These tables represent the relationships between x and y for two different sets of data. Which statements correctly describe the relationships between x and y for each table? Responses Table A represents an additive relationship because y is 1.5 more than x, and Table B represents a multiplicative relationship because y is 3 times x. Table A represents an additive relationship because , y, is 1.5 more than , x, , and Table B represents a multiplicative relationship because , y, is 3 times , x, . Table A represents a multiplicative relationship because y is 2.5 times x, and Table B represents an additive relationship because y is 2 more than x. Table A represents a multiplicative relationship because , y, is 2.5 times , x, , and Table B represents an additive relationship because , y, is 2 more than , x, . Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times x. Both data sets represent multiplicative relationships. In Table A, , y, is 2.5 times , x, , and in Table B, , y, is 3 times , x, . Both tables represent additive relationships. In Table A, y is 1.5 more than x, and in Table B, y is 2 more than x. Both tables represent additive relationships. In Table A, , y, is 1.5 more than , x, , and in Table B, , y, is 2 more than , x, . Table A x 1 2 3 4 y 2.5 5.0 7.5 10.0 Table B x 1 2 3 4 y 3 6 9 12
Answers
Correct expression is,
Table A represents an additive relationship because y is 5.5 more than x.
Table B represents a multiplicative relationship because , y, is 4.5 times x.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
These tables represent the relationships between x and y for two different sets of data.
Hence, The equation for table A is,
Two points from the table A are, (1, 6.5) and (2, 7.5)..
Thus, The equation fop table is,
y - 6.5 = (7.5 - 6.5) / (2 - 1) (x - 1)
y - 6.5 = 1 (x - 1)
y - 6.5 = x - 1
y = x - 1 + 6.5
y = x + 5.5
Thus, Table A represents an additive relationship because y is 5.5 more than x.
Hence, The equation for table B is,
Two points from the table A are, (1, 4.5) and (2, 9)..
Thus, The equation fop table is,
y - 4.5 = (9 - 4.5) / (2 - 1) (x - 1)
y - 4.5 = 4.5 (x - 1)
y - 4.5 = 4.5x - 4.5
y = 4.5x
Thus, Table B represents a multiplicative relationship because , y, is 4.5 times , x,.
Therefore, We get;
Correct expression is,
Table A represents an additive relationship because y is 5.5 more than x.
Table B represents a multiplicative relationship because , y, is 4.5 times x.
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Related Questions
Officials at a metropolitan transit authority want to get input from people who use a certain bus route about a possible change in the schedule. They randomly poll 20 riders from each bus route. The type of sampling method used is: A. Simple random sample B. Stratified random sample C. Cluster sample D. Systematic sample
Answers
Answer: so u do 1 + n = 21
Step-by-step explanation:
21
Answer:
Step-by-step explanation:
SRS
2. Determine a line that is parallel to the line y=-5x-5 passes through the point (1, 2). Which
of the following is an equation of this line?
Answers
Answer: y = 5x - 3
Step-by-step explanation:
The lines need the same slope
2 = 5(1) + b
2 = 5 + b
-5 -5
-3 = b
y = 5x - 3
A large data set contains information on all registered republicans in the United States. The following information is recorded.- Name
- Age
- Gender
- Home address
- Whether they voted or not in 2016 presidential election
Which of the following questions could not be answered based solely on the information in this data set?answer choicesa. What percent of registered republican voters are male?b. Which state had the most registered republican voters vote in the 2016 presidential election?c. What is the average age of registered republican voters?d. How many registered republicans voted for Gary Johnson in the 2016 presidential election.
Answers
The question which could not be answered based solely on the information in this data set is How many registered republicans voted for Gary Johnson in the 2016 presidential election? So, correct answer is option (d).
We have a large data consists of information on all registered republicans in the United States. The information of voters which present in data are Name, Gender, Age, Home address, Whether they voted or not in 2016 presidential election. We have to determine the question which answer is not possible on basis of this data. Let's consider the options one by one.
a) Here, gender and voters who vote or not in 2016 election, so it is easy to determine the percent of registered republican voters are male.
b) Address details and the information of voters who vote or not, helps to determine the state which had the most registered republican voters vote in the 2016 election.
c) The Age and registered voter information that he vote or not is used to determine the average age of registered republican voters.
d) Now, there is no information regarding the voters choice for voting their votes. So, it not determined that how many voters voted for Gary Johnson in the 2016 presidential election. This is write choice here.
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a researcher for an organization that collects and reports on crime has data on the murder rates for 10 states from a certain year. the murder rate is the number of murders per 100,000 inhabitants. the murder rate sample data are reproduced below. use a ti-83, ti-83 plus, or ti-84 to calculate the sample standard deviation and the sample variance of the murder rates. round your answers to one decimal place. murders per 100k inhabitants 7.1 9 5.6 2.5 4.8 7 3.6 2.1 6.1 helpcopy to clipboarddownload csv provide your answer below: $$standard deviation
Answers
The sample standard deviation of murder rates is approximately 2.2, and the sample variance is approximately 4.9. The standard deviation and variance are measured in the same units as the original data (murders per 100,000 inhabitants), squared and unsquared.
