Please help! Correct answer only!

You can play a game with a wheel whose rim is divided into equal sections marked with the numbers from 1 to 10. If you play, the attendant will spin the wheel and a ball will land in a random section. If the number the ball lands on is odd, you win $25. If the number the ball lands on is even, you win nothing. If you play the game, what is the expected payoff?

$___

The interest on the loan is: $375.44

The maturity value is: $4,775.44.

Maturity value and interest on a loan can be calculated as follows:

Maturity value: it is the amount of the loan plus the interest charged on it. It can be calculated using the formula:

MV = P + I

where MV is the maturity value, P is the principal (original loan amount), and I is the interest charged on the loan.

Interest: it is the amount charged by the lender for the use of their money. It can be calculated using the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the term of the loan (in years or days).

Therefore:

Exact interest: 4,400 * 6% * 172/365 = $375.44

Maturity value: 4,400 + 375.44 = $4,775.44

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Chance is 1/10

Given that the die has 20 different numbers, ranging from 1-20, we are to determine the chance that the top side will be either a 9 or a 10.When throwing a die with a different number of faces or sides, each face has an equal chance of showing up as the top side. Thus, to determine the chance that the top side will be either a 9 or a 10, we need to find the probability of rolling a 9 or 10.To calculate the probability of a single event occurring, we divide the number of favorable outcomes by the total number of possible outcomes. Thus, in this case, the probability of rolling a 9 or a 10 would be:Probability of rolling a 9 or a 10= number of favorable outcomes/ total number of possible outcomesNumber of favorable outcomes: 2 (since there are only 2 sides of the die that have a 9 or a 10)Total number of possible outcomes: 20 (since there are 20 different numbers on the die)Probability of rolling a 9 or a 10 = 2/20 = 1/10Therefore, the chance that the top side will be either a 9 or a 10 is 1/10.

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The summation is Σ(xᵢ-4)², i=1,2,3...

What is summation ?

When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labelled "+" is defined can all be added together, in addition to numbers.

Series are summations of infinite sequences. They are related to the idea of limit but are not covered in this article.

Let x serve as the definition of a score.

Each score will be xi, i.e. x1, x2, x3, x4... for the first four consecutive scores, and so on.

By deducting 4 from each score, you get xi-4.

Squaring the Resulting Value = (xi-4)²

The sum of the squared numbers is equal to (xi-4)²

where i=1, 2, 3.

Σ(xᵢ-4), The set of instructions written in summation notation is 2.

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Σ(xᵢ-4)² is the set of instruction expressed in summation notation.

What is Summation Notation?

The summation symbol, S, tells us to add up the sequence's components. To the right of the summation sign is a typical component of the sequence that is being summed. An index that appears below the summation sign designates the variable of summation.

Let a score be defined by x,

Each score will be xᵢ i.e. x₁, x₂, x₃, x₄... for the first four consecutive scores and so on.

Subtracting 4 from each score = xᵢ-4

Squaring the Resulting Value = (xᵢ-4)²

The sum of the squared numbers = Σ(xᵢ-4)², i=1,2,3...

Σ(xᵢ-4)² is the set of instruction expressed in summation notation.

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The equation of line t in slope intercept form is 5y - 3x = -1

The equation of line s is y=3/5x + 2/5

This is in the slope intercept form

y = mx + c

where m represents the slope of the line

The slope of the line  y=3/5x + 2/5 is 3/5

The slope of two parallel line is same

The slope of line t is 3/5, it passes through the points (2, 1)

The equation of the line is

y - y₁ = m(x - x₁)

y - 1 = 3/5 (x - 2)

5y - 5 = 3x - 6

5y - 3x = -6 + 5

5y = 3x  -1

y = 3/5 x - 1/5

Therefore, the equation of line t in slope intercept form is 5y - 3x = -1

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By using the formula for mean and variance, it can be calculated that

Mean of X = 25

Variance of X = 51.67

What is mean and variance?

Suppose there is a data set. Mean gives the average of the values of the data set

Variance is the square of the sum of deviation from mean.

Let x be the total; of the numbers on the two card

Possible values of X= 15, 20, 25, 30, 35

P(X = 15) = \(\frac{2}{12}\)

P(X = 20) = \(\frac{2}{12}\)

P(X = 25) = \(\frac{4}{12}\)

P(X= 30) = \(\frac{2}{12}\)

P(X = 35) = \(\frac{2}{12}\)

Mean of X =

\(15 \times \frac{2}{12} + 20 \times \frac{2}{12} +25 \times \frac{4}{12} + 30 \times \frac{2}{12} + 35 \times \frac{2}{12}\\\\\frac{300}{12}\\\\25\)

Variance of X =

= \((225 \times \frac{2}{12} + 400 \times \frac{2}{12}+625 \times \frac{4}{12}+900 \times \frac{2}{12}+1225 \times \frac{2}{12}) - (25)^2\\\\\frac{8000}{12} - 625}\\\\666.67 - 625\\\\51.67\)

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Complete Question

In a box are four cards numbered 5, 10, 15, 20. two cards are taken out at random without replacement, and X is the total; of the numbers on the two card. Find the mean and variance of X .

