An Izod impact test was performed on 20 specimens of PVC pipe. The sample mean is and the sample standard deviation is s = 0.22. Find a 99% lower confidence bound on the true Izod impact strength. Assume the data are normally distributed.

Answer:

C) The mean is 22 and the standard deviation is 100.

Step-by-step explanation:

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 expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

If [tex] X\ sim N(\mu_x =5, \sigma_x =25)[/tex]

And the random variable Y =2+4X.

If we are interested in find the mean and the standard deviation for this new variable we need to apply the concepts of expected value and Variance of random variables.

Using the concept of expected value we have:

[tex]E(Y) =E(2+4X) = E(2) +E(4X)= 2+ 4E(X) =2+4(5) =2+20=22[/tex]

So on this case the [tex]E(Y) =\mu_Y =22[/tex]

Using the concept of variance we have:

[tex]Var(Y)=Var(2+4x)=Var(2)+Var(4X)+2Cov(2,4X)[/tex]

But since 2 is a constant we don't have variance for this and the [tex]Cov(2,4x)=0[/tex] because the covariance of a random variable with a constant is zero. So applying these concepts we have:

[tex]Var(Y)= Var(4x)=4^2 Var (X)= 16 \sigma^2_x =16(25^2)=10000[/tex]

And then if we need the standard deviation we just need to take the square root:

[tex]sd(Y) = \sqrt{10000}=100[/tex]

So the best option for this case would be:

C) The mean is 22 and the standard deviation is 100.

Answer:

Option c) is correct.

Step-by-step explanation:

Given :

[tex]\mu_x = 5[/tex]  and  [tex]\sigma_x = 25[/tex]

Y = 2 + 4X

Calculation:

This problem can be solved by using concept of expected value and variance of random variables.

By expected value concept,

[tex]\rm E(Y) = E(2 + 4X)= E(2) + E(4X)= 2 + 4E(X)=2+4(5)=22[/tex]

Therefore, [tex]\mu_y = 22[/tex]

By variance concept,

[tex]\rm Var(Y)= Var(2+4X)=Var(2)+Var(4X)+2Cov(2,4X)[/tex]

[tex]\rm Cov(2,4X)=0[/tex]

Var(2) = 0

Therefore,

[tex]\rm Var(Y) = Var(4X)= 4^2Var(X)= 16\sigma_x^2=16(25^2)=10000[/tex]

Therefore,

Standard deviation(Y) = [tex]\sqrt{10000}[/tex] = 100

Hence, option c) is correct.

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Answer:

56 pentagon.

Step-by-step explanation:

Here is the complete question: Eight point lies on the circle. How many pentagons can you make using five points as vertices?

Given: Five points on vertices.

Using the combination formula to find the number of pentagon.

[tex]_{r}^{n}\textrm{C} = \frac{n!}{r!(n-r)!}[/tex]

⇒ [tex]_{8}^{5}\textrm{C}= \frac{8!}{5!(8-5)!}[/tex]

⇒[tex]_{8}^{5}\textrm{C}= \frac{8!}{5!\times 3!} \\\\_{8}^{5}\textrm{C} = \frac{8\times 7\times 6\times5\times4\times3\times2\times1}{5\times4\times3\times2\times1\times3\times2\times1} = \frac{336}{6}[/tex]

∴ [tex]_{8}^{5}\textrm{C}= 56[/tex]

∴ With eight point lies on circle, we can make 56 pentagons using five points as vertices

Answer:

4 out of 10 or 4/10 is my answer

Answer:

The fraction will be 4/10, or 2/5.

The percentage will be 40%.

Step-by-step explanation:

The fraction and percentage will be the number of black pens divided by the total number of pens.

We can find the total number of pens by adding all the pens in each color together.

2 + 4 + 3 + 1 = 10

The total number of pens is 10. The number of black pens is 4.

The fraction will be 4/10, or 2/5.

The percentage will be 40%.

I hope this helps. Happy studying. :)

Answer: the correct option is A

Step-by-step explanation:

We want to find 95% confidence interval for the mean of the weight of pretzels.

