Vic works at a hardware store. He sells 144 bolts for $70.56. What is the constant of proportionality

True. If y is a differentiable function of u and u is a differentiable function of x, then the chain rule states that y is a differentiable function of x.

The chain rule states that if y is a function of u and u is a function of x, then the derivative of y with respect to x is equal to the derivative of y with respect to u multiplied by the derivative of u with respect to x. This means that if y is a differentiable function of u and u is a differentiable function of x, then y is also a differentiable function of x.

In mathematics, a function is said to be differentiable at a point if it is possible to define the derivative of the function at that point. The derivative of a function is a measure of how the function changes as its input (or independent variable) changes. It is defined as the limit of the difference quotient, which is a measure of the rate of change of the function over a small interval around the point of interest.

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Answer:

The temperature at noon was -10ºF + 15º = 5ºF.

Then, from noon to 7:00 pm, there were 7 hours, during which the temperature dropped 25º. Therefore, the temperature at 7:00 pm was:

5ºF - 25º = -20ºF.

So, the temperature at 7:00 pm was -20ºF.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer would be -30°F

\(8^{3} \cdot 8^{-7} =8^{-4}=\boxed{\frac{1}{8^4}}\)

Answer:

2 3/4

Step-by-step explanation:

There are 16 ounces in a pound so 8 ounces is 1/2 a pound.

1 1/2 + 1/2 + 3/4

2 + 3/4

2 3/4

Answer:

1, 4, and 7

Step-by-step explanation:

The rest are equal to angle 2

Answer:

50 units

Step-by-step explanation:

this is a walk around problem

the sides of the triangles are 19, 13, and 18

perimeter = 19 + 13 + 18

p = 50 units

Answer:

3

Step-by-step explanation:

its the median, just see which one is in the middle by crossing out one dot on each side until you get to the middle

Answer:

The equation that can be used to describe the possible distances of the Earth from the Sun, with the distances given in million of miles is;

d = 93 ± 1.6

Step-by-step explanation:

The parameters given are;

The mean distance of the Earth from the Sun, d = 93 million

The amount by which the distance varies = 1.6 million

Therefore, the equation that can be used to describe the possible distances of the Earth from the Sun, with the distances given in million of miles is  given as follows;

d = 93 ± 1.6

Therefore, the range of values for the distance of the Earth from the Sun can be presented as follows;

93 - 1.6 ≤ d ≤ 93 + 106

Which gives

91.4 ≤ d ≤ 94.6

After deducting the amounts for Federal tax, Social Security, and other deductions, the net pay for working 40 hours at an hourly wage of $8.95 is $276.61. Option A.

To calculate the net pay, we need to subtract the deductions from the gross pay.

Given:

Hours worked = 40

Hourly wage = $8.95

Federal tax deduction = $35.24

Social Security deduction = $24.82

Other deductions = $21.33

First, let's calculate the gross pay:

Gross pay = Hours worked * Hourly wage

Gross pay = 40 * $8.95

Gross pay = $358

Next, let's calculate the total deductions:

Total deductions = Federal tax + Social Security + Other deductions

Total deductions = $35.24 + $24.82 + $21.33

Total deductions = $81.39

Finally, let's calculate the net pay:

Net pay = Gross pay - Total deductions

Net pay = $358 - $81.39

Net pay = $276.61

Therefore, the net pay for 40 hours worked at $8.95 an hour with deductions for Federal tax of $35.24, Social Security of $24.82, and other deductions of $21.33 is $276.61. SO Option A is correct.

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Note the correct and the complete question is

What is the net pay for 40 hours worked at $8.95 an hour with deductions for Federal tax of $35.24, Social Security of $24.82, and other deductions of $21.33?

A.) $276.61

B.) $326.25

C.) $358.00

D.) $368.91

The empirical rule, also known as the 68-95-99.7 rule, provides a rough estimate of the percentage of values that fall within a certain number of standard deviations from the mean in a normal distribution.

According to the empirical rule, approximately 68% of the area under a normal curve is within 1 standard deviation of the mean, approximately 95% of the area is within 2 standard deviations of the mean, and approximately 99.7% of the area is within 3 standard deviations of the mean.

To match the probabilities to the range for the empirical rule, we can use the following table:

Within 1 standard deviation of the mean: 68%

Within 2 standard deviations of the mean: 95%

Within 3 standard deviations of the mean: 99.7%

It's important to note that the empirical rule is only an approximation and may not be accurate for all normal distributions.

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As per the given situation, Michael is option (b) 6 years old now.

The unitary method can be used to solve this problem. To use this method, we must first decide which quantity represents the unit, in this case the unit is one year.

We can then write the given information in terms of the unit. Norman is 12 years older than Michael, and in 6 years, he will be twice as old as Michael. This can be rewritten as 12 units + 6 units = 2(6 units).

This equation can be solved using the unitary method to find that Michael is 6 years old, making answer B the correct answer

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Answer:

24 gallons of 50% grape juice

Step-by-step explanation:

if you have 1 gallon of 50% grape juice and 1 gallon of 25% grape juice, the resulting combination will be 2 gallons of 75/2% (or 37.5%) grape juice.

