Audrey needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4. 25 hours and charged her $156 for parts. The total was $347. 25. What was the cost of labor, per hour?

\(\huge\fbox\purple{ANSWER} \)

\( \mathsf\pink{v = l \times w \times h}\)

\( \mathsf \purple{{72in}^{3} = c \times 4in \times 3in}\)

\( \mathsf \pink{ {72in}^{3} = c \times 12 {in}^{2} }\)

\( \mathsf \purple{ \frac{72 {in}^{3} }{ {12in}^{2} } = c \times \frac{12 {in}^{2} }{ {12in}^{2} } }\)

\( \mathsf \pink{6in = c}\)

\( \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }\)

\( \boxed{ \pink✠\underline{ \boxed{ \sf{Volume \: of \: Rectangular \: prism=length × width × height.}}} \pink✠}\)

\(\rule{80mm}{2.5pt}\)

\( \qquad \sf \: ➛ 72 = c \times 4 \times 3 \\ \qquad \sf \: ➛72 = c \times 12 \\ \qquad \sf \: ➛transporting \: 12 \: in \: divide \\ \qquad \sf \: ➛ \frac{72}{12} = c \\ \qquad \sf \: ➛ \cancel\frac{72}{12} = c \\ \qquad \sf \: ➛6 = c\)

\(\rule{80mm}{2.5pt}\)

★ Hence "c" (length) of Rectangular prism (shipping carton) is

\(\boxed{ \blue✜\underline{ \boxed{ \sf{length(c)= 6inch \green✓}}} \blue✜}\)

Hope it helps !

(a) To sketch a graph of the speed over a 3-second time span, we need to know the equation that describes the relationship between speed and time. Without this information, we cannot create an accurate graph.

(b) To find the volume of blood that passes along the artery in one second, we need to use the formula Q = A * v, where Q is the flow rate, A is the cross-sectional area of the artery, and v is the speed of blood flow. The cross-sectional area of the artery is given by A = pi * r^2, where r is the radius of the artery.

Thus, substituting the given values, we get:

A = pi * (5mm)^2 = 78.54 mm^2

v = 0.2 + 0.1 sin(2pit/0.8) (using the given information)

Q = A * v = 78.54 * (0.2 + 0.1 sin(2pit/0.8))

To find the volume of blood that passes along the artery in one second, we need to evaluate Q at t = 1 second, so we get:

Q = 78.54 * (0.2 + 0.1 sin(2pi1/0.8)) = 31.39 mm^3/s

Therefore, the volume of blood that passes along the artery in one second is approximately 31.39 cubic millimeters.

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Step-by-step explanation:

1/2 + 1/4

2/4 + 1/4= 3/4

1 - 3/4 = 1/4 is left

Answer:

There is 1/4 left

Step-by-step explanation:

Find the amount of cake left.

The entire cake is 1

1-1/2 - 1/4

Get a common denominator of 4

1 *4/4 = 4/4

1/2 *2/2 = 2/4

Using the common denominator

4/4 - 2/4 - 1/4

2/4 - 1/4

1/4

There is 1/4 left

Answer:

P(A) = 0.95

P(B) = 0.05

P(C) = 0.85

P(D) = 0.15

P(E) = 0.15

P(F) = 0.85

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

(4-5)-(13-18+2)

=-1-(13-18+2)

=-1-(-5+2)

=-1(-3)

=2

Answer:

A. 85%

   135%

B.15%

C.24 gallons

Step-by-step explanation:

A.

B.80-12=68.00    80X15%=12.00

C.6x4=24

The scale factor of TRAP to EZYD is 1.25.

Dilation is the increase or decrease in the size of a figure by a scale factor of k. If k > 1 it is an increase and if k < 1, it is a decrease.

To find the scale factor of TRAP to EZYD:

Scale factor = ZE / TR = 15 / 12 = 1.25

The scale factor of TRAP to EZYD is 1.25.

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The value of x is (5 ± √153)/4.

