The stem-and-leaf plot displays the amount of time, in minutes, that 10 players spent practicing their serving skills for an upcoming tennis tournament.


1| 2, 2, 9
2| 0, 2, 6
3| 1, 1
4| 0
5|
6| 8
Key: 3|1
means 31


Part A: Calculate the mean, median, mode, and range for the data given. Show your work.

Part B: Should the tennis players report the mean or median value to show they are less prepared for the tournament? Explain based on the scenario.

All three values (I, II, and III) are solutions to the inequality, so the correct answer is "I, II and III."

To solve the inequality -10 + 3x ≥ -4, we can follow these steps:

Add 10 to both sides of the inequality:

3x ≥ 6

Divide both sides by 3:

x ≥ 2

Now, let's check which of the given values satisfies the inequality:

I. 8:

x ≥ 2, and 8 ≥ 2, so 8 is a solution.

II. 2:

x ≥ 2, and 2 ≥ 2, so 2 is also a solution.

III. 6:

x ≥ 2, and 6 ≥ 2, so 6 is a solution as well.

All three quantities (I, II, and III) fulfill the requirements of the inequality; hence, the right you have to select is "I, II and III."

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The value of the infinite series expression [tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] is -30.

Given information:

[tex]\sum^{124}_{i = 1}a_i = -10[/tex]  and [tex]\sum^{124}_{i = 1} b_i = -20[/tex].

The required series form can be rearranged as,

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) &= 29\sum^{124}_{i = 1}a_i - 13\sum^{124}_{i = 1}b_i[/tex]

Substitute the provided values of [tex]\sum^{124}_{i = 1}a_i = -10[/tex]  and [tex]\sum^{124}_{i = 1} b_i = -20[/tex].

We get,

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = 29(-10) - 13(-20)

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = -290+ 260

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = -30.

As a result, the required value is -30.

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Area= 69π or 216.77 square units.

Remember that the formula for the area of a circle is the following:

[tex]A=\pi r^{2}[/tex]; where "r" is the radius of the circle.

Hence, the area of the white circle is:

[tex]A_{WC} =\pi (10)^{2} =100\pi[/tex]

Here you can use the same formula, just need to change the value of the radius:

[tex]A_{RC} =\pi (13)^{2} =169\pi[/tex]

[tex]A_{RC} -A_{WC} =169\pi -100\pi =69\pi[/tex]

The area of the shaded region is 69π or 216.77 square units, approximately.

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Answer:

2((4.5)(6) + (4.5)(4) + (6)(4))

= 2(27 + 18 + 24) = 2(69) = 138 square cm

The mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.

To calculate the mean excess return of the value-weighted index portfolio, we need to first calculate the total market capitalization of the three stocks:

Total Market Cap = $3,000 + $2,000 + $1,500 = $6,500

Next, we can calculate the weight of each stock in the index portfolio as follows:

Weight of Stock A = $3,000 / $6,500 = 0.4615

Weight of Stock B = $2,000 / $6,500 = 0.3077

Weight of Stock C = $1,500 / $6,500 = 0.2308

The capitalization-weighted beta of the portfolio can then be calculated as the sum of the product of each stock's weight and its beta:

Beta of Index Portfolio = (0.4615 x 0.15) + (0.3077 x 0.95) + (0.2308 x 1.7) = 1.081

The mean excess return of the index portfolio can be calculated using the single-index model as:

Mean Excess Return = Beta of Index Portfolio x Standard Deviation of Market-Index Portfolio

= 1.081 x 18%

= 19.458%

Finally, we need to adjust for the risk-free rate to obtain the actual mean return of the index portfolio. If the risk-free rate is 2%, then the mean return of the index portfolio would be:

Mean Return = Mean Excess Return + Risk-Free Rate

= 19.458% + 2%

= 21.458%

Therefore, the mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.

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The requried measure of the side QT in triangle SQT is 59 units.

A figure is shown with two triangles, SQT and SQR.

