There are a total 12,715 seats in an arena. Of the total,
7,512 seats are currently occupied by spectators. How
many seats, to the nearest percent, are currently oc-
cupied?
A. 12
B. 52
C. 59
D. 61
E. 75

The expression can be simplified as 2.09 × 10⁻⁹.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

We have to evaluate (23)⁻³ . (34)⁻³.

We have a rule of exponent that,

aⁿ . bⁿ = (a . b)ⁿ

Applying the rule,

(23)⁻³ . (34)⁻³ = (23 × 34)⁻³

                      = 782⁻³

We have another rule of exponent that,

a⁻ⁿ = 1 / aⁿ

So, 782⁻³ = 1 / 782³ = 2.09 × 10⁻⁹

Hence the simplified form is 2.09 × 10⁻⁹.

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Answer:

linear function

Step-by-step explanation:

The given function is linear function.

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3\(x\) - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with g(\(x\)), this function can be written as g(\(x\) )= 3\(x\) - 2.

A linear function is of the form g(\(x\)) = m\(x\) + b where 'm' and 'b' are real numbers. Here,

Given:

y = 800 - 114.29\(x\)

year     accumulated          

            depreciation    

0          0                      

1          114.29              

2          228.58                

3          342.87                

4          457.16                  

5          571.45                  

6          685.74                  

7          800          

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The probability that a patient testing positive for avian influenza with this test is actually infected with avian influenza is approximately 0.803 or 80.3%

To determine the probability, we can use Bayes' theorem. Let's assume that we have 10,000 patients tested. Out of these, 4% (or 400) patients will be infected with avian influenza, and the remaining 96% (or 9,600) will not have the infection.

Out of the 400 infected patients, the test will correctly identify 98% of them, which is 392 patients. However, there will be a false positive rate of 1% among the 9,600 non-infected patients, which is 96 patients.

So, the total number of patients testing positive will be 392 + 96 = 488. Out of these, 392 patients are truly infected, which gives us the probability of a patient testing positive being infected as 392/488 ≈ 0.803.

Therefore, the probability that a patient testing positive for avian influenza with this test is actually infected with avian influenza is approximately 0.803 or 80.3%.

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we make the table using 3 any numbers for x and replacing on the function

x=-1

x=0

x=1

Table

place the points and joint it

the function is growth since it can be seen in the graph

Domain

We can see on graph the line can be any value of x because horizontally it has no beginning or end

Range

We can see the smallest value that the graph could take is -4 and the May is not defined so it is infinite

Y intercept

point where x = 0 and the line touches the y axis

the point is

Asymptote

horizontal or vertical line that the nape line will touch

our asymptote lies on the value of y = -4, why the line never touches this value

Among the options given in the question, the following are the properties of the linear correlation coefficient:

The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

If r=−​1, then a perfect negative linear relation exists between the two variables.

Properties of linear correlation coefficient:

Linear correlation coefficient is a value calculated from given data and used to measure the strength of linear relationship between two variables, for instant between x and y variables.

The sign of this coefficient (r) indicates the direction linear relationship will take between x and y. Below are some properties of the linear correlation coefficient:

Now, the properties of the linear correlation coefficient among the given ones in the question are:

b. The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

d. A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

f. If r=−​1, then a perfect negative linear relation exists between the two variables.

Hence, options b, d and f are correct.

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To convert a fraction into a decimal you have to divide the numerator by the denominator. For example, to convert 39/8, you need to divide 39 by 8, which is equal to 4.875.

Answer:

yes

Step-by-step explanation:

There are 67 integers from 1 to 250 that are not divisible by any of the numbers 2, 3, 5, and 7. To find the number of integers from 1 to 250 that are not divisible by any of the numbers 2, 3, 5, and 7, we can use the principle of inclusion-exclusion.

Step 1: Find the number of integers divisible by each individual number.

- Number of integers divisible by 2: 250/2 = 125

- Number of integers divisible by 3: 250/3 = 83 (rounded down)

- Number of integers divisible by 5: 250/5 = 50

- Number of integers divisible by 7: 250/7 = 35 (rounded down)

Step 2: Find the number of integers divisible by each pair of numbers.

- Number of integers divisible by both 2 and 3: 250/(2*3) = 41 (rounded down)

- Number of integers divisible by both 2 and 5: 250/(2*5) = 25

- Number of integers divisible by both 2 and 7: 250/(2*7) = 17 (rounded down)

- Number of integers divisible by both 3 and 5: 250/(3*5) = 16 (rounded down)

- Number of integers divisible by both 3 and 7: 250/(3*7) = 11 (rounded down)

- Number of integers divisible by both 5 and 7: 250/(5*7) = 7 (rounded down)

Step 3: Find the number of integers divisible by all three numbers (2, 3, 5) using the principle of inclusion-exclusion.

- Number of integers divisible by both 2, 3, and 5: 250/(2*3*5) = 8 (rounded down)

Step 4: Find the number of integers divisible by all four numbers (2, 3, 5, 7) using the principle of inclusion-exclusion.