We can use a TI-83, TI-83 Plus, or TI-84 to calculate the sample standard deviation and variance of the murder rates:
Enter the following information into a list: Enter the data into L1 by pressing STAT, then ENTER.Determine the standard deviation of the sample: STAT, CALC, and 1-VarStats are the commands. Enter L1 into the list and hit ENTER. The Sx value represents the standard deviation (s).Determine the sample variance: The sample variance is equal to the square of the sample standard deviation. To get the sample variance (s2), we can square the Sx value calculated in step 2.We get the following results using this method:
2.209 is the sample standard deviation (s).
4.877 sample variance (s2) (rounded to three decimal places)
As a result, the sample standard deviation of the murder rates is about 2.2, and the sample variance is about 4.9. It should be noted that the standard deviation and variance are measured in the same units as the original data (murders per 100,000 inhabitants), squared and unsquared.
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The overhead reach distances of adult females are normally distributed with a mean of 205 cm and a standard deviation of 8.6 cm.
a. Find the probability that an individual distance is greater than 218.40 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 203.20 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
Answers
a) The probability that an individual overhead reach distance is greater than 218.40 cm is about 0.0594.
b) The probability that the mean for 20 randomly selected overhead reach distances is greater than 203.20 cm is about 0.7930.
c) The central limit theorem applies and we can use the normal distribution to approximate the sampling distribution of the sample means.
What is Probability :Probability is a way to evaluate how likely something is to happen. Several things are difficult to forecast with absolute confidence.
Now in the given question ,
a. To find the probability that an individual distance is greater than 218.40 cm, we can use the z-score formula:
z = (x - μ) / σ
where x is the individual distance, μ is the mean overhead reach distance, and σ is the standard deviation of the overhead reach distances. Plugging in the values given, we have:
z = (218.40 - 205) / 8.6
z = 1.56
Using a standard normal table or calculator, we can find the probability that a z-score is greater than 1.56 to be approximately 0.0594. Therefore, the probability that an individual overhead reach distance is greater than 218.40 cm is about 0.0594.
b. To find the probability that the mean for 20 randomly selected distances is greater than 203.20 cm, we need to use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normal, with a mean of μ and a standard deviation of σ / sqrt(n), where n is the sample size. In this case, we have:
μ = 205
σ = 8.6
n = 20
So the standard deviation of the sample means is:
σ / sqrt(n) = 8.6 / sqrt(20) = 1.923
Next, we need to find the z-score corresponding to a mean of 203.20 cm:
z = (203.20 - 205) / 1.923
z = -0.82
Using a standard normal table or calculator, we can find the probability that a z-score is greater than -0.82 to be approximately 0.7930. Therefore, the probability that the mean for 20 randomly selected overhead reach distances is greater than 203.20 cm is about 0.7930.
c. The normal distribution can be used in part (b) because of the central limit theorem. Even though the sample size is less than 30, the sampling distribution of the sample means will still be approximately normal if the population distribution is normal or if the sample size is large enough. In this case, we are told that the population distribution of overhead reach distances is normal, so the central limit theorem applies and we can use the normal distribution to approximate the sampling distribution of the sample means.
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For each example, state whether the one-sample, two-independent-sample, or related-samples t test is most appropriate. If it is a related-samples t test, indicate whether the test is a repeated-measures design or a matched-pairs design. A professor tests whether students sitting in the front row score higher on an exam than students sitting in the back row. A graduate student selects a sample of 25 participants to test whether the average time students attend to a task is greater than 30 minutes. A researcher matches right-handed and left-handed siblings to test whether right-handed siblings express greater emotional intelligence than left-handed siblings. A principal at a local school wants to know how much students gain from being in an honors class. He gives students in an honors English class a test prior to the school year and again at the end of the school year to measure how much students learned during the year.
Answers
All the sample tests are stated below:
1) A two-independent-sample t test.
2) A one-sample t test.
3) A related-samples t test.
4) A related-samples t test.
What is Sample Test ?It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing. A sample must be representative of the entire population and must not be biased toward any one trait.
A professor runs an experiment to see if front-row students perform better on an exam than back-row pupils.
This is a two-independent-sample t test, as there are two distinct groups (students in the front row and students in the back row) and the professor is interested in comparing the mean exam scores between them.
To determine whether students spend more than 30 minutes on an activity on average, a graduate student chooses a sample of 25 participants.
This is a one-sample t test, as there is only one group of participants and the graduate student is interested in comparing the mean time students attend to a task to a specific value (30 minutes).
To determine whether right-handed siblings exhibit higher emotional intelligence than left-handed siblings, a researcher pairs up right- and left-handed siblings.
This is a related-samples t test using a matched-pairs design, as the researcher is interested in comparing emotional intelligence scores of right-handed and left-handed siblings who are matched based on certain criteria (in this case, being siblings).
A local school's principal is curious to discover how much an honors class benefits the children there. He administers tests to honors English students before the start of the school year and again at the conclusion of the year to gauge their progress.
