Karin has $ 70 in a savings account that earns 10% interest, compounded annually. To the nearest cent, how much interest will she earn in 3 years ?

Answer:

The Answer Is A. I believe

If a large airline wants to estimate its average number of unoccupied seats per flight over the past year Then a 92% confidence interval for the population mean number of unoccupied seats per flight is (10.334, 12.266) seats.

To construct a confidence interval for the population mean number of unoccupied seats per flight, we will use the following formula CI = X ± z*(σ/√n)

Where:

X = sample mean = 11.3 seats

σ = sample standard deviation = 4.3 seats

n = sample size = 300

z = z-score corresponding to the desired confidence level of 92%, which we can look up in a standard normal distribution table or use a calculator. For a 92% confidence level, the z-score is 1.75.

Plugging in the values, we get:

CI = 11.3 ± 1.75*(4.3/√300)

CI = 11.3 ± 0.966

Therefore, the 92% confidence interval for the population mean number of unoccupied seats per flight is (10.334, 12.266) seats. This means we can be 92% confident that the true population means a number of unoccupied seats per flight falls within this interval.

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Since A and B are mutually exclusive, the probability of A occurring given that B has already occurred is 0. This means that P(A | B) = 0.

P(A ∩ B) = 0, since the events are mutually exclusive.

P(A | B) = 0, since the probability of A given B is 0 when A and B are mutually exclusive.

Since A and B are mutually exclusive, they cannot both occur at the same time. This means that the probability of them both happening at the same time is 0. As a result, P(A ∩ B) = 0.

Since A and B are mutually exclusive, the probability of A occurring given that B has already occurred is 0. This means that P(A | B) = 0.

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Answer: 0.2 cm/yr

Step-by-step explanation:

simply divide centimeters by years

25.0 cm ÷ 125 yr

0.2 cm/yr ... answer



The rate of uplift is 0.2 cm/yr

hope that helps...

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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The value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

According to the given question.

We have an equation

2x + 2/y = 4w + 2

Since, we have to find the value of x for the given equation

2x + 2/y = 4w + 2

Thereofore,

2x + 2/y = 4w + 2

⇒ 2(x + 1)/y = 2(2w + 1)    (taking 2 common from both the sides)

⇒ (x + 1)/y = 2w + 1

⇒ (x + 1) = y(2w + 1)         (multiplying both the sides by y)

⇒ x + 1 = 2yw + y

⇒ x = 2yw + y - 1         ( subtracting 1 both the sides)

Hence, the value of x is 2yw + y - 1 for the given equation 2x + 2/y = 4w + 2.

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Answer:

196 tickets

Step-by-step explanation:

The total expenses to put on a 3-day production of a play is $980. Each ticket to go and watch the play is going to be sold for $5. The producer sells x number of tickets, x number of tickets would cost 5x. Therefore to find the number of tickets the producer must sell so as to make a profit the money generated from selling the tickets must be more than the cost of production. Therefore we use the formula:

5x ≥ 980

Dividing through by 5:

x ≥ 980

x ≥ 980/5

x ≥ 196

Therefore the producer must sell at least 196 tickets so as to make a profit

Step-by-step explanation:

-3p+6p is 3p

-3 + 6 = 3

So when you simplify the equation you get 3p

The option that will provide the best combined miles per gallon is the third option: buying a new hybrid that will get double the mileage of the present hybrid.

1. Option 1: Keeping the old hybrid: Using this option means keeping the old hybrid, whose gas mileage is 35 miles per gallon. Using the same vehicle for both the daily commute and the weekend trip, the total weekly mileage would be:

20 miles x 5 days = 100 miles100 miles + 400 miles = 500 miles per week

Using 35 miles per gallon for the hybrid, the gas consumption for the week is:500 miles ÷ 35 miles per gallon = 14.29 gallons of gasoline per week.

2. Option 2: Buying a new hybrid: Using this option involves purchasing a new hybrid with a higher gas mileage of 50 miles per gallon. Using the same vehicle for both the daily commute and the weekend trip, the total weekly mileage would be: 20 miles x 5 days = 100 miles100 miles + 400 miles = 500 miles per week

Using 50 miles per gallon for the new hybrid, the gas consumption for the week is:

500 miles ÷ 50 miles per gallon = 10 gallons of gasoline per week.

3. Option 3: Buying a new hybrid that gets double the mileage: Using this option entails buying a new hybrid that gets twice the gas mileage of the current hybrid. Since the SUV's gas mileage stays the same, the hybrid's gas mileage should now be 70 miles per gallon.

Using the same vehicle for both the daily commute and the weekend trip, the total weekly mileage would be:

20 miles x 5 days = 100 miles100 miles + 400 miles = 500 miles per week

Using 70 miles per gallon for the new hybrid, the gas consumption for the week is:500 miles ÷ 70 miles per gallon = 7.14 gallons of gasoline per week.

The option that will provide the best combined miles per gallon is the third option: buying a new hybrid that will get double the mileage of the present hybrid.

