How many ways can 4 people each choose a piece of cake from 7 total (no sharing).

The probability that Jeff has to play the game exactly 5 times i.e he keeps playing until he wins prize is (0.25)⁵.

We have, a fast-food restaurant runs a promotion which consists some food items with games pieces. 1 in 4 game pieces is a winner. This means, probability of winning game or sucess (p) = 1/4 . Since number of trials is fixed, trials are independent and probability of success is constant in each trial, we can use Binomial distribution. The Binomial distribution probability formula is

P(X= x) = ⁿCₓ(p)ˣ(1-p)⁽ⁿ⁻ˣ⁾

where,n --> number of trials

p --> probability of success

x --> number of times for a specific outcome within n trials

ⁿCₓ --> number of combinations

we have calculate the probability that he has to play the game exactly 5 times, i.e

x = 5 . Jeff keeps playing until he wins and he wins when he play exactly 5 times so,n= 5

Now, plugging all known values in above formula we get,

P(X= 5) = ⁵C₅(0.25)⁵(1-0.25)⁰

=> P(X= 5) = ⁵C₅(0.25)⁵(0.75)⁰

=> P(X= 5) = 1× (0.25)⁵× 1 = (0.25)⁵

Hence, required probability is (0.25)⁵

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As per the Newton's method, the equal ration of the Pizza is 3: 2: 3

In math, Newton's method states that a technique for solving equations of the form f(x)=0 by successive approximation

Here we have given that three calculus students entered a pizza parlor. they were quite hungry and ordered an entire pie, instead of having the pizza maker cut the pie in the usual manner they asked her to slice the pie into three equal areas using only two parallel slices.

And we need to find these slices be made in order to accomplish this

Here let us assuming that the pizza has unit radius, and the area of the pizza is π and each piece has to have area π/3.

Therefore, the given details is enough to find the height of a circle segment such that its area is one third of the original circle,

As per the Newton's method, we get the value of h as,

=> h ≈ 0.735068 ≈ 4492/6111,

Therefore the three slices have widths approximately proportional to 3:2:3.

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The value of θ will -45° or 26.56°

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

Given that, cosec²θ = cotθ + 3

Solving for θ,

∵ cosec²θ = cot²θ+1

∴ cot²θ+1 = cotθ + 3

cot²θ-cotθ-2 = 0

Factorizing and solving, we get

(cotθ+1)(cotθ-2) = 0

cotθ+1 = 0

cotθ = -1

θ = -45°

or, cotθ-2 = 0

cotθ = 2

θ = 26.56°

Hence, The value of θ will -45° or 26.56°

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The linear function is  f(x) = 3x -5.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given linear function expression,

f(x) = mx + b

From the table,

x = -2

then, 1 = -2m +b       ......equation 1

Put x = 0

then, b = -5

Substitute the value of b to the equation 1, we get

m = 3

Finally, the function is f(x) = 3x -5

Therefore, the linear function is  f(x) = 3x -5

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Answer: x

≥

3

−

3

y

Step-by-step explanation:

Answer:

64 divided by 2= 32 80 divided by 32= 2.5

Tritan purchased a new car in 2000 for $22,800. The value of the car ha been depreciating exponentially at a constant rate then the Cost of the car in year 2016 will be $2811.

Cost price of the car = $22800

Value of the car has been depreciating exponentially, so the formula for value   of the car after t years,

Here P(t) = Final value after t years

A = Cost price or initial value

r = rate of depreciation

t = duration in years

r = 100(1 - 0.87737)

r = 12.26%

Now cost of the car in year 2016 (After 16 years)

P(16)  = 2810.99

       = $2811

Therefore, cost of the car in year 2016 will be $2811.

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Answer: a)

Step-by-step explanation:

To find [tex]\frac{dy}{dx}[/tex], we will have to use implicit differentiation, and because the base is [tex]dx[/tex], we will take the deriviative of both sides with respect to [tex]x[/tex].

