Find the area of the saved region. The graph depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 91

Answers

Answer 1

The area of the shaded region is 0.725746882.

What is a cumulative distribution function?

The probability distribution of random variables is described using the cumulative distribution function. The probability for a discrete, continuous, or mixed variable may be described using it. The cumulative probability for a random variable is calculated by adding the probability density function.

Given:

The graph depicts the IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 91.

From the diagram,

the critical value is 91.

The formula to calculate the z-score is,

z = (x - u) / s,

Substituting the given values to the formula,

the given values are;

x = critical value = 91

u = mean = 100

s = standard deviation = 15

Thus,

z = (x - u) / s

z = -0.6

P(z > -0.6 ) = 0.725746882

Therefore, the area is 0.725746882.

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Find The Area Of The Saved Region. The Graph Depict IQ Scores Of Adults, And Those Scores Are Normally

Related Questions

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x​, is found to be 97​, and the sample standard​ deviation, s, is found to be 13. ​(a) Construct a 90​% confidence interval about μ if the sample​ size, n, is 27. ​(b) Construct a 90​% confidence interval about μ if the sample​ size, n, is 18. ​(c) Construct an 80​% confidence interval about μ if the sample​ size, n, is 27. ​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed?

Answers

a) 90% confident that the true population mean μ is between 91.01 and 102.99.

b) 90% confident that the true population mean μ is between 92.26 and 101.74.

c) 80% confident that the true population mean μ is between 93.79 and 100.21.

d) Using Central Limit Theorem to approximate the population mean as normally distributed, the confidence intervals can still be computed using the same formula as before.

(a) To construct a 90% confidence interval about μ when n = 27, we use the formula:

x ± z × (s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the z-score that corresponds to the desired confidence level (in this case, z = 1.645 for a 90% confidence level). Plugging in the values given, we get:

97 ± 1.645 × (13/√27)

which simplifies to:

(91.01, 102.99)

Therefore, we are 90% confident that the true population mean μ is between 91.01 and 102.99.

(b) To construct a 90% confidence interval about μ when n = 18, we use the same formula as before, but with a different z-score (since the sample size is smaller). In this case, we use z = 1.734, and we get:

97 ± 1.734 × (13/√18)

which simplifies to:

(92.26, 101.74)

Therefore, we are 90% confident that the true population mean μ is between 92.26 and 101.74.

(c) To construct an 80% confidence interval about μ when n = 27, we use the same formula as before, but with a different z-score (since the confidence level is different). In this case, we use z = 1.282, and we get:

97 ± 1.282 × (13/√27)

which simplifies to:

(93.79, 100.21)

Therefore, we are 80% confident that the true population mean μ is between 93.79 and 100.21.

(d) The confidence intervals in parts (a)-(c) assume that the population is normally distributed. If the population is not normally distributed, we cannot rely on these intervals to accurately estimate the true population mean. However, if the sample size is sufficiently large (usually n > 30), we can use the Central Limit Theorem to approximate the population mean as normally distributed, and the confidence intervals can still be computed using the same formula as before. If the sample size is small and the population is not normally distributed, other methods may be needed to construct a confidence interval, such as bootstrapping or using a non-parametric approach.

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what is the unknown number in sequence 2 in the chart? What rule can you write that relates sequence 2 to sequence 1

Answers

The tenth term of the second sequence is 80 and sequence 2 is formed by multiplying by 2 to sequence 1. Then the correct option is C.

What is an arithmetic sequence?

Let a₁ be the first term and d be a common difference. Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

From the table, the first term of the first sequence is 4 and the first term of the second sequence is 8. If the first sequence is multiplied by 2 then we obtain the second sequence.

The common difference of the second sequence is given as,

d = 16 - 8

d = 8

Then the tenth term of the second sequence is given as,

a₁₀ = 8 + (10 - 1) x 8

a₁₀ = 8 + 72

a₁₀ = 80

The tenth term of the second sequence is 80 and sequence 2 is formed by multiplying by 2 to sequence 1. Then the correct option is C.

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The complete question is attached below.

