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3 years ago

Write the standard equation of a circle with center (-9,-4) and radius 15.

Mathematics

1 answer:

Oksi-84 [34.3K]3 years ago

5 0

Answer:

Equation of a circle:

radius = the sq. rt of (x - h)^2 + (y - k)^2

Plug in the values for the center of a circle and the radius:

15 = the sq. rt of (x + 9)^2 + (y + 4)^2

(x + 9)^2 + (y + 4)^2 = 225

The answer is A or the first one.

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from 2002 to 2012, the number of a particular make of cars sold at a dealership yearly declined to 500. The number is expected t

Alinara [238K]

To determine the number of cars that will be sold by the year 2020, we will use the equation,

N = (N1)(1 - r)^(t)

where N1 is the starting number of cars, r is the rate of the decrease, and t is the number of years from 2012. Substituting the konwn values,

N = (500)(1 - 0.028)^(8)
N = 398.38

The closest integer to the calculated value is 398. Thus, the answer is 398 cars.

3 0

2 years ago

40 is 50% of what number?<br> A. 20<br> B. 40<br> C. 60<br> D. 80

Alex787 [66]

Answer:

D. 80

Step-by-step explanation:

multiply 40 by 2 cause its 50 percent

5 0

2 years ago

Read 2 more answers

If you have $.25 on your debit card do you have enough money to buy a Baseball glove Yes or no

Novosadov [1.4K]

Answer:

no, depends on what the ball costs but no because its .25 (meaning cents) not 25.00 (meaning dollars)

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2$

$n = 2401$

The minimum sample size is 2401.

4 0

2 years ago

The radius of the cone is 5 in and y = 13 in. What is the volume of the cone in terms of π?

olga nikolaevna [1]

Answer:

The volume of the cone is;

100 π inches^3

Step-by-step explanation:

To calculate the volume, we need the height

We can get the height from the slant height and the radius

Mathematically, we use Pythagoras’ theorem for this as the slant height, the radius and the height forms a right-angled triangle

The right-angled triangle has the slant height as its hypotenuse

By the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides

Let the height be h

Thus;

12^2 = 5^2 + h^2

169= 25 + h^2

h^2 = 169-25

h^2 = 144

h = √1144 inches = 12 inches

The volume of the cone is;

1/3 * π * r^2 * h

= 1/3 * π * 5^2 * 12

= 100 π inches^3

4 0

2 years ago