please help 20 points and brainlyist

Please Help 20 Points And Brainlyist

Answers

Answer 1

a) 1. The backpack weight sample mean is 6.375 pounds.

a) 2. The backpack weight sample mean is 6.375 pounds.

a) 3. The backpack weight sample mean is 6.625 pounds.

b) The range of the sample means is between 6.375 and 6.625, which approaches 0.250 pounds, plus or minus.

c) Since the students are using the sample means to estimate the mean backpack weight of their schoolmates, the true statements are A. and D.

The farther the range of the sample means is from O, the less confident they can be in their estimate.

What is a sample mean?

A sample mean is a statistic computed from a sample of data or variables.

The sample mean represents the average value of the sample data.

What is a range in statistics?

The range describes the difference between the largest number and the smallest number.

Thus, based on the range of the sample means, the farther it is from 0, the less confident the students can be in their estimate.

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Related Questions

Which of the following measurements would be MOST likely to have a negative exponent in scientific notation?
a. The distance the Earth is from the sun in meters.
b. The length of a needle in millimeters
c. The length of a football field in inches.
d. The length of an amoeba in meters.

Answers

The measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

Given four measurements:

The distance the Earth is from the sun in meters.The length of a needle in millimetersThe length of a football field in inches.The length of an amoeba in meters.

We are required to choose one measurement which would most likely to have a negative exponent in scientific notation.

A negative exponent is defined as the multiplicative inverse of the base,raised to the power which is of the opposite sign of tthe given power.It is expressed as [tex]e^{-x}[/tex].

We know that exponent shows continuous growth or continuous decay.

Among all the measurement the measurement which is most likely to have a negative exponent in scientific notation is the length of an amoeba in meters because among all the option amoeba can grow continously or decay continuously.

Hence the measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

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Which of the following terms is best described as the point halfway between
the endpoints of a line segment?
O
O
A. Ordered pair
B. Vertex
OC. Coordinate
O
D. Midpoint
SUBMIT

Answers

Answer:

D. Midpoint...

Step-by-step explanation:

I hope it helps You:)

At noon, ship a is 40 nautical miles due west of ship b. ship a is sailing west at 18 knots and ship b is sailing north at 17 knots. how fast (in knots) is the distance between the ships changing at 5 pm? (note: 1 knot is a speed of 1 nautical mile per hour.)

Answers

The distance between the ships changing at 92.29 Knots

Using the position of ship A as the reference point, at time t measured in hours past noon, ship A is 18 t miles west of this point and ship B is 40 + 17t north of this point. The distance between ships is then

                              [tex]d(t) = \sqrt{(18t)^{2} + (40+17t)^{2} } \\[/tex]

The rate of change of distance is -

                              [tex]\frac{dd}{dt} = \frac{36t + 2(40 + 17t)17}{2\sqrt{18t^{2} + (40 + 17t) } }[/tex]

after putting t = 5 into this rate of change ,

we get, answer = 92.29

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A farmer with 1200 meters of fencing wishes to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What are the dimensions of the field that produce the largest area

Answers

The perimeter of a given figure is a measure of the addition of each individual length of the sides of the figure. Thus the dimensions that would produce the largest area of the field are; length = 300 m, and width = 200 meters.

The perimeter of a given figure is a measure of the addition of each length of the sides of the figure. It always has the unit as that of the given sides of the figure.

So in the given question, the perimeter of the fence required = 1200 meters.

Thus, let the length of the enclosed rectangle be represented by l and its width by w. Thus,

Perimeter = 2l + 3w

1200 = 2l + 3w

Thus, let l be equal to 300, we have;

1200 = 2(300) + 3w

1200 - 600 = 3w

w = 200

Thus the dimensions of the field that would produce the largest area are; length = 300 m and width = 200 m.

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The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds.

Answers

The domain is the water balloon's height increasing will be (0, 2), staying the same will be (2, 4), decreasing the fastest will be (6, 10), and the height of the water balloon at 16 seconds the will be 0.

What is a slope?A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run or horizontal change.Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates. Find the difference between these two points' x-coordinates. Subtract the difference between the x and y coordinates from the difference between the two.The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds.

