2. A carnival game uses a fair spinner with 16 sections. There are 2 white sections, 4 red sections, and 10 blue sections on the spinner. Part A Find the probability of each event. Express your answer as a fraction in simplest form. P(blue) = = P(green) = P(red) =​

Hello there. To solve this question, we'll find how many times George's grandpa is older than his grandson.

First, this is also called the ratio of the ages between George and his grandpa.

To find this, we divide their ages in the order Grandpa : Grandson as following:

Simplify the fraction by a factor of 8

This is how many times George's grandpa is older than him.

The algebraic expression for the area of desert in Africa is 5 x

Algebraic expressions are expressions that are comprised of variables, terms, factors, coefficients, and constants.

They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc.

From the information given, we have;

This can be expressed as;

Area of desert in Africa = 5 x

Thus, the algebraic expression for the area of desert in Africa is 5 x

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Answer:

301.6cm^2

Step-by-step explanation:

3x+2x+x+90°=360(sum of shoes in circle equals 360°)

6x+90=360

6x=360-90

6x=270

divide both sides by 6

6x/6=270/6

x=45°

therefore 3x=3*45

=135

Area of the shaded sector

area of a sector =β(tita) /360*πr^2

=3x/360*πr^2

=3*45/360*πr^2

135/360*πr^2

Let π be 22/7

note r=16

0.375*22/7*(16)^2

0.375*22/7*256

0.375*3.143*256

ANS=301.728

The measurement closest is 301.6cm^2

Iron Man will travel a distance of 273.12 meters before he touches the ground after passing you. So, this is the long answer to the given problem.

Step 1: Initial velocity (u) = 39.0 m/s Initial displacement (s) = -403 m (because he is moving in the downward direction)Acceleration (a) = 9.8 m/s² (due to gravity)

Step 2: We can use the formula for displacement: `s = ut + (1/2)at²`Where t is the time taken.

Step 3: Substituting the given values of u, s, and a, we get:-403 = 39t + (1/2) × 9.8 × t²-403 = 39t + 4.9t²

Step 4: We have a quadratic equation now, let's solve it.4.9t² + 39t - 403 = 0Using the quadratic formula: `t = (-b ± sqrt(b² - 4ac)) / 2a`Where a = 4.9, b = 39, and c = -403

Step 5: Solving the above equation, we get two values oft = 7.14 s and t = -9.32 s As time cannot be negative, we reject the negative value of t.So, Iron Man will take 7.14 seconds to reach the ground.

Step 6: Now, let's calculate the distance traveled by Iron Man to reach the ground.`s = ut + (1/2)at²` (from step 2)`s = 39 × 7.14 + (1/2) × 9.8 × 7.14²`= 273.12 meters.

Therefore, Iron Man will travel a distance of 273.12 meters before he touches the ground after passing you. So, this is the long answer to the given problem.

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Answer:

1. MAD for Jada's data set = 1

Step-by-step explanation:

Mean Absolute Deviation = sum of the distances of each data value from the mean ÷ number of data value

Jada's data set is given as: 4, 4, 4, 6, 6 ,6

Mean = 5

✔️Find the distance between each data value form the mean

4 = |4 - 5| = 1

4 = |4 - 5| = 1

4 = |4 - 5| = 1

6 = |6 - 5| = 1

6 = |6 - 5| = 1

6 = |6 - 5| = 1

✔️Find the sum of the distances of each data value from the mean

1 + 1 + 1 + 1 + 1 + 1 = 6

✔️Find the MAD:

MAD = 6/6

MAD = 1

A. The arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone boothe.

B. The arrival rate per hour must increase by at least 1.6 customers per hour to justify a second telephone booth under the new criterion.

To get the how much arrival rate must increase, we must get the expected waiting time for a customer.

Assuming;

X is the number of customers who arrive per hour

Y is the length of a phone call in minutes.

Then, X follows a Poisson distribution with λ = 4 (since 4 customers per hour use the phone on average)

Y follows a negative exponential distribution with mean μ = 5 (since the mean length of a phone call is 5 minutes).

Total time is given as sum of waiting time and length of call;

T = W + Y

The waiting time W is the difference between the time a customer arrives and the time that the phone becomes available. waiting time follows a uniform distribution where mean= 1/λ (since the arrivals follow a Poisson process);

Then we have;

E(W) = 1/(2λ) = 1/8 hours

The expected total time T that a customer spends at the phone booth is:

E(T) = E(W) + E(Y) = 1/8 + 5/60 = 11/48 hours

For a second telephone booth to be justifiable, new customer that arrives must wait 3 minutes or longer for the phone.

