Teen Cigarette Use Is Down The US Centers for Disease Control conducts the National Youth Tobacco Survey each year. The preliminary results1 of 2019 show that e-cigarette use is up among US teens while cigarette use is down. We examined e-cigarette use in Exercise 3. 137 and here we estimate cigarette use. In the sample of 1582 teens, 92 reported smoking a cigarette in the last 30 days

The probability that the first 5 seasons you receive in the mail are the first 5 seasons that were made, in the correct order is given as follows:

p = 1/30240.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

5 seasons are going to be shown from a set of 10, and the order is relevant, hence the permutation formula is used to obtain the total number of outcomes, as follows:

P(10, 5) = 10!/5!

P(10, 5) = 30240.

Only one of the outcomes has the correct seasons and order, hence the probability is given as follows:

p = 1/30240.

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The net present value of this investment, assuming a required 8% return, is approximately $13,829.

To calculate the net present value (NPV) of this investment, we'll first find the present value of the net cash flows and the salvage value, then subtract the initial investment.

For the net cash flows, we'll use the Present Value of Annuity (PVA) formula:

PVA = Net Cash Flow * [(1 - (1 + r)^(-n)) / r]

Where:
- Net Cash Flow is $11,000
- r is the required return (0.08)
- n is the number of years (7)

PVA = 11,000 * [(1 - (1 + 0.08)^(-7)) / 0.08]
PVA = 11,000 * 4.99271
PVA ≈ $54,920

Next, we'll find the present value of the salvage value at the end of year 7:

PV_salvage = Salvage Value / (1 + r)^n
PV_salvage = 6,700 / (1 + 0.08)^7
PV_salvage ≈ $3,909

Now, we can calculate the NPV by adding the present values and subtracting the initial investment:

NPV = (PVA + PV_salvage) - Initial Investment
NPV = (54,920 + 3,909) - 45,000
NPV ≈ $13,829

The net present value of this investment, assuming a required 8% return, is approximately $13,829.

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We can see here that the equation of the blue line is: y = -x -1.

Finding the value(s) of the variable(s) that make the equation true is the aim of an equation. These numbers are referred to be the equation's roots or solutions.

Finding an equation's answers may require algebraic manipulation, substitution, factoring, or other techniques, depending on how difficult the problem is.

The two points can be seen as thus:

(-1, 0) (0, -1)

Slope = -1.

Suppose, y = -x + a       (1, 0)

0 = - (-1) + a

a = -1

Thus, the equation is y = -x -1.

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The limit of Ln as n approaches infinity is -1/2, and it can be expressed as the definite integral ∫0¹ (x - 1) dx over the interval [0, 1].

To express the limit of Ln as n approaches infinity as a definite integral, we can use the definition of the definite integral as the limit of a Riemann sum. We can divide the interval [0, 1] into n subintervals of equal width Δx = 1/n, and evaluate Ln as the limit of the Riemann sum:

Ln = 1/n * [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]

where f(x) = x - 1 is the function being integrated.

Taking the limit as n approaches infinity, we have:

lim(n→∞) Ln = lim(n→∞) 1/n * [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]

= ∫0¹ (x - 1) dx

where we have used the fact that the limit of the Riemann sum is equal to the definite integral of the function being integrated.

Therefore, the limit of Ln as n approaches infinity is equal to the definite integral of (x - 1) over the interval [0, 1].

So,

lim(n→∞) Ln = ∫0¹ (x - 1) dx = [x¹ - x] from 0 to 1

= [1/2 - 1] - [0 - 0]

= -1/2

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According to the above, the fishing population is divided into 53% prefer fresh water and 47% prefer salt water.

To find the percentage of people that make up each group, we must find the total number of people who were surveyed:

228 + 245 + 242 + 285 = 1,000

Once we find the total number of people who took the survey, we can find the percentage of each value by making rules of three as shown below:

Age 30 and younger and Saltwater fishing:

1,000 = 100%

228 = ?%

228 * 100 / 1,000 = 22.8%

Age 30 and younger and Freshwater fishing:

1,000 = 100%

245 = ?%

245 * 100 / 1,000 = 24.5%

Over 30 years old and Saltwater fishing:

1,000 = 100%

242 = ?%

242 * 100 / 1,000 = 24.2%

Over 30 years old and Freshwater fishing:

1,000 = 100%

285 = ?%

285 * 100 / 1,000 = 28.5%

To find the other percentages we must find the total number of fishermen by age ranges and by fishing preference:

Age ranges

228 + 245 = 473

242 + 285 = 527

1,000 = 100%

473 = ?%

473 * 100 / 1,000 = 47.3%

1,000 = 100%

527 = ?%

527 * 100 / 1,000 = 52.3%

Fishing mode preferences

228 + 242 = 470

245 + 285 = 530

1,000 = 100%

530 = ?%

530 * 100 / 1,000 = 53%

1,000 = 100%

547 = ?%

470 * 100 / 1,000 = 47%

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The value of x in the similar figures is 2.33

When two figures have the same shape but their sizes are different, then such figures are called similar figures

The two polygons are similar

We have to find the value of x

Let us form a proportional equation

4590/21=510/x

4590x=21×510

4590x=10710

Divide both sides by 4540

x=10710/4590

x=2.33

Hence, the value of x in the similar figures is 2.33

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(a) With 98% confidence, the true average student loan debt for university students in Canada falls between $25,883.5 and $26,116.5.

(b) No, this does not contradict the reported average of $26,500.

(a) To construct a 98% confidence interval, we can use the formula:

CI = [tex]\bar{x}[/tex] ± z* (σ/√n)

where [tex]\bar{x}[/tex] is the sample mean, σ is the population standard deviation (unknown), n is the sample size, and z* is the z-value from the standard normal distribution that corresponds to the desired level of confidence (98% in this case).

Substituting the given values, we get:

CI = 26,000 ± 2.33 * (500/√64)
CI = 26,000 ± 116.5
CI = (25,883.5, 26,116.5)

Therefore, we can say with 98% confidence that the true average student loan debt for university students in Canada falls between $25,883.5 and $26,116.5.

(b) No, this does not contradict the reported average of $26,500. The reported average is within the confidence interval we calculated, which means that it is a plausible value for the true average. The sample mean of $26,000 is slightly lower than the reported average, but this could be due to random sampling error.

Overall, we cannot make a definitive conclusion about the true average based on this sample alone, but we can say with 98% confidence that it falls within the range of $25,883.5 to $26,116.5.

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The length of SQ to the nearest tenth of a foot is approximately 2.1 feet.

To find the length of SQ, we can use trigonometry. First, we can find the measure of angle R by subtracting the measures of angles Q and S from 180°:

R = 180° - 90° - 6° = 84°

Then, we can use the sine function to find the length of SX (which is equal to SQ):

sin(Q) = SQ / RS

sin(6°) = SQ / 20

SQ = 20 * sin(6°)

SQ ≈ 2.07 feet (rounded to the nearest tenth of a foot)

Therefore, the length of SQ to the nearest tenth of a foot is approximately 2.1 feet.

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If Polly reduced the price and sold 3 of the remaining necklaces for £8 each, she sold the remaining necklaces for £6.70 each.

First, let's find the original cost of the necklaces:
50 necklaces * £5 = £250

Now, let's calculate the profit Polly made:
£250 * 70% = £175

So, the total amount she made from selling the necklaces is:
£250 + £175 = £425

Polly sold 40% of the necklaces for £11 each:
50 necklaces * 40% = 20 necklaces
20 necklaces * £11 = £220

She sold 3 necklaces for £8 each:
3 necklaces * £8 = £24

Now let's find the amount left after selling these necklaces:
£425 - £220 - £24 = £181

Polly has 50 - 20 - 3 = 27 necklaces remaining. Let's find the price at which she sold each of the remaining necklaces:
£181 / 27 = £6.70

So, Polly sold the remaining necklaces for £6.70 each.

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This function is an example of exponential decay because the base of the exponential term (2/7) is between 0 and 1. and the y-intercept is 8.

To find the y-intercept, we need to evaluate the function when x=0, which gives:

y = 8 (2/7)^0 = 8

The given function is an example of exponential decay. In an exponential function, if the base of the exponent is between 0 and 1, the function shows exponential decay, and if it is greater than 1, the function shows exponential growth.

In the given function y = 8 (2/7)^x, the base of the exponent is 2/7, which is less than 1. This means that as the value of x increases, the value of the function decreases at a decreasing rate, which is the characteristic of exponential decay.

To find the y-intercept of the function, we can substitute x=0 in the given function. When x=0, we have:

y = 8 (2/7)^0

y = 8 x 1

y = 8

This means that the y-intercept of the function is (0, 8), which is the point where the function intersects the y-axis. In this case, it represents the initial value of the function when x=0.

