The length of a rectangle is 4 inches less than twice its width. If the perimeter of the rectangle is 64 inches, what are the dimensions of the rectangle?

Show work please

Answer:

The p-value of the test is 0.4966 > 0.05, which means that we cannot conclude, at the 0.05 level of significance, that there is a difference.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

To US and Canada:

37 overweight out of 256. So

[tex]p_1 = \frac{37}{256} = 0.1445, s_1 = \sqrt{\frac{0.1445*0.8555}{256}} = 0.022[/tex]

Europe:

41 overweight out of 246. So

[tex]p_2 = \frac{41}{246} = 0.1667, s_2 = \sqrt{\frac{0.1667*0.8333}{246}} = 0.0238[/tex]

Test if there is a difference between the proportion of all items on English Air flights to the U.S. and Canada which are overweight (p1) and the proportion of all items on English Air flights within Europe which are overweight (p2):

At the null hypothesis, we test if there is no difference, that is, if the subtraction of the proportions is 0.

[tex]H_0: p_1 - p_2 = 0[/tex]

At the alternate hypothesis, we test if there is difference, that is, if the subtraction of the null hypothesis is different of 0.

[tex]H_1: p_1 - p_2 \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]X = p_1 - p_2 = 0.1445 - 0.1667 = -0.0222[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.022^2 + 0.0238^2} = 0.0324[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.0222 - 0}{0.0324}[/tex]

[tex]z = -0.68[/tex]

P-value of the test:

The p-value of the test is the probability of the sample proportion differing from 0 by at least 0.0222, which is P(|z| > 0.68), which is 2 multiplied by the p-value of z = -0.68.

Looking at the z-table, z = -0.68 has a p-value of 0.2483

0.2483*2 = 0.4966

The p-value of the test is 0.4966 > 0.05, which means that we cannot conclude, at the 0.05 level of significance, that there is a difference.

Answer:

%37.5

Step-by-step explanation:

9514 1404 393

Answer:

  (b)  -30x²√(2x)

Step-by-step explanation:

Squares can be removed from under the radical.

Answer:

The answer is b on edg

Step-by-step explanation:

Just took the assignment

Answer:

Below - 13

Above 35

Step-by-step explanation:

Given the 5 number summary :

1, 5, 11, 17, 20

Minimum = 1

Q1 = 5

Q2 = 11

Q3 = 17

Maximum = 20

Lower Outlier = Q1 - 1.5*IQR

Upper Outlier = Q3 + 1.5*IQR

IQR = Q3 - Q1 = 17 - 5 = 12

LOWER = 5 - (1.5 * 12) = 5 - 18 = - 13

UPPER = 17 + (1.5 * 12) = 17 + 18= 35

Answer:

respuesta 0.2

Step-by-step explanation:

espero que te sirvan ( ꈍᴗꈍ)

Answer:

a

Step-by-step explanation:

Your answer should be 27 square units

Answer: 54

Step-by-step explanation:

Answer:

9y+7=2y+98

5y=91

y=91\5

Answer:

That would be E. trapezoid

Step-by-step explanation:

Answer:

E is the answer thank me later

Answer:

x = sqrt(17)

Step-by-step explanation:

Angle B is 90 degrees; the line BC is a radius of circle C and line AB is a tangent line of BC. Since they must be perpendicular, angle B is 90 degrees.

Now use the pythagorean theorem to solve for x.

c=9, a = 8, b= x

a^2+b^2=c^2

8^2+x^2=9^2

x=sqrt(81-64)

x=sqrt(17)

Answer:

a (a - b)

Step-by-step explanation:

[tex]2a^{2}-3ab+b^{2} from 3a^{2} + 2ab - b^{2}[/tex]

Now, as [tex]2a^{2}-3ab+b^{2}[/tex] is from [tex]3a^{2} + 2ab - b^{2}[/tex]

so it will be subtracted :

[tex]3a^{2} + 2ab - b^{2}[/tex] [tex]-2a^{2}-3ab+b^{2}[/tex]

= [tex]a^{2} - ab[/tex]

= a (a - b)

Answer:

B) 119.1

Step-by-step explanation:

First, find your circle area

[tex]A=\pi r^{2} \\A=\pi 7^{2} \\A=153.9[/tex]

Then get the area of the square, we will worry about the tringles on each side in the last step.

l=12

w= 14 (Radius of circle times 2)

A=wl

A=14*12

A=168

Now the triangle

h=14 (Radius of circle times 2)

b=(27 - 12) / 2 = 7.5 ( total length 27 minus 12 divided, by 2 since there's 2 triangles on each side.