Given:

When x=0,

When x=1,

When x=2,

When x=-1,

When x=-2,

Option A is the correct answer.

Therefore, the minimum size box needed to pack 120,000 staples is a rectangular prism with dimensions 20 x 10 x 10 centimeters (length x width x height) and a volume of 500 cubic centimeters.

Volume is the measure of the amount of space occupied by a three-dimensional object, such as a solid, liquid, or gas. It is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). For example, the volume of a rectangular prism can be calculated by multiplying the length, width, and height of the prism together, while the volume of a sphere can be calculated using a formula involving the radius of the sphere.

Here,

To determine the minimum size box needed to pack 120,000 staples given that 100 staples are packed into each small box, we need to find the number of small boxes required and then calculate the volume of the large box required to pack them.

The number of small boxes required can be found by dividing the total number of staples by the number of staples in each box:Number of small boxes = 120,000/100 = 1,200

Now, to determine the volume of the large box needed, we need to know the dimensions of a single small box. Let's assume that each small box is a rectangular prism with dimensions length (l), width (w), and height (h). We don't know these dimensions, but we can assume that the ratio of length to width to height is 2:1:1, which is a common shape for small boxes.

Let L, W, and H be the dimensions of the large box. We can calculate these dimensions as follows:

L = 2l (since the length of the large box will be twice the length of a small box)

W = w (since the width of the large box will be the same as the width of a small box)

H = h (since the height of the large box will be the same as the height of a small box)

The volume of the large box is then given by:

Volume = LWH

Substituting the values of L, W, and H, we get:

Volume = 2lwh

To find the minimum size box needed, we need to minimize the volume subject to the constraint that 1,200 small boxes must fit inside. This can be done using calculus, but it turns out that the minimum volume occurs when the dimensions of the large box are equal to the dimensions of the small box. Therefore, we can assume that:

l = 10 cm (since each small box contains 100 staples, and we can assume that the staples are packed in a 10 x 10 x 10 array)

w = 5 cm (since the width of the small box is half the length)

h = 5 cm (since the height of the small box is also half the length)

Substituting these values into the formula for the volume of the large box, we get:

Volume = 2lwh

= 2(10)(5)(5)

= 500 cubic centimeters

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Answer:

6 and 7

Step-by-step explanation:

Answer:

6&7

Step-by-step explanation:

6*6=36

7*7=49

The possible values of x in the figure are given as follows:

x > 3/2.

The possible values of x are obtained verifying if the given dimensions form a triangle, and the condition is that the sum of the lengths of the two smaller sides has to be greater than the length of the greatest side.

For the triangle given in the image, the dimensions are given as follows:

Hence, applying the condition, the inequality to obtain the values of x is given as follows:

2x + 4x - 3 > 4x.

Then, solving the inequality, the possible values of x in the triangle are given as follows:

2x + 4x - 3 > 4x

2x > 3

x > 3/2.

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Answer:

Step-by-step explanation:

Answer:

I think this should be C.

Step-by-step explanation:

Answer:

the moment of inertia of the uniform cylinder is 0.154 kg * m^2.

Step-by-step explanation:

Answer:

Justin did not eat 7/12 of the pizza

Step-by-step explanation:

Marc eats 1/6 × 24 = 4, 24 - 4 = 20 left over

Claudine eats 1/4 × 20= 5, 20 - 5 = 15 left over

Sylvia eats 1/3 × 15 = 5, 15 - 5 = 10 left over

Justin eats 10.

24 - 10 = 14

Justin did not eat 14/24 = 7/12

In right triangle ABC, side AB is 8 units and BC is 8 units.

A right angled triangle is a triangle with one of the angles as 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.

Given that, ∠BAD=∠BCD=45°

By using angle sum property of triangle in triangle ABD,

We get ∠ABD=45°

By using angle sum property of triangle in triangle BCD,

∠CBD=45°

So, AB = 8 units and BC= 8 units

Therefore, in right triangle ABC, side AB is 8 units and BC is 8 units.

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Answer:

3 negative 3 positive

Step-by-step explanation:

-3+3=0

Answer:

8 and 4

Step-by-step explanation:

8 x 4= 32

8+4 = 12

There is insufficient evidence to reject the null hypothesis, and we cannot conclude that the actual overall mean diameter of the ball bearings is not 4.300 mm.

The standard deviation (s) of the ball bearings' diameters is given as 0.005 mm, indicating the variability in the measurements. The overall mean diameter (µ) is specified as 4.300 mm. A sample of 81 ball bearings (n) has a sample mean of 4.299 mm. To determine whether there's reason to believe that the actual overall mean diameter is not 4.300 mm, we need to conduct a hypothesis test.

