What is the location of the point on the number line that is of the way from
A= -4 to B= 17?
A. 3
B. 7
C. 9
OD. 5

The correct matches are:

-1: 0

-2: 0

X: 14/3

0: 0

6: Not used

= 2² + 2x - 5: Not used

To match the representations with their respective average rates of change, we need to calculate the average rate of change for each function over the interval (0, 3) and compare it to the given values.

Let's calculate the average rate of change for each function:

Function: 2² + 2x - 5

To find the average rate of change, we need to calculate the difference in function values divided by the difference in x-values:

Average rate of change = (f(3) - f(0)) / (3 - 0)

Average rate of change = ((2² + 2(3) - 5) - (2² + 2(0) - 5)) / 3

Average rate of change = (13 - (-1)) / 3

Average rate of change = 14 / 3

Match: X = 14/3

Function: -1

Since the function is constant, the average rate of change is 0.

Match: 0

Function: 2

Since the function is constant, the average rate of change is 0.

Match: 0

Function: 3

Since the function is constant, the average rate of change is 0.

Match: 0

Function: -2

Since the function is constant, the average rate of change is 0.

Match: 0

Function: -3

Since the function is constant, the average rate of change is 0.

Match: 0

Therefore, the correct matches are:

-1: 0

-2: 0

X: 14/3

0: 0

6: Not used

= 2² + 2x - 5: Not used

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When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

The statement "There is one outlier, indicating an abnormally large number of books were checked out on that day" is true based on the data set.

To determine if there are any outliers in the given data set of the number of books checked out from a library during the first two weeks of the month, we can examine the values and look for extreme values that deviate significantly from the rest of the data.

The data set is as follows:

19, 10, 15, 99, 12, 18, 15, 16, 12, 13, 18, 17, 19, 13

To identify outliers, we can use different methods, such as the interquartile range (IQR) or z-scores. Let's calculate the IQR to determine if there are any outliers:

Arrange the data set in ascending order:

10, 12, 12, 13, 13, 15, 15, 16, 17, 18, 18, 19, 19, 99

Calculate the first quartile (Q1) and third quartile (Q3):

Q1 = 13 (median of the lower half)

Q3 = 18 (median of the upper half)

Calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 18 - 13 = 5

Define the lower and upper boundaries for outliers:

Lower bound = Q1 - 1.5 * IQR = 13 - 1.5 * 5 = 5.5

Upper bound = Q3 + 1.5 * IQR = 18 + 1.5 * 5 = 25.5

Based on these calculations, any value below 5.5 or above 25.5 would be considered an outlier.

Looking at the data set, we can see that there is indeed one outlier, which is the value 99. It is significantly larger than the rest of the values and falls above the upper bound.

Therefore, the statement "There is one outlier, indicating an abnormally large number of books were checked out on that day" is true based on the data set.

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The graph of the solution to the inequality is attached as image to this answer.

The piece-wise defined function h(x) represents different values of y (the output) depending on the value of x (the input). Each interval of x has a different value assigned to it.

In this particular case, the inequality statements define the intervals for x and their corresponding output values.

Let's break it down:

- For values of x that are greater than -3 and less than or equal to -2, h(x) is assigned the value of -1.

- For values of x that are greater than -2 and less than or equal to -1, h(x) is assigned the value of 0.

- For values of x that are greater than -1 and less than or equal to 0, h(x) is assigned the value of 1.

- For values of x that are greater than 0 and less than or equal to 1, h(x) is assigned the value of 2.

Any values of x outside of these intervals are not defined in this piece-wise function and are typically represented as "not a number" (NaN).

For example, if you were to evaluate h(-2.5), it falls within the first interval (-3 < x ≤ -2), so h(-2.5) would be equal to -1. Similarly, if you were to evaluate h(0.5), it falls within the fourth interval (0 < x ≤ 1), so h(0.5) would be equal to 2.