Part A:

As seen from the graphic, increase from 0 to 2 sec.

The domain is (0, 2), where the height of the water balloon increases.

Part B:

The water balloon stays the same from 2 to 4 sec.

The field means that the height of the water balloon remains the same (2, 4).

Part C:

Height decreasing fasted at 4 to 6 sec.

Because the slope is steepest downward from 4 to 6 sec as comfort to 6 to 10 sec.

The domain is where the height of the water balloon decreases rapidly (6, 10).

Part D:

The balloon's height will be almost near the ground as resistance will play its role.

But it will almost touch the ground.

The height of the water balloon will be 0 in 16 seconds.

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How do I solve it I am running low on time it says it wrong don’t know

Answers

x > 1 is the required solution of the given inequality - 3x + 7 < 4. This can be obtained by solving the inequality the same way as we solve an algebraic equation.

Solve the inequality:

The inequality can be solved as the same way as we solve an algebraic equation.

Combine the terms with variables to one side and constants to other side.To multiply the whole inequality with negative terms we reverse the sign of the inequality.

Here in the question the inequality to be solved is given:

- 3x + 7 < 4

By subtracting 7 from both sides of the inequality we get,

⇒ - 3x + 7 - 7 < 4 - 7

⇒ - 3x < - 3

To make the side of the inequality with variable x positive we multiply the whole equation with - 1, then we have to reverse the sign of inequality since we have to multiply the whole inequality with a negative term,

we get,

⇒ 3 x > 3

Now finally by dividing the whole inequality by 3 we get,

x > 1

The number line representation can be done by marking values from 1 to numbers greater than 1.

Hence x > 1 is the required solution of the given inequality - 3x + 7 < 4.

 

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18. A tennis player uses up 800 calories every hour. In 1 hour and 15 minutes, how many calories does this player use? (A) 900 (B) 1000 (C) 1100 (D) 1200​

Answers

(C) 1000,
An hour = 60 minutes,
60/4= 15 minutes
The tennis player uses 800 calories, so 800/4 =200 calories
1 hour 15 minutes= 60 minutes + 15 min.
= 800 cal. + 200 cal.
=1000calories

Shira's math test included a survey question asking how many hours students spent studying for the test. The scatter plot below shows the relationship between how many hours students spent studying and their score on the test. A line was fit to the data to model the relationship.

Which of these linear equations best describes the given model?

Answers

Answer:

Part 1) Option B. y = 10x + 45

Part 2) The score is 95

Step-by-step explanation:

Linear equation that best describes the given model

Let

x ---> number of hours students spent studying

y ---> their score on the test

Looking at the line that was fit to the data to model the relationship

The slope is positive

The y-intercept is the point (0,45)

For x=1, y=55 ----> point (1,55)

Find the slope

The formula to calculate the slope between two points is equal to

substitute the points (0,45) and (1,55)

Find the equation of the line in slope intercept form

we have

substitute

Part 2) Estimate the score for a student that spent 5 hours studying.

For x=5 hours

substitute in the linear equation and solve for y

To conduct a test of hypothesis with a small sample, we make an assumption that?

Answers

To conduct a test of hypothesis with a small sample, we make an assumption that the population is normally distributed .

What is normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The normal distribution appears as a "bell curve" on a graph.

A probability bell curve is more properly described as the normal distribution.The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has a kurtosis of 3 and zero skew.Not all symmetrical distributions are normal, but all normal distributions are symmetrical.Natural occurrences frequently resemble the usual distribution.

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The length of plot is 8 meters more than its breath. If its perimeter is 80 metres, find its length and breath.

Answers

Answer:

length = 24 meters
breadth = 16 meters

Step-by-step explanation:

Let L be length and B be breadth

From the first fact we get the equation
L = B + 8         (1)

We know that perimeter = 2(L+B) and this is given as 80

So 2(L+B) = 80

L + B = 80/2 = 40
or
L = 40 - B              (2)

If we add equations (1) and (2) we can eliminate B

We get 2L = B + 8 + 40 - B =48

L = 48/2 = 24

Substituting for L in equation (1) we get

24 = B + 8  ==>

B = 24-8 =16

Cross-check

Perimeter = 2 (L+B) = 2(24 + 16) = 2(40) = 80

Hence check OK

A solid right pyramid has a regular hexagonal base with an area of 5.2 cm2 and a height of h cm.which expression represents the volume of the pyramid?(5.2)h cm3(5.2)h cm3(5.2)h cm3(5.2)h cm3

Answers

volume of pyramid = 1/3(5.2)h cm3

What is a Prism?

