8. The heights of female students at North Shore High School are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. About how many students in a random sample of 1000 female students could we expect to have heights less than 167.5 cm

The MOST accurate definition of standard deviation is the mean absolute deviation of the sum of the squared deviation from the average. Option 4

Standard deviation can be defined as a statistic tool that measures the dispersion of a dataset in relation to its mean and is calculated as the square root of the available variance of the set.

It is calculated as the square root of the given variance.

Thus, the MOST accurate definition of standard deviation is the mean absolute deviation of the sum of the squared deviation from the average.

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The rewritten equation for the given equation is [tex]x=\frac{h+g}{-f}[/tex]. So, option C is correct.

A linear equation given in the form ax + b = c can be rewritten to solve for x as below:

ax + b = c

⇒ ax = c - b

∴ x = (c - b)/a

So, here the basic operations such as addition, subtraction, multiplication, and division are used on both sides to rewrite the given equation for solving x.

Given equation is -fx - g = h

Step 1: Adding 'g' on both sides

-fx - g + g = h + g

⇒ -fx = h + g

Step 2: Dividing by '-f' on both sides

-fx = h + g

⇒ -fx/-f = (h + g)/-f

∴ x = (h + g)/-f

Therefore, the rewritten equation to solve for x is x = (h + g)/-f.

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Disclaimer: The given question was incomplete in the portal. Here is the complete question.

Question: Select the correct answer. which equation is correctly rewritten to solve for x?

Equation: -fx = h + g

A. x = (g - h)/f

B. x = (h - g)/-f

C. x = (h + g)/-f

D. x = (h + g)/f

The value of 2+8+32+128…..,n=9 is 174762

The series is given as:

2+8+32+128…..,n=9

Start by calculating the common ratio (r)

r = 8/2

r = 4

The sum of the series is then calculated as:

[tex]S_n = \frac{a *(r^n - 1)}{r -1}[/tex]

This gives

[tex]S_9 = \frac{2 *(4^9 - 1)}{4 -1}[/tex]

Evaluate the difference

[tex]S_9 = \frac{2 *( 262143)}{3}[/tex]

Evaluate the quotient

[tex]S_9 = 174762[/tex]

Hence, the value of 2+8+32+128…..,n=9 is 174762

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A square is a plane shape that has an equal length of sides. The required answers to the questions are;

i. Yes, the area of a square and its length of sides are directly proportional.

ii. Yes, the perimeter and length of the side of a square are directly proportional.

A square is a plane shape that has an equal length of sides, with four internal right angles. The area of a square can be determined as:

Area = length x length

        = [tex](length)^{2}[/tex]

This implies that the value of area of a given square depends on the value of its length. So that the area and length of sides of a square are directly proportional.

If the value of its length increases, then the value of its area increases, viz-a-viz. Then the area and length of the sides of a square are directly proportional.

The perimeter of a square is the sum of the length of its individual sides. Thus, the perimeter of a square can be determined by:

perimeter = 4 x length

Thus the value of the length determines the value of its perimeter. If the length of its sides increases, so is that of the perimeter. Therefore, the length and perimeter of a square are directly proportional.

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The centre angle of circular sector is n = 90 degrees (approximately).

A sector is referred to as a component of a circular made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radius of the circle at its ends.

A piece of pizzas can be used as an analogy for the form of a circle's sector.

The formula for finding the angle formed at the circular sector in radian is;

Let 'n' be the centre angle.

Let 'l' be the slant height of the cone which is equal to radius of circular sector.

Let 'r' be the radius of the cone.

First, calculate the total length of the circular sector say 'L' which is equal to the circumference of the circular base of the cone.

circumference = 2[tex]\pi[/tex]r

                        = 2×3.14×1

                        = 6.28

Now,

centre angle = length of circular sector/radius of circle

n = L/l

n = 6.28/4

n = 1.57 radian

Convert radian in degree as;

n = (1.57×180)/[tex]\pi[/tex]

n = 89.95

n = 90 degrees (approximately)

Therefore, the angle made by the circular sector is 90 dergees.

