The five winning basketball scores totaled 500 points. Three scores, 81, 112 and 97 were recorded in the team log. Jacki estimated that the other scores had to be 100 and 110. Why are Jacki’s estimates reasonable? A. It is reasonable because that is the average of the numbers. B. It is reasonable because there are five numbers. C. It is reasonable because those are even numbers. D. It is reasonable because all the scores equal 500.

The value of the angle QSR in the given circle containing lines and tangents is 120 degrees.

A circle is a two-dimensional geometric object made up of all points on a plane that are equally spaced from a central fixed point. The radius of a circle is the distance from the centre to any point on the circle. One of the most fundamental and significant geometric forms, the circle has many uses in mathematics, science, and engineering, including the study of trigonometry, coordinate geometry, and calculus. Moreover, circles are utilised in numerous practical contexts, including the creation of wheels, gears, and lenses as well as the simulation of physical phenomena like the motion of planets and electrons.

The measure of angle QSR is determined using the formula:

angle QSR = arc a + arc b / 2

Here, arc a = 150 and arc b = 90 thus:

angle QSR = 150 + 90 / 2

angle QSR = 240 / 2 = 120 degrees.

Hence, the value of the angle QSR in the given circle containing lines and tangents is 120 degrees.

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5x² - 25x - 30 has a common factor with 4x² - 25x + 6, which is (x - 6).

option C.

To find the common factor of two polynomials, we can use the method of polynomial factorization.

First, let's factor the polynomial 4x² - 25x + 6:

4x² - 25x + 6 = (4x - 1)(x - 6)

Now, let's factor each of the answer choices:

We can see that only choice C has a common factor with 4x² - 25x + 6, which is (x - 6). Therefore, the answer is C.

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The most appropriate representation to show the relationship between the number of chapters and the total pages of a book would be a scatter plot titled "School Library".

with the x-axis labeled "Number of Chapters" ranging from 0 to 20 and the y-axis labeled "Total Pages" ranging from 0 to 275 with points at (3, 18), (4, 38), (5, 45), (8, 85), (10, 76), (12, 145), (13, 138), (14, 160), (16, 180), and (20, 220).

A scatter plot is a graph used to display the relationship between two variables. In this case, the two variables are the number of chapters and the total number of pages in a book. The plot consists of dots, each representing a single data point. The x-axis represents the independent variable, which in this case is the number of chapters. The y-axis represents the dependent variable, which is the total number of pages. By plotting each data point on the graph, it is easier to visualize the relationship between the two variables.

A line graph is not appropriate for this situation because it suggests a continuous relationship between the two variables, which is not the case here. The number of chapters and total pages are discrete variables, and there is no natural order to the data points that would justify connecting them with a line.

The first scatter plot option is not appropriate because it shows the y-axis ranging up to 450, which is much higher than the maximum value of 275 for the total pages in this data set. This exaggerates the differences between the data points and can be misleading.

The chosen scatter plot is appropriate because it clearly shows the relationship between the number of chapters and the total pages of a book. It is easy to see that as the number of chapters increases, the total pages also tend to increase. The scatter plot also helps to identify any outliers or patterns in the data that may not be apparent from just looking at the numbers. It is a visual tool that helps to quickly understand the data and draw conclusions from it.

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Answer:

a. 9/16 or 0.5625

b. 1.331 or 1331/1000

Step-by-step explanation:

I’m assuming you meant a^2 and b^3

Recall the definitions for congruence and similarity.

similar - the shapes are the same shape but are different sizes

congruent - the shapes are identical

Now if you have two polygons, assuming that they are identical to start out with (If not you won't be able to solve the problem. Do you see why?) and you perform the operations to one of them, the translation and the rotation will not change anything. But the dilation will make one shape 1/2 as big as the other. So in this case the two polygons are similar but not congruent.

Angles corresponding with ∠8 are ∠4 and ∠12.

In geometry, corresponding angles are angles that are in the same relative position at the intersection of two lines when a third line crosses them. When two lines are intersected by a third line, they form pairs of corresponding angles that are congruent, meaning they have the same measure.