This is a related-samples t test using a repeated-measures design, as the principal is interested in comparing the test scores of the same group of students before and after taking the honors English class to measure how much they learned during the year.
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Adding and Subtracting Polynomials
Feb 09, 10:57:07 AM
Find the sum of 9x² + 5x + 8 and 9x – 7.
-
Answers
9x² + 14x +1 is the sum of polynomials 9x² + 5x + 8 and 9x – 7.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
We need to find the sum of 9x² + 5x + 8 and 9x – 7.
Summation is the addition of a sequence of any kind of numbers.
So add 9x² + 5x + 8 and 9x – 7.
9x² + 5x + 8 + 9x – 7.
Add the like terms
9x² + 14x +1
Hence, 9x² + 14x +1 is the sum of polynomials 9x² + 5x + 8 and 9x – 7.
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Rewrite 92 and 146 as product of their prime factor
Answers
92 and 146 as product of their prime factor are 2^2 * 23 and 2 * 73
How to rewrite the expressionFrom the question, we have the following parameters that can be used in our computation:
92 and 146
Prime factorization of 92:
92 = 2 x 2 x 23
Prime factorization of 146:
146 = 2 x 73
So, we have
Product = 2 * 2 * 23 * 2 * 73
This gives
Product = 2^3 * 23 * 73
Hence, the expression is 2^3 * 23 * 73
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Can you find out the area of these shapes
Answers
1) The Area of the first compound shape is given as = 52cm
2) The area of the second shape is given as = 47cm
Note that the method for deriving this area of the shapes is by dividing them into "regular" shapes as shown in the attached images.
What is a compound shape?
A compound form is created by combining simple shapes. It's also known as a "composite" or "complex" form.
For Shape A:
We have a triangle and a rectangle when the compound shape is de-regularized.
The dimensions of the triangle are:
Base 8cm
Height 3cm
Since the area of a triangle is given as:
1/2 B * H,
The area of the triangle is = 1/2 * 8 * 3cm
= 12cm
For the rectangle, the area of a rectangle is given as L * B. Since
L = 8cm and
B = 5cm
The area = 8* 5 = 40cm
The total area of Shape A = 40cm + 12cm
= 52cm
For Shape B:
We have two rectangles and one right-angled triangle when the shape is "converted".
The dimensions of rectangle 1 are:
L = 3
B = 2
Area = 6
The dimensions of rectangle 2 =
L = 8cm
B = 4cm
Area = 32cm
The dimension of the Right angled triangle is:
Base = 6cm
Height = 3cm (that is 7-4)
Thus:
The area of the triangle is:
1/2 * 6* 3
= 9cm
Thus the total area of the second shape is:
= 32 + 6 + 9
= 47cm
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Steps by steps to divide 44 divided by 2,876
Answers
Answer:
44 ÷ 2,876 = 0.01528 (rounded to five decimal places)
Step-by-step explanation:
To divide 44 by 2,876, we can use long division. Here are the steps:
Write 44 under the long division symbol (÷) and 2,876 outside the symbol.
___
2,876 | 44
Since 2 is smaller than 44, we can't divide 2,876 by 44, so we need to add a decimal point and a zero to the quotient and bring down the next digit of the dividend (4).
___
2,876 | 44.0
___
2,876 | 44.0
4
We see that 28 is the largest multiple of 2,876 that is less than or equal to 440. We write 28 above the line, and multiply 2,876 by 28 to get 80,528. We subtract 80,528 from 440, which gives us a remainder of 4.
28
___
2,876 | 44.0
4 4 0
- 3 4 2 8
-------
8 4
Since we have a remainder of 4, we can't bring down any more digits from the dividend, so we add a decimal point and a zero to the quotient and bring down a zero to make the dividend 40. We repeat the process of finding the largest multiple of 2,876 that is less than or equal to 400, writing it above the line, multiplying it by 2,876, subtracting the result from the dividend, and bringing down the next digit.
28. 0
___
2,876 | 44.0
4 4 0
- 3 4 2 8
-------
8 4
8 3 6
- 8 0 4
-------
3 2
We have a remainder of 32, and we can't bring down any more digits from the dividend, so we add a decimal point and a zero to the quotient and bring down another zero to make the dividend 320. We repeat the process of finding the largest multiple of 2,876 that is less than or equal to 3,200, writing it above the line, multiplying it by 2,876, subtracting the result from the dividend, and bringing down the next digit.
28. 00
___
2,876 | 44.0
4 4 0
- 3 4 2 8
-------
8 4
8 3 6
- 8 0 4
-------
3 2
2 8 2
- 2 8 7 6
-------
6
We have a remainder of 6, and we can't bring down any more digits from the dividend, so we have our final answer:
44 ÷ 2,876 = 0.01528 (rounded to five decimal places)
44
÷ 2,876
Step 2: Determine the first digit of the quotient by dividing the first digit of the dividend by the divisor. Write this digit on top of the division bar.
- The first digit of 44 is 4.
