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OverLord2011 [107]
3 years ago
9

The perimeter of the rectangle below is 72 units. Find the value of y

Mathematics
1 answer:
ss7ja [257]3 years ago
6 0

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

2(3y+2)+2(4y-1) = 72\\6y+4+8y-2=72\\14y+2=72\\14y=70\\y=5

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The mean annual income for people in a certain city is 37 thousand dollars, with a standard deviation of 28 thousand dollars. A
Aloiza [94]

Answer:

P( 31 < \bar X< 41)

And we can ue the z score formula given by:

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

And using this formula we got for the limits:

z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515

z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01

So we want to find this probability:

P(-1.515

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".  

Solution to the problem

Let X the random variable that represent the annual income of a population, and for this case we know the following info:

\mu=37 and \sigma=28  and we are omitting the zeros from the thousand to simplify calculations

We select a sample size of n=50>30.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

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

And we want to find this probability:

P( 31 < \bar X< 41)

And we can ue the z score formula given by:

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

And using this formula we got for the limits:

z = \frac{31-37}{\frac{28}{\sqrt{50}}}= -1.515

z = \frac{41-37}{\frac{28}{\sqrt{50}}}= 1.01

So we want to find this probability:

P(-1.515

4 0
3 years ago
HELPPP Provide the missing statements and reasons for the following proof:
agasfer [191]

The missing statements and reasons in the proof showing that ∠1 is supplementary to ∠2 are:

S2: ∠2 ≅ ∠3

R2: corresponding angles

S3: m∠2 ≅ m∠3

R3: Definition of congruent angles

R5: Definition of supplementary angles

S7: m∠1 + m∠2 = 180°

S8: ∠1 is supplementary to ∠2

Given the proof to show that ∠1 is supplementary to ∠2, thus:

Since lines m and n are parallel to each other,

∠2 and ∠3 are corresponding angles, so, ∠2 ≅ ∠3 based on the corresponding angles theorem.

Since ∠1 and ∠3 form a linear pair, they are supplementary to each other.

By substitution, we would have m∠1 + m∠2 = 180°.

Therefore, we can conclude that ∠1 is supplementary to ∠2.

In summary, the missing statements and reasons in the proof showing that ∠1 is supplementary to ∠2 are:

S2: ∠2 ≅ ∠3

R2: corresponding angles

S3: m∠2 ≅ m∠3

R3: Definition of congruent angles

R5: Definition of supplementary angles

S7: m∠1 + m∠2 = 180°

S8: ∠1 is supplementary to ∠2

Learn more about supplementary angles on:

brainly.com/question/12919120

5 0
2 years ago
Doug makes a parallelogram-shape sign for his shop.
suter [353]
It is the area of two triangle and one rectangle
area of a triangle is 1/*b*h
A=1/2*1.9*2.8=2.66 ft^2 multiply it by 2 as we have 2 triangle= 5.32 ft^2

Area of a rectangle=w*l=3.2*2.8 =8.96 ft^2
Add them =8.96+5.32=14.28ft^2

4 0
3 years ago
Read 2 more answers
If jimmy has 15 cookies and has 3 friends and wants to share how will he do it
8090 [49]

Answer:

If he includes himself then:

Split up the cookies into 4 equal parts.

\frac{15}{4}  = 3.75

3.75 cookies each if he includes himself.

If he does not include himself:

Split up the cookies into 3 equal parts

\frac{15}{3}  = 5

5 cookies each if he shares to his friends without including himself.

3 0
3 years ago
Which of the following statements
irga5000 [103]

Answer:

tqweryetqwewrqfvwrq

Step-by-step explanation:

5 0
3 years ago
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