a principal data about the distance, in miles that his teachers and bus drivers live from the school, the box plots below show these data. based on the box plots, which statement is true?

The quadratic function f(x) = 2x² - 16x + 24 can be rewritten in the vertex form f(x) = 2(x - 4)² + 4.

Given the function in the question:

f(x) = 2x² - 16x + 24

To determine the vertex form f(x) = a(x-h)² + k, we need to complete the square.

Factor out the leading coefficient of 2:

f(x) = 2x² - 16x + 24

f(x) = 2(x² - 8x + 12)

To complete the square, we need to add and subtract the square of half of the coefficient of x:

f(x) = 2[(x² - 8x + 16) - 4] + 8

Since (x² - 8x + 16) is a perfect square trinomial, we factored as (x - 4)².

f(x) = 2[(x - 4)² - 4] + 8

Now we can simplify and rewrite in the desired form:

f(x) = 2(x - 4)² - 4 + 8

f(x) = 2(x - 4)² + 4

Therefore, the vertex form is f(x) = 2(x - 4)² + 4.

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The standard deviation of the sample mean differences is, 16.98.

Since, We know that;

Standard deviation is defined to be the square root of the population variance of the vector. The sample standard deviation s is defined to the square root of the sample variance of the vector.

Here, The standard deviation of the sample mean differences should be calculated using the standard deviations of the two populations.

In order to see how they differ, we need to first subtract them from each other,

So, we get:

21.2 - 17.6 = 3.6

We then divide this number with the first standard deviation as follows:

⇒ 3.6/21.2 x 100

⇒ 16.98

Therefore, the standard deviation of the sample mean is, 16.98.

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The solution is, Option 4 is correct., the graph represents the following system of inequalities.

Explanation:

We are given two inequality y<-x-4 and y>2x-3.

We need to choose correct graph from given choices.

First we draw the graph of each equation

Equation 1: y<-x-4

We draw the graph using slope intercept form.

Slope=-1 and y-intercept (0,-4)

Test point (0,0). Put (0,0) into equation 1 y<-x-4

We get . This is false statement. Graph will shade away from point (0,0).

Equation 2: y<2x-3

We draw the graph using slope intercept form.

Slope=2 and y-intercept (0,-3)

Take test point (0,0). Put (0,0) into equation 2, y>2x-3

We get . This is true statement. Graph will shade towards the point (0,0).

Please take a look attachment for the graph.

Option 4 is correct.

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complete question:

Which graph represents the following system of inequalities?

y < -x - 4

y > 2x - 3

Answer:

y=-3

Step-by-step explanation:

Answer:

Y = - 3

Step-by-step explanation:

So lets help you out here.....

First of all you should set up how you have to solve, let do this step by step...

Step 1 : 2y + 3y - 18 = - 33

Step 2 : Combine like terms... (2y + 3y = 5y)

Step 3 : Set up your new equation (5y - 18 = - 33)

Step 4 : Subtract negative 18 by negative 33 (- 18 - 33 = -15)

(PS: In a calculator - 18 - 33 is -51 but the 18 is also a negative so it would be - 15)

Step 5 : Divide (- 15 / 5 = - 3)

And that is how you solve this problem, have a great day!!!!!!

The figures that complete the two-way frequency table are attached accordingly.

Let represent the table like this:


                      Chcken       Veggie             Tuna               Total

Seltzer            38                 45                     A                    90
Iced Tea           B                  C                        D                    E
Total                 75                 F                       G                    160

NOte that:

A = 90 - 38 - 45 = 7
B = 75 - 38 = 37
E = 160-90 = 70
C = D + 11
D + 11 + D = 70-37
2D = 33-11
D=22/2

D=11

Thus C = 22
F = 45 + C
F = 45 + 22
F = 22


G = A + D = 18

?thus, the completed two-way frequency table is:


                    Chcken       Veggie             Tuna               Total

Seltzer            38                 45                     7                    90
Iced Tea           B                  22                     11                    70
Total                 75                 67                    18                    160

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The area of the composite figure in this problem is given as follows:

A = 87 ft².

When we want to obtain the area of a composite figure, we must add the areas of all the components of the figure.

The figure in this problem is composed as follows:

The areas are calculated as follows:

Hence the area of the composite figure is given as follows:

A = 10 x 6 + 6 x 3 + 0.5 x 6 x 3

A = 87 ft².

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The probability of dying from heart disease is 0.1667 or 16.67%.

The odds in favor of an event are defined as the ratio of the probability of the event occurring to the probability of the event not occurring. In this case, the odds in favor of dying from heart disease are 1 to 5.

