Syd chooses two different primes, both of which are greater than 10, and multiplies them. The resulting product is less than 400. How many different products could Syd have ended up with?

Answer:

B

Step-by-step explanation:

[tex]\frac{4(x+3)(x+1)}{(x+5)(x-5)}[/tex] ← substitute x = 3 into the expression

= [tex]\frac{4(3+3)(3+1)}{(3+5)(3-5)}[/tex]

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

= [tex]\frac{96}{-16}[/tex]

= - 6

Answer:

45°, 60°, and 75°

Step-by-step explanation:

Note:

The sum of the angles in a triangle is always 180°.

For the Question :

if the three angles of the triangle are 3x, 4x, and 5x, then we have the equation:

3x + 4x + 5x = 180°

Combining like terms, we get:

12x = 180

Dividing both sides by 12, we get:

x = 15°

Therefore, the angles of the triangle are:

3x = 3 * 15 = 45°

4x = 4 * 15 = 60°

5x = 5 * 15 = 75°

So, the exact sides of each angle of the triangle are 45°, 60°, and 75° respectively.

Answer:

45°, 60°, and 75°

Step-by-step explanation:

3x + 4x + 5x = 180°

12x = 180

x = 15°

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

3x = 3 * 15 = 45°

4x = 4 * 15 = 60°

5x = 5 * 15 = 75°

Answer:

  745

Step-by-step explanation:

You want the original number of books in the library if adding 298 children's books increased the fraction of children's books from 2/5 to 4/7.

We often like to work problems like this in terms of "ratio units." Here, we'll let x represent the number of books in a ratio unit. This means the number of children's books is originally 2x, and the total number of books is originally 5x. Then we have ...

  (2x +298)/(5x +298) = 4//7

Cross multiplying gives ...

  7(2x +298) = 4(5x +298)

  3(298) = 6x . . . . . . . . . . . . . subtract (14x+4(298))

  149 = x

  745 = 5x . . . . . . the original number of books in the library

There were 745 books in the library at first.

__

Additional comment

If we let x represent the original number of library books, then the arithmetic involves more fractions. You would have an equation like ...

  2/5x +298 = 4/7(x +298)

<95141404393>

a. To calculate the present value of investment A at a discount rate of 21 percent, we need to find the present value of each cash flow and then sum them up. The present value of each cash flow can be calculated using the formula PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

Using the given cash flows and the discount rate of 21 percent, we have:

PV = 11,000 / (1 + 0.21)^1 + 11,000 / (1 + 0.21)^2 + 11,000 / (1 + 0.21)^3 + 11,000 / (1 + 0.21)^4 + 11,000 / (1 + 0.21)^5 + 11,000 / (1 + 0.21)^6

Calculating this expression will give us the present value of investment A.

b. Similarly, to calculate the present value of investment B, we use the same formula and substitute the cash flows for investment B:

PV = 11,000 / (1 + 0.21)^1 + 11,000 / (1 + 0.21)^2 + 11,000 / (1 + 0.21)^3 + 11,000 / (1 + 0.21)^4

c. For investment C, we use the formula with the cash flows for investment C:

PV = 16,000 / (1 + 0.21)^1 + 48,000 / (1 + 0.21)^2

Calculating these expressions will give us the present values of investments B and C, respectively.

The present values of investments A, B, and C are $37,461.97, $29,930.99, and $48,003.16 respectively.

To calculate the present value of the cash flows from every investment, we use the present value of annuity formula: PV = C * [(1 - (1 + r)^-n ) / r], where PV is the present value, C is the constant cash flow per period, r is the discount rate, and n is the number of periods.

(a) Investment A: C = $11,000, r = 21% or 0.21, n = 6 years. PV = $11,000 * [(1 - (1 + 0.21)^-6) / 0.21] = $37,461.97.

(b) Investment B: C = $11,000, r = 21% or 0.21, n = 4 years. PV = $11,000 * [(1 - (1 + 0.21)^-4) / 0.21] = $29,930.99.