Therefore, This function is an example of exponential decay because the base of the exponential term (2/7) is between 0 and 1. and the y-intercept is 8.

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The fraction, David used 13/8 cups of blueberries for the pancakes.

Let's solve it step-by-step using the given information.

1. David has 3 1/2 cups of blueberries.
2. He uses 1/4 cup for a breakfast smoothie.
3. He uses 1/2 of the remaining blueberries for pancakes.

Step 1: Calculate the remaining blueberries after making the smoothie.
3 1/2 - 1/4 = (7/2) - (1/4)

To subtract the fractions, they need a common denominator, which in this case is 4.

(7/2) * (2/2) - (1/4) = (14/4) - (1/4) = 13/4 cups

Step 2: Calculate the amount of blueberries used for the pancakes.
David uses 1/2 of the remaining blueberries for the pancakes, so:

(13/4) * (1/2) = 13/8 cups

David uses 13/8 cups of blueberries for the pancakes.

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Answer:

Based on the given information, we can conclude that the graph represents a quadratic function. The vertex of the parabola is located at (0, 9) and the function passes through several points including (-4, -7), (-3, 0), (3, 0), and (4, -7).

To find the equation of the function, we need to determine the value of "a" in the equation f(x) = ax^2 + bx + c. Since the vertex is located at (0, 9), we know that the x-coordinate of the vertex is 0. Therefore, we can use the vertex form of the equation, which is f(x) = a(x - 0)^2 + 9, or simply f(x) = ax^2 + 9.

Next, we can use one of the given points to solve for "a". Let's use the point (-3, 0).

0 = a(-3)^2 + 9

0 = 9a - 9

9 = 9a

a = 1

Therefore, the value of "a" in the equation of the function is B. 1.

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The width of the swamp is 12 feet, and the length is 50 feet.

length is 10 less than 5 times its width. We can write that as:

Equation for length:

L = 5W - 10

We also know that the perimeter of the swamp is 124 feet. The formula for the perimeter of a rectangle is:

Perimeter = 2(Length + Width)

So, we have:

124 = 2(L + W)

Now, we can substitute the expression for L from the first equation into the second equation:

124 = 2((5W - 10) + W)

Now, we can solve for W:

Step 2: solving for width

124 = 2(6W - 10)

62 = 6W - 10

72 = 6W

W = 12

Now that we have the width (W = 12 feet), we can find the length by plugging the width back into the equation for L:

Step 1: solving for length

L = 5W - 10

L = 5(12) - 10

L = 60 - 10

L = 50

So, the width of the swamp is 12 feet, and the length is 50 feet.

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The swamp has a perimeter 124 feet the length L of the swamp is 10 less than 5 times it width What are the length and the width of the swamp

To find the slope of the tangent line to the polar curve, we need to find the derivative of the equation with respect to θ.

First, we can convert the polar equation into rectangular coordinates using the conversions rcos(θ) = x and rsin(θ) = y:
rcos(θ) = (1-2sin(θ))cos(θ)
r = x/cos(θ)
x/cos(θ) = 1 - 2sin(θ)
x = cos(θ) - 2sin(θ)cos(θ)
y = sin(θ) - 2sin^2(θ)

Next, we can find the derivative of y with respect to x using the chain rule:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dθ = cos(θ) - 4sin(θ)cos(θ)
dx/dθ = -sin(θ) - 2cos^2(θ)
Plugging in the value of e for θ, we get:
dy/dθ = cos(e) - 4sin(e)cos(e)
dx/dθ = -sin(e) - 2cos^2(e)

Finally, we can find the slope of the tangent line by taking the ratio of dy/dθ to dx/dθ:
slope = (cos(e) - 4sin(e)cos(e)) / (-sin(e) - 2cos^2(e))
This is the slope of the tangent line to the polar curve at the point specified by the value of e.
Hi! I'd be happy to help you with your question. To find the slope of the tangent line to the polar curve r = 1 - 2sin(θ) at a specific value of θ, we'll first need to convert the polar equation into Cartesian coordinates.
Let's recall the conversion formulas:
x = r*cos(θ)
y = r*sin(θ)