Which is the graph of f(x) = square root 4x

Answers

The graph of the function is attached

How to determine the graph of the function

From the question, we have the following parameters that can be used in our computation:

f(x) = square root 4x

This can be expressed as

f(x) = √(4x)

Take the square root of 4

So, we have the following representation

f(x) = 2√x

This means that the graph f(x) = √(4x) and f(x) = √(4x) are the same

Next, we plot the graph

See attachment for the graph of f(x)

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bo is buying a board game that usually cost b dollars

Answers

The amount to be paid by Bo is 0.82B

What is percent?

A percent of a number is the 100th part of it.

Given that, the board game costs B dollars. Price is reduced by 18%.  we need to calculate the final bill.

Cost of game = B dollars

Discount = 18% = 0.18

Discount amount = 0.18B

Final cost = B-0.18B

Amount to pay = 0.82B

Hence, the amount to be paid by Bo is 0.82B

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The complete question is:-

Bo is buying a board game which usually costs B dollars. The game is on sale, and the price has been reduced by 18% There are different ways of thinking about how to calculate Bo's final bill. Match the expressions to their meanings.

Find an infinite set of positive integers such that the sum of any two distinct elements has an even number of distinct prime factors

Answers

One possible set of positive integers that satisfies the given condition is the set of powers of 2, i.e., {2, 4, 8, 16, 32, ...}.

To see why this set works, note that any two distinct powers of 2 have a different binary representation, differing in at least one bit. This means that their sum will have one more "1" bit in its binary representation than either of the two numbers being added.

Since any prime number greater than 2 is odd, it follows that the sum of any two distinct powers of 2 will have an even number of distinct prime factors, namely the powers of 2 that appear in its binary representation.

First, let's note that every positive integer can be uniquely expressed as a product of prime powers, e.g., 36 = 2^2 * 3^2. The prime factors of an integer are the primes that appear in its prime factorization, e.g., the prime factors of 36 are 2 and 3.

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what part of 18 is 4

Answers

22.22 repeating.
Steps:
4/18 x 100= 22.22

(d) If we take 1000 samples of size n = 75 from the population of all copayments for a
month's supply of topical painkiller ointment for regular users and plot the sample means on
a dotplot, describe the shape you would expect to see in the plot and where it would be
centered.
The shape of the plot will be?
and the center will be at?

Answers

hola i can help... all you have to do is grab a calculator and add 100 to each number, them sbract them by 302

plese help asap pleaaaaaaaaaase!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer: 63

63-15=48

Step-by-step explanation:

Which constants could each equation be multiplied by to eliminate the x-variable using addition in this system of
equations?
2x+3y=25
-3x+4y=22

Answers

To eliminate the x-variable using addition in this system of equations we must multiply 3(2x + 3y = 25) and 2(- 3x + 4y = 22).

What are the three types of solutions for a system of linear equations?

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Given, A system of equations 2x + 3y = 25 and - 3x + 4y = 22.

Now, To eliminate the x-variable using addition we have to multiply equation (i) by 3 and equation (ii) by 2 which results in,

6x + 9y = 75 and - 6x + 8y = 44,        (6x + (-6x) would cancel out).

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9. 0/10 points Previous Answers EppDiscMaths 2.2.035. My Notes Ask Consider the following statement. Sam will be allowed on Signe's racing boat only if he is an expert sailor. Rewrite the statement in if-then form in two ways, one of which is the contrapositive of the other. Use the formal definition of "only if." (Select all that apply.) If Sam is not an expert sailor, then he will be allowed on Signe's racing boat. If Sam is allowed on Signe's racing boat, then he is not an expert sailor. If Sam is allowed on Signe's racing boat, then he is an expert sailor. If Sam is not allowed on Signe's racing boat, then he is an expert sailor. If Sam is an expert sailor, then he will not be allowed on Signe's racing boat. If Sam is not an expert sailor, then he will not be allowed on Signe's racing boat. Need Help? Read It Talk to Tutor

Answers

If Sam is not an expert sailor, then he will not be allowed on Signe's racing boat. and If Sam is allowed on Signe's racing boat, then he is an expert sailor.

are both correct if-then forms of the given statement, with the first being the contrapositive of the second. The other options are not correct if-then forms.

The original statement is "Sam will be allowed on Signe's racing boat only if he is an expert sailor." This statement can be rewritten in if-then form using the formal definition of "only if," which means "if and only if" or "implies and is implied by."

One possible if-then form is "If Sam is not an expert sailor, then he will not be allowed on Signe's racing boat." This is the contrapositive of the original statement, which means that it is logically equivalent to the original statement. It asserts that if Sam is not an expert sailor, then he cannot be on Signe's racing boat.

