a local lighthouse is 170ft tall. During a visit to the lighthouse, Tommy who is 5ft tall, cast a shadow that is 1.8ft long. How long in ft is the lighthouse shadow​

Answer: the slope is 1

Step-by-step explanation:

slope is rise divided by run

Answer:

52.37 52.4 when  rounded

Step-by-step explanation:

Answer:

OPTION B

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

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As per the coordinate, the equation of the tangent line is  y = (-1/2)x - 3.

In this problem, we are given the equation of a circle, x² + y² = 20, which represents all the points on the plane that are equidistant from the origin (0,0) with a distance of √20 or a radius of

=> √20/2 = 2√5.

Now, let's consider point A. We know that it lies on the circle, so it must satisfy the equation x² + y² = 20. Additionally, we are told that its y-coordinate is -4. Using this information, we can substitute y=-4 into the equation of the circle to get

=> x² + (-4)² = 20,

which simplifies to x² = 4.

Thus, point A has coordinates (±2, -4), and we can determine which one is correct by looking at the circle's equation.

Next, let's consider point B. We are told that its x-coordinate is √10. Since point B lies on the circle, it must also satisfy the equation

=> x² + y² = 20.

Using this equation, we can substitute x=√10 to get

=> (√10)² + y² = 20,

which simplifies to y² = 10. Thus, point B has coordinates (√10, ±√10).

To find the y-intercept, we can use the fact that point A lies on the tangent line. Substituting the coordinates of point A into the equation of the tangent line, we get -4 = (-1/2)(±2) + b, which simplifies to b = -3. Thus, the equation of the tangent line at point A is y = (-1/2)x - 3.

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Complete Question:

A point A lies on the circle with the equation x² + y² = 20 and has y-coordinate -4

A point B lies on the circle and has x-coordinate √10

A tangent line set at A intersects the tangent at B at point C

Find the equation of the tangent line.

Answer: y = 4x

Step-by-step explanation:

I would say y = 4x because all of these equations have a constant involved except for that.

Answer:

28-8-4x=0

x=5

5 days

Step-by-step explanation:

28-8=20 problems left

then 4 each day

Answer:

2.4 hours

Step-by-step explanation:

Let x = hours riding on bike

One cyclist covers 10 miles for every hour, so multiply x by 10 like this: 10x

Other cyclist covered 15 miles for every hour, so multiply x by 15 like this: 15x

They will both add up to 60

10x + 15x = 60

25x = 60

Divide both sides by 25

25x/25 = 60/25

x = 2.4

Answer:

2x+14

Step-by-step explanation:

Answer:

2x + 14

Step-by-step explanation:

Step 1:

2 × x + 2 × 14

Answer:

2x + 14

Hope This Helps :)

bye the question

greatest common factor means which is common factor in all three numbers as 18,36,45

Step-by-step explanation:

here,

therefore the greatest common factor of 18,36 and 45 is 3.

Keenan's z-score is 0.71, rounded to the nearest hundredth.

The z-score measures how many standard deviations an individual's score is from the mean, and can be calculated using the formula:

z = (x - μ) / σ

where x is the individual's score, μ is the mean score, and σ is the standard deviation.

For Keenan's exam:

z = (80 - 77) / 4.2

z = 0.71

Therefore, Keenan's z-score is 0.71, rounded to the nearest hundredth.

Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.

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Answer:

Step-by-step explanation:

you do -8 x 14, which will give you -112, and then divide -112 by -7. The negatives will cancel out and you can do 112 divided by 7, which is 16.

so, x = 16

Answer:14=7x/-8

   14(-8)=7x

   -112/7 =x

    -16=x

Step-by-step explanation:

Answer:

If an object on Mercury weighed 25lb, it would weigh 75lb on Earth

(25 * 3 = 75)

The answer is b  

:")

We have 3 = (4/3)π(3r^2)(dr/dt). Now we can solve for dr/dt, the rate of change of the radius.

To find the rate at which the radius is increasing, we need to use the relationship between volume and radius of a sphere. The volume of a sphere is given by V = (4/3)πr^3, where V represents the volume and r represents the radius.

