Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. F(x) = 0 x < 0 x2 49 0 ≤ x < 7 1 7 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 5). (b) Calculate P(4.5 ≤ X ≤ 5). (c) Calculate P(X > 5.5). (d) What is the median checkout duration ? [solve 0.5 = F()]. (e) Obtain the density function f(x). (f) Calculate E(X). (g) Calculate V(X) and ????x. (h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].

Answer:

3j + 3m + 21

Step-by-step explanation:

Normally, they would each travel 3 miles, so the total would normally be 3j + 3m. However, for today, Jared ran another 21 miles, so 21 miles is added to the total.

Total distance = 3j + 3m + 21

Answer:

(3j) + (3m + 21)

Step-by-step explanation:

Since every time Jared goes running he runs 3 miles we should multiply j by 3. So we will have: 3j

Since every time Malia goes running she runs 3 miles we should multiply m by 3. So we will have 3m

But this month Jared ran an extra 21 miles so we will have to add that after we have multiplied both j and m by 3.

Since we want the total distance they ran that month, we need to add all of these distances.

This will give us 3j + 3m + 21.

In the answer options 3j is inside a parenthesis as well as 3m + 21. Since inside the parenthesis we only have addition and the order which we add doesn't really make a difference, the parenthesis were unnecessary but they won't affect the answer.

None of the other options are equal to $1,136.42. Answer: $1,100.42

The amount of interest paid in the first year of a five-year amortization schedule is to be determined, given the following table for months 1 through 12, and the four options a.

$1,100. 42, b. $1,010. 16, c. $1,188. 34, and d. $1,241. 18 as possible answers to the question.

To determine the amount of interest paid in the first year of a five-year amortization schedule, we must first find the sum of the interest payments for the first twelve months.

Using the information given in the problem, the total amount of interest paid for the first year is calculated as follows:

Total interest paid in the first year = $99.03 + $97.73 + $96.42 + $95.10 + $93.78 + $92.44 + $91.09 + $89.73 + $88.36 + $86.98 + $85.58 + $84.18= $1,136.42

Therefore, after one year of payments, the total amount paid to interest is $1,136.42.

Therefore, the correct answer is option a. $1,100. 42.

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the options that are polynomials are:

3.9x³-4.1x² + 7.3

x²y²-4x³+12y

4-x²

A polynomial is an expression of the form:

p(x) = aₙ*xⁿ + ...+ a₂*x² + a₁*x  + a₀

Where all the exponents of the variable are whole numbers, and in this case we have only one variable x, but we could have any number of variables.

With that in mind, the options that are polynomials are:

3.9x³-4.1x² + 7.3

x²y²-4x³+12y

4-x²

These 3 expressions are polynomials.

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Triangle properties include triangle inequality, angle sum, congruence, exterior angle theorem, and isosceles triangle theorem.

1. Triangle Inequality: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. Angle Sum of a Triangle: The sum of the angles of a triangle is always equal to 180°.

3. Congruence of Triangles: If two triangles have all three sides equal, then they are congruent (the same size and shape).

4. Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

5. Isosceles Triangle Theorem: If two sides of a triangle are equal in length, then the angles opposite those sides are also equal in measure.

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The five properties of triangle is listed below.

The term triangle is defined as the polygon with three angle, sides and vertices.

Here we have to list down the properties of triangle.

The basic five properties of triangle are as follows:

1) in geometry, total amount of space inside the triangle is called the area of a triangle. And it is measured by square units.

2) The property of perimeter of a triangle is equal to the sum of all three sides of the triangle.

3) And the another property states that sum of the length of the two sides of a triangle is greater than the length of the third side.

4) according to the angle, the property states that sum of the angles of a triangle is always 180 degrees.

5) If angles of an equilateral triangle are equal and has a measure of 60⁰ each.

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Jack ate 1/10 cup more strawberries than Leo

The problem states that Leo ate 3/5 cup of strawberries, and Jack ate 7/10 cup of strawberries. We need to find out how much more Jack ate than Leo.

To solve this problem, we first need to find a common denominator for the two fractions. The denominator is the bottom number of a fraction, which represents the total number of equal parts that make up a whole.

The smallest common denominator for 5 and 10 is 10. We can convert the fraction 3/5 into an equivalent fraction with a denominator of 10 by multiplying both the numerator and denominator by 2. This gives us 6/10.

Now, we have two fractions with the same denominator: 6/10 and 7/10. To find out how much more Jack ate than Leo, we can subtract the fraction representing what Leo ate from the fraction representing what Jack ate:

7/10 - 6/10 = 1/10

Therefore, Jack ate 1/10 cup more strawberries than Leo did.

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Answer:

\(\huge\boxed{\sf Yes.}\)

Step-by-step explanation:

y = 6x - 9 ---------------(1)

y = 2x + 3 --------------(2)

So,

x = 3, y = 9

Put this in Eq. (1) to verify.

