Ben wants to compare the scores of this year's basketball games to the scores of last year's games. He made the following double stem-and-leaf plot to make
his comparison.
Comparison of
Basketball Scores
Between the Last
Two Years
Last
Year
995
97753
6654
9
Stem
OB. 20
OC 16.
0
1
2
3
4
5
What is the difference between the median score this year and the median score last year?
OA 18
OD. 17
This
Year
999
7889
456778
233
2

Answer:

Let x, x + 1, and x + 2 be the three numbers.

x^2 + (x + 2)^2 = x^2 + x^2 + 4x + 4

= 2x^2 + 4x + 4

= 2x^2 + 4x + 2 + 2

= 2(x^2 + 2x + 1) + 2

= 2(x + 1)^2 + 2

The new area of the figure after the dilation with a scale factor of 4 will be 400 units²

We have,

When a figure is dilated by a scale factor of k, its area is multiplied by k².

So,

If the original area of the figure = 25 units²

Dilated by a scale factor = 4

The new area.

= (4²)(25 units²)

= 16(25 units²)

= 400 units²

Therefore,

The new area of the figure after the dilation with a scale factor of 4 will be 400 units².

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1. AB is a tangent, the triangle is a right triangle

2. AB is  not a tangent, the triangle is not a right triangle and hence not a Pythagorean triple

3. arc RS = 100 degrees

4. arc ST =  80 degrees

5. arc RTS = 260 degrees

6. arc RST = 180degrees

7. x = 3

8. x = 7

A tangent will obey Pythagorean triple hence we have that

AB^2 = AC^2 + BC^2

1. AB^2 = 24^2 + 10^2 = 676

AB = sqrt (676) = 26. hence AB is a tangent

2. AB^2 = 8^2 + 11^2 = 185

AB = sqrt (185) = 13.6. hence AB is not a tangent

Length of arc

3. arc RS = 100 degrees (central angle equals intercepted arc)

4. arc ST = 180 - arc RS = 180 - 100 = 80 degrees

5. arc RTS = 180 + arc ST = 180 + 80 = 260 degrees

6. arc RST = 180degrees (semicircle)

Value of x

7. x + 8 = 5x - 4

8 + 4 = 5x - x

12 = 4x

x = 3

8. 4x + 5 = 6x - 9

4x - 6x = -9 - 5

-2x = -14

x = 7

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Answer:

x ≤ [tex]\sqrt[2]{2}[/tex]

Step-by-step explanation:

x² ≤ 8

[tex]\sqrt{x^{2} }[/tex] ≤ [tex]\sqrt{8}[/tex]

x ≤ [tex]\sqrt[2]{2}[/tex]

Answer:

2.75

Step-by-step explanation:

To find the mean absolute deviation for a set of data, we first need to find the mean (average) of the data set. Then, for each data point, we find the absolute value of the difference between the data point and the mean. Finally, we take the mean of those absolute differences.

Step 1: Find the mean

Mean = (6+7+10+12+13+4+8+12)/8 = 72/8 = 9

Step 2: Find the absolute differences

|6-9| = 3

|7-9| = 2

|10-9| = 1

|12-9| = 3

|13-9| = 4

|4-9| = 5

|8-9| = 1

|12-9| = 3

Step 3: Find the mean of the absolute differences

Mean absolute deviation = (3+2+1+3+4+5+1+3)/8

Mean absolute deviation = 22/8

Mean absolute deviation = 2.75

Therefore, the mean absolute deviation for the given data set is 2.75.

The value of sin 75 without using a calculator is 1/4(√2 +√6)

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

sin(75)

This can be expanded as

sin(75) = sin(45 + 30)

Using the sine rule, we have

sin(75) = sin(45)sin(30) + cos(45)cos(30)

Evaluate the trigonometry ratios

So, we have

sin(75) = √2/2 * 1/2 + √2/2 * √3/2

So, we have

sin(75) = √2/4 + √6/4

Evaluate the sum

sin(75) = 1/4(√2 +√6)

Hence, the value is sin(75) = 1/4(√2 +√6)

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The value of length y is,

y = 4 cm

And, The area of the shaded part is, 20 cm²

We have to given that;

A figure is shown in image.

Hence, We get;

The value of y is,

y = 4 cm

And, The area of the shaded part is,

⇒ 4 × 5

⇒ 20 cm²

Thus, The value of length y is,

y = 4 cm

And, The area of the shaded part is, 20 cm²

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Answer:

  0.67 million miles per day

Step-by-step explanation:

You want the average rate of change of the function d(t) = ∛(6t²) on the interval [4, 8], where d is in millions of miles, and t is in days.

The average rate of change of the function on the interval [a, b] is given by ...

  rate of change = (d(b) -d(a))/(b -a)

As the table in the attachment shows, this is approximately ...

  rate of change = (7.268 -4.579)/(8 -4) ≈ 0.67

The average rate of change on the interval 4 ≤ t ≤ 8 is about 0.67 million miles per day.

