Kelly makes $10 more per hour than her regular pay when she is working overtime. Yesterday, she worked 8 regular hours and 4 overtime hours and earned $160. What is kelly's regular pay per hour?.

Using translation concepts, we have that:

4. The type is f(x + k), with k = 3, and a horizontal shift.

5. The type is kf(x), with k = 5 and a vertical stretch.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For graph 4, we have function g(x) is a shift left of 3 units of function f(x), hence:

The type is f(x + k), with k = 3, and a horizontal shift.

For graph 5, we have that for each value of x, g(x) = 5f(x), hence:

The type is kf(x), with k = 5 and a vertical stretch.

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Answer:

50.25

Step-by-step explanation:

100.50/2=50.25

Answer:

50.25

explanation:

Answer:

f(x) "down" by "3" units

Step-by-step explanation:

Edge 2020

Answer:

it would be 210 feet but u can't put feet into hours

Step-by-step explanation:

We know that the volume of a rectangular box is given by length times width times height. So, we have:

V = x * (x - 5) * (x + 2) = 180

Briefly defined, what is rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

We can use this equation to find the length of the box.

Expanding the equation:

x^3 - 5x^2 + 2x = 180

Solving for x using a calculator or an algebraic equation solver we can find that x = 9.52

So the length of the box is 9.52 inches.

The answer is B. 9.52 in

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Answer:

2d^0.7

Step-by-step explanation:

Answer:

648

Step-by-step explanation:

8×3^4=648

8×81=648

Answer:

Hope it helps!

Step-by-step explanation:

To find the inverse of a function, we can follow these steps:

Replace f(x) with y.

Swap x and y.

Solve for y.

So, for the function y = x^2 - 10x, we can start by replacing f(x) with y:

y = x^2 - 10x

Next, we swap x and y:

x = y^2 - 10y

Now we solve for y. Rearranging the equation, we get:

y^2 - 10y - x = 0

Using the quadratic formula, we can solve for y:

y = (10 ± √(100 + 4x)) / 2

Therefore, the inverse of y = x^2 - 10x is:

y = (10 ± √(100 + 4x)) / 2

The equation of the line that passes through the point (8, 5) and perpendicular to y = −12x +7 is y = (1/12)x + 13/3.

We know that,

The product of the slopes of two perpendicular lines is -1.

The slope intercept form of a line is given by :-

y = mx + c

Comparing it with y = -12x + 7

We get,

m = -12 (slope of the line)

c = 7 (y-intercept of the line)

Let the slope of the line perpendicular to the given line be n.

Hence, we can write,

(-12)*n = -1

n = 1/12

Also, the line passes through (8,5).

Hence, we can write,

5 = (1/12)(8) + c

5 = 2/3 + c

c = 5 - 2/3 = 13/3

Hence, the equation of the line is given by :-

y = (1/12)x + 13/3

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Answer: 5.7 inches

Step-by-step explanation:

To find the width of the home in the scale drawing, we can use algebra to solve for w.

First, we can simplify the equation w/0.6 = 9.5 by multiplying both sides by 0.6:

w/0.6 * 0.6 = 9.5 * 0.6

w = 5.7 inches

Therefore, the width of the home in the scale drawing is 5.7 inches.

The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer:

Option A.

Step-by-step explanation:

See attachment.

Basically, the reason why I left it at cm(3) was because that's the standard unit for volume, any length of measurement to the third power.

Answer:

$3.10/package x 5 packages = $15.50

If Marissa gives the clerk $20, her change will be:

$20 - $15.50 = $4.50

Therefore, Marissa will receive $4.50 in change.

The answer is A - $4.50.

Answer:

-2

Step-by-step explanation:

Answer:

4/25

Step-by-step explanation:

Its 4/25 as a fraction

ANSWER: THERE ARE TWO SOLUTIONS TO GET THE ANSWER

THE FIRST ONE IS FACTOR BY GROUPING AND THE SECOND SOLUTION IS SOLVING USING THE QUADRATIC FORMULA.

STEP BY STEP SOLUTION:

FACTOR BY GROUPING

(5x +9) (x -9)

WRITE IN STANDARD FORM

5x^2 - 36x -81

SOLVE USING THE QUADRATIC FORMULA

Solve the equation for x by finding a,b, and c of the quadratic then applying the quadratic formula.

X= 9, -9/5

I HOPE IT HELP YOU :)

The bounds for a 95% confidence interval could be option (B) 72 and 79

We know that the 98% confidence interval has bounds of 73 and 80. This means that if we were to repeat the same experiment many times, we would expect that 98% of the time, the true population mean would fall within this range.

To find the bounds for a 95% confidence interval, we can use the fact that a higher confidence level corresponds to a wider interval, and a lower confidence level corresponds to a narrower interval.