The graph of the piece-wise function h(x) consists of horizontal line segments connecting the specified values of y for each interval, resulting in a step-like pattern.

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The units of each product that Cane should produce to maximize profits will be 62000 units of Beta and 7600 units of

Alpha.

               Alpha Beta

Selling price 130 90

Variable cost 78 48

Contribution margin 52 42

Pound per unit 5 2

Contribution margin per pound 10.4 21

                      Pound                   Unit

Beta 62000*2 = 124000 62000

Alpha 38000 38000/5 = 7600

Total 162000

Maximum contribution margin = (38000*10.4+124000*21) = 2999200

Highest price = 10.4+5 = 15.40 per pound

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The simplified form of the expression 1200 × 1260 ÷ 800 in standard form is 1890.

To simplify the given expression, we perform the multiplication and division operations according to the order of operations (PEMDAS/BODMAS).

First, we perform the multiplication: 1200 × 1260 = 1,512,000.

Next, we perform the division: 1,512,000 ÷ 800 = 1890.

The result, 1890, is in standard form.

In standard form, a number is expressed as a product of a number between 1 and 10 (inclusive) and a power of 10. In this case, 1890 is already in the appropriate format and does not require any further modification.

Therefore, the simplified form of the expression 1200 × 1260 ÷ 800 is 1890 in standard form.

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Answer:

19, 14, 38

Step-by-step explanation:

Let x, y, and z be each number respectively:

[tex]x+y+z=71\\z=2x\\y=x-5\\\\x+y+z=71\\x+(x-5)+2x=71\\2x-5+2x=71\\4x-5=71\\4x=76\\x=19\\\\y=x-5\\y=19-5\\y=14\\\\z=2x\\z=2(19)\\z=38[/tex]

Therefore, the three numbers are 19, 14, and 38.

Answer:

n = -1/8

Step-by-step explanation:

n + 3/4 = 5/8

n = 5/8 - 3/4

n = 5/8 - 6/8

n = -1/8

So, n = -1/8

Answer$535.50

Step-by-step explanation:

15% is equal to .15

So, multiply 600.00x .15=90

                   600.00 - 90.0=510.
                   510. 00x .05=25.50

                   510.00+25.50=535.50

                   Your answer is $535.5

The line of reflection for the image of triangle DEF is the y-axis.

To determine the line of reflection for the image of triangle DEF, we need to find the axis along which the reflection occurred. We can do this by examining the coordinates of the corresponding points before and after the reflection.

Given that D' is located at (3, 5) after the reflection, we can compare the x-coordinates of D and D'. The x-coordinate of D is -3, and the x-coordinate of D' is 3. We notice that there is a change in sign, indicating a reflection across the y-axis.

Therefore, the line of reflection for the image of triangle DEF is the y-axis.

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Answer:

Midpoint = (-1, -1/2)

Step-by-step explanation:

We can find the midpoint using the midpoint formula which is given by:

M = (x1 + x2) / 2, (y1 + y2) / 2, where

Thus, we can plug in (-9, -1) for (x1, y1) point and (7, 0) for (x2, y2) in the midpoint formula:

M = (-9 + 7) / 2, (-1 + 0) / 2

M = (-2) / 2, (-1) / 2

M = -1, -1/2

Thus, (-1, -1/2) is the midpoint of the line segment with endpoints (-9, -1) and (7, 0).

Answer:

h(x) = -x - 4

Step-by-step explanation:

Given:

f(x) = 8x - 2

g(x) = 9x + 2

Substituting these values into the equation h(x) = f(x) - g(x)

h(x) = (8x - 2) - (9x + 2)

Simplify

h(x) = 8x - 2 - 9x - 2

Combining like terms

h(x) = (8x - 9x) - (2 + 2)

h(x) = -x - 4

Hope this helps.

The measure of center that the student should give to their teacher is the median.