__

Additional comment

Mercury has an orbit of about 88 days at a distance of roughly 36 million miles from the Sun. Already at that distance, the General Theory of Relativity comes into play, making predictions from Newtonian physics somewhat problematic. It is unlikely this formula has any relation to reality for t much less than 200.

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The answer to the above question is [tex]\sqrt{77}/22[/tex]

A surd is an irrational number, that is, a number that cannot be expressed as a simple fraction or ratio of two integers.

Given the expression:

[tex]\frac{\sqrt{7} }{2\sqrt{11} }[/tex]

Multiply both numerator and denominator by a factor. In this case our factor is [tex]\sqrt{11}[/tex]

Then we have:

= [tex]\frac{\sqrt{7} }{2\sqrt{11} }*\frac{\sqrt{11} }{\sqrt{11} }[/tex]

This gives us:

=  [tex]\frac{\sqrt{7} * \sqrt{11} }{2\sqrt{11} * \sqrt{11} }[/tex]

This should give us:

= [tex]\frac{\sqrt{77} }{2*11 }[/tex][tex]\frac{\sqrt{77} }{22 }[/tex]

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Solution: 11/5 as a mixed number is 2 1/5.

Answer: 9

Step-by-step explanation:-1 plus 9 equals 8

Answer: y = 9

Step-by-step explanation:

First of all, you right out your equation

x + y = 8

Secondly, you sub in the values you have

-1 + y = 8

Then you can swap your answer and y

-1 + 8 = y

Work out the answer

-1 + 8 = 9

Answer is y = 9

Answer:

To find out how many 1 1/2 foot boards can be cut from a 12 foot long board, we need to divide the length of the board by the length of each board.

First, we need to convert 1 1/2 feet to an improper fraction.

1 1/2 = (2 x 1 + 1) / 2 = 3/2

So, each board is 3/2 feet long.

Next, we divide the length of the 12 foot long board by the length of each board:

12 / (3/2) = 12 x 2/3 = 24/3 = 8

Therefore, 8 boards of length 1 1/2 feet can be cut from a 12 foot long board.

Step-by-step explanation:

The explicit rule for the sequence -4/3, 1, -4/5, -2/3, -4/7 is -4(2 + n)

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

-4/3, 1, -4/5, -2/3, -4/7

In the above sequence, we can see that 1 is added to the denomiator of the previous term to get the new term

Take for instance

2nd = -4/(3 + 1) = -1

3rd = -4/(3 + 2) = -4/5

4th = -4/(3 + 3) = -4/6 = -2/3

4th = -4/(3 + 7) = -4/7

Hence, the explicit rule is -4(2 + n)

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Based on the equation, we own 100 shares of JP Morgan Emerging Markets Bond Fund and 900 shares of Fidelity Conservative Income bond fund.

The portfolio is worth $10,000 in total:

$100x + $10y = $10,000

We can now use elimination to find x:

$1100x + $110y = $110,000 -($100x + $10y = $10,000)

$1000x = $100,000 x = 100

As a result, we own 100 shares of JP Morgan Emerging Markets Bond Fund. To solve for y, we can plug this number back into the original equation:

$100x + $10y = $10,000

$100(100) + $10y = $10,000

$10y = $9,000 y = 900

As a result, we have 900 shares of Fidelity Conservative Income bond fund

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The future value or the total amount due at time t for the loan is $5112.50.

To find the future value or the total amount due at time t for a loan with a principal P, a simple interest rate r, and a period of time t, we can use the formula for calculating simple interest;

A=P + (P × r × t)

where; A = future value or total amount due at time t

P = principal amount

r = simple interest rate

t = time period (in years)

Given the values; P = $5000

r = 4.5% (or 0.045 as a decimal)

t = 6 months (or 0.5 years)

We can substitute these values into the formula and calculate the future value;

A = 5000 + (5000 × 0.045 × 0.5)

A = 5000 + 112.5

A = $5112.50

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The volume of the large solid is equal to 8/25 cm³.

In Mathematics, the volume of a cube can be calculated by using the following formula:

V = m³

Where:

By substituting the given points into the formula for the volume of a cube, we have the following;

Volume of cube, V = m³

Volume of cube, V = (1/5)³

Volume of cube, V = 1/125 cm³.

For the volume of the large solid, we have:

Volume of large solid = 5 × 2 × 4 × 1/125

Volume of large solid = 8/25 cm³.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The area of the polygon to the nearest tenth is 80.7 in²

A polygon any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. Examples of polygon include ; triangle, quadrilateral, pentagon e.t.c

The area of a polygon is expressed as;

A = 1/2nsa

where n is the number of side

a is the apothem

s is the side length

Side length = apothem × 2tan(180/n)

n = 12

s = 5 × 2tan(180/12)

s = 5 × 2tan15

s = 2.679

Area = 1/2 × 12 × 5 ×2.679

= 80.7 in²(nearest tenth)

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As per the given percentage, the value of the loan 10 years after it starts is £4506.32.

