Andrea collected data for a school project, but accidentally spilled her coffee on her page. She knows that the values represented a linear function. For this function, what is the value of y when x = 0?.

The height of the streetlight is 30 feet.

Let's call the height of the streetlight "h".

When the person is 16 feet from the streetlight, the length of their shadow will be 16 feet * (6 feet / h) = 96 feet / h.

When the person is 5 feet from the tip of the streetlight's shadow, the length of the streetlight's shadow will be h * (16 feet / 5 feet) = 3.2 * h.

Since the length of the person's shadow starts to appear beyond the streetlight's shadow when they are 5 feet from the tip of the streetlight's shadow, we know that 96 / h > 3.2 * h.

Solving for h, we get:

96 / h > 3.2 * h

96 > 3.2h

30 > h

So, the height of the streetlight is less than 30 feet.

To determine the exact height of the streetlight, we can use the equation:

96 / h = 3.2 * h

96 = 3.2h

30 = h

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complete question:

a six foot person walks from the base of a streetlight directly toward the tip of the shadow cast by the streetlight. when a person is 16 feet from the streetlight and 5 feet from the tip of the streetlight's shadow, the person's shadow starts to appear beyond the streetlight's shadow. what is the height of the streetlight?

Professor evaluation in this case is an example of a discrete random variable. A discrete random variable takes on a countable number of distinct values.

In this case, the scores 1, 2, 3, 4, and 5. The variable represents the outcome of a specific event (the evaluation of a professor) and can only assume these specific values. Each score has a certain probability associated with it, reflecting the likelihood of that score being given by the students.

As it is a discrete random variable, there is no intermediate value between the possible scores, and the probability distribution can be represented by a probability mass function.

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The solution to the differential equation dx/dt = 3x(x - 8), with the initial condition x(0) = 1, involves finding the function x(t) that satisfies the equation.

To solve the given differential equation, we can separate variables and integrate. Rearranging the equation, we have dx/(x(x - 8)) = 3dt. Now, we can integrate both sides.

Integrating the left side requires partial fraction decomposition. We can express the integrand as A/x + B/(x - 8), where A and B are constants. By finding a common denominator and equating the numerators, we get A(x - 8) + Bx = 1. Expanding and equating coefficients, we find A = -1/8 and B = 1/8.

Substituting these values back into the integral, we have (-1/8)∫(1/x)dx + (1/8)∫(1/(x - 8))dx = 3∫dt. Simplifying, we obtain -(1/8)ln|x| + (1/8)ln|x - 8| = 3t + C, where C is the constant of integration.

To determine the value of the constant C, we use the initial condition x(0) = 1. Plugging in t = 0 and x = 1, we get -(1/8)ln|1| + (1/8)ln|1 - 8| = 3(0) + C. This simplifies to C = -(1/8)ln|7|.

Finally, we can write the solution as -(1/8)ln|x| + (1/8)ln|x - 8| = 3t - (1/8)ln|7|. This equation represents the solution x(t) to the given initial value problem.

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The value value of x is at the 40th percentile of the distribution is 0.65.

The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation

Given:- μ\(_X\)=0,σ\(_X\)=1

We can standardize the random variable: Z=(X−μx)/σx,

Then the equation is P(X≤ x )=Φ(x−μx/σx)=Φ(x−0/1)=0.4

Inverse function

Ф\(\\^{-1}\)(0.4) = \(\frac{x-0}{1}\)

From the table we get,

Ф\(^{-1}\) = 0.65

Thus

\(\frac{x-40}{10}\) = 0.65

x -0 = 0.65

x = 6.5

Thus the value value of x is at the 40th percentile of the distribution is 0.65

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The rate at which the people are moving apart 2 hours after the man starts walking is 0 ft/s.

Let's set up a coordinate system to solve the problem. We'll place point P at the origin (0, 0) and the woman's starting point at (-100, 0). The man starts walking south, so his position at any time t can be represented as (0, -5t).

The woman starts walking north, so her position at any time t can be represented as (-100, 4t).

After 2 hours (or 2 * 3600 seconds), the man's position is (0, -5 * 2 * 3600) = (0, -36000), and the woman's position is (-100, 4 * 2 * 3600) = (-100, 28800).

To find the distance between them, we can use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Distance = √((-100 - 0)^2 + (28800 - (-36000))^2)

        = √(10000 + 12960000)

        = √(12970000)

        ≈ 3601.2 feet

To find the rate at which the people are moving apart, we need to find the rate of change of distance with respect to time. We differentiate the distance equation with respect to time:

d(Distance)/dt = d(√((x2 - x1)^2 + (y2 - y1)^2))/dt

Since the x-coordinates of both people are constant (0 and -100), their derivatives with respect to time are zero. Therefore, we only need to differentiate the y-coordinates:

d(Distance)/dt = d(√((0 - (-100))^2 + ((-36000) - 28800)^2))/dt

              = d(√(100^2 + (-64800)^2))/dt

              = d(√(10000 + 4199040000))/dt

              = d(√(4199050000))/dt

              = (1/2) * (4199050000)^(-1/2) * d(4199050000)/dt

              = (1/2) * (4199050000)^(-1/2) * 0

              = 0

Therefore, the rate at which the people are moving apart 2 hours after the man starts walking is 0 ft/s.

