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. (8 points)

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. (4 points)

Answer:

(- 8, 2 )

Step-by-step explanation:

y = [tex]\frac{1}{2}[/tex] x + 6 → (1)

y = - [tex]\frac{3}{4}[/tex] x - 4 → (2)

substitute y = [tex]\frac{1}{2}[/tex] x + 6 into (2)

[tex]\frac{1}{2}[/tex] x + 6 = - [tex]\frac{3}{4}[/tex]x - 4

multiply through by 4 ( the LCM of 2 and 4 ) to clear the fractions

2x + 24 = - 3x - 16 ( add 3x to both sides )

5x + 24 = - 16 ( subtract 24 from both sides )

5x = - 40 ( divide both sides by 5 )

x = - 8

substitute x = - 8 into either of the 2 equations and evaluate for y

substituting into (1)

y = [tex]\frac{1}{2}[/tex] (- 8) + 6 = - 4 + 6 = 2

solution is (- 8, 2 )

The two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.

Since the two buses are traveling towards each other at constant speeds, we can use the formula for finding the time two objects meet when traveling at constant speeds in opposite directions:

t = (d2 - d1)/(v1 + v2)

Where t is the time they meet, d1 is the distance the first bus travels, d2 is the distance the second bus travels, v1 is the speed of the first bus, and v2 is the speed of the second bus.

In this case, d1 is the distance between NY and Boston (approx. 200 miles), d2 is the distance between Boston and NY (also approx. 200 miles), v1 is the speed of the first bus (200 miles in 5 hours, or 40 miles/hour), and v2 is the speed of the second bus (200 miles in 5 hours, or 40 miles/hour).

Plugging these values into the formula, we get:

t = (200 - 200)/(40 + 40)

t = 0/80

t = 0

Hence, the two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.

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Answer:

[tex]x = \frac{9}{ \sqrt{2} } = \frac{9 \sqrt{2} }{2} [/tex]

statement B and D  are true. to determine which of the statements is true, we need to perform the indicated operations and simplify the expressions for the volumes of the boxes.

what is expressions ?

In computer programming, an expression is a combination of values, variables, and operators that produces a result or value. Expressions can be simple or complex, and they can be used in a variety of contexts, such as assigning values to variables, performing calculations, and making logical decisions.

In the given question,

To determine which of the statements is true, we need to perform the indicated operations and simplify the expressions for the volumes of the boxes.

The volume of the oak box is 2x³ + 5x² - 3xc*m³.

The volume of the maple box is 2x³ + 9x² - 2x - 24c*m³.

A. The oak box has a volume 4x² + x 24c*m³ greater than the maple box.

To compare the volumes, we need to subtract the volume of the maple box from the volume of the oak box:

(2x³ + 5x² - 3xcm³) - (2x³ + 9x² - 2x - 24cm³)

= 2x³ - 4x² + 2x + 24c*m³

Therefore, statement A is not true.

B. The maple box has a volume 4x² + x - 24c*m³ greater than the oak box.

To compare the volumes, we need to subtract the volume of the oak box from the volume of the maple box:

(2x³ + 9x² - 2x - 24cm³) - (2x³ + 5x² - 3xcm³)

= 4x² + x - 24c*m³

Therefore, statement B is true.

C. The total volume of 1 oak box and 1 maple box is 4x³ + 14x² + 5x + 24c*m³.

To find the total volume, we need to add the volumes of the oak and maple boxes:

(2x³ + 5x² - 3xcm³) + (2x³ + 9x² - 2x - 24cm³)

= 4x³ + 14x² - x - 27c*m³

Therefore, statement C is not true.

D. The total volume of 2 maple boxes is 4x³ + 18x² + 4x + 48c*m³.

To find the total volume of 2 maple boxes, we need to multiply the volume of 1 maple box by 2:

2(2x³ + 9x² - 2x - 24cm³) = 4x³ + 18x² - 4x - 48cm³

Therefore, statement D is true.

In summary, the correct statements are:

B. The maple box has a volume 4x² + x - 24c*m³ greater than the oak box.

D. The total volume of 2 maple boxes is 4x³ + 18x² + 4x + 48c*m³.

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Answer:

8) ]-infinity ,1]

9) ]-infinity,-2[

Answer:

8) x ≤ 1     9) x < -2

Hope this helps.

Answer:

5 3/8 ft

Step-by-step explanation:

5 7/8 - 1/4 = 5 7/8 - 4/8 = 5 3/8

Answer:

We can use the continuous compounding formula to solve this problem:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.

In this problem, we know the final amount (A = $1255.66), the interest rate (r = 4% = 0.04), and the time (t = 4 years). We want to find the initial amount (P).