E(W) ≥ 1/20

To get λ,

1/(2λ) ≥ 1/20

λ ≤ 10

This means that, the arrival rate per hour must increase to at least 10 customers per hour to justify a second telephone booth.

b. Getting how much the arrival rate per hour must increase to justify a second telephone booth under the new criterion,

we need to find the probability that a customer has to wait at all.

Let P(W > 0) be the probability that a customer has to wait.

P(W > 0) = 1 - P(W = 0)

The waiting time W follows a uniform distribution with mean 1/λ, so we have:

P(W = 0) = 1 - λ/4

The length of a phone call Y follows a negative exponential distribution with mean 5 minutes = 1/12 hours, so we have:

P(Y > t) = e^(-μt) = e^(-t/12)

The probability that a customer has to wait is given as;

P(W > 0) = 1 - P(W = 0) = λ/4

To justify a second telephone booth, the probability of having to wait at all must exceed 0.6. so we have;

P(W > 0) > 0.6

λ > 2.4

The arrival rate per hour must increase by at least 2.4 - 4 = 1.6 customers per hour to justify a second telephone booth under the new criterion.

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Answer:

11%

Step-by-step explanation:

find the price of the shirts before markup by dividing 10800 by 400

You get 27, which you will subtract 30 by, getting you 3.

Divide this number by 27

.11

The amount of water that would be saved by the energy saving shower is 32 gallons. Option C

It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.

The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.

We can be able to attest that we have that the previous number of gallons that would be dispersed in the first  instance is;

7 gal/min * 8 mins

= 56 gallons

In the other case we use the equation for the energy saving shower;

y = 3(8)

= 24 gallons

We would now save;

56 gallons - 24 gallons

= 32 gallons of water

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Missing parts;

A standard shower head in Marty's house dispenses 7 gallons of water per minute. Marty changed this shower head to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new shower head.

y = 3x

How much water does Marty save each day with the change in shower heads if he uses the shower for 8 minutes each day?

A. 4 gallons

B . 12 gallons

C . 32 gallons

D . 53 gallons

The mean of the fitted exponential distribution is 66.67.

To find the mean of the fitted exponential distribution, we first need to estimate the parameter lambda using maximum likelihood estimation.

The probability density function of the exponential distribution is given by

f(x; lambda) = lambda * exp(-lambda * x)

where x is the claim size and lambda is the parameter to be estimated.

The likelihood function for the observed data is the product of the individual probabilities of each claim

L(lambda) = lambda^n * exp(-lambda * sum(x_i))

where n is the number of observed claims and x_i is the i-th claim size.

The log-likelihood function is given by:

ln L(lambda) = n * ln(lambda) - lambda * sum(x_i)

To estimate the parameter lambda, we need to maximize the log-likelihood function with respect to lambda:

d/d(lambda) ln L(lambda) = n/lambda - sum(x_i) = 0

Solving for lambda, we get

lambda = n / sum(x_i)

Substituting the observed values, we get

lambda = 6 / (20 + 45 + 50 + 80 + 100 + 2*100) = 0.015

Therefore, the estimated parameter of the fitted exponential distribution is lambda = 0.015.

The mean of the exponential distribution is given by

E(X) = 1/lambda

Substituting the estimated value of lambda, we get

E(X) = 1/0.015 = 66.67

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Answer:

answer was 3)

Step-by-step explanation:

Because function was star with 1,2,3,4,

The constraint optimization problem can be solved by determining the expressions for x' and y' and confirming the second-order condition using the bordered Hessian Matrix. The value function and the Envelope Theorem can be used to analyze the effects of changes in income and prices on the optimal value of u(x, y).

To find the expressions for x' and y', we set up the Lagrangian function:

\(L(x, y, \lambda) = 2x^2 + y - \lambda (p_x * x + p_y * y - M)\)

Taking partial derivatives with respect to x, y, and λ, we get:

\(\partial L/\partial x = 4x - \lambda p_x = 0\\\partial L/\partial y = 1 - \lambda p_y = 0\\p_x * x + p_y * y = M\)

Solving these equations simultaneously, we find the optimal values of x and y. Differentiating the first-order conditions, we obtain the second derivative expressions, denoted as 2". The bordered Hessian matrix can be used to confirm the second-order condition for part (a).

To derive the value function, we substitute the optimal values of x and y into the utility function: u(x, y) = 2(x')² + y'.

Suppose the income increases by one unit. We can determine the effect on the optimal value of u(x, y) by using the value function and considering the change in the optimal values of x and y.

Applying the Envelope Theorem, we can evaluate the change in the optimal value of u(x, y) by taking the derivative of the value function with respect to income, while keeping the prices constant.