Since in the question we are given to RS = ST 81, QR = v + 33, and QT = 3v 19,

As RS = St and SQ is a common side both the triangle are congruent, QT = QR

v + 33 = 3v - 19
52 = 2v
v = 26

Now,
QT = 3(26) - 19
QT = 59

Thus, the requried measure of the side QT in triangle SQT is 59 units.

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(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.

(ii) The axioms of probability are:

the non-negativity (that the probability of an event is greater than or equal to zero), and

the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).

(iii) When two fair dice are thrown the probability of getting:

a) The sum of 9 = 1/9

b) Two odd numbers = 1/4

c) two prime numbers = 1/9

d)  two factors of 12 = 1/9

(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.

To find probability when two dice are thrown, we have:

(a) The sum of 9:

We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways

A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.

(b) Two odd numbers:

We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).

possible outcomes = 9,

So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.

(c) Two prime numbers

We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)

possible outcomes = 4,

So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.

(d) Two factors of 12:

We count the number of ways and divide by the total possible outcomes.

The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways

possible outcomes = 6

Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12

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Answer:

The answer would be 3.5 in decimal form.

Answer:

The answer is 55/12

Step-by-step explanation:

8-41/12

(8×12+1×(-41))/12

(96-41)/12

55/12

Answer:

Hii^^ Here's your answers:
5 hrs=$150 earned
7 hrs=$210 earned
9 hrs=$270 earned

Step-by-step explanation:

30x = amount earned
x = hours

Answer:(5,150) (7,210) (9,270)

Step-by-step explanation: For each hour she works, she earns 30 dollars.

Number of hours: Money she earns

1:30

X stands for the amount of money she earns. So for 5 hours, we can write this:

5:X

To get from 1:30 to 5:x, you multiply by 5. 1x5=5. So you multiply 30x5 and get 150. Do the same for the other situations, and you get:

5:150

7:210

9:270

To plot them on the graph, the number of hours she works is x, and the money she earns is y.

So, put these on the graph:

(5,150)

(7,210)

(9,270)

The value of the expression is 2x³ + 3x² - 27x + 40

It is important we know that algebraic expressions are described as expressions that are composed of factors, constants, variables, coefficients and terms.

Algebraic expressions are also made up of arithmetic operations, such as;

From the information given, we have;

1. (x + 5)(2x² -7x + 8)

expand the bracket

2x³ - 7x² + 8x + 10x² -35x + 40

collect like terms

2x³ - 7x² + 10x² + 8x - 35x + 40

Add the like terms

2x³ + 3x² - 27x + 40

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Answer:

90 children's tickets and 200 adult tickets were sold.

Step-by-step explanation:

Let's use the variables c and a to represent the number of children's and adult tickets sold, respectively.

From the problem, we know that:

The total number of tickets sold is 290: c + a = 290

The total revenue from ticket sales is $2250: 5c + 9a = 2250

We now have two equations with two unknowns. We can use substitution or elimination to solve for c and a. Here's one way to use elimination:

Multiply the first equation by 5 to get 5c + 5a = 1450

Subtract the above equation from the second equation to eliminate c: 5c + 9a - (5c + 5a) = 2250 - 1450

Simplify: 4a = 800

Solve for a: a = 200

Substitute a = 200 into the first equation to solve for c: c + 200 = 290

Simplify: c = 90

Therefore, 90 children's tickets and 200 adult tickets were sold.

The solution is,  $ 12833 .59 will he have in the account after 5 years.

Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment, but also on any interest that has previously accrued. In other words, it is interest that is earned on both the initial principal and any interest that has been added to it over time.

by the question.

We can use the formula for compound interest to solve the problem:

A = P

where:

A = final amount (x in this case)

P = principal or initial amount ($10,000.00)

r = annual interest rate (5% in this case)

n = number of times the interest is compounded per year (12, since it's compounded monthly)

t = time in years (5, since Tyrone opened the account 5 years ago)

Substituting the values given, we get:

A = $ 12833 .59

The solution is,  $ 12833 .59 will he have in the account after 5 years.