- Number of integers divisible by 2, 3, 5, and 7: 250/(2*3*5*7) = 1 (rounded down)

Step 5: Use the principle of inclusion-exclusion to find the total number of integers not divisible by any of the given numbers.

Total = Number of integers - (Sum of number of integers divisible by individual numbers) + (Sum of number of integers divisible by pairs of numbers) - (Number of integers divisible by all three numbers) + (Number of integers divisible by all four numbers)

Total = 250 - (125 + 83 + 50 + 35) + (41 + 25 + 17 + 16 + 11 + 7) - 8 + 1

Calculating this expression, we find:

Total = 250 - 293 + 117 - 8 + 1 = 67

Therefore, there are 67 integers from 1 to 250 that are not divisible by any of the numbers 2, 3, 5, and 7.

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Ther work done by the gas is approximately 1077.94 ft-lb (rounded to two decimal places).

To find the work done by the gas, we can use the formula:

Work = ∫ P dV

Where P is the pressure and dV is the change in volume.

Given that the pressure is inversely proportional to the volume, we can express the relationship as:

P = k/V

Where k is a constant.

To find the value of k, we can use the initial conditions:

P = 1300 pounds per square foot (at V = 4 cubic feet)

Substituting these values into the equation, we get:

1300 = k/4

Solving for k, we find:

k = 5200

Now, we can integrate the equation to find the work done:

Work = ∫ (5200/V) dV

Integrating, we get:

Work = 5200 ln|V| + C

Applying the initial and final volume conditions, we have:

Work = 5200 ln|5| - 5200 ln|4|

Calculating this expression, we find:

Work ≈ 5200 ln(5/4) ≈ 1077.94 ft-lb

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Answer:

B i think

Step-by-step explanation:

Answer:

x = 13

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 5² + 12² = 25 + 144 = 169 ( take the square root of both sides )

x = \(\sqrt{169}\) = 13

Answer:

a²+b²=c²

5²+12²= c²

25+144=c²

169=c²

\( \sqrt{169 =} \sqrt{c} \)

13=c

Answer:

11. c > 5

12. option 1

Step-by-step explanation:

The person who ate more is Joe.

Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.

Here p, called the numerator and q, called the denominator, are real numbers.

Total number of cookies = 12

Fraction that Joe ate = 2/3

Fraction that Peggy ate = 1/3

From the fractions itself, we can say that Joe ate more since the numerator is bigger for the fraction that Joe ate.

Number of cookies that Joe ate = 2/3 × 12 = 8

Number of cookies that Peggy ate = 1/3 × 12 = 4

Hence the number of cookies is more eaten by Joe.

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The system of equations is:

x + y = 10

4x + 3y = 36

The solution is x = 6 and y = 4.

A)

Let's define the variables:

We can write the system of equations:

x + y = 10

4x + 3y = 36

Isolate x on the first equation to get:

x = 10 - y

Replace that in the other one:

4*(10 - y) + 3y = 36

40 - 4y + 3y = 36

40 - y = 36

40 - 36 = y

4 = y

And thus, the value of x is:

x = 10 - y = 10 - 4 = 6

They bought 6 cheese wafers and 4 chocolate ones.

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Answer:

x = 3, y = 1

Step-by-step explanation:

By substitution since y = -2x + 7, substitute that for the 2nd y so

-2x +7 = 3x - 8, so x = 3, then substitute the 3 in any of the equations, so y = -2(3) + 7 is equal to 1

If you use elimination you can subtract the two equations from each other to get rid of the y so

y = -2x + 7

-y = -3x + 8

so 0 = -5x + 15, 5x = 15, x=3

Answer:

x=-2, -6

Step-by-step explanation:

factor the expression

y=x^2+ 8x + 12

y= (x+2)(x+6)

set the equation equal to 0, since you are finding zeros, or solutions

0=(x+2)(x+6)

split the equation into two parts

0=(x+2) and 0=(x+6)

solve the equations

you should get 2 zeros

x=-2, -6

The time listened to each CD is 52.5 minutes or 0.9 hours

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

Number of hours drive on the road trip = 3(1/2) hours

Number of CDs listened to in 3(1/2) hours = 4

We can write as,

3(1/2) hours = 4 CDs

3(1/2) can be written as 7/2.

Divide both sides by 4.

7/2 hours = 4 CDs

(7/2)/4 = 4/4 CDs

7/8 hours = 1 CDs

0.9 hours = 1 CDs

52.5 minutes = 1 CD

Thus,

The time listened to each CD is 52.5 minutes.

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Answer:

149.25

Step-by-step explanation:

Man I did the question and i got it wrong so after the second time of getting it wrong it gave me the answer.

Explanatory variables in a regression model are typically considered to be random when they are subject to variability or uncertainty. There are several reasons why explanatory variables may be treated as random:

Measurement error: Explanatory variables may be measured with some degree of error or imprecision. This measurement error introduces randomness into the values of the variables. Accounting for this randomness is important to obtain unbiased and accurate estimates of the regression coefficients.