(c) Investment C has 2 cash flows: $16,000 at end of year 1 and $48,000 at end of year 3. We calculate their present value separately and sum those up. PV = $16,000 / (1 + 0.21)^1 + $48,000 / (1 + 0.21)^3 = $13,223.14 + $34,780.02 = $48,003.16.

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Answer:

[tex]\sf \angle PDT \cong \angle XF\:\!K[/tex]

[tex]\sf m\angle PDT = m\angle XF\:\!K[/tex]

Step-by-step explanation:

From inspection of the given diagram, we can see that ∠NAZ is congruent to ∠YBR, since they are both labelled 47°.

We use identical tick marks to indicate congruent angles. Therefore, as ∠NAZ and ∠MCS both have one tick mark, this means they are congruent. So the measure of ∠MCS is also 47°.

The remaining two angles, ∠PDT and [tex]\sf \angle XF\:\!K[/tex], do not have a tick mark. This indicates that these angles are congruent (and different to the other three angles).

The symbol ≅ is used to show congruency. If we want to represent angle PDT is congruent to angle [tex]\sf XF\:\!K[/tex], we write it as [tex]\sf \angle PDT \cong \angle XF\:\!K[/tex].

This literally means "angle PDT is congruent to angle [tex]\sf XF\:\!K[/tex]".

If two angles are congruent, then their angle measures are equal.

When the angle measures are equal we write it as [tex]\sf m\angle PDT = m\angle XF\:\!K[/tex].

The "m" means "measure", the "∠" means "angle", and "=" means "is equal to". So [tex]\sf m\angle PDT = m\angle XF\:\!K[/tex] means "the measure of angle PDT is equal to the measure of angle [tex]\sf XF\:\!K[/tex]".

The inverse of the function y = x³ - 27 is

[tex]y = \sqrt[3]{x - 3} [/tex]

The correct answer choice is option D.

y = x³ - 27

Reduce 27 to a number with cubic power

y = x³ - 3³

y = (x - 3)³

[tex]y = \sqrt[3]{x - 3} [/tex]

Hence, y = x³ - 27 is cubic root of x minus 3.

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The table that represents a linear function is (a)

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

The table of values

By definition;

A linear function is a function that has a constant rate of change

From the options, we have

(a) as x increase by 1, y constantly increase by 4

This means that table (a) is a linear function

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Answer:

A

Step-by-step explanation:

There are 6 numbers from -10 to +10 that can be obtained by adding and using each number or its opposite exactly once.

To find the number of possible sums that can be obtained by adding the positive and negative integers from 1 to 4, we can consider the possible combinations.

The four positive integers are 1, 2, 3, and 4, and their sum is +10.

The four negative integers are -1, -2, -3, and -4, and their sum is -10.

To determine the possible sums, we can combine the positive and negative integers in various ways. Each number or its opposite can be used exactly once.

Here are the possible combinations:

1 + (-2) + (-3) + (-4) = -8

1 + (-2) + (-4) + (-3) = -8

1 + (-3) + (-2) + (-4) = -8

1 + (-3) + (-4) + (-2) = -8

1 + (-4) + (-2) + (-3) = -8

1 + (-4) + (-3) + (-2) = -8

From the given example, we can observe that a sum of -8 can be obtained. Similarly, we can calculate the sums for other combinations.

In total, there are 6 different sums that can be made in this way.

Therefore, if you add and use each number or its opposite exactly once, you can get 6 numbers from -10 to +10.

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Derek should drill E 5.14 feet up to wall from C.

If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.

Using the triangle proportionality theorem,

Therefore,

let

EC = x

4 / 3 = x / 9 - x

cross multiply

4(9 - x) = 3x

36 - 4x = 3x

36 = 3x + 4x

36 = 7x

divide both sides of the equation by 7

x = 36 / 7

x = 5.14 feet up the wall from C

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Each person received 1/4 gallon of water.

To determine how much water each person received, we can divide the total amount of water (3/4 gallon) equally among the three hikers.

Since there are three hikers, we need to divide the total amount of water by 3.

Dividing 3/4 gallon by 3, we perform the following calculation:

(3/4 gallon) ÷ 3 = (3/4 gallon) × (1/3) = (3/12) gallon

So, each person received 3/12 gallon of water.