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The correct question is-

The slant height and radius of a cone are 4 and 1, respectively. Unrolling the curved surface gives a circular sector with center angle n degrees. Find n.

As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution whenever the sample size is large.

Thus, as a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution when the sample size is large and each element is selected independently from the same population.

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Answer:

I don't know.i don't know

The probability that two of three football games will go to into overtime is 0.08

From the question, we have the following parameters about the probability

Sample size, n = 3

Proportion that goes to overtime, p = 18%

Number that goes into overtime, x = 2

The probability that two of three football games will go to into overtime is calculated using the following binomial probability

P(x) = nCx * p^x * (1 - p)^(n -x)

Substitute the known values in the above equation

P(2) = 3C2 * (18%)^2 * (1 - 18%)^(3 -2)

Express 18% as decimal

P(2) = 3C2 * (0.18)^2 * (1 - 0.18)^(3 -2)

Evaluate the difference

P(2) = 3C2 * (0.18)^2 * (0.82)^1

Evaluate the combination expression

P(2) = 3 * (0.18)^2 * (0.82)^1

Evaluate the exponent

P(2) = 3 * 0.0324 * (0.82)

Evaluate the product

P(2) = 0.079704

Approximate

P(2) = 0.08

Hence, the probability that two of three football games will go to into overtime is 0.08

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Answer:

the 4th answer option. W = 153°, P = 71°

Step-by-step explanation:

PQRS ~ TUVW

that means both figures are similar.

and that means that the angles at the corresponding vertexes are the same, and all 4 corresponding sides (and any other pair of corresponding lines like diagonals) have the same scaling factor.

we see due to the proportions of the different parts of the shapes

U corresponds to Q.

T corresponds to P.

W corresponds to S.

V corresponds to R.

therefore, as the angle at S = 153°, so is W.

and as the angle at T = 71°, so is P.

Answer:

A=P(1+in)

A=13000(1+6/100×9)

A=press calculator

Answer:

13

Step-by-step explanation:

2(x-4+8)=34

x-4+8=17

x+4=17

x=13

The statement when a person convicted of a crime appeals a conviction, he or she asks a higher court to examine the trial court's decisions to determine whether the proper procedures were followed is True.

Appeal occur when a person convicted of a crime want another court to reverse a decisions or to examine and re-check the judgement or outcome of a trial court outcome because the convicted person was not satisfied with the outcome or the result  of the trial court .

Hence, the statement is true because an offender  that was convicted of a crime can tend to files an  appeal with a higher court or appellate court so as to examine the trial court's decisions.

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Answer:

f[g(4)] = 4

Step-by-step explanation:

Given table:

[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} x & -6 & -4 & 1 & 3 & 4\\\cline{1-6} f(x) & 4 & -1 & -6 & 1 & 3 \\\cline{1-6} g(x) & 1 & 4 & 3 & -4 & -6 \\\cline{1-6}\end{array}[/tex]

f[g(4)] is a composite function.

When calculating composite functions, always work from inside the brackets out.

Begin with g(4):  g(4) is the value of function g(x) when x = 4.

From inspection of the given table, g(4) = -6

Therefore, f[g(4)] = f(-6)

f(-6) is the value of function f(x) when x = -6.

From inspection of the given table, f(-6) = 4

Therefore, f[g(4)] = 4

As we can see

So

Answer:

[tex]\frac{23}{90}[/tex]

Step-by-step explanation:

we require 2 equations with the recurring digit placed after the decimal point.

let x = 0.2555.. ( multiply both sides by 10 and 100 )

10x = 2.555... (1)

100x = 25.555.... (2)

subtract (1) from (2) thus eliminating the recurring digits

90x = 23 ( divide both sides by 90 )

x = [tex]\frac{23}{90}[/tex]

Answer:

[tex]\sf \dfrac{23}{90}[/tex]

Step-by-step explanation:

  x = 0.25555.....  --------------(I)

Number of non-recurring digits is 1. So, multiply equation (I) by 10.

10x = 2.5555.... --------------(II)

Number of recurring digits is 1. So, multiply equation (II) by 10.

