a probability distribution has a mean of 22 and a standard deviation of 2. use chebychev's inequality to estimate the probability that an outcome of the experiment lies between 13 and 31. a) 0.9506 b) 0.9917 c) 0.0494 d) 0.0083 e) 0.2222 f) none of the above

The  null and alternative hypothesis test the economist's claim is-

H₀: u = 863 ,H₁: u < 863

What is hypothesis test?

A applied math hypothesis test may be a technique of applied math abstract thought accustomed decide whether or not the info at hand sufficiently support a selected hypothesis. Hypothesis testing permits us to create probabilistic statements regarding population parameters.

Main body:

Let ц =average calories of virginia school lunches

The average calories in the school lunch is 863

Here the economists claims that after the testing period ends, the average caloric content in the lunches were dropped

The null hypothesis is H₀ц = 863

Means H₀ ;The average caloric content in the school lunch is 863

The alternative hypothesis is H₁ц <863

Hence , H₁; the average caloric content in the lunches was dropped.

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Answer:

  NK = 26

Step-by-step explanation:

You have a triangle with the centroid identified and all medians drawn. You are given IK = 52 and want NK, where point N is the intersection of median JN with side IK.

The centroid of a triangle is the point where the medians intersect. It divides each median in the ratio 2:1.

A median of a triangle joins a vertex with the midpoint of the opposite side. Here, that means point N is the midpoint of side IK.

IK is given as length 52, so each half of that segment is 52/2 = 26.

  IN = NK = 26

95% confidence interval for true average degree of polymerization is  [430.87 ; 446.07] and this interval suggest that 441 is a plausible value for true average degree of polymerization and also this interval does not suggest that 451 is a plausible value.

Given :

The total number of values given is, n = 17

Mean, μ₀ = 438.47

Standard Deviation, σ = 14.79

The normal distribution is given by: N (438.47 ; 14.79)

If Cl  is 95% then  is 5% and  is 2.5%

α/2 = 0.025

Now, use t-statistics distribution with (n -1) degree of freedom

                         df = 16

So, the t score for 0.025 and 16 s from t-table 2.120.

CI = [ μ₀ ± [tex]t_{\alpha /2}[/tex] ; (n-1) × σ/ √n]

⇒ CI = [μ₀ ± 2.120 × 14.79/√17

⇒ CI = [ μ₀ ± 7.60]

⇒ CI = 430.87 ; 446.07]

Yes, the interval suggests that 441 is a plausible value for true average degree of polymerization.

No, the interval does not suggest that 451 is a plausible value.

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Answer:

36

I looked it up on

If 2 is the cost of one pen and 6 is the cost of one pencil, compute the ordered pair (2,6)

When Mia buys 4 pens and 1 pencil, she has $5 left; the number of dollars she starts with is 4a+b+5.

When she buys 2 pens and 2 pencils, she has $3 left; the number of dollars she starts with is 2a+2b+3.

Since those two expressions represent the same number, set them equal to each other and simplify to get an equation in a and b.

4a+b+5=2a+2b+3

2a-b=-2 [1]

They can purchase 7 pens and 4 pencils with their entire budget if Edward shows up with the same amount of money that Mia did.

The two of them have twice as much money as Mia did in the beginning, and they can buy 7 pens and 4 pencils with the money they have left over. To get a second equation in a and b, write an equation that says that and simplify it.

7a+4b = 8a+2b+10

a-2b=-10 [2]

solving both the equations 1 and 2:

2a-b = -2 - [1]

a-2b = -10 -[2]

a = 2 , b= 6

if 2 is the cost of one pen and 6 is the cost of one pencil, compute the ordered pair (2,6)

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Answer:

Interval notation to inequality notation

In fractional form, the answer is 397/55 and in decimal form it is 7.2181.

The equation can be written as 22/5+k= -31/11

transferring 22/5 to the R.H.S., the sign will turn negative.

thus, k=-31/11-22/5

Further solving the equation by taking L.C.M. of 11 and 5 which comes to 55,

k=(155+242)/55

we get the value of k= 397/55

If we convert the given value of k into decimal, it can also be written as, 7.2181.