Prism is a three dimensional figure. A prism is a 3-dimensional shape with two identical shapes (bases) facing each other.

we know that,

The volume of the pyramid is equal to

volume = (1/3) × base area × height

we have height = h cm

area of base = 5.2 cm^2

substitute in the formula

                       v = 1/3 × 5.2 × h

                        volume = 1.73h cm^3

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Use the figure to the right to find the value of PT. T is the midpoint of PQ
PT=3x+3 TQ=7x-9

Answers

If T is the midpoint of PQ and PT = 3x+3, TQ = 7x-9, then PT = 12 units.

Determining the Value of PT

It is given that,

T is the midpoint of PQ ........ (1)

PT=3x+3 ......... (2)

TQ=7x-9 .......... (3)

From (1), the distance from P to T and the distance from T to Q will be equal.

⇒ PT = TQ [Since, a midpoint divides a line into two equal segments]

Hence, equating the equations of PT and TQ given in (2) and (3) respectively, equal, we get the following,

3x + 3 = 7x - 9

or 7x - 9 = 3x + 3

or 7x - 3x = 9 + 3

or 4x = 12

or x = 12/4

⇒ x = 3

Substitute this obtained value of x in equation (2)

PT = 3(3) + 3

PT = 9 + 3

PT = 12 units

Thus, if T is the midpoint of PQ, then the measure of PT and TQ is equal to 12 units.

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Find using appropriate Properties:
6/7 x -2/3 + 3/5 + 5/8 x -6/7

Answers

The simplified form of the expression is given as 83x/56 -(97/105)

Finding the value of unknown variables

Alphabets are usually represented as unknown variables in a equation or expression.

Given the following expression shown below

6/7 x -2/3 + 3/5 + 5/8 x -6/7

Collect the like terms to have;

6/7 x+ 5/8 x  -2/3 + 3/5 -6/7

Simplify

48x+35x/56 - (70-63 + 90)/105

The final expression will be given as;

83x/56 -(97/105)

Hence the simplified form of the expression is given as 83x/56 -(97/105)

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if a + b is equals to 5 and a x b is equal to 6 then what is the value of a and b​

Answers

Answer: 2 and 3, or 3 and 2

Step-by-step explanation:

a + b = 5 so a = 5 - b

Substitute a = 5 - b into ab = 6; (5 - b)b =  6

5b - [tex]b^{2}[/tex] = 6

[tex]b^{2}[/tex] - 5b + 6 = 0

(b - 2)(b - 3) = 0

So b is either 2 or 3

So a is either 3 or 2 depending on what b is

d= the square root of 4h/5 make h the subject of the formula

Answers

[tex]d = \sqrt{ \frac{4h}{5} } \\ square \: both \: sides \\ d {}^{2} = \frac{4h}{5} \\ multiply \: both \: sides \: by \: 5 \\ 5d {}^{2} = 4h \\ divide \: both \: sides \: by \: 4[/tex]

[tex]h = \frac{5d {}^{2} }{4} [/tex]

Find the number of ways of delivering five letters to five houses so that no house gets
a correct letter.

Answers

Using the Fundamental Counting Theorem, it is found that there are 1024 ways of delivering the letters.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem, each house has a correct letter, however the letter cannot be used for the house, hence the parameters are given as follows:

n1 = n2 = n3 = n4 = n5 = 5 - 1 = 4.

Thus the number of ways is:

N = 4 x 4 x 4 x 4 x 4 = 4^5 = 1024.

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PLEASE HELP FAST!

A cylinder and a cone have the same volume. The cylinder has radius x
and height y. The cone has radius 1/2x. Find the height of the cone in terms of y.

Answers

The height of the cone in terms of y is h = 12x⁴y

How to find the volume of a cone and cylinder?