- Divide 4 by 2,876: 4 ÷ 2,876 = 0.0013916... (rounded to 0.0014)
- Write 0 on top of the division bar as the first digit of the quotient:
0
-----
2,876
Step 3: Multiply the divisor (2,876) by the first digit of the quotient (0). Write the result under the dividend.
0
-----
2,876
0
Step 4: Subtract the result of Step 3 from the dividend (44). Write the difference underneath.
0
-----
2,876
0
-----
44
Step 5: Bring down the next digit of the dividend (4) and write it next to the result from Step 4.
0
-----
2,876
0
-----
44
4
Step 6: Determine the next digit of the quotient by dividing the new two-digit number (the result of Step 5) by the divisor. Write this digit next to the 0 in the quotient on top of the division bar.
- The two-digit number is 44.
- Divide 44 by 2,876: 44 ÷ 2,876 = 0.0152994... (rounded to 0.0153)
- Write 0.015 (or just 0, since it's less than 1) next to the 0 in the quotient:
0.01
-----
2,876
0
-----
44
4
Step 7: Multiply the divisor (2,876) by the next digit of the quotient (0 or 1, depending on the result of Step 6). Write the result under the last number subtracted.
0.01
-----
2,876
0
-----
44
4
28
Step 8: Subtract the result of Step 7 from the last number subtracted. Write the difference underneath.
0.01
-----
2,876
0
-----
44
4
28
--
16
Step 9: Bring down the next digit of the dividend (0) and write it next to the result from Step 8.
0.01
-----
2,876
0
-----
44
4
28
--
16
0
Step 10: Determine the next digit of the quotient by dividing the new two-digit number (the result of Step 9) by the divisor. Write this digit next to the previous digits in the quotient on top of the division bar.
- The two-digit number is 16.
- Divide 16 by 2,876: 16 ÷ 2,876 = 0.0055629... (rounded to 0.0056)
- Write 0.005 (or just 0, since it's less than
PLEASE HELP:
light travels at a speed of 1.86 x 10^5 miles per second. it takes about 15,000 seconds for the light to reach Neptune. write your answer in scientific notation.
Answers
The distance that the light travels in the scientific notation will be 2.79 × 10⁹ miles.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
The light travels at a speed of 1.86 × 10⁵ miles per second. And it takes about 15,000 seconds for the light to reach Neptune.
Then the number of miles is given as,
1.86 × 10⁵ = d / 15,000
d = 1.86 × 10⁵ × 15,000
d = 2.79 × 10⁹ miles
The distance that the light travels in the scientific notation will be 2.79 × 10⁹ miles.
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Does anyone know the answer to these?
Answers
The slopes of the lines are listed below:
Case 1: m = 1
Case 2: m = - 4 / 5
Case 3: m = - 4
Case 4: m = 5
Case 5: m = 2 / 7
Case 6: m = - 1
Case 7: m = 0
Case 8: m = NaN (Not a Number)
Case 9: m = 3 / 5
Case 10: m = - 8 / 3
How to determine the slope of a line
In this question we find ten cases of lines, whose slopes must be determined according to the following rules:
If the line is parallel with the x-axis, then its slope is zero.If the line is parallel with the y-axis, then its slope is undefined. If the line is oblique, then the slope is determined by secant line formula:m = Δy / Δx
Now we proceed to determine the slope for each case:
Case 1
m = (5 - 0) / [0 - (- 5)]
m = 1
Case 2
m = (- 3 - 1) / [0 - (- 5)]
m = - 4 / 5
Case 3
m = (- 3 - 1) / (1 - 0)
m = - 4
Case 4
m = [1 - (- 4)] / (1 - 0)
m = 5
Case 5
m = (3 - 1) / [0 - (- 7)]
m = 2 / 7
Case 6
m = (0 - 3) / (3 - 0)
m = - 1
Case 7
m = 0
Case 8
m = NaN (Not a Number)
Case 9
m = [- 1 - (- 4)] / (5 - 0)
m = 3 / 5
Case 10
m = (- 4 - 0) / (1.5 - 0)
m = - 4 / 1.5
m = - 8 / 3
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Math Question...............
Answers
Answer:12.90
Step-by-step explanation:
A number line goes from 0 to 10. A closed circle is shown at point 0 and 5. Point 0 is labeled Start and point 5 is labeled Finish.
A 5-mile race takes place along a straight course. The number line shows the distance, in miles, from start to finish. The race director would like to place a water station along the course such that the distance from the start to the water station and the water station to the finish line is in a 7:5 ratio. Where would the water station be located? Round to the nearest tenth of a mile, if necessary.
The water station will be placed about
miles from the start.
Answers
The water station would be located at 2.92 miles. Round to the nearest tenth of a mile, the answer is 2.9 miles.
What is the distance?Distance is a numerical value that quantifies "how much ground an object has traveled" while in motion. Distance is calculated as the sum of a person's movement and time.
Call the distance between the starting point and the water station x. 5 - x meters separate from the water station from the finish line.
We may write the following equation because we are aware that the ratio between these two lengths is 7:5.
x / (5 - x) = 7/5
Expanding and solving for x, we get:
5x = 7(5) - 7x
12x = 35
x = 35/12 = 2.92 miles
Therefore, the distance of the water station would be 2.9 miles.
