Answer:
Given:
n = 1003
[tex] p' = \frac{462}{1003} = 0.4606 [/tex]
q = 1 - 0.4606 = 0.5394
a) The sample size and count.
Here the sample size is the number that took part in the poll. It is denoted as n = 1003.
The count is the number that answered yes. Count = 462
b) The sample proportion.
The formula for sample proportion is: [tex] p' = \frac{x}{n} [/tex]
Therefore, sample proportion =
[tex] p' = \frac{462}{1003} = 0.4606 [/tex]
c) The relationship between population proportion and sample proportion.
Since the sample size is greater than 30 (n>30), the sample size is large. Hence, for a large sample, the population proportion is approximately equal to the sample proportion.
This means the population proportion, p = 0.4606
Answer:
A) Sample size n=1003
Count x=462
B) Sample proportion p=0.46
C) The population proportion can be estimated with a confidence interval, with the information given by the sample proportion.
The 95% confidence interval for the population proportion is (0.429, 0.491).
Step-by-step explanation:
A) The sample size include all the adult that answer the poll. The sample size is then n=1003.
The count is the number of adults that answer Yes in this case. The count is x=462.
B) The sample proportion can be calculated dividing the count by the sample size:
[tex]p=\dfrac{x}{n}=\dfrac{462}{1003}=0.46[/tex]
C) The population proportion is not known. It can only be estimated with the information given by samples of that population. The statistical inference is the tool by which the sample information can be used to estimate the population characteristics.
With the sample proportion p we can estimate a confidence interval for the population proportion.
We can calculate a 95% confidence interval.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.46*0.54}{1003}}\\\\\\ \sigma_p=\sqrt{0.00025}=0.0157[/tex]
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0157=0.031[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.46-0.031=0.429\\\\UL=p+z \cdot \sigma_p = 0.46+0.031=0.491[/tex]
The 95% confidence interval for the population proportion is (0.429, 0.491).
We have 95% that the population proportion is within this interval
\begin{aligned} &y=2x +1 \\\\ &x-y=-3 \end{aligned} y=2x+1 x−y=−3 Is (2,5)(2,5)left parenthesis, 2, comma, 5, right parenthesis a solution of the system?
Answer:
Yes
Step-by-step explanation:
Given the system of equations
[tex]\begin{aligned} &y=2x +1 \\\\ &x-y=-3 \end{aligned}[/tex]
We want to determine if (2,5) is a solution of the system.
We can do this by substitution of the given point into the equations and see if it holds.
Given (x,y)=(2,5), x=2, y=5
In the first equation
y=2x+1
5=2(2)+1
5=5
Therefore, the point (2,5) satisfies the first equation.
In the second equation
[tex]x-y=2-5=-3[/tex]
Since our result (-3) is equal to the Right Hand Side, the point also satisfies the second equation.
Therefore, (2,5) is a solution of the system.
Drew has two cats. One cat weighs 17 pounds, and the other one weighs 12 1/2 pounds. Audrey’s dog weighs 33 pounds. What is the difference in ounces between Audrey’s dog and the combined weights of Drew’s cats?
Answer: 3.5 pounds
Step-by-step explanation:
17+12.5=29.5
33-29.5=3.5
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
5 ≥ p
Step-by-step explanation:
Add 5 to both sides:
0 ≥ p - 5
+5 + 5
________
5 ≥ p
Answer:
p <= 5
Step-by-step explanation:
Let's solve your inequality step-by-step.
0≥p−5
Step 1: Flip the equation.
p−5≤0
Step 2: Add 5 to both sides.
p−5+5≤0+5
p≤5
Answer:
p≤5
Write an equation to represent the following statement. The quotient of 36 and 3 is j. Solve for j (I mark brainiest whoever asks)
Answer:
36 ÷ 3 = j
Step-by-step explanation:
The quotient of 36 and 3 is '36 ÷ 3'.
'Is j' would be '= j'.
Put it together, and you get:
36 ÷ 3 = j
'j = 12'
[tex]\frac{36}{3} = j\\\\\text {Divide the two numbers: }36/3 = 12\\\boxed {12=j}[/tex]
Brainiest Appreciated
The series 14 + 6 + (–2) + (–10) + . . . + (–154) is arithmetic. How many terms are in the series?
Answer:
22
Step-by-step explanation:
In the series 14 + 6 + (–2) + (–10) + . . . + (–154)
The gap between entities is 8.
Therefore number of entities between -10 and -154 = (154 - 10)/8 =18
Total number of terms in the series = 18 + 4 = 22
There are 22 terms in the given arithmetic series.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
In the given arithmetic series 14 + 6 + (–2) + (–10) + . . . + (–154)
The common difference between entities is 8.