Substituting the known values into the formula, we get:

1255.66 = Pe^(0.04*4)

Simplifying the exponent:

1255.66 = Pe^0.16

Dividing both sides by e^0.16:

1255.66 / e^0.16 = P

Using a calculator to evaluate e^0.16, we get:

1255.66 / 1.17351087099 = P

Simplifying:

P = $1069.44

Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).

Step-by-step explanation:

compounded continuously, given that there is $1255.66 in the account after four years, we can use the formula:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.

Substituting the known values into the formula, we get:

1255.66 = Pe^(0.04*4)

Simplifying the exponent:

1255.66 = Pe^0.16

Dividing both sides by e^0.16:

P = 1255.66 / e^0.16

Using a calculator to evaluate e^0.16, we get:

P = 1069.44

Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).

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Answer:

We can use the continuous compounding formula to solve this problem:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.

In this problem, we know the final amount (A = $1255.66), the interest rate (r = 4% = 0.04), and the time (t = 4 years). We want to find the initial amount (P).

Substituting the known values into the formula, we get:

1255.66 = Pe^(0.04*4)

Simplifying the exponent:

1255.66 = Pe^0.16

Dividing both sides by e^0.16:

1255.66 / e^0.16 = P

Using a calculator to evaluate e^0.16, we get:

1255.66 / 1.17351087099 = P

Simplifying:

P = $1069.44

Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).

Step-by-step explanation:

compounded continuously, given that there is $1255.66 in the account after four years, we can use the formula:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.

Substituting the known values into the formula, we get:

1255.66 = Pe^(0.04*4)

Simplifying the exponent:

1255.66 = Pe^0.16

Dividing both sides by e^0.16:

P = 1255.66 / e^0.16

Using a calculator to evaluate e^0.16, we get:

P = 1069.44

Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).

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Answer: x = 9 units

Step-by-step explanation:

[tex]f(x)=\displaystyle\sum_{n=1}^{\infty}c_n\cdot x^n \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\sum_{n=1}^{\infty}c_n\cdot n\cdot x^n\implies n\sum_{n=1}^{\infty}c_n\cdot x^n\implies n\cdot f(x)\quad \textit{assuming "n" is an constant}[/tex]

Applying PEMDAS the correct expression showing where to insert brackets to make it correct are:

i. 3 × (5 + 2) + 2 = 23;      ii. (12 ÷ 4) + 2 = 5

i. 3 × (5 + 2) + 2 = 23

In this expression, we need to prioritize addition over multiplication, as per the order of operations (PEMDAS or BODMAS).

Therefore, we should add 5 and 2 first and then multiply the result by 3. Adding the brackets around 5 + 2 forces the addition to be done before multiplication, resulting in the correct answer.

ii. (12 ÷ 4) + 2 = 5

In this expression, we need to prioritize division over addition. Therefore, we should divide 12 by 4 first and then add the result to 2. Adding brackets around 12 ÷ 4 forces the division to be done before addition, resulting in the correct answer.

To understand where to insert brackets, you need to follow the order of operations, which is a set of rules that dictates the order in which arithmetic operations should be performed. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)

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Answer:

  5.35 grams

Step-by-step explanation:

Given that a 12 grams of a substance will decay exponentially to 7 grams in 2 hours, you want to know the amount remaining after 3 hours.

The amount remaining can be described by ...

  remaining = (initial amount)·(decay factor)^(t/(decay interval))

  remaining = 12(7/12)^(t/2) . . . . where t is in hours

After 3 hours, the amount remaining is ...

  remaining = 12(7/12)^(3/2) ≈ 5.35 . . . . grams

About 5.35 grams will remain after 3 hours.

__

Additional comment

The half-life is about 2.572 hours.

The algebraic expression can be simplified to 4p√2q³r

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

The expression can be simplified as follow:

2√(8p²q³r) = 2 * √8 * √p² √(q³r)

                  = 2 * √(4 * 2) * p √(q³r)

                  = 2 * √4 * √2 * p √(q³r)

                  = 2 * 2 * √2 * p √(q³r)

                  = 4p√2q³r

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Question in English

Could you help me solve this? I have the answer what I need is the procedure. Thank you so much

2√8p²q³r

Answer:

x = (y-z)/3

Step-by-step explanation:

z = 3x + y

3x = z - y

x = (z - y)/3

The kite is approximately 18.57 yards high above the edge of the pond.

The Pythagorean theorem would be used to solve the prob;lem that we have here

The theorye tell us that the squatre of the hypotenuse is the same as the sum of the square of the other two sides

The formula is written as

c^2 = a^2 + b^2

In this case:

c = 37 yards (length of the string)

a = 32 yards (distance from where the kite is tied to the ground to the edge of the pond)

b = height of the kite above the edge of the pond (which we need to find)

Now, plug the values into the Pythagorean theorem:

37^2 = 32^2 + b^2

1369 = 1024 + b^2

Subtract 1024 from both sides:

b^2 = 345

Now, take the square root of both sides to solve for b:

b = √345

= 18.57 yards

The kite is approximately 18.57 yards high above the edge of the pond.

