Answer:
g(11) = 101
Step-by-step explanation:
g(r) = -20 + 11r
So in g(11), we just need to replace 'r' with '11'
g(11) = -20 + 11 (11)
--> g(11) = -20 + 121 = 101
--> g(11) = 101
Please comment down below if 8(11) wasn't a typo. I thought it was, so I replaced 8 with g. If that was intentional, I'll edit my answer as soon as possible.
Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 101 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 12.9 and a standard deviation of 3.2. What is the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
The 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is (12.4,13.3).
Given that a sample of 101 cookies and per cookie in the sample has a mean of 12.9 and a standard deviation of 3.2.
From the given information,
Let n=101 represents the size of the sample.
Let [tex]\bar{x}[/tex]= 12.9 represents the mean of the sample.
Let s= 3.2 represents the standard deviation of the sample.
Degrees of freedom:
df = n-1
df= 101-1
df= 100
The critical value of t at 0.2 level of significance with 100 degrees of freedom is,
[tex]\begin{aligned}t_{cric}&=t_{(\frac{\alpha}{2}, n-1)}\\ &=t_{(0.2,100)}\\ &=1.2900\end[/tex]
The 80% confidence interval for the number of chocolate chips per cookie for Big chip cookies is computed as follows:
[tex]\begin{aligned}CI_{80\%}&=\bar{x}\pm t_{(\frac{\alpha}{2},n-1)}\left(\frac{s}{\sqrt{n}}\right)\\ &=12.9\pm 1.2900\left(\frac{3.2}{\sqrt{101}}\right)\\ &=12.9\pm 1.2900\times 0.3184\\ &=12.9\pm 0.410736\\ &=12.489264,13.310736\end[/tex]
Hence, the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies when the mean is 12.9 and standard deviation is 3.2 is (12.4,13.3).
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3.5.3 Test (CST): Functions
Does this graph show a function? Explain how you know.
-5
5-
OA. No; there are y-values that have more than one x-value.
B. No; the graph fails the vertical line test.
OC. Yes; there are no y-values that have more than one x-value.
D. Yes; the graph passes the vertical line test.
Jhy
Answer:
D
Step-by-step explanation:
It pass the vertical line test.
Hope this helps <3
As per the given graph, the graph fails the vertical line test. The correct option is B.
What is graph?A graph is a visual representation of data that uses lines, bars, or other symbols to show how different values are related to each other.
Graphs are often used to display information in a way that is easy to understand and interpret.
The vertical line test is a way to determine whether a given graph represents a function.
According to this test, if any vertical line intersects the graph at more than one point, then the graph does not represent a function.
In the given graph, we can see that there are some vertical lines that intersect the graph at more than one point, such as the vertical line passing through x = 2.
Therefore, the graph does not pass the vertical line test and does not represent a function.
Thus, the correct answer is B.
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1. Which one of the following statements expresses a true proportion? A. 3:49:12 OB. 2:1 1:2 OC. 54:9 = 6:3 OD. 7:98:9
Answer:
3:4 9:12
Step-by-step explanation:
Rewrite the ratios as fractions. 3:4 becomes 3/4, and 9:12 becomes 9/12, which simplifies to 3:4. Therefore A is a true proportion.
Find the missing length indicated. i need help with steps
The measure of the missing length from the given diagram is 25
Triangular altitude theoremAccording to the theorem, the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse.
According to the given diagram, the expression below will be used to determine the value of x
x/60 = 60/144
Cross multiply yo have:
144x = 60 * 60
Simplify the result to have
144x = 3600
Divide both sides by 144
144x/144 = 3600/144
x = 3600/144
x = 25
Hence the measure of the missing length from the given diagram is 25
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Select all of the following true statements if R = real numbers, N = natural numbers, and S = {10, 11, 12,...}.
