−13,9,9,−13,5,−13,9


Calculate the value of the sample standard deviation. Round your answer to one decimal place.

The variance and standard deviation for the given frequency of pupils per teacher in some states of US is

Variance= 4.62 = 4.6

Standard Deviation = 2.14 = 2.1

The frequency distribution shows the average number of pupils per teacher in some states of the United States.

Variance(σ²) is a measure of dispersion. A measure of dispersion is a quantity that is used to check the variability of data about an average value. Data can be of two types - grouped and ungrouped. When data is expressed in the form of class intervals it is known as grouped data. On the other hand, if data consists of individual data points, it is called ungrouped data. The sample and population variance can be determined for both kinds of data.

The standard deviation(σ) of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.

That means Standard Deviation = √variance.

For the given data the sum of frequencies(ni) = 1+16+11+7+1+2= 38.

Midpoint(mi) is 12,15,18,21,24,27.

ni * mi = 12,240,198,147,24,54.

Sum of ni * mi = 675.

Mean (u) =  17.76

mi - u    is -5.76,-2.76,0.24,3.24,6.24,9.24.

(mi - u)^2 is 33.17,7.61,0.057,10.49,38.93,85.37.

Sum of (mi - u)^2 = 175.62.

Variance = Sum of (mi - u)^2 / sum of frequencies

=> 175.62/38

=> 4.62 = 4.6.

Standard deviation = √variance.

=> √4.62

=> 2.14 = 2.1.

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The simplification of the expression 20(6) - 7 using the laws of equation gives 113

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

20(6) - 7

Firstly, solve the equation inside the bracket to get:

120 - 7

Taking the difference of the two terms gives:

113

The simplification of the expression 20(6) - 7 using the laws of equation gives 113

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Answer:

For 12a - 37 > 0 answer is   a > 37/12

For 6a ≤ 42 answer is a ≤ 7

Step-by-step explanation:

The domain and the range of the graph in interval notation are (-∝, ∝) and [-3, ∝) respectively

The domain of the function is the set of input values of the graph while the range of a function is the set of output values of the graph.

The graph represents the given parameter

Based on the definition above, the range of a function is the set of y values of the graph while the domain is the set of x values of the graph

On the graph, we can see that:

The x values extend indefinitely on the graph;

This means that the domain is (-∝, ∝)

While y values start from -3 and increases up

This means that the range is [-3, ∝)

Hence, the domain and the range of the function in interval notation are (-∝, ∝) and [-3, ∝) respectively

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The perimeter of the walkway in terms of y will be y = 50 + 8x. The slope will be 8.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

Given that the length and width of a rectangular garden are 15 meters and 10 meters, respectively. A walkway of width x surrounds the garden.

The perimeter will be calculated as:-

Perimeter = 2 ( W + L )

Perimeter = 2 [ ( 15 + 2x ) + ( 10 + 2x ) ]

Perimeter = 2 ( 10 + 2x + 15 + 2x )

Perimeter  = 2 ( 25 + 4x )

y = 50 + 8x

Compare the equation with the general form of the equation:-

y = 50 + 8x

y = mx + c

Slope = 8

Therefore, the perimeter of the walkway in terms of y will be y = 50 + 8x. The slope will be 8.

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The value of f(x) when x equals -5 is 15. Option D

A function can be defined as an expression, law or rule that explains the relationship between two variables;

Given the function;

f(x) = 5x + 40

To determine the value of the function when x = - 5, we have to substitute the value of x as -5 in the function.

