Imagine that you are told that the probabilities of certain outcomes are independent of one another. What does this mean

Answer:

After 3 years, the value of the car is 72900

Step-by-step explanation:

Original Price = 100,000

Annual depreciation is 10%

So, the car has 90% less of its original value after 1 and so on,

we have the formula,

\(V = P(R)^n\)

here P is the orginal value, P = 100,000

R is the rate at which the value changes so, R = 0.9

n is the number of years, n = 3

V is the value after n years.

So,,,,,,

\(V = P(R)^n\\V = (100000)(0.9)^3\\V = 72900\)

Given, a new car is bought for 100,000, and annual depreciation is 10%. To find the value of the car after 3 years we have to calculate the total depreciation of the car over 3 years and then subtract it from the original cost of the car.

Solution:Year 1 depreciation = 10% of the original cost= 10/100 × 100,000= 10,000Cost of car after 1 year= Original cost - Depreciation= 100,000 - 10,000= 90,000Year 2 depreciation = 10% of the remaining cost= 10/100 × 90,000= 9,000Cost of car after 2 years= Remaining cost after year 1 - Depreciation in year 2= 90,000 - 9,000= 81,000Year 3 depreciation = 10% of the remaining cost= 10/100 × 81,000= 8,100Cost of car after 3 years= Remaining cost after year 2 - Depreciation in year 3= 81,000 - 8,100= 72,900Hence, the value of the car after 3 years is 72,900.

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Answer:

can u add a picture please?

Step-by-step explanation:

To solve this problem, we need to set up a system of equations based on the given information. Let's assume that the farmer needs x cubic yards of mix a and y cubic yards of mix b.

For phosphoric acid, the equation would be:
x * pounds of phosphoric acid in mix a + y * pounds of phosphoric acid in mix b = pounds of phosphoric acid required

For nitrogen, the equation would be:
x * pounds of nitrogen in mix a + y * pounds of nitrogen in mix b = pounds of nitrogen required

For potash, the equation would be:
x * pounds of potash in mix a + y * pounds of potash in mix b = pounds of potash required

We can solve this system of equations using substitution or elimination method. Once we find the values of x and y, we can calculate the total cost.

Since the question asks for the answer in more than 100 words, I'll provide an explanation for the solution process.

1. Set up the equations using the given information.
2. Solve the system of equations to find the values of x and y.
3. Substitute the values of x and y into the cost equation to find the total cost.

The solution to the problem is to blend x cubic yards of mix a and y cubic yards of mix b to meet the minimum monthly requirements at a minimum cost. The total cost can be calculated by substituting the values of x and y into the cost equation.

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The length of the ribbon to the nearest tenth is 50.3 inches.

To find the length of the ribbon that surrounds the edge of a circular hat that has a radius of 8 inches, we can use the formula for the circumference of a circle.

The formula for the circumference of a circle is given by the following:

C = 2πr

Where C represents the circumference of the circle, π represents the constant value of pi which is approximately equal to 3.14, and r represents the radius of the circle.

Given that the circular hat has a radius of 8 inches, we can use this value to find the circumference of the circle.

Hence, we have: r = 8 inches

C = 2πr

C = 2π(8)C = 16π

The length of the ribbon that surrounds the edge of the circular hat is equal to the circumference of the circle. Therefore, the length of the ribbon is:16π ≈ 50.3 inches (to the nearest tenth)

Therefore, the length of the ribbon to the nearest tenth is 50.3 inches.

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To find the equation of the tangent plane to the surface at the given point (6, 8, ln(10)), we need to use the gradient vector.