Now, substitute the polar curve equation into these formulas:
x = (1 - 2sin(θ))*cos(θ)
y = (1 - 2sin(θ))*sin(θ)
To find the slope, we need the derivative of y with respect to x, which is dy/dx. To do this, we'll first find dy/dθ and dx/dθ.
Differentiating both x and y with respect to θ:
dx/dθ = -2cos(θ)^2 + 2sin(θ)cos(θ)
dy/dθ = -2sin(θ)^2 + 2sin(θ) - 2sin(θ)cos(θ)
Now, we find the derivative of y with respect to x:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dx = (-2sin(θ)^2 + 2sin(θ) - 2sin(θ)cos(θ)) / (-2cos(θ)^2 + 2sin(θ)cos(θ))

Now, you can plug in the specific value of θ for which you want to find the slope of the tangent line to the polar curve, and simplify the expression to obtain the final answer.

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The proper options provided for the required equation of a circle is

At the center of the circle there rests a y-axis, so its x-coordinate is equal to 0.

The formula for a specified circle with coordinates (0, k) and radius r is  

(x - 0)² + (y - k)² = r²

Therefore, the equation ends up categorically signified by:

x2 + (y – 3)2 = 36

x2 + (y + 8)2 = 36

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Answer:

-7x^2 + 15x +7

Step-by-step explanation:

-7x^2 + 5x + 10 - (-10x + 3)

-7x^2 + 5x + 10 + 10x -3.......when u distribute it multiple by -1

-7x^2 + 15x +7 ...... simplify by collecting like term.

The best point estimate is 15 hours. The 95% confidence interval for the population mean is (14.71, 15.29).

The best point estimate of the population mean is the sample mean, which is 15 hours since it was stated in the problem that the average time spent by college students on computer gaming is 15 hours.

To calculate the 95% confidence interval for the population mean, we use the formula:

CI = [tex]\bar{X}[/tex] ± z*(σ/√n)

where [tex]\bar{X}[/tex] is the sample mean, z is the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96), σ is the population standard deviation (given as 3), and n is the sample size (given as 350).

Plugging in the values, we get:

CI = 15 ± 1.96*(3/√350)

Simplifying, we get:

CI = 15 ± 0.29

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The coordinates of the point 1 / 4 of the way from A to B is (-2, -0.5).

To find the coordinates of the point that is 1/4 of the way from point A to point B, we can use the following formula:

Point P = (1 - t) x A + t x B

Given the coordinates of points A (-4, -2) and B (4, 4):

P x = (1 - 1/4) x Ax + (1/4) x Bx

P x = (3/4) x (-4) + (1/4) x 4

P x = -3 + 1

P x = -2

P y = (1 - 1/4) x Ay + (1/4) x By

P y = (3/4) x (-2) + (1/4) x 4

P y = -1.5 + 1

P y = -0.5

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The monthly payment for a new car priced at $24,530 with the given terms is $630.15.

Calculating the down payment:

20% of $24,530

= 0.20 × 24,530

= $4,906.

Subtracting the down payment from the car price:

= $24,530 - $4,906

= $19,624 (amount to finance).

Adding the 8% TT&L (tax, title, and license) to the amount to finance:

  8% of $24,530

= 0.08 × 24,530

= $1,962.40.

So, the total amount to finance

= $19,624 + $1,962.40

= $21,586.40.

Converting the annual interest rate of 3.16% to a decimal:

  3.16% / 100

= 0.0316.

Calculating the monthly interest rate:

 0.0316 / 12

= 0.002633.

Calculating the total number of payments: 36 months.

Using the monthly payment formula:

P = (PV * r * (1 + r)^n) / ((1 + r)^n - 1),

where P is the monthly payment,

           PV is the present value or amount to finance,

          r is the monthly interest rate, and

          n is the total number of payments.
Now, pluggin  in the values:

P = ($21,586.40 × 0.002633 × (1 + 0.002633)³⁶) / ((1 + 0.002633)³⁶ - 1)

= $630.15.

The monthly payment for the new car will be approximately $630.15.

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The probability that Lucky will get different colored socks is 1/6 or 1 out of 6.

To solve this problem, we can use the concept of probability and combinations.

Step 1: Determine the total number of possible outcomes.

When Lucky selects two socks without replacement, there are a total of 13 socks in the bag (5 red + 8 blue). So, the total number of possible outcomes is given by selecting 2 socks out of 13, which is represented as C(13, 2) or 13 choose 2.