In the given figure;

Lines r,s,t and u are parallel lines.

Angles ∠8 and ∠12 are in corresponding angle  ( line t and u are parallel ands line intersect it)

Angle ∠4 and ∠8 are corresponding angle (line r and s are parallel and t line intersect it)

Hence, Angles corresponding with ∠8 are ∠4 and ∠12.

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Step-by-step explanation:

draw a triangle then label corners a and b. spread them 120 degrees apart and there you have it.

The area of the triangle is: 24 unit²

What is an area ?

Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is typically measured in square units, such as square meters or square feet. The area of a shape is calculated by multiplying its length by its width, or by using a specific formula for the shape.

We can find the area of the triangle by using the formula:

Area = 1/2 * base * height

where the base is the distance between points A and B, and the height is the distance from point C to the line containing AB.

The distance between points A and B is 4 units (since they have the same x-coordinate). To find the height, we can use the equation of the line containing AB, which is:

y = 4x - 3

Substituting x = 4 (the x-coordinate of point C) gives us:

y = 4(4) - 3 = 13

So the height is 13 - 1 = 12 units.  

Therefore, the area of the triangle is:

Area = 1/2 * base * height

= 1/2 * 4 * 12

= 24

So the answer is not one of the given choices. The correct answer is 24.

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Answer please mark as brainliest:

Allstars typically have the tallest players.

Step-by-step explanation:

To determine which team typically has the tallest players, we can compare the measures of center for each team. The measures of center we can use are the mean and median.

Using a calculator or a spreadsheet, we can calculate the mean and median for each team:

Allstars mean: (73+62+60+63+72+65+69+68+71+66+70+67+60+70+71)/15 = 67.1 inches

Allstars median: arrange the heights in order from smallest to largest: 60, 60, 62, 63, 65, 66, 67, 68, 69, 70, 70, 71, 71, 72, 73. The median is the middle value, which is 68 inches.

Champs mean: (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)/15 = 66.4 inches

Champs median: arrange the heights in order from smallest to largest: 58, 60, 60, 62, 65, 67, 67, 68, 69, 69, 70, 70, 70, 75. The median is the middle value, which is 67 inches.

Based on the measures of center, we can see that the Allstars have a higher mean and median height than the Champs. Therefore, we can conclude that the Allstars typically have the tallest players.

Answer:

[tex] \frac{1}{3} [/tex]

The answer is B

Step-by-step explanation:

There are six outcomes in total (numbers: 1; 2; 3; 4; 5 and 6)

The number she had spinned must be greater than 4 (that means there are two favorable outcomes: 5 and 6)

n = 6

m = 2

[tex]p = \frac{m}{n} = \frac{2}{6} = \frac{1}{3} [/tex]

This is the original expression x(x + 1) =  [tex]x^{2}[/tex]  + x  that we started with, so we can be confident that our factorization is correct.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

To factorize an expression means to write it as a product of factors. In this case, we want to write [tex]x^{2}[/tex] + x as a product of factors. One way to do this is to look for common factors that we can take out of both terms in the expression.

In this case, the only common factor in both   [tex]x^{2}[/tex]  and x is x itself. Therefore, we can take out an x from both terms to get:

x(x + 1)

This is the fully factorized form of the expression  [tex]x^{2}[/tex]  + x. It shows that  [tex]x^{2}[/tex]  + x can be written as a product of two factors: x and (x + 1).

We can verify that this is correct by multiplying out the two factors:

x(x + 1) =  [tex]x^{2}[/tex]  + x

Therefore, This is the original expression x(x + 1) =  [tex]x^{2}[/tex]  + x  that we started with, so we can be confident that our factorization is correct.

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Answer:

+ or - (7)

Step-by-step explanation:

5-|p+6|= -8

-|p+6|=-8-5

|p+6|= 13

p+6 = + or - (13)
so case 1
p+6 = 13
p = 7
case 2

p+6 = -13
p+ -7

The monthly payment on a purchase of a $10,000 car at 5.9% for 4 years is: C. $234.39.