 100x = 25.5555...... (III)

Subtract equation (II) from (III)

     100x = 25.5555........

       10x =    2.5555.......

    -             -                      

         90x = 23

             x = 23/90

Answer:

12, 14, 16, 18

Step-by-step explanation:

(x + (x+2) + (x+4) + (x+6))/4 = 15

^ solve algebraically

you'll get (4x+12)/4 = 15

then: 4x + 12 = 60

then 4x = 60-12

then 4x = 48

then x = 12

x is 12 so then do substitution

so you get

12 + (12+2) + (12+4) + (12+6)

12, 14, 16, 18

Answer:

? = 120°

Step-by-step explanation:

the central angle is the same as the arc that subtends it , that is

? = 120°

Answer:

  3 1/2 quarts

Step-by-step explanation:

The fraction of the lemonade that is water can be determined from the ratio of water to lemon juice. That fraction of a gallon is the quantity of interest.

Of the 7+1 = 8 parts that make up the lemonade, 7 of those are water. That is, water is 7/8 of the lemonade.

Of the 4 quarts of lemonade, the quantity that is water will be ...

  (7/8)(4 quarts) = 7/2 quarts = 3 1/2 quarts . . . of water

Using it's concept, the domain of the function represented by the graph is all real numbers.

The domain of a function is the set that contains all possible input values for the function.

In this problem, a parabola is used, which has no restriction such as an even root or a fraction, hence the domain is all real values.

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The measure of BC from the figure shown is 26

A line is the distance between two points. From the given line AC;

AC = AB + BC

Given the following parameters

AC = 8x - 20

AB = 3x - 1

Required
Length BC

Substitute

8x-20 = 3x-1 + BC
BC = 8x-20 -(3x - 1)

BC = 8x - 20 - 3x + 1

BC = 5x - 19

Since  B is the midpoint of AC, then;

AB = BC
3x - 1 = 5x - 19

-2x = -18

x = 9

Determine the length of BC

BC = 5(9) - 19
BC = 45 - 19
BC = 26

Hence the measure of BC from the figure shown is 26

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The more on these factors forecasters must rely, the more innovative a new product or service design is: Subjective Estimates.

Option (e) is correct.

A subjective estimate is a specific type of estimate that is founded on a person's subjective evaluation or in-depth comprehension of the possibility of a specific outcome.

A subjective estimate only takes into account the subject's ideas and prior experiences rather than employing data or exact calculations.

Individual subjective evaluations are highly biased and differ from person to person.

Contrarily, a subjective estimate is incredibly prone to revision, even when only one person's viewpoint is taken into account.

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Answer:

2/3

Step-by-step explanation:

1/3 cup powdered sugar

2/6 cup brown sugar

Reduce 2/6 to 1/3.

1/3 + 1/3 = 2/3

The three consecutive integers are 5, 6, and 7.

What are consecutive integers?

Whole numbers that follow one another without a gap are known as consecutive integers. A few examples of consecutive integers are 15, 16, and 17, 1,2 and 3, and so on.

Finding the Consecutive Integers

Let the three consecutive integers be a, a + 1, and a + 2.

These three consecutive integers are to be such that two times the first integer when added to three times the second integer minus the third integer, it is equal to 21.

⇒ 2a + 3(a+1) - (a+2) = 21

2a + 3a + 3 - a -2 = 21

5a - a + 3 - 2 = 21

4a + 1 = 21

4a = 20

a = 20/4

a = 5

∴ a+1 = 5+1

a+1 = 6

And, a+2 = 5 + 2

a +2 =7

Hence, the three consecutive integers come out to be 5, 6, and 7

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Using linear function concepts, it is found that the volume of each marble is of 0.05 liters.

A linear function is modeled by:

y = mx + b

In which:

The linear function that gives the volume of water, when n marbles are inserted into the tank, is given by:

w = 32 - 0.05n

The slope of -0.05 means that for each marble inserted, there are 0.05 liters less for water, hence the volume of each marble is of 0.05 liters.