Since the hybrid's mileage has doubled, its gas consumption will be less than half that of the old hybrid, and it will consume the least amount of gas per week compared to the other two options.

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Explanation:

All direct proportion equations are straight lines that go through the origin.

In this case, the constant of proportionality is 5 because of the following

Each x,y set of values are selected from the points in the graph. The equation of the green line is y = 5x with slope 5 and y intercept 0.

Furthermore, that slope 5 indicates that the unit rate is 5 gallons per minute.

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Answer:10:05

Step-by-step explanation:

subtract 45 from 50!

Answer:

She started the test at 10:05 am

Step-by-step explanation:

Take the end time and subtract the time of the test

10:50-45 = 10:05

She started the test at 10:05 am

Answer:65.6

Step-by-step explanation:

So $0.25 per yard

16.4/$0.25=65.6

Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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Answer: The expression (6-√)(15-√) can be simplified by using the distributive property of multiplication over addition:

(6-√)(15-√) = 6 * 15 + 6 * (-√) + (-√) * 15 + (-√) * (-√)

Expanding the first two terms:

6 * 15 = 90

6 * (-√) = -6√

Next, we'll use the identity for the product of two square roots:

(-√) * 15 + (-√) * (-√) = 15√ - √^2

Since the square root of a positive number is positive, √^2 = √. So:

15√ - √^2 = 15√ - √

Putting everything together:

(6-√)(15-√) = 90 - 6√ + 15√ - √

Combining like terms:

(6-√)(15-√) = 90 + 9√

So, the expression (6-√)(15-√) without a perfect square factor in the radicand is:

(6-√)(15-√) = 90 + 9√

Therefore, the answer is:

(6-√)(15-√) = A. 35 + 9√.

Step-by-step explanation:

The ladder demanded for Hill 2 must be no less than 108.27 meters high.

In order to find the necessary height of the ladder for Hill 1, we can employ an equation-based method:

height = tan(60 degrees) * 50 meters

height = 28.87 meters

From this calculation, it follows that a ladder is required that is at least 28.87 meters tall in order to climb Hill 1.

For Hill 2, using the same technique, we ascertain the required minimum ladder height:

tan(75 degrees) =height / 40 meters

height = tan(75 degrees) * 40 meters

height = 108.27 meters

Consequently, the ladder demanded for Hill 2 must be no less than 108.27 meters high.

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To find the average change in Michelle's position each minute, we need to calculate the total change in her position and divide it by the total time elapsed.

The initial position is -2.1 m and the final position is -38.6 m, resulting in a total change of: Total change = Final position - Initial position = -38.6 m - (-2.1 m) = -38.6 m + 2.1 m  = -36.5 m. The time elapsed is 6 1/4 minutes, which can be expressed as a mixed fraction or an improper fraction: Time elapsed = 6 1/4 minutes = 25/4 minutes. Now, we can calculate the average change in position per minute: Average change per minute = Total change / Time elapsed=  (-36.5 m) / (25/4 min) = (-36.5 m) * (4/25 min) ≈ -5.84 m.

Therefore, the average change in Michelle's position each minute is approximately -5.84 meters.

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Answer:

Step-by-step explanation:

First let us get the equation of the coordinates

y-y0 = m(x-x0)

Using the coordinates ( - 3, 2 ), ( - 1, 0 )

m = 0-2/-1-(-3)

m = -2/2

m = -1

Substitute m = -1 and (-1, 0) into the formula

y - 0 = -1(x+1)

y = -x-1

f(x) = -x-1

Since f(x) = 2

2 = -x-1

-x = 2+1

-x = 3

x = -3

Hence the value of x is -3

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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Answer:the first one is d and the third one is 65% and I think the second one is 5 hours

Step-by-step explanation:

(PLZ READ )all you have to do to get the answer for the first one is divide for example on D it says 1 and then 5 and 2 and 10 first you divide 1 by 5 then 2 by ten and if they ALL have the same answer then they are proportional even if one does not have the same as All the rest it is not proportional.

and for the third one you can search it up

Answer:

Step-by-step explanation:

Find the exact value using trigonometric identities.

Exact Form:

241

200

Decimal Form:

1.205

Mixed Number Form:

1

41

200

The required probability for P(x<92) is 0.15866.

Given that,
Sample score = X =  92
Mean = μ = 98
Standard deviation = σ = 6
p(x ≤ 92 ) is to be determined

Probability can be defined as the ratio of favorable outcomes to the total number of events.

z = (X - μ) / σ
z = (92 - 98) / 6
z = - 1

Now
Probability,
p(x < 92) = P(z = -1)
p(x < 92)  = 0.15866   (from z score table)

Thus, The required probability for P(x<92) is 0.15866.

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That the equation of the line is y = 7x - 50.

The equation of a line with slope m passing through the point (x1, y1) is given by: y - y1 = m(x - x1).

In this case, the line has a slope of 7 and passes through (8, 6). Therefore, we can plug in the values for m, x1, and y1 into the equation above to find the desired equation.

