Work sheet is pretty hard giving 20 points

The actual speed (along the road) of the red car is 8.37 feet per second

Let's call the distance between the police car and the red car "x" at time t. Then, we know that:

x^2 = 40^2 + (140 - vt)^2

Where

We are given that dx/dt (the rate at which x is decreasing) is -85 ft/s, so:

d/dt [x^2] = d/dt [40^2 + (140 - vt)^2]

2x(dx/dt) = 0 - 2v(140 - vt)

Substituting dx/dt = -85 and solving for v, we get:

2x(−85) = −2v(140−vt)

−170x = −280v + 2v^2t

v^2t = 140v - (85/2)x

Now, we can differentiate the equation x^2 = 40^2 + (140 - vt)^2 with respect to time to get:

2x(dx/dt) = 2(140 - vt)(-v)

Substituting dx/dt = -85 and solving for x, we get:

-170x = -2v(140 - vt)

x = (140v - vt^2)/85

Substituting this expression for x into the equation we derived earlier, we get:

v^2t = 140v - (85/2)((140v - vt^2)/85)

v^2t = 140v - 70(2v - t^2)

v^2t = 140v - 140v + 70t^2

v^2t = 70t^2

v = sqrt(70t^2)/t = sqrt(70) = 8.37 ft/s (rounded to two decimal places)

Therefore, the actual speed (along the road) of the red car is 8.37 feet per second

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Answer:

378in^2 i think

Step-by-step explanation:

The sales tax on 250 dollars purchase is: $3865

We are told that sales tax is directly proportional to retail price. Thus:

S ∝ p

Any item that sells for 158 dollars has a sales tax of 10.22 dollars. Thus:

158 = 10.22k

where k is constant of proportionality

Thus:

k = 158/10.22

k = 15.46

Thus, the equation is:

S = 15.46p

Sales tax on 250 dollars purchase is:

S = 15.46 * 250

S = $3865

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The length of the shadow would be approximately 41.7 feet if the angle of elevation from the horizontal to the sun is 38° at this time.

If the angle of elevation from the horizontal to the sun is 38°, then the tangent of that angle is equal to the opposite side (the height of the tree) divided by the adjacent side (the length of the shadow).

Therefore, we can set up the equation using trigonometric function tangent as,
tan(38°) = height of tree / length of shadow

Solving for the length of the shadow, we get:
length of shadow = height of tree / tan(38°)

Plugging in the given height of the tree (32 feet) and using a calculator to find the tangent of 38°, we get:
length of shadow = 32 / tan(38°) = 41.7 feet (rounded to one decimal place)

Therefore, the length of the shadow would be approximately 41.7 feet at this time.

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Answer:

8 13/15

Step-by-step explanation:

Multiply the fractions so they both have the least common denominator:

5 2/3 = 5 10/15

3 1/5 = 3 3/15

Now, you can add the two mixed numbers:

[tex]5 \frac{10}{15} + 3 \frac{3}{15} = 8 \frac{13}{15}[/tex]

This is your final answer.

The value of x is 18.4 and the value of y is 22.5 in the cube

From the question, we have the following parameters that can be used in our computation:

The diagram of a cube.

Each edge of the cube = 13 units.

The diagonal of each face is x units long

So, we have

x^2 = 13^2 + 13^2

Evaluate

x = 18.4

The diagonal of the cube is y units long.

So, we have

y^2 = 13^2 + 13^2 + 13^2

Evaluate

y = 22.5

Hence, the value of x is 18.4 and the value of y is 22.5

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Answer: 61,6 in.

Step-by-step explanation:

To find the area of trapezoids with parallel bases, we add the length of the lower base to the length of the upper base.

Then we multiply this value by the height.

Finally, we divide the resulting value by [tex]2[/tex].

The scatter plot that has a pattern that is best fit by y = x^2 has a property that displays a nonlinear pattern

From the question, we have the following parameters that can be used in our computation:

Equation of the best fit of the scatter plot: y = x^2

As a general rule

Any equation that has a degree other than 1 is a non linear equation

This means that the property it displays is a nonlinear pattern

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Let's start by setting up some equations to represent the given information.