9 = 6(3) - 9

9 = 18 - 9

9 = 9 [Equation satisfied]

Now, put x = 3, y = 9 in Eq. (2)

9 = 2(3) + 3

9 = 6 + 3

9 = 9 [Equation satisfied]

Since, both the equations are satisfied by the values of x and y, we can say that x = 3 and y = 9 is the solution to the system.

\(\rule[225]{225}{2}\)

Answer: Yes, it is a solution

Step-by-step explanation:

Plug (x,y) values into the equations.

Plug in (3,9)

y=6x-9  ---->.  (9)=6(3)-9 ----> 9=18-9 ----->   9=9

y=2x+3 ------>.  (9)=2(3)+3 ----> 9=6+3 ----> 9=9

When know (3,9) is a solution because each side has the same value.

Example:

8=9 Not a solution

5=5 A solution

Answer:

The new price for one pound of apples is $1.44

Step-by-step explanation:

A 10% discount from $1.60 is $0.16, which can be found by multiplying $1.60 by 0.10. To figure out the new price, use the equation: $1.60 - $0.16= $1.44

Answer:

1/12 is the reciprocal of 12.

Step-by-step explanation:

A reciprocal of a number is simply the inverse of it (in simple terms, the numerator and denominator switch places).

Therefore, the inverse (or reciprocal) of 12/1 is 1/12.

Answer:

D

Step-by-step explanation:

when x=1, y should = 2

2(1)=2

so y=2x is correct

Answer:

<4 step by step explanation

The required value of the upper limit for both the integral are,
4. a = -1 or a = 1/2
5. b = 1

The limit of a sum can be used to express the definite integral of any function, or if the interval [a, b] has an antiderivative F, the definite integral of the function is the difference of the values at points a and b.

Here,

4.
Given expression,
\(= \int _{-2}^{a}x^2dx = 7/3\\= [x^3]_{-2}^a = 7 / 3\\= a^3 + 8 / 3 = 7/3\\a=-1,\:a=\frac{1}{2}-\frac{\sqrt{3}}{2}i,\:a=\frac{1}{2}+\frac{\sqrt{3}}{2}i\)

Since as mentioned that a must be greater than -2 so the considered value of a is, a = -1 and a = 1/2, and a graph of the area of the expression is shown,

Similarly,
5.
b = 1
A graph of the area under the given integration has been shown.

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The sum of two square roots of 2 and 1/4 is the result having radical as (8√2 + 1)/4

The symbol √ is used to represent or show that a number is a radical. Radical expression is defined as any expression containing a radical (√) symbol

The square root 2 = √2

two square root of 2 = √2 + √2

two square root of 2 = 2√2

sum of two square roots of 2 and 1/4 = 2√2 + 1/4

adding in one fraction by taking LCM of the denominators, we have;

sum of two square roots of 2 and 1/4 = (4×2√2 + 1)/4

sum of two square roots of 2 and 1/4 = (8√2 + 1)/4

Therefore, the radical expression (8√2 + 1)/4 is the sum of two square roots of 2 and 1/4.

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Yes, simulations can indeed be a practical alternative to calculating probabilities based on formal rules. Simulations allow us to replicate a procedure or event using randomization to generate outcomes similar to those we are interested in studying.

By repeatedly running the simulation, we can gather data and observe the frequency of specific outcomes, which can provide an estimate of the probability of those outcomes occurring.

In the example you mentioned, instead of calculating the probability of getting exactly 5 boys in 10 births using complex calculations, a simulation approach can be employed. By simulating the process using coins or a random number generator, where heads represent boys and tails represent girls, we can perform numerous trials and count the occurrences of obtaining 5 heads (boys) in 10 tosses (births). By recording and analyzing the results of these simulated trials, we can approximate the probability of getting exactly 5 boys in 10 births.

Simulations offer a practical and efficient way to estimate probabilities, especially in situations where direct calculations may be challenging or time-consuming. They allow us to model and understand complex systems and make informed decisions based on observed frequencies and patterns.

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3/6 because absolute value of any number has to be positive and you have to subtract the 2 answers to find the distance

According to the Pythagorean Theorem, for a Right triangle:

Where "a" is the hypotenuse and "b" and "c" are the legs of the Right triangle.

Let's check the side lengths given in each option:

A) The hypotenuse would be:

So, if you apply the Pythagorean Theorem, you get:

These side lenghts do not form a Right triangle.

B) Since all the sides of this triangle have equal length, it is not a Right triangle, but an Equilateral triangle.

C) The hypotenuse of this triangle would be:

Then, applying the Pythagorean Theorem, you get:

These side lenghts form a Right triangle.

The answer is: Option C

The result is consistent with the previous calculation, and option C, 3.682, is the correct answer.

To calculate log4 57 to the nearest thousandth, we can use a scientific calculator or a logarithmic table.

Using a calculator, we can find the logarithm of 57 to the base 4 directly:

log4 57 ≈ 3.682

Therefore, the correct answer is option C: 3.682.

