a street light is mounted at the top of a 15-foot tall pole. a man 6 feet tall walks away from the pole with a speed of 5 ft/sec along a straight path. how fast is the tip of his shadow moving when he is 40 feet from the pole?

Answer:

A)

Step-by-step explanation :

This question isn't too hard, but you would have to use similar triangles.

Answer:

x = 13

Step-by-step explanation:

vertical angles are congruent , then

∠ B = ∠ A , that is

6x - 8 = 5x + 5 ( subtract 5x from both sides )

x - 8 = 5 ( add 8 to both sides )

x = 13

This confidence interval suggests that we are 90% confident that the population mean lies between $273 and $658.

This confidence interval provides us with an estimate of the population mean with 90% confidence. This confidence interval suggests that we are 90% confident that the population mean lies between $273 and In other words, we can be 90% sure that the population mean falls within this range. This confidence interval does not tell us the actual population mean, but it provides us with an estimate of where the population mean is likely to lie. Furthermore, it also provides us with an indication of the degree of uncertainty associated with our estimate.

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Answer:

sorry I don't know now how to read

Kenji and Ramon are at a distance of 750 m after a time interval of 1 hour from each other.

Kenji runs for a total time of 60 minutes + 15 minutes = 75 minutes.

Ramon runs for a total of 60 minutes.

Now, we find the total distance covered by Kenji and Ramon in the time intervals of 75 minutes and 60 minutes respectively.

Kenji runs a total distance of 150 meters/minute * 75 minutes = 11250 meters.

Ramon runs a total distance of 200 meters/minute * 60 minutes = 12000 meters.

Now, we find the difference in their distances.

The distance between Kenji and Ramon is 12000 meters - 11250 meters = 750 meters.

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Complete Question:

Kenji and Ramon are running cross country. Kenji run at a rate of 150 meter per minute and Ramon runs at a rate of 200 meters per minute. If Kenji starts 15 minutes before Ramon, how far apart are they after one hour?

The two sequence A and sequence B both are correct.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that triangle UVW and Triangle ABC are congruent.

A transformation is a way of changing the size or position of a shape.

Every point in the image is the same distance from the mirror line as the original shape.

Triangle UVW made a 180 degrees of rotation about point V and then a triangle along the directed line segment VB.

This is same as translation along the directed line segment UA then about 180 degrees rotation about point A.

Hence, the two sequence A and sequence B both are correct.

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The function that models the data in the given table is: D. y = -2x + 10.

The function that models the data of a table can be expressed in the slope-intercept form as y = mx + b, where:

Find the slope of the function using two pairs of values from the table, (6, -2) and (10, -10):

Slope (m) = change in y / change in x = (-10 - (-2)) / (10 - 6)

Slope (m) = -8 / 4

Slope (m) = -2

Find the y-intercept (b) by substituting m = -2 and (x, y) = (6, -2) into y = mx + b:

-2 = -2(6) + b

-2 = -12 + b

-2 + 12 = b

10 = b

b = 10

To write the function, substitute m = -2 and b = 10 into y = mx + b:

y = -2x + 10

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Answer:

y = 4x - 2

Step-by-step explanation:

y = 4x + b

-6 = 4(-1) + b

-6 = -4 + b

b = -2

y = 4x - 2

Answer:

[tex]y - (-6) = 4(x - (-1))[/tex] or [tex]y = 4x - 2[/tex]

Step-by-step explanation:

We can use point slope form: [tex]y - y_{1} = m(x - x_{1})[/tex], where [tex](x_1, y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.

We plug in (-1, -6) and 4 to get:  which simplifies to [tex]y + 6 = 4(x + 1)[/tex]

If we want to express this in the form y = mx + b, we have to do a little rearranging. [tex]y + 6 = 4(x + 1)[/tex] becomes [tex]y + 6 = 4x + 4[/tex] and then we subtract 6 from both sides to get: [tex]y = 4x - 2[/tex]

Answer:

Step-by-step explanation: To find the measure of angle ACB, we can use the Pythagorean Theorem: AB^2 + AC^2 = BC^2.