Since we want a narrower interval for a 95% confidence level, we can expect the bounds to be closer to the sample mean. We can calculate the sample mean as the midpoint of the 98% confidence interval

(sample mean) = (lower bound + upper bound) / 2 = (73 + 80) / 2 = 76.5

Next, we can use the formula for a confidence interval:

(sample mean) ± (z-score) × (standard error)

where the z-score depends on the desired confidence level, and the standard error depends on the sample size and sample standard deviation. Since we don't have this information, we can assume that the sample size is large enough (i.e., greater than 30) for the central limit theorem to apply, and we can use the formula

standard error = (width of 98% CI) / (2 × z-score)

For a 98% confidence interval, the z-score is 2.33 (found using a standard normal distribution table or calculator). Plugging in the values, we get

standard error = (80 - 73) / (2 × 2.33) = 1.70

Now, we can use this standard error to calculate the bounds for a 95% confidence interval

(sample mean) ± (z-score) × (standard error) = 76.5 ± 1.96 × 1.70

Simplifying, we get

(lower bound) = 76.5 - 3.33 = 73.17

(upper bound) = 76.5 + 3.33 = 79.83

Therefore, the correct option is (B) 72 and 79

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Answer:

f(x) = 4x + 48

Step-by-step explanation:

Replace the positions of x and y and isolate y to find the inverse of a function.

y = 1/4x – 12

x = 1/4y – 12

x + 12 = y/4

4(x + 12) = y

4x + 48 = y

f(x) = 4x + 48

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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585 miles per 9 hours

Step-by-step explanation:

715miles per 11 hours

/11 to determine miles per hour

65 miles per 1 hour

× 9 to determine miles per 9 hours

585 miles per 9 hours

Answer:

Nina's rate in MPH:  12.706 miles per hour

Nina is faster than Sophia.

Step-by-step explanation:

For this problem, we will convert feet per second into miles per hour, and then compare Nina's rate to Sophia's rate.

We are given Nina rides at 63360 feet in 3400 seconds.  To convert this to miles per hour, we need to know that there are 5280 feet in 1 mile, and 3600 seconds in 1 hour.  Now that we now these conversions, let's find the rate in miles per hour.

(63360 feet / 3400 seconds) * (1 mile / 5280 feet) * (3600 seconds / 1 hour) = 12.706 miles per hour.

So we know that Nina rides her bike at 12.706 miles per hour and are given that Sophia rides her bike in 10 miles in 1 hour.

With this, we can say Nina rides faster than Sophia by 2.706 miles per hour (12.706 - 10).

Cheers.

Answer:

9)x=11 y=3

11)x=18 y=5

Step-by-step explanation:

9) 9x+25=13x+19                   13x-19+17y+5=180

   9x+44=13x                         129+17y=180

   44=4x                                 17y=51

   11=x                                     y=3

11) 49+3x=7x-23                    3x=11y-1

Answer:

Step-by-step explanation:

Y= 4x+3 make x the subject

4x = y - 3

x = (y-3)/4

The equation ( ∂P/∂E )T = -P( ∂P/∂V )T - T( ∂T/∂V )P represents a relationship involving partial derivatives of pressure (P), energy (E), and volume (V) with respect to temperature (T).

In the given equation, the left-hand side represents the partial derivative of pressure with respect to energy at constant temperature ( ∂P/∂E )T . On the right-hand side, the equation involves two terms. The first term, -P( ∂P/∂V )T , represents the negative product of pressure (P) and the partial derivative of pressure with respect to volume at constant temperature ( ∂P/∂V )T . The second term, -T( ∂T/∂V )P , represents the negative product of temperature (T) and the partial derivative of temperature with respect to volume at constant pressure ( ∂T/∂V )P .

This equation suggests a relationship between the changes in pressure, energy, and volume, with temperature held constant. It states that the rate of change of pressure with respect to energy is determined by the combined effects of the partial derivatives of pressure with respect to volume and temperature. By understanding this equation and its implications, one can analyze and interpret the behavior of the variables involved in the thermodynamic system.

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Answer:

4/3

Step-by-step explanation:

\(4x-3y=0\\-3y=-4x\\3y=4x\\y=\frac{4}{3}x\\\\\)

We know, y directly varies with x

hence,

\(y\ \alpha \ x\\\)

remove the sign of proportionality

\(y=kx\)

now compare with the above equation we get the value of k = 4/3

Answer:

Step-by-step explanation:

A 10= 4 plus 6

Answer:

1.50

Step-by-step explanation:

To find the mean of the probability distribution, we need to multiply each value of hours studied by its corresponding probability, then add up the products.

Mean = (0.5 x 0.07) + (1 x 0.2) + (1.5 x 0.46) + (2 x 0.2) + (2.5 x 0.07)

Mean = 0.035 + 0.2 + 0.69 + 0.4 + 0.175

Mean = 1.5

Therefore, the mean of the probability distribution is 1.5.

Answer:

D

Step-by-step explanation:

1.50 on edge (if that guys right)