Find the area of sector DEF (show work please)

18,234.9+516.1 show your work

butalik [34]

Answer:

18,751

Step-by-step explanation:

18 234 . 9

516 . 1

----------------

18 751 . 0

----------------

3 0

2 years ago

Read 2 more answers

The larger of two numbers is 7 times the smaller number. Three times the larger number is 7 more than 4 times the smaller number

Juliette [100K]

Let the smaller number be x.

Given, the larger number is 7 times the smaller number.

So, the larger number = 7x.

Given, 3 times the larger number is 7 more than 4 times the smaller number.

So we can write the equation as,

$3(7x) = 4(x)+7$

$3(7x) = 4x+7$

$21x = 4x+7$

Now we have to move 4x to the left side by subtracting 4x from both sides.

$21x-4x = 4x-4x+7$

$21x-4x = 7$

$17x = 7$

To get x, we will divide both sides by 17. We will get,

$\frac{17x}{17} = \frac{7}{17}$

$x = \frac{7}{17}$

So the smaller number = $\frac{7}{17}$

The larger number = $7(\frac{7}{17} )$ = $\frac{49}{17}$

So we have got the required numbers.

Smaller number = $\frac{7}{17}$ and larger number = $\frac{49}{17}$ .

4 0

3 years ago

1. Kari is making copies at a local copy store of the program for her school play. She makes 52 copies and the total cost is $6.

Leona [35]

The first one is 2.78% second one is 3.8% third one is 4.5% and it will be 378

8 0

3 years ago

Given a point (-3, 6) and a line y= 2x − 8, what is the slope of the line?

Eddi Din [679]

The slope is 2.

Since the line "y = 2x − 8" follows slope-intercept form (y = mx + b), and the slope is always m, we know that the value of the slope is 2.

6 0

3 years ago

A study was conducted and two types of engines, A and B, were compared. Fifty experiments were performed using engine A and 75 u

USPshnik [31]

Answer:

a) -6 mpg.

b) 2.77 mpg

c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Gas mileage A: Mean 36, standard deviation 6, sample of 50:

So

$\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485$

Gas mileage B: Mean 42, standard deviation 8, sample of 50:

So

$\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314$

Distribution of the difference:

Mean:

$\mu = \mu_A - \mu_B = 36 - 42 = -6$

Standard error:

$s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142$

A. Find the point estimate.

This is the difference of means, that is, -6 mpg.

B. Find the margin of error

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = zs = 1.96*1.4142 = 2.77$

The margin of error is of 2.77 mpg

C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)

The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg

The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg

The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

8 0

2 years ago