The gradient vector of the surface h(x, y) = ln√(x^2 + y^2) is given by:

∇h = (∂h/∂x, ∂h/∂y)

To find the partial derivatives, we differentiate h(x, y) with respect to x and y:

∂h/∂x = (∂/∂x)(ln√(x^2 + y^2)) = (1/√(x^2 + y^2)) * (∂/∂x)(√(x^2 + y^2))

= (1/√(x^2 + y^2)) * (x/(√(x^2 + y^2)))

∂h/∂y = (∂/∂y)(ln√(x^2 + y^2)) = (1/√(x^2 + y^2)) * (∂/∂y)(√(x^2 + y^2))

= (1/√(x^2 + y^2)) * (y/(√(x^2 + y^2)))

Evaluating these partial derivatives at the given point (6, 8, ln(10)), we have:

∂h/∂x = (6/(√(6^2 + 8^2))) = 3/5

∂h/∂y = (8/(√(6^2 + 8^2))) = 4/5

Now, we can use these values along with the point (6, 8, ln(10)) to write the equation of the tangent plane using the point-normal form:

(x - 6)(∂h/∂x) + (y - 8)(∂h/∂y) + (z - ln(10)) = 0

Substituting the values, the equation of the tangent plane is:

(x - 6)(3/5) + (y - 8)(4/5) + (z - ln(10)) = 0

Simplifying the equation will give the final form of the tangent plane equation.

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Part 1: A = 0, B = 2, C = 3, D = 0, E = -2

Part 2: The derivative f'(3) is 6.

Part 3: The equation of the tangent line to the curve y = f(x) at x = 3 is y = 6x – 15.

This equation of the tangent line can be found by substituting x = 3 into the simplified difference quotient expression C + Dh + Eh2 , and then taking the limit as h approaches 0.

This expression can then be rearranged to give the equation of the line, which is y = 6x – 15. The equation of the tangent line gives the slope of the line at the given point, in this case x = 3. The slope of the line is 6, which is the same as the derivative of the function at the given point.

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The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.

To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.

For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.

For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.

To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:

Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.

Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.

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Answer:

126

Step-by-step explanation:

a = 14 x 9

a = 126\(in^{2}\)

Answer:

266

Step-by-step explanation:

A = bh

A = 14(19)

A = 266

Answer:

1.625

Step-by-step explanation:

8 1/8 is also known as 8.125

Divide

8 1/8 by 5 inches which gives you an answer of 1.625

This is the sine model, y that represents the height above the ground of one of the blades of the windmill at any given time t.

Given that the blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. Let's find the sine model, y. Let's begin by writing the sine function where y represents the height above the ground of one of the blades of the windmill at any given time t and the constant 30 represents the height of the axis. Let's take A to be the amplitude of the function since the blades oscillate between a minimum height of 20 feet above the ground and a maximum height of 40 feet above the ground. Let's also take T to be the period of the function since the blades complete two full rotations in one minute or 2π radians in one period.T = 1 minute = 2π radians per period∴ T = 2π/1 = 2πA = (40 − 30)/2 = 5

To obtain the vertical shift, let's find the average of the minimum and maximum heights since the sine function oscillates above and below the horizontal axis:y = Asin(ωt) + b Where A is the amplitudeω is the angular frequency b is the vertical displacement of the graph

The vertical shift, b = (20 + 40)/2 = 30Since the blades are completing two full rotations in one minute, we can convert this to radians per second as shown:2 rotations = 4π radians2 rotations per minute = 4π radians per minute4π radians per minute = 4π/60 radians per secondω = 4π/60 radians per second

Substituting the values into the sine function, we obtain:y = 5sin[(4π/60)t] + 30Explanation:To summarize the given problem, the blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. We are to write a sine model, y. From the above explanation, we have found the amplitude (A), period (T), angular frequency (ω), and vertical displacement (b) of the sine function. We then substituted these values into the general form of the sine function to obtain the specific sine model:y = 5sin[(4π/60)t] + 30

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Answer:

4

Step-by-step explanation:

add 12 to 20 then divide 32 by 8

Answer:

-p^4

Step-by-step explanation:

The term with highest degree goes first in standard form.