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Answer:

0.1%

Step-by-step explanation:

138 into a percent=1.38%

156 into a percent=1.56%

175 into a percent=1.75%

1.38-1.56=0.18

1.56-1.75=0.19

0.19-0.18= 0.1%

The increase in volunteers from year 1 to year 2 is 13.04 % and the increase from year 1 to year 3 is 26.81 %.

The percentage can be defined as a relative value that represents the hundredth part of any quantity.

Given that the number of volunteers in a program during year 1, year 2 and year 3 are 138, 156 and 175 respectively.

The percentage of increase in volunteers from year 1 to year 2 is given below.

Volunteers (%) = \(\dfrac {156-138}{138} \times 100\)

Volunteers (%) = 13.04%

The percentage of increase in volunteers from year 1 to year 3 is given below.

Volunteers (%) = \(\dfrac {175-138}{138} \times 100\)

Volunteers (%) = 26.81 %

Hence we can conclude the increase in volunteers from year 1 to year 2 is 13.04 % and the increase from year 1 to year 3 is 26.81 %.

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Answer:

A reflex angle is an angle greater than a straight angle and less than a circle. ... Some examples of the measures of reflex angles in degrees are:.

Step-by-step explanation:

hope it helps!

Answer:

lol same facts though

Step-by-step explanation:

Answer:

Your future doesn't really depend on school to be honest, but school is one of the options to a great future. Even college and etc dropouts become successful.

Answer:

16

Step-by-step explanation:

each sheep has about 6.42 pounds of wool so if you do 100/6.42 you get 15.5 but there isn't half sheeps so you round up to 16

Answer:

D

Step-by-step explanation:

The sum of the ratios = 4 + 3 = 7

The ratio of blue paint to the total paint = 4/7

The ratio of yellow paint to the total paint = 3/7

Pints of blue paint needed to make  21 pints of the green paint = 4/7 x 21 = 12 pints

Pints of yellow paint needed to make  21 pints of the green paint = 3/7 x 21 = 9 pints

The area of the composite figure is the sum of the area of all rectangle which 700cm²

To find the area of the composite figure, we need to divide the figure into small parts and the find the area.

In this problem, we can divide the figure into different rectangular parts

Area of a rectangle; length * width

1. A = L * W = 10 * 5 = 50 cm²

2. A = L * W = 10 * 5 = 50 cm²

3. A = L * W = 20 * 30 = 600cm²

The area of the composite figure is the sum area of the rectangles.

A = 50 + 50 + 600 = 700cm²

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Answer:

Step-by-step explanation:

sin A = \(\frac{opposite side}{Hypotenuse}\)

Sin 29 = \(\frac{y}{500}\)

0.4848 * 500 = y

y = 242.4 ft

Answer:

Y=242.4

Step-by-step explanation:

due to the association property the angle at the bottom left is 29 degrees

since sine property is oposite over hypothesis we get

sine(29)=y/500

500sin(29)=y

Y=242.4

Answer:

Step-by-step explanation:

The equation is actually y=mx+b

M is the slope

B is the Y-intercept

Y=14x+b

Answer:

y = 14x

Step-by-step explanation:

equation: y = mx

Slope(m) = 14

Since the line passes through the origin, there is no y-intercept, so the equation is in y = mx form. Since we're given the slope(m), all we have to do is rewrite the equation with the given value of m:

y = 14x

Answer:

where's the picture at?

Answer:

Step-by-step explanation:

our lengths are:

7.5a-1.5b,  3.5a+4.5b, 6.5c+2a, 8.5-6.5c

P=7.5a+3.5a+2a-1.5b+4.5b+6.5c-6.5c+8.5=16a+3b+8.5

Answer:

No

Step-by-step explanation:

d = (x_2 - x_1)^2 + (y_2-y_1)^2

If any two points on  both triangles have the same measure then they are congruent.

41

52

Answer:

Step-by-step explanation:

The order of letters in "figure's name" is important

NEPK ≅ VXSR

A). KN (4th and 1st) ≅ RV (4th and 1st)

NEPK ≅ VXSR

G). NE (1st and 2nd) ≅ VX (1st and 2nd)

NEPK ≅ VXSR

D). PK (3rd and 4th) ≅ SR (3rd and 4th)

NEPK ≅ VXSR

F). EP (2nd and 3rd) ≅ XS (2nd and 3rd)

Answer:

z < ¾

Step-by-step explanation:

Or z < 0.75

...........