Number of samples. n = 15 bags

Mean, u = 10.2

Standard deviation, s = 0.25

We will use the t- test

Degree of freedom = n - 1 = 15 - 1= 14

Alpha, a = (1-confidence interval )/2

a = (1-0.95)/2 = 0.025

Looking at the t-distribution table, the corresponding z value is 2.131

Confidence interval = z × standard deviation/√n

Confidence interval = 2.131 × 0.25/√15

Confidence interval = 0.13755545851

Approximately 0.138

At 95% confidence interval,

The lower end is 10.2 - 0.138 = 10.062 Approximately 10.06

The upper end is 10.2 - 0.138 = 10.338. Approximately 10.34

Answer:

A) 4x - 2y + 3z = - 3

B) 2x - 3y + 2z = 1

C) 6x    + 10z = -2

Multiply A) by -1.5

A) -6x  +3y -4.5z = 4.5  Then adding to B)

B) 2x - 3y + 2z = 1

D) -4x -2.5z = 5.5  then we add this to C)

C) 6x + 10z = -2  Now we multiply D) by 1.5

D) -6x -3.75z = 8.25  Adding C) + D)

6.25z = 6.25

z = 1  Then putting z = 1 into A) and B)

A) 4x - 2y + 3 = - 3  equals A) 4x -2y = -6

B) 2x - 3y + 2 = 1  equals B) 2x -3y = -1 we divide A) by -2

A) -2x + y = 3  then adding to B

B) 2x - 3y  = -1

-2y  = 2

y = -1

FINALLY solving for x we'll use equation A)

A) 4x - 2*-1 + 3*1 = - 3

A) 4x +2 + 3 = -3

A) 4x = -8

x = -2

(Yes, it's just that easy. LOL)

Step-by-step explanation:

Answer:x+y=58

Step-by-step explanation:

Sum means addition

For this case we must write a quadratic equation of the form:

[tex]x ^ 2 + bx + c = 0[/tex]

We have two roots:

[tex]x_ {1} = - 7\\x_ {2} = 1[/tex]

Thus, we can rewrite the equation in a factored form as:

[tex](x + 7) (x-1) = 0[/tex]

If we apply distributive property we have:

[tex]x ^ 2-x + 7x-7 = 0[/tex]

Different signs are subtracted and the major sign is placed.

[tex]x ^ 2 + 6x-7 = 0[/tex]

Answer:

The quadratic equation is:

[tex]x ^ 2 + 6x-7 = 0[/tex]

Answer: Our required probability is 0.48.

Step-by-step explanation:

Since we have given that

Probability that days are cloudy in January = 51%

Probability that days are cloudy and foggy = 25%

So, we need to find the probability that a randomly selected day in January will be foggy if it is cloudy.

So,P( Foggy|cloudy) is given by

[tex]\dfrac{P(Foggy\cap cloudy)}{P(cloudy)}\\\\=\dfrac{25}{51}\\\\=0.48[/tex]

Hence, our required probability is 0.48.

Answer:

Step-by-step explanation:

The triangle given is aright angle triangle. This is because one if its angles is 90 degrees. The other two angles add up to give 180 degrees. Looking at the right angle triangle, taking the 8 degree angle as the reference angle, the length of the adjacent side is 82, the length of the opposite side is t. Applying trigonometric ratio,

Tan # = opposite side / adjacent side.

# = 8 degrees

Tan 8 = t/82

t = 82 tan8

t = 82 × 0.1405

t = 11.521

Answer:

B. 22.5m^2

Step-by-step explanation:

To find the area of a trapezoid, you must use the formula:

1/2 × height × (base 1+ base 2)

1. 1/2 × 5m × (8+1)

2. 1/2 x 5m x (9)

3. Switch it around to make it easier to solve

5m × 9× 1/2 (We can do this because of the commutative property.)

4. 45m × 1/2 = 45 ÷ 2 = 22.5m^2

In the context of the problem, this means that the area of the trapezoid is 22.5m^2.

Answer: it will take him 4.5 hours to cover same distance

Step-by-step explanation:

Marathon runner covered the whole distance in 4 hours running at a constant speed of 8.1 km per hour.

Speed = distance / time

Distance = speed×time

Therefore, distance covered by the marathon runner in in 4 hours, running at a speed of 8.1 km per hour is

8.1 × 4 = 32.4 kilometers

if he decreased the speed to 7.2 km per hour, the distance remains 32.4 kilometers. Therefore,

At 7.2 km per hour, the time it would take him to cover the same distance would be

Distance/ speed = 32.4/7.2 = 4.5 hours

Answer:

Factory made 4 batches of granola bars yesterday.