Answer: -p^4

Answer:

-\(p^{4}\)

Step-by-step explanation:

standard form means highest exponent to lowest exponent regardless of the terms coefficient.  

In mathematics, "\(a^2\)" denotes the square of a number or variable "a." It is calculated by multiplying "a" by itself.

4For example, if "a" is 5, then a^2 would be 5*5, which equals 25. When "a" represents a positive number, its square is always positive.

If "a" is negative, its square is still positive since a negative multiplied by a negative results in a positive.

In geometrical terms, if "a" represents the length of the side of a square, then a^2 represents the area of that square. This notation is part of the general concept of exponentiation.

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The Question in English

What does a^2 mean in mathematics

Answer: To use the method of completing the square to solve the quadratic equation x^2 + x + 9 = 0, we can follow these steps:

Move the constant term to the right-hand side of the equation:

x^2 + x = -9

Add the square of half the coefficient of the x-term to both sides of the equation:

x^2 + x + (1/2)^2 = -9 + (1/2)^2

x^2 + x + 1/4 = -35/4

Rewrite the left-hand side as a square:

(x + 1/2)^2 = -35/4 + 1/4

(x + 1/2)^2 = -34/4

Take the square root of both sides:

x + 1/2 = ±sqrt(-34/4)

Solve for x:

x = -1/2 ± sqrt(-34)/2

So the number that needs to be added to "complete the square" is (1/2)^2 = 1/4.

Step-by-step explanation:

The basis of solutions using the Frobenius method for the differential equation xy" + (1 – 2x)y' + (x - 1)y = 0 is y₁(x) = a₀x⁻ⁿ, y₂(x) = aₙx⁻ⁿ, and y₃(x) = aₙ₊₁x²⁻ⁿ, where a₀, aₙ, and aₙ₊₁ are constants and n is a non-negative integer.

To find a basis of solutions using the Frobenius method, we assume that the solution can be expressed as a power series:

y(x) = ∑[n=0 to ∞] aₙ\(x^{n+r}\),

where aₙ represents the coefficients and r is a constant to be determined. Let's begin by differentiating the series:

y'(x) = ∑[n=0 to ∞] aₙ(n+r)\(x^{n+r-1}\),

y''(x) = ∑[n=0 to ∞] aₙ(n+r)(n+r-1)\(x^{n+r-2}\).

Substituting these derivatives into the given differential equation, we have:

xy" + (1 – 2x)y' + (x - 1)y = 0

∑[n=0 to ∞] aₙ(n+r)(n+r-1)\(x^{n+r}\) + ∑[n=0 to ∞] aₙ(n+r)\(x^{n+r}\) - 2x∑[n=0 to ∞] aₙ(n+r)\(x^{n+r-1}\) + ∑[n=0 to ∞] aₙ\(x^{n+r}\) - ∑[n=0 to ∞] aₙ\(x^{n+r}\) = 0.

∑[n=1 to ∞] aₙ(n+r-1)\(x^{n+r}\) = ∑[n=0 to ∞] aₙ(n+r)\(x^{n+r}\) * \(x^r\).

Finally, for the third term, we'll differentiate the series:

-2x∑[n=0 to ∞] aₙ(n+r)\(x^{n+r-1}\) = -2x∑[n=0 to ∞] aₙ(n+r)\(x^n * x^r\).

Now, we can combine the terms:

∑[n=0 to ∞] (aₙ(n+r)(n+r-1) + aₙ(n+r) - 2aₙ\((n+r))x^n * x^r\) = 0.

Since this equation should hold for all values of x, the coefficients of each power of x must be zero. Therefore, we obtain the following recurrence relation:

aₙ(n+r)(n+r-1) + aₙ(n+r) - 2aₙ(n+r) = 0.

Simplifying the equation, we have:

aₙ[(n+r)(n+r-1) + (n+r) - 2(n+r)] = 0.

aₙ(n+r)(n+r-1+1-2) = 0.

aₙ(n+r)(n+r-2) = 0.