If you prefer to verify the result using logarithmic properties, you can do so as follows:

Let's assume log4 57 = x. This means \(4^x\) = 57.

Taking the logarithm of both sides with base 10:

log (\(4^x\)) = log 57

Using the logarithmic property log (\(a^b\)) = b \(\times\) log a:

x \(\times\) log 4 = log 57

Dividing both sides by log 4:

x = log 57 / log 4

Using a calculator to evaluate the logarithms:

x ≈ 3.682

Thus, the result is consistent with the previous calculation, and option C, 3.682, is the correct answer.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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Answer:

(9 x 100) + (5 x 10) +  (0 x 1) + (9/10) + (5/100)

hope this helps brainliest <3

Answer:

Step-by-step explanation:

Answer:

daddy chill

Step-by-step explanation:

what does te guy say?

The firm's weighted average cost of capital is 15.074%

To calculate the weighted average cost of capital (WACC), we need to follow these steps:

1. Determine the weight of each component of the capital structure (debt, preferred stock, and common stock) by dividing the value of each component by the total capital.
2. Multiply the weight of each component by its respective cost.
3. Sum the weighted costs to obtain the WACC.

Here's the step-by-step calculation:

1. Calculate the weights:
Debt weight = $1,083 / $5,032 = 0.215
Preferred stock weight = $268 / $5,032 = 0.053
Common stock weight = $3,681 / $5,032 = 0.732

2. Calculate the weighted costs:
Weighted cost of debt = 0.215 x 5.5% = 0.011825
Weighted cost of preferred stock = 0.053 x 13.5% = 0.007155
Weighted cost of common stock = 0.732 x 18% = 0.13176

3. Sum the weighted costs to find the WACC:
WACC = 0.011825 + 0.007155 + 0.13176 = 0.15074 or 15.074%

Therefore, we can state that the firm's weighted average cost of capital is 15.074%.

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Answer:  66% of 110 is 72.6

Step-by-step explanation:

Because i said so

use oak national academy.

it really helped me.

Answer:

try mathswatch videos(this is u need to pay or you can use someones username and password for the videos if ur a school student) or oak nation (this one is free)

Step-by-step explanation:

Primer numbers can only be divided by one and itself.

The equation is given as:

\(\mathbf{abc = 105}\)

Assume a =  5.

So, we have:

\(\mathbf{5bc = 105}\)

Divide through by 5

\(\mathbf{bc = 21}\)

Assume b = 7

\(\mathbf{7c = 21}\)

Divide through by 7

\(\mathbf{c = 3}\)

So, we have:

\(\mathbf{a = 5, b = 7, c = 3}\)

The sum is represented as:

\(\mathbf{a + b + c =5 + 7 + 3}\)

\(\mathbf{a + b + c =15 }\)

Hence, the sum of a, b and c is 15.

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The statement suggests that the worst-case time complexity of Insertion Sort is approximately proportional to n²/2, while the average-case time complexity is approximately proportional to n²/4.

The worst-case and average-case time complexities of Insertion Sort indicate that the algorithm's performance is quadratic, with the average case being more efficient than the worst case due to a smaller constant factor.

The worst-case time complexity refers to the scenario where the input array is in reverse order or nearly sorted in reverse order. While the average-case time complexity represents the average performance of the algorithm over all possible inputs.

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Answer:

4.2M - 2.9M= 1300000

1.3/2.9x100= 44.83%

Answer:

59%

Step-by-step explanation:

2900000÷4200000× 100

Answer:

Step-by-step explanation:

The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.

Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.

Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.

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The annual percentage rate (apr) = 8% and the monthly payment is around (c) $99.64

The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR). APR is a percentage that expresses the actual annual cost of borrowing money throughout the course of a loan or the revenue from an investment. This does not account for compounding and includes any fees or additional expenditures related to the transaction. Consumers can evaluate lenders, credit cards, or investment goods using the APR as a benchmark figure.

Given interest charge =$425.13

Total borrowing amount = $3162

now lets simplify by using the above values

[{(425.13/3162)/3*365}*365]*(100)

APR = 8%

And monthly payment is

= (3162+425.13)/36

= (3587.13)/36

= $99.64.

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The length of IKE is 2x - 12.

A condition on a variable that is true for just one value of the variable is called an equation.

Since KITE is a kite, we know that KT = IT and KE = IE. Let's call the length of these diagonals d. Then we have:

KT + TI = d

KE + EI = d

Substituting in the given values, we get:

x + 6 + 2x = d

2x + IE = d

Solving for d in the first equation, we get:

3x + 6 = d

Substituting this into the second equation, we get:

2x + IE = 3x + 6

Solving for IE, we get:

IE = x + 6

Therefore, IKE is equal to:

IKE = IT - IE

IKE = (d - KT) - (x + 6)

IKE = (3x + 6 - x - 6) - (x + 6)

IKE = 2x - 12

So, the length of IKE is 2x - 12.

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