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4 years ago

Circle A has area 500 in2. The diameter of circle B is three times the diameter of circle A. Estimate the area of circle B.

Mathematics

2 answers:

stich3 [128]4 years ago

7 0

Answer:

456.5

Step-by-step explanation:

VladimirAG [237]4 years ago

3 0

Answer:

why was this question up for so long

Step-by-step explanation:

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What is the vertex of the parabola whose equation is y = (x + 1)^2 + 3?

dalvyx [7]

The y-value of the vertex is positive 3, as shown by the +3 on the right hand side of the equation, and the x-value is -1, from the (x+1)^2 (remember, when the number is inside the brackets, flip the sign) The vertex would be (-1, 3)

If you are looking for a rigorous answer (calculus), we must find the mininum point of the equation: f(x) = (x+1)^2 + 3 f
f'(x) = 2(x+1) = 2x + 2
2x + 2 = 0
x = -1
f(1) = (-1 + 1)^2 + 3
f(1) = 0 + 3 = 3
(-1, 3)

5 0

3 years ago

The circumference of a circle is 15π ft. What is the area, in square feet? Express your answer in terms of π.

DerKrebs [107]

Answer:

Area of the circle is 56.25π square feet.

Step-by-step explanation:

Given that:

The circumference of a circle is 15π ft.

To Find:

What is the area, in square feet?

We know that:

Circumference of a circle = 2πR
Area of a circle = πR²

Where,

Radius is denoted as R.

Finding the radius of the circle:

Circumference of a circle = 15π

⟶ 2πR = 15π

⟶ 2πR = 2π × 7.5

Cancelling 2π.

⟶ R = 7.5

∴ Radius of the circle = 7.5 ft.

Finding the area of the circle:

⟶ Area = πR²

⟶ Area = π(7.5)²

⟶ Area = π × 7.5 × 7.5

⟶ Area = π × 56.25

⟶ Area = 56.25π

∴ Area of the circle = 56.25π ft.²

7 0

3 years ago

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 30,393 miles, with a standard

Pie

Answer:

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem:

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 30393, \sigma = 2876, n = 37, s = \frac{2876}{\sqrt{37}} = 472.81$

What is the probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

This probability is the pvalue of Z when X = 30393 + 339 = 30732 subtracted by the pvalue of Z when X = 30393 - 339 = 30054. So

X = 30732

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{30732 - 30393}{472.81}$

$Z = 0.72$

$Z = 0.72$ has a pvalue of 0.7642.

X = 30054

$Z = \frac{X - \mu}{s}$

$Z = \frac{30054 - 30393}{472.81}$

$Z = -0.72$

$Z = -0.72$ has a pvalue of 0.2358

0.7642 - 0.2358 = 0.5284

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

4 0

3 years ago

You are riding a roller coaster when a shoe falls off your foot. The function y=200−16t^2 represents the height y (in feet) of t

pickupchik [31]

A graphing calculator shows it takes 3.25 seconds for the shoe to hit the building.

_____
200 -16t^2 = 31
169 = 16t^2
√(169/16) = t
t = 13/4 = 3 1/4