With this, we have;

f(-5) = 5(-5) + 40

Now, expand the bracket

f(-5) = -25 + 40

Add the values, we have;

f(-5) = 15

We can see that the value of the function with the input of the variable x as -5 is 15

Thus, the value of f(x) when x equals -5 is 15. Option D

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Answer:

Step-by-step explanation:

x + 139 + 37 + 53 = 360

              x + 229 = 360

                       x = 360-229

                       x = 131 degrees

The solution of the system of equations are x = 7 and y = 77

Given data

y = 9x + 14

y = 6x + 35

solving using substitution method to solve the simultaneous equation we have

y = 9x + 14  equation 1

y = 6x + 35  equation 2

equating the both equations will give

9x + 14  = 6x + 35

9x - 6x = 35 - 14

3x = 21

x = 7

plugging x = 7 into equation 1

y = 9x + 14

y = 9 * 7 + 14

y = 63 + 14

y = 77

The solution of the system of equations are x = 7 and y = 77

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Answer:

If it takes one minute to use 5.7 calories, it’ll take 190/5.7 minutes to use 190 calories. This simplifies to 100/3 minutes. So this person must walk for 33 minutes and 20 seconds to use 190 calories (assuming the rate of calorie usage remains constant throughout).

Step-by-step explanation:

3xy² - x²

x = 2, y = 3

well, we simply replace every variable in the expression by the actual value and calculate.

3×2×3² - 2² = 6×9 - 4 = 54 - 4 = 50

Answer:

Step-by-step explanation:  You could try to times 15 by each side or add them or turn it into an expression like E*15=0

The appropriate way to calculate the monthly rent over time is 1190 × 1.017^n.

From the information, it was stated that the monthly rent for the first house is $1,190, and the Bainters can expect it to increase 1.7% every year and that the Bainters want to calculate their monthly rent over time.

Therefore, the appropriate expression will be:

= 1190 × (1 + 1.7%)^n

where n = number of years

= 1190 × 1.017^n

Therefore, the appropriate way to calculate the monthly rent over time is 1190 × 1.017^n.

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The solution to the linear equation is v = -36

Here we have a simple linear equation:

v/3 + 3 = v/4

To solve this, we need to isolate the variable v.

First, let's move all the terms with "v" to the left and the terms without to the right side, so we get:

v/3 - v/4 = -3

Now we can solve this:

4v/12 - 3v/12 = -3

v/12 = -3

v = -3*12

v = -36

The solution to the linear equation is v = -36

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Answer: D

Step-by-step explanation: It said the grandparents were less than 89 years old, if it said that the grandparents that were 89 and younger had remembered that's when you would use a solid circle because the 89 would be included. But since 89 isn't included then it's an open circle.

The probability that Nacho will get all 4 questions wrong will be 0.3164.

From the information, Nacho takes a multiple choice test, the test has 4 questions and each question has 4 choices.

The probability of getting the correct option is 1 out of 4 which is 0.25 and the incorrect option is 0.75.

Therefore, the probability that Nacho will get all 4 questions wrong will be:

= (0.75)⁴

= 0.3164

Therefore, the probability that Nacho will get all 4 questions wrong will be 0.3164.

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The transforming the winner's age to a z-score is 1.03 and z-score is below the mean age of the winners.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Mean = (Sum of all the observations/Total number of observations).

Given:

Population mean,

μ=27.7 years

Population standard deviation,

σ=3.2 years

Winner's age =31 years

According to given question we have

If "x" represents the age of the winner then the z-score for "x":

z=x−μ/σ

a) Transforming the winner's age to a z-score

 z=31−27.7/3.2

   =1.03

(b) Interpretation of the z-score:

The winner's age of 31 years is 1.03 standard deviation below the mean age of the winners.

Therefore, the transforming the winner's age to a z-score is 1.03 and z-score is below the mean age of the winners.

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To find the

a) Transforming the winner's age to a z-score

(b) Interpretation of the z-score

is missing

Answer:8977/1000

Step-by-step explanation:

The value of 8.977 as a ratio of two integers would be equal to 8977/1000  

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We need to Write 8.977 as a ratio of two integers.