To calculate the monthly payment for a car loan, we can use the formula:

M = P [ i(1 + i)^n / ((1 + i)^n – 1) ]

Where:

M = Monthly payment

P = Principal (he amount of the loan)

i = Monthly interest rate (annual interest rate divided by 12)

n = Number of months in the loan term

Using this formula with the given information, we get:

P = $10,000

i = 5.9% / 12 = 0.004917

n = 4 years x 12 months/year = 48 months

M = $10,000 [ 0.004917(1 + 0.004917)^48 / ((1 + 0.004917)^48 – 1) ]

M = $234.39 (rounded to the nearest cent)

Therefore, the answer is option C.

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The caloric content in candy A is 269 and that of candy B is 255.

The caloric content is the quantity of energy required to increase the temperature of one liter of water by one degree. A calorimeter was initially used to determine a food's calorie count.

Let us consider:

Caloric content of Candy A = x

Caloric content of Candy B = y

We can thereby make two equations:

Eqn 1: 1x + 2y = 779

Eqn 2: 2x + 1y = 793

By elimination method, we have

2x + 4y = 1558

Solving for x by subtracting with Eqn 2, we have,

3y = 765

y = 765 ÷ 3

y = 255.

Now substituting the value of y in Eqn 2, we have:

2x + 1y = 793

2x + 1 × 255 = 793

2x + 255 = 793

2x = 793 - 255

2x = 538

x = 538 ÷ 2

x = 269.

Hence caloric content in candy A is 269 and that of candy B is 255.

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The shaded part of the figure in choice B is divided into three equal parts

There are 12 equal parts in total so each activity takes up 1/12.

What is the fraction?

A fraction is a part of a whole or a ratio of two numbers expressed with a horizontal line between them.

Part A: The shaded part of the figure in choice B

is divided into three equal parts

there are three kinds of activities

Part B: According to the choice B of part A. there are 12 equal parts in total so each activity takes up 1/12.

figure in all the parts of the choice up to B of part A, get 12 equal parts

Hence, The shaded part of the figure in choice B is divided into three equal parts

There are 12 equal parts in total so each activity takes up 1/12.

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Libby is correct in claiming that a function with a domain of all real numbers and is increasing everywhere must have all real numbers as its range.

Libby is correct. If a function is increasing throughout its domain, the y-values become greater as x approaches infinity.

This is because the function can take any y-value without restriction as x approaches positive or negative infinity.

The domain of the function is all real numbers, it means that the function is increasing for every x-value, and there are no limits to how large or small x can be.
The given function has a domain of all real numbers, which means it is defined for any value of x.
The function is increasing throughout its domain, which means that as x increases, the y-value of the function also increases.

Conversely, as x decreases, the y-value of the function decreases.
Since there is no restriction on the x-values in the domain, we can let x approach positive infinity to find the largest possible y-value, and negative infinity to find the smallest possible y-value.
As x approaches positive infinity, the y-value of the function keeps increasing without any upper limit, meaning that the function can take any arbitrarily large positive y-value.
Similarly, as x approaches negative infinity, the y-value of the function keeps decreasing without any lower limit, meaning that the function can take any arbitrarily large negative y-value.
Therefore, the range of the function must include all real numbers since the function is able to take any positive or negative y-value without restriction.

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Answer: the term 27 ; a27=a1+(n-1)d. a27=38+(27-1)(-7)

Step-by-step explanation:

Given a1=38,a17=-74. a17=a1+(n-1)d. =38+(17-1)d. -74=38+16d. -74-38=16d. -112=16d. d= -7. the term 27 ; a27=a1+(n-1)d. a27=38+(27-1)(-7).