Let's say the price of a postcard is "x" cents.

Then, according to the problem statement, the price of an envelope is 8 times cheaper than the notepad, which means the price of an envelope is (1/8)th of the price of the notepad. So the price of an envelope is (1/8)*y cents, where "y" is the price of the notepad in cents.

Also, we know that the price of an envelope is 2 cents more expensive than the price of a postcard, so we can write:

(1/8)*y = x + 2 ...(Equation 1)

We also know that there are 15 postcards and 10 envelopes in the purchase, so the total cost of the postcards and envelopes is:

15x + 10[(1/8)*y] ...(Equation 2)

Finally, we have a notepad that costs "y" cents. So the total cost of the purchase is:

15x + 10[(1/8)*y] + y ...(Equation 3)

We are given that the total cost of the purchase is 1 dollar and 68 cents, which is equal to 168 cents. So we can write:

15x + 10[(1/8)*y] + y = 168 ...(Equation 4)

Now we have four equations (Equation 1, Equation 2, Equation 3, and Equation 4) with three variables (x, y, and 168). We can solve for x and y by using a system of equations.

From Equation 1, we can solve for y in terms of x:

(1/8)*y = x + 2

y = 8x + 16

Substituting this expression for y into Equations 2 and 3, we get:

15x + 10[(1/8)*y] = 15x + 10(8x + 16) = 160x + 160

15x + 10[(1/8)*y] + y = 15x + 8x + 16 = 23x + 16

Substituting these expressions into Equation 4, we get:

23x + 16 = 168

Solving for x, we get:

x = 6

Substituting this value for x into Equation 1, we can solve for y:

(1/8)*y = x + 2 = 6 + 2 = 8

y = 64

So the price of a postcard is 6 cents, the price of an envelope is (1/8)*64 + 2 = 10 cents, and the price of a notepad is 64 cents

The intercepts of the equation are: D. D. x-intercept (-7/4, 0), y-intercept (0,7).

The x-intercept of an equation is simply the value of x when the corresponding value of y equals zero. Also, this is where the line of the equation cuts across the x-axis on a graph.

The y-intercept of an equation, on the other hand, is the value of y when the corresponding value of x equals zero. It is the point where the line of the equation cuts across the y-axis on a graph.

Thus, given the equation y = 4x + 7, the y-intercept is:

y = 4(0) + 7

y = 7

The x-intercept is:

0 = 4x + 7

-4x = 7

x = 7/-4

x = -7/4

The correct option is: D. x-intercept (-7/4, 0), y-intercept (0,7).

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Answer: No.

Step-by-step explanation:

The graph doesn't represent a linear, exponential, or quadratic function.

An example of a linear function is a straight line.

An example of a quadratic function is like a smile.

An example of an exponential function is a curved line.

So hence, this doesn't represent a function.

Reply below if you have any questions of concerns.

You're welcome!

- Nerdworm

Answer:

Step-by-step explanation:

The possible outcomes for the coin toss being tails and the card chosen being 1, 2, or 3 are:

-T1

-T2

-T3

Therefore, there are three possible outcomes for the event that the coin toss is tails.

The equation represents the line of best fit is y = -2x + 22.

A mathematical statement that represents a relationship between two or more quantities is typically expressed using symbols, numbers, and mathematical operations. Equations are used to express mathematical relationships, make predictions, and solve problems. An equation typically consists of an expression on each side of an equal sign (=), indicating that the values on both sides are equivalent.

According to the given information:

To determine the equation of the line of best fit in the scatter plot, we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

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

Given that the line of best fit goes through points (5, 12) and (9, 4), we can calculate the slope (m) using the formula:

m = [tex]\frac{(y_{2}-y_{1})}{(x_{2}-x_{1} ) }[/tex]

Plugging in the values from the given points, we get:

m = [tex]\frac{(4-12)}{(9-5)}[/tex]

m = -8 / 4

m = -2

So, the slope of the line of best fit is -2.