I guessed you would need about 1.5 times of the 50 % mixture to make the 25% mixture into 50 %.  I checked, 1.5 times 16 is 24, so I calculated what is the average concentration (24*50 + 16*25)/40, and I got 40 so that guess was correct.

Answer:

y=x/2−63

Step-by-step explanation:  6x+3y=-63     3y=6x-63= y=2/x-63  

Answer:

The slope of a line perpendicular to the line whose equation is 6x+3y=-63 will be: 1/2

Step-by-step explanation:

We know that the slope intercept-form of the line equation is

\(y=mx+b\)

where m is the slope and b is the y-intercept

Given the equation

\(6x+3y=-63\)

simplifying the equation to write in the slope-intercept form

\(y=-2x-21\)

Thus, the slope = -2

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be:

\(\frac{-1}{-2}=\frac{1}{2}\)

Therefore, the slope of a line perpendicular to the line whose equation is 6x+3y=-63 will be: 1/2

Answer:

7

Step-by-step explanation:

\(s = {a}^{2} \: thus \: a = \sqrt{s } = \sqrt{49} = 7\)

The answer would be 2x1=x so x would be 2

Step-by-step explanation:

Answer:

x = 7, - 8

Step-by-step explanation:

x^2 + x - 56 = 0

x^2 + 8x - 7x - 56 = 0

x ( x + 8 ) - 7 ( x + 8 ) = 0

( x - 7 ) ( x + 8 ) = 0

x - 7 = 0

x = 7

x + 8 = 0

x = - 8

The given statement "In performing a lower-tailed z-test for one mean, the value of the test statistic was z=0.51, which would yield a p-value of 0.695." is true because we perform null hypothesis.

In a lower-tailed z-test for one mean, we test a null hypothesis that the population mean (μ) is greater than or equal to a certain value, against an alternative hypothesis that the population mean is less than that value.

To perform the test, we calculate the z-test statistic using the sample mean, sample standard deviation, sample size, and the hypothesized population mean. If the calculated z-test statistic falls in the rejection region (below the critical value), we reject the null hypothesis and conclude that the population mean is less than the hypothesized value.

In this case, the calculated z-test statistic is 0.51, which falls in the non-rejection region (above the critical value) for a lower-tailed test with a significance level of 0.05. Therefore, the p-value is greater than 0.05, and we do not reject the null hypothesis. The statement that the p-value is 0.695 is consistent with this conclusion.

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The equation of the line that meets the following conditions are as follows;

5. y + 2 = 3(x - 4).

6. y - 7 = -3/2(x + 5)

7. y + 8 = -20/7(x - 4).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (4, -2) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 3(x - 4)

Part 6.

At data point (-5, 7) and a slope of -3/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 7 = -3/2(x + 5)

Part 7.

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (12 + 8)/(-3 - 4)

Slope (m) = -20/7

At data point (4, -8) and a slope of -20/7, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 8 = -20/7(x - 4).

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Answer:

c

Step-by-step explanation:

the graph shows a constant speed an no change in distance

Answer:

Statistical inference

Step-by-step explanation:

The monthly interest rate you will be paying is approximately $2,583.33, and (b) the alternative loan is less attractive than the one from the car dealer, with the lender needing to charge an interest rate of approximately 2.31% to match the car dealer's rate.

(a) Calculation of the interest rate you will be paying every month:

Given:

The car will cost = $150,000

Amount to be paid upfront = 40%

Interest rate per annum = 2%

Loan tenure (no of years) = 5 years

Loan tenure (no of months) = 5 x 12 = 60 months

Using the formula to calculate the interest rate you will be paying every month:

Interest Rate = (Loan amount x interest rate per annum x Loan tenure (no of years) + loan amount) / Loan tenure (no of months)

Substituting the given values in the formula:

Interest Rate = (150000 x 2 x 5 / 100 + 150000) / 60

Interest Rate = (15000 + 150000) / 60

Interest Rate ≈ $2,583.33

Therefore, the interest rate that you will be paying every month is approximately $2,583.33.

(b) (i) You are able to secure financing for your car from another source. You will have to pay 3% per annum on this loan. The lender requires you to pay monthly for 5 years. Is this loan more attractive than the one from the car dealer?

Given:

Interest rate per annum = 3%

Loan tenure (no of years) = 5 years

Loan tenure (no of months) = 5 x 12 = 60 months

Using the formula to calculate the interest rate you will be paying every month:

Interest Rate = (Loan amount x interest rate per annum x Loan tenure (no of years) + loan amount) / Loan tenure (no of months)

Substituting the given values in the formula:

Interest Rate = (150000 x 3 x 5 / 100 + 150000) / 60

Interest Rate = (22500 + 150000) / 60

Interest Rate ≈ $2,916.67

The monthly payment amount is higher than the car dealer's, so this loan is not more attractive than the one from the car dealer.