What is the area of a rectangle?

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

Here, we have

Given: Area of rectangle = 61

Equation : A(x) = 2x² - 5x

We have to find the value of x.

A(x) = 16

16 = 2x² - 5x

2x² - 5x - 16 = 0

we apply here factorization and we get

= (-b ± √b²-4ac)/2a

=  (5 ± √5²+4(2)(16))/2(2)

= (5 ± √25+128)/4

= (5 ± √153)/4

Hence, the value of x is (5 ± √153)/4.

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Selling insurance is not risky for an insurance company that insures many thousands of 21-year-old men due to the principle of large numbers and the concept of risk pooling.

The principle of large numbers states that as the number of individuals in a risk pool increases, the actual outcomes tend to approach the expected outcomes. In the case of life insurance for \(21-year-old\) men, while it is true that there is a high probability that each individual insured will live, the insurance company can rely on the law of large numbers to ensure that the overall outcomes align with their expectations.

When an insurance company insures many thousands of 21-year-old men, the law of large numbers comes into play. While it is true that some individuals may die at a young age, the insurance company can accurately predict the mortality rates and life expectancies for large groups based on actuarial data. This allows them to calculate premiums that are sufficient to cover the expected payouts in the event of death.

By pooling the risk of many individuals together, the insurance company can spread the financial risk across the entire pool. While some individuals may experience unfortunate events and their beneficiaries receive payouts, the premiums paid by the larger group of insured individuals ensure that the insurance company can cover these payouts and still make a profit.

In the case of the 21-year-old men, the insurance company can rely on statistical data, mortality tables, and actuarial calculations to determine the appropriate premiums that will cover the expected payouts and still provide a profit for the company. This allows the insurance company to manage the risk effectively and ensure their long-term financial stability.

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Answer:

10

Step-by-step explanation:

8 is closest to 10 therefore 8 rounds up to 10

Answer:

B

Step-by-step explanation:

Graph shrinks, that means for every x value there is a higher y value. So coefficient of x is definitely more than 1. Try to substitute x = 1 to (9x)^2 and (3x)^2.

(3(1))^2 = 9

Step-by-step explanation:

First find 28% of $19.50:

($19.50) / (100) × (28) = $5.46

Now minus the 285 from the original price:

($19.50) - ($5.46) = $14.04

The answer is $14.04

Hope it helped :)

The study would use a simple random sampling because it would be easy to randomly select. The study would use cluster sampling because the of fall into naturally occurring subgroups. The study would use stratified sampling because it would be important to have members from each segment of the population.

The study is a sample survey, because the population is for it to be practical to record all of the responses.

a. The study would use a simple random sampling because it would be easy to randomly select members of the population. Simple random sampling is a type of probability sampling that is used when the population is homogenous and every member has an equal chance of being selected for the sample.

b. The study would use cluster sampling because the members of the population fall into naturally occurring subgroups. Cluster sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into naturally occurring subgroups.

c. The study would use stratified sampling because it would be important to have members from each segment of the population. Stratified sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into segments or strata based on certain characteristics.

d. The study is a sample survey, because the population is too large for it to be practical to record all of the responses. Sample survey is a type of survey that collects data from a sample of the population, rather than the entire population. This is often done when the population is too large or when it is not practical to survey the entire population.

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Answer:

Step-by-step explanation:

Triangle LMN is similar to Triangle OMP, so you can write a proportion (that is two ratios, or fractions, equal to each other)

LM is to OM as LN is to OP

the equation looks like this:

LM/OM = LN/OP

Fill in the numbers you know

28/10 = 26/OP

Cross multiply and solve for OP

26*10 = 28*OP

260 =28*OP

Divide both sides by 28

260/28 = OP

9.3 = OP

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Total flowers sold = 200

Flowers are :

Carnations, Roses, and Gerber daisies

Carnations = c

Roses = r

Daisies = d

20 fewer roses than daisies ; r = d - 20

Total sales = $453

c = $1.50 each ; r = 3.75 each ; d = 2.25 each

c + d + d - 20 = 200

c + 2d = 220 - - (1)

