Sam can wash 2 1/7 loads of laundry in 3/5 of an hour. How many loads of

What is the perimeter of a square with sides that measure 2x + 3 units?

PtichkaEL [24]

Answer:

8x+12

Step-by-step explanation:

We know that squares have equal sides. To calculate perimeter, just add up all of the 4 sides.

2x+3+2x+3+2x=3+2x+3

Add like terms:

8x+12

You could also multiply by four:

4(2x+3)

Use distributive property:

8x+12

8 0

3 years ago

A recent survey describes the total sleep time per night among college students as approximately Normally distributed with mean

marin [14]

Answer:

a) $\sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981$

b) We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

c) $z = \frac{6.9-6.72}{0.0981}= 1.835$

And we can use the z normal table or excel and we got:

$P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent the total sleep time of a population, and for this case we know the distribution for X is given by:

$X \sim N(6.72,1.26)$

Where $\mu=6.72$ and $\sigma=1.26$

(a) What is the standard deviation for the average time in hours? (Round your answer to four decimal places.)

For this case the sample mean have the following distirbution

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the deviation is given by:

$\sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981$

in minutes?= (Round your answer to three decimal places.)

(b) Use the 95 part of the 68–95–99.7 rule to describe the variability of this sample mean. (Round your answer to four decimal places.)

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

(c) What is the probability that your average will be below 6.9 hours? (Round your answer to four decimal places.)

For this case we can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And we can find the z score for 6.9 and we got:

$z = \frac{6.9-6.72}{0.0981}= 1.835$

And we can use the z normal table or excel and we got:

$P(Z$

4 0

3 years ago

FUNCTION OR NOT /// ALGEBRA I

guapka [62]

Answer:

First figure: The graph is not a function

Second figure:

Statement 1: It is false

Statement 2: It is false

Statement 3: It is right

Step-by-step explanation:

First graph is not a function.

The domain of it is ⇒ 0 ≤ x < 3 , 3 < x ≤ 6 , 6 ≤ x < 9

From the domain ⇒ x = 6 has two corresponding values of y⇒ 3 and 4

∴ It is not a function because every x must have one and only one

corresponding value of y

Second figure

{(3 , 6) , (4 , 6) , (5 , 7) , (6 , 8) , (7 , 10) , (8 , 10)}

Statement 1: It is false because we use x-value to check function or not.

The relation is a function because every x-value has one corresponding

y-value

Statement 2: It is false because 3 ≤ x ≤ 8 means we will use for x all real numbers from 3 to 8 not only the integers 3 , 4 , 5 , 6, ,7 , 8

The domain of this function is { 3 , 4 , 5 , 6 , 7 , 8 }

Statement 3: It is right because the range is the y-value and all the y-value in the function are 6 , 7 , 8 , 10

5 0

3 years ago

Which explanation shows why this is a parallelogram?

svetoff [14.1K]

Answer:

One pair of opposite sides are parallel and congruent

Step-by-step explanation:

As you can see, segment HE and GF are both marked as parallel and congruent

5 0

3 years ago

Masha is making a scale diagram of the front face of an aquarium. The face is shaped like a rectangle. She uses a scale of 1 cen

dangina [55]

14 feet because 5+5+2+2 equals 14

4 0

3 years ago