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Answer:

.05 liters

Step-by-step explanation:

The area of the new rectangle will be 25 times that of the original

A rectangle is a 2D shape that has 4 sides and equal interior angles

If rectangle has a width of 2.45 feet and a length of 6.5 feet, then;

Width = 2.45 feet

Length = 6.5feet

A = 2.45 * 6.5

A = 15.925 square feet

If each side of the rectangle is increased by a factor of 5, hence;

W1 = 5(2.45) = 12.25feet

L1 = 5(6.5) = 32.5 feet

Determine the area of the new rectangle

A = 12.25 * 32.5

A = 398.125 square feet

Ratio of the area

A1/A = 398.125/15.925

A1 = 25A

Hence the area of the new rectangle will be 25 times that of the original

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A and B are independent events if the probability of getting a red convertible is 0.08

The given parameters are:

P(A) = 0.20

P(B) = 0.40

The events are independent, if

P(A and B) = P(A) * P(B)

So, we have:

P(A and B) = 0.20 * 0.40

Evaluate

P(A and B) = 0.08

Hence, A and B are independent events if the probability of getting a red convertible is 0.08

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Complete question

A video game randomly chooses your car color and type. The probability of getting a red car is 0.20, and the probability of getting a convertible is 0.40.

Event A = You get a red car.

Event B = You get a convertible.

A and B are independent events if _____.

A.The probability of getting a red car or a convertible is 0.60.

B.The probability of getting a red car or a convertible is 0.08.

C.The probability of getting a red convertible is 0

D.The probability of getting a red convertible is 0.08

The equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.

Slope of the line KL = (8 - 0)/(-6 - 6) = 8/(-12) = -2/3.

Using the formula of the slope of the line passing through the points (x₂, y₂) and (x₁, y₁), as m = (y₂ - y₁)/(x₂ - x₁).

The slope of the line parallel to the line KL will be equal to the slope of KL.

Thus, the slope of the required line is m = -2/3.

The required line also passes through point M (-4, -2).

Thus, the equation of the required line will be,

y - (-2) = (-2/3)(x - (-4)) {Using the equation of the line passing through the point (x₁, y₁) and a slope m, as y - y₁ = m(x - x₁)},

or, y + 2 = (-2/3)(x + 4),

or, 3(y + 2) = -2x - 8,

or, 2x + 3y = -6.

From the given points, only the point (-6, 2) satisfies the equation.

Thus, the equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.

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The provided question is incomplete. The complete question is:

"On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point could be on the line that is parallel to line KL and passes through point M?

(–10, 0)

(–6, 2)

(0, –6)

(8, –10)"

The value is J = 1.71*10^-6 kmol/m^2.s

According to the given conditions we get,

The length the tube l= 0.20m

The diameter of the tube d= 0.01m

The total pressure inside the tube P= 101.32kPa

The partial pressure of CO2 at the first end is

P1= 456mm Hg = 60794.832 Pa

The partial pressure of CO2 at the other end is

P2= 76mm Hg = 10132.472 Pa

The temperature is T = 298 K

The diffusion coefficient D= 1.67* 10^-5 m^2/s

Generally the molar flux of CO2 is mathematically represented as

J= D{p1-p2} / R.T

Here R is the gas constant with value R= 8.314 j/kmol

So we get J= 1.71 * 10^-3 mol/m^2.sec

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The age of the father is 57 years old

Total age = Average age x Population

Average of the four children = 15

Population = 4

Total age of the four children = 15 x 4

Total age of the four children = 60 years

If the parents are added:

Population = 6

Average age = 25

Total age = 25 x 6

Total age = 150 years

Total age of the parents = 150 - 60

Total age of the parents = 110 years

The father is 4 years older than his wife

Let the age of the father be x

The age of the wife = x - 4

x + x - 4 = 110

2x = 114

x = 114/2

x = 57

Therefore, the age of the father is 57 years old

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Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Prime numbers between 20 - 29 = 23 and 29.

There are 2 prime numbers out of these 10.

Therefore,

P(choose prime number) = [tex]\frac{2}{10} \\=\frac{1}{5}[/tex]