1.50c + (d - 20)(3.75) + 2.25d = 453

1.50c + 3.75d - 75 + 2.25d = 453

1.50c + 6d = 528 - - - (2)

From (1)

c = 220 - 2d

1.5(220 - 2d) + 6d = 528

330 - 3d + 6d = 528

330 + 3d = 528

3d = 528 - 330

d = 198/3

d = 66

66 × 2.25 = $148.5

c = 220 - 2(66)

c = 88

88 * 1.50 = $132

r = d - 20

r = 66 - 20

r = 46

46 × $3.75 = $172.5

Answer:

7.6032,7.63,7.6

Sorry if I am wrong.

Step-by-step explanation:

The UCL (Upper Control Limit) using sigma = 3 for this process would be 30. The UCL utilizing sigma=3 for this process would be 28.036.

In statistical process control, the upper control limit (UCL) is utilized as a device to identify when to stop a process due to a high variation.

A process that exceeds its UCL will result in defective or inconsistent items, which should be avoided.

Marble Inc. produces high-end countertops from a variety of materials. The company employs the process of randomly selecting one countertop to count the number of blemishes as a means of monitoring the quality of its production processes.

The formula for calculating UCL is as follows: UCL = average of blemishes + 3 × standard deviation For ten samples with a different number of blemishes in each sample, the UCL is determined.

Using the given formula for UCL using sigma= 3: UCL = (2+3+4+5+6+7+8+9+10+17)/10 + 3 × √[(2-9.1)² + (3-9.1)² + (4-9.1)² + (5-9.1)² + (6-9.1)² + (7-9.1)² + (8-9.1)² + (9-9.1)² + (10-9.1)² + (17-9.1)²]/10UCL = 28.036

From the above calculations, the UCL utilizing sigma=3 for this process would be 28.036.

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Answer:

10^24

Step-by-step explanation:

Answer:

x^4 - 6x^3 + 5x^2 + 24x - 36

Step-by-step explanation:

So what you want to do is solve for x. The way we do this is by multiplying x^2 (from the first set of parenthesis) and multiply it with all of the things in the second set of parenthesis. So it's going to look like this:

x^2 (x^2 -6x +9)

When we multiply a variable by the same variable, we keep the single variable and add the exponents. So now it's going to look like this:

x^4 - 6x^3 + 9x^2

Now the first part of the equation is done. When we move on to the second part, you will do -4(x^2 -6x +9). Again, we are going to use the distributive property to get the second part of the equation so that it looks like this:

-4x^2 + 24x - 36

Now we can put the two parts together. When we do this, you can line up the ones that have the same exponent. This is because they have to be in the order that they are given. After we do this, it will look like this:

x^4 - 6x^3 + 5x^2 + 24x - 36

Usually you will end up with one less term than when you started with. For example, if you start with 6 terms, you should end with 5.

Hope this helps!

To find the inverse Laplace transform of F(s) = (s^2 - 4s + 8) / (2s - 1), we can use partial fraction decomposition followed by applying the inverse Laplace transform to each term.

First, let's perform the partial fraction decomposition:

F(s) = (s^2 - 4s + 8) / (2s - 1)

= (A / (2s - 1)) + (B / (s - 2))

Multiplying both sides by the denominators and simplifying, we get:

s^2 - 4s + 8 = A(s - 2) + B(2s - 1)

Expanding the right side and equating coefficients, we find:

For the s term: -4 = -2A + 2B

For the constant term: 8 = 2A - B

Solving these equations, we get A = 3 and B = 2.