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Find the directional derivative of f(x,y,z)=xy+z^3 at the point (2,3,1) in the direction of a vector making an angle of 3π/4 with ∇f(2,3,1). Expert Answer.
Answers
The directional derivative of f(x, y, z) = [tex]xy+z^{3}[/tex] at the point (2, 3, 1) in the direction of a vector making an angle of 3π/4 with the gradient of f at that point is √2 (3cos(3π/4) + 2sin(3π/4)).
To find the directional derivative of f(x, y, z) = xy + z^3 at the point (2, 3, 1) in the direction of a vector making an angle of 3π/4 with the gradient of f at that point, we need to calculate the gradient of f at that point and then use it to find the dot product with the given direction vector.
The gradient of f at the point (2, 3, 1) is given by ∇f(2, 3, 1) = (y, x, 3z^2) = (3, 2, 3).
The direction vector in the direction of 3π/4 with the gradient can be found as follows:
Let [tex]d = (cos(3\pi /4), sin(3\pi /4), 0)[/tex]
The directional derivative of f in the direction d at the point (2, 3, 1) is given by
∇f(2, 3, 1) . d = [tex](3, 2,3).(cos(3\pi /4), sin(3\pi /4),0)[/tex]
= [tex]3cos(3\pi /4)+2sin(3\pi /4)[/tex]
= √2 (3cos(3π/4) + 2sin(3π/4))
So the directional derivative of f in the direction of a vector making an angle of 3π/4 with the gradient of f at (2, 3, 1) is √2 (3cos(3π/4) + 2sin(3π/4)).
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Girl Scout cookies are available only for a few weeks every year. They are mostly sold door-to-door and from tables at strip malls. Some cookie flavors are very popular, while others don't sell as well and are changed from year to year.The following analysis of variance was made to compare the popularity of each type of cookie, based on sales of 4 cookie flavors by 8 girl scouts in the same troop.COOKIE.............N....Mean....StdevDo-si-dos..........8.....8.33......3.39Samoas.............8....23.00....15.23Tagalongs.........8......9.17......2.23ThinMints..........8....51.00.....26.11Pooled StDev = 11.02Compute the margin of error to compare all pairs of means with Bonferroni's procedure with 94% family confidence.
Answers
The margin of error to compare all pairs of means with Bonferroni's procedure with 94% family confidence are [9.17, 20.17], [-4.66, 6.34] and [37.17, 48.17]. The margin of error for the difference in means between Samoas and Tagalongs is approximately 14.97.
To compute the margin of error to compare all pairs of means with Bonferroni's procedure with 94% family confidence, we need to use the formula:
Margin of error = t* (Sqrt (MSE/n))
Where t* is the critical value for a two-tailed t-test with a significance level of alpha = (1 - 0.94)/2 = 0.03,
degrees of freedom (df) = N - k,
where N is the total sample size (N = n * k = 8 * 4 = 32)
and k is the number of groups (k = 4), and MSE is the mean square error from the analysis of variance (ANOVA).
To find the critical value t* from the t-distribution table or calculator,
we need to look up the value of t for alpha/2 = 0.03/2 = 0.015 and df = 32 - 4 = 28, which is approximately 2.5.
The mean square error MSE is calculated by dividing the residual sum of squares (SSR) by the degrees of freedom within (dfw), which is
N - k = 32 - 4 = 28.
From the ANOVA table, we have:
SSR = 3458.08
dfw = 28
MSE = SSR/dfw = 3458.08/28 = 123.50
Now we can compute the margin of error for each pair of means with a 94% family confidence level, which means that the overall family
error rate is alpha = 1 - 0.94 = 0.06, and
the individual error rate for each comparison is alpha/k(k-1)/2 = 0.06/6 = 0.01.
For Do-si-dos vs. Samoas, the difference in means is 23 - 8.33 = 14.67. The margin of error is:
t* (Sqrt (MSE/n)) = 2.5 * (Sqrt (123.50/8)) = 5.50
The 94% family confidence interval for this comparison is [14.67 - 5.50, 14.67 + 5.50] = [9.17, 20.17].
For Do-si-dos vs. Tagalongs, the difference in means is 9.17 - 8.33 = 0.84. The margin of error is:
t* (Sqrt (MSE/n)) = 2.5 * (Sqrt (123.50/8)) = 5.50
The 94% family confidence interval for this comparison is [0.84 - 5.50, 0.84 + 5.50] = [-4.66, 6.34].
For Do-si-dos vs. Thin Mints, the difference in means is 51 - 8.33 = 42.67. The margin of error is:
t* (Sqrt (MSE/n)) = 2.5 * (Sqrt (123.50/8)) = 5.50
The 94% family confidence interval for this comparison is [42.67 - 5.50, 42.67 + 5.50] = [37.17, 48.17].
For Samoas vs. Tagalongs, the difference in means is 9.17 - 23 = -13.83. The Margin of error = 2.326 * 11.02 * √(1/8 + 1/8) ≈ 14.97
Therefore, the margin of error for the difference in means between Samoas and Tagalongs is approximately 14.97.