In statistics, the median is a measure of central tendency that represents the middle value in a dataset when it is ordered from least to greatest. It divides the dataset into two equal halves, where half the values are smaller than the median and half are larger.

The median is useful because it is not influenced by extreme values or outliers in the dataset, unlike the mean (average). It provides a representative value that indicates the central position of the data.

The median is a better measure of center in this case since the data is skewed. The value of median is not affected by skewness

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The period of the function in this problem is given as follows:

5 units.

A periodic function is a function that has the behavior repeating over intervals in the domain of the function.

Then the period of the function has the concept defined as the difference between two points in which the function has the same behavior.

Two consecutive peaks of the graph of the function in this problem are given as follows:

Input of 1 and input of 6.

Hence the period of the function is given as follows:

6 - 1 = 5 units.

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Answer:

the two numbers are 20 and 1.

Answer:

tourist: 28%

non-tourist: 72%

Step-by-step explanation:

total: 50

tourists: 14

non-tourists:50 - 14 = 36

tourist percentage: 14/50 × 100% = 28%

non-tourist percentage: 36/50 × 100 = 72%

The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.

The sequence is defined by the following formula:
a1 = 1, a2 = 3,
and
an = (-1)nan - 1 + an - 2 for n ≥ 3.
To find the third term (a3), we substitute n = 3 into the formula:
a3 = (-1)(3)(a3 - 1) + a3 - 2.
Next, we simplify the equation:
a3 = -3(a2) + a1.
Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:
a3 = -3(3) + 1.
Simplifying further:
a3 = -9 + 1.
Therefore, the third term (a3) is equal to -8.
To find the fourth term (a4), we substitute n = 4 into the formula:
a4 = (-1)(4)(a4 - 1) + a4 - 2.
Simplifying the equation:
a4 = -4(a3) + a2.
Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:
a4 = -4(-8) + 3.
Simplifying further:
a4 = 32 + 3.
Therefore, the fourth term (a4) is equal to 35.
To find the fifth term (a5), we substitute n = 5 into the formula:
a5 = (-1)(5)(a5 - 1) + a5 - 2.

Simplifying the equation:
a5 = -5(a4) + a3.
Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:
a5 = -5(35) + (-8).
Simplifying further:
a5 = -175 - 8.
Therefore, the fifth term (a5) is equal to -183.
In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.

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Answer:

The equation of this line is y = -4.

Answer:

y=-4

Step-by-step explanation:

zero slope m=0

y-y1=m(x-x1)

y-(-4)=0(x-(-9))

y+4=0

y=-4

The midpoint of AB is M(1,2). If the coordinates of A are (8,-4), The coordinates of point B are (-6, 8).

To find the coordinates of point B, we can use the midpoint formula, which states that the midpoint between two points (x₁, y₁) and (x₂, y₂) is given by:

Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

We are given the midpoint M(1, 2) and the coordinates of point A (8, -4). Let's denote the coordinates of point B as (x, y).

Using the midpoint formula, we can set up the following equations:

1 = (8 + x) / 2 (equation 1)

2 = (-4 + y) / 2 (equation 2)

Let's solve these equations to find the values of x and y.

From equation 1:

2 = 8 + x

x = 2 - 8

x = -6

From equation 2:

4 = -4 + y

y = 4 + 4

y = 8

Therefore, the coordinates of point B are (-6, 8).

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Answer:

B = (-6, 8)

Step-by-step explanation:

To find the coordinates of B, given the coordinates of A and the coordinates of the midpoint of AB, use the Midpoint formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint formula}\\\\$M(x,y)=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]

Let A = (x₁, y₁) = (8, -4)

Let B = (x₂, y₂)

Given M is (1, 2), substitute the points into the midpoint formula:

[tex](1,2)=\left(\dfrac{x_2+8}{2},\dfrac{y_2-4}{2}\right)[/tex]

[tex](1,2)=\left(\dfrac{x_2}{2}+4,\dfrac{y_2}{2}-2\right)[/tex]