Sampling variability: In many cases, the data used to estimate the regression model are obtained through sampling. The values of the explanatory variables in the sample may differ from the true population values due to random sampling variability. Treating the explanatory variables as random helps capture this uncertainty and provides more robust inference.

Random assignment in experiments: In experimental studies, researchers often manipulate or assign values to the explanatory variables randomly. This random assignment ensures that the variables are not influenced by any underlying factors or confounders. Treating the explanatory variables as random reflects the randomization process used in the experiment.

By considering the explanatory variables as random, we acknowledge and account for the inherent variability and uncertainty associated with them. This allows for a more comprehensive and accurate modeling of the relationships between the explanatory variables and the response variable in regression analysis.

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Answer:

80

Step-by-step explanation:

The sum of the interior angles of a triangle is 180.  Subtract out the 2 angles that you know.

180 - 70 - 30 = 80

Answer: The answer is 226.2 feet.

Step-by-step explanation: The formula to find the total surface area of a cylinder is 2\(\pi\) x radius squared x height. If you use the formula you will get 226.19 feet as your answer and I rounded that to 226.2 feet.

UR MOM

Answer:

We can use the formula for the area of a rectangle, which is:

Area = length x width

We know that the width of the rectangle is 5 centimeters and the area is 65 square centimeters. Substituting these values into the formula, we get:

65 = length x 5

To solve for the length, we can isolate it by dividing both sides of the equation by 5:

65/5 = length

Simplifying the left side, we get:

13 = length

Therefore, the length of the rectangle is 13 centimeters.

Step-by-step explanation: :)

Answer:

1.5 °C

Step-by-step explanation:

-2.5, -1, -0.5, 0, 3, 4, 4.5, 5

median is the middle number in the list of numbers

The value of p(10) we get as  123.

What is Quadratic polynomial ?

A quadratic polynomial is a polynomial of degree 2, which means that it is a polynomial expression in one variable (usually written as x) that contains only terms of the form ax² + bx + c, where a, b, and c are constants. The highest exponent of the variable x in a quadratic polynomial is 2.

We are given a table of values for the quadratic polynomial p. Since p is a quadratic polynomial, it can be written in the form:

p(x) = ax² + bx + c

where a, b, and c are constants.

To find the value of p(10), we need to substitute x = 10 in the above equation and simplify:

p(10) = a(10)² + b(10) + c

p(10) = 100a + 10b + c

We don't know the values of a, b, and c, but we can use the values in the table to set up a system of equations.

From the table, we can see that:

p(0) = c = 3

p(1) = a + b + c = 6

p(2) = 4a + 2b + c = 11

Solving this system of equations, we get:

a = 1

b = 2

c = 3

Therefore, the quadratic polynomial p is:

p(x) = x² + 2x + 3

To find p(10), we substitute x = 10 in the above equation:

p(10) = (10)² + 2(10) + 3

p(10) = 100 + 20 + 3

p(10) = 123

Therefore, the value of p(10) is 123.

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Answer:

Because is cannot be evenly divided by 2.

Answer:

Step-by-step explanation:

47.1 should be your answer, the formula to finding the circumference of a circle is 2 x pi x r and in this case, r is 7.5 because thats half of 15. So 2 x 3.14 is 6.28 x 7.5 is 47.1

The problem involves finding a fundamental set of real solutions for the given systems of differential equations with complex eigenvalues. The matrices A are provided for each system.

For the matrix A = [[-4, -8], [4, 4]], the complex eigenvalues can be found by solving the characteristic equation. Once the eigenvalues are obtained, the corresponding eigenvectors can be calculated. The real solutions of the system can be obtained by taking the real parts of the eigenvectors and exponentiating them with the eigenvalues.

Similarly, for the matrix A = [[-1, -2], [4, 3]], the eigenvalues and eigenvectors can be determined. The real solutions can be obtained by taking the real parts of the eigenvectors and multiplying them with the exponentials of the eigenvalues.

For the matrix A = [[-1, 1], [-5, -5]], the eigenvalues and eigenvectors need to be found. Then the real solutions can be obtained by taking the real parts of the eigenvectors and exponentiating them with the eigenvalues.

The matrix A = [[0, 4], [-2, -4]] requires finding the eigenvalues and eigenvectors. The real solutions can be obtained by taking the real parts of the eigenvectors and multiplying them with the exponentials of the eigenvalues.

For the matrix A = [[-1, 3], [-3, -1]], the eigenvalues and eigenvectors need to be determined. The real solutions can be obtained by taking the real parts of the eigenvectors and exponentiating them with the eigenvalues.

Finally, for the matrix A = [[3, -6], [3, 5]], the eigenvalues and eigenvectors can be found. The real solutions can be obtained by taking the real parts of the eigenvectors and multiplying them with the exponentials of the eigenvalues.

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