C(13, 2) = (13!)/(2!(13-2)!) = (13 * 12)/(2 * 1) = 78

Step 2: Determine the number of favorable outcomes.

For Lucky to get different colored socks, there are two cases to consider: selecting a red sock first and a blue sock second, or selecting a blue sock first and a red sock second.

Case 1: Red sock first, then blue sock:

The number of ways to select one red sock out of five is C(5, 1) = 5. After selecting one red sock, there are eight blue socks remaining, and Lucky needs to select one blue sock out of eight, which is C(8, 1) = 8.

Case 2: Blue sock first, then red sock:

The number of ways to select one blue sock out of eight is C(8, 1) = 8. After selecting one blue sock, there are five red socks remaining, and Lucky needs to select one red sock out of five, which is C(5, 1) = 5.

So, the total number of favorable outcomes is 5 + 8 = 13.

Step 3: Calculate the probability.

The probability of getting different colored socks is the ratio of the number of favorable outcomes to the total number of possible outcomes:

P(Different Colored Socks) = Number of Favorable Outcomes / Total Number of Possible Outcomes

= 13 / 78

= 1/6

Therefore, the probability that Lucky will get different colored socks is 1/6 or 1 out of 6.

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The number of tire rotations depends on the distance traveled by the wheel and the circumference of the tire. Different tire sizes would change the circumference of the tire, and therefore the number of rotations of the wheel

1. Compare the original rotations _______ vs new rotations _________.

Without knowing the original and new rotations, answer cannot be provided

2.The number of tire rotations depends on the distance traveled by the wheel and the circumference of the tire. If the wheel traveled a greater distance, the number of rotations would increase, and if it traveled a shorter distance, the number of rotations would decrease. Similarly, if the tire's circumference increased, the number of rotations would decrease, and if the circumference decreased, the number of rotations would increase.

3. Different tire sizes would change the circumference of the tire, and therefore the number of rotations of the wheel. A larger tire size would result in fewer rotations for the same distance traveled, while a smaller tire size would result in more rotations for the same distance traveled. Therefore, when changing tire sizes, it's important to consider the effect on speedometer readings and potential changes in vehicle handling

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The number of parking spaces that the parking lot has is 32 parking spaces.

To start, we must ascertain the parking lot's length designed exclusively for parking spaces. Bearing in mind that 28 feet at one end of each row is left unmarked, this distance is subtracted from the overall parking lot length:

316 feet - 28 feet  = 288 feet

It is now established that the width of each space assigned to a car is equal to nine feet. Consequently, dividing the previously determined length used for parking by the allotted width per car will determine the total number of available parking spaces:

288 feet / 9 feet = 32 parking spaces

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Therefore , the solution of the given problem of equation comes out to be False.

In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.

Here,

False.

The order of operations we use to solve two-step equations is the same order we use to solve every other mathematical statement,

which is commonly recalled by the acronym PEMDAS. (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).

The fundamental distinction is that we are carrying out the operations against the equation's representation. For instance, consider the following equation:

=> 2x + 5 = 11

To get the following result, we would first subtract 5 from both sides, then divide by 2.

=> x = 3

In order to "undo" the operations that were carried out on the variable in the original equation, we are utilising the same series of operations as usual, but in reverse order.

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The circumference of the cake board is 35π cm.

The diameter of the round cake is 30 cm, which means its radius is 15 cm. The diameter of the circular cake board is 5 cm longer than that of the cake, which means its diameter is 30 + 5 = 35 cm. Therefore, the radius of the cake board is 17.5 cm.

The circumference of a circle is given by the formula:

[tex]$$C = 2 \pi r$$[/tex]

where [tex]$r$[/tex] is the radius of the circle. Using this formula, we can find the circumference of the cake board:

[tex]$$C = 2 \pi \cdot 17.5 = 35 \pi$$[/tex]

Therefore, the circumference of the cake board is 35π cm.

In other words, if you were to wrap a string or ribbon around the edge of the cake board, it would need to be 35π cm long.

This is an important measurement to consider when decorating or transporting a cake, as it can help ensure that the cake is centered on the board and that there is enough room for any additional decorations or trimmings.

In summary, the circumference of the cake board is 35π cm.

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The volume of the cylinder is 3811.7 cubic units when the radius is 9 and the width is 15.