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The coefficient of determination is: 88%

The following table shows the calculations:

X Y X^2 Y^2 XY

22 3 484 9 66

17 4 289 16 68

41 21 1681 441 861

5 1 25 1 5

36 16 1296 256 576

19 7 361 49 133

24 14 576 196 336

6 4 36 16 24

8 2 64 4 16

52 32 2704 1024 1664

35 23 1225 529 805

Total 265 127 8741 2541 4554

Sample size: n=11

Now,

(a)

The coefficient of correlation is :

r=[tex]\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=0.94[/tex]

(b)

The slope of the regression equation is 0.63

S.

and intercept of the equation will be

[tex]b_{0}=\frac{1}{n}(\sum y - b_{1} \sum x)=-3.729965\approx -3.73[/tex]

So the regression equation will be

y'=-3.73+0.63*x

(c)

The coefficient of determination is: 88%

Regression is a statistical analytical method that investigates correlations between two or more variables. Its widespread usage stems from its ability to forecast or assess the value of one contingent variable using one or many independently varying variables.

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The possible number of combinations are 9,720.

In mathematics, a combination is a way of selecting a subset of items from a larger set, where the order of selection does not matter. The number of combinations of size k that can be chosen from a set of n items is denoted by the symbol C(n,k) or sometimes by ⁿCk, and is given by the formula:

C(n,k) = n! / (k! ×(n - k)!)

A number is a mathematical concept used to represent quantity or value. It can be a whole number, such as 1, 2, 3, or a decimal, such as 1.5 or 3.14. Numbers are used in various mathematical operations, such as addition, subtraction, multiplication, and division. They are also used in everyday life for counting and measuring.

There are a total of 9,720 possible combinations for a 4-number computer cable lock where each space can be any number 0-9, except for the restriction that all four numbers cannot be the same. To arrive at this number, we can first calculate the total number of possible combinations without the restriction, which is 10⁴ = 10,000. Then we subtract the number of combinations where all four numbers are the same, which is simply 10 (i.e. 0000, 1111, 2222, etc.), to get 9,990. Finally, we subtract the number of combinations where all four numbers are the same and also subtract the number of combinations where three out of four numbers are the same (which is simply 10×4 = 40 since there are 10 possible values for the repeated number and 4 possible positions for it), which gives us a final count of 9,720.

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He completed volunteering in 39 hours 40 minutes in 4 weeks

How to determine this

If Ken volunteers 1 hr 25 mins each day

i.e 1 hr 25 mins = 1 days

By converting 1 hr 25 mins to mins

When 60 mins = 1 hr

1 hr 25 mins = 60 + 25 = 85 mins

How many hours of volunteering is completed in 4 weeks

Let x represent the numbers of hours

i.e x = 4 weeks

By converting 4 weeks to days

When 7 days = 1 week

4 weeks = 4 * 7 days

= 28 days

So, when 85 mins = 1 day

x mins = 28 days

x = 28 days * 85 mins/1 day

x = 2380 mins

By converting it back to hour

When 60 mins = 1 hour

2380 mins = x

x = 2380/60 hour

x = 39 hours 40 mins

Therefore, the hours that can be completed in 4 weeks is 39 hours 40 minutes

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The rectangle's height is 2 in, and the rectangle's base is 5 x 2+ 3 = 30 in, whose area is given as 68in².

It has two pairs of equal-length sides that are at right angles to each other. It is the most common type of quadrilateral, and it can be found in everyday objects like windows, doors, and tabletops.

To solve this problem, we need to use the formula for the area of a rectangle (A = l x w), where A is the area, l is the length, and w is the width. We also know that the base is 3 inches shorter than 5 times the height. Therefore, we can set up the equation to solve for the height and the base of the rectangle as follows:

A = l x w

A = (h + 3) x (5h)

A = 5h² + 3h

5h²  + 3h = 68

h= -2 (as height can not be in negative)

h= 2

By using the quadratic formula, we can solve for the height, h, which is equal to 2.

Therefore, the rectangle's height is 2 in, and the rectangle's base is 5 x 2+ 3 = 30 in.

This problem was solved by using the quadratic equation to solve for the height of the rectangle, which was then used to solve for the base.

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The surface area of the hexagonal pyramid is  740 metres².