Answer: 7

Step-by-step explanation: number adds up by 7

Answer:

x⁻²· x⁻²

Step-by-step explanation:

x⁻⁴ = x⁻²· x⁻² = x⁽⁻² ⁺ ⁻²⁾ = x⁻⁴

Answer:

here you go

Step-by-step explanation:

The percent of change from 8,000 to 6,000 can be calculated using the formula:

�������;�ℎ����=���;�����−���;��������;�����×100Percent;change=Old;ValueNew;Value−Old;Value×100

Substituting the given values, we get:

�������;�ℎ����=6,000−8,0008,000×100Percent;change=8,0006,000−8,000×100

Therefore, there is a decrease of 20% from 8,000 to 6,000.

Answer:  decreases 6000 to 8000 = 33.33

x-    

6000−50005000×100 = 20%

Step-by-step explanation:hope that helps have a great day and stay safe (;

By answering the presented question, we may conclude that So, the equation python is 176 inches longer than the garter snake.

In mathematics, an equation is a claim that two expressions are equivalent. Two sides that are separated by the algebraic symbol (=) make form an equation. As an illustration, the claim "2x + 3 = 9" makes the statement "2x plus 3 equals the quantity "9." Finding the value or values of the variable(s) necessary for the equation to be true is the goal of equation solving. Equations can include one or more parts and be straightforward or complex, regular or nonlinear. The formula "x2 + 2x - 3 = 0" raises the variable x to the second power. In many different branches of mathematics, including algebra, calculus, and geometry, lines are used.

Let's use "P" to represent the length of the python in inches.

P = 9(22):

P = 198

Therefore, the python is 198 inches long.

198 - 22 = 176

So, the python is 176 inches longer than the garter snake.

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a. The function n(p) that represents the cost of the paints with the 15% discount is n(p) = 6.99p - 0.15(6.99p).

b. The 15% discount reduces the cost of the paints from 34.95 to 29.70.

Discount is term used for reduction in the original price of a good or service. It is a common practice used by retailers and businesses to attract customers.

a. The function n(p) that represents the cost of the paints with the 15% discount is given by:

n(p) = 6.99p - 0.15(6.99p)

= 5.94p

b. The cost of purchasing 5 paints before the discount is 6.99 x 5 = 34.95.

The cost of purchasing 5 paints after the discount is 5.94 x 5 = 29.70.

Therefore, the 15% discount reduces the cost of the paints from 34.95 to 29.70.

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The length of FG is 40 units.

What are parallel lines?

Two or more lines that are consistently parallel to one another and that are located on the same plane are referred to as parallel lines. No matter how far apart parallel lines are, they never cross. The relationship between parallel and intersecting lines is the reverse. The lines that never meet or have any possibility of meeting are known as parallel lines.

Since FG is parallel to CD, triangles CDE and FGE are similar. Thus, we can set up the following proportion:

CE/CD = FG/FE

Substituting the given values, we get:

32/16 = FG/20

Simplifying the left side, we get:

2 = FG/20

Multiplying both sides by 20, we get:

FG = 40

Therefore, the length of FG is 40 units.

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Function composition is a mathematical concept that involves combining two or more functions to create a new function. A real-life example of function composition might involve a company that uses a software program to calculate payroll. The program might use one function to calculate an employee's hourly rate based on their salary, and another function to calculate their total hours worked based on their timecard data. These two functions could be combined using function composition to create a new function that calculates the employee's total pay.

As for multiplying a binomial with a trinomial, here's an example:

(2x + 3)(4x² + 5x - 6)

To solve this, we use the distributive property of multiplication, which involves multiplying each term in one set of parentheses by each term in the other set of parentheses. We can break this down into three separate multiplications:

2x (4x² + 5x - 6) = 8x³ + 10x² - 12x

3 (4x^2 + 5x - 6) = 12x² + 15x - 18

Adding these two results together, we get:

(2x + 3)(4x² + 5x - 6) = 8x³ + 22x² + 3x - 18

Therefore, the product of the binomial (2x + 3) and the trinomial (4x² + 5x - 6) is 8x³ + 22x² + 3x - 18.

[tex] \: [/tex]

Therefore , the solution of the given problem of triangle comes out to be the desired outcome is demonstrated.

If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.