Therefore, the number of entities between -10 and -154
= (154 - 10)/8
=18
The Total number of terms in the series = 18 + 4 = 22
Hence, there are 22 terms in the given arithmetic series.
Learn more about arithmetic sequence here:
https://brainly.com/question/3702506
#SPJ2
A population of 100 insects tripled in size every month. Write a function formula to represent the insect population after x months
Answer:
3x+100
Step-by-step explanation:
A 2-kilogram bag of sugar costs $5.09. What is the unit price, rounded to the nearest cent?
Answer:their is something wrong in the question
Step-by-step explanation:
What is the formula for the area of a triangle?
The formula to find the area of a triangle is :
1/2 base*height
For instance:
base=4 cm
height=5cm
area of traingle=1/2*b*h
=1/2*4*5
=10cm^2
Hope it helps...
Good luck on your assignment
What advantages do money market accounts offer a depositor compared to other types of savings accounts? Answer in
complete sentences.
Answer:
Step-by-step explanation:
Money markets accounts offer a annual percentage yield which is higher compared to other types of savings accounts
These accounts also require a higher minimum deposits to get a higher rate
These accounts may also be insured and secured by the Federal Deposit Insurance Corp in banks and the National Credit Union Administration in credit unions.
They are also relatively easy to access.
graphic designworks employed three different sales people last year Person 1 earned 3500 in the first quarter person 2 earn 6500 in the first quarter and Person 3 earned 8000 in the first quarter what are the maximum FUTA deduction for the first quarter
A.1054.00
B. 620.00
C.1116.00
D.899.00
Answer:
B im not to sur tho tell me if you got it
Answer:
1054.00
Step-by-step explanation:
There are about 237 milliliter in 8 oz how many mililiters in 15 oz
Answer:
443
Step-by-step explanation:
Answer:426.196
Step-by-step explanation:
Evaluate √-75 where s = -3
PLS I NEED HELP ASAP!!!!
When Rachel put gas in her car she records the distance and she has driven since her last fill up and then number of gallon of gas that her car has used. she use this information to predict the amount of gas in her car we used to travel to different distance.Complete the equation so that it models the relationship between the number of gallons of gas that the Car uses Jeannie and the number of miles the car has driven D click the arrow to choose on the answer from each menu
Answer:
we need picture
Step-by-step explanation:
Answer:
G 0.04 Times D
Step-by-step explanation:
Find the perimeter of a parallelogram whose base is 8cm and another side is 12cm
A parallelogram
P=2(a+b)
The answer is 64
P=2(a+b)=2·(24+8)=64
To be honest, I really don’t understand this and need someone to help me out.
Answer:
A.
Explaintion:
n=13. 13+2 = 15
I hope this helps ( :
Answer: B
Step-by-step explanation:
because 4 is the number of (n) plus the 2
What is the range of values for the measurement 300 ± 2%?
PLEASE HELP ??
What is the length of x?
Answer:
[tex]1\dfrac{3}{5}[/tex]
Step-by-step explanation:
Because these two triangles are similar:
[tex]\dfrac{4}{5}=\dfrac{x}{2}\\x=\dfrac{8}{5}=1\dfrac{3}{5}[/tex]
Hope this helps!
Write a trinomial with 3x as the GCF of its terms.
Answer:
3x (x² + x + 1)
You could write any trinomial like this
What is equivalent to 84 1/4
Answer:
[tex] \frac{337}{4} [/tex]
Step-by-step explanation:
[tex]84 \frac{1}{4} = \frac{84 \times 4 + 1}{4} = \frac{336 + 1}{4} = \frac{337}{4} [/tex]
Wyatt analyzed the data from his science experiment and found that the MAD was greater than the IQR. What does this tell you about the variability of the data?
a
The average of the data is closer to the least value than it is to the greatest value.
b
The middle 50% of the data is spread out more than the average variation.
c
The average variation is spread out more than the middle 50% of the data.
d
The average of the data is closer to the greatest value than it is to the least value.
Answer:
The correct option is C
Step-by-step explanation:
The average variation is spread out more than the middle 50% of the data.
Point A is at (2,-8) and the point C is at (-4,7). Find the coordinates of point B on AC such that the ratio of AB to BC is 2:1.
Answer:
The coordinates of point B are (-2, 2)
Step-by-step explanation:
We have two points: A and C.
The coordinates for A are (2, -8) and the coordinates for C are (-4, 7).
