An apple pie is divided into eight equal slices with each slice being 280 calories. How much calories are in the entire pie

Identify the equation of the circle D with center D(−8,−1) and radius 3.

REY [17]

Answer:

(h+8)^2 + ( y +1)^2 = 9

Step-by-step explanation:

The equation of a circle can be written as

(x-h) ^2 +(y-k) ^2 = r^2

where (h,k) is the center and r is the radius

(h- -8)^2 + ( y - -1)^2 = 3^2

(h+8)^2 + ( y +1)^2 = 3^2

(h+8)^2 + ( y +1)^2 = 9

8 0

3 years ago

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What is the area of a circle that has a diameter of 16in

rjkz [21]

Answer:

A=πr2

A=π8^2

A=π* 8* 8

A= 64π

A= 64x3.14

A= 200.96 in^2

Step-by-step explanation:

8 0

2 years ago

Simplify 3/x²+14x+48 divided by 3/10x+60

stira [4]

C. 10/x+8
The easy way to do it would be to take it one step at a time.

8 0

3 years ago

Read 2 more answers

A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. Consider the sample m

love history [14]

Answer:

a) The expected value of the sample mean weight is 20.4 pounds.

b)The standard deviation of the sample mean weight is 0.123.

c) There is a 14.46% probability the sample mean weight will be less than 20.27.

d) This value is $c = 20.6153$ .

Step-by-step explanation:

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 $\frac{\sigma}{\sqrt{n}}$ .

Problems of normally distributed samples can be 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.

In this problem, we have that:

A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. This means that $\mu = 20.4, \sigma = 1.23$

Consider the sample mean weight of 100 watermelons of this variety. This means that $n = 100$ .

a. What is the expected value of the sample mean weight? Give an exact answer.

By the Central Limit Theorem, it is the same as the mean of the population. So the expected value of the sample mean weight is 20.4 pounds.

b. What is the standard deviation of the sample mean weight? Give your answer to four decimal places.

By the Central Limit Theorem, that is:

$s = \frac{\sigma}{\sqrt{n}} = \frac{1.23}{\sqrt{100}} = 0.123$

The standard deviation of the sample mean weight is 0.123.

c. What is the approximate probability the sample mean weight will be less than 20.27?

This is the pvalue of Z when $X = 20.27$ .

Since we are working with the sample mean, we use $s$ instead of $\sigma$ in the Z score formula

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

$Z = \frac{20.27 - 20.4}{0.123}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446.

This means that there is a 14.46% probability the sample mean weight will be less than 20.27.

d. What is the value c such that the approximate probability the sample mean will be less than c is 0.96?

This is the value of $X = c$ that is in the 96th percentile, that is, it's Z score has a pvalue 0.96.

So we use $Z = 1.75$

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

$1.75 = \frac{c - 20.4}{0.123}$

$c - 20.4 = 0.123*1.75$

$c = 20.6153$

This value is $c = 20.6153$ .

6 0

2 years ago

Two mechanics worked on a car. The first mechanic worked for 5

ArbitrLikvidat [17]

<u>Answer:</u>

$50 and $115

<u>Step-by-step explanation:</u>

We know that,

the sum of the two rates = $165 per hour

Let x and (165 - x) represent the $/hour of the 15hr and 5hr mechanics respectively.

Then combining their charges together to get:

$(x*15)hour+(165-x)*5 hour=1325$

Solving for x to get:

$15x-5x+825=1325$

$10x=500$

$x=50$

So the rate charged per hour by one mechanic is $50 and for the other mechanic = $(165-50)=$ $115.

8 0

3 years ago