So, we can set up the following equation:

Odds in favor of dying from heart disease = probability of dying / probability of not dying

1/5 = probability of dying / probability of not dying

We can solve for the probability of dying by cross-multiplying:

probability of dying = odds in favor of dying from heart disease / (odds in favor of dying from heart disease + 1)

probability of dying = 1 / (1 + 5)

probability of dying = 1/6

Therefore, the probability of dying from heart disease is 0.1667 or 16.67%.

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1) For the following set of test scores for a history class, 100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40, it would be better for the teacher to consider D) The mean because it is higher and the teacher wants to feel good about the students.

2) The mode of these data about the high temperatures in Orlando for the past 8 days would be 90.

3) The median of these data about the high temperatures in Orlando for the past  8 days would be 80.

The mean, mode, and median are three centers of measurement.

The mean refers to the average value in the data set, obtained as the quotient of the total value divided by the number of items.

The mode refers to the value that occurs most in the data set.

Lastly, the median is the middle value for a data set arranged in descending or ascending order.

1. Test Scores:

100, 45, 60, 60, 50, 50, 45, 95, 60, 55, 40

Total value = 660

Number of data items = 11

Mean = 60 (660 ÷ 11)

Median = 55

Mode = 60

2. High Temperature:

91, 90, 90, 90, 84, 82, 81, 90

Total Value = 698

Number of data items = 8

Mean = (87.25 (698 ÷ 8)

Median = 90

Mode = 90

3. High Temperature:

91, 90, 90, 90, 84, 82, 81,90

Median = 80 (81, 82, 84, 90, 90, 90, 90, 91)

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The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is K -  273.15. Therefore, the correct option is option C.

Temperature is a unit of warmth or coldness that can be defined in the context of any number of arbitrary scales. It indicates the direction through which the energy from heat will naturally flow, i.e., through a hotter (body) to a colder (body) body. Temperature cannot be the same as a thermodynamic system's energy; for instance, a blazing match is significantly hotter than an iceberg.

K = C + 273.15

K - 273.15 = C + 273.15 - 273.15

K -  273.15 = C

Therefore, the correct option is option C.

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Your question is incomplete but most probably your full question was,  

The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15.

When solved for C, the equation is

C = K – 273.15

C = 273.15 – K

C = K + 273.15

C = 273.15K

The probability that at least one of the three users is more careful is 0.936.

We need to find the probability that a single randomly selected Internet user is more careful, which is 0.60.

The probability that none of the three users are more careful is (0.40)^3 = 0.064.

Therefore, the probability that at least one of the three users is more careful is 1 - 0.064 = 0.936.

Rounding to three decimal places, the answer is 0.936.

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Answer:

5y= -3x +15

Step-by-step explanation:

y=mx+c is slope Intercept form where M is slope and c is Intercept

1) The scale factor of dilation is 1/3

2) The orientation is preserved in dilation of A to A'

3) The congruence is not preserved in dilation of A to A'

We know that the scale factor is nothing but the ratio of the size of the transformed image to the size of the original image.

Here from the attached graph we can observe that the square A is transformed to A'

The side length of square A is 18 units and the side length of square A' is 6

So, the scale factor would be,

r = A' / A

r = 6/18

r = 1/3

We know that a dilation preserves the shape and orientation of the figure, but changes the size of he figure.

So, the dilations do not preserve congruence, as it changes the size of a figure.

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Answer:

Step-by-step explanation:

hello :

let : x ,x+1 ,x+2   three consecutive integers

x +x+1 +x+2 = 108

3x =105

x = 105/3

x = 35

35  ,  36  , 37

The equation with the following y-intercepts are matched

a) c ⁢ x + b ⁢ y = a: (0, a/b)

b) c ⁢ x + a ⁢ y = b: (0, b/a)

c) b ⁢ x + a ⁢ y = c: (0, c/a)

d) a ⁢ x + b ⁢ y = c: (0, c/b)

Given data ,

Let the set of equations be represented by

c ⁢ x + b ⁢ y = a

c ⁢ x + a ⁢ y = b

b ⁢ x + a ⁢ y = c

a ⁢ x + b ⁢ y = c

Now , the y-intercept of the equation is when the value of x = 0

So , when x = 0

The y intercepts of the equation are

c ⁢ x + b ⁢ y = a: (0, a/b)

c ⁢ x + a ⁢ y = b: (0, b/a)

b ⁢ x + a ⁢ y = c: (0, c/a)

a ⁢ x + b ⁢ y = c: (0, c/b)

Hence , the equations are solved

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- To answer a question about a sale transaction on rental property that closes on December 16, you need to calculate how much rent the landlord owes to the buyer for the remaining days of December.