Next, we can substitute the slope and one of the given points (5, 12) into the slope-intercept form to solve for the y-intercept (b):

12 = -2(5) + b

12 = -10 + b

b = 12 + 10

b = 22

So, the y-intercept of the line of best fit is 22.

Thus, the equation of the line of best fit is:

y = -2x + 22.

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The amount(volume) of water that will be needed to fill the pool is 144 ft³.

Volume is the space occupied by a solid shape.

To calculate the amount(volume) of water that will be needed to fill the pool, we use the formula below

Formula:

Where:

From the diagram in the question,

Given:

Substitute these values into equation 1

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The total area of the given figure is 525 cm² respectively.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

The area of a plane figure is the area that its perimeter encloses.

The quantity of unit squares that cover a closed figure's surface is its area.

So, first, we will divide the figure into 2 parts which will be the triangle and the rectangle, and then add their area to get the total area as follows:

Triangle:

1/2 * b * h

1/2 * 15 * 20

15 * 10

150 cm²

Rectangle:

l*b

15*25

375 cm²

The total area of the figure: 375 + 150 = 525 cm²

Therefore, the total area of the given figure is 525 cm² respectively.

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Answer:

Equation:  250(1 + 0.028t) = 500

Answer:  36 years

Step-by-step explanation:

The equation we can use to solve this problem is the simple interest formula:

[tex]\boxed{A = P (1 + rt)}[/tex]

where:

Given the initial investment is $250 at an interest rate of 2.8%, and Edward wants to double his money:

Substite these values into the equation:

[tex]500=250(1+0.028t)[/tex]

Swap sides:

[tex]250(1+0.028t)=500[/tex]

Now solve for t:

[tex]\implies \dfrac{250(1+0.028t)}{250}=\dfrac{500}{250}[/tex]

[tex]\implies 1+0.028t=2[/tex]

[tex]\implies 1+0.028t-1=2-1[/tex]

[tex]\implies 0.028t=1[/tex]

[tex]\implies \dfrac{0.028t}{0.028}=\dfrac{1}{0.028}[/tex]

[tex]\implies t=35.71428571...[/tex]

Assuming the interest is applied annually on the anniversary of the account opening, it will take Edward 36 years to double his money with a 2.8% simple interest rate.

Answer:

196

Step-by-step explanation:

There are 7 choices for the first spot.

4 choices for the second spot. And 7 choices for the third spot, which cannot be 6,7,8--so it can be 0,1,2,3,4,5 or 9 (7choices)

7 × 4 × 7 is 196

There are 196 possibilities for the three digit area code with this plan.

Answer:

The area should be 0.5 * b * h

Step-by-step explanation:

B stands for the base of the triangle and H is the height

The solution equates to f(x) = 6x + 8.

Reiterating the same statement without reiteration, it is observed that f'(x) equals ƒ""(x), ultimately resulting in a value of 6. Subsequently, we can derive a complete expression for f(x) where C represents an integration constant.

It should be noted that to find this constant, since f(-1) = 2, plugging in x as -1 and f(x) as 2 into the above equation results in:

2 = 6(-1) + C

C = 8

As such, we can confirm that the entire expression of f(x) is simply 6 times x added to 8. Validating this answer, when assessing f(0) or f(1) , either result should match the given values from our initial problem which they do. Hence, the solution equates to:

f(x) = 6x + 8.

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Answer:

B. 200 students

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the number of seconds it will take for the planes to be at the same altitude, we need to set the altitude equations for both planes equal to each other and solve for time:

2639 + 35.25t = h    (altitude equation for Plane A)

0 + 80.75t = h       (altitude equation for Plane B)

where h is the altitude of both planes when they are at the same altitude, and t is the number of seconds that have passed.

Setting the two equations equal to each other and solving for t, we get:

2639 + 35.25t = 80.75t

45.5t = 2639

t = 58

Therefore, it will take 58 seconds for the planes to be at the same altitude.

To find their altitude at that time, we can substitute t = 58 into either of the altitude equations and solve for h:

2639 + 35.25t = h

2639 + 35.25(58) = h

h = 4818.5

Therefore, when the planes are at the same altitude, their altitude will be approximately 4818.5 feet.