Equate the x-coordinates and solve for x₂:

[tex]\begin{aligned}1&=\dfrac{x_2}{2}+4\\\\1-4&=\dfrac{x_2}{2}+4-4\\\\-3&=\dfrac{x_2}{2}\\\\-3\cdot 2&=\dfrac{x_2}{2}\cdot 2\\\\-6&=x_2\\\\x_2&=-6\end{aligned}[/tex]

Equate the y-coordinates and solve for y₂:

[tex]\begin{aligned}2&=\dfrac{y_2}{2}-2\\\\2+2&=\dfrac{y_2}{2}-2+2\\\\4&=\dfrac{y_2}{2}\\\\4\cdot 2&=\dfrac{y_2}{2}\cdot 2\\\\8&=y_2\\\\y_2&=8\end{aligned}[/tex]

Therefore, the coordinates of B are (-6, 8).

The value of x, representing the length of the hypotenuse AC, is 3√2 units.

In a right triangle ABC, with angle ABC measuring 45 degrees and side AB having a length of 3 units, we can use trigonometric ratios to find the length of the hypotenuse AC, represented by x.

Since angle ABC is 45 degrees, we know that it is a special right triangle, specifically a 45-45-90 triangle.

In such a triangle, the lengths of the sides are in a specific ratio: 1:1:√2.

In this case, side AB is 3 units, which represents the length of one of the legs. By the ratio mentioned earlier, the hypotenuse AC (x) will be √2 times the length of AB.

Therefore, we have:

AC = AB [tex]\times[/tex] √2

AC = 3 [tex]\times[/tex] √2

AC = 3√2 units

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In the class , each child needs to pay (n * p) / y shillings to cover the cost of the lost books.

In the given scenario, there is a class of "y" children, and "n" mathematics books were lost, each costing "p" shillings. The teacher decides to distribute the cost of the lost books equally among all the children.

To find out how much money each child needs to pay, we need to divide the total cost of the lost books by the number of children in the class.

The total cost of the lost books can be calculated by multiplying the number of lost books ("n") by the cost of each book ("p").

Total cost = n * p

To distribute the cost equally among all the children, we divide the total cost by the number of children ("y"):

Cost per child = Total cost / Number of children

Substituting the values, we get:

Cost per child = (n * p) / y

Therefore, each child in the class needs to pay (n * p) / y shillings to cover the cost of the lost books.

It's important to note that this calculation assumes that the total cost is evenly distributed among all the children, regardless of whether they were responsible for losing the books or not.

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Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

[tex]{\implies 0.5x + 0.1(70) = 0.4(70 + x)}[/tex]

Simplifying the equation:

[tex]\qquad\implies 0.5x + 7 = 28 + 0.4x[/tex]

[tex]\qquad\quad\implies 0.1x = 21[/tex]

[tex]\qquad\qquad\implies \bold{x = 210}[/tex]

[tex]\therefore[/tex] We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]

Answer:

C. (n+5)(n-5)

Step-by-step explanation:

Select the expression that is equivalent to (n²-25)

Let's check each option. A and B are wrong, so we only check C & D.

C. (n + 5) (n - 5)

n² - 5n + 5n - 25

n² - 25

D. (n - 5)²

(n - 5) (n - 5)

n² - 5n - 5n + 25

n² - 10n + 25

So, the correct answer is C. (n+5)(n-5)

The critical value tₕ for a confidence level of 0.99 and a sample size of 22 is approximately 2.831.

To find the critical value tₕ for a given confidence level and sample size, we can use a t-distribution table or a statistical software.

For a confidence level of 0.99, we need to determine the critical value tₕ such that the area under the t-distribution curve to the right of tₕ is equal to (1 - c) / 2. In this case, (1 - c) / 2 = (1 - 0.99) / 2 = 0.005.