Step-by-step explanation:

Given:

1 batch of granola bar is made of 1/8 barrel of raisins.

1/8 barrels can be rewritten as 0.125 barrels.

Hence we can say 1 batch of granola bar is made of 0.125 barrels.

Also Given:

Yesterday Factory used 1/2 barrel of raisins.

1/2 barrels can be rewritten as 0.5 barrels.

Hence we need to find how much batches of granola bars were made using 0.5 barrels of raisins.

Now,

For 0.125 barrels raisins = 1 batch of granola bar

for 0.5 barrels of raisins = Batches of granola bar for 0.5 barrels of raisins

By Using Unitary method we get;

Batches of granola bar for 0.5 barrels of raisins = [tex]\frac{1\times 0.5}{0.125}=4[/tex]

Hence Factory made 4 batches of granola bars yesterday.

Answers:

1a) The next four terms are: 513, -728, 1001, -1330

1b) The direct formula is [tex]a_n = (-1)^n*n^3+1[/tex]

================================================

Explanation:

It helps to start with part B first. The direct formula will help us find the next four terms in a very efficient manner.

Start with the sequence {0, 9, -26, 65, -124, 217, -342}

Subtract 1 from each term to get this new sequence {-1, 8, -27, 64, -125, 216, -343}, which closely resembles the sequence {1, 8, 27, 64, 125, 216, 343}. This is the sequence of perfect cubes. The only difference is that each term alternates from positive to negative and vice versa.

So we will have an n^3 as part of the equation and also a (-1)^n as part of the equation. The (-1)^n portion allows us to alternate in signs. Put together we have (-1)^n*n^3 so far

The last thing we do is add 1 to this so that we undo the operation "subtract 1" we did earlier to the original list.

Therefore the formula is [tex]a_n = (-1)^n*n^3+1[/tex]

--------------------

To help verify we have the right formula, plug in n = 1 and we get

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_1 = (-1)^1*1^3+1[/tex]

[tex]a_1 = 0[/tex]

and plug in n = 2 to get

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_2 = (-1)^2*2^3+1[/tex]

[tex]a_2 = 9[/tex]

and so on. I'll let you check the other terms

--------------------

Let's find the terms a8,a9,a10,a11

This is simply a matter of plugging n = 8, n = 9, n = 10, and n = 11

Plug in n = 8

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_8 = (-1)^8*8^3+1[/tex]

[tex]a_8 = 513[/tex]

Repeat for n = 9

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_{9} = (-1)^9*9^3+1[/tex]

[tex]a_{9} = -728[/tex]

Repeat for n = 10

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_{10} = (-1)^{10}*10^3+1[/tex]

[tex]a_{10} = 1001[/tex]

Repeat for n = 11

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_{11} = (-1)^{11}*11^3+1[/tex]

[tex]a_{11} = -1330[/tex]

Answer:

The equation is I = 65 - 15d and it's continuous

Step-by-step explanation:

First, let's discart the options. The last two options cannot be because if you solve for I in those equations, you'll get the following:

65 = I - 15d

I = 65 + 15d

Now, suppose that after 1 day, you want to know the length of the bread:

I = 65 + 15(1) = 80

This is impossible because the bread is being cut and it's not growing each afternoon. Therefore these options, wheter is discrete or continuous are discarted.

The correct equation to use is then

I = 65 - 15d

Now, how do you know if the graph is continuous or discrete?. A graph is continuous when all the points belonging to a set, can take any value within an interval. A discrete graph all the values belonging to a set, are distinct and separate one of another, in other words, the values are unconnected.

In this case, if you graph this equation, you have the following (see attached graph)

As you can see, all the values are connected and continuous.

Answer : B

Step-by-step explanation:

Answer:

Tan33=x/y

y= x/Tan33

Tan40=(10+x)/y

y= (10+x)/Tan40

Therefore

x/Tan33 = (10+x)/Tan40

xTan40-xTan33 =10Tan33

x= 10Tan33/(Tan40-Tan33)

x=34.2m

Step-by-step explanation:

Answer:

95% confidence Interval would be between $18.775 and $20.225.

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

And margin of error (ME) around the mean calculated as

ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where

Using the numbers, we get:

ME=[tex]\frac{1.96*5}{\sqrt{64} }[/tex] =1.225

Then 95% confidence Interval would be 20±1.225 or between $18.775 and $20.225

Answer:

The confidence interval is between 18.775 and 21.225.

