Graph the given data set and describe what kind of model best describes the data. Then write a function that models
the data.
X y
-2,-1
-1,-2
0,-1
1,2
2,7

Equation to find b is 0.05b = 5.10.

Let's use the variable b to represent the cost of the haircut.

According to the problem, the tip was 5% of the cost of the haircut, which can be written as:

0.05b = 5.10

To solve for b, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.05:

b = 5.10 ÷ 0.05

b = 102

So the cost of the haircut was $102. We can check this by calculating 5% of $102, which gives us a tip of $5.10, as stated in the problem.

Therefore, the equation to find b, the cost of the haircut, is:

0.05b = 5.10

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The volume of sphere A is 256π/3 cm³.

The volume of sphere B is  288π cm³.

The volume of sphere C is   2048π/3 cm³.

The volume of each sphere is calculated as follows;

V = ⁴/₃ πr³

where;

Volume of sphere A;

V = ⁴/₃ πr³

V = ⁴/₃ π(4³) = 256π/3 cm³

Volume of sphere B;

V = ⁴/₃ πr³

V = ⁴/₃ π(6³) = 288π cm³

Volume of sphere C;

V = ⁴/₃ πr³

V = ⁴/₃ π(8³) = 2048π/3 cm³

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Answer:

Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2.

Step-by-step explanation:

The range is the simplest measure of variability and is the difference between the largest and smallest values. In this case, the largest value is 20 and the smallest value is 2, so the range is:

Range = 20 - 2 = 18

However, since there are some extreme values (2 and 20), it may be better to use a measure of variability that is less affected by outliers. The interquartile range (IQR) is a good measure of variability that is less affected by extreme values.

To find the IQR, we need to find the median of the data set. The median is the middle value when the data is arranged in order. In this case, the data set has an even number of values, so the median is the average of the two middle values:

Median = (10 + 12) / 2 = 11

Next, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set. In this case, the lower half of the data set is {2, 10, 10} and the upper half of the data set is {12, 12, 20}.

Q1 = Median of lower half = 10

Q3 = Median of upper half = 12

So, the IQR is:

IQR = Q3 - Q1 = 12 - 10 = 2

Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2.

Answer:

84.5 square units.

Step-by-step explanation:

The formula to calculate the area of a trapezoid is:

Area = (base 1 + base 2) * height / 2

Using the measurements you provided, we can calculate the area of the trapezoid as follows:

Area = (12 + 14) * 6.5 / 2

Area = 26 * 6.5 / 2

Area = 169/2

Area = 84.5

Therefore, the area of the trapezoid is 84.5 square units.

The measure of the angle ∠6 as 57 degrees.

Same-side interior angles are pairs of angles that are on the same side of the transversal and between the two parallel lines. When two parallel lines are intersected by a transversal, the same-side interior angles are supplementary, which means that they add up to 180 degrees. This is known as the Same-Side Interior Angles Theorem.

Now, let's apply this theorem to the given problem. We are given that ∠4 is 123 degrees and we need to find the measure of ∠6. Since ∠4 and ∠6 are same-side interior angles, we know that they add up to 180 degrees. We can use this information to set up an equation:

∠4 + ∠6 = 180

Substituting the value of ∠4 as 123 degrees, we get:

123 + ∠6 = 180

To solve for ∠6, we can subtract 123 from both sides of the equation:

∠6 = 180 - 123

Simplifying the right-hand side of the equation, we get:

∠6 = 57

Therefore, the measure of ∠6 is 57 degrees.

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Complete Question:

Same-side interior angles always add up to 180°. If ∠4 and ∠6 are same-side interior angles, what is the measure of ∠6 where the value of ∠4 is 123 degrees?

The claim that the population mean is less than 125 (Option E) would

the interval tends to refute.

The 90% confidence interval for the population mean is 135 to 160. This means that if we were to repeat the process of taking samples from the same population and constructing a 90% confidence interval, we would expect 90% of the intervals to contain the true population mean.

With this in mind, let's consider each claim:

A. The interval does not rule out the possibility that the population mean is more than 110, as 110 is less than the lower bound of the interval.

B. The interval does not rule out the possibility that the population mean is less than 150, as 150 is greater than the upper bound of the interval.

