3 Aaron has a pencil that is
foot long. He has a pen that
is 0.7 foot long. Measured
in
feet, how much longer is Aaron's
pencil than the pen?

Answer:

The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).

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

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

Subtraction of normal variables:

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

A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N.

This means that [tex]\mu_1 = 6.1, s_1 = \frac{0.7}{\sqrt{125}} = 0.0626[/tex]

In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N.

This means that [tex]\mu_2 = 5.8, s_2 = \frac{1}{\sqrt{75}} = 0.1155[/tex]

Distribution of the difference:

[tex]\mu = \mu_1 - \mu_2 = 6.1 - 5.8 = 0.3[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0626^2+0.1155^2} = 0.1314[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = zs[/tex]

[tex]M = 1.645*0.1314 = 0.22[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 0.3 - 0.22 = 0.08N

The upper end of the interval is the sample mean added to M. So it is 0.3 + 0.22 = 0.52N

The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).

[tex](1 + \sqrt{2^{4} }) = 5[/tex]

[tex](1 - \sqrt{2^{4} } ) = - 3[/tex]5--3=8

Answer:

63

Step-by-step explanation:

Mode is the number that is repeated the most, in this case its 63

Answer:

24

Step-by-step explanation:

i did it

9514 1404 393

Answer:

  y = 11.2 in

Step-by-step explanation:

The product of segment lengths to the near and far intersection points of the secant with the circle are the same for all secants from the same external point. Here, there are three, so we have the relations ...

  9×9 = 5(5+y) = x(x+19)

Then the value of y can be found as ...

  81/5 = 5+y

  16.2 -5 = y = 11.2

__

The value of x is a little trickier, as a quadratic is involved.

  81 = x² +19x

  81 + 90.25 = x² +19x +90.25 . . . . complete the square

  171.25 = (x +9.5)²

  x = √171.25 - 9.5 ≈ 3.58625...

__

Additional comment

For the purpose here, the tangent can be considered to be a degenerate case of a secant in which the two points of intersection with the circle are the same point. For the purpose of this calculation, the length of the tangent is squared. (The distance to the points of intersection is the same.)

I find it easier to remember one rule, rather than a separate rule for tangents. With some imagination, the same rule can be applied when the "secants" meet inside the circle. In that case, they are called "chords".

We have shown the value for x because we suspect some versions of this question may ask for x instead of y. (Rounding may be required in that case.)

Answer:

[tex]A=\frac{215*x}{2}-x^2)[/tex]

Step-by-step explanation:

From the question we are told that:

Total length of building side [tex]x=25feet[/tex]

Perimeter of  fence in [tex]P=190feet[/tex]

Generally the perimeter of the display area is given as mathematically given by

[tex]2L+2B=P+x\\2L+2B=190+25[/tex]

Therefore

[tex]2L+2B=215[/tex]

[tex]L+B=\frac{215}{2}[/tex]

[tex]B=\frac{215}{2}-L[/tex]

Generally the Area of the display area A is given as mathematically given by

[tex]Area A=L*B[/tex]

[tex]Area A=L*(\frac{215}{2}-L)[/tex]

[tex]Area A=\frac{215*L}{2}-L^2)[/tex]

Length L in terms of x

[tex]Area A=\frac{215*x}{2}-x^2)[/tex]

Answer:

456.9

Step-by-step explanation:

Answer:

182

Step-by-step explanation:

Add 178 + 209 + 159 = 546

Then divide 546 by 3 = 182

Answer:

Sorry for the wait.

Step-by-step explanation:

5. the two bottom angles are the same btw

[tex]2x+2x+x-15=180\\5x-15=180\\5x-15+15=180+15\\5x=195\\5x/5=195/5\\x=39[/tex]

6. straight lines are 180

[tex]3x+17+x-9=180\\4x+8=180\\4x+8-8=180-8\\4x=172\\4x/4=172/4\\x=43[/tex]

7. another 180

[tex]2x-4+3x+5+2x+11=180\\7x-10=180\\7x-10+10=180+10\\7x=190\\7x/7=190/7\\x=27.14\\[/tex]

8. 90 degree angle

[tex]x+x+4+3x-9=90\\5x-5=90\\5x-5+5=90+5\\5x=95\\5x/5=95/5\\x=19[/tex]

Answer:

a

Step-by-step explanation:

Answer:

Hi how are you doing today Jasmine

Answer: 7/17

add all the marbles to get the total

6 + 7 + 4 = 17

there are 7 blue marbles so

7/17

Answer:

A

Step-by-step explanation:

How you find x is you do 27-8. You get 19. If you do 19+8 and think of 19 as x, you get 27. This is why A is correct

Answer:

Step-by-step explanation:

Answer:

40.4

Step-by-step explanation:

Use the formula if you have one, (AS = 2Ab (a+b+c)h)

Then apply.

Answer:

D

Step-by-step explanation:

The other graphs are functions.