A. -15∈N
B. N⊂R
C. S⊂N
D. ∅⊂N
E. N∈S
F. {10.11.12,...}⊆S
The true statements are:
B. N⊂R
C. S⊂N
D. ∅⊂N
F. {10.11.12,...}⊆S
Subsets and SetsNote that:
All real numbers are numbers that can be found on the real number lineNatural numbers are positive whole numbersAll natural numbers are subsets of real numbersThe null set (∅) is a subset of every setA set is a proper subset of itselfFollowing the points highlighted above, the true statements in the given options re:
B. N⊂R
C. S⊂N
D. ∅⊂N
F. {10.11.12,...}⊆S
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Find the median for the scores 91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95, 72, 75
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What does \boxed{median} mean in math?}}[/tex]
[tex]\boxed{\text{Median}}\rightarrow\textsf{ is the number in the middle.}[/tex]
[tex]\huge\textbf{How do you find the \boxed{median}?}[/tex]
[tex]\text{You can found it by putting the numbers from \bf least to greatest.}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\text{Find the median for the scores 91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95,}\\\text{72, 75}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\text{91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95, 72, 75}[/tex]
[tex]\huge\textbf{Rearrange the problems to:}[/tex]
[tex]\text{69,71,71,71,72,74,75,82,87, 89,89,91,95,95}[/tex]
[tex]\huge\textbf{The expression:}[/tex]
[tex]\mathsf{\dfrac{75 + 82}{2} = median}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{\dfrac{75 + 82}{2} = median}[/tex]
[tex]\mathsf{\dfrac{157}{2} = median}[/tex]
[tex]\mathsf{257\div2 = median}[/tex]
[tex]\mathsf{78.5 = median}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{78.5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Measure the length of this segment in inches.
Answer:
3 [tex]\frac{3}{4}[/tex] inches
Answer: I'm pretty sure it's 3 5/8, it's the S that's blocking the view but it gotta be 3 5/8.
Step-by-step explanation: PLS MAKE ME BRAINLIST
1. Name a career that requires data-analysis skills. Describe how data analysis is
used in this career. Be specific in your examples.
The career that requires data analysis skills is a data scientist because the skills helps in computing and analyzing large amounts of data from several sources.
Data analysis skillsData analysis skills are known as technical skills used by a data analyst to report insights and analyze data.
Some data analysis skills include;
Data VisualizationData CleaningPythonSQL and NoSQLMachine LearningLinear Algebra and CalculusMATLABA career that requires data analysis skills is a data scientists
A data scientist is one that computes and analyzes large amounts of data from different sources and makes useful interpretations from it.
The skills such career needs include statistics, calculus, probability, programming, excel, visualization, database management, and machine earning.
There is also need for a high level of accuracy when solving problems.
Thus, the career that requires data analysis skills is a data scientist because the skills helps in computing and analyzing large amounts of data from several sources.
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"The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200, with 200 being the highest level of motivation. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 30 students who are at least 29 years of age, and their mean was 135.2"
Calculate the observed test statistic (Zobt or Tobt) for hypothesis test. Round up to the second decimal place.
Using the z-distribution, the observed test statistic is given as follows:
z = 3.69.
What are the hypothesis tested?At the null hypothesis, it is tested if older students have the same mean as the general population, that is:
[tex]H_0: \mu = 115[/tex]
At the alternative hypothesis, it is tested if they have a greater mean, that is:
[tex]H_0: \mu > 115[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.For this problem, the parameters are:
[tex]\overline{x} = 135.2, \mu = 115, \sigma = 30, n = 30[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{135.2 - 115}{\frac{30}{\sqrt{30}}}[/tex]
z = 3.69.
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How did the temperature change if it increased by 50% and then decreased by 33 1/3%
The temperature does not change after the percentage increase and decrease.
What is the change in the temperature?
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
Assume the initial temperature is 10.
Temperature after the 50% increase : (1 + 0.5) x 10 = 15
Temperature after the 33 1/3% decrease : (1 - 0.333) x 15 = 10.00
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What are the coordinates of the y-intercept of the line -3x+2y=6?