The cylinder and the cone have the same volume.

Volume of a cylinder = πr²h

where

r = radiush = height

Therefore,

Volume of a cylinder = πx²y

volume of a cone = 1 / 3 πr²h

where

r = radius of the coneh = height of the cone

Therefore,

πx²y = 1 / 3 × π × (1 / 2x)² × h

πx²y = πh / 12x²

πx²y × 12x² / π = h

h = 12x⁴y

Therefore, the height of the cone in terms of y is h = 12x⁴y

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Determine whether the given set of functions is linearly independent on the interval (−[infinity], [infinity]). f1(x) = x, f2(x) = x2, f3(x) = 6x − 2x2 linearly dependent linearly independent

Answers

The given set of functions are not linearly independent.

Given,

[tex]f_{1} (x) = x\\f_{2} (x) = x^{2} \\f_{3} (x) = 6x-2x^{2}[/tex]

We need,

[tex]c_{1} f_{1} (x)+c_{2} f_{2} (x)+c_{3} f_{3}(x)=0[/tex]

Substituting the values in equation we get,

[tex]c_{1} x+c_{2} x^{2} +c_{3} (6x-2x^{2} )=0\\[/tex]

Computing the equation we get,

[tex]c_{1} x+c_{2} x^{2} +c_{3} 6x-c_{3} 2x^{2}=0[/tex]

[tex](c_{1} +6c_{3} )x+(c_{2} -2c_{3} x^{2} =0[/tex]

This resolves to two equations

[tex](c_{1} +6c_{3})x =0\\(c_{2} -2c_{3} )x^{2} =0[/tex]

These will have an infinite set of solutions:

[tex]c_{1} =-6c_{3} \\c_{2} =2c_{3}[/tex]

Two functions are said to be linearly independent if neither function is a constant multiple of the other.

Here, it is clear that the given functions are not linearly independent.

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all common factors of 24

Answers

Answer:

The all common Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24


To the nearest whole number, what is the surface area of the right triangular prism?

Answers

Answer: 797.4 m²

Step-by-step explanation:

The surface area is just the total of the areas of each face of of a solid. In this solid, we have 2 triangles and 3 rectangles.

Triangles

We know that the two triangles of this solid are congruent, so they will have the same area. Since the area of a triangle is [tex]\frac{1}{2}bh[/tex], two triangles would have an area of [tex]bh[/tex]. Hence, the total area is

[tex]A=9 * 15\\A=135[/tex]

Rectangles

The area of a rectangle is lw, where l is the length and w is the width. Let's find the total area of all of them.

[tex]A=9*16+15*16+17.4*16[/tex]

All of the areas are a product of some number and 16. This makes sense as the length of this prism is 16. We can un-distribute this 16 to make the calculation easier.

[tex]A=16(9+15+17.4)\\A=16(41.4)\\A=662.4[/tex]

Total

We can add both totals to get the total surface area of the solid.

[tex]135+662.4\\=797.4[/tex]

The surface area of this right triangular prism is 797.4 m².

can someone help? will award brainliest​

Answers

Answer:

B

Step-by-step explanation:

The beginning temperature is -12 and then it rises 5 degrees each hour at the end of the game it is 32 degrees.

The answer is B

The temperature at the beginning of the hockey tournament is -12
degrees and rises five degrees each hour. At the end of the hockey
tournament the temperature is 32 degrees.

Solve the following quadratic equation for all values of a in simplest form.
5(x − 6)² — 29 = −19

Answers

Answer:

[tex]X1 = 6-\sqrt{2} , X2 = 6+\sqrt{2}[/tex]

Step-by-step explanation:

Answer: x= √2 + 6, - √2 + 6

Step-by-step explanation:

The area of a painting is 4081 c m squared.

If the width of the painting is 53 cm, what is its length, in centimeters?

Type your numerical answer below (without units). If necessary, round to the nearest integer.

Answers

Answer:

49,2

Step-by-step explanation:

i dont practice math in english so the variables might be a little different!! The little L with the squiggly is supposed to represent length

The length of the painting is 77 cm if the area of the painting is 4081 sq cm and the width is 53 cm.

The area of a rectangle is the product of the length and width of the same rectangle.