We have to find the coordinates of the point B, that satisfies the condition that the distance AB is 2 times the distance BC.
We also know that B is a point of the line AC.
We can calculate the line AC as a linear function y=mx+b.
The slope m is:
[tex]m=\dfrac{y_c-y_a}{x_c-x_a}=\dfrac{7-(-8)}{-4-2}=\dfrac{15}{-6}=-2.5[/tex]
Then, the y-intercept b can be calculated using the coordinates of one of the points, in this case point A:
[tex]y=-2.5x+b\\\\b=y_a+2.5x_a=-8+2.5*2=-8+5=-3[/tex]
Then, we know that B is a point of the linear function y=-2.5x-3, within the range x ∈ (-4; 2).
To have a ratio AB to BC of 2 to 1, we can divide the length of the line AC in 3 parts, and the point B will be located in the end of the segment nearer to point C.
In the picture attached, you can see the division of the segment AC in three parts and the location of point B=(x, y).
Applying the Thales theorem, we can divide the segment in the y-axis in three and calculate y, and the same for the x-axis.
Then, the coordinate y for the point B is:
[tex]y=y_c-(y_c-y_a)/3\\\\y=7-[7-(-8)]/3=7-15/3=7-5=2\\\\\\x=x_c-(x_c-x_a)/3\\\\x=-4-(-4-2)/3=-4-(-6)/3=-4+2=-2[/tex]
Then, the point B has coordinates (-2, 2).
We can verify the distances as:
[tex]AB=\sqrt{(2-(-2))^2+((-8)-2)^2}=\sqrt{16+100}=\sqrt{116}\\\\\\BC=\sqrt{((-2)-(-4))^2+(2-7)^2}=\sqrt{4+25}=\sqrt{29}\\\\\\\dfrac{AB}{BC}=\dfrac{\sqrt{116}}{\sqrt{29}}=\sqrt{\dfrac{116}{29}}=\sqrt{4}=2[/tex]
Answer: (-2,2)
Step-by-step explanation:
Calculate the perimeter
Answer:
Sqare = 6+6+6+6 = 6*4 = 24
Rectangle = 6+6+18+18 = 12+36 = 48
24+48 = 72
The perimeter is 72.
Choose the correct option :
1: set A = { 1,5,6,7 } and set B = { 0,1,7,15 } . what is the A U B ?
a) A U B = { 0,1,5,6,7,15 }
b) A U B = {0,1,1,5,6,7,15}
c) A U B = { 1,5,6,7,15}
d) A U B = { 1, 7 }
2: which equation shows the identity property of multiplication ?
a) a+a+a+= 3× a
b) ( a + b ) + 4 = a + ( 4 + b )
c) a ( b + c ) = ab + ac
d) a×1 = a
3: which is an example of associative property of addition ?
a) 7+ 0 = 7
b) (3+9) + 8 = 3 + ( 9+ 8)
c) 5 + ( -5 ) = 0
d) 4+ 3 = 3 +4
4: which property of addition is used in the following ?
( 9+8 ) + 5 = 9 + ( 8+ 5 )
a) associative property
b) closure property
c) distributive property
d) commutative property
5: which property is used in the following expression ?
( 2 × 6 ) × 4 = 6 × ( 4 × 2 )
a) distributive property of multiplication
b) commutative property of addition
c) associative property of addition
d) associative property of multiplication
6: which property is used in the following ?
2×( 4+3 ) = 2 x 4 + 2 × 3
a) commutative property
b) distributive property
c) associative property
d) none of the above
7: which is an example of identity property of addition ?
a) (4+6) + 2 = 4 + ( 6 + 2 )
b) 9+ 0 = 9
c) 8× 1 = 8
d) 7+ 4 =4+ 7
8: which of the following does NOT show the commutative property of addition ?
a) ab = ba
b) 3x + 4y = 4y + 3x
c) a+ b =b+ a
d) 8+ x = x + 8
9: which operation will not change the value of any nonzero number ?
a) dividing by zero
b) adding one
c) multiplying by zero
d) multiplying by one
10: which property of addition does 2 + 0= 2 illustrate ?
a) commutative property
b) zero property
c) distributive property
d) identity property
please give me the full answer i will mark brainliest
Answer:
1. a
2. d
3. b
4.a
5 d
6. b
7. b
8.a
9. d
10. a
A sample of 50 impossible whoppersandwiches have a mean fat content of 37.6g and standard deviation of 4.9g . A sample of 58 regular whopper sandwiches have a mean fat content of 39.3g and standard deviation of 2.7g. Use a 0.05 significance level to test the claim that the mean fat content for the impossible whopper is less than the mean fat content for the regular whopper.
(Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.)
USE A 0.05 SIGNIFICANCE LEVEL TO TEST THE CLAIM:
H0: μ1____ μ2For Q17(circle one: equal to, less than, greater than, not equal to )
H1 : μ1____ μ2For Q18(circle one: equal to, less than, greater than, not equal to )
Test Statistic t=__________ Q19(ROUND TO 2 DECIMAL PLACES)
P-value: p =_____________ Q20(ROUND TO 4 DECIMAL PLACES)
Decision/Conclusion: _________________________________Q21(CIRCLE ONE BELOW) Reject H0, There is sufficient evidence to warrant the rejection of the claim.
OR
Fail to Reject H0, There is not sufficient evidence to warrant the rejection of the claim.
Construct an appropriate confidence interval ( ______________ Q22, _______________ Q23) (ROUND TO 3 DECIMAL PLACES)
Answer:
Step-by-step explanation:
H0: μ1____ μ2For Q17(circle one: equal to, less than or equal to, greater than or equal to, not equal to )
H1 : μ1____ μ2For Q18(circle one: equal to, less than, greater than, not equal to )
Formula for calculating the the test:
t = [ (x₁ - x₂) - d ] / sqrt[(s₁²/n₁) + (s₂²/n₂)]
where x₁ = 37.6, x₂ = 39.3, d = 0 assuming equality = 37.6 - 39.3 = -1.7
s₁² = 4.92 = 24.01, s₂² = 2.72 = 7.29, n₁ = 50, n₂ = 58.
thus, t = [ (-1.7) - (0)] / √(24.01/50) + (7.29/58)
t = (-1.7) / (0.4802 + 0.1257)
t = -1.7 / 0.6059
t = -2.8057. = -2.81
P value:
Lets find the degree of freedom:
DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }
DF = (24.01/50 + 7.29/58)² / {[(24.01 / 50)² / 50-1)] + (7.29/58)² / 58-1)]}
DF = (0.4802 + 0.1257)² /{[ (0.4802)²/49] + (0.1257)²/57)]}
DF = (0.6059)²/ (0.00471 + 0.00028)
DF = 0.3671 / 0.00499 = 75.37
Thus, P value = 0.9968 using a t distribution calculator.
Decision/Conclusion: Since the P value 0.9968 is greater than α (.05), Fail to Reject H0, There is not sufficient evidence to warrant the rejection of the claim.
What is the value of g(1⁄2) when g(x) = 2x2? What is the input? What is the output?
Answer:
[tex]g(\frac{1}{2}) = 0.5[/tex]
The input is [tex]x = \frac{1}{2}[/tex] and the output is [tex]g(x) = g(\frac{1}{2}) = 0.5[/tex]
Step-by-step explanation:
Suppose we have a function g(x) = a. The input is the value of x and the output is the value of g.
In this question:
[tex]g(x) = 2x^{2}[/tex]
We want g(1/2) = g(0.5). So
[tex]g(0.5) = 2*(0.5)^{2} = 2*0.25 = 0.5[/tex]
[tex]g(\frac{1}{2}) = 0.5[/tex]
The input is [tex]x = \frac{1}{2}[/tex] and the output is [tex]g(x) = g(\frac{1}{2}) = 0.5[/tex]
The following 96% confidence interval based on a sample of 32 students was formed to estimate the population mean time that students will require to complete a particular examination: 62.4 ± 12.6 minutes. Which one of the following interpretations is correct for this confidence interval?A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutesB) We are 96% confident that the sample mean time (62.4 minutes) equals the true mean timeC) We are 96% confident that the population mean time required by students who take this test is 62.4 minutesD) We are 96% confident that the sample mean time (62.4 minutes) is correctE) We are 4% confident that an individual student taking this test will require less than 49.8 minutes or more than 75.0 minutes
Answer:
A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes
Step-by-step explanation:
x% confidence interval is between a ± b.
a is the sample mean.
b is the margin of error.
Interpretation: We are x% sure that the population mean is between a-b and a+b.
In this question:
96% confidence interval for the mean time that students will require to complete a particular examination. Between 62.4 - 12.6 = 49.8 minutes and 62.4 + 12.6 = 75 minutes.
The correct interpretation is that we are 96% sure that the population mean is in this interval.