Volume = π × radius² × height

Substitute the given values:
Volume = π × (9)² × 15

Squaring the radius:
Volume = π × 81 × 15

Multiplying the values together:
Volume = π × 1215

Calculating the volume using the approximate value of π (3.14):
Volume ≈ 3.14 × 1215

Calculating the final volume:
Volume ≈ 3811.7 cubic units

So, the volume of the cylinder with a radius of 9 and a height of 15 is approximately 3811.7 cubic units.

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a) It is verified that the situation is binomial

b. Probability of exactly coining 4 times is 1.83 × 10⁻³

c. Probability of winning atleast 3 times is 0.0234

d. Mean number of wins is 0.555

The total number of outcomes per toss is 6×6×6=216

a) Number of trails n = 20

Probability of win P = 6/216 = 1/36

Probability of lost Q = 1 - P

= 1 - 1/36

= 35/36

The outcome has two possibilities with P = 1/36, Q = 35/36  and with n = 20 times. Hence, it is binomial.

(B) Probability of exactly coining 4 times

[tex]P= C^{20}_{4} P^4Q^{16}[/tex]

= 4845 × (1/36)⁴ × (35/36)¹⁶

= 1.83 × 10⁻³

(C) Probability of winning atleast 3 times

[tex]P= 1-C^{20}_{0} P^0Q^{20}-C^{20}_{1} P^1Q^{19}-C^{20}_{2} P^2Q^{18}[/tex]

= 1 - 1 × (1/36)⁰ × (35/36)²⁰ - 20 × (1/36)¹ × (35/36)¹⁹ - 190 × (1/36)² × (35/36)¹⁸

= 1 - 0.5692 - 0.3252 - 0. 0882

= 0.0234

(D) Mean number of wins = nP

= 20 × (1/36)

= 0.555

a) It is verified that the situation is binomial

b. Probability of exactly coining 4 times is 1.83 × 10⁻³

c. Probability of winning atleast 3 times is 0.0234

d. Mean number of wins is 0.555.

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R= 1 and the interval of convergence is (-1, 1].

To find the radius of convergence, we can use the ratio test:

lim n→∞ |(-1)^n x^(n+1) Vn+5| / |(-1)^n x^n Vn+5| = lim n→∞ |x|

This limit exists for all x, and it equals 1 when |x| = 1. Therefore, the radius of convergence is R = 1.

To determine the interval of convergence, we need to check the endpoints x = -1 and x = 1 separately.

When x = -1, the series becomes:

∑ (-1)^n (Vn+5)

This is an alternating series with decreasing terms, so it converges by the alternating series test.

When x = 1, the series becomes:

∑ (-1)^n (Vn+5)

This is again an alternating series with decreasing terms, so it also converges by the alternating series test.

Therefore, the interval of convergence is (-1, 1].

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Answer:  325

Step-by-step explanation:

15*30-5*5-20*5=325

Answer: 875 square feet.

Step-by-step explanation: (25x30)+(5x20)+25

The area of the shaded region of the circle is A = 57,918.5 feet²

Given data ,

First, we need to find the area of the quarter circle:

Area of quarter circle = (1/4)  π ( r )²

= (1/4)  π ( 290 )²

= 66,018.5 feet²

Next, we need to find the area of the square:

Area of square = side²

= 90²

= 8,100 feet²

Now, we can find the area of the shaded section by subtracting the area of the square from the area of the quarter circle:

Area of shaded section = Area of quarter circle - Area of square

= 66,018.5 feet² - 8,100 feet²

= 57,918.5 feet²

Hence , the area of the shaded section of the field is 57,918.5 feet²

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The relationship between the amount of time spent practicing shooting free throws and the percentage made in a game can be described as a positive correlation.

As a basketball player dedicates more time to practicing free throws, their skill and accuracy in making these shots during a game typically improve.

Consistent practice is crucial for developing muscle memory and fine-tuning shooting techniques, which contribute to a higher success rate in making free throws during games. This increased success rate is reflected in the percentage of free throws made in a game, an essential factor that can influence the outcome of the match.

However, it is important to note that the correlation is not always linear. For example, a player who practices for hours on end may experience diminishing returns due to fatigue or lack of focus. Additionally, other factors such as pressure, game context, and individual differences in learning abilities can affect the percentage of free throws made in a game.

In conclusion, investing time in practicing free throws generally leads to an improvement in a player's in-game performance. While there are external factors that may influence the success rate, the positive correlation between practice time and the percentage of free throws made in a game emphasizes the importance of consistent and focused training for basketball players.

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