To derive [tex]y[/tex] with respect to [tex]x[/tex], just derive the term with respect to y then multiply the term with [tex]\frac{dy}{dx}[/tex].

So [tex]\frac{d}{dx} x^{2}[/tex] is just [tex]2x[/tex], [tex]\frac{d}{dx} y^{2}[/tex] is [tex]2y \frac{dy}{dx}[/tex], and  [tex]\frac{d}{dx} 289[/tex] is 0. Now substitue each term with it's deriviative.

[tex]2x + 2y \frac{dy}{dx} = 0[/tex]

Now, just solve for  [tex]\frac{dy}{dx}[/tex] when [tex]x[/tex] is 8 and [tex]y[/tex] is 15

[tex]2(8) + 2(15)\frac{dy}{dx} = 0[/tex]

[tex]16 + 30\frac{dy}{dx} = 0[/tex]

[tex]\frac{dy}{dx} = \frac{-16}{30} = \frac{-8}{15}[/tex]

So the answer is choice a)

Answer:

Correct Statement : The y- intercept of Function A is greater than the y- intercept of Function B

Answer:

1. m<AOB = 50 degree

2. m<COD = 90 degree

3. m<BOD = 130 degree

4. m<AOD = 180 degree

Step-by-step explanation:

1. We see that <AOB has one leg at 0 and the other leg at 50 degrees, so the <AOB is 50 degrees.

2. We see that <COD has one leg at 0 and the other leg at 90 degrees, so the <COD is 90 degrees

3. We see that <BOD has one leg at 50 and the other leg at 180 leg, so the <BOD is 180 - 50 = 130 degree

4/ We see that <AOD has one leg at 0 and the other leg at 180 degrees, so the <AOD is 180 - 0 = 180 degrees

The required solutions are as follows,
1. Angle e = Angle a
2. Angle f = Angle c
3. Ange a, b, and c add up to 180°.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

here.
Angle e = Angle and as they are alternate angles,
Angle f = Angle c as they are alternate angles,

Ange a, b, and c add up to 180°. as they lie on a straight line.
Therefore angles e, f, and b also be added to  180°

Thus, the solution of the angles is shown above.

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Answer:

Step-by-step explanation:

3x - 19 = 2x + 1

x - 19 = 1

x = 20

2(20) + 1 + 5y + 19 = 180

40 + 1 + 5y + 19 = 180

41 + 5y + 19 = 180

5y + 19 + 41 = 180

5y + 60 = 180

5y = 120

y = 24

Answer:

1

Step-by-step explanation:

For function f(x), the average rate of change from x = a to x = b is:

average rate of change = (f(b) - f(a))/(b - a)

Here we have:

f(a) = f(-3) = -2.88

f(b) = f(2.5) = 2.62

average rate of change = (2.62 - (-2.88))/(2.5 - (-3)) = 1

Answer:

£2.53 just divide£7.60by 3

The instantaneous rate of change of f(x) = x³ − 5 at (2,3) is (b) 12

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

Function: f(x) = x³ − 5

Point = (2, 3)

Differentiate the function to get the instantaneous rate

This is represented as

f'(x) = 3x²

Substitute 2 for x in the equation

The 2 is coming from the x-coordinate in (2, 3)

So, we have

f'(2) = 3(2)²

Evaluate

f'(2) = 12

Hence, the instantaneous rate of change is 12

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Answer:

x⁵ - 1/3x² -1

Step-by-step explanation:

In order to write polynomials in standard form:

1) Find the degree (power) of each term

2) Arrange them in descending order (largest to smallest)

We have : -1 + x⁵ - 1/3x²

The degree of -1 is 0 since there is no power.

The degree of x⁵ is 5.

The degree of - 1/3x² is 2.