Answer:
y-intercept: (0,3)
Step-by-step explanation:
To find the y-intercept, we set x to equal 0, giving the equation:
-3(0)+2y = 6
0+2y = 6
y = 3
3. The time for a swing to move forward and backward can be determined by the formula
T = 2√√√15₁
T represents the time, in seconds, taken by the swing to move through one
complete cycle (forward and back) and L represents the length of the rope supporting the swing.
9.8
Determine the length of the rope supporting a swing that takes 3.4 seconds to move through one
complete cycle. Show all steps and round the answer to the nearest tenth of a metre.
Step-by-step explanation:
T = 2×pi × sqrt(L/9.8)
now we know the time the swing should take for a complete back and forth cycle : 3 4 seconds.
the only unknown variable is now L (the length of the rope) :
3.4 = 2×pi × sqrt(L/9.8)
3.4/(2pi) = sqrt(L/9.8)
(3.4/(2pi))² = L/9.8
3.4²/(4pi²) = L/9.8
11.56/(4pi²) = L/9.8
2.89/pi² = L/9.8
9.8 × 2.89/pi² = L = 2.869618563... m ≈ 2.9 m
I need help with this geometry question asap!
Answer:
True
Step-by-step explanation:
Lines in three dimensions can be one of ...
coincidentparallelintersecting (at one point)skewCoplanarLines are coplanar when a plane can be defined that includes the entirety of both of them. In the attached image, lines m₁ and n intersect and both lie in the gray plane. They are coplanar.
Lines m and m₁ are parallel, and both are contained in the turquoise plane. They are coplanar. A plane can always be drawn that will contain a pair of parallel lines. That is, any two parallel lines must be coplanar.
The lines m and n in the figure are skew, non-intersecting and non-parallel. They cannot be contained in a single plane.
__
Additional comment
Three or more parallel lines may not be coplanar. They will only definitely be coplanar when considered in pairs.
A train is traveling at a speed of 60 miles per hour. What happens to the number of miles when the number of hours
changes?
O When the number of hours increases, the number of miles decreases.
O When the number of hours increases, the number of miles increases.
O When the number of hours decreases, the number of miles increases.
O When the number of hours decreases, the number of miles stays the same.
Intro
Done
When the number of hours decreases, the number of miles increases.
What is the relationship between number of hours and number of miles travelled?
Average speed is the total distance travelled per time.
Average speed = total distance / total time
There is an inverse relationship between the distance travelled and the time travelled. If time increases, the distance travelled decreases.
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In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 22.4 and a standard deviation of 5.1. Complete parts (a) through (d) below.
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 19.
The probability of a student scoring less than 19 is.
(Round to four decimal places as needed.)
(b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 17.7 and 27.1.
The probability of a student scoring between 17.7 and 27.1 is.
(Round to four decimal places as needed.)
(c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than 33.1.
The probability of a student scoring more than 33.1 is
3.1
is.
(Round to four decimal places as needed.)
(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
OA. None of the events are unusual because all the probabilities are greater than 0.05.
B. The event in part (c) is unusual because its probability is less than 0.05.
C. The events in parts (a) and (b) are unusual because its probabilities are less than 0.05.
D. The event in part (a) is unusual because its probability is less than 0.05.
Help me solve this
Using the normal distribution, we have that:
a) The probability of a student scoring less than 19 is 0.2709 = 27.09%.
b) The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.
c) The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.
d) The correct option is: B. The event in part (c) is unusual because its probability is less than 0.05.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 22.4, \sigma = 5.1[/tex]
Item a:
The probability is the p-value of Z when X = 19, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 22.4}{5.1}[/tex]
Z = -0.67.
Z = -0.67 has a p-value of 0.2709.
The probability of a student scoring less than 19 is 0.2709 = 27.09%.
Item b:
The probability is the p-value of Z when X = 27.1 subtracted by the p-value of Z when X = 17.7, hence:
X = 27.1:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{27.1 - 22.4}{5.1}[/tex]
Z = 0.92.
Z = 0.92 has a p-value of 0.8212.
X = 17.7:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.7 - 22.4}{5.1}[/tex]
Z = -0.92.
Z = -0.92 has a p-value of 0.1788.
