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3 years ago

5

Lia has $24. Lia and her brother together have a total of $45. The solution of the equation 24 + x = 45 is the amount of money,

x, that Lia's brother has. How much money does Lia's brother have?

2 answers:

sp2606 [1]3 years ago

8 0

Answer:

x=21

Step-by-step explanation:

45-24=21

Julli [10]3 years ago

6 0

Answer:

21$

Step-by-step explanation:

24+x=45

-24 -24

x=21$

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A circular tablecloth has a diameter of 70 inches. Max wants to add a decorative fabric around the edge of the tablecloth.Approx

JulijaS [17]

Answer:

219.8

Step-by-step explanation:

you multiply 70 and 3.14 and get 219.8

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2 years ago

Problem: The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72

Lisa [10]

Answer:

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

1) 0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2) 0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3) 0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4) 0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.

Step-by-step explanation:

To solve these questions, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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

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

The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches.

This means that $\mu = 38.72, \sigma = 3.17$

Sample of 10:

This means that $n = 10, s = \frac{3.17}{\sqrt{10}}$

Compute the probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

This is 1 subtracted by the p-value of Z when X = 40. So

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

By the Central Limit Theorem

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

$Z = \frac{40 - 38.72}{\frac{3.17}{\sqrt{10}}}$

$Z = 1.28$

$Z = 1.28$ has a p-value of 0.8997

1 - 0.8997 = 0.1003

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

$\mu = 266, \sigma = 16$

1. What is the probability a randomly selected pregnancy lasts less than 260 days?

This is the p-value of Z when X = 260. So

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

$Z = \frac{260 - 266}{16}$

$Z = -0.375$

$Z = -0.375$ has a p-value of 0.3539.

0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less?

Now $n = 20$ , so:

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

$Z = \frac{260 - 266}{\frac{16}{\sqrt{20}}}$

$Z = -1.68$

$Z = -1.68$ has a p-value of 0.0465.

0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less?

Now $n = 50$ , so:

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

$Z = \frac{260 - 266}{\frac{16}{\sqrt{50}}}$

$Z = -2.65$

$Z = -2.65$ has a p-value of 0.0040.

0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?

Sample of size 15 means that $n = 15$ . This probability is the p-value of Z when X = 276 subtracted by the p-value of Z when X = 256.

X = 276

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

$Z = \frac{276 - 266}{\frac{16}{\sqrt{15}}}$

$Z = 2.42$

$Z = 2.42$ has a p-value of 0.9922.

X = 256

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

$Z = \frac{256 - 266}{\frac{16}{\sqrt{15}}}$

$Z = -2.42$

$Z = -2.42$ has a p-value of 0.0078.

0.9922 - 0.0078 = 0.9844

0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.

8 0

3 years ago

Triangle ABC has been rotated 90° to create triangle DEF. Write the equation, in slope-intercept form, of the side of triangle A

Ket [755]

the equation in the slope-intercept of the side of triangle ABC that is perpendicular to segment EF is y = x + 1

<h3>How to determine the equation</h3>

From the figure given, we can deduce the coordinates of the sides

For A

A ( 4,2)

For B

B ( 4, 5)

C ( 1, 2)

D ( 2, -4 )

E ( 5, -4)

F ( 2, -1)

The slope for BC

Slope = $\frac{y2 - y1}{x2 - x1}$

Substitute the values for both B and C coordinates, we have

Slope = $\frac{2- 5}{1 - 4}$

Find the difference for both the numerator and denominator

Slope = $\frac{-3}{-3}$

Slope = 1

We have the rotation for both point ( 0, 1)

y - y1 = m ( x - x1)

The values for y1 and x1 are 1 and 0 respectively and the slope m is 1

Substitute the values

y - 1 = 1 ( x - 0)

y - 1 = x

Make 'y' the subject of formula

y = x + 1

Thus, the equation in the slope-intercept of the side of triangle ABC that is perpendicular to segment EF is y = x + 1

Learn more about linear graphs here:

brainly.com/question/4074386

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4 0

2 years ago

The diameters of ball bearings are distributed normally. The mean diameter is 87 millimeters and the standard deviation is 6 mil

devlian [24]

Answer:

69.14% probability that the diameter of a selected bearing is greater than 84 millimeters

Step-by-step explanation:

According to the Question,

Given That, The diameters of ball bearings are distributed normally. The mean diameter is 87 millimeters and the standard deviation is 6 millimeters. Find the probability that the diameter of a selected bearing is greater than 84 millimeters.

In a set with mean and standard deviation, the Z score of a measure X is given by Z = (X-μ)/σ

we have μ=87 , σ=6 & X=84

Find the probability that the diameter of a selected bearing is greater than 84 millimeters

This is 1 subtracted by the p-value of Z when X = 84.

So, Z = (84-87)/6

Z = -3/6

Z = -0.5 has a p-value of 0.30854.

⇒1 - 0.30854 = 0.69146

0.69146 = 69.14% probability that the diameter of a selected bearing is greater than 84 millimeters.

Note- (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 p-value, we get the probability that the value of the measure is greater than X)

7 0

3 years ago

I need help with question 18 PLS!!!!

dolphi86 [110]

Answer:

162

Step-by-step explanation:

( -a ) ( b ) ( -a + b )

-6 ( 3 ) ( -6 + -3 )

-6 ( 3 ) ( -9 )

- 18 ( -9 )

162

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3 years ago