Now arranging them in descending order:

x⁵ has the largest degree, followed by - 1/3x² and then -1, so the polynomial in standard form is:

x⁵ - 1/3x² -1

Answer:

y=5x

Step-by-step explanation:

If y is 25 and x is 5

25 = 5 (5)

25=25

The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The line t that passes through the points (0, 2) and (8, -4) is given as,

(y - 2) = [(- 6 - 2) / (8 - 0)](x - 0)

y - 2 = - 0.75x + 0

y = -0.75x + 2

The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.

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Answer:

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

Given:

Find the discount:

Find the discount %:

Answer:

no

Step-by-step explanation:

we can test it

10=7(1)+5

10=7+5

10=12

not a solution

hopes this helps

The function available capacity for the four classes is 40 seats each. The protection level for class 1 is 40 seats, meaning that 40 seats are protected for class 1. 40 + 40 + 40 + 40 = 160

The booking limits for the four fare classes in a flight are given as 40, 40, 40, and 40, respectively. This means that the available capacity for these four classes is 40 seats each. The protection level for class 1 is 40 seats, meaning that 40 seats are specifically reserved for passengers in class 1. This ensures that passengers in class 1 are guaranteed at least 40 seats on the flight. The protection level for the other classes is also 40 seats each, ensuring that at least 40 seats are available for each class. This allows airlines to ensure that all of their classes have sufficient seating capacity for their passengers. 40 + 40 + 40 + 40 = 160

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Answer:

To calculate how long it will take for the plane to reach 18,000 ft, first find the difference between the plane's current altitude and its target altitude:

35,600 ft - 18,000 ft = 17,600 ft

Then, divide this difference by the rate of descent to find the time it will take for the plane to reach its target altitude:

17,600 ft / 3,200 ft/mile = 5.5 miles

Since the rate of descent is given in feet per mile, this result is equivalent to the time it will take for the plane to reach its target altitude. Therefore, it will take the plane 5.5 miles (or a similar amount of time) to reach 18,000 ft.

The function which can be used to find the relation between distance and time is f(t) = 130t.

As we know the train travels 260 kilometers in 2 hours,

then the distance traveled in one hour will be 130 kilometers.

distance = 130

when time = 0 ,

distance also = 0 , as the train has not started moving yet.

Then , the function which can tell bout the  relation will be ,

f(t) = 130t

where d = f(t)

Distance is a scalar quantity which tells us about how far an object is from its starting position. Distance don't have a direction.

The distance unit of measurement in the SI

SI unit of distance is meter  in the International System of Units.

Using this as the fundamental unit and a few formulae, a large number of different derived units or quantities are produced, including volume, area, acceleration, and speed.

Distance is measured also  using the C.G.S. and M.K.S in metric unit system.

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Answer: If the prices paid for a model of a new car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500, it means that the majority of the prices paid for the car will fall within a certain range around the mean. Specifically, approximately 68% of the prices paid will be within one standard deviation of the mean, which in this case would be between $16,500 and $17,500. Approximately 95% of the prices paid will be within two standard deviations of the mean, which would be between $16,000 and $18,000. And approximately 99.7% of the prices paid will be within three standard deviations of the mean, which would be between $15,500 and $18,500. This shows that the prices paid for the car are relatively consistent, with only a small percentage falling outside of the range determined by the mean and standard deviation.

Step-by-step explanation:

Answer:

d = 0

Step-by-step explanation:

7.5d = 2.5d

Divided both sides by factors and we get

d = 0

Answer:

60

Step-by-step explanation:

To find the least common multiple of 15 and 12, we can list the multiples of 15 and 12 and find the smallest number that appears in both lists:

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...

The least common multiple of 15 and 12 is 60, so Cameron and Brooks will go to the grocery store on the same day every 60 days.

Answer:

x = -3

Step-by-step explanation:

See the picture below

Answer: 11

Step-by-step explanation: To raise the winning percentage to 75%, the team needs to win 3 more games out of 4, for a total of 3/4=75% of the games. Since the team has already won 8 games, they need to win 8+3=11 games in a row to raise the winning percentage to 75%