The pyramid above is an hexagonal pyramid. The surface area of the pyramid can be found as follows:

Therefore,

surface area of the hexagonal pyramid = A + 1 / 2 ps

where

Therefore,

A = base area = 1 / 2 p a

where

Hence,

p = 10(6) = 60 metres

a = 5√3 metres

A = base area = 1 / 2 × 60 × 5√3 = 150√3 metres

Therefore,

surface area of the hexagonal pyramid = 150√3 + 1 / 2 × 60 × 16

surface area of the hexagonal pyramid = 150√3 + 480

surface area of the hexagonal pyramid = 739.807621135

surface area of the hexagonal pyramid = 740 metres²

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The surface area of the hexagonal pyramid is  740 metres².

The pyramid above is an hexagonal pyramid. The surface area of the pyramid can be found as follows:

Therefore,

surface area of the hexagonal pyramid = A + 1 / 2 ps

where

Therefore,

A = base area = 1 / 2 p a

where

Hence,

p = 10(6) = 60 metres

a = 5√3 metres

A = base area = 1 / 2 × 60 × 5√3 = 150√3 metres

Therefore,

surface area of the hexagonal pyramid = 150√3 + 1 / 2 × 60 × 16

surface area of the hexagonal pyramid = 150√3 + 480

surface area of the hexagonal pyramid = 739.807621135

surface area of the hexagonal pyramid = 740 metres²

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The coordinates of P when written as a fraction and as a decimal, is:

Point P has the coordinates of ( 3/4 , 5/6 ) which means that it is already in fraction form as it has both a numerator and a denominator for the x and ya values.

We can then convert these fractions to decimal form as shown :

x - value : 3 ÷ 4 = 0.75

y - value : 5 ÷ 6 = 0.83

In decimals, it is:

(0.75, 0.83)

In conclusion, as a fraction, point P is ( 3 / 4, 5 / 6 ), and as a decimal, point P is ( 0.75, 0.83 ).

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The  expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign is A)  [tex]x^2+2x+1[/tex].

What is area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Here the given square shaped traffic sign side length a = x+1

We know that, area of square = [tex]a^2[/tex] square unit.

Then, area of the square shaped traffic sign is

=> A = [tex](x+1)^2[/tex]

=> A = [tex]x^2+2x+1[/tex]

Hence the  expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign is A)  [tex]x^2+2x+1[/tex].

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If the boat travel north at 30 km per hour .  the equivalent speed in still water required to achieve an actual speed of 30 km/h is 30.1 km/h.

Finding the boat's true speed using Pythagoras' theorem using this  formula

Speed = √((30 km/h)^2 + (4/√(2) km/h)^2)

Let plug in the formula

Speed = √(900 + 8) km/h

Speed = √(908) km/h

Speed = 30.1 km/h

Speed = 30 km/h ( Approximately)

Therefore  the speed is 30km/h.

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To find the angle of depression, we can use the tangent function in trigonometry. In this situation, we have a right triangle where the height (opposite side) is 400 feet, and the distance (adjacent side) is 18,410 feet.

tan(angle) = opposite / adjacent

tan(angle) = 400 / 18,410

Now, we'll use the arctangent (inverse tangent) function to find the angle:

angle = arctan(400 / 18,410)

angle ≈ 1.25 degrees

The angle of depression from the top of the lighthouse to the waterline of the ship is approximately 1.25 degrees, rounded to the nearest hundredth of a degree.

Answer:

1 over 3 would juts be 1/3

Answer:

A tangent is a line that touches the curve or a circle at a point..

That this is just an estimate of the true proportion of all voters who would vote for Brown, based on the sample of 350 voters surveyed. The true proportion could be different, due to sampling variability.

What is Statistic?

A statistic is a numerical measure that summarizes some aspect of a dataset. It is a way to describe a sample of data in a concise and meaningful way. Common examples of statistics include measures of central tendency such as the mean, median, and mode, as well as measures of variability such as the range, standard deviation, and variance.

The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is the sample proportion, which is the number of voters who said they'd vote for Brown divided by the total number of voters surveyed:

Number of votes who said they'd vote for brown

    total number of surveyed

= 109/350

=0.31

Therefore, based on the sample of 350 voters surveyed.

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Answer:

12 units.

Step-by-step explanation:

Convert the expression to vertex form:

d(t)=3t^2-12t+0

= 3(t^2 - 4t)

= 3[(t - 2)^2 - 4]

= 3(t-2)^2 - 12.

Minimum value = 12.

Answer: 130

Step-by-step explanation:

The problem is asking for an expression that is equivalent to the addition of 91 and 39. An expression is a combination of numbers, variables, and mathematical operations that does not have an equal sign. In this case, the expression we are looking for should evaluate to the same value as the sum of 91 and 39, which is 130.

To obtain this expression, we simply add 91 and 39, since the sum of these two numbers is equivalent to the expression we are looking for. Adding 91 and 39, we get:

91 + 39 = 130

Therefore, the expression that is equivalent to 91 plus 39 is simply 130.

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