The problem states that helium is being pumped into the balloon at a rate of 3 cubic feet per second. Since the rate of change of volume is given, we can differentiate the volume equation with respect to time (t) to find the rate at which the volume is changing: dV/dt = (4/3)π(3r^2)(dr/dt).

We know that dV/dt = 3 cubic feet per second, and we need to find dr/dt, the rate of change of the radius. Since we're interested in the rate of change after 2 minutes, we convert the time to seconds: 2 minutes = 2 × 60 seconds = 120 seconds.

Plugging in the values, we have 3 = (4/3)π(3r^2)(dr/dt). Now we can solve for dr/dt, the rate of change of the radius.

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Answer:

Slope intercept form: y=mx+b

The m above always represents the slope of the equation.

The slope of y= -7x-14 is   -7

Answer:

250 mph

Step-by-step explanation:

d = rt

180 min = 3 hr.

750 = 3r

r = 250 mph

Check the picture below.

a circle has a total of 360°, if we divide that evenly by 5, like in the case of this polygon, namely PENTAgon, each central angle will just be 72°, as you see in the picture.

\((f\circ g)(x)=f(g(x))=f(x-3) \\ \\ =3(x-3)^2+5(x-3)+13 \\ \\ =3(x^2 -6x+9)+5(x-3)+13 \\ \\ =3x^2 -18x+27+5x-15+13 \\ \\ =\boxed{3x^2 - 13x +25}\)

Simplifying the expression, -(4x³+x²) + 2(x³ - 3x²), the simplest form would be: B. -2x³ - 7x².

To simplify the expression, -(4x³+x²) + 2(x³ - 3x²), do the following:

Apply the distributive property to eliminate the parentheses

-4x³ - x² + 2x³ - 6x²

Combine like terms together

-4x³ + 2x³ - 6x² - x²

-2x³ - 7x²

Thus, simplifying the expression, -(4x³+x²) + 2(x³ - 3x²), the simplest form would be: B. -2x³ - 7x².

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Answer:

What is the question from Solving inequalities unit portfolio task 2-3?

Step-by-step explanation:

Comment it down below and I will solve it! :D

Answer:

1/12

Step-by-step explanation:

1/4*3

Answer:

x = \(\sqrt{3}\)/6

Step-by-step explanation:

30-60-90 triangles have legs in the ratio of 1 : \(\sqrt{3}\) : 2

create a proportion:  (6 ÷\(\sqrt{3}\)) = (1÷x)

cross-multiply:  6x = \(\sqrt{3}\)

divide by 6

Answer:

9

Step-by-step explanation:

4-x = 5(16-x)

44-x = 80-5x

4x = 36

x = 9

The company should not buy the machine.

To determine if the company should buy the machine, we need to calculate the net present value (NPV) of the investment.

First, we need to calculate the present value (PV) of the additional income the machine will generate over its lifespan. Using the formula PV = FV / e^(rt), where FV is the future value, r is the annual interest rate, and t is the number of years, we get:

PV = $7,000 / e^(0.01 x 6) = $6,439.61

Next, we need to calculate the PV of the initial investment of $44,000. Since this is a one-time cost, we can simply use the present value formula:

PV = $44,000 / e^(0.01 x 0) = $44,000

Now we can calculate the NPV by subtracting the PV of the initial investment from the PV of the additional income:

NPV = $6,439.61 - $44,000 = -$37,560.39

Since the NPV is negative, the investment is not worth it. In other words, the cost of the machine outweighs the benefits of the increased production. Therefore, the company should not buy the machine.

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Answer:

\(120-2.614\frac{5}{\sqrt{130}}=118.85\)    

\(120+2.614\frac{5}{\sqrt{130}}=121.15\)    

Step-by-step explanation:

Information given

\(\bar X= 120\) represent the sample mean

\(\mu\) population mean (variable of interest)

s=5 represent the sample standard deviation

n=130 represent the sample size  

For this case we can't set a margin of error just with a % since they not specify 1.13% respect to something for this case we can omit this value

Confidence interval

The confidence interval for the mean is given by the following formula:

\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\)   (1)

The degrees of freedom are given by:

\(df=n-1=130-1=129\)

The Confidence level is 0.99 or 99%, the significance would be \(\alpha=0.01\) and \(\alpha/2 =0.005\), and the critical value would be \(t_{\alpha/2}=2.614\)

And replacing we got:

\(120-2.614\frac{5}{\sqrt{130}}=118.85\)    

\(120+2.614\frac{5}{\sqrt{130}}=121.15\)    

The statement that best describes the sampling distribution of sample means is normal with a mean of 625 and a standard deviation of 4.45. So, correct option is A.