Similarly, if the price of y increases by one unit, we can analyze the impact on the optimal value of u(x, y) using the Envelope Theorem and considering the change in the optimal values of x and y, with the price of y denoted as p.

These steps will help us understand the changes in the optimal values of u(x, y) under different scenarios based on the given utility function, prices, and income.

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You are approximately 29.25 meters away from your starting point. To find the distance from your starting point after walking 16 m straight east and then 24.5 m straight south, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the eastward distance of 16 m and the southward distance of 24.5 m form the two sides of a right triangle. Let's call the distance you are from your starting point (the hypotenuse) as "d."

Using the Pythagorean theorem, we have:

\(d^2 = (16^2) + (24.5^2)\)

\(d^2\) = 256 + 600.25

\(d^2\)= 856.25

Taking the square root of both sides, we find:

d = √856.25

d ≈ 29.25

Therefore, you are approximately 29.25 meters away from your starting point.

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Answer:

5

Step-by-step explanation:

The total amount of interest earned by the investment in n years is 100 times the product of the annual interest rate and the time period i.e., I = 100 * x * n

The total amount of interest earned by an investment can be calculated using the simple interest formula:

I = P * r * t

Where:

I = the total amount of interest earned

P = the principal investment amount

r = the annual interest rate as a decimal

t = the time period in years

In this case, the principal investment amount is $10,000, the annual interest rate is x percent (as a decimal, x/100), and the time period is n years. So, the total amount of interest earned can be represented by:

I = 10,000 * (x/100) * n

Simplifying this expression, we get:

I = 100 * x * n

Therefore, the total amount of interest earned by the investment in n years is 100 times the product of the annual interest rate and the time period. The units of this value will be dollars, since it represents the amount of interest earned.

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Answer:

20 kph

Step-by-step explanation:

Step 1:

10 : 30         Ratio

Step 2:

60 mins in hour        

Step 3:

10 : 30 = x : 60        Equation

Step 4:

30x = 600       Multiply

Step 5:

x = 600 ÷ 30         Divide

Answer:

x = 20

Hope This Helps :)

Answer:

001,23,83,88,112,132,667

Step-by-step explanation:

Are you kidding me that you need help on this?

Answer:

Step-by-step explanation:

2 + 1/3 = 2 1/3 = 7/3

35 = 35/1

35/1 : 7/3 = 35/1 × 3/7 = 105/7 = 15

The rise-over-run formula for the slope of a straight line is the basis of the high-low method.

What is slope of a straight line?

The slope of a straight line by joining two points is the rise over run formula. The subtraction between the two points of the y-coordinates is called the rise. And the subtraction between the two points of the x-coordinates is called the run. The slope can be calculated by dividing the rise by run.

The slope of a line either goes in the upward direction or in the downward direction or left direction or right direction. It determines the direction of the line. When the straight line goes in the upward direction, it means the rising line and slope is positive. When it goes in the downward direction, it means a falling line and slope is negative.

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The partial fraction decomposition of X₁(s) is (A / (s - r₁)) + (B / (s - r₂)) + (C / (s - r₃)).

To express the fraction X₁(s) = (s² + 4s + 3s) / (s³ + 5s² + 2s + 8) in partial fraction form, we need to decompose the rational function into simpler fractions. The general form of a partial fraction decomposition is:

X₁(s) = (A / (s - r₁)) + (B / (s - r₂)) + (C / (s - r₃))

where A, B, and C are constants, and r₁, r₂, and r₃ are the roots of the denominator polynomial.

To find the roots of the denominator, we set the denominator equal to zero and solve for s:

s³ + 5s² + 2s + 8 = 0

The roots of this cubic polynomial can be found using numerical methods or factoring techniques. Let's assume the roots are r₁, r₂, and r₃.

Then, we can express X₁(s) in partial fraction form as:

X₁(s) = (A / (s - r₁)) + (B / (s - r₂)) + (C / (s - r₃))

where A, B, and C are the constants we need to determine.

To find the values of A, B, and C, we can multiply both sides of the equation by the denominator (s³ + 5s² + 2s + 8) and simplify. This will give us a system of equations that we can solve to find the values of A, B, and C.

(s³ + 5s² + 2s + 8) * X₁(s) = A + B(s - r₁) + C(s - r₂)(s - r₃)

Expanding the left side and comparing coefficients, we get:

s² + 4s + 3s = A + (B + C) * s² + (-B * (r₁ + r₂ + r₃) + C * (r₁r₂ + r₁r₃ + r₂r₃)) * s + B * r₁r₂ + C * r₁r₃ * r₂r₃

By comparing the coefficients of the powers of s on both sides, we obtain a system of equations. Solving this system will give us the values of A, B, and C.