So the correct answer is:
A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes
Answer:
The confidence interval for the true mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The confidence interval for this case i given by:
[tex] 62.4 -12.6 \leq \mu \leq 62.4+12.6[/tex]
[tex] 49.8 \leq \mu \leq 75.0[/tex]
For this case we can conclude that the true mean for the time that students will require to complete a particular examination is between 49.8 and 75.0 minutes. And the best option for this case by:
A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes
Step-by-step explanation:
The confidence interval for the true mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The confidence interval for this case i given by:
[tex] 62.4 -12.6 \leq \mu \leq 62.4+12.6[/tex]
[tex] 49.8 \leq \mu \leq 75.0[/tex]
For this case we can conclude that the true mean for the time that students will require to complete a particular examination is between 49.8 and 75.0 minutes. And the best option for this case by:
A) We are 96% confident that the population mean time required for all students who take this test is somewhere between 49.8 and 75.0 minutes
the perimeter of a square is equal to the perimeter of an equilateral triangle the length of a side of the square is given by the x and lenghth of a side of equilaterel triangle is given x+1 which equation can be used to find the value of x?
Answer:
x = 3
Step-by-step explanation:
We are told that the length of a side of the square is x.
Now, perimeter of square = 4 × side length
Perimeter of square = 4x
Also,we are told that the triangle is equilateral and a side is (x + 1).
Thus, perimeter of triangle = 3(x + 1)
Since we are told that the perimeter of the square is equal to that of the equilateral triangle. Thus;
4x = 3(x + 1)
4x = 3x + 3
Subtract 3x from both sides to get;
4x - 3x = 3
x = 3
Answer:
pretty sure it's C
Step-by-step explanation:
1. An AP Statistics class starts a project to estimate the average number of hours a student at their high school sleeps per night. Their high school has 1200 students, and they take a sample of the first 120 students that arrive at school on a particular day. They ask each of the 120 students how many hours of sleep they got the night before and then calculate an average. Which of the following statements is an accurate description of the elements of this survey?
Answer:
(C) Sample: the 120 students surveyed. Population: the 1200 students at the high school. Parameter of interest: the average number of hours a student at this high school sleeps per night.
Step-by-step explanation:
The correct answer is (C). The sample is a subset of the population, and the parameter is a characteristic of the population of interest.
The city of Omaha decided to build a new parking garage in hopes of luring more people to the Old Market district.The city will pay for the parking garage through parking fees. For a random sample of 42 weekdays, daily fees collected averaged $126 with a standard deviation of $16. The consultant who advised the city on the project estimated the potential parking revenues to be $135 per day, though the city believes that estimate is too high. Perform a hypothesis test (by hand) using α=0.05 to check the advisor's claim that the revenue would be $135 per day. Include the following:
1. Write your hypotheses in both symbols and words.
2. Test an appropriate hypothesis "by hand" using an alpha level of 0.05. Assume conditions are met (so don't check them). Be sure to include the correct probability notation and use the editor for all work.
3. Support your test with the corresponding confidence interval, again "by hand". Use the editor to show all steps.
4. Write your 3-part final conclusion using the test results and interval results. Include a sentence that states whether the test and interval results agree.
Answer:
Given:
Mean, u = 135
Sample size, n = 42
Sample mean, x' = 126
Standard deviation = 16
Significance level = 0.05
1) The null and alternative hypotheses:
H0 : u = 135 (the revenue per day is $135)
H1 : u < 135 (the revenue per day is less than $135)
2) In this case, we have a left tailed test.
Let's use the formula:
[tex] = \frac{x' - u}{s/ \sqrt{n}} = \frac{126 - 135}{16 / \sqrt{42}} = -3.645 [/tex]
t = - 3.645
Critical value: at a significance level of 0.05, left tailed test,
tcritical = -1.683
We reject null hypothesis, H0, since t calculated, -3.645 is less than tcritical, -1.683.
3) Given, a = 0.05, df = 41, left tailed test,
t-value = 2.02
For the corresponding confidence interval, we have:
[tex] CI = (x' - \frac{t * \sigma}{\sqrt{n}}, x' + \frac{t * \sigma}{\sqrt{n}}) [/tex]
[tex] CI = (126 - \frac{2.02 * 16}{\sqrt{42}}, 126 + \frac{2.02 * 16}{\sqrt{42}}) [/tex]
CI = (121.014, 130.986)
4) Conclusion:
We reject the estimated potential revenue advised by the consultant, H0, as it is too high, because the t-calculated falls in rejection region(i.e, less than critical value), also the upper limit of the confidence interval is less than $135.
Suppose corn chips cost 21.5 cents per ounce . If a bag cost $2.91, how many ounces of chips
Answer:
13 ounces
Step-by-step explanation:
291/21.5=13.5348837209