I need help with all 4 questions plz

Answer:

The 90% confidence interval for the difference of the population means is approximately (-17.98, -2.02).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

Boys:

Mean of 75, sample of 45, standard deviation of 25.

This means that [tex]\mu_B = 75, s_B = \frac{25}{\sqrt{45}}[/tex]

Girls:

Mean of 85, sample of 30, standard deviation of 17.

This means that [tex]\mu_G = 85, s_G = \frac{17}{\sqrt{30}}[/tex]

Distribution of the difference of mean grades of boys and girls:

[tex]\mu = \mu_B - \mu_G = 75 - 85 = -10[/tex]

[tex]s = \sqrt{s_B^2+s_G^2} = \sqrt{(\frac{25}{\sqrt{45}})^2+(\frac{17}{\sqrt{30}})^2} = 4.85[/tex]

Confidence interval:

As stated, the critical value is [tex]z = 1.645[/tex]

The margin of error is of:

[tex]M = zs = 1.645*4.85 = 7.98[/tex]

Lower bound:

[tex]\mu - M = -10 - 7.98 = -17.98[/tex]

Upper bound:

[tex]\mu + M = -10 + 7.98 = -2.02[/tex]

The 90% confidence interval for the difference of the population means is approximately (-17.98, -2.02).

Answer:

Step-by-step explanation:

Given:

The dimensions of the box are (w+5) inches, (w+4) inches, (2w) inches.

To find:

The expression that describes the volume of the box.

Solution:

We know that the volume of a rectangular prism is:

[tex]V=length\times breadth \times height[/tex]

Substituting the given values, we get

[tex]V=(w+5)\times (w+4) \times 2w[/tex]

[tex]V=(w^2+5w+4w+20)2w[/tex]

[tex]V=(w^2+9w+20)2w[/tex]

Using distribution property, we get

[tex]V=(w^2)2w+(9w)2w+(20)2w[/tex]

[tex]V=2w^3+18w^2+40w[/tex]

Therefore, the volume of the box is [tex]2w^3+18w^2+40w[/tex] cubic inches.

Note: All the options are incorrect.

Answer:

B

Step-by-step explanation:

The formula for the area of a triangle is given as:

A = ½*base*height

A = ½*b*h

A = (bh)2

If we know the area (A) and the base, to find the height, the following would be done:

Divide both sides by b

A/b = h/2

Multiply both sides by 2

[tex] \frac{A}{b} * 2 = h [/tex]

As we can see here, to find the base, we would divide the area by the vase, then multiply what we get by 2.

Answer:

[tex]x=12.07[/tex]

Step-by-step explanation:

From the question we are told that:

Mean [tex]\=x =12cm[/tex]

Standard deviation [tex]\sigma=0.04[/tex]

Significance level [tex]\alpha=5\%=0.05[/tex]

Therefore

Confidence level [tex]95\%=0.95[/tex]

From table [tex]P(z<1.645)=0.95[/tex]

Generally the equation for Z-score is mathematically given by

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]x=z\sigma+\mu[/tex]

[tex]x=1.645*0.04+12[/tex]

[tex]x=12.07[/tex]

Answer:

V=lwh /3

Step-by-step explanation:

Answer:

3 days

Step-by-step explanation:

well, in 2 days mitch can jar 12 liters of jam right? but 12 is divisible by 2. so let’s just do that to help us out later, 12 / 2 = 6

now that we have that, let’s make sure. in 1 day he can jar 6, in 2 he can jar 12.

that seems right! so now, can we add 6 to 12 to make 18? yep! how many more times do we need to add 6? 1 time. so 12 + 6 = 18. every 6 liters is 1 day. so 1 day + 1 day + 1 day (18 liters) is 3 days total!

hope this helped you!

Answer:

720

Step-by-step explanation:

I think you just have to do

6x8x3x5

Answer:

There's 3 questions which one do I answer?

Step-by-step explanation:

Answer:

Mean - 1.5

Median - 1.5

Step-by-step explanation:

Median = middle number

Means = all numbers added up and divided by how many are there

Answer:

15.25 km =15,250 m

so Jada ran further

Answer:

Jada ran farther

Step-by-step explanation:

First, convert 8,500 to kilometers.