Answer:

y = -5x + 31

Step-by-step explanation:

To find the equation of a line parallel to the line 5x + y = 5, we first need to rearrange it in slope-intercept form, which is

y = -5x + 5. (We see that the slope of this line is -5)

A line parallel to this line will have the same slope of -5. Now, we need to find the equation of a line that passes through the point (8,-9) with slope -5.

We can use the point-slope form of the line to find the equation. The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

Substituting the values we have, we get:

y - (-9) = -5(x - 8)

Simplifying this equation, we get:

y + 9 = -5x + 40

y = -5x + 31

Therefore, the equation of the line parallel to 5x + y = 5 that passes through the point (8, -9) is y = -5x + 31.

The solution to the given simultaneous equation y = -x + 10 ; y = -x + 12 is zero.

y = -x + 10

y = -x + 12

Subtract both equations

y - y = -x -(-x) + 10 -12

0 = -x + x - 2

0 = 0 - 2

0 = -2

In conclusion, zero is the solution to the equation

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Only 17 is a solution of the equation 3q = 51 among the values in the set {15, 16, 17}.

To check if a value is a solution of the equation 3q = 51, we substitute the value for q and check if the equation is true.

Let's check each value in the set {15, 16, 17}:

For q = 15, 3q = 3(15) = 45, which is not equal to 51. Therefore, 15 is not a solution of the equation 3q = 51.

For q = 16, 3q = 3(16) = 48, which is not equal to 51. Therefore, 16 is not a solution of the equation 3q = 51.

For q = 17, 3q = 3(17) = 51, which is equal to 51. Therefore, 17 is a solution of the equation 3q = 51.

Therefore, only 17 is a solution of the equation 3q = 51 among the values in the set {15, 16, 17}.

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It can be seen that if the circumference were smaller, the area would decrease, as it is proportional to the square of the radius.

Given the circumference (C) of the hub cap as 83.90 cm, we can find the radius (r) using the formula C = 2 * π * r,

where π = 3.14.

Thus, r ≈ 13.363 cm.

To find the area (A), use the formula A = π * r^2, yielding A ≈ 560.509 cm². Rounded, the area is about 561 cm².

Therefore, it can be seen that if the circumference were smaller, the area would decrease, as it is proportional to the square of the radius.

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The concentration of H⁺ ions at a pH of 7 is 1 x 10⁻⁷ M.

Ion concentration refers to the amount of ions that are present in a solution or a medium, expressed in terms of their concentration.

The concentration of ion with pH of 7 is calculated as follows;

pH = -log[H⁺]

[H⁺] = 10^(-pH)

The given pH = 7, so the ion concentration is calculated as;

[H⁺] = 10⁻⁷

[H⁺]  = 1 x 10⁻⁷ M

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Answer:

(1/2)(12)(16) + (1/2)π(6^2)

= (96 + 18π) square cm

= about 152.55 square cm

Carmine's loan balance after two years would be approximately $13,827.72.

In mathematics, the term "loan" typically refers to a sum of money that is borrowed by one party from another with the agreement to repay it with interest over time. Loans are a common financial concept used in various areas of mathematics, such as finance, economics, and business.

"Compounded quarterly" refers to a method of calculating interest or investment growth where the interest is added to the principal and then reinvested or recalculated at the end of each quarter (every three months) within a given time period.

To calculate Carmine's loan balance after two years, we need to use the compound interest formula, which is given by:

A = P ×[tex](1+r/n)^{nt}[/tex]

Where:

A = the loan balance after t years

P = the initial principal amount (loan amount) = $11,500

r = annual interest rate = 8% or 0.08 (expressed as a decimal)

n = number of times interest is compounded per year = 4 (since it is compounded quarterly)

t = time in years = 2 (since Carmine made no payments for the first two years)

Putting the values into the formula, we get:

A = 11,500 × (1 + 0.08/4)⁸

A = 11,500 × (1 + 0.02)⁸

A = 11,500 × (1.02)⁸

A ≈ $13,827.72

So, Carmine's loan balance after two years would be approximately $13,827.72.

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