Here,

Area is equal to (sum of parallel edges) / 2 * (distance between them)

=>  WXYZ area equals (WZ plus XY) / 2 * hS

=>  (XM / XY)2 equals Area of WXM / Area of WXY

=>  XM / XY = 1/2

=>  WXM area divided by WXY area equals (1/2)2 = 1/4.

=>  WXY plus WXM together make up the area of WXYZ.

=>  WXY / 2 + WXM / 4 equals (WZ + XY) / 2 * h

=> WZ * h equals WXY * h plus 2 * WXM:

=>  (WZ - WXY) / 2 * h equals WXM

=>  WXYZ area equals (WZ plus XY) / 2 * h

=>  (WZ+WXY+(WZ-WXY)) / 2 * h

=> (2WZ) / 2 * h

=>  WZ * h

=> WXYZ Area equals 2 * WXM Area

Thus, the desired outcome is demonstrated.

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Answer:

10.14 inches square

a) The probability that in the next eight tries, the number of free throws he will make exactly 8 is equals to the 0.27249.

b) The probability that in the next eight tries, the number of free throws he will make exactly 5 is equals to the 0.08386.

We have a professional basketball player makes 80% of the free throws he tries.

let X be the number of free throws he will make in the next 8 tries. He makes 80% of the free thwors he tries. So, for binomial distribution, X~Bin(8,0.80)

so the probability mass function of X is P[X =x] = ⁸Cₓ 0.85ˣ (1-0.85)⁽⁸⁻ˣ⁾, x = 0,1, 2,..8

P[ X = x] = 0 otherwise.

a) So, the probability that he makes exactly 8 throws isP,(X=8)

= ⁸C₈(0.85)⁸ (1- 0.85)⁰

=0.27249

b) the probability that he makes exactly 5 throws is, P[X=5]

=⁸C₅0.855(1-0.85)⁽⁸⁻³⁾=56×0.855×0.153

=0.08386

Hence required probability is 0.083.

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Difference between interval measurement and ratio measurement is Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point. So, option C is correct.

Interval measurement uses numeric values with equal intervals.

This means that the difference between any two adjacent values on the scale is always constant.

However, the zero point on this scale is arbitrary, meaning it does not represent the absence of the characteristic being measured.

Ratio measurement, on the other hand, also uses numeric values with equal intervals, but it has an absolute zero point.

This means that the zero point on a ratio scale represents the complete absence of the characteristic being measured.

As a result, ratio scales can be used to perform more advanced mathematical operations, such as multiplication and division.
To summarize, the main difference between interval and ratio measurement lies in the zero point of their scales. Interval measurement scales have an arbitrary zero point, whereas ratio measurement scales have an absolute zero point.

The correct choice is option C . Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point.

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Question:-

Which of the following statements describes the difference between interval measurement and ratio measurement?

A) Ratio measurement is used for continuous data, whereas interval measurement is used for noncontinuous data.

B) Interval measurement uses numeric values with equal intervals, whereas ratio measurement uses numeric values with unequal intervals.

C) Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point.

D) Ratio measurement uses numeric values without fixed meaning, whereas interval measurement uses numeric values with fixed meaning.

Hence, x = 5 - an is the answer to the equation x + a = 5 for any value of a as the problem in order to solve the x + a = 5 equation family.

A simple formula is a declaration that two forms are equal. It has two sides, the lower half (LHS) and the right-hand side (RHS), which are divided by the equal sign (=). In order to prove that an equation is correct, one or more uncertain variables may exist.

For instance, the solution 3x + 5 = 14 has a single unknowable variable, x. We must rearrange the equation to find the value of x by carrying out actions that preserve equality, such as deducting 5 from both sides of the equation:

given

We must isolate x on one side of the problem in order to solve the x + a = 5 equation family. By taking an away from both sides, we may accomplish this:

x + a - a = 5 - a

By condensing the left side, we obtain:

x = 5 - a

Hence, x = 5 - an is the answer to the equation x + a = 5 for any value of a as the problem in order to solve the x + a = 5 equation family.

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