0.8212 - 0.1788 = 0.6424.
The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.
Item c:
The probability is one subtracted by the p-value of Z when X = 33.1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33.1 - 22.4}{5.1}[/tex]
Z = 2.1.
Z = 2.1 has a p-value of 0.9821.
1 - 0.9821 = 0.0179.
The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.
Item d:
Probabilities less than 0.05 are unusual, hence the correct option is:
B. The event in part (c) is unusual because its probability is less than 0.05.
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The table shows various values of a linear function f (x).
x –4 0 2 5 9 13
f (x) –11 1 7 16 28 40
What is f –1(13)?
40
38
13
4
The value of f –1(13) is 4
How to determine the inverse value?The table of values is given as:
x –4 0 2 5 9 13
f (x) –11 1 7 16 28 40
A linear function is represented as:
y = mx + b
Where b represents the y-intercept and m represents the slope
From the graph, when x = 0, y = 1.
This means that b = 1
So, we have
y = mx + 1
Also from the graph, when x = 2, y = 7.
So, we have:
7 = 2m + 1
Subtract 1 from both sides
7 - 1 = 2m + 1 - 1
Evaluate the difference
6 = 2m
Rewrite the above equation as:
2m = 6
Divide both sides of the equation by 2
m = 3
Substitute m = 3 in y = mx + 1
y = 3x + 1
The notation f –1(13) implies that y = 13
So, we have
13 = 3x + 1
Subtract by 1
3x = 12
Divide by 3
x = 4
Hence, the value of f –1(13) is 4
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Write the following in simplified radical form.
3/40
Answer:
3.42
Step-by-step explanation:
Question Find the area of a trapezoid whose height is 6 ft and whose bases are 9.7 ft and 6.3 ft.
Answer:
48 Square feet
Step-by-step explanation:
A=((a+b)/2)*h,
((6.3+9.7)/2)*6=48ft^2
Which histogram represents the data? 1,2,12,14,15,16,18
Option b) is correct
In statistics, a histogram is a graphical representation of the distribution of data. A histogram is represented by a set of rectangles, adjacent to each other, where each column represents a certain type of data. Statistics is a stream of mathematics that is used in various fields. When figures are repeated in statistical data, this repetition is known as frequency and can be written in the form of a table, called a frequency distribution. Frequency distributions can be displayed graphically using different types of graphs and one of them is a histogram.
A histogram chart is used under certain conditions. They are:
Data should be numeric.
A histogram is used to check the shape of the data distribution.
It is used to check if the process changes from one period to another.
It is used to determine whether the output differs when it involves two or more processes.
It is used to analyze whether the given process meets the customer's requirements.
The data 1,2,12,14,15,16,18 is given
We need to find the histogram which best fits to the given data
Total number that falls between 0-9 is 2
Total Number that falls between 10-19 is 5
Total Number that falls between 20-29 is 1
Total Number that falls between 30-39 is 5
Total Number that falls between 40-49 is 3
Total Number that falls between 50-59 is 1
Hence the histogram is obtained
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16
A Ferris wheel with a radius of 25 m makes 2 rotations every minute.
a. State the period of the Ferris wheel.
b. Complete a tables of values showing the height above the ground for 2 rotations of
Ferris wheel by assigning the correct variables
c. Graph 2 rotations of the Ferris wheel. (Hint: Time Vs Height above the platform)
d. State the amplitude of the Ferris wheel.
The period of this Ferris wheel can be calculated as 30 seconds. The amplitude is 25
How to solve for the period.a. We have 60 seconds in a minute
In a minute it makes 2 rotations. The period = 60 secs / 2 rotations
= 30 seconds
b. We have h = 25 - 25cos [tex]\frac{25}{30} t[/tex]
25 - 25cos[tex]\frac{25}{15} t[/tex]
We would have the table in the attachment
d. Amplitude
= max - min / 2
= 50 - 0 / 2
= 25
How many three-digit multiples of 5 have three different digits?
There are 180 numbers which are three-digit multiples of 5.