(ii) Suppose the lender requires you to set aside $10,000 as security to be deposited with the lender until the loan matures and repayment is made. What interest rate must the lender charge for it to be equivalent to the interest rate charged by the car dealer?

Let x be the interest rate that the lender must charge.

Using the formula of compound interest, we can find the interest charged by the lender as follows:

150000(1 + x/12)^(60) - 10000 = 150000(1 + 0.02/12)^(60)

150000(1 + x/12)^(60) = 150000(1.0016667)^(60) + 10000

(1 + x/12)^(60) = (1.0016667)^(60) + 10000/150000

(1 + x/12)^(60) = (1.0016667)^(60) + 0.066667

Taking the natural logarithm on both sides:

60(x/12) = ln[(1.0016667)^(60) + 0.066667]

x ≈ 2.31%

Thus, the lender must charge approximately a 2.31% interest rate to be equivalent to the interest rate charged by the car dealer.

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y = mx + b

m = slope or rate of change

b = y-intercept

x = input

y = output

Answer:

x= input

y= output

Step-by-step explanation:

Answer:

The answer is 1086 in³

Step-by-step explanation:

When a hollow plastic ball is projected into the air, there is air resistance opposing its motion. The magnitude of the ball's acceleration is not equal to zero. At time t, the ball is moving up and to the right at a 45-degree angle to the horizontal.

The acceleration of the ball can be determined by considering the forces acting on it. Since there is air resistance opposing the ball's motion, its acceleration is less than the acceleration due to gravity (g). Therefore, the statement "a < g" best represents the magnitude and direction of the ball's acceleration at time t. This means that the ball's acceleration is directed downward but is smaller than the acceleration due to gravity. The presence of air resistance affects the ball's motion and causes its acceleration to be less than the acceleration due to gravity.

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In the parallelogram, the coordinates form of the vectors WX, XY, WZ, OZ are (18,3), (24, 21), (2x, y)  and (0,0).

The term coordinate in math is known as the set of values that represents the exact position on the coordinate plane

Here we know that WXYZ is a parallelogram and the position vectors of W, X and Y are (2,1), (6,3) and (4,7) respectively.

Then the value of the coordinate vectors are calculated as,

=> WX = (2,1) x (6,3) = (18, 3)

And the value of XY is calculated as,

=> XY = (6,3) x (4,7) = (24, 21)

And we know that the value of Z is (x, y), then the vector is calculated as,

=> WZ = (2,1) x (x, y) = (2x, y)

Finally the value of OZ is calculated as,

=> OZ =(0,0)  x (x , y) = (0, 0)

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The value of Sin2t is 1/4 and cos2t is (15/16)^1/2  and tan2t is 1/(15)^1/2.

According to the statement

we have given that the sint=1/8 then we have to find the exact value of

sin(2t) , cos(2t) , and tan(2t).

Here the value of Sint = 18

then sin2t becomes

sin2t = 2*1/8 then

sin2t = 1/4.

And

(Cos2t)^2 = 1 - (Sin2t)^2

(Cos2t)^2 = 1 - 1/16

(Cos2t)^2 = (16 - 1)/16

(Cos2t)^2 = 15/16

(Cos2t) = (15/16)^1/2

then

tan2t = sin2t/cos2t

tan2t = (1/4)/(15)^1/2 / 4

tan2t = 1/(15)^1/2

these are the values of given terms.

So, The value of Sin2t is 1/4 and cos2t is (15/16)^1/2  and tan2t is 1/(15)^1/2.

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Equation of line DC is y = -1/2 x - 8

Equation of line AD is y = 2x + 2

Equation of line BC is y = 2x - 8

The equation of the line 2y + x = 4 is arranged in slope intercept form to have

y = -x/2 + 2

The slope is -1/2

with a slope of -/2 and points (0, -8) line DC is written as

y - -8 = -1/2 (x - 0)

y + 8 = -1/2 x

y = -1/2 x - 8

Equation of line AD

line AD is a perpendicular line  to line DC hence the slope is negative reciprocal of the slope of line DC

slope = 2

point A(0, 2) line AD is written as

y - 2 = 2 (x - 0)

y - 2 = 2x

y = 2x + 2

Equation of line BC

line BC is a parallel to line AD hence the slopes are equal

slope = 2

point C (0, -8) line AD is written as

y - - 8 = 2 (x - 0)

y + 8 = 2x

y = 2x - 8

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Answer:

7

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

To find the maximum area of the lawn that can be watered by the sprinkler, we can use the formula for the area of a circle:

A = πr^2

Given that the radius of the sprinkler's spray is 22ft, we can substitute this value into the formula:

A = 3.14 * (22)^2

A ≈ 3.14 * 484

A ≈ 1519.76

Rounded to the nearest tenth, the maximum area of the lawn that can be watered by the sprinkler is approximately 1519.8 ft^2.\(\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}\)

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Answer: A

Step-by-step explanation:

Answer:

5 sqrt xy

Step-by-step explanation:

Edge 2020