[tex]A=h\frac{b}{2} \\A=14\frac{7.5}{2} \\A=52.5[/tex]

Now add 2 triangles, the square and substract the circle

52.5+52.5+168 = 273

273 - 153.9 = 119.1 in^2

Answer:

35

Step-by-step explanation:

Here we see 5 black keys for every 7 white keys.

So the ratio is 5:7

If we need 49 white keys, find the amount we scale the original ratio by:

    49/7 = 7

So we are scaling by a factor of 7.

The number of black keys would be 5 * the scale of 7. = 35

So there should be 35 black keys.

Using proportions, it is found that 35 black keys appear on a portable keyboard with 49 white keys.

The rule of three is:

7 white keys - 5 black keys

49 white keys - x black keys

Applying cross multiplication:

[tex]7x = 49 \times 5[/tex]

Simplifying both sides by 7:

[tex]x = 7 \times 5 = 35[/tex]

Hence, 35 black keys will appear.

A similar problem, also involving proportions, is given at https://brainly.com/question/24372153

Answer:

C. ASA Similarity

Step-by-step explanation:

Using the Angle-Side-Angle Similarity Theorem is the only thing we can do because looking above we see that we know two angles and one side. Hence, this can be the only theorem that is fit for these two triangles.

Answer:

the closest answer is the last option, so I would say that is the correct one.

Step-by-step explanation:

4.5 x 4.5 x π =

20.25 x π =

63.6172....

Answer:

D

hope this helps

have a good day :)

Step-by-step explanation:

m > 10.33 hope this helps

Answer:

3/20

1/5

Step-by-step explanation:

Sample space :

10 - faced die :

(1, 2, 3, 4,5, 6, 7,8, 9, 10)

Coin = (H, T)

P(H) = 1/2

Multiple of 3 = 3, 6, 9 = 3

P(Multiple of 3) = 3 / 10

P(H and multiple of 3) = 1/2 * 3/10 = 3 /20

2.)

P(tail) = 1/2

Prime numbers = (2, 3, 5, 7) = 4

P(A prime number) = 4 / 10

P(tail and prime number) = 1/2 * 4 /10 = 4 /20 = 1/5

Answer:

A, Reflection across the y-axis and translation 3 units down

Answer:

A reflection across the y-axis and translation 3 units down

Step-by-step explanation:

Answer:

no. of packs in one box = 18

no. of boxes = 7

total no. of packs of socks = 18*7

=126

Answer:

126 packs

Step-by-step explanation:

1 box = 18 packs

7 boxes = ? packs

7 * 18 = 126 packs

Answer:

2^5

Step-by-step explanation:

1^10 = 1 (1*1*1*1*1....)

5^2 = 25 (5*5)

2^5 = 32 (2*2*2*2*2)

3^3 = 27 (3*3*3)

Answer:

430ml

Step-by-step explanation:

there are 1000ml in 1L so take 0.43 times with 1000 to find the answer

Answer:

x=8,y=-2/3

Step-by-step explanation:

make x the subject of formula

x=7+3y

substitute into the first equation

4(7+3y)+3y=18

28+12y+3y=18

28+15y=18

15y=18-28

15y=-10

y=-10/15=-2/3

since y=-2/3, substitute y into x=7+3y

x=7+3(-2/3)

x=7-2

x=5

Answer:

a) 3, 2, 0, -1

b) 7, 1, -9, -10

c) 6, 2, -1, -3, -12

d) 8, 2, 0, -2, -4

Answer:

C

Step-by-step explanation:

This is the answer because you have to use the formula of volume

which is L x W x H then you get your answer

Answer:

Choose 1 answer: Multiply/divide both sides by the same non-zero constant. Multiply/divide both sides by the same variable expression.

Step-by-step explanation:

Answer:

Multiply/divide both sides by the same non-zero constant

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

100 - 3.1 = 96.9

142000 - 96.9 = 1410903.1