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Suppose annual salaries for sales associates from a particular store have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $37,500 is
Answers
With a mean of $32,500 and a standard deviation of $2,500. The z-score for a sales associate who earns $37,500 is 2.
The z-score, also known as a standard score, is a measure of how many standard deviations a given value is from the mean. It is used to standardize the data and make it easier to compare and interpret. The formula for the z-score is:
z = (x - μ) / σ
where x is the value of interest, μ is the mean, and σ is the standard deviation.
In this case, the mean annual salary for sales associates from a particular store is $32,500 and the standard deviation is $2,500. We want to find the z-score for a sales associate who earns $37,500. Plugging in the values, we get:
z = ($37,500 - $32,500) / $2,500 = 2
This means that the sales associate's salary is 2 standard deviations above the mean.
Interpreting the z-score can help us understand how unusual or typical a given value is in comparison to the mean. In this case, a z-score of 2 indicates that the sales associate's salary is relatively high compared to the mean, but it is not an extremely high salary.
We can use a standard normal table to find the proportion of the data that falls below a given z-score, or to find the corresponding value for a given proportion of the data.
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A spam filer is designed by screening commonly occurring phrases in spam. Suppose that 60% of email is spam. In 20% of the spam emails, the phrase "free gift card" is used. In non-spam emails, 99.5% of them do not mention "free gift card". What is the probability that a newly arrived email which does mention "free gift card", is not spam?
Answers
The probability that a newly arrived email which does mention "free gift card", is not spam is 0.0165.
Let S be the event that an email is spam, and let F be the event that an email mentions "free gift card". We want to find P(S' | F), the probability that the email is not spam given that it mentions "free gift card".
We can use Bayes' theorem to find P(S' | F):
P(S' | F) = P(F | S') P(S') / P(F)
We can calculate each of these probabilities as follows:
P(F | S') = the probability that a non-spam email mentions "free gift card". From the problem, we know that this probability is 0.005 (i.e., 99.5% of non-spam emails do not mention "free gift card").
P(S') = the probability that an email is not spam. From the problem, we know that this probability is 0.4 (i.e., 60% of emails are spam, so 40% are not spam).
P(F) = the probability that an email mentions "free gift card". This can be calculated using the law of total probability:
P(F) = P(F | S) P(S) + P(F | S') P(S')
= 0.20 × 0.60 + 0.005 × 0.40
= 0.121
In the first term, we use the given probability that 20% of spam emails mention "free gift card". In the second term, we use the probability that 0.5% of non-spam emails mention "free gift card".
Plugging these values into Bayes' theorem, we get:
P(S' | F) = 0.005 × 0.4 / 0.121 ≈ 0.0165
Therefore, the probability that a newly arrived email which does mention "free gift card" is not spam is approximately 0.0165 or 1.65%.
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The step function f(x) is graphed.
What is the value of f(0)?
• -2
• -1
• 0
• 1
Answers
The value of f(0) is -2.
Option A is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
From the graph, we see that,
f(x) = -1 for -1 ≤ x < 0
Similarly,
f(x) = -2 for 0 ≤ x < 1 _____(1)
Now,
The value of f(x) at x = 0.
From (1),
f(0) = -2
Thus,
The value of f(0) is -2.
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I will give brainliest and ratings if you get this correct
Answers
Answer:
[tex]\textsf{Increasing}: \quad (- \infty, -1) \cup (1, \infty)[/tex]
[tex]\textsf{Decreasing}: \quad(-1, 1)[/tex]
[tex]\textsf{Minimum}: \quad (1, -4)[/tex]
[tex]\textsf{Maximum}: \quad (-1, 0)[/tex]
Step-by-step explanation:
[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}}\implies f'(x) > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies f'(x) < 0[/tex]
Given function:
[tex]f(x)=x^3-3x-2[/tex]
Differentiate the given function:
[tex]\implies f'(x)=3x^2-3[/tex]
To find the interval where f(x) is increasing, set the differentiated function to more than zero:
[tex]\implies 3x^2-3 > 0[/tex]
[tex]\implies 3(x^2-1) > 0[/tex]
[tex]\implies x^2-1 > 0[/tex]
[tex]\implies x^2 > 1[/tex]
[tex]\implies x < -1, \;\;\; x > 1[/tex]
So the interval on which function f(x) is increasing is:
[tex](- \infty, -1) \cup (1, \infty)[/tex]
To find the interval where f(x) is decreasing, set the differentiated function to less than zero:
[tex]\implies 3x^2-3 < 0[/tex]
[tex]\implies 3(x^2-1) < 0[/tex]
[tex]\implies x^2-1 < 0[/tex]
[tex]\implies x^2 < 1[/tex]
[tex]\implies -1 < x < 1[/tex]
So the interval on which function f(x) is decreasing is:
[tex](-1, 1)[/tex]
To find the relative extrema, set the differentiated function to zero and solve for x:
[tex]\implies 3x^2-3=0[/tex]
[tex]\implies 3(x^2-1)=0[/tex]
[tex]\implies x^2-1=0[/tex]
[tex]\implies x^2=1[/tex]
[tex]\implies x=-1,\;\;x=1[/tex]
To find the y-coordinates of the relative extrema, substitute the found values of x into the function and solve for y:
[tex]\implies f(-1)=(-1)^3-3(-1)-2=0[/tex]
[tex]\implies f(1)=(1)^3-3(1)-2=-4[/tex]
Therefore the minimum and maximum points of the function are:
[tex]\textsf{Minimum}: \quad (1, -4)[/tex]
[tex]\textsf{Maximum}: \quad (-1, 0)[/tex]
10. Which is the bigger portion, ½ of a 12 inch pizza, or % of a 9 inch pizza? Give a reason for your
answer.