According to the statement
we have to find the three digit numbers which are multiples of 5.
we know that three digit numbers are start from 100 to 999 and in 1 line of counting means 100 to 110 there are 2 numbers are multiples of 5.
Here we use Multiplication method to find the number of digit which are a multiple of 5.
It means there are two numbers which are multiples of 5 in the one line of counting and there are 90 lines of counting from 100 to 999.
So, it means the answer will become
2*90 = 180.
So, There are 180 numbers which are three-digit multiples of 5.
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Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
Volume: Answer, yd3
Answer:
The volume is
[tex]339.4 {yd}^{3} [/tex]
Step-by-step explanation:
The solution is in the image
32. What is the perimeter of a regular octagon with a side length of 7 units?
11 units
35 units
49 units
56 units
Answer:
56
Step-by-step explanation:
solution
Here
P=8a=8·7=56
Answer:
56 units
Step-by-step explanation:
the perimeter of a rectangular octagon with sides of length a
is equal to: 8 × a
Then
the perimeter of a regular octagon with a side length of 7 units
is equal to: 8 × 7 = 56 units
if f(x) = 3(x+5)+4/x, what is f(a+2)?
Answer:
A
Step-by-step explanation:
Substitute a + 2 for x:
f(a + 2) = 3 [ (a + 2) + 5 ] + 4 / (a + 2)
= 3 [ a + 7 ] + 4 / (a + 2)
Answer:
A.
Step-by-step explanation:
I need help with this slope
Answer:
Step-by-step explanation:
First, the y-intercept is -3 so from -3 the slop to the next point is 4/1.
A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 572 ft. Find the width of the walkway, (x in the diagram below), if the garden is 14 ft. wide by 18 ft. long. Factoring or the quadratic equation formula can be used. a) 5) Solve for the specified variable A = 1/(a+b)h for a 6) Solve for x 14 feet x+10_I 33 Jeet b) A=1/(a+b)h for a
Match each expression to the scenario it represents.
Expressions
Scenario
the price of a game that’s been discounted
18% off its list price (x)
arrowRight
the price of a toy that sells for 18% more
than the amount (x) needed to build the toy
arrowRight
the volume of water remaining in a tank after
of its original volume (x) is drained out
arrowRight
the total amount of flour in a bakery after receiving new stock equal to of its current stock (x)
arrowRight
The expression matched with each scenario is;
Scenario 1: 0.82x
Scenario 2: 1.18x
Scenario 3: 7/10x
Scenario 4: 13/10x
AlgebraThe price of a game that’s been discounted
18% off its list price (x)
Total price = x
Discount = 18%x = 0.18x
New price = x - 0.18x
= 0.82x
The price of a toy that sells for 18% more
than the amount (x) needed to build the toy
Original price = x
Percentage increase = 18%x = 0.18x
New price = x + 0.18x
= 1.18x
The volume of water remaining in a tank after 3/10 of its original volume (x) is drained out
Original volume = x
Volume drained = 3/10x
New volume = x - 3/10x
= 7/10x
The total amount of flour in a bakery after receiving new stock equal to 3/10 of its current stock (x)
Original stock = x
New stock = 3/10x
Total stock = x + 3/10x
= 13/10x
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The non-parallel sides of a trapezoid are called the
Answer:
Step-by-step explanation:
the legs
Factor the expression.
3r2 – 75
Answer:
3(r + 5)(r - 5)
Step-by-step explanation:
Both 3 and 75 are divisible by 3, so we take out a 3.
3(r^2 - 25)
Next, we can factor r^2 - 25. It's a difference of squares.
3(r + 5)(r - 5)
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AC and BD intersect at point E which is inside the circle. Find the measure of Arc AB if Arc CD = 60 degrees and Angle CED = 35 degrees.
Th measure of arc AB will be 60 degrees
Circle theoremThe figure shown shows a circle with lines AC and BD intersecting the circle at the point E
From the figure given the measure of the arc AB is congruent to the arc CD.Given that the measure of arc CD is 60 degrees, hence the measure of arc AB will also be 60 degrees
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