Graph A is a linear function, and C is an Absolute Value Function.

Graph B also seems to be a function.

However- I can only narrow it down to B or C.  I apologize if my answer is not correct.

Answer:144

Step-by-step explanation:

Use a calculator

or 1/2 x 288 =  288/2 = 144

Answer: 144

Step-by-step explanation:

I'm assuming that the "x" in this statement is a multiplication symbol.

Multiplying any number by 1/2 or 0.5 is the same thing as dividing it by 2.

Therfore the answer is 288/2 which is 144.

Answer:

4/5 is the slope

Answer:

(-5,-4) or (-4, -5)

Step-by-step explanation:

Answer:

[tex]1 \to 22 \to 0.176[/tex]

[tex]2 \to 13 \to 0.104[/tex]

[tex]3 \to 18 \to 0.144[/tex]

[tex]4 \to 29 \to 0.232[/tex]

[tex]5 \to 37 \to 0.296[/tex]

[tex]6 \to 6 \to 0.048[/tex]

Step-by-step explanation:

Given

[tex]n = 125[/tex]

See attachment for proper table

Required

Complete the table

Experimental probability is calculated as:

[tex]Pr = \frac{Frequency}{n}[/tex]

We use the above formula when the frequency is known.

For result of roll 2, 4 and 6

The frequencies are 13, 29 and 6, respectively

So, we have:

[tex]Pr(2) = \frac{13}{125} = 0.104[/tex]

[tex]Pr(4) = \frac{29}{125} = 0.232[/tex]

[tex]Pr(6) = \frac{6}{125} = 0.048[/tex]

When the frequency is to be calculated, we use:

[tex]Pr = \frac{Frequency}{n}[/tex]

[tex]Frequency = n * Pr[/tex]

For result of roll 3 and 5

The probabilities are 0.144 and 0.296, respectively

So, we have:

[tex]Frequency(3) = 125 * 0.144 = 18[/tex]

[tex]Frequency(5) = 125 * 0.296 = 37[/tex]

For roll of 1 where the frequency and the probability are not known, we use:

[tex]Total \ Frequency = 125[/tex]

So:

Frequency(1) added to others must equal 125

This gives:

[tex]Frequency(1) + 13 + 18 + 29 + 37 + 6 = 125[/tex]

[tex]Frequency(1) + 103 = 125[/tex]

Collect like terms

[tex]Frequency(1) =- 103 + 125[/tex]

[tex]Frequency(1) =22[/tex]

The probability is then calculated as:

[tex]Pr(1) = \frac{22}{125}[/tex]

[tex]Pr(1) = 0.176[/tex]

So, the complete table is:

[tex]1 \to 22 \to 0.176[/tex]

[tex]2 \to 13 \to 0.104[/tex]

[tex]3 \to 18 \to 0.144[/tex]

[tex]4 \to 29 \to 0.232[/tex]

[tex]5 \to 37 \to 0.296[/tex]

[tex]6 \to 6 \to 0.048[/tex]

Answer:

200

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

Answer:

you need more information to answer this, it's either 84 or 56 since it's in acute angle. looks closer to 84

Answer:

11,143.3

Step-by-step explanation:

Density measures the number of people per unit area

Density = population / area

1,579,000 / 141.7  = 11,143.30

Answer:

Summary. The Addition Property states that: a=bis equivalent toa+c=b+cora−c=b−c Basically, whatever you do to one side of the equal sign, you have to do to the other side.

Hope this helps!!! :)

Answer:

3

Step-by-step explanation:

You can put 3 in 9 three times

Answer:

Step-by-step explanation:

==

Answer:

I think it's 64 in

I hope it's helps you

Answer:

tan theta = 8/15

Step-by-step explanation:

Sin is equal to opposite over hypotenuse. So it means that the side opposite from theta is 8, and the hypotenuse is 17.

To find the value of the adjacent side from theta, use the Pythagorean Theorem.

a^2 + b^2 = c^2

8^2 + b^2 = 17^2

64 + b^2 = 289

Subtract 64.

b^2 = 225

Take the square root.

b = 15.

So that means:

the side opposite from theta is 8,

the side adjacent from theta is 15,

the hypotenuse is 17.

Now we take tan, opposite over adjacent, and use the values from the triangle.

tan = opposite / adjacent

tan = 8/15.

Answer:

Step-by-step explanation:

When you are taking off percentages from numbers, you first want to make the percent a number. This step is super simple. Just divide the 18 by 100

This gets you 0.18

Now multiply

84 * 0.18 = 15.12

So 15.12 is the discount

Then take 84 and subtract 15.12

84 - 15.12 = 68.88

So 68.88 is the sell price

Answer:

n/4-6

Step-by-step explanation:

n/4-6

This is the expression because we need to divide n by 4 and subtract 6

The number is 68

68 divided by 4= 17

17-6=11