C. The interval does not rule out the possibility that the population mean is between 140 and 150, as both of these values fall within the interval.

D. The interval does not rule out the possibility that the population mean is more than 140, as 140 is less than the upper bound of the interval.

E. The interval refutes the claim that the population mean is less than 125, as 125 is less than the lower bound of the interval.

Therefore, the answer is (E) The population mean is less than than 125.

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Answer:

Step-by-step explanation:

These three graphs have a greater rate of change than the equation y=1/2 x+3.

What is equation?

An equation is an expression that states the equality of two things using mathematical symbols. It is a statement of balance between two elements, usually represented by numbers or variables. Equations are used to solve problems in many fields, including biology, chemistry, physics, engineering, and economics. Equations can be written in a variety of ways, such as linear, quadratic, and polynomial equations, and each type has a unique set of properties. Equations are useful for understanding the relationships between different variables and for predicting outcomes.

Graphs A, D, and F all have a greater rate of change than y=1/2 x+3.

Graph A has a slope of 2, which is double that of y=1/2 x+3 (1).

Graph D has a slope of 4, which is quadruple that of y=1/2 x+3 (1).

Finally, Graph F has a slope of 6, which is six times that of y=1/2 x+3 (1).

Therefore, these three graphs have a greater rate of change than the equation y=1/2 x+3.

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Answer: 65.25 u²

Step-by-step explanation:

I'm going to flip the triangle so c is at the bottom.  i draw a height from <C down to c so that I create a right triangle and I will use trig to find h

they gave me b (hypotenuse) and <A and i want that new h we drew which is opposite <A

sin A = b/h

sin 65 = 18/h    cross multipy to bring h up

h=18/sin65

h=16.31

Area= 1/2 b h     b=base=c=8

=1/2 (8)(16.31)

=65.25 u²

The commutative property of multiplication is as shown x × y = y × x .

The given values of x and y are:

x = a + bi and y = c + di

By the commutative property which states that it is a binary operation in which ab=ba whenever you change the order of the operands.

Therefore,

x = a + bi and y = c + di

Now, x × y = (a + bi) × (c + di)

 = ac + adi + bci + bdi²

= ac - bd + i(ad + bc)

Now, y × x = (c+ di) × (a + bi)

 = ac + bci + adi + bdi²

= ac - bd + i(ad + bc)

Therefore,  x × y = y × x

and when ab = ba then the property is known as commutative property.

Hence commutative property of multiplication is as shown above.

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The function f(x) is a logarithmic function with a vertical asymptote at x = -8. The range of the function is from negative infinite to positive infinity, and it is increasing on it's entire domain. The end behavior of the function on the left side is that as x -> -8^+, y -> -∞, and to the right side, is that as x -> +∞, y -> +∞.

The function starts being defined at x = -8, hence the vertical asymptote of the function is given as follows:

x = -8.

The range of the function is the set containing all values assumed by y on the graph, hence it is in fact from negative infinity to positive infinity, and the function is increasing on it's entire domain.

The end behavior is the values on the extreme left and extreme right of the graph.

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If the area of a square of side (4x-1) is equal to 49, the perimeter of the square is 12 units.

We can start by using the formula for the area of a square, which is side squared, to solve for the side of the square. In this case, we know that the area of the square is 49, so we can set up the equation as follows:

(4x-1)² = 49

Expanding the left side of the equation, we get:

16x² - 8x + 1 = 49

Subtracting 49 from both sides, we get:

16x² - 8x - 48 = 0

Dividing both sides by 8, we get:

2x² - x - 3 = 0

We can solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values of a, b, and c from our equation, we get:

x = (-(-1) ± √((-1)² - 4(2)(-3))) / 2(2)

x = (1 ± √(25)) / 4

x = (1 ± 5) / 4

x = 1 or x = -3/2

Since the side of a square cannot be negative, we can only use the solution x = 1.

Therefore, the side of the square is 4x-1 = 4(1)-1 = 3.