To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 3 in this case:

(3/12 gallon) ÷ 3/3 = (3/12) gallon × (1/3) / (1/3) = (1/4) gallon

Therefore, each person received 1/4 gallon of water.

As a decimal, 1/4 gallon is equal to 0.25 gallons.

Hence, each person received 0.25 gallons of water.

In conclusion, each person in the hiking group received 1/4 gallon or 0.25 gallons of water at the rest area.

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Bi-monthly and extra principal payments on loans or investments relate to the time value of money by accelerating repayment and reducing overall interest.

Making bi-monthly and extra principal payments on a loan or investment relates to the time value of money by accelerating the repayment process and potentially reducing the overall interest paid.

Bi-monthly payments involve paying half of the monthly amount every two weeks, resulting in 26 payments per year instead of 12. This shorter interval reduces the outstanding balance more frequently, leading to faster interest reduction and loan payoff.

The time value of money concept recognizes that money available today is worth more than the same amount in the future.

Extra principal payments involve paying more than the required amount towards the loan or investment principal. By reducing the principal faster, the interest charged on the remaining balance decreases, thereby saving money in the long run.

The time value of money acknowledges that reducing debt or increasing investment value earlier provides greater financial benefits due to the potential for compounding growth or savings over time.

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The two trains will meet at a distance of 875 kilometers from the station.

To determine the distance at which the two trains will meet, we need to calculate the time it takes for the second train to catch up to the first train.

Let's assume the distance from the station where they meet is 'd' kilometers.

The first train has been traveling for 2 hours before the second train starts, so by the time the second train starts, the first train has already covered a distance of (125 km/h) * (2 hours) = 250 kilometers.

Now, let's consider the time it takes for the second train to catch up to the first train. The relative speed between the two trains is (175 km/h - 125 km/h) = 50 km/h.

To cover the initial distance of 250 kilometers between the trains, it will take the second train (250 km) / (50 km/h) = 5 hours.

During this time, the first train continues to move north at a speed of 125 km/h, covering a distance of (125 km/h) * (5 hours) = 625 kilometers.

Therefore, the total distance from the station where the two trains meet is 250 kilometers (initial distance) + 625 kilometers (distance covered by the first train) = 875 kilometers.

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The range of the quadratic function g(x) = 3x² - 24x + 44 is [-4, ∝)

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

g(x) = 3x² - 24x + 44

The vertex (x) is calculated as

x = 24/(2 * 3)

x = 4

So, we have

g(4) = 3 * 4² - 24 * 4 + 44

g(4) = -4

The leading coefficient is positive

So, we have

g(4) ≥ -4

As an interval, we have

[-4, ∝)

Hence, the range is [-4, ∝)

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Answer:

Step-by-step explanation:

To determine the mean and median of the distribution of masses, we first need to calculate the midpoint of each class interval. The midpoint is found by taking the average of the lower and upper limits of each interval. Then, we multiply the midpoint by the corresponding frequency and sum up the results. Finally, we divide the sum by the total frequency to find the mean.

Here is the calculation:

Class Interval   |  Midpoint (x)  |  Frequency (f)  |  f * x

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

30-34.9               |    32.5               |         5                 |   162.5

35-39.9               |    37.5               |         9                 |   337.5

40-44.9               |    42.5               |         7                 |   297.5

45-49.9               |    47.5               |         6                 |   285

50-54.9               |    52.5               |         4                 |   210

55-59.9               |    57.5               |         4                 |   230

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

Total                      |                                  |       35               |   1,522.5

Mean = (Sum of (f * x)) / (Sum of f) = 1,522.5 / 35 ≈ 43.5 kg

To find the median, we need to arrange the masses in ascending order. The cumulative frequency (cf) is calculated by summing up the frequencies as we move down the list. The median is the value that falls in the middle when the cumulative frequency reaches half of the total frequency.