Given that:

The area of the painting, A = 4081 cm².

The width of the painting, b = 53 cm.

To find the length of the painting, use the following formula to obtain the area of the rectangle:

Area = length × breadth

Let the length of the painting is l, then

A = l × b

4081 = l × 53

l = [tex]\frac{4081}{53}[/tex]

l = 77

Thus, the length of the painting is 77 cm.

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My family was so excited to see the new movie, Thor: Love and Thunder. I decided to go and take my
two boys and four of their friends. The adult ticket price was $11.00 and only 3 of the kids were able to
get the children's ticket price. If the total bill was $62.00, how much was each children's ticket?

Answers

Answer:$6

Step-by-step explanation:

If only 3 got the children's price, that means there were 4 adult tickets.
4*11=44

62-44=18

18/3=6

$6 per child ticket

Omar recorded the number of hours he worked each week for a year. below is a random sample that he took from his data. 13, 17, 9, 21 what is the standard deviation for the data? standard deviation: s = startroot startfraction (x 1 minus x overbar) squared (x 2 minus x overbar) squared ellipsis (x n minus x overbar) squared over n minus 1 endfraction endroot.

Answers

The standard deviation exists as the positive square root of the variance.

So, the standard deviation = 4.47.

How to estimate the standard deviation?

Given data set: 13 17  9 21

To calculate the mean of the data.

We know that mean exists as the average of the data values and exists estimated as:

Mean [tex]$=\frac{13+17+9+21}{4} \\[/tex]

Mean [tex]$=\frac{60}{4} \\[/tex]

Mean = 15

To find the difference of each data point from the mean as:

Deviation:

13 - 15 = -2

17 - 15 = 2

9 - 15 = -6

21 - 15 = 6

Now we have to square the above deviations we obtain:

4, 4, 36, 36

To estimate the variance of the above sets:

variance [tex]$=\frac{4+4+36+36}{4}$[/tex]

Variance [tex]$=\frac{80}{4}$[/tex]

Variance = 20

The standard deviation exists as the positive square root of the variance. so, the standard deviation [tex]$=\sqrt{20 }=4.47$[/tex].

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Answer:

4.4

Step-by-step explanation:

The answer above is correct.

factorise completely
2x²+8+6

Answers

Use GCF
2( x^2 +4 +3)
Combine like terms
2 ( x^2 +7)
Can’t simplify further
Answer:: 2 ( x^2 +7)

Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

⨠ add 8 and 6

[tex]\sf{2x^2+14}[/tex]

⨠ factor the 2 out

[tex]\sf{2(x^2+7)}[/tex]

Since we cannot simplify this more, we know that we've simplified completely.                                                                                   [tex]\small\pmb{\sf{Frozen \ melody}}[/tex]

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference
2. Also, let b1, b2, b3, ... be a sequence of positive integers in geometric progression with common
ratio 2. If a1 = b1 = c, then the number of all possible values of c, for which the equality

2(a1 + a2 + ⋯ + an

) = b1 + b2 + ⋯ + bn

holds for some positive integer n, is _____

Answers

Since [tex]a_1,a_2,a_3,\cdots[/tex] are in arithmetic progression,

[tex]a_2 = a_1 + 2[/tex]

[tex]a_3 = a_2 + 2 = a_1 + 2\cdot2[/tex]

[tex]a_4 = a_3+2 = a_1+3\cdot2[/tex]

[tex]\cdots \implies a_n = a_1 + 2(n-1)[/tex]

and since [tex]b_1,b_2,b_3,\cdots[/tex] are in geometric progression,

[tex]b_2 = 2b_1[/tex]

[tex]b_3=2b_2 = 2^2 b_1[/tex]

[tex]b_4=2b_3=2^3b_1[/tex]

[tex]\cdots\implies b_n=2^{n-1}b_1[/tex]

Recall that

[tex]\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n[/tex]

[tex]\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

It follows that

[tex]a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n +  n(n-1)[/tex]

so the left side is

[tex]2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n[/tex]

Also recall that

[tex]\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}[/tex]

so that the right side is

[tex]b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)[/tex]

Solve for [tex]c[/tex].