To determine the perimeter of the square, we can use the formula for the perimeter of a square, which is 4 times the length of one side. In this case, the length of one side is 3, so the perimeter of the square is:

4 x 3 = 12

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The required volume and total surface area of the pentagonal pyramid are 15√3

Using the Pythagorean theorem, we can find s:

s² = (3√2)² + (s/2)²

s²2 = 18 + (s²/4)

3s²/4 = 18

s² = 24

s = 2√6

Now, we can find the area of each triangle:

Area of triangle = (1/2) * apothem * side

Area of triangle = (1/2) * 3√2 * 2√6

Area of triangle = 3√3

The total area of the base pentagon is 5 times the area of each triangle:

Area of base = 5 * 3√3

Area of base = 15√3

Now, we can find the volume of the pentagonal pyramid:

V = (1/3) * Base Area * Height

V = (1/3) * 15√3 * 3

V = 15√3

To find the surface area of the pentagonal pyramid,
Area of triangular face = (1/2) * side * slant height
The slant height is the distance from the midpoint of one of the sides of the pentagon to the apex of the pyramid.
slant height² = height² + (s/2²
slant height² = 9 + 6
slant height = √15

Now, we can find the area of each triangular face:
Area of triangular face = (1/2) * 2√6 * √15
Area of triangular face = 3√10

There are five triangular faces, so the total area of the triangular faces is:

Total area of triangular faces = 5 * 3√10
The total area of triangular faces = 15√10

Adding the area of the pentagonal base, we get the total surface area:

Total surface area = 15√3 + 15√10

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well, hmmm keeping in mind that complex roots never come all by their lonesome, their sister always comes along, namely their conjugate, so if we have the complex roots of "i" or namely "0 + i", we also have her sister "0 - i", and if we have "1 - 2i", she also came with "1 + 2i", and we also have the root of 5, and that'd give us the fifth degree polynomial, so

[tex]\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = 1-2i &\implies x -1+2i=0\\ x = 1+2i &\implies x -1-2i=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -1+2i )( x -1-2i )( x -5 ) = \stackrel{0}{y}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2-i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill[/tex]

[tex]( x -1+2i )( x -1-2i )\implies \stackrel{ \textit{difference of squares} }{( [x -1]+2i )( [x -1]-2i )} \\\\\\ (x-1)^2 -(2i)^2\implies (x^2-2x+1)-4i^2\implies (x^2-2x+1)-4(-1) \\\\\\ x^2-2x+1+4\implies x^2-2x+5 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{so we can say}}{a(x^2+1)(x^2-2x+5)(x-5)=y}\hspace{5em}\textit{we also know that } \begin{cases} x=0\\ y=-75 \end{cases} \\\\\\ a(0^2+1)(0^2-2(0)+5)(0-5)=-75\implies -25a=-75 \\\\\\ a=\cfrac{-75}{-25}\implies a=3 \\\\[-0.35em] ~\dotfill[/tex]

[tex]3(x^2+1)(x^2-2x+5)(x-5)=y\implies 3(x^3-5x^2+x-5)(x^2-2x+5)=y \\\\\\ 3(x^5-7x^4+16x^3-32x^2+15x-25)=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} 3x^5-21x^4+48x^3-96x^2+45x-75=y \end{array}}~\hfill[/tex]

Check the picture below.

Answer:

Yes, you need to find the GCF (greatest common factor) to solve this word problem.

The greatest common factor of 35 and 42 is 7. So you can create 7 teams with equal number of boys and girls on each team without leaving anyone out

Step-by-step explanation:

To find the point P on the line y=3x that is closest to the point (50,0), we need to use the formula for the distance between a point and a line. This formula is:

distance = |Ax + By + C| / sqrt(A^2 + B^2)

Where A, B, and C are the coefficients of the equation of the line in the form Ax + By + C = 0.

In this case, the equation of the line y=3x can be written as -3x + y = 0. So we have:

A = -3, B = 1, C = 0

Now we can plug in the values of (50,0) and solve for x and y to find the point P that is closest to it:

distance = |-3x + y| / sqrt((-3)^2 + 1^2)
distance = |-3x| / sqrt(10)

To minimize the distance, we need to minimize |-3x|. This occurs when x = 0. So the point P that is closest to (50,0) is the point (0,0).
To find the point P on the line y = 3x that is closest to the point (50, 0), we need to minimize the distance between P and (50, 0).