Thus, the value of k can b expressed in both numerical and fractional forms.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using ( 0,0) and (1,1 ). the slope is 1 and the y intercept is 0 because the line cuts the y axis at the origin. The equation of the line is y=1x

The null hypothesis states that the probability of reader has personal computer is 0.52 whereas alternative hypothesis states opposite

Its given that

The probability that readers has a personal computer = 0.52

The null hypotheses is that the proportion of readers who own a personal computer is equal to 0.53

Null hypotheses = H₀: p = 0.55

The alternate hypotheses is that the proportion of readers who own a personal computer is not equal to 0.55

Alternate hypotheses = H₁: p ≠ 0.55

Determine the  type of test:

Since the alternate hypothesis states that the proportion of readers who own a personal computer is different, therefore it is a two-tailed test.

To determine the z-score,

Given level of significance : ∝ = 0.05

So, the z-score at 0.05

Z-score = 1.960 (two tailed)

We Reject H₀ if Z > 1.960

And we accept H₀ if Z < 1.960

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Answer: 27.1875 pounds

Step-by-step explanation:

To find out how many pounds are in 435 ounces, we need to divide the number of ounces by the number of ounces per pound. Since 1 pound is equal to 16 ounces, we can divide 435 ounces by 16 ounces per pound to get the number of pounds. This gives us 435 ounces / 16 ounces/pound = 27.1875 pounds.

Therefore, there are approximately 27.1875 pounds in 435 ounces.

Answer:

27.1875 pounds

Step-by-step explanation:

1 pound = 16 ounces,

x pounds = 435 ounces

x = 435 ounces * 1 pound / 16 ounces

x = 27.1875 pounds

Answer:

Step-by-step explanation: 70 2.5 60

Answer:

p(x)=x^2 -17 x + 84

Step-by-step explanation:

p(x)=(x-7)(x-12)

 = x^2-17x+84

Answer:

I can't see the number line, but I'll say 15,000

The solution is, 15000 when 15,490 rounded to the nearest thousand.

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

here, we have,

given that, 15,490

now, we have to rounded to the nearest thousand.

we get, 490 < 500

so, it is 15000

Hence, The solution is, 15000 when 15,490 rounded to the nearest thousand.

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More students received a 94 than any other score on the test. So, option B is the correct answer.

The mode of any given data set is the value that occurs in the given data set the most. This is that one value that occurs more than any other value in any given data set. From the given problem, we can easily understand that 94 is the mode of the set since it is the average score. This means that more students received a 94 than any other score on the test.

The first option is not the correct answer because we have not been told that 99 was the highest score on the test. We have also not been told no student scored below 50 or that a score of 91 was slightly below average.

This means option B is the correct answer.

The question you might be looking for is -

The mode score on the 6th-grade math test was 94! Which of these interpretations must be correct?

a. 99 was the highest score on the test.

b. More students received a 94 than any other score

c. No student scored below a 50

d. A score of 91 was slightly below average.

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Answer:

1420

Step-by-step explanation:

its in the question

Making b the subject in the formula for area of a trapezium, A, given by A = (a+b)÷2 h is found to be b = 2A/h - a

The given expression for area of trapezium is A = (a+b)÷2*h

b is solved for as follows

A = (a+b)÷2*h

A = h * (a+b)/2

divide through by h

A/h = (a+b)/2

multiply through by 2

2A/h = (a + b)

2A/h = a + b

b = 2A/h - a

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The correct option d. 0.109, for the probability of the event: exactly 6 heads out of 8.

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

The probability of getting one head = 1/2.

p = 0.5.

Thus, the probability of getting one tail = 1/2

q = 0.5

Thus, for exactly 6 heads

P(X = 6) =  ⁸C₆. (0.5)⁶ (0.5)²

P(X = 6) = 0.109

Thus, the probability of the event: exactly 6 heads on flipping coin 8 times is 0.109.

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The false statement out of given four option is (a)conserves around 9 cubic yards in landfill space.

Area is characterized as the complete space taken up by a level (2-D) surface or state of an item. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Region. Presently, envision your square is comprised of more modest unit squares

That's what first explanation expresses "conserves around 9 cubic yards in landfill space "

Yet, here unit of landfill space is off-base. Since landfill space is an amount that in every case express in region. Unit of region in the proclamation articulation ought to be square yards not cubic yards

The excess amounts units are reliable with what they address.

Subsequently, When 500 telephone directories are reused, then, at that point,  false statement is option  (a) Monitors around 9 cubic yards in landfill space.

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The solution set of the given inequality -7x < -21 is {x | x > 3}.

For the stated question-

The given inequality is-

-7x < -21

Dividing both side by -1 will change the direction of the sign.