Substituting in the given values for AB and AC, we get: 10.2^2 + 4.9^2 = BC^2

Solving for BC, we get: BC = √(10.2^2 + 4.9^2)

Substituting this value back into the equation for the Pythagorean Theorem, we get:

AB^2 + AC^2 = (√(10.2^2 + 4.9^2))^2

Simplifying this equation, we get:

AB^2 + AC^2 = 10.2^2 + 4.9^2

This equation is already in the correct form, so we can solve for ∠ACB directly:

∠ACB = tan^-1(AC/AB)

Substituting in the given values for AC and AB, we get:

∠ACB = tan^-1(4.9/10.2)

Using a calculator, we find that tan^-1(4.9/10.2) is approximately equal to 26.7°.

Rounded to 3 significant figures, this value is 26.7°.

Fred's pay for the specified week, with a rate of $11.25 for regular hours and time and a half for overtime, and number of hours worked of 48.5 hours is presented by completing the attached table as follows;

Rate: $11.25, regular hours: 40, overtime: N/A, total: $450

Rate: $16.875, regular hours: N/A, overtime: 8.5, total: $143.4375

Gross: $593.4375

A payment rate is the amount of payment or money that is received in a unit of time.

The amount Fred earns per hour = $11.25

The number of regular hours Fred works per week = 40

The rate at which he is paid for overtime = Time and a half

The number of hours Fred works in the specified week = 48.5 hours

Therefore, the amount Fred earns for working overtime = 1.5 × $11.25 = $16.875

The amount Fred earns for regular hours during the specified week = 40 × $11.25 = $450

The number of overtime hours Fred works for during the week = 48.5 - 40 = 8.5

The amount Fred earns for the overtime work = 8.5 × $16.875 = $143.4375

Fred's gross payment for the week is therefore; $450 + $143.4375 = $593.4375

The table can therefore be completed by plugging in the above values as follows;

Rate: $11.25, regular hours: 40, overtime: N/A, total: $450

Rate: $16.875, regular hours: N/A, overtime: 8.5, total: $143.4375

Gross: $593.4375

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The line integral of the vector field in the figure is zero. This is due to the fact that the vector field is perpendicular to the curve c, and therefore, the integral of the dot product of the vector field and the tangent vector along the curve c is zero.

1. The line integral of a vector field is the integral of the dot product of the vector field and the tangent vector of the curve along the curve.

2. The vector field in the figure is perpendicular to the curve c.

3. The dot product of two perpendicular vectors is zero.

4. Therefore, the integral of the dot product of the vector field and the tangent vector along the curve c is zero.

5. Hence, the line integral of the vector field in the figure is zero.

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the impact on the error probability of part is on  Decreasing trends of the test procedure

A Type II error is when we fail to reject a false null hypothesis. Higher values of α make it easier to reject the null hypothesis, so choosing higher values for α can reduce the probability of a Type II error.

The consequence here is that if the null hypothesis is true, increasing α makes it more likely that we commit a Type I error (rejecting a true null hypothesis).

So using lower values of α can increase the probability of a Type II error.

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Answer:

There's 413.1ml of liquid in the bottle

The z-score to the nearest tenth for the following blood pressure readings is 45.14%.

What is blood pressure ?

The force of moving blood exerted on the walls of blood arteries is known as blood pressure. The heart's action of pumping blood through the circulatory system is mostly responsible for this pressure. The pressure in the major arteries is meant when the word "blood pressure" is used without qualifier.

As the data is normally distributed we can use standard normal z table to estimate the answers.

Z = (x-mean)/s.d

Given mean = 121.

S.d = 15.

P(X<142).

Z = (142-121)/15 = 1.4

From z table,

P(z<1.8) = 0.9641 ~ 96.41%

P(X>130).

Z = (130-121)/15 = 0.6

From z table,

P(z>0.6) = 0.8849

P(112<X<130) = P(X<130)-P(X<112).

P(X<130).

Z = (130-121)/15 = 0.6

From z table,

P(z<0.6) = 0.7257

P(X<112).