Step-by-step explanation:

Answer:

47.72% of students scored between 563 and 637 on the exam .

Step-by-step explanation:

The percentage of the students scored between 563 and 637 on the exam

= The percentage of the students scored lower than 637 on the exam -

the percentage of the students scored lower than 563 on the exam.

Since 563 is the mean score of students on the Statistics course, 50% of students scored lower than 563. that is P(x<563)=0.5

P(x<637)=P(z<z*) where z* is the z-statistic of the score 637.

z score can be calculated using the formula

z*=[tex]\frac{X-M}{s}[/tex] where

Then z*=[tex]\frac{637-563}{37}[/tex] =2

P(z<2)=0.9772, which means that 97.72% of students scored lower than 637 on the exam.

As a Result, 97.72%-50%=47.72% of students scored between 563 and 637 on the exam

Answer: No, the percentage of the fleet out of compliance is not different from their initial thought.

Step-by-step explanation:

Since we have given that

n = 22

x = 5

So, [tex]\hat{p}=\dfrac{x}{n}=\dfrac{5}{22}=0.23[/tex]

he company initially believed that 20% of the fleet was out of compliance. Is this strong evidence the percentage of the fleet out of compliance is different from their initial thought.

so, p = 0.2

Hypothesis would be

[tex]H_0:p=\hat{p}\\\\H_a:p\neq \hat{p}[/tex]

So, the t test statistic value would be

[tex]t=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\\\t=\dfrac{0.23-0.20}{\sqrt{\dfrac{0.2\times 0.8}{22}}}\\\\\\t=\dfrac{0.03}{0.085}\\\\t=0.353[/tex]

Degree of freedom = df = n-1 = 22-1 =23

So, t{critical value} = 2.080

So, 2.080>0.353

so, we will accept the null hypothesis.

Hence, No, the percentage of the fleet out of compliance is not different from their initial thought.

Final answer:

A hypothesis test can be conducted to determine whether the percentage of the fleet out of compliance is different from the initial belief of 20% by using a null hypothesis of p = 0.20 and an alternative hypothesis of p ≠ 0.20, followed by a Z-test for proportions.

Explanation:

To determine whether there is strong evidence that the percentage of the fleet out of compliance is different from the company's initial belief of 20%, we should set up a hypothesis test. The null hypothesis (H₀) is that the true proportion of cars that are out of compliance is equal to 20% (H₀: p = 0.20). The alternative hypothesis (Ha) is that the true proportion of cars that are out of compliance is different from 20% (Ha: p ≠ 0.20).

Using the sample data of 5 failures out of 22 tested, a statistical test such as the Z-test for proportions can be conducted to determine if we should reject the null hypothesis. This would involve calculating the test statistic comparing the sample proportion to 0.20 and then finding the p-value to make a decision based on the chosen significance level, usually 0.05. If the p-value is below the significance level, we would reject the null hypothesis, indicating that there is evidence that the percentage of the fleet out of compliance is different from 20%.

Answer:

6:8

Step-by-step explanation:

Answer:

Step-by-step explanation:

A) 2x³ +x² -18x -9 = x²(2x +1) -9(2x +1) = (x² -9)(2x +1) = (x -3)(x+3)(2x +1)

__

B) x³ +3x² -x -3 = x²(x +3) -1(x +3) = (x² -1)(x +3) = (x -1)(x +1)(x +3)

__

C) 4x³ -16x² -x +4 = 4x²(x -4) -1(x -4) = (4x² -1)(x -4) = (2x -1)(2x +1)(x -4)

_____

In each case, the third-level factoring mentioned in step 4 is the factoring of the difference of squares: a² -b² = (a -b)(a +b).

_____

The step-by-step is exactly what you need to do. It is simply a matter of following those instructions. You do have to be able to recognize the common factors of a pair of terms. That will be the GCF of the numbers and the least powers of the common variables.