So, we can rewrite F(s) as:

F(s) = (3 / (2s - 1)) + (2 / (s - 2))

Now, we can apply the inverse Laplace transform to each term:

L{3 / (2s - 1)} = 3/2 * L{1 / (s - 1/2)} = 3/2 * e^(t/2)

L{2 / (s - 2)} = 2 * L{1 / (s - 2)} = 2 * e^(2t)

Therefore, the inverse Laplace transform of F(s) is given by:

f(t) = (3/2) * e^(t/2) + 2 * e^(2t)

In conclusion:

The inverse Laplace transform of F(s) = (s^2 - 4s + 8) / (2s - 1) is f(t) = (3/2) * e^(t/2) + 2 * e^(2t).

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Answer:

13.89 miles

Step-by-step explanation:

Since we are calculating for hypotenuse, reference Pythagorean Theorem:

a^2 + b^2 = c^2

12^2 + 7^2 = c^2

144 + 49 = 193

square root of 193 = 13.89 (If rounded to hundredths place)

Answer:

√(193) miles

Step-by-step explanation:

7²+12²=x²

49+144=x²

193=x²

x=√(193) miles

Answer:

b. $6,524.96

Step-by-step explanation:

$1,631.24 x 4 equals $ $6,524.96

Given:

Amount Marty spent per day = $3

Number of days = 14

Remaining amount = $68

Since the amount left depends on the number

Maximizing the sum or mean difference between the residuals squared, do not accurately describe the goal of the least squares regression line.

The least squares regression line minimizes the sum of the residuals squared. This means that it aims to minimize the difference between the observed values and the predicted values squared.

This is done by finding the line that has the smallest overall distance from the data points.

The other options, such as maximizing the sum or mean difference between the residuals squared, do not accurately describe the goal of the least squares regression line.

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The least squares regression line minimizes the sum of the residuals squared.

In regression analysis, the least squares regression line is a line that best fits a set of data points by minimizing the sum of the squared differences between the observed values and the predicted values.

The residuals are the differences between the observed values and the predicted values, and squaring them ensures that negative and positive differences are both considered.

By minimizing the sum of the squared residuals, the least squares regression line finds the line that is closest to all the data points.

For example, let's say we have a dataset of 10 data points.

The least squares regression line is determined by finding the line that minimizes the sum of the squared differences between the observed values and the predicted values for each data point.

This means that the line is positioned in a way that it is as close as possible to all the data points, minimizing the overall error.

By minimizing the sum of the residuals squared, the least squares regression line provides the best fit to the data and can be used to make predictions or analyze relationships between variables.

It is widely used in various fields, including statistics, economics, and social sciences.

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Answer:

8/50

Step-by-step explanation:

2/10 x 4/5 = 8/50

Hope that helps!

The key features of the graph of the exponential function are given as follows:

The y-intercept of a function gives the value of the function when it crosses the y-axis, that is, when x = 0, hence it is the initial number of mammals, which is of 120.

As x goes to infinity, the number of mammals will never be of zero but it will get very close to zero, hence the line y = 0 is the horizontal asymptote of the graph.

The graph is shown by the image given at the end of the answer.

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Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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Answer:

-11

Step-by-step explanation:

Triangles have 180 degrees

using the vertical angle theory we know that 80 and 60 are angles

We can subtract them from 180 to get 40 left

this minus 51 is -11

x is -11

The intrinsic value of the PUT option is $0. It means the option has no inherent value based on the given information.

To determine the intrinsic value of a PUT option, we compare the strike price (X) with the current market price (S) of the underlying asset. If the strike price is higher than the market price, the intrinsic value is the difference between the strike price and the market price. However, if the market price is higher than the strike price, the intrinsic value is $0.

In the given information, we have the following data:

- Strike price (X): $90

- Market price (S): $47.78

Since the market price is lower than the strike price (47.78 < 90), the intrinsic value of the PUT option is $0. This means that exercising the option would not result in any profit because it is currently out of the money.

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The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.

The chain rule formula can be stated as follows:

If y = f(g(x)), then the derivative of y with respect to x is given by:

dy/dx = (df/dg) * (dg/dx)

In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.

The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:

dy/dx = (df/dg) * (dg/dh) * (dh/dx)

This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.

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