7x > 21

Now, divide both side by 7

7x/7 > 21/7

x > 3 (solution set)

Thus, the solution set of the given inequality -7x < -21 is {x | x > 3}.

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Answer: -5,4

Step-by-step explanation:

2,1 x 2 = 4,2

-3,2 x 3 = -9,6

-9,6

- 4,2 = -5,4

A repeated-measures test's null hypothesis is that the population as a whole will have a mean difference of μD = 0.

What is Null Hypothesis?

In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening.

The t statistic is calculated from the difference between the sample parameter in question and the value of the corresponding population parameter assumed under the null hypothesis. If the hypothesis is true, the difference between the values (and the corresponding t statistic) is expected to be zero.

A repeated-measures test's null hypothesis is that the population as a whole will have a mean difference of μD = 0.

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1) The equation of a line passing through the point (5, 9) in point slope form is;  (y - 9) = 3(x - 5)

2) The equation that is parallel and passing through (0, 4) is; y = ¹/₂x + 4

3) The equation of the line parallel to y - 7 = 7(x - 3) and passing through the point (4, 2) is; (y - 2) = 7(x - 4)

4) Thus, the equation of the line parallel to y = -7x - 2and passing through (-9, -12) is; y = -7x - 75

The general equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

1) We are given the equation of a line as;

y = 3x + 5

where;

slope = 3

y-intercept = 5

Thus, the equation of a line passing through the point (5, 9) in point slope form is;

(y - y₁) = m(x - x₁)

Thus; (y - 9) = 3(x - 5)

2) Equation of a line is given as;

y = (1/2)x

Thus, the equation that is parallel and passing through (0, 4) is;

y - 4 = (1/2)(x - 0)

y - 4 = ¹/₂x

y = ¹/₂x + 4

3) We are given the equation;

y - 7 = 7(x - 3)

y - 7 = 7x - 21

y = 7x - 14

Thus, equation of the line passing through the point (4, 2) is;

(y - 2) = 7(x - 4)

4) We are given the equation;

y = -7x - 2

Thus, the equation of the line parallel and passing through (-9, -12) is;

y + 12 = -7(x + 9)

y = -7x - 63 - 12

y = -7x - 75

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Answer:

2.91666667 dozen marbles can be purchased.

Step-by-step explanation:

To get this answer, you divide $140, by how much it costs per dozen, so $48.

Thus, you can purchase 2.91666667 dozen marbles, with $140.

The time that it takes for a ride of 24 miles is given as follows:

1.6 hours.

To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the desired numeric value.

The distance in this problem is given as the multiplication of the velocity of 15 miles per hour and the time in hours, as follows:

d = 15h.

The variable h can be isolated, thus giving the time in hours for a distance of d miles, as follows:

h = d/15.

The time for a distance of 24 miles is obtained replacing the lone instance of d by 24, as follows:

h = 22

d = 1.6 hours.

The problem asks for the time for a distance of 24 miles.

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Answer:

26.9%

Step-by-step explanation:

538/2000 =  0.269

Multiply this by 100 to get the percentage

= 26.9%

Kevion and Samantha like to collect stamps and if Kevion has 45 stamps then Samantha has 45*3-2= 129 stamps.

The fundamental methods for mixing numbers or algebraic expressions to carry out mathematical computations are known as mathematical operations. These operations include multiplication, division, exponentiation, multiplication, and subtraction. More complex operations, such square roots, logarithms, and trigonometric functions, are available in addition to these fundamental operations. Mathematical operations are employed in a wide collection of disciplines, from elementary arithmetic to intricate computations in engineering and physics. We can use these operations to resolve issues and generate predictions based on mathematical models. We may better comprehend the world around us and make more precise predictions about what will happen in the future by applying mathematical procedures.

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0.1116 is the area under the standard normal curve using the given z-score.

The standard score in statistics is the number of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed.

Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.

The 90th percentile's z-score is 1.2816, as calculated by the Percentile to Z-Score Calculator.

Therefore, a student's z-score would be deemed "excellent" if it was greater than or equal to 1.2816.

So, the area under the standard normal curve will be:

Find the z-scores by looking at the table's intersection of the 0.9 down and 0.07 across columns, which is 0.1660.

Similarly, find -0.5 down and 0.09 across to get 0.2776.

Add them together now: 0.2776 - 0.1660 = 0.1116

Therefore, 0.1116 is the area under the standard normal curve using the given z-score.

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