Arranged Masses: 30, 30, 30, 30, 30, 35, 35, 35, 35, 35, 35, 35, 35, 35, 40, 40, 40, 40, 40, 40, 40, 45, 45, 45, 45, 45, 45, 50, 50, 50, 50, 55, 55, 55, 55

Cumulative Frequency: 5, 14, 21, 27, 31, 35

Since the total frequency is 35, the median will be the value at the (35/2 = 17.5)th position. Since it falls between the 17th and 18th values, we take the average of those two values.

Median = (40 + 40) / 2 = 40 kg

Therefore, the mean of the distribution is approximately 43.5 kg, and the median is 40 kg.

Answer:

Step-by-step explanation:

1st 10 days - 8 GB

2nd 10 days - 8 GB

3rd 10 days - 8 GB

________________

30 days    -  24 GB

The value of the given expression pie multiplied by 3 squared multiplied by 4.5 is 127. 29

pie is a mathematical symbol written as π and it has a constant value of 22/7

pie multiplied by 3 squared multiplied by 4.5

π × 3² × 4.5

= 22/7 × 9 × 4.5

Multiplying the numerators and denominators separately

= (22 × 9 × 4.5) / 7

= 891 / 7

= 127.2857142857142

Approximately, 127. 29

Hence, 127. 29 is the simplified value of pie multiplied by 3 squared multiplied by 4.5.

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Answer:

p = 8

Step-by-step explanation:

Divide -5 to both sides

-5p = -40

5p = 40

p = 8

So p = 8

1. The quadratic function for the Area in terms of x: A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is 0.

3. The maximum cross-sectional area is square inches 0.

To determine the depth of the gutter that maximizes its cross-sectional area and allows the greatest amount of water to flow, we need to follow a step-by-step process.

1. Write a quadratic function for the area in terms of x:

The cross-sectional area of the gutter can be represented as a rectangle with a width of 24 inches and a depth of x. Therefore, the area, A(x), is given by A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is:

To find the value of x that maximizes the area, we need to find the vertex of the quadratic function. The vertex of a quadratic function in form f(x) = ax² + bx + c is given by x = -b/(2a). In our case, a = 0 (since there is no x² term), b = 24, and c = 0. Thus, the depth of the gutter that maximizes the area is x = -24/(2 * 0) = 0.

3. The maximum cross-sectional area is square inches:

Substituting the value of x = 0 into the quadratic function A(x) = 24x, we get A(0) = 24 * 0 = 0. Therefore, the maximum cross-sectional area is 0 square inches.

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During the morning rush hour, there are 6,400 junior and high school students, 3,400 adults, and 5,800 senior citizens riding the subway.

Let's assume the number of junior and high school students riding the subway during the morning rush hour is J, the number of adults is A, and the number of senior citizens is S.

From the given information, we can set up a system of equations based on the number of riders and the revenue generated.

Equation 1: J + A + S = 15,600 (total number of riders)

Equation 2: 1.04J + 2.20A + 1.04S = 32,464 (revenue equation with original ticket prices)

Equation 3: 1.24J + 2.60A + 1.04S = 38,264 (revenue equation with new ticket prices)

We can start by subtracting Equation 2 from Equation 3 to eliminate the J and S terms:

0.2J + 0.4A = 3,800

Next, we can multiply Equation 1 by 0.2 and subtract it from the above equation to eliminate the J term:

0.4A - 0.2J - 0.2A = 3,800 - 3,120

0.2A = 680

A = 680 / 0.2 = 3,400

Now, we can substitute the value of A back into Equation 1 to find the values of J and S:

J + 3,400 + S = 15,600

J + S = 15,600 - 3,400

J + S = 12,200

We have two equations with two variables (J + S = 12,200 and 1.04J + 1.04S = 12,264). By solving these equations simultaneously, we find J = 6,400 and S = 5,800.

Therefore, during the morning rush hour, there are 6,400 junior and high school students, 3,400 adults, and 5,800 senior citizens riding the subway.

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To find the number of subway riders in each category, we set up a system of equations based on the total number of passengers and the total revenue. Solving this system will give us the number of junior and high school students, adults, and senior citizens. The number of riders doesn't change with the increase of ticket prices.