Now, we have three cases to consider:

Case 1: aₙ = 0

If aₙ = 0, then the coefficient of \(x^n\) is zero, and we can move on to the next value of n.

Case 2: n+r = 0

If n+r = 0, then r = -n. In this case, the solution becomes:

y₁(x) = a₀\(x^r\) = a₀\(x^{-n}\).

Case 3: (n+r)(n+r-2) = 0

If (n+r)(n+r-2) = 0, then we have two solutions:

Solution 1: n+r = 0

In this case, r = -n. The solution becomes:

y₂(x) = aₙ\(x^r\) = aₙ\(x^{-n}\).

Solution 2: n+r-2 = 0

In this case, r = 2-n. The solution becomes:

y₃(x) = aₙ₊₁\(x^r\) = aₙ₊₁\(x^{2-n}\).

Therefore, we have three linearly independent solutions:

y₁(x) = a₀\(x^{-n}\),

y₂(x) = aₙ\(x^{-n}\),

y₃(x) = aₙ₊₁\(x^{2-n}\).

We can identify the series expansions of known functions as follows:

y₁(x) = a₀\(x^{-n}\) is a series expansion of a constant function.

y₂(x) = aₙ\(x^{-n}\) is a series expansion of \(x^{-n}\), which is a generalized power function.

y₃(x) = aₙ₊₁\(x^{2-n}\) is a series expansion of \(x^{2-n}\), which is another generalized power function.

These solutions form a basis for the given differential equation using the Frobenius method.

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A decrease of 316 gallons is represented as -316, and -948 : 3 = -316 represents the problem.

Given that a pump runs for 3 hours, removing an equal number of gallons of water each hour, and after 3 hours, the water in the koi pond has decreased by 948 gallons, and Ken says the water in the pond decreased by 316 gallons each hour, to determine which statement best explains why Ken is correct, the following calculation must be performed:

Therefore, a decrease of 316 gallons is represented as -316, and -948 : 3 = -316 represents the problem.

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Answer:

The Completing the Square Method basically "forces" the existence of a perfect square trinomial in order to easily factor an equation where factoring by grouping is impossible.

For

x

2

−

8

x

−

15

, the first step would be to make the equation equal to zero and add 15 to both sides.

x

2

−

8

x

=

15

Next, we need to turn the binomial on the left side of the equation into a perfect trinomial. We can do this by dividing the coefficient of the "middle x-term", which would be

−

8

, in half then squaring it.

−

8

2

=

−

4

and

(

−

4

)

2

=

16

We then add the result to both sides of the equation.

x

2

−

8

x

+

16

=

15

+

16

Now, we can factor the perfect square trinomial and simplify

15

+

16

.

(

x

+

4

)

2

=

31

Now, we subtract

31

from both sides of the equation.

(

x

+

4

)

2

−

31

In order to factor these terms, both of them need to be the "squared version of their square rooted form" so that the terms stay the same when factoring.

(

x

+

4

)

2

−

√

31

2

Now, we can factor them. Since the expression follows the case

a

2

−

b

2

, where, in this case,

a

=

(

x

+

4

)

and

b

=

√

31

, we can factor them by following the Difference of Squares Formula:

a

2

−

b

2

=

(

a

+

b

)

(

a

−

b

)

.

Your final answer would be:

(

(

x

+

4

)

+

√

31

)

(

(

x

+

4

)

−

√

3

Answer:

m = 13

Step-by-step explanation:

(-9, -6) (-8,7)

The slope is rise/run or ( y2 - y1) / (x2 - x1)

We see the y increase by 13 and the x increase by 1, so the slope is

13/1 or 13

So, m = 13

If she weeded 40% of her garden in 8 minutes, we can add another 40% weeded if we add 8 more minutes -

40% + 40% = 80%

8 + 8 = 16 minutes

We need 20% more to reach 100% of her garden. Since 20% is ½ of 40%, we just divide the rate in half -

40%(÷2) in 8(÷2) minutes = 20% in 4 minutes

80% + 20% = 100%

16 + 4 = 20 minutes

Therefore, it takes Paula 20 minutes to weed her entire garden.