Answers
½ of a 12 inches pizza represents the bigger portion.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
½ of a 12-inch pizza, then the area is given as,
A = (π / 2) x (12 / 2)²
A = 56.52 square inches
30% of a 9-inch pizza. Then the area is given as,
A = 0.30 x π (9 / 2)²
A = 19.0755 square inches
½ of a 12 inches pizza represents the bigger portion.
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i^{11} + i^{16} + i^{21} + i^{26} + i^{31}
Answers
Answer:
Below
Step-by-step explanation:
For this , I will assume i = [tex]\sqrt{-1}[/tex]
i^{11} + i^{16} + i^{21} + i^{26} + i^{31} =
- i +1 +i -1 - i = - i
find the sum please helpppppp
Answers
The value of the sum notation is 729
How to determine the sum notationFrom the question, we have the following parameters that can be used in our computation:
The sum notation
From the notation, we have the following values
First term, a = 972
Common ratio, r = -1/3
The sum is then represented as
Sum = a/(1 -r)
So, we have
Sum = 972/(1 + 1/3)
Evaluate
Sum = 729
Hence. the sum is 729
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Please help !! I need help
Answers
Answer:
Step-by-step explanation:
197.97
According to a survey, 56% of young Americans aged 18 to 29 say the primary way they watch television is through streaming services on the internet. Suppose a random sample of 350 Americans from this group is selected. Would it be surprising to find that more than 70% of the sample watched television primary through streaming services? (Include z-score)
Answers
Answer:
The z-score is a statistical measure that describes how far a sample estimate is from the population parameter in standard deviation units. It is calculated by taking the difference between the sample estimate and the population parameter, and dividing it by the standard deviation of the sampling distribution of the estimate. The resulting z-score can be used to calculate the probability of observing a sample estimate as extreme or more extreme than the one obtained, assuming the null hypothesis is true.
In this case, the sample estimate is the proportion of individuals who watch television primarily through streaming services, which is 70%, and the population parameter is the proportion of all individuals who watch television primarily through streaming services, which is 56%. The sample size is 350. The null hypothesis is that there is no difference between the sample and population proportions, and the alternative hypothesis is that the sample proportion is greater than the population proportion.
To calculate the z-score, we need to determine the standard error of the sampling distribution of the proportion. The standard error is a measure of the variability of sample estimates due to random sampling variation. It is calculated by taking the square root of the population proportion times one minus the population proportion, divided by the sample size. In this case, the standard error is:
standard error = sqrt[(0.56 * (1 - 0.56)) / 350] = 0.028
The z-score can now be calculated as:
z-score = (0.7 - 0.56) / 0.028 = 5.19
This z-score is quite large, indicating that the sample estimate is more than 5 standard errors away from the population parameter. This suggests strong evidence against the null hypothesis, as the probability of observing a sample estimate as extreme or more extreme than the one obtained is very low, assuming the null hypothesis is true.
In other words, the result of observing a sample proportion of 70% or above is highly unlikely to have occurred by chance alone, assuming that the true population proportion is 56%. This result provides evidence in support of the alternative hypothesis, which states that the sample proportion is greater than the population proportion.
Please Help Me...
Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity.
$300 invested quarterly for 15 years at a 4.5% interest rate compounded quarterly.
The accumulated amount will be $_________?
(Round to the nearest cent as needed.)
Answers
In 15 years the investment will be worth $586.99.
What is compounding?Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.
It is the result of reinvesting interest, or adding it to the loaned capital, rather than paying it out or requiring payment from the borrower, so that interest is earned on the principal sum plus previously accumulated interest in the following period.
In finance and economics, compound interest is the norm.
To find how much will the investment be worth in 20 years:
Given -
Initial investment = $300.
Interest rate = 4.5%.
Interest applied = quarterly.