Let P(x, y) be a point on the line y = 3x. The distance between P and (50, 0) is given by the distance formula:

D = sqrt((x - 50)^2 + (y - 0)^2)

Since y = 3x, we can rewrite the distance formula as:

D = sqrt((x - 50)^2 + (3x)^2)

To minimize the distance, we can minimize the square of the distance (D^2), as it avoids dealing with the square root:

D^2 = (x - 50)^2 + (3x)^2

Now, we can find the derivative of D^2 with respect to x and set it to 0 to find the critical points:

d(D^2)/dx = 2(x - 50) + 2(3x)^2 * 6x = 0

Solve this equation to find the x-coordinate of the point P. Then, use y = 3x to find the corresponding y-coordinate. Finally, you'll have the coordinates of the point P that is closest to (50, 0).

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The student's parents will pay half of the first-year cost, which is $12,000.

The academic scholarship will pay an additional $500, leaving the student with a remaining cost of $24,000 - $12,000 - $500 = $11,500 for the first year.

If the student wants to pay off the remaining $11,500 by the end of 12 months, they will need to save an average of $958.33 per month.

Therefore, the minimum amount that the student will need to save every month is approximately $958.33.

4√5+2√5

4+2(√5)

6√5

option C

Answer: Each piece of poster board with be 0.78 cents each.

Step-by-step explanation: In order to find x, you need to figure out why 35 pieces of poster boards came up to a total of $27.30.

You will divide in this situation. If you divide $27.30 by 35 poster boards, you should get 0.78 as the result, representing the cost of each poster board.

Answer:

x = 5

Step-by-step explanation:

10^5=

(10 x 10) x 10 x 10 x 10=

(100 x 10)x 10 x 10=

(1000 x 10) x 10=

(10,000 x 10) = 100,000

To solve the equation 10^x = 100,000, we need to isolate x on one side of the equation. We can do this by taking the logarithm of both sides of the equation with base 10:

log(10^x) = log(100,000)

Using the logarithmic property log(a^b) = b*log(a), we can simplify the left side of the equation:

x*log(10) = log(100,000)

Since log(10) = 1, we can simplify further:

x = log(100,000)

Using a calculator, we can evaluate the logarithm to get:

x = 5 + log(10)

x = 5 + 1

x = 6

Therefore, the solution to the equation 10^x = 100,000 is x = 6.

On solving the query we can say that This stage consists just of arithmetic multiplication and does not include any specific properties of numbers.

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

The expression's step is justified by the distributive property. The distributive property of multiplication over addition asserts that for any three integers a, b, and c, a(b + c) = ab + ac. This is the particular property we are employing.

Here are the facts:

2(5 + 17) = 2(5) + 2(17)

which is equivalent to:

2(5 • 17) = (2 • 5) 17

The distributive principle of multiplication over addition is used in this phase.

Then, we further simplify by multiplying 2 by 5 to get 10, which results in:

(2 • 5) 17 = 10 • 17 = 170.

This stage consists just of arithmetic multiplication and does not include any specific properties of numbers.

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On solving the query we can say that This stage consists just of arithmetic multiplication and does not include any specific properties of numbers.

What is function?

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

The expression's step is justified by the distributive property. The distributive property of multiplication over addition asserts that for any three integers a, b, and c, a(b + c) = ab + ac. This is the particular property we are employing.

Here are the facts:

2(5+17)=2(5) + 2(17)

which is equivalent to:

2(5+17)= 44

The distributive principle of multiplication over addition is used in this phase. Then, we further simplify by multiplying 2 by 5 to

get 10, which results in:

(2×5) 17 = 10× 17 = 170.

This stage consists just of arithmetic multiplication and does not include any specific properties of numbers.

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It makes sense to begin with the y-intercept when sketching the graph of y = mx + b because the y-intercept is the point at which the line intersects the y-axis, where x = 0. This point gives us a starting point for the graph and allows us to plot a single point before determining the slope of the line. Once we have the y-intercept, we can use the slope to find additional points on the line, and then connect the points to create the graph of the line.

Answer:

Step-by-step explanation:

When graphing a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept, it makes sense to begin with the y-intercept instead of the slope because the y-intercept gives us a point on the y-axis where the line crosses it.

In the case of the equation y = X + 2, the y-intercept is the point (0,2) on the y-axis, which is a point we can easily plot on the graph. Once we have plotted the y-intercept, we can then use the slope, which is 1 in this case, to find another point on the line by moving one unit to the right along the x-axis and one unit up along the y-axis. We can then draw a straight line through these two points to complete the graph of the line.