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The pattern that can be used to represent a triangular number is T(n) = 1 + 2 + 3 + ... + n.

A number that can take the form of an equilateral triangle is called a triangular number. By definition, it represents the sum of positive integers up to n consecutive natural numbers. The pattern for such a calculation is expressed as follows:

T(n) = 1 + 2 + 3 + ... + n.

Triangular numbers exhibit many engaging properties and are applicable across various mathematical and real-world contexts.

In conclusion, the pattern used to represent a triangular number is T (n) = 1 + 2 + 3 + ... + n.

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Answer:

The correct answer is C

Step-by-step explanation:

The statements can be arranged correctly as follows:

1. Word Form shows a number written in words.

2. Standard form shows a number written using digits.

3.  Digit is one of the numerals from 0 to 9

4. Place value the position of a digit in a number, which determines its value.

5.  Period each three-digit part of a whole number, separated by commas

6. Expanded form shows a number written as an addition statement

We can determine the terms by first understanding the mathematical meanings. Word form is a term used in math to denote expressions written in word B.

Also, the standard form is a way of shortening large numerical values using digits. Digits are single numbers that run between 0 to 9 and they make up the higher values of numbers.

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From the data given, we can see that as you move upward in the atmosphere from sea level, the temperature generally decreases such as from 28 degree to negative degree.

This is because earth atmosphere is heated from bottom-up by the Earth's surface, so, the nearest air to the ground is warmer than the air at higher altitudes. When we climb higher, the air pressure decreases and this causes the air to expand and cool.

This decrease in temperature with increasing altitude is known as the adiabatic lapse rate, but this is known to vary depending on factors such as humidity and atmospheric conditions.

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187, 500 ml are needed to prepare 750 mg from 1:250.

We have to find amount in ml to prepare 750 mg from 1:250.

let the amount needed in ml be x.

Using proportion

1/750 = 250 / x

x= 750 . 250

x= 187, 500 ml

Thus, to prepare 750 mg 187,500 ml is needed.

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Answer:

Think about the PEMDAS rules for order of operations.

Multiplication comes before addition or subtraction, so first we have "the product of a number and 5" - that's 5x. Then "six more" than that would be 5x + 6. "Equals" means the "=" sign, so the final answer is 5x + 6 = 8.

The volume of the pyramid is  9333 cubic centimetres

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

Base dimensions = 40 cm by 20 cm

Height = 35 cm

The volume of the pyramid is calculated as

Volume = Product of Base dimensions and Height/3

substitute the known values in the above equation, so, we have the following representation

Volume = 40 * 20 * 35/3

Evaluate

Volume = 9333

Hence, the volume is 9333

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The value of f(j) when

1. j = -1 is 11

2. j = 0 is 10

3. j = 1 is 11

4 . j = 2 is 14

A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

For example, here j is a variable and f(j) is the function of 'j'.

f(j) = j²+10

Therefore , when j = -1

f(j) = -1)² + 10

f(j) = 1+10 = 11

When j = 0

f(j) = 0²+10

= 0+10 = 10

when j = 1

f(j) = 1²+10

= 1+10 = 11

When j= 2

f(j) = 2²+10

= 4+10

= 14

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The quantity of cats that will be in the pet daycare when there are 40 dogs would be = 120 cats.

Ratio can be defined as the comparison of two values that shows the amount of one value that can be found in the other value.

The initial amount of dogs = 20

The initial amount of cats = 60

The final amount of dog = 40

The final amount of cats = ?