Answer:

Answer

If we add 76+(-90)-(-48)=34

The sum to infinity of the sequence is -2.25

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

3, -1, 1/3, -1/9

Using the above as a guide, we have the following:

First term, a -3

Common ratio, r = -1/3

The sum to infinity is then calculated as

Sum = a/1 - r

So, we have

Sum = -3/(1 + 1/3)

Evaluate

Sum = -2.25

Hence, the sum is -2.25

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To flush twice the volume of water contained in the system, you would need to flush 18.2 gallons x 2 = 36.4 gallons of water through the system.

To calculate the volume of water contained in the system, you would use the formula for the volume of a cylinder: V = πr^2h, where r is the radius of the pipe (half the diameter), h is the length of the pipe, and π is approximately 3.14.

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Step-by-step explanation:

84/6= 84÷6/6÷6

14/1= 14 points

Answer:

39=6t+3f+e

39=19f+1

5 touchdowns, 3 extra points, and 2 field goals.

Step-by-step explanation:

e=f+1

6t=15f

39= 6t   +3f   +e

       ^       ^      ^

39=(15f)+(3f)+(f+1)           |             e=f+1                     |                      6t=15f

39=19f+1                         |             e=2+1                    |                      6t=15(2)

38=19f                            |             e=3                        |                      6t=30

f=2                                  |                                            |                      t=5

\( : \implies \sf 9x + 3 = - 33\)

\( : \implies \sf 9x = - 33 - 3\)

\( : \implies \sf 9x = - 36\)

\( : \implies \sf x = \dfrac{ - 36}{9} = - 4\)

\( \therefore \sf x = -4 \)

Answer:

\(\frac{dy}{dx}\) = - \(\frac{3}{2}\)

Step-by-step explanation:

differentiating implicitly, using the product rule for the term - 5y²

3x² - 5y² - 1 = 0 ( differentiate implicitly with respect to x )

6x - 10y \(\frac{dy}{dx}\) - 0 = 0 ( subtract 6x from both sides )

- 10y \(\frac{dy}{dx}\) = - 6x ( divide both sides by - 10y )

\(\frac{dy}{dx}\) = \(\frac{-6x}{-10y}\) = \(\frac{3x}{5y}\)

substitute (5, - 2 )

\(\frac{dy}{dx}\) = \(\frac{3(5)}{5(-2)}\) = \(\frac{15}{-10}\) = - \(\frac{3}{2}\)

Answer:

\(\dfrac{\text{d}y}{\text{d}x}=-\dfrac{3}{2}\)

Step-by-step explanation:

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

To find dy/dx for 3x² - 5y² - 1 = 0, differentiate each term with respect to x.

Begin by placing d/dx in front of each term of the equation:

\(\implies \dfrac{\text{d}}{\text{d}x} 3x^2-\dfrac{\text{d}}{\text{d}x} 5y^2-\dfrac{\text{d}}{\text{d}x} 1=\dfrac{\text{d}}{\text{d}x} 0\)

Differentiate the terms in x only (and constant terms):

\(\implies 6x-\dfrac{\text{d}}{\text{d}x} 5y^2-0=0\)

\(\implies 6x-\dfrac{\text{d}}{\text{d}x} 5y^2=0\)

Use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 6x-10y\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation to make dy/dx the subject:

\(\implies 10y\dfrac{\text{d}y}{\text{d}x}=6x\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{6x}{10y}\)

Now we have differentiated the given equation with respect to x, substitute the given point (5, -2) into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{6(5)}{10(-2)}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{30}{-20}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{3}{2}\)

Therefore, the value of dy/dx at point (5, -2) is -3/2.

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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System of Equations

Given the system of equations:

x + z = 6

2x + 4z = 1

To solve the system by the elimination method, we must make the coefficients of one variable opposite.

It's required to eliminate the z-term which means we must make the coefficients of z opposite on both equations.

The coefficient of z is 4 in the second equation, so to eliminate the variable, we must multiply the first equation by -4 as follows:

-4x - 4z = -24

Now when we add both equations, the z is eliminated.

Answer: Multiply equation A by −4.

The cost of the pyramid shape sign is $240.

A pyramid is a 3D figure that has a base made of a polygon and faces that are all triangular and connected. The conventional shape of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this section, let's study more about pyramids.

We know the volume of a pyramid is (1/3)×length of the bese×width of the base×height.

∴ The volume of the pyramid with base length of 6feet, base width of 3feet and height 5 feet is,

= (1/3)×6×3×5 cubic feet.

= 30 cubic feet.

Given, The aluminum costs $8 per cubic foot.

∴ The total cost of the pyramid is = (30×8) = $240.

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Answer:

Step-by-step explanation:

See image