The sampling distribution of sample means is the distribution of all possible sample means that could be obtained from a population of a given size. The Central Limit Theorem (CLT) states that if the sample size is sufficiently large (usually n > 30), the sampling distribution of sample means will be approximately normal, regardless of the distribution of the population.

In this case, the population is the distribution of SAT math scores of students taking Calculus I with a mean of 625 and a standard deviation of 44.5. If random samples of 100 students are repeatedly taken, the sampling distribution of sample means will also be normal due to the CLT.

The mean of the sampling distribution of sample means will be the same as the population mean of 625, while the standard deviation of the sampling distribution of sample means will be the population standard deviation divided by the square root of the sample size, which is 44.5/√100 = 4.45.

Therefore, correct option is A.

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Answer:71

Step-by-step explanation:1775/25

Answer:

71 bags

Step-by-step explanation:

Each bag: 20 pennies

Pennies count: 1775

Final Answer: 71 bags

Explain:

1775 / 25 = 71

Answer:

y = -3x + 12/2

Step-by-step explanation:

Step 1: Add -x to both sides

x + 2/3 + -x = 4 + -x

2/3y = -x + 4

Step 2: Divide both sides by 2/3

2/3y ÷ 2/3 = -x + 4 ÷ 2/3

y = -3x + 12/2

Signal a) is not absolutely band-limited and so, its Nyquist sampling rate cannot be determined. Signal b) is absolutely band-limited with an absolute bandwidth of B Hz, and its Nyquist sampling rate is 2B.

Let x(l) be a band-limited signal with absolute bandwidth B Hz. For each of the signals below, we need to determine whether the signal is absolutely band-limited, and if so, express the Nyquist sampling rate for the signal in terms of B.

a) x(0) + x(t - 1)dx(t)dt:For this signal, let us apply the Fourier transform. The Fourier transform of the first term is 2πX(ω)δ(ω), and that of the second term is e^(-jω)X(ω).

Thus, X(ω) = 2πX(ω)δ(ω) + e^(-jω)X(ω)On rearranging this expression, we get: X(ω) = [1 / (1 - 2πδ(ω))]e^(-jω)Therefore, the signal is not absolutely band-limited because it has components at all frequencies.

Hence, the Nyquist sampling rate cannot be determined.b) x:For this signal, let us consider its Fourier transform. Its Fourier transform will be a scaled version of the Dirac comb function, centered at ω = 0, with a spacing of 2π. Hence, X(ω) = 2πBδ(ω).

The signal is absolutely band-limited with absolute bandwidth B Hz, and hence, the Nyquist sampling rate will be 2B. The Nyquist sampling rate is twice the absolute bandwidth, and so, the sampling rate for this signal will be 2B Hz.

Thus, the answer to the question is as follows:Signal a) is not absolutely band-limited and so, its Nyquist sampling rate cannot be determined. Signal b) is absolutely band-limited with an absolute bandwidth of B Hz, and its Nyquist sampling rate is 2B.

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The given statement the purpose of process control to detect assignable causes of variation is true because helps improve efficiency, productivity, and customer satisfaction by managing and correcting such causes.

The purpose of a process control is to detect when assignable causes of variation are present. This is done through the use of control charts, which are used to monitor the process and identify any deviations from the expected process behavior.

When an assignable cause of variation is detected, it can be addressed and corrected, helping to ensure that the process remains stable and produces consistent, high-quality products or services.

By detecting and addressing assignable causes of variation, process control helps to prevent problems before they occur, leading to improved efficiency, productivity, and customer satisfaction.

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