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Find the surface area of the composite figure. 5.cm idem 10cm 8cm 4cm 24 12cm If you'd like, SA = [Ml] cm2 jest calculator. 4cm 5cm

Answers

To find the surface area of the composite figure, we need to break it down into simpler shapes and add up their surface areas. From the given dimensions, we can see that the composite figure consists of two rectangular prisms and a triangular prism.

The dimensions of the rectangular prism are 10 cm (length), 8 cm (width), and 24 cm (height). Therefore, its surface area is:

SA1 = 2lw + 2lh + 2wh

SA1 = 2(10 cm)(8 cm) + 2(10 cm)(24 cm) + 2(8 cm)(24 cm)

SA1 = 160 cm^2 + 480 cm^2 + 384 cm^2

SA1 = 1024 cm^2

The dimensions of the triangular prism are 5 cm (base), 12 cm (height), and 8 cm (length). Therefore, its surface area is:

SA2 = lb + 2[(1/2)bh + lh]

SA2 = (8 cm)(5 cm) + 2[(1/2)(5 cm)(12 cm) + (8 cm)(12 cm)]

SA2 = 40 cm^2 + 240 cm^2 + 96 cm^2

SA2 = 376 cm^2

The dimensions of the rectangular prism on top are 4 cm (length), 5 cm (width), and 12 cm (height). Therefore, its surface area is:

SA3 = 2lw + 2lh + 2wh

SA3 = 2(4 cm)(5 cm) + 2(4 cm)(12 cm) + 2(5 cm)(12 cm)

SA3 = 40 cm^2 + 96 cm^2 + 120 cm^2

SA3 = 256 cm^2

To find the total surface area of the composite figure, we add the surface areas of the three shapes:

Total surface area = SA1 + SA2 + SA3

Total surface area = 1024 cm^2 + 376 cm^2 + 256 cm^2

Total surface area = 1656 cm^2

Therefore, the surface area of the composite figure is 1656 cm^2.

an amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. two alternative loading/unloading methods have been proposed. to account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. use the following data to test for any significant effect due to the load

Answers

The signficant changes that are happening as per the information provided in the question will be as follows:

1. The p-value for Factor A is 0.4194 option e. greater than 0.10.

2. The conclusion with respect to Factor A will be option b. Factor A is not significant.

3. The conclusion with respect to Factor B will be option b. Factor B is not significant.

4. The p-value for the interaction of factors A and B is 0.1621 option e. greater than .10

5. There is no effect of decreasing the waiting time and changing the loading and unloading methods  between the rides.

Here, we are going to perform two-way ANOVA Observation

A       B               C                

41, 43, 49 52, 44, 46 50, 46, 48

49, 50, 48 50, 46, 48 48, 44, 46          

Sums of row and column

A      B        C          Row total (xa)

133     142   144                    419

147     144   138                    429

Col total (xb)

280   286 282                    848

For A,

∑x²=412+432+492+...+482+442+462=40088

∑x²b/ra =1/3⋅2(280²+286²+282²)

=1/6(78400+81796+79524)

=1/6(239720)

For B,

=39953.3333

∑x²a/rb=1/3⋅3(419²+429²)

=1/9(175561+184041)

=1/9(359602)

For C,

=39955.7778

∑∑x²ab/r=  1/3(133²+142²+144²+147²+144²+138²)

=1/3(17689+20164+20736+21609+20736+19044)

=1/3(119978)

=39992.6667

For D,

(∑x)²/rab

=(848)²/3⋅2⋅3

=719104/18

=39950.2222

Sum of squares total

SST=∑x²-(∑x)²/n

Now we subtract A and D

=(A)-(D)

=40088-39950.2222

=137.7778

Sum of squares between rows will be,

SSA=∑x²a/rb-(∑x)²/n

Now, we subtract C and D

=(C)-(D)

=39955.7778-39950.2222

=5.5556

Sum of squares between columns

SSB=∑x²b/ra- (∑x)²/n

Now, we subtract B and D

=(B)-(D)