Z = (112-121)/15 = -0.6

From z table,

P(z<-0.6) =0.2743

Required answer is 0.7257-0.2743 = 0.4514 ~ 45.14%

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The rate of interest  for the given data can be found as 6%.

Simple interest can be defined as a form of interest in which the percent rate is applied on the same principal for a given period of time. The amount can be calculated by adding the interest to the principal.

The given data as per the question is as below,

P = $4000, t = 6 years and Interest = $1440.

Suppose the rate of interest be r% per annum.

Substitute all the values in the expression for simple interest (P × r × t)/100 as follows,

1440 = (4000 × 6 × r)/100

⇒ r = 6%

Hence, the rate of interest is obtained as 6%.

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We can begin by rewriting the problem:

3/4 - 1/2p > 5/4

Let’s solve accordingly through steps:

1. Subtract 3/4

-1/2p > 2/4

2. Divide both sides by the coefficient

-1/2 / -1/2 = p

2/4 / -1/2 = -1

3. Simplify & Switch Signs

p < -1

The answer to Part A is p < -1.

Part B: On a number line, this answer would be graphed by plotting a point at -1 and drawing an arrow that goes to the left direction to show that p is less than -1.

Answer:

[tex](4,-3)[/tex]

Step-by-step explanation:

The solution is where the graphs intersect.

Answer:

x( x-4)(x+2)

Step-by-step explanation:

x^3-2x^2-8x

First factor out the greatest common factor x

x( x^2 -2x -8)

What 2 numbers multiply to -8 and add to -2

-4*2 = -8

-4+2 = -2

x( x-4)(x+2)

The graph is a parabola with its touching the x-axis at (3,0)

A parabola is a curve where any point is at an equal distance from:

a fixed point (the focus ), and

a fixed straight line (the directrix )

its general equation is y = a(x – h)² + k or x = a(y – k)² +h. Here (h, k) denotes the vertex. y = a(x – h)2 + k is the regular form. x = a(y – k)2 +h is the sidewise form.

Given here (x-3)² + 4 = -4/9(x(x-6))

simplifying this we get

9(x²-6x+13) = -4 (x(x-6))

13x²-78x+117 = 0

(x-3)² = 0

thus it has a root at x=3

The graph is attached showing the parabola  touching the x-axis at (3,0)

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Answer:

4

Step-by-step explanation:

gradient = slope = m = rise / run

  from the origin (0,0) this line rises '12' and has a run of '3'

             12/3 = 4

Approximately 50% percentage of people age 65 or older take at least five prescription medicines daily in the United States.

In the United States, approximately 50% percentage of people aged 65 or older take at least five prescription medicines daily. This figure is based on data from the Centers for Disease Control and Prevention (CDC) which track and analyze the health and healthcare of the US population. The CDC found that in 2015, those ages 65 or older reported taking an average of 14.7 prescriptions per person, which is an increase from the average of 13.7 prescriptions per person in 2010. Of those aged 65 or older, 50% reported taking at least five medications daily, while 25% reported taking at least 10 medications daily. The data also showed that seniors were more likely to take multiple medications if they had chronic conditions such as diabetes, high blood pressure, and heart disease. This highlights the importance of closely monitoring and managing medication use, especially among seniors, to ensure that their medications are appropriate and safe.

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Answer:

Your answer is -13x + 20

Step-by-step explanation:

2x - 5*(3x - 4)

Discribute the -5.

2x + [ (-5)(3x) + (-5)(-4) ]

2x + [ (-15x +20) ]

2x - 15x + 20

- 13x + 20

The gradient vector field of f is ∇(f) = (xi+yj)/√(x^2+y^2) ans sketch is given below.

In the given question, we have to find the gradient vector field of f and sketch it.

f(x,y)= √(x^2+y^2)

To find the gradient, it's just the partial derivatives for x and y

∇(f) = ∂f/∂x i + ∂f/∂y j

In this case, we have

∂f/∂x = x/√(x^2+y^2) and ∂f/∂y = y/√(x^2+y^2). So

∇(f) = x/√(x^2+y^2) i + x/√(x^2+y^2) j

We can write it as

∇(f) = (xi+yj)/√(x^2+y^2).