[tex]2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}[/tex]

Now, the numerator increases more slowly than the denominator, since

[tex]\dfrac{d}{dn}(2n(n-1)) = 4n - 2[/tex]

[tex]\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2[/tex]

and for [tex]n\ge5[/tex],

[tex]2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2[/tex]

This means we only need to check if the claim is true for any [tex]n\in\{1,2,3,4\}[/tex].

[tex]n=1[/tex] doesn't work, since that makes [tex]c=0[/tex].

If [tex]n=2[/tex], then

[tex]c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0[/tex]

If [tex]n=3[/tex], then

[tex]c = \dfrac{12}{2^3 - 6 - 1} = 12[/tex]

If [tex]n=4[/tex], then

[tex]c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N[/tex]

There is only one value for which the claim is true, [tex]c=12[/tex].

Assume that thermometer readings are normally distributed with a mean of 0 C and a standard deviation of 1.00 C. A thermometer is randomly selected and tested. For the case​ below, draw a​ sketch, and find the probability of the reading.​ (The given values are in Celsius​ degrees.)

Between 1.50 and 2.25

1. Choose the correct graph
2.the probability of getting a reading between 1.50 and 2.25

Answers

The probability of getting a reading between 1.50 and 2.25 is; 0.00546

How to find the probability from z-score?

We are given the following information in the question:

Mean; μ = 0 °C

Standard Deviation; σ = 1 °C

We are given that the distribution of thermometer readings is a bell shaped distribution that is a normal distribution.

Formula for z-score is;

z = (x' - μ)/σ

P(Between 1.50 degrees and 2.25 degrees) is expressed as;

P(1.5 ≤ x ≤ 2.25)

= P((1.5 - 0)/1 ≤ z ≤ (2.25 - 0)/1))

= P(z ≤ 2.25) -  P(z < 1.5)

= 0.0546 = 5.46%

The graph that correctly describes this is the first graph

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QUICK!!!
The total arm and blade of a windshield wiper is 12 in. long and rotates back and forth through an angle of 90 degrees. The shaded region in the figure is the portion of the windshield cleaned by the 9​-in. wiper blade. What is the area of the region​ cleaned?

answer with the last three decimal places (no rounding)

Answers

The area of the region is: 63.585 square inches.

What is the area of the region​ cleaned?

If we have a circle of radius R, the area of said circle is:

A = pi*R^2

Particularly, if we have a section of the circle defined by an angle θ, the area of that region is:

A = (θ/2pi)*pi*R^2 = (θ/2)*R^2

In this case we have:

θ = 90° = pi/2

R = 9in

Replacing that we get:

A = (pi/4)*(9in)^2 = (3.14/4)*(9in)^2 = 63.585 in^2

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The navy reports that the distribution of waist sizes among male sailors is approximately normal, with a mean of 32.6 inches and a standard deviation of 1.3 inches. part a: a male sailor whose waist is 34.1 inches is at what percentile? explain your reasoning and justify your work mathematically. (5 points) part b: the navy uniform supplier regularly stocks uniform pants between sizes 30 and 36. anyone with a waist circumference outside that interval requires a customized order. describe what this interval looks like if displayed visually. what percent of male sailors requires custom uniform pants? show your work and justify your reasoning mathematically. (5 points) (10 points)

Answers

Using the normal distribution, it is found that:

a. A male sailor whose waist is 34.1 inches is at the 87.5th percentile.

b. 5.7% of male sailors requires custom uniform pants.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 32.6, \sigma = 1.3[/tex]

For item a, the percentile is the p-value of Z when X = 34.1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (34.1 - 32.6)/1.3

Z = 1.15

Z = 1.15 has a p-value of 0.875.

Hence 87.5th percentile.

For item b, the proportion who does not require an special order is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 30, hence:

X = 36:

Z = (36 - 32.6)/1.3

Z = 2.62

Z = 2.62 has a p-value of 0.996.

X = 30:

Z = (30 - 32.6)/1.3

Z = -2

Z = -2 has a p-value of 0.023.

0.996 - 0.023 = 0.943.

Hence the proportion who requires an special order is:

1 - 0.943 = 0.057.

5.7% of male sailors requires custom uniform pants.

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