- You can use a formula called prorated rent to calculate the amount of rent that is proportional to the number of days that the buyer owns the property. Prorated rent splits the amount between the previous and new owners of a rental property.

- The formula for prorated rent is: Prorated Rent = (Monthly Rent / Number of Days in Month) x Number of Days Rent Owed

- In your case, the monthly rent is $713, the number of days in December is 31, and the number of days rent owed is 16 (from December 16 to December 31). The closing day is the buyer's, so the landlord owes rent for that day as well.

- Plugging these values into the formula, you get: Prorated Rent = (713 / 31) x 16 = 368.26

- This means that the landlord owes $368.26 to the buyer for the remaining days of December.

I hope this helps you answer your question.

Answer: The jar that would experience the greatest pressure is Jar D.

This is because the pressure of a gas is directly proportional to its temperature (according to the ideal gas law). Since all four jars have the same number of gas molecules, the jar with the highest temperature (Jar D) would have the greatest pressure.

Step-by-step explanation:

Answer:

-21

Step-by-step explanation:

4×(-4)+35÷(-7)

Plus and minus together makes minus

Multiplication and division goes first

-16-5= - 21

The probability that they are the 2 oldest people in the group is 0.011

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.

The probability of an event A is denoted by P(A)

From the question above, let us calculate the probability.

The probability that the first person selected is the oldest is 1/10.

Then, the probability that the second person selected is the second oldest is 1/9, since there are only 9 people left to choose from.

Therefore, the probability of selecting the two oldest people in the group is:

1/10 * 1/9 = 1/90

So, the probability of selecting the two oldest people in the group is 1/90 or approximately 0.011 or 1.1%.

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1/7 square units make up the entire area under the curve from x = 7 to infinity.

To find the area under the curve [tex]y = x^{-2}[/tex] from x = 7 to x = t, we can integrate the function with respect to x:

[tex]\int\limits^7_t x^{(-2)} dx = [-x^{(-1)}] = [-1/t + 1/7][/tex]

To evaluate this expression for t = 10 and t = 100, we substitute these values:

[-1/10 + 1/7] = 0.0428 (rounded to four decimal places)

[-1/100 + 1/7] = 0.1328 (rounded to four decimal places)

To find the total area under the curve from x = 7 to infinity, we can integrate the function with respect to x from 7 to infinity:

[tex]\int\limits^7_t {x} x^{(-2)} dx \\= [-x^{(-1)}] \\= [0 - (-1/7)] \\= 1/7[/tex]

Therefore, the total area under the curve from x = 7 to infinity is 1/7 square units.

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The angles in the triangle are;

A = 26.67°, B = 29.06°, C = 124.27°

We know that we have the triangle as ΔABC  and a-13.9, b-15.2, c-25.7

Using the Cosine rule;

a^2 = b^2 + c^2 - 2ac CosA

(13.9)^2 = (15.2)^2 + (25.7)^2 - 2(15.2 * 25.7)Cos A

193.21 = 891.35 - 781.28CosA

193.21 -  891.35 =  - 781.28CosA

Cos A = 193.21 -  891.35 /  - 781.28

A = Cos-1 (193.21 -  891.35 /  - 781.28)

A = 26.67°

Then;

c^2 = a^2 + b^2 - 2abCosC

(25.7)^2 = (13.9)^2 + (15.2)^2- 2(13.8 * 15.2)CosC

660.49 = 424.25 - 419.52CosC

660.49 -  424.25 = - 419.52CosC

C= Cos-1 (660.49 -  424.25 / - 419.52)

C = 124.27°

Then B;

180 - ( 26.67° + 124.27°)

= 29.06°

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The quotient of the expressions 99 m² n³-81m³n²-18mn and 3mn is 33mn² - 27m²n - 6

From the question, we have the following parameters that can be used in our computation:

99 m² n³-81m³n²-18mn

__________________

3mn

To find the quotient of the expressions, we simply divide each term of the numerator by 3mn

Using the above as a guide, we have the following:

99 m² n³-81m³n²-18mn

__________________      = 33mn² - 27m²n - 6

3mn

Hence, the solution is 33mn² - 27m²n - 6

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Answer:

x= -18

Step-by-step explanation:

-2/3x + -21/4 = 27/4

-8x-63=81

-8x-63+63=81+63

-8x=144

-8x/-8 = 144/-8

x=-18

The diameter of the circle is 396 units.