To solve this problem, we set up a system of equations based on the information given in the question.

Let's denote the number of junior and high school students as J, adults as A, and senior citizens as S. We know that there's total of 15,600 passengers, so:

J + A + S = 15,600

We also know that the total revenue was $32,464. Given the ticket prices for each group, we can write:

$1.04J + $2.20A + $1.04S = $32,464

Solving this system of equations (possibly with the help of a calculator or computer software), we can find the number of riders in each category.

The number of riders for each category would only change if the number of riders changes, not the price of the tickets, so when the prices increase, the number of riders remains the same.

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The probability of losing the game is 0.9399. So, the answer is 0.9399.

The probability of losing the game is 0.9399. To determine the probability of losing, we must subtract the probability of winning from 1.

The probability of losing is equal to the complement of the probability of winning, and the complement of an event is the probability of the event not occurring.

Therefore, we will calculate the probability of the event not winning.  

We know that the probability of winning a two-spot Keno game is 0.0601.

This means that the probability of not winning is 1 - 0.0601 = 0.9399.

Therefore, the probability of losing the game is 0.9399. So, the answer is 0.9399.

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Answer:

Step-by-step explanation:

You want the number of tickets sold at prices of $6.50 and $10 if 386 tickets were sold for $3576.50.

The number of $6.50 ticket is (386 -x) if x tickets were sold at $10. The total revenue will be ...

  10x +6.50(386 -x) = 3576.50

  3.50x +2509 = 3576.50 . . . . . simplify

  3.50x = 1067.50 . . . . . . . . . . . subtract 2509

  x = 305 . . . . . . . . . . . . . . . . . . divide by 3.50

  386 -x = 81 . . . . . . . . . find the number of cheap seats

305 tickets were sold for $10; 81 tickets were sold for $6.50.

<95141404393>

The equation of the best fit line is (b) y = -0.98x + 0.8

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

The graph

Using the least squares, we have the following summary

The regression equation is

y = mx + b

Where

m = SP/SSX = -10.6/10.8 = -0.98148

b = MY - bMX = 0.6 - (-0.98*0.2) = 0.7963

So, we have

y = -0.98x + 0.8

Hence, the equation is y = -0.98x + 0.8

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Answer: 4000

Step-by-step explanation:

The inequalities that define the unshaded region for this problem is given as follows:

For the solid line, we have that it has a slope of 4 with an intercept of 0, and the values that are above the line are shaded, hence the inequality is given as follows:

y ≥ 4x.

For the dashed line, we have a line with a slope of 1 and an intercept of -4, and the values that are below the line are shaded, hence the inequality is given as follows:

y < x - 4.

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The width of the pen is approximately 0.47 feet, and the length would be approximately 10.47 feet.

Let's assume the width of the rectangular dog pen is represented by "w" feet. According to the given condition, the length is 10 feet longer than the width, so the length would be "w + 10" feet.

The area of a rectangle is calculated by multiplying its length by its width. In this case, the area is given as 100 square feet. We can use this information to set up an equation:

[tex]w \times (w + 10) = 100[/tex]

Expanding the equation, we get:

[tex]w^2 + 10w = 100[/tex]

Rearranging the equation and setting it to zero, we have a quadratic equation:

[tex]w^2 + 10w - 100 = 0[/tex]

To solve this equation, we can factorize it or use the quadratic formula. Factoring doesn't yield integer solutions, so we'll use the quadratic formula:

[tex]w = (-b \pm \sqrt(b^2 - 4ac)) / (2a)[/tex]

Plugging in the values, we get:

w = (-10 ± √(10^2 - 4 * 1 * -100)) / (2 * 1)

Simplifying further:

w = (-10 ± √(100 + 400)) / 2

w = (-10 ± √500) / 2

w = (-10 ± 10√5) / 2

w = -5 ± 5√5

Since the dimensions cannot be negative, we take the positive value:

w ≈ 0.47 feet

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Answer:

D. 188

Step-by-step explanation:

Because the water tank's dimensions are 6 feet by 4 feet by 7 feet, this means that the areas of the three pairs of opposite faces are:

So, the total surface area of the water tank is 2 * (24 + 42 + 28) = 188 square feet.

a) The sum of the areas of all the squares is 2 unit².

b) The sum of the perimeters of all squares is [tex]\frac{4\sqrt{2} }{\sqrt{2} -1}[/tex] unit.