Since the sample size is 22, we have n - 1 degrees of freedom, which is 22 - 1 = 21. We need to find the critical value tₕ with 21 degrees of freedom that corresponds to an area of 0.005 in the upper tail of the t-distribution.

Using a t-distribution table or a statistical software, we find that the critical value tₕ is approximately 2.831.

Therefore, the critical value tₕ for a confidence level of 0.99 and a sample size of 22 is approximately 2.831.

It is important to note that the critical value may vary slightly depending on the specific t-distribution table or statistical software used. However, the value obtained above is a reasonable approximation based on commonly used tables or software.

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The statement "1 is NOT in the domain" is true because for the function f(x), the expression x - 7 results in division by zero when x equals 1, which makes 1 not a valid input for the function.

To determine if a value is in the domain of a function, we need to consider any restrictions or limitations on the input values.

For the function f(x) = √(x - 7), the square root function is defined only for non-negative values.

Therefore, the expression (x - 7) inside the square root must be greater than or equal to zero. In other words, x - 7 ≥ 0.

Solving this inequality, we find x ≥ 7.

This means that any value of x that is greater than or equal to 7 is in the domain of f(x).

However, the statement is asking specifically about the value 1.

Since 1 is less than 7, it does not satisfy the inequality x ≥ 7 and is therefore not in the domain of f(x).

Similarly, for the function g(x) = 4x - 8, there are no restrictions on the domain.

Any real number can be substituted into the function, including the value 1.

Therefore, the statement "1 isn't in the domain of f(0) g" is not accurate.

It is true that 1 is not in the domain of f(x), but it is in the domain of g(x).

In summary, the correct statement is that "1 is not in the domain."

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Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

The expression that is equivalent to x√6 is option C, 62/37/3.The correct choice is C. 62/37/3.

To find an expression that is equivalent to √(6x²), we need to simplify the square root.

Using the properties of square roots, we know that the square root of a product is equal to the product of the square roots. Therefore, we can simplify the expression as follows:

√(6x²) = √6 * √(x²)

The square root of x² is simply x, and the square root of 6 cannot be simplified further. Therefore, the expression can be simplified as:

√(6x²) = x√6

Among the given options, the expression that is equivalent to x√6 is option C, 62/37/3.

Therefore, the correct choice is C. 62/37/3.

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A triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4) and J′ at (−3, −5). The translation direction is 2 units to the left. The number of units of the image of triangle JKL is 2 units to the left only.

Given that a triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4) and J′ at (−3, −5). We have to determine the translation direction and the number of units of the image of triangle JKL. Let's first find the translation direction to determine the image of triangle JKL.

Seeing the position of J and J', we can determine that the translation was made in the left direction because J has moved from the point (-1,-5) to (-3,-5). Thus, the translation direction is 2 units to the left. Now, let's calculate the number of units of the image of triangle JKL.

Let's draw a rough sketch of the triangle JKL and locate its vertices J(-1,-5), K(-2,-2), and L(2,-4).To find the number of units of the image of triangle JKL, we need to find the horizontal and vertical distances between the vertices of the original triangle and its image.

We can use the horizontal distance between J and J′ as a reference to calculate the remaining distances. J has moved 2 units to the left, so the horizontal distance between J and J′ is 2. Now, let's calculate the vertical distance between J and J′. The coordinates of J and J′ are (-1,-5) and (-3,-5), respectively.

The difference between the y-coordinates of J and J′ is 0, which means that J and J′ are on the same horizontal line. Therefore, the vertical distance between J and J′ is 0. Hence, the image of the triangle JKL has moved 2 units to the left and 0 units vertically. Thus, the number of units of the image of triangle JKL is 2 units to the left only.

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Answer:

2

DNE

-3

3

Step-by-step explanation:

(1) DNE because it is not continuous

(2) DNE because it is not continuous

(3) -3 because at 4, f(x) = -3

(4) x can be any value of -5-2k (where k is a positive integer) or 3. So you can just put 3.