So, the table of 15 years will be as follows:
using the formula we get,
Therefore, in 15 years the investment will be worth $586.99
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In the process of producing engine valves, the valves are subjected to a first grind. Valves whose thicknesses are within the specification are ready for installation. Those valves whose thicknesses are above the specification are reground, while those whose thicknesses are below the specification are scrapped. Assume that after the first grind, 75% of the valves meet the specification, 20% are reground, and 5% are scrapped. Furthermore, assume that of those valves that are reground, 90% meet the specification, and 10% are scrapped.
a)Find the probability that a valve is ground only once. Round the answer to two decimal places.
b)Given that a valve is not reground, what is the probability that it is scrapped?
c)Find the probability that a valve is scrapped. Round the answer to three decimal places.
d)Given that a valve is scrapped, what is the probability that it was ground twice?
e)Find the probability that the valve meets the specification (after either the first or second grind).
f)Given that a valve meets the specification (after either the first or second grind), what is the probability that it was ground twice?
g)Given that a valve meets the specification, what is the probability that it was ground only once?
Answers
The probabilities are (a) 0.8 (b) 0.125 (c) 0.12 (d) 0.1667 (e) 0.88 (f) 0.2045 (g) 0.795
Let A = meet specification, B = reground and C = scrapped
index 1 indicates the value was not reground and index 2 indicates that value was reground before obtaining the situation.
P(A₁) = 70% = 0.7
P(B) = 20% = 0.2
P(C₁) = 10% = 0.1
P(A₂/B) = 90% = 0.9
P(C₂/B) = 10% = 0.1
(a) Probability that a valve is ground only once = 1 - P(B)
= 1 - 0.2 = 0.8
(b) a valve is not reground, the probability that it is scrapped
P(A₁∪C₁)
P(A₁) + P(C₁) = 0.1 + 0.7 = 0.8
P(C₁/A₁∪C₁) = 0.1/0.8 = 0.125
(c) Probability that a valve is scrapped
P(C₁) + P(B) × P(C₂/B) = 0.1 + 0.2 × 0.1
= 0.12
(d) a valve is scrapped, the probability that it was ground twice
P(B/C) = P(B∩C)/P(C)
= [tex]\frac{0.2\times 0.1}{0.12}[/tex]
P(B/C) = 0.1667
(e) the probability that the valve meets the specification (after either the first or second grind)
P(A) = P(A₁) + P(B) × P(A₂/B)
P(A) = 0.7 + 0.2 × 0.9 = 0.88
(f) P(B/A) = P(A₂)/P(A)
= 0.18/0.88 = 0.2045
(g) valve meets the specification, probability that it was ground only once
1 - P(B/A) = 1 - 9/14
= 0.795
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A rectangular pyramid has a volume of 525 cubic feet. It has a base of 25 feet by 18 feet. Find the height of the pyramid.
Volume of a Pyramid: V=1/3Bh
What is the height of the pyramid in cubic feet?
Answers
We know that the formula for the volume of a pyramid is given as:
V = (1/3)Bh
where V is the volume, B is the area of the base, and h is the height of the pyramid.
So, substituting the given values, we have:
525 = (1/3)(25*18)h
Multiplying both sides by 3, we get:
1575 = 450h
Dividing both sides by 450, we get:
h = 1575/450
Simplifying this, we get:
h = 3.5
Therefore, the height of the pyramid is 3.5 feet.
Answer: The height is 3.5 cubic feet
Step-by-step explanation:
We have to find the area of the base first so multiply 25 and 18 feet together. You will get 450
Now you can make an equation.
525 = (1/3)*450*h
Multiply the 1/3 and the 450 together to get 150
Your equation is now 525 = 150h
Divide 150 on both sides to isolate h
You now have 3.5 = h
The students in Colleen's class got to choose whether to visit the zoo or the aquarium. 24 students went to the zoo and 3 students went to the aquarium. What is the ratio of the number of students who went to the aquarium to the total number of students?
Answers
The solution is, the ratio of the number of students who went to the aquarium to the total number of students is 1:9.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
here, we have,
24 students went to the zoo and 3 students went to the aquarium.
i.e. we get,
24 students went to the zoo
3 went to the aquarium
so, total no. of students = 24+ 3
= 27
then, we have,
the ratio of the number of students who went to the aquarium to the total number of students is = 3 : 27
= 1: 9
Hence, The solution is, the ratio of the number of students who went to the aquarium to the total number of students is 1:9.
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find the area of the given circle. round to the nearest tenth. a circle with radius measuring 3 point 5 centimeters. (Use 3.14 for π)
Answers
The formula for the area of a circle is A = πr^2, where r is the radius.
The area of the circle with a radius of 3.5 centimeters is approximately 38.5 square centimeters.
Substituting r = 3.5 centimeters and using π ≈ 3.14, we get:
A = 3.14 × (3.5)^2
A = 38.465 square centimeters (rounded to the nearest tenth)
Consequently, the radius of the circle is 3.5 centimetres, and its area is roughly 38.5 square centimeters.
The area of a circle is the measure of the region enclosed by the circle in a two-dimensional space. It is the amount of space inside the circle and is typically measured in square units, such as square centimeters (cm²) or square meters (m²). The formula to calculate the area of a circle is:
Area = π x radius²
Where π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, which is approximately 3.14159, and radius is the distance from the center of the circle to any point on the circumference. The area formula can also be expressed in terms of the diameter:
Area = π x (diameter/2)²
This formula tells us that the area of a circle depends on the length of its radius or diameter, and it allows us to calculate the area of any circle given either of these two measurements.
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