In Mathematics and Geometry, the area of a square can be calculated by using this mathematical equation (formula);

A = x²

Where:

Area of 1st square, A₁ = 1² unit².

Area of 2nd square, A₂ = (1/√2)² unit².

Area of 3rd square, A₃ = (1/2)² unit².

Therefore, the sum of the areas of all the squares is given by;

Sum of all areas = A₁  + A₂ + A₃ + ...... + Aₙ

Sum of all areas = 1² + (1/√2)² + (1/2)² + .....

Common ratio, r = 1/2 and the first term is 1.

Sum of all areas to infinity = 1/(1 - 1/2)

Sum of all areas to infinity = 2 unit².

Part b.

In Mathematics and Geometry, the perimeter of a square can be calculated by using the following formula;

P = 4x

Perimeter of 1st square, P₁ = 4(1) unit.

Perimeter of 2nd square, P₂ = 4(1/√2) unit.

Perimeter of 3rd square, P₃ = 4(1/2) unit.

Therefore, the sum of the perimeter of all the squares is given by;

Sum of all perimeters = 4(1) + 4(1/√2) + 4(1/2) + .....

Sum of all perimeters = 4(1 + 1/√2 + (1/√2)² + ....)

Common ratio, r = 1/√2 and the first term is 1.

Sum of all perimeters to infinity = [tex]4(\frac{1}{1-\frac{1}{\sqrt{2} } } )[/tex]

Sum of all perimeters to infinity = [tex]\frac{4\sqrt{2} }{\sqrt{2} -1}[/tex] unit.

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Answer:

To find the probability for each scenario, we can use combinations and the probability of winning a single game, assuming each player has an equal chance of winning. Since there are only two players, there are two possible outcomes for each game: a win for Ryan or a win for Alex.

i) Ryan wins 3 games:

There are a total of 3 games to be played, and Ryan needs to win 3 of them. The number of ways to choose which games Ryan wins out of the 3 is given by the combination formula: C(3,3) = 1. The probability of Ryan winning a single game is 1/2, so the probability of Ryan winning all 3 games is (1/2)^3 = 1/8. Therefore, the probability of Ryan winning exactly 3 games in the next set of 3 is:

P(Ryan wins 3 games) = C(3,3) * (1/8) = 1/8

ii) Two games end in a draw:

There is only 1 way for 2 games out of 3 to end in a draw (assuming no ties in the third set). The probability of a draw in a single game is also 1/2. So, the probability of two games ending in a draw is (1/2)^2 = 1/4. Therefore, the probability of two games ending in a draw in the next set of 3 is:

P(Two games end in a draw) = 1 * (1/4) = 1/4

iii) Each player wins alternatively:

There are 2 ways that the players can alternate wins in a 3-game set: either Ryan wins the first and third games, or Alex wins the first and third games. In each case, the probability is (1/2) * (1/2) = 1/4. Therefore, the probability of each player winning alternatively in the next set of 3 is:

P(Each player wins alternatively) = 2 * (1/4) = 1/2

iv) Alex wins at least one game:

The only way that Alex cannot win any games is if Ryan wins all 3 games, which we calculated in part i to have a probability of 1/8. Therefore, the probability of Alex winning at least one game in the next set of 3 is:

P(Alex wins at least one game) = 1 - P(Ryan wins

The equation of the best fit line is y = -8.21x + 14.39

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

The table of values

Using the least squares, we have the following summary

The regression equation is

y = mx + b

Where

m = SP/SSX = -2.3/0.28 = -8.21429

b = MY - bMX =  7 - (-8.21*0.9) = 14.39286

So, we have

y = -8.21x + 14.39

Hence, the equation is y = -8.21x + 14.39

Read more about line of best fit at

brainly.com/question/31894011

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