This is a unitary vector field everywhere, with the exception of the origin, where it is undefined, where we can see it as the vector xi+yj divided by the magnitude √(x^2+y^2). From the starting point, the direction is outward.

The sketch is given below:

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Answer:            

Step-by-step explanation:

The confidence interval for the given poll is; 51% to 57%

We are given that;

Sample proportion; p = 54% = 0.54

Margin of error; E = 3% = 0.03

Now, formula for confidence interval of proportions is;

p ± E

where;

p is sample proportion

E is margin of error

Thus;

CI = 0.54 ± 0.03

CI = (0.54 - 0.03), (0.54 + 0.03)

CI = (0.51, 0.57)

We conclude that the confidence interval is CI = (0.51, 0.57)

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Answer:

3.75 Hours or 225 Minutes

Step-by-step explanation:

5/4 = 1.25 So it takes 1.25 hours to do an assignment

1.25 x 3 = 3.75

Which equals 225 Minutes

Answer: 3.75 or 3 3/4

Step-by-step explanation:

This is a unit rate problem

A unit rate is a rate for one of something. (i.e, 1 pencil for 4 notebooks)

So first, to find the time needed for one assignment, we divided 5 hours by 4 hours.

5/4 = 1.25 (1 and 1/4)

Now we multiply the unit rate by 3.

1.25 times 3 = 3.75, or 3 3/4.

The rate of change of S for the weekly sales is :

-250 000e⁻°·⁵t

Given:

the sales of the product is :

S = 500,000e^-0.5t

where S is the weekly sales in the dollars and t is the number of weeks since end of the campaign.

we are asked to find the rate of sales dS/dt = ?

that is the rate of sales of delay.

Given:

S = 500,000e^-0.5t

dS/dt =(500,000)e^-0.5t + 500,00 (e^-0.5t)

= 0 +  500,00 (e^-0.5t)

= - 250 000 e^0.5t

therefore, dS/dt = - 250 000 e^0.5t

Hence we get the required answer.

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M will increase from 24 to 56

The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. It is symbolised by the proportional sign ().

According to the direct proportion formula, if y is directly proportional to x, we can state that y = kx, where k is a constant. Y = kx also serves as the direct proportion equation's general form.

When one quantity increases or declines, the other quantity also rises or falls in direct proportion. On the other hand, in indirect or inverse proportion, if one quantity rises, the other one falls, and vice versa.

m= 8p

When p = 3        

 m =3 × 8 =24

When p = 47      

  m=8× 7 = 56

So M will increase from 24 to 56

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Answer:

{ No SIMPLIFIED: [tex]\frac{9}{12} inches[/tex] }
{ SIMPLIFIED: [tex]\frac{3}{4} inches[/tex] }

Step-by-step explanation:

If we want to know about the plant grows, we need to add the fractions in 3 weeks with this solution:
[ The inch of the plant 1st week ] + [ The inch of the plant 2nd week ] + [ The inch of the plant 3rd week ] = [ The inch of the plant in 3 weeks ]

Look at the denominator of 3 weeks, it is 12 and the numerators are 1,3,5
To plus the fraction we remain the denominator and plus the numerators together which we can result in this equation:
[tex]\frac{1}{12}[/tex] + [tex]\frac{3}{12}[/tex] + [tex]\frac{5}{12}[/tex] = [tex]\frac{1 + 3 + 5}{12}[/tex] = [tex]\frac{9}{12}[/tex] { SIMPLIFIED: [tex]\frac{9 : 3 }{12 : 3} = \frac{3}{4}[/tex] }
So then we see that if you choose no simplified then: Michael's plant grow  [tex]\frac{9}{12}[/tex] inches in 3 weeks or you could choose the simpliflied one then: Michael's plant grow [tex]\frac{3}{4}[/tex] inches in 3 weeks.

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