8,500 ÷ 1,000 = 8.5

15.25 > 8.5

Have a wonderful day!

Answer:

2 solutions

-1 and 2

Step-by-step explanation:

Answer:

(-4,-4)

YW :))

Or you could of just looked it up cause thats what I did!!

Answer:

C. Associative property of multiplication

Step-by-step explanation:

The associative property of multiplication states that the way in which factors are grouped in a multiplication problem does not change the product.

Answer:

228525-Look below for steps:)

Step-by-step explanation:

Step 1:

6925

*   33

______

Step 2:

5*3=15

carry the one

3*2+1=7

9*3=27

carry the 2

6*3+2=20

SO your first number is 20775 but we are NOT done yet!

add a zero below 5

5*3=15

carry the one

3*2+1=7

9*3=27 carry the 2

then 6*3+2=20

then add 207750+20775

which equals....

228525

so 228525 is your answer!!!

I really do hope this made sense!

Have a great day!

- Hailey: D

(NOTHING IS COPIED AND PASTED!!!!!)

Answer:

85

Step-by-step explanation:

Answer:

Step-by-step explanation:

A hypotenuse is calculated on a triangle with a right angle. The hypotenuse is the side opposite the sides with the right angle. The equation is a^2 + b^2=c^2 where the hypotenuse is the square root of c.

Answer:

For this process, the capability index is 0.4444

Step-by-step explanation:

Given the data in the question;

Lower specification limit = 22.8 mm

Upper specification limit = 23.2 mm

The standard deviation σ = 0.15 mm

Mean μ = 23

capability index Cpk = ?

Now, Using the formula;

Cpk = min{ [(USL - μ)/3σ], [(μ - LSL)/3σ]

where USL is the Upper specification limit, LSL is the Lower specification limit, σ is the standard deviation, μ is the mean

so we substitute

Cpk = min{ [(23.2 - 23 )/(3×0.15)], [(23 - 22.8)/(3×0.15)] }

Cpk = min{ [0.2 / 0.45 ], [0.2 / 0.45] }

Cpk = min{ [ 0.4444 ], [0.4444] }

Therefore, for this process, the capability index is 0.4444

Answer:

there is no profit there is loss because CP is greater than SP

Step-by-step explanation:

loss=CP-SP

=Rs480-Rs420

=Rs60

loss%=loss/cp*100%

=60/480*100%

=6000/480

=12.5%

Step-by-step explanation:

1. E

2. G

3. I

4. J

5. H

6. F

7. A

8. D

9. B

10. C

Answer:

yes

Step-by-step explanation:

because in order to create a right triangle all of its sides must be different

Answer:

Yes

Step-by-step explanation:

Using the Pathagerum theorm (C**2 = A**2 + B**2)

The hypotinuse as always the longest side except for an equal lateral triangle. So if it is a right angle triagle so if true then,

13**2 =  5**2 + 12**2

169 = 25 + 144

169 = 169

so it is true (YES).

Answer:

tanx=b/c

sinx=b/a

cosx=c/a

Step-by-step explanation:

Answer:

REVENGE

Step-by-step explanation:

Answer:

2v + 5u

Step-by-step explanation:

9514 1404 393

Answer:

  A) a + s = 297

  B) 30a +20s = 6050

  C) 286 students

  D) 11 adults

Step-by-step explanation:

A) Total people is the sum of the numbers of adults and students:

  a + s = 297

__

B) Total revenue is the sum of revenue from each class of attendees:

  30a +20s = 6050

The solution is ...

  30a + 20(297 -a) = 6050 . . . there were 297-a students

  10a = 110 . . . . . . . . . . . . . . . . subtract 5940

  a = 11

  s = 297 -11 = 286

__

C) 286 students attended.

__

D) 11 adults attended.

addtion

becuase when you add the number of boys and girls together you get  the overall number of the class.

Answer: properties would be multiplication and the answer would be 40%

Step-by-step explanation: You can use cross multiplication to identify the answer to this.

She will need 6 yards. the permiter is 16 which 5 wouldnt be enough