=39953.3333-39950.2222

=3.1111

Sum of squares between columns

SSAB=∑∑x²ab/r-(∑x)²/n-SSA-SSB

Now we subtract B, D and Sum of squares between columns

=(B)-(D)-SSA-SSB

=39992.6667-39950.2222-5.5556-3.1111

=33.7778

The residual value of sum of squares Error,

SSE=SST-SSA-SSB-SSAB

=137.7778-5.5556-3.1111-33.7778

=95.3333

ANOVA table

Source. Sums    Degrees Mean Squares Square

of squares of freedom variation freedom

                       SS              DF          MS              F        

A         SSA=5.5556     a-1=1 MSR=5.5556    0.6993   0.4194 (p-value)

B            SSB=3.1111      b-1=2 MSC=1.5556    0.1958

0.8247 (p-value)

AB       SSAB=33.7778   2   MSAB=16.8889   2.1259 0..1621 (p-value)

Error (residual) SSE=95.33      12         MSE= 7.9444            

Total of SST=137.7778      will be    17  

In conclusion,

1. F for between columns, the critical value F(1,2) at 0.05 level of significance will be 4.7472. As computed that FR=0.6993<4.7472

H0 has been accepted, thus, there is no significant difference between rows.

P value is 0.4194 > 0.05. Hence, we fail to reject H0

2. F for between columns, the critical value F(2,2) at 0.05 level of significance will be 3.8853. As computed, FC=0.1958<3.8853. Thus, H0 is accepted and there is no significant difference between columns. P value is 0.8247 > 0.05. Hence, we fail to reject H0

3. The interaction between the Factors AB, there is no sufficient evidence to support the claim of interaction between the factors. Thus, P value is 0.1621 > 0.05. Hence, we fail to reject H0.

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Note that the full question is:

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/ unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use α = .05. Use both p-Value and Critical-Value approaches.Type of Ride

Roller Coaster Screaming Demon Log Flume

Method 1 41 52 50

43 44 46

49 46 48

Method 2

49 50 48

51 46 44

47 48 46

1. The p-value for Factor A is:__________.

a. less than .01

b. between .01 and .025

c. between .025 and .05

d. between .05 and .10

e. greater than .10Item 18

2. What is your conclusion with respect to Factor A?

a. Factor A is significant

b. Factor A is not significant

3. The p-value for Factor B is:_______.

a. less than .01

b. between .01 and .025

c. between .025 and .05

d. between .05 and .10

e. greater than .10

3. What is your conclusion with respect to Factor B?

a. Factor B is significant

b. Factor B is not significant

4. The p-value for the interaction of factors A and B is:_______.

a. less than .01

b. between .01 and .025

c. between .025 and .05

d. between .05 and .10

5. What is your recommendation to the amusement park?

The probability of obtaining a head when a certain coin is flipped is about 0. 65. Which of the following is closest to the probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times?O 0.14
O 0.37
O 0.39
O 0.60
O 0.65

Answers

The probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times is 0.370

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

"Information available from the question"

The parameters are:

Sample size, n = 25

Probability of success, p = 0.65

Number of success, x ≤ 15

The probability is represented using the following binomial formula:
[tex]P(x) =n_C_x*p^x*(1-p)^n^-^x[/tex]

Using the above formula, we have:

P(x ≤ 15) = 0.370

Hence, the probability is 0.370

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Compute each matrix sum or product if it is defined. If an expression is​ undefined, explain why. Let A= 3 0 −2 4 −5 2 ​, B= 8 −4 1 2 −3 −4 ​, C= 2 3 −3 2 ​, and D= 2 5 −2 5 .
−2​A, B−2​A, ​AC, CD

Answers

The solution is,

-2A = (-6, -8, 0, 8, 2, -8)

B - 2A = (2, -7, -4, 3, 4, -12)

AC is undefined.

CD = (3, 2, 12, 5)

What is matrix?

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

here, we have,

Given the matrices:

A = (3 4 0 -4 -1 4)

B = (8 1 -4 -5 2 -4)

C = (1 -1 3 1)

D = (3 -2 4 5)

We are required to compute the following

-2A, B - 2A, AC, CD

For -2A:

-2(3 4 0 -4 -1 4)

= (-6, -8, 0, 8, 2, -8)

For B - 2A:

Because B - 2A = B + (-2A),

we have:

(8 1 -4 -5 2 -4) + (-6, -8, 0, 8, 2, -8)

(2, -7, -4, 3, 4, -12)

For AC:

(3 4 0 -4 -1 4)(1 -1 3 1)

This is undefined.

For CD:

(1 -1 3 1)(3 -2 4 5)

= (3, 2, 12, 5)

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Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.[1 h 43 6 8]

Answers

The value of h such that the matrix is the augmented matrix of a consistent linear system is 2

For the given matrix to be the augmented matrix of a consistent linear system, we need to check whether the matrix is in row echelon form or not. If the matrix is in row echelon form and the last row is not all zeros, then the linear system is consistent.

We can use elementary row operations to transform the matrix into row echelon form.

[tex]\left[\begin{array}{ccc}1&h&4\\3&6&8\end{array}\right][/tex]

R2 <- R2 - 3R1

[tex]\left[\begin{array}{ccc}1&h&4\\0&6-3h&-4\end{array}\right][/tex]

The matrix is in row echelon form. Now, we need to check whether the last row is all zeros or not.

If 6-3h = 0, then the last row will be all zeros, which implies that the linear system is inconsistent.

If 6-3h ≠ 0, then the last row will not be all zeros, which implies that the linear system is consistent.

Therefore, we need to solve the equation 6-3h = 0 to determine the value of h that makes the linear system consistent.

6-3h = 0

3h = 6

h = 2

So, the value of h that makes the matrix the augmented matrix of a consistent linear system is h = 2.

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Brandon has a certain amount of money. If he spends $24, then he has of the original amount left.
How much money did Brandon have originally?

Answers

Brandon have a total of $32 originally

How much money did Brandon have originally?

From the question, we have the following parameters that can be used in our computation:

When he spends $24, he has 3/4 of the original amount left

Using the above as a guide, we have the following:

24 = Original * 3/4

Make "Original" the subject of the formula

So, we have the following representation

Original = 24/(3/4)

Evaluate the expression

Original = 32

Hence, the amount is $32

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Do the ratios 5/10 and 6/12 form a proportion

Answers

Answer:

Step-by-step explanation:

if we simplify both of them,

5/10=1/2

and

6/12=1/2

then it means they are equal

Which best describes the composition of transformations that maps JKLM to PQRS?

Answers

Answer:

D

Step-by-step explanation:

The notation is not what I am used to, but I think that I understand.  To go from the large figure to the smaller figure.  You need to dilate your figure by 1/3 .  The length of the big figure is 6 and 1/3 of that is a length of 2.  The width of the big figure is 3.  !/3 of that is 1 and that is what I see on the smaller figure.

Assuming the center of the dilation is point J.  If you move the shrunken figure 2 to the left and 5 down, it would fit right on top of the smaller figure.

The correct translation rule is given as -

(D_1/3 . T_<-2,-5> ) JKLM.

What is translation?

Translation is defined as the movement of graphical image over the two

dimensional plane. In genera, we can write the translation as -

(x, y) → (x ± k, y ± a)

here, we have,

Given is the composition of transformations that maps JKLM to PQRS.

Firstly →

The image is first translated according to the rule -

(x, y) → (x - 2, y - 5).

Secondly -

The image is then dilated by the scale factor -

{K} = 1/3.

Therefore, the correct translation rule is given as -

(D_1/3 . T_<-2,-5> ) JKLM.

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Which expression represents the distance
between point J and point K?
|-9|+|-2| |6|+|-9|
|-9|-|-2|
16|-|-2|
-10
10+ y
0
-10-
-J (6,-2)
K (6,-9)
10

Answers

The expression showing the distance between point J and point K is |-9|-|-2|

What is distance between points?

Distance between two points is the length of the line segment that connects the two given points.

Given that, two points J(6, -2) and k(6, -9), we need to find the distance between them,

The distance between two pints is given by,

D = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here, the points are, (6, -2) and (6, -9)

Therefore,

|JK| = [tex]\sqrt{(0-0)^2+(-9+2)^2}[/tex]

|JK| = √7²

|JK| = 7 units

Therefore, the expression showing the distance between point J and point K is |-9|-|-2|

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Gold Corp. has an ROE of 12% and a payout ratio of 20%.
What is its sustainable growth rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answers

The sustainable growth rate is calculated by subtracting the payout ratio from the ROE.

The sustainable growth rate is calculated by subtracting the payout ratio from the ROE. To calculate the sustainable growth rate for Gold Corp., we must first calculate the retention ratio. The retention ratio is calculated by subtracting the payout ratio from 100%. In this case, the retention ratio would be 100% - 20% = 80%. The sustainable growth rate is then calculated by multiplying the retention ratio by the ROE. In this case, the equation would be 80% * 12% = 9.6%. The sustainable growth rate for Gold Corp. is 9.6%, which can be rounded to 9.6%.

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Use the t-table to find the t-score that cuts off 2.5% in the upper tail for a t-distribution with 24 degrees of freedom
a: 1.711
b: 2.064
c: 2.492
d: 2.069

Answers

We can see from a t-table with right-tail probabilities that the probability value that is closest to 2.5% is 0.0250, which is represented by a t-score.

The row in the table that corresponds to the number of degrees of freedom (df) must be found before the column that corresponds to the desired level of significance or alpha value in order to use the t-table to determine a t-score that cuts off a specific percentage in the upper tail for a t-distribution with a given number of df.

Since there are 24 degrees of freedom in this situation, we need to identify the t-score that removes 2.5% of the upper tail. We will be looking at the column for the right-tail probabilities because this test has one tail (upper tail), making it a one-tailed test.

Therefore, We can see from a t-table with right-tail probabilities that the probability value that is closest to 2.5% is 0.0250, which is represented by a t-score.

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Which of the following best describes the relationship between the amount of time spent snoozing and the amount of time slept?

A. no association
B. positive association
C. positive and negative association
D. negative association

Answers

Answer: It is D.

Step-by-step explanation:

1Caleb started saving money in a cookie jar. He started with $25 He adds $10 to the cookie jar each week. Write an equation where wis the number of weeks Caleb
saves his money andt is the total amount in dollars in the cookie jar. Determine which variable is the independent variable and which is the dependent variable. Then, graph the total amount in the cookie jar for w being less than 6 weeks.

Answers

The linear equation is y = $25 + $10*w, and its graph is on the image at the end.

How to write the equation?

Here we know that he started with $25 He adds $10 to the cookie jar each week. Then we can model this with a linear equation:

y = $25 + $10*w

Where w is the number of weeks.

Now we want to graph this, to do so, we just need to find two points on the line.

if w = 0

y = $25 + $10*0 = $25

if w = 6

y = $25 + $10*6 = $85

So we need to graph the points (0, 25) and (6, 85) and connect them witha  line.

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Given the sample data x: 23 17 15 30 25
(a) Find the range.
(b) Verify that sum of x= 110 and sum of x^2= 2568
(c) Use the results of part (b) and appropriate computation formulas to compute the sample variances s^2 and sample standard deviation s.
(d) Use the defining formulas to compute the sample variance s^2 and sample standard deviation s.
(e) Suppose the given data comprise the entire population of all x values. Compute the population variance ơ^2 and population standard deviation ơ.

Answers

The range of the given data is 15, the sum is 110, variance is 37.

The sample variance is a value that measures the variability of values in the data set and how much the observed values deviate from the value of the mean or central value of the data set.

X=[23,17,15,30,25]

(a)

The value of the range is the difference between the maximum value and minimum value:

range=30-15=15

(b)

Sum(x)= 23+17+15+30+25=110

the sum of x2 = [tex]23^2+17^2+15^2+30^2+25^2=2568[/tex]

(c)

from part (b)

[tex]s^2=\sum x_i-nX^2]/[n-1]\\\\=[2568-5(22)^2][5-1]\\\\=37[/tex]

(d)

Using the definition of the variance, first we calculate the mean,

u=110/5=22

u=22

[tex]v^2=\frac{1}{n-1}\sum (x_i-u)^2\\\\=148/4\\=29.6\\s=6.083.[/tex]

e)

The value of population variance is v =5.44

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Find the mean absolute deviation (MAD) of the data in the bar chart below.
Please answer

Answers

Mean absolute deviation of the data is 1.

What is mean absolute deviation?

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

Given, In bar chart

Number of artists n = 4

Number of albums for Lil Shane x₁ = 7

Number of albums for Ben Raises x₂ = 9

Number of albums for Nicky x₃ = 6

Number of albums for Underdog x₄ = 6

Mean of the number of albums

μ = (7 + 9 + 6 + 6)/4 = 28/4 = 7

|μ - x₁| = |7 - 7| = 0

|μ - x₂| = |7 - 9| = |-2| = 2

|μ - x₃| = |7 - 6| = 1

|μ - x₄| = |7 - 6| = 1

Mean absolute deviation = ∑|x - μ|/n

= (0 + 2 + 1 + 1)/4

= 1

Hence, 1 is the mean absolute deviation (MAD) of the data in the bar chart.

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Read the following paragraph and answer the question. "Emest Cline is an American Screenwriter and author. Emest was born in 1972. He started his writing career in 1992
doing spoken word poetry. His best known works include 'Dance Monkey Dance' and 'When I Was a Kid. He then moved to film, as the screenwriter of the film Fanboys. He then released one of the most entertaining novels of all time, Ready Player One. Today Cline is still working, writing for many projects." Why type of informational text is this?
A. Biography
B. Autobiography
C. Essay
D. Memoir

Answers

Biography, as it provides a brief overview of the life and career of Emest Cline.

What is Biography ?

A biography is a written account of another person's life, typically written by someone else. It often includes information about the person's background, education, career, accomplishments, and other significant events and experiences throughout their life. Biographies can also provide insights into a person's personality, character, and motivations, as well as the historical or cultural context in which they lived.

Given ,

Emest Cline is an American Screenwriter and author. Emest was born in 1972. He started his writing career in 1992

doing spoken word poetry. His best known works include 'Dance Monkey Dance' and 'When I Was a Kid. He then moved to film, as the screenwriter of the film Fanboys. He then released one of the most entertaining novels of all time, Ready Player One. Today Cline is still working, writing for many projects.

The type of informational text that this paragraph is is A.

Therefore, Biography, as it provides a brief overview of the life and career of Emest Cline.

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Show your work, and graph the piecewise function below.

Answers

For x ≤ -1, the function is given by f(x) = 4x + 1. This is a linear function with a slope of 4 and y-intercept of 1. The graph of this part of the function is a straight line passing through (0, 1) with a steep slope, extending towards negative x-values.

What is function?

In mathematics, a function is a rule that associates each element in one set (called the domain) to a unique element in another set (called the range). Functions are one of the most important concepts in mathematics and have a wide range of applications in various fields.

A function is usually denoted by a letter, such as f(x), where x is an element in the domain and f(x) is the corresponding element in the range. The domain of a function is the set of all possible values of x for which the function is defined, and the range is the set of all possible values of f(x).

To graph the piecewise function f(x), we will graph each part of the function separately.

For -1 < x < 2, the function is given by f(x) = -2x - 3. This is also a linear function with a slope of -2 and y-intercept of -3. The graph of this part of the function is a straight line passing through (-1, 1) with a gentle slope, extending towards positive x-values until it reaches x=2.

For x ≥ 2, the function is given by f(x) = 5. This is a horizontal line at y=5, which is a constant function. The graph of this part of the function is a horizontal line at y=5 starting from x=2.

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Plans were made for a rectangular garden to be planted outside a library. The plans use a scale of 1.6cm=2cm. If the Girardeau is 14cm by 10cm on the scale, find the actual dimensions

Answers

The actual dimensions of the rectangular garden are 17.5 cm by 12.5 cm

How to determine the actual dimensions

From the question, we have the following parameters that can be used in our computation:

Scale: 1.6 cm = 2 cm

A scale is the ratio of the size of the drawing to the size of the actual object.

Given that the dimension is

14 cm by 10 cm


Using the above as a guide, we have the following equation

Actual = 14 * 2/1.6 cm by 10 * 2/1.6 cm

Evaluate

So, we have the following representation

Actual = 17.5 cm by 12.5 cm

Hence, the actual is 17.5 cm by 12.5 cm

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What is the square root of 7 to the nearest hundredths

Answers

The square root of 7 is approximately 2.65 when rounded to the nearest hundredth.

The ratio of students to teachers is 72 : 3. Which statement describes this relationship?
Responses
A There are 3 students for each teacher.There are 3 students for each teacher.
B There are 8 students for every 9 teachers.There are 8 students for every 9 teachers.
C There are 36 students for every 2 teachers.There are 36 students for every 2 teachers.
D There are 24 students for each teacher.

Answers

D. There are 24 students for each teacher.

You can simplify the ratio of 72 : 3 by dividing 72 by 3

72/3=24

Therefore, for every 24 students there is 1 teacher
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