The length of the arc is 0.83π units.  

The length of an arc of a circle is given by the formula:

L = θ/360 * πd

where θ is the measure of the angle and is the diameter of the circle

Given: θ = 80° and L = 88π

L = θ/360 * πd

88π = 80/360 * π * d

88 = 80/360 * d

80 * d = 88 * 360

80d = 31680

80d = 31680/80

d = 396 units

PART 2

If  θ = 25°, r = 6 (from the image above). Thus, d = 2 * 6 = 12

L = θ/360 * πd

L = 25/360 * π * 12

L = 0.83π units

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a) The number of ways that four people can be selected from this group of fifteen is: 1365 ways

b) The number of ways that four Republicans can be selected from the eight Republicans is: 70 ways

c) The probability that the selected group will consist of all republicans is: 5.13%

The selection of people from a given list can be done in the following way: if we want to select r people from a list of n people, then we can do so in:

nCr = n!/(r!(n - r)!)

In the first part of the question, we don't need to decide on specific people from each group, but in the subsequent parts, it becomes an added restriction.

A. This can be done in:

15C4 = 15!/(4!(15 -4!)

= 1365 ways

B. This can be done in:

8C4 = 8!/(4!(8 - 4)!)

= 70 ways

C. The chances that all are republicans is a measure of the ratio of the answer in the first question to the second:

70/1365 = 0.0513 = 5.13%

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Trapezium T is reflected across line x = 3 to form trapezium U and reflected across line x = 7 to form tralpelzium V

The figure is attached

Reflection across a line is a geometric transformation which mirrors a point, shape or figure exactly across a pre-defined plane known as the Line of Reflection.

In other words, the size and general outline are kept in tact while orientations are adjusted. Furthermore, each corresponding point on either side of the Line of Reflection is found to be equidistant from the said axis and lies along a perpendicular line.

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The area of the entire space is 38.57 units².

We have,

From the figure,

Total area.

= Semicircle + Rectangle + Trapezium + Rectangle

Now,

Semicircle:

Radius = 2 units

Rectangle:

Length = 4 units

Width = 3 units

Trapezium:

Parallel sides = 5 units and 3 units

Height = 1 unit

Rectangle:

Length = 2 units

Width = 5 units

Now,

Area of the entire space.

= πr² + 4 x 3 + 1/2 x 1 x (5 + 3) + 2 x 5

= 22/7 x 2 x 2 + 12 + 1/2 x 1 x 8 + 10
= 88/7 + 12 + 4 + 10

= 12.57 + 12 + 4 + 10

= 12.57 + 26

= 38.57 units²

Now,

1 unit = 7 feet

So,

= 38.57 X 7² feet²

= 1889.93 feet²

Thus,

The area of the entire space is 38.57 units².

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Answer:

Since f is increasing over its domain, we know that if a > b, then f(a) > f(b). Therefore, we have:

2x + 3 > 3x - 2

Solving for x, we get:

x < 5

So the solution set is:

Df = [3, infinity) intersect (-infinity, 5) = [3, 5)

Therefore, the inequality is true for all x in the interval [3, 5).

Since f is increasing over its domain, we know that if a > b, then f(a) > f(b). Therefore, we have:

x^2 - 2 < y^2 - 2

Simplifying, we get:

x^2 < y^2

Taking the square root of both sides, we get:

|x| < |y|

So the solution set is:

Df = [3, infinity)

|x| < |y| means that either x < y or -x < y. Therefore, the solution set can be divided into two parts:

Part 1: x^2 - 2 < 0, i.e., x is in the interval (-sqrt(2), sqrt(2)). For this part, we have:

Df intersect (-sqrt(2), sqrt(2)) = empty set

Part 2: x^2 - 2 >= 0, i.e., x is outside the interval (-sqrt(2), sqrt(2)). For this part, we have:

Df intersect (-infinity, -sqrt(2)] union [sqrt(2), infinity) = [3, infinity)

Therefore, the inequality is true for all x in the interval [3, infinity) except for the interval (-sqrt(2), sqrt(2)).

Step-by-step explanation:

Answer:

$7000

Step-by-step explanation:

For simple interest,

I = Prt,

where I = amount of interest earned

P = principal amount, the amount of the investment

r = annual interest rate (convert percent to decimal for calculations)

t = time (number of years)

I = Prt

We know I, r, and t, and we need to solve for P.

1120 = P × 4% × 4

Convert percent to decimal.

1120 = P × 0.04 × 4

Multiply on the right side.

1120 = 0.16P

Divide both sides by 0.16

7000 = P

Answer: $7000