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3 years ago

The diameter of a dinner plate is 13 inches. What is the approximate area of the plate to

Mathematics

1 answer:

allsm [11]3 years ago

7 0

Step-by-step explanation:

The formula for the area of a circle is pi x radius squared. So since we know the diameter we can take that and half it giving us radius. Than we plug radius in the formula, so 6.5 squared is 42.25. You than multiply it by pi, and not 3.14 because theirs a possibility of being a couple units off when rounding, and after multiplying it you'll be left with the answer of 132.73

Answer: 132.73

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Which statements are true for the functions g(x) = x^2 and h(x) =-x^2? Check all that apply

Sloan [31]

Answer:

h(x) is the NEGATIVE of g(x)

Step-by-step explanation:

Where are the statements? Please share them next time.

h(x) is the NEGATIVE of g(x): h(x) = -x^2 = -g(x)

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3 years ago

Angle b and Angle g are known as alternate ___________ angles.

Afina-wow [57]

Alternate exterior angles because the are OUTSIDE of the parallel lines

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3 years ago

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Solve the system by substitution. y=−3x-2 -7x+3y=10 PLEASE HELP

enyata [817]

Y=-3x-2
subsitute -3x-2 for y
-7x+3(-3x-2)=10
distribute
a(b+c)=ab+ac
3(-3x-2)=-9x-6

-7x-9x-6=10
add like terms
-16x-6=10
add 6
-16x=16
multiply -1
16x=-16
divide 16
x=-1

subsitute
y=-3x-2
y=-3(-1)-2
y=3-2
y=1

x=-1
y=1

(x,y)
(-1,1)

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3 years ago

Time spent using e-mail per session is normally distributed, with mu equals 11 minutes and sigma equals 3 minutes. Assume that

liq [111]

Answer:

a) 0.259

b) 0.297

c) 0.497

Step-by-step explanation:

To solve this problem, it is important to know 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:

$\mu = 11, \sigma = 3$

a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 25, s = \frac{3}{\sqrt{25}} = 0.6$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

$Z = \frac{11.2 - 11}{0.6}$

$Z = 0.33$

$Z = 0.33$ has a pvalue of 0.6293.

X = 10.8

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

$Z = \frac{10.8 - 11}{0.6}$

$Z = -0.33$

$Z = -0.33$ has a pvalue of 0.3707.

0.6293 - 0.3707 = 0.2586

0.259 probability, rounded to three decimal places.

b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.5 and 11 minutes?

Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So

X = 11

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

$Z = \frac{11 - 11}{0.6}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5.

X = 10.5

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

$Z = \frac{10.5 - 11}{0.6}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033.

0.5 - 0.2033 = 0.2967

0.297, rounded to three decimal places.

c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 100, s = \frac{3}{\sqrt{100}} = 0.3$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

$Z = \frac{11.2 - 11}{0.3}$

$Z = 0.67$

$Z = 0.67$ has a pvalue of 0.7486.

X = 10.8

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

$Z = \frac{10.8 - 11}{0.3}$

$Z = -0.67$

$Z = -0.67$ has a pvalue of 0.2514.

0.7486 - 0.2514 = 0.4972

0.497, rounded to three decimal places.

5 0

3 years ago

What is DA equal to? Brainiest if correct and please show your answer.

Naddik [55]

Answer:

<h2>DA is equal to 25 or BA</h2>

Step-by-step explanation:

ABC

ADC

Since we know that line CA is equal to line CA because of reflexive property
Angle BAC and DAC are equal because of definition of an angle bisector
Angle ABC and ADC are equal because of definition of an angle bisector
This will give us ASA, proving to us that all sides and angles are congruent (this was already given to us)
So, if BA is 25, and we know that BA is congruent to DA, this tells us that DA is 25

5 0

1 year ago