Once we have the values of A, B, and C, we can substitute them back into the partial fraction expression:

X₁(s) = (A / (s - r₁)) + (B / (s - r₂)) + (C / (s - r₃))

This completes the partial fraction decomposition of X₁(s).

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Courtney would take 8 hours to type a 50-page paper on her own. This is because the amount of time it takes to type a paper is directly proportional to the number of pages in the paper.

Kirsten and Courtney together took 6 hours to type 50-page paper. This means they both worked for 3 hours each.

Therefore, Courtney would take 8 hours to type a 50-page paper on her own.

Kirsten and Courtney worked together to type a 50-page paper in 6

hours. This means that each of them worked for 3 hours each. Thus, it would take Courtney 8 hours to type a 50-page paper on her own. To put it into perspective, she would need to work for double the time she worked with Kirsten to finish the paper alone. As such, it would take Courtney 8 hours to type a 50-page paper if she were to do it alone. This is because the amount of time it takes to type a paper is directly proportional to the number of pages in the paper. Consequently, Courtney would need to put in 8 hours of work to type a 50-page paper.

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Answer:

48 children

Step-by-step explanation:

For every 5 adults there are 2 children.

so for every 1 adult there is 2/5 of a child.

So number of children = 120 * 2/5

= 240/5

= 48.

PART A

We were told that the price of a T-shirt is $50

T shirt and backpack is $100

T shirt, backpack and sportsball is $125

If If Brennan's parents give him a $ 75 donation, let x represent the amount of money that he would still need to win the prize of a T -shirt , backpack , and sports ball. It means that

t + 75 = 125

Thus, the equation ito

The amount you should pay for a bond with a face value of $1000 is $719.6.

Find the price of the bond using the formula for the present value of an annuity with semi-annual payments:

P = [C x (1 - (1 / (1 + r/n)^(nt))) x (1 + r/n)^t] / (r/n)

where,

P = price of the bond

C = coupon payment

r = required rate of return

n = frequency of interest payments (in this case 2 for semi-annual)

t = time to maturity (in this case 20 semi-annual periods)

Substituting the given values in the formula:

P = [55 x (1 - (1 / (1 + 0.10/2)^(2*10)))) x (1 + 0.10/2)^20] / (0.10/2) = 719.6

Therefore, the price of the bond that pays a semi-annual coupon of 5.5% with a face value of $1000 and matures in 10 years, with a required rate of return of 10% is $719.6.

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The equation is: 3x^3 = 4x + 8

The form is ax^2 + bx + c = 0

Rewrite the given equation to equal 0:

Subtract 3x^2 from both sides to get:-3x^2 + 4x + 8  = 0

Now give each letter their value:

a = -3, b = 4, c = 8

(a) The function f = 1A is f-measurable.

(b) For every m ∈ N (m > 1), the set Em is f-measurable.

(a) To show that f = 1A is f-measurable, we need to show that the preimage of any Borel set B in R is f-measurable. Since f can only take values 0 or 1, the preimage of any Borel set B is either the empty set, X, A or X \ A, all of which are f-measurable. Therefore, f is f-measurable.

(b) To show that Em is f-measurable, we need to show that its complement E^c_m is f-measurable. Let E^c_m be the set of points that belong to less than m sets Ak.

Then E^c_m is the union of all intersections of at most m-1 sets Ak. Since each Ak is f-measurable, any finite intersection of at most m-1 sets Ak is also f-measurable. Hence, E^c_m is f-measurable, and therefore Em is also f-measurable.

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Answer:

x = 6

Step-by-step explanation:

Okay 16x - 6 is alternate interior to the 90 degrees angle.  Alternate interior is like if you make a slanted line \ like that those endpoints will be congruent.

So you would write the equation like this.

16x - 6 = 90 (add 6 on both sides)

16x = 96 (divide both sides by 16)

x = 6

I hope this helps ya!!

Answer:

Step-by-step explanation:

A) Two similar solids have a scale factor of 3:5. If the height of solid I is 3 cm, find the height of solid II (B) If the surface area of 1 is 54π cm, fine

If you draw all diagonals of a regular hexagon you have 5⋅6=30 possible triangles, but 5 of those are the same (the equilateral triangles) so we have 30−5=25 possible triangles.

In terms of geometry, a hexagon is a closed, six-sided polygon in two dimensions. A hexagon has six angles and six vertices. Hexa and gonio both denote the number six. A hexagon can be found in the shapes of a honeycomb, a football, a pencil face, and floor tiles. a standard hexagonal 2D geometric polygon with six equal-length sides and six equal-sized angles. All of the lines are closed, and there are no curving edges. A regular hexagon has 720 degrees of internal angles. Additionally, these shapes have six rotating and six reflective symmetries.

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