Answer:

Step-by-step explanation:

The slope is the ratio of the change in y to the change in x:

  m = ((b+3) -b)/((a +3) -a) = 3/3 = 1

The point-slope form of the equation of a line through point (h, k) with slope m is ...

  y -k = m(x -h)

Here, we have (h, k) = (a, b) and m=1, so the equation in point-slope form is ...

  y -b = x -a

Adding b puts this in slope-intercept form:

  y = x + (b-a)

Answer:

$6

Step-by-step explanation:

so you add 16 15 and 20 to see how much you earned in total, to get 51 dollars. we subtract 12 because we used it at the movies and get 39 dollars in total. now we subtract this from 45 to see how much more we need to get 6.

equation: 45-(15+16+20-12)........this equals 6 as well

You need to earn more money to buy a $45 video game and it is equal to $6.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.

It is given that , you earn some money by doing different works. The earn money from different works is given.

By mowing the lawn money earned = $16

For babysitting money earned = $15

Money earned for the allowance = $20

So , the total money earned is :

= $16 + $15 + $20

= $51

Now , you have spend $12 at the movie theatre. That meant the money now left is :

= $51 - $12

= $39

You need to buy a video game which costs $45. So , you need to earn some more money which is :

= $45 - $39

= $6

Therefore , you need to earn more money to buy a $45 video game and it is equal to $6.

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Answer:

  200 students were in the program

Step-by-step explanation:

The parent should know how to figure ...

  170/85% = total/100%

This is the same as ...

  total = 170/0.85 = 200

200 students were in the program.

_____

Critical Thinking

There are three declarative statements here. There is no question. We have made up a question to answer.

Another possible answer to the non-question could be, "The parent can ask his student how many students were in the program."

Answer:

Step-by-step explanation:

20

cause i said so

Answer: tangent of A = 2.4

Cotangent of B = 0.4167

Step-by-step explanation:

Answer:

[tex]\displaystyle \frac{5}{12} = cot∠B \\ 2\frac{2}{5} = cot∠A[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ \\ \\ \frac{10}{24} = cot∠B → \frac{5}{12} = cot∠B \\ \\ \frac{24}{10} = cot∠A → 2\frac{2}{5} = cot∠A[/tex]

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

Rejection of aspirin argument is more dangerous because the incorrect dosage of aspirin may cause more severe adverse reactions than the incorrect dosage of vitamin C. It would be prudent to use a lower level of significance to test the aspirin argument.

Answer: 12 trillion dollars

Step-by-step explanation: The government started with 10 trillion than collected 8 trillion in taxes, reducing their debt to 2 trillion dollars. Then the government spent 10 trillion dollars and now their debt is 12 trillion dollars.

Answer:

12

Step-by-step explanation:

Answer:

Option B. 8 mi, 9 mi, 2 mi

Step-by-step explanation:

The option A doesn't have a set of numbers which could be the lengths of the sides of a triangle. The numbers 1,9,10 mean that the longest side is exactly the sum of the others. The only possible way is they lie in the same line, no triangle is formed

Option C gives the numbers 1,9,11. It's impossible to have a side of 11 when you have the sum of the others less than 11. The maximum extension of the other sides (forming a line) won't be enough to reach the length of 11

Option D is also infeasible for the same reason as the option A. The three lines must be aligned to be connected in its extremes

Option B is the only one who can provide a set of possible lengths of a triangle since the sum of the shortest sides is greater than the third. If we open wide enough the angle between the 2 mi side and the 8 mi side, we would eventually connect the 9 mi side and form a triangle

Answer:

The 40% marked up price of refrigerator is  $1260.

Step-by-step explanation:

The cost price of the refrigerator  = $900

Now, the mark up should be 40%

Calculating the markup on the cost price , we get

40 % of $900  =  [tex]\frac{40}{100}  \times 900 = 360[/tex]

or, 40 % mark up = $360

Now, the Marked up cost = Cost Price + Marked up Price

                                          = $900 + $360 = $1260

Hence, the 40% marked up price of refrigerator is $1260.

Answer:

A is the answer

Step-by-step explanation:

If you fail to agree on the actual cash value, amount of loss, or cost of repair or replacement, either can make a written demand for appraisal. ... The two appraisers will then set the amount of loss, stating separately the actual cash value and loss to each item.

When the insured tenant and the insurance company fail to agree on the amount of loss; Choice A is what happens: Either the tenant or the company can request an appraisal, so that an impartial third party determines the amount of loss.

Discussion:

Situations such as in the question may arise when quantifying the amount of loss in an insurance situation.

In such scenarios; the best option is for either the tenant or the company can request an appraisal, so that an impartial third party determines the amount of loss.

The essence of this, is to ensure fairness in quantification of the amount of loss.

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