Starting with the y-intercept also makes sense because it gives us a sense of the vertical position of the line before we consider its slope. This can be helpful in cases where the y-intercept is a large or small number, as it can affect the scale of the graph and make it easier to read. Additionally, starting with the y-intercept can help us to quickly identify whether the line intersects the y-axis or not, and at what point.

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =42\\ r=13 \end{cases}\implies A=\cfrac{(42)\pi (13)^2}{360} \\\\\\ A=\cfrac{1183\pi }{60}\implies \implies A\approx 61.94[/tex]

Answer:

To determine Martha's monthly pension, we need to use the formula provided by the Merrick Oaks School District for calculating the annual pension benefit:

Annual Pension Benefit = (Years of Service x Average of Last Three Annual Salaries) / 55

where 55 is the "pension factor" used by the district.

Using this formula, we can calculate Martha's annual pension benefit as follows:

Annual Pension Benefit = (18 x $100,000) / 55

Annual Pension Benefit = $32,727.27

Therefore, Martha's annual pension benefit is $32,727.27.

To calculate her monthly pension, we simply divide the annual pension benefit by 12:

Monthly Pension Benefit = $32,727.27 / 12

Monthly Pension Benefit ≈ $2,727.27

Therefore, Martha's monthly pension benefit would be approximately $2,727.27 if she retires after 18 years of service.

Step-by-step explanation:

The first 3 common denominators of 5/24 and 5/8 are the same as the first 3 lowest multiples of 24, which are;  24, 48, and 72

The lowest common multiples of two numbers are the smallest multiples that are common to two numbers.

The first 3 common denominators of 5/24 and 5/8 can be found from the first three lowest common multiples of 24 and 8 as follows;

The first three lowest multiples of 24 are 24, 48, and 72

The first three lowest multiples of 8 are 8, 16, and 24

Therefore, the first three common denominators of 5/24 and 5/8 are 24, 48, and 72

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The alternative hypothesis μ ≠ 0 would indicate a two-tailed test.

Option  C is the correct answer.

We have,

A two-tailed test is a statistical test where the alternative hypothesis is that the population parameter is not equal to a specific value.

In this case,

The alternative hypothesis of μ ≠ 0 indicates that the population mean can be either greater than or less than zero, leading to two possible outcomes

in the test. It means that the test will check if the population mean is significantly different from zero in either direction.

This is in contrast to a one-tailed test, where the alternative hypothesis is directional and indicates that the population parameter is either greater than or less than a specific value.

Thus,

The alternative hypothesis μ ≠ 0 would indicate a two-tailed test.

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The complete question.

Which of the following alternative hypotheses would indicate a two-tailed test?

μ  > 0

μ < 0

μ ≠ 0

μ = 0

[tex]\textit{Pythagorean Identities} \\\\ \sin^2(\theta)+\cos^2(\theta)=1\implies \cos^2(\theta )=1-\sin^2(\theta ) \\\\ 1+\cot^2(\theta)=\csc^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{1-\sin^2(\theta )}{1+\cot^2(\theta )}~~ = ~~\sin^2(\theta )\cos^2(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1-\sin^2(\theta )}{1+\cot^2(\theta )}\implies \cfrac{\cos^2(\theta )}{\csc^2(\theta )}\implies \cfrac{\cos^2(\theta )}{ ~~ \frac{1}{\sin^2(\theta )} ~~ }\implies \cos^2(\theta )\sin^2(\theta )[/tex]

Approximately 5% of students spent their day off playing outside.

To find the percentage of students who spent their day off playing outside, we first need to determine the total number of students. We can do this by adding the number of votes for each activity:

Sleeping: 24

Playing Games 56

Playing Outside: 8

Shopping: 45

Fun Projects: 17

Total Votes (Students) = 24 + 56 + 8 + 45 + 17 = 150

Now we can calculate the percentage of students who spent their day off playing outside:

Percentage = (Number of students who played outside / Total number of students) * 100

Percentage = (8 / 150) * 100 = 0.0533 * 100 = 5.33%

Now, we'll round to the nearest percent:

Percentage ≈ 5%

So, approximately 5% of students spent their day off playing outside.

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