Answer:

Equation of this line is y = 1

Step-by-step explanation:

We have to write an equation of a line passing through (0,1) and slope 0.

Standard equation of a line in slope form is y = mx + c

Where m = slope and c = y intercept.

Since m = 0

so y = c is the equation.

This line passes through (0,1)

so equation will be Y = 1

Equation of this line is y = 1

Step-by-step explanation:

Hope this helps:)

Answer:

y = 1

Step-by-step explanation:

Answer:

The Company should choose to get the cylinder packages  ( V = 42.39 in³ )

Step-by-step explanation:

The volume of a cylinder of radius of circumference 1.5 in  and h = 1.5*4

h  =  6 in   is:

V(c)  =  π *r²*h   =  π * (1.5)²*6   =   π *2.25*6

V(c)  = 42.39 in³

Now V(p) =  Square of the base ( of side 3 in) * h

h  =  6 in

V(p)  =  (3)²*6

V(p)  =  54 in³

If we compare these two volumes we see that the volume of the cylinder is small than that of the square prism

Answer:

7/50

Step-by-step explanation:

Answer:

112 seconds

Step-by-step explanation:

According to my calculations girl here to tell you how.

40*14=560

560/5=112

if 14 is hours and 40 is minutes, multiplying and dividing by five gives you

*DRAMATIC MUSIC*

112 seconds

Answer:

176 minutes

Step-by-step explanation:

14 hours equals 840minutes + 40 minutes = 880 minutes

880/5=176

Answer:

I'm not sure if B. is incorrectly written but the answer would be

65c + 90s \(\geq\)600

Step-by-step explanation:

since he needs AT LEAST 600$ then the sign should look like that. 65 dollars per car, and c represents the amount of cars, and 90 per SUV and s represents how many SUVS

B. 65c + 90s ≥ 600 is the correct option.

Our friend really wants to buy the newest cell phone which will cost him $600. He gets a job detailing cars and SUVs and plans to save all the money he earns.

Inequality can be defined as the relation of the equation contains the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,

If he gets paid $65 to detail a car and $90 to detail an SUV

The inequality form for above condition so he can earn at least $600

= 65c + 90s ≥ 600, where c = cars and s = SUV

Thus, the required inequality is given by 65c + 90s ≥ 600.

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The distance AD is 49 miles.

As per the given values of speed and time, we will calculate the distance AC. Firstly equalising the units.

As per the known fact, 60 minutes = 1 hour

30 minutes = (1/60)×30

30 minutes = 0.5 hour

Now, speed, distance and time are related as -

Speed = distance ÷ time

Distance = speed × time

Distance = 62 × 0.5

Distance = 31 miles

So, AC = 31 miles and BC = 25 miles.

Therefore, AB = AC - BC

AB = 31 - 25

AB = 6 miles

The distance AD = AC + CD

AD = 31 + 3 × AB

AD = 31 + 3 × 6

AD = 31 + 18

AD = 49 miles

Therefore, the distance between AD is 49 miles.

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The complete question is attached.

Answer:

the awnswer is 5.032\

Step-by-step explanation:

Answer:

3/32

Step-by-step explanation:

5/8 = (5 x 4)/(8 x 4) = 20/32

20/32 - 17/32 = 3/32

Answer:

a 5/8 inch socket is 50% bigger than a 17/32 inch socket

Step-by-step explanation:

17 - 5 = 12

32 - 8 = 24

Then divide to find the percent;

12 / 24

you would get 0.5 or 50%

so, a 5/8 inch socket is 50% bigger than a 17/32 inch socket

Answer:

3/13 which is 0.23 as a decimal

Step-by-step explanation: