There are seven different books to choose from. In how many ways can you arrange these books on three different shelves of a bookcase?

When comparing the given numbers 7.17 x 10^4 and 8.17 x 10^5, we find that 7.57 x 10^4 is the number that lies between them.

To determine this, we compare the given numbers and look for the smallest number that is greater than 7.17 x 10^4 and the largest number that is smaller than 8.17 x 10^5.

Let's break down the given numbers:
7.17 x 10^4 is equivalent to 71700 (since 10^4 = 10,000).
8.17 x 10^5 is equivalent to 817,000 (since 10^5 = 100,000).

We can see that 7.57 x 10^4 is greater than 71700 but smaller than 817000, making it the number that falls between the two given values.

Therefore, the correct answer is C. 7.57 x 10^4.
To summarize, when comparing the given numbers 7.17 x 10^4 and 8.17 x 10^5, we find that 7.57 x 10^4 is the number that lies between them.

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(fg)(x)= x³ - 7x² - 9x + 8

domain is (-∞,∞)

Given: f(x)= x-8, g(x)= x² +1x - 1

To find (fg)(x) we multiply f(x) and g(x)

(fg)(x) = f(x) * g(x)

(fg)(x)= (x-8) (x²+x-1)

(fg)(x)= x³ + x² - x - 8x² - 8x +8

(fg)(x)= x³  - 7x²  - 9x + 8

we know, domain for all cubic function is set of all real numbers

domain is (-∞,∞)

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Answer:

24.5

Step-by-step explanation:

Subtract 28 from 90 then divide that by 4 :)

Answer:

15.5

Step-by-step explanation:

Since it is a 90° angle, you do 90 - 28

62

62/4 = 15.5

We are required to determine the conditional odds ratios between race and whether a murder victim, given gender, and interpret the data provided. Here, we are given data on murder rates in the United States, based on which we can calculate the conditional odds ratios. The probability of being a murder victim can be represented by P(MV), and the probability of not being a murder victim can be represented by P(NMV). Also, the probabilities of being a nonwhite or white male or female can be represented by P(NW M), P(W M), P(NW F), and P(W F) respectively.

The conditional odds ratios for murder victims, given gender, and race can be calculated as follows:Conditional odds ratio for nonwhite males:
Odds of being a murder victim for nonwhite males: P(MV | NW M) / P(NMV | NW M)P(MV | NW M) = 0.0263 and
P(NMV | NW M) = 1 - P(MV | NW M) = 0.9737
Therefore, odds of being a murder victim for nonwhite males = P(MV | NW M) / P(NMV | NW M) = 0.0263 / 0.9737 = 0.02705
Odds of being a murder victim for white males: P(MV | W M) / P(NMV | W M)P(MV | W M) = 0.0049 and P(NMV | W M) = 1 - P(MV | W M) = 0.9951
Therefore, odds of being a murder victim for white males = P(MV | W M) / P(NMV | W M) = 0.0049 / 0.9951 = 0.00491
Conditional odds ratio for nonwhite females: Odds of being a murder victim for nonwhite females:
P(MV | NW F) / P(NMV | NW F)P(MV | NW F) = 0.0072 and P(NMV | NW F) = 1 - P(MV | NW F) = 0.9928
Therefore, odds of being a murder victim for nonwhite females = P(MV | NW F) / P(NMV | NW F) = 0.0072 / 0.9928 = 0.00726
Odds of being a murder victim for white females: P(MV | W F) / P(NMV | W F)P(MV | W F) = 0.0023 and P(NMV | W F) = 1 - P(MV | W F) = 0.9977
Therefore, odds of being a murder victim for white females = P(MV | W F) / P(NMV | W F) = 0.0023 / 0.9977 = 0.00231
The odds ratios for males versus females, given race and murder victim status, can be represented as follows: Conditional odds ratio for nonwhite victims: Odds ratio for nonwhite males versus nonwhite females:
0.02705 / 0.00726 = 3.726
Odds ratio for white males versus white females: 0.00491 / 0.00231 = 2.124
Odds ratio for nonwhite males versus nonwhite females: 0.0263 / 0.0072 = 3.653

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Amy and Vince must save approximately $323.45 at the beginning of each month to have the $18,000 they need for their trip to Europe in five years  if they can get 5.5% interest in their savings account.

We know that Amy and Vince want to save $18,000 in five years and can earn 5.5% interest in their savings account, we need to adjust the interest rate to a monthly rate.

First, let's calculate the monthly interest rate (r) from the annual interest rate:

r = (1 + annual interest rate)^(1/12) - 1

= (1 + 0.055)^(1/12) - 1

= 0.0045107

Next, let's calculate the number of periods (n) in months:

n = 5 * 12

= 60 months

Using the future value of an ordinary annuity formula, we can solve for the monthly savings (PMT):

PMT = FV / [((1 + r)^n - 1) / r]

where:

FV = Future Value (desired savings amount)

r = Monthly interest rate

n = Number of periods

FV = $18,000

PMT = 18,000 / [((1 + 0.0045107)^60 - 1) / 0.0045107]

≈ $323.45

Therefore, Amy and Vince must save approximately $323.45 at the beginning of each month to have the $18,000 they need for their trip to Europe in five years.

Therefore, the correct option is $323.45.

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Answer:

B

Step-by-step explanation:

When the number 410 is changed to 310 in the list of student numbers for the 10 schools in the district:

(a) The mean increases by 0.9.

(b) The median decreases by 7.

(a) The mean is calculated by summing up all the values and dividing by the total number of values.

Let's compare the mean before and after the change in the number 410.

Before the change:

Mean = (170 + 194 + 303 + 309 + 316 + 330 + 368 + 371 + 379 + 410) / 10 = 308

After the change (410 changed to 310):

Mean = (170 + 194 + 303 + 309 + 316 + 330 + 368 + 371 + 379 + 310) / 10 = 308.9

Comparing the mean before and after the change, we can see that the mean increases by 0.9.

(b) The median is the middle value of a sorted dataset. In this case, the median is the value that separates the lower half from the upper half when the numbers are arranged in ascending order.

Before the change:

Median = 316

After the change (410 changed to 310):

Median = 309

Comparing the median before and after the change, we can see that the median decreases by 7.

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The numbers of students in the 10 schools in a district are given below. (Note that these are already ordered from least to greatest.) 170, 194, 303, 309, 316, 330, 368, 371, 379, 410 Suppose that the number 410 from this list changes to 310. Answer the following. (a) What happens to the mean? It decreases by It increases by It stays the same. It decreases by It increases by It stays the same. (b) What happens to the median

Answer:

ok

Step-by-step explanation:

If dr. Robinson rejects the null hypothesis after observing a test statistic that exceeds the critical value at the .05 level, there is a 5% chance that the null hypothesis is actually true.

This refers to the hypothesis that there is no significant difference between specified populations, where any observed difference is due to sampling or experimental error.

Hence, we can see that if dr. Robinson rejects the null hypothesis after observing a test statistic that exceeds the critical value at the .05 level, there is a 5% chance that the null hypothesis is actually true.

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The two numbers are x = 3.43 and y = 22.57.

What is a linear equation in two variables?

An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Let the first number be x and the second number be y. Then we can write the given information as a system of equations:

x + y = 26

(2/5)x + (3/8)y = 10

To solve this system, we can eliminate one of the variables by multiplying the first equation by 8 and the second equation by 5, then subtracting the resulting equations:

8x + 8y = 208

10x + 15y = 50

Subtracting these equations gives us:

-2x - 7y = -158

Dividing both sides by -7, we get:

x + y = 22.57

Substituting this back into the first equation, we get:

x + 22.57 = 26

Solving for x, we get:

x = 26 - 22.57

= 3.43

Substituting this back into the original equation x + y = 26, we get:

3.43 + y = 26

Solving for y, we get:

y = 26 - 3.43

= 22.57

Hence, the two numbers are x = 3.43 and y = 22.57.

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Answer:

(2,4)

Step-by-step explanation:

Answer:

1440.1 in^2

Step-by-step explanation:

I drew a picture with work; hopefully this is the equation you're using in the lesson.

Answer:

2a

Step-by-step explanation:

up at the top is the answer

Answer:

-8 +12i

Step-by-step explanation:

(1 + 9i)-(9 - 3i)

Distribute the minus sign

(1 + 9i)-9 + 3i

Combine like terms

1-9  +9i +3i

-8 +12i

Steps to solve:

(1 + 9i)-(9 - 3i)

~Distribute negative sign to left side

(1 + 9i) - 9 + 3i

~Combine like terms

-8 + 12i

Best of Luck!

Answer:

Y-intercept is 0

Step-by-step explanation:

The line crosses at 0,0

x intercept is 0

Y intercept is 0

Answer:

5/8 is smaller.

Step-by-step explanation:

A ratio is just a different type of fraction, a 5:8 ratio means 5/8 which is 0.625. A 7:9 ratio equals 7/9 which is 0.777777

Then to compare them you see which is smaller or bigger.

0.77777  is bigger than 0.625 so we know that 0.77777777 which was the 7:9 ratio is the bigger one.

Answer: 3 3/4

Step-by-step explanation:

From the question, we are informed that Jerome use 3 1/4 gallons of gasoline while driving from school to his baseball game.

Assuming that he originally had 7 gallons in his car, the amount of gasoline he have left will be:

= 7 - 3 1/4

= 3 3/4 gallons

To approximate the area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method, we can use the following formula:

Approximate Area = Δx * [f(x1) + f(x2) + f(x3) + f(x4)]

where Δx is the width of each subinterval and xi represents the right endpoint of each subinterval.

In this case, the interval [2, 4] is divided into four equal subintervals, so Δx = (4 - 2) / 4 = 0.5.

Now, let's evaluate the function at the right endpoints of the subintervals:

f(2.5) = 1/(2.5)^2 = 0.16

f(3) = 1/(3)^2 = 0.1111

f(3.5) = 1/(3.5)^2 = 0.0816

f(4) = 1/(4)^2 = 0.0625

Substituting these values into the formula:

Approximate Area = 0.5 * [0.16 + 0.1111 + 0.0816 + 0.0625]

Approximate Area = 0.5 * 0.4152

Approximate Area = 0.2076

Therefore, the approximate area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method is approximately 0.2076.

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Answer:

The intermediate step in the form;

is;

Explanation:

Given the quadratic equation;

solving by completing the square;

Factorizing;

Therefore, the intermediate step in the form;

is;

The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.

The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.

Here, we will solve this system of equations using inverse of the matrix method as follows:

We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].

The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33]  where,

d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,

d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,

d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,

d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,

d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,

d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,

d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,

d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,

d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.

We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]

Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]

Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.

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Answer:

(a) False

(b) False

(c) True

Step-by-step explanation:

(a) If we had measured the heights of the men and women in centimeters (1 inch= 2.54 cm), the correlation coefficient would have been 2.54 times larger.

No, since changing the units of measurement does not change the correlation coefficient

(b) There is a strong negative association between the heights of men and women because women are always smaller than the men they date.

Negative association means that as one variable increases, the other decreases, Here, we see that as the heights of the men increase, the height of the women do not reliably decrease, hence there is no strong negative asscoiation

(c) There is a positive association between the heights of men and women.

We see from the values given that as the heights of men increase, so do the heights of women and vise versa, so there is a positive association between the heights of men and women

Answer:

\(\boxed{\text{2. 4.7 units}}\)

Step-by-step explanation:

Assume your triangle has the dimensions shown below.

Before we can use the Law of Sines, we must find ∠C.

1. Calculate ∠C

\(\begin{array}{rcl}A + B + C & = & 180^{\circ}\\66^{\circ} + 76^{\circ} + C & = & 180^{\circ}\\142^{\circ} + C & = & 180^{\circ}\\C & = & 38\, ^{\circ}\\\end{array}\)

2. Calculate b

Use the Law of Sines

\(\begin{array}{rcl}\dfrac{b}{\sin B } & = & \dfrac{c}{\sin C}\\\\\dfrac{b}{\sin 76^{\circ}} & = & \dfrac{3}{\sin 38^{\circ}}\\\\\dfrac{b}{0.9703} & = & \dfrac{3}{0.6157}\\\\ & = & 4.873\\b & = & 0.9703\times 4.873\\& = & \boxed{\mathbf{4.7}}\\\end{array}\)

Pythagorean theorem tells us how the side lengths of right triangles are related.

The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.

This relationship can be written as the equation:

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

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Answer:

35 as a fraction is 7/20

Step-by-step explanation:

Answer:

11/35

Step-by-step explanation:

To identify the restaurant with the distribution closest to normal for sodium, we can calculate the goodness-of-fit measures, such as the Anderson-Darling test or the Shapiro-Wilk test, for each restaurant's sodium distribution and select the one with the highest p-value indicating the closest agreement to normality.

To answer the probability questions and identify the restaurant with the distribution closest to normal for sodium, we need access to the dataset and perform statistical calculations using R programming language. Unfortunately, as a text-based AI, I don't have direct access to external datasets or the capability to execute code. However, I can provide you with an outline of the steps you can follow to conduct the analysis:

1. Load the dataset: Import the dataset containing information about the restaurants, including the variable of interest (sodium levels).

2. Probability questions: Formulate two probability questions related to the dataset. For example:

  a) What is the probability that a randomly selected restaurant has sodium levels above a certain threshold?

  b) What is the probability that a randomly selected restaurant has sodium levels within a specific range?

3. Theoretical normal distribution: Assuming that the sodium variable follows a normal distribution, calculate the probabilities using the theoretical normal distribution. You will need to estimate the mean and standard deviation from the dataset.

4. Empirical distribution: Calculate the probabilities using the empirical distribution. This involves computing the sample mean and sample standard deviation from the dataset and using these estimates to calculate the probabilities.

5. Compare the results: Compare the probabilities obtained from the theoretical normal distribution and the empirical distribution. Assess the agreement between the two methods by examining the differences in probabilities.

6. Identify closest to normal distribution: Analyze the sodium variable for each restaurant and assess which restaurant's distribution exhibits the closest resemblance to a normal distribution. This can be done by visually inspecting histograms or using statistical tests such as the Shapiro-Wilk test.

By following these steps and implementing the necessary code in R, you will be able to answer the probability questions and determine which restaurant's sodium distribution is closest to normal.

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The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

---------------------------------------------------------------------------

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

---------------------------------------------------------------------------

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

---------------------------------------------------------------------------

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

---------------------------------------------------------------------------

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

---------------------------------------------------------------------------

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

---------------------------------------------------------------------------

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

---------------------------------------------------------------------------

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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Answer:

idkjjjlhy of do it si or