We begin with stating the null hypothesis (H₀) as: µ = 4.300 mm, and the alternative hypothesis (H₁) as: µ ≠ 4.300 mm. To conduct the hypothesis test, we can use the Z-test since the sample size is large (n ≥ 30). The Z-test statistic is calculated as:

Z = (sample mean - µ) / (s / √n)

Plugging in the values:

Z = (4.299 - 4.300) / (0.005 / √81) ≈ -1.8

Now, we need to find the p-value associated with this Z-score. The p-value helps us to determine the likelihood of observing a sample mean as extreme as 4.299 mm, given that the null hypothesis is true. A low p-value (typically, p < 0.05) would indicate that there is evidence to reject the null hypothesis in favor of the alternative hypothesis.

In this case, the p-value associated with a Z-score of -1.8 is approximately 0.072, which is greater than 0.05. Therefore, there is insufficient evidence to reject the null hypothesis, and we cannot conclude that the actual overall mean diameter of the ball bearings is not 4.300 mm.

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a and c are directly proportional to each other when a and b are directly proportional and b and c are directly proportional.

If a and b are directly proportional and b and c are directly proportional, it means that their ratios are equal. Direct proportionality implies that as one variable increases, the other also increases in proportion and as one variable decreases, the other also decreases in proportion.

Mathematically, this can be written as

a = kb and b = mc, where k and m are constants of proportionality.

Multiplying these two equations gives: a = kbm

Substituting the value of b from the second equation in the first equation, we get: a = kmc

Therefore, a and c are also directly proportional to each other with a constant of proportionality km.

Thus, if a increases by a certain factor, c will also increase by the same factor.

If a and b are directly proportional and b and c are directly proportional, then it can be concluded that a and c are directly proportional as well.

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Therefore, the average number of machines waiting for service is 0.083 (rounded to three decimal places).

To calculate the average number of machines waiting for service, we can use the concept of the M/M/1 queue, where arrivals follow a Poisson distribution and service times follow a negative exponential distribution.

In this case, the arrival rate (λ) is 1 breakdown every 4 working days, and the service rate (μ) is 1 repair job per day.

The utilization factor (ρ), which represents the system's utilization, can be calculated as ρ = λ/μ = (1/4)/(1) = 1/4.

The average number of machines waiting for service (Lq) can be calculated using the formula Lq = ρ² / (1 - ρ).

Plugging in the values, we have Lq = (1/4)²/ (1 - 1/4) = 1/12.

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Answer: -c^12+9c^4

Step-by-step explanation:

Answer: 81 c^4 - c^12

Step-by-step explanation:

(9c^2+c^6)(9c^2-c^6)

Step-by-step explanation: (9c^2+c^6)(9c^2-c^6)

This is the difference of squares

(a+b) (a-b) = a^2 - b^2

(9c^2) ^2 - ( c^6)^2

81 c^4 - c^12

Answer:

1, 3 &4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Work Shown:

9/12 = (x+4)/(2x)

9(2x) = 12(x+4)

18x = 12x+48

18x-12x = 48

6x = 48

x = 48/6

x = 8

Answer:

Step-by-step explanation:

I need the statements please.

(a) The marginal density functions fX and fY is FY(y) = 3y(2y+1)

(b)The probability that X + Y ≤ 1 is P(X + Y ≤ 1) = 5/16

(a) To discover the negligible thickness work of X, we coordinated the joint thickness work with regard to y over the extent of conceivable values of y:    

fX(x) = ∫ f(x,y) dy = ∫ 3(2−x)y dy,   0<x<2

Assessing the necessary, we get:

fX(x) = (3/2)*(2-x)²,   0<x<2

To discover the negligible thickness work of Y, we coordinated the joint thickness work with regard to x over the extent of conceivable values of x:

FY(y) = ∫ f(x,y) dx = ∫ 3(2−x)y dx,   0<y<1

Assessing the necessary, we get:

FY(y) = 3y(2y+1),   0<y<1

(b) To calculate the likelihood that X + Y ≤ 1, we got to coordinate the joint thickness work over the locale of the (x,y) plane where X + Y ≤ 1:

P(X + Y ≤ 1) = ∫∫ f(x,y) dA,   where A is the locale X + Y ≤ 1

We will modify the condition X + Y ≤ 1 as y ≤ 1−x. So the limits of integration for y are to 1−x, and the limits of integration for x are to 1:

P(X + Y ≤ 1) = \(∫0^1 ∫0^(1−x)\) 3(2−x)y dy dx

Evaluating the inner integral, we get:

\(∫0^(1−x)\) 3(2−x)y dy = (3/2)*(2−x)*(1−x)²

Substituting this into the external indispensably, we get:

P(X + Y ≤ 1) = ∫0^(3/2)*(2−x)*(1−x)²dx

Assessing this necessarily, we get:

P(X + Y ≤ 1) = 5/16

Hence, the likelihood that X + Y ≤ 1 is 5/16.

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Answer:

Hey! I hope this helps. I used ratio, I divided $28.50 by 2 to find out how much she worked for in an hour then I multiplied by 15.

Answer:

15% should be the answer because 60 + 25 is 85 and the remaining is classic rock which is 15%

The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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