That is;

20 dogs = 60 cats

40 dogs = X cats

make X the subject of formula;

X = 40×60/20

= 2400/20

= 120 cats

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The equivalent value of the expression is A = 12 + 6x + 6x + 6y

Given data ,

Let the expression be represented as A

Now , the value of A is

A = 6(2 + x + x + y)

On simplifying the equation , we get

A = 6 ( 2 ) + 6x + 6x + 6y

On further simplification , we get

A = 12 + 6x + 6x + 6y

Hence , the expression is A = 12 + 6x + 6x + 6y

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The complete question is attached below :

which expression uess exactly terms and is equivalent to 6(2 + x + x + y)

Yes , y varies directly with x as a proportion of k = 2.5

Given data ,

Let the values of x = { 2 , 6 , 18 }

Let the values of y = { 5 , 15 , 45 }

Now , the proportion equation is y = kx

On simplifying , we get

k = 5/2

k = 2.5

Therefore , the proportionality constant is k = 2.5

Hence , the proportion is y = 2.5 ( x )

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The number of pages that can be printed in half a minute is 90 pages

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

The graph represents a  proportional relationship

Where

x = minutes

y = pages

When the time is half a minute, we have

x = 0.5

So, we have the following ordered pair

(0.5, y)

From the question. we have

(4, 720)

So, we have

(0.5, y) = (4, 720)

Express as an equation

So, we have

y/0.5 = 720/4

This gives

y = 0.5 * 720/4

Evaluate

y = 90

Hence, the number of pages is 90

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Yes , Han is correct as the a circle with a longer arc length has a larger central angle

Given data ,

Let the arc length of the circle A = 6π units

Let the radius of the circle A = 15 units

Let the arc length of circle B = 2π units

Let the radius of the circle B = 5 units

Now , The length of an arc in a circle is determined by both the radius of the circle and the central angle that subtends the arc. The formula for calculating the length of an arc in a circle is given by:

Arc length = (Central angle / 360 degrees) x (2πr)

Though two circles' radii differ, they may nevertheless have distinct arc lengths even though their centre angles are the same. Similar to this, if the radii of two circles are adjusted properly, two circles with differing central angles can nevertheless have the same arc length.

Hence , the central angle is solved

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The value of c as per the law of cosines, to the nearest tenth, is 5.1 units.

Given information:

a = 8, b = 9 C = 34°.

To find the value of C:

According to the Law of Cosines, for any triangle ABC:

c² = a² + b² - 2ab cos(C)

Substituting the given values:

c² = 8² + 9² - 2(8)(9) cos(34°)

c² = 64 + 81 - 144 cos(34°)

c² = 145 - 144 cos(34°)

Taking the square root of both sides:

c = √(145 - 144 cos(34°))

Using a calculator:

c ≈ 5.1 units (rounded to the nearest tenth)

Therefore, the value of c is approximately 5.1 units.

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On solving the "equation" written as "5x² - 8x + 12 = 3x + 10" by using "factoring-method" , the "solutions" are x = 1/5 and x = 2.

To solve "5x² - 8x + 12 = 3x + 10" by using the "factoring-method", it should first be rearranged in "standard-form", where one side of the equation is = 0,

First, we combine the constant terms on the right side of the quadratic:

⇒ 5x² - 8x + 2 = 3x,

⇒ 5x² - 11x + 2 = 0,  Now, we factor the quadratic expression on the left side of the equation as :

⇒ 5x² - 10x -x + 2 = 0,

⇒ 5x(x - 2) -1(x - 2) = 0,

⇒ (5x - 1)×(x - 2) = 0

By applying the zero product property, we know that either "5x - 1 = 0" or "x - 2 = 0";

⇒ 5x - 1 = 0 , We get x = 1/5,

⇒ x - 2 = 0, We get x = 2;

Therefore, the solution are x = 2, and x = 1/5.

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The given question is incomplete, the complete question is

Solve the quadratic-equation "5x² - 8x + 12 = 3x + 10" by factoring.

Answer:

Step-by-step explanation:

The population density of the neighborhood is 12000 people per square mile.

Total number of people = 1250

Number of city blocks = 30

Length of the block, l = 1/16 mile

Width of the city block, w = 1/18 mile

Area of one block, A = l x w

A = (1/16) x (1/18)

A = 1/288 square mile

Total area of all the 30 blocks, A' = 30 x A

A' = 30/288 square mile

So, the population density,

D = Total no.of people/A'

D = 1250/(30/288)

D = 1250 x 288/30

D = 12000 people per square mile.

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