We know that negative divided by a negative is positive, then;

8.977 can be written as;

8977/1000

Therefore, The value of 8.977 as a ratio of two integers can be written as

8977/1000

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Answer: 1. -4<n<4

2. n<-3 or n>19

3. n<=-36 or n>=44

Step-by-step explanation:

n=number

units from a number is measured using absolute value sign

1. 4 units from 0: |n-0|<4 ==> |n|<4

n<4, n>-4 ==> -4<n<4

2. 11 units from 8: |n-8|>11

n-8>11

n-8+8>11+8

n>19

n-8<-11

n-8+8<-11+8

n<-3

n<-3 or n>19

3. half a number is at 2 units from 20:  |n/2-2|>=20

n/2-2>=20

n/2>=22

n>=44

n/2-2<=-20

n/2<=-18

n<=-36

n<=-36 or n>=44

The area is 108yd2(square yards).

In the given triangle a base

24yd and the corresponding height of 6 yds are given, so to calculate the area we can use:

A=12×b×h

If we substitute the given numbers we get:

A=[tex]\frac{1}{2}[/tex]×24×18

=12×9

=108

The units of base and height are the same (yards), so the calculated area is in yd2

The area is the quantity that expresses the extent of a region on the plane or on a curved surface. the world of a plane region or plane area refers to the area of a shape or planar lamina, while area refers to the area of an open surface or the boundary of a three-dimensional object. The area is often understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the quantity of paint necessary to cover the surface with a single coat. it's the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).

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Answer:

12.87

Step-by-step explanation:

Since we know that line CD is a perpendicular bisector, triangle ACD is a right triangle, and thus we can apply the Pythagorean theorem to determine the length of side CD. Since the Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the adjacent sides, we can plug in the values of side AD and AC.

As side CD is the bisector of side AB, sides AD and DB are both half the length of side AB, so:
AD = 11/2
AD = 5.5

We now know two values of our equation, and thus we can solve for the missing third value.

5.5^2 + b^2 = 14^2
14^2 - 5.5^2 = b^2
196 - 30.25 = b^2
165.75 = b^2
[tex]\sqrt{165.75} = b[/tex]
b = 12.87

Answer:

(9p^4+10)(9p^4−10)

Answer:

s = √77

it is not rational since 77 not a perfect square

Step-by-step explanation:

area = s^2 = s * s = 77

==> s = √77

We use Integers in everyday life when we solve real-world problems.

Let’s understand a real-life problem using integers.

Christian borrowed $1000 to buy a computer. After some time, she has paid back $250. How much does Christian still owe?

First, we will write a simple equation to represent the problem.

Let the amount that Christian still owes = 'x'

1000 = 250 + x

Now, we will rearrange the equation to isolate .

Then, solve for x.

The answer is 750.

Christian still owes = $750.

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Answer:

6.505

Step-by-step explanation:

[tex]\frac{7}8}[/tex]  Put in your calculator 7 ÷ 8 and you will get .875  

So, 10 [tex]\frac{7}{8}[/tex] is 10.875  now subtract this from 4.37.  You can line up the decimals and then subtract or just have the calculator do this for you, if you are allowed.

10.875 - 4.37 = 6.505

Answer:

[tex]\frac{\pi r^2}{2}[/tex]

Step-by-step explanation:

The area of a semicircle is half the area of a circle

The area of a circle is [tex]\pi r^2[/tex], where r is the radius of the circle, and [tex]\pi[/tex] is a mathematical constant, approximately 3.14. The area of the semicircle is half the area of the circle, or [tex]\frac{\pi r^2}{2}[/tex].

The rule for the cost function c(x) that gives the total daily cost of producing x bags of pretzels will be 1200 + 0.4x

b. The revenue function will be 1.80x.

c. The profit function p(x) is 1.4x - 1200.

It should be noted that fixed cost = 1200

Also, it costs 40 cents to produce each bag of pretzels. Therefore, the cost function will be:

= 1200 + 0.4(x)

= 1200 + 0.4x

The revenue function will be:

= Price × Quantity

= 1.80 × x

= 1.8x

c. The profit function p(x) will be:

= Revenue - Cost

= 1.8x - 1200 + 0.4x

= 1.4x - 1200

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Answer:

A. You can write the number as a Ratio of two entegers

D. You know what the next number is