We know the values of P and A for the first two years. So, we can use these values to find the value of r. Let's use the formula for the first year:

2645 = 2500(1 + r/1)¹ˣ¹

Simplifying the equation, we get:

1 + r = 2645/2500

1 + r = 1.058

r = 0.058 or 5.8%

Therefore, the interest rate per annum is 5.8% (to 1 decimal place).

Now, let's move on to finding the value of the loan after 10 years. We can use the same formula for compound interest, but we need to substitute the values of P, r, n, and t accordingly. Here's the formula:

A = P(1 + r/n)ⁿˣ

Where:

P = 2500

r = 0.058

n = 1 (as the interest is compounded annually)

x = 10

Substituting these values, we get:

A = 2500(1 + 0.058/1)¹ˣ¹⁰

A = 2500(1.058)¹⁰

A = 4506.32

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Answer:

look at the photo

Step-by-step explanation:

The probability of getting hearts or face cards is 25/52.

We know that, Probability of an event = Number of favorable outcomes/Total number of outcomes.

Total number of outcomes = 52 cards

Number of hearts = 13

Number of face cards = 12

Probability getting hearts = 13/52

Probability getting face cards = 12/52

P(Hearts or Face card) = 13/52 + 12/52

= 25/52

Therefore, the probability of getting hearts or face cards is 25/52.

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We can factor each of the given terms so that 4x^2 shows up

8x^5 = 4x^2*2x^3

12x^3 = 4x^2*3x

20x^2 = 4x^2*5

This shows how 4x^2 is the GCF of 8x^5, 12x^3, and 20x^2

-----------------

Here's how to find the GCF of terms involving variables.

First, find the GCF of the coefficients 8, 12 and 20.

List the prime factorizations

Then circle "2*2" since it is found in all three factorizations. Do not circle 3 because it's not found in 8 or 20. Do not circle 5 since it's not found in 8 or 12.

Therefore, the GCF of {8,12,20} is 2*2 = 4.

As for the variable terms, we look for the smallest exponent.

The exponents for x^5, x^3, x^2 are 5,3,2 in that order. The smallest exponent is 2, so x^2 is part of the GCF.

----------------

Summary:

We found the GCF of the coefficients was 4.

The GCF of the variable terms was x^2

That's how we arrive at the GCF of 4x^2

The coordinates of point B are given as follows:

B(-7, 6).

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

For this problem, we have that M(-6,2) is the midpoint of A(-5,-2) and B(x,y).

Then the x-coordinate of point B is obtained as follows:

(x - 5)/2 = -6

x - 5 = -12

x = -7.

The y-coordinate of point B is obtained as follows:

(y - 2)/2 = 2

y - 2 = 4

y = 6.

Hence the coordinates of B are given as follows:

B(-7, 6).

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Answer:

  total deposits: $35,100

Step-by-step explanation:

You have the value of an annuity earning 5% with payments of $65 a month for 45 years as $131,718.42. You want to know the total value of payments.

12 payments per year of $65 for 45 years will have a total value of ...

  12·65·45 = 35100

Total deposits will be $35,100.

The three things that a personality test can tell you are:

A. How you prefer to interact with others.

C. What you might enjoy in a career.

D. How you recharge your energy.

A personality test is a tool used to assess and measure an individual's traits, characteristics, and patterns of behavior.

It may be a series of questions or statements that the individual must respond to.

The results are used to determine the person's strengths and weaknesses, their communication and social interaction (like if they are extrovert or introvert), how they process information and decision-making, etc.

They can also tell of an individual's preferred methods of finding balance in their lives, like spending time alone or with friends and families, being in nature, etc.

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The solution to a trignometric equation sin²x - 1 = 0 is x = { π/2,  3π/2}

Consider a trignometric equation,

sin²x - 1 = 0

We need to solve this trigonometric equation  for all values of angle x such that 0≤ x < 2π

Consider equation,

sin²x - 1 = 0

sin²x = 1

Takin square root,

sin(x) = ±1

when sin(x) = 1, then x = π/2

and when sin(x) = -1 then x = 3π/2

Therefore, required values of angle x = { π/2,  3π/2}

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Answer:  3/8.

Step-by-step explanation: f 4 + 12 = 16,   12 / 2 = 6, 6 / 16 = 3 / 8

There is a financial advantage of $ 1,187,520.

Incremental Costs and Revenues will be as follows

Increment in sales = 82,000 units × 40% = 32,800 units

and, Selling Price

= (32,800 units × $62 per unit)

= $ 2,033,600

Direct materials

= $ 7.50 × 32,800 units

= 246,000

Direct labor

= $ 9.00 × 32800

= $295,200

and, Variable manufacturing overhead

= 2.40 x 32800

= $78, 720

So, the contribution is

= 2,033,600 - (246000 + 285200 + 78720)

= 1,423,680

Now, Variable selling expenses

= 32800 x 3.7

= 121,360

and, Fixed Selling Expenses

= 32800 x 3.5

= 114,800

So, Net income = 1, 187, 520

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