Substituting in 7 for m, 8 for x1, and 6 for y1, we can rewrite the equation as: y - 6 = 7(x - 8).

Simplifying, we find that the equation of the line is y = 7x - 50.

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By definition of the volume of cube, the side length of the cubic quart container is approximately equal to 9.818 centimeters.

A quart means a quarter of gallon and is equal to 946.353 cubic centimeters. The volume of the cube is equal to the cube of the side lengt, then:

x³ = 946.353

x = ∛946.353

x ≈ 9.818

By definition of the volume of cube, the side length of the cubic quart container is approximately equal to 9.818 centimeters.

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Answer:

4(5b-4)

Step-by-step explanation:

(20b-16)/4

4(5b-4)

Answer:

4(5b - 4)

Step-by-step explanation:

20b - 16 ← factor out 4 from each term

= 4(5b - 4)

Answer:

Step-by-step explanation:

\(-16 + 9 - (-2) + (-5)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:\:\\-16+9=-7\\\\=-7-\left(-2\right)+\left(-5\right)\\\\=-7+2+\left(-5\right)\\\\-7+2=-5\\\\=-5+\left(-5\right)\\\\=-10\)

B. - 10

Hi there !

-16 + 9 - (-2) + (-5) =

- (-) = +

+ (-) = -

= - 16 + 9 + 2 - 5

= - 10

Good luck !

The distance between Johannesburg to Pietermaritzburg is 420 km. The journey will take 6 hours.

What is the meaning of average speed?

The total distance traveled by the object in a given time interval is the average speed. A scalar quantity is average speed. It is represented by magnitude and lacks direction.

Given that the average speed of a truck is 70km/h.

The distance that truck travels a distance of 420km.

The formula of speed is:

Average speed = Distance/time

Rewrite the formula:

Time =  Distance/Average speed

Now putting average speed = 70km/h and Distance  = 420 km:

Time = 420 km/ (70km/h)

Time = 6 hours

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The correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.

The correct methods for "thinking out computation" (mental arithmetic) are a, b, and c.

a) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15. This method is correct because it breaks down the calculation into smaller, easier-to-manage parts.

b) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21. This method is also correct because it simplifies the calculation by subtracting 10 first, and then subtracting the remaining 7.

c) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997. This method is correct because it simplifies the calculation by multiplying 1000 by 3 first, and then subtracting 1 three to get the correct answer.

d) 150 ÷ 3 Think: what equals 150 x 3, that's 450. This method is incorrect because it is actually doing the opposite operation (multiplication instead of division) and therefore does not result in the correct answer. The correct method would be to think about how many times 3 can go into 150, which is 50.

In conclusion, the correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.

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The correct methods for "thinking out computation" (mental arithmetic) are:
A) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15
B) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21
C) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997
D) 150 ÷ 3 Think: what equals 150 x 3, that's 450

All four methods of "thinking out computation" provided in the question are correct and valid.

Method (a) is using the "doubles" method, which is a common mental arithmetic technique. By recognizing that 7+7 is 14, it is easy to add 1 more to get 15.

Method (b) is using the "subtracting by tens" method. By recognizing that 38 minus 10 is 28, it is easy to subtract 7 more to get 21.

Method (c) is using the distributive property of multiplication. By recognizing that 999 is very close to 1000, we can multiply 3 by 1000 and then subtract 3 to get 2997.

Method (d) is using the inverse operation of multiplication. By recognizing that 150 is a multiple of 3, we can think of 150 as 3 times some unknown number, and then determine that number by dividing 150 by 3. The answer is 50, which is the same as thinking of what equals 150 times 3 (450).

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Answer:

area is 60.75 m^2

Step-by-step explanation:

The factor form of the quadratic equations are listed below:

Case 13: (b - 4) · (b - 2)

Case 14: (n + 4) · (n + 2)

Case 15: 2 · (n + 9) · (n - 6)

Case 16: 5 · (n + 2)²

Case 17: 2 · (k + 5) · (k + 6)

Case 18: (a - 10) · (a + 9)

Case 19: (p + 10) · (p + 1)

Case 20: 5 · (v - 2) · (v - 4)

Case 21: 2 · (p + 2) · (p - 1)

Case 22: 4 · (v - 2) · (v + 1)

Case 23: (x - 10) · (x - 15)

Case 24: (v - 5) · (v - 2)

Case 25: (p + 6) · (p - 3)

Case 26: 6 · (v + 10) · (v + 1)

In this problem we find quadratic equations of the form a · x² + b · x + c, whose factor form is introduced below:

a · x² + b · x + c = a · x² + a · (- r₁ - r₂) · x + a · r₁ · r₂ = a · (x - r₁) · (x - r₂)

Where r₁, r₂ are real roots.

Now we proceed to present the factor form of each quadratic equation:

Case 13

b² - 6 · b + 8 = (b - 4) · (b - 2)

Case 14

n² + 6 · n + 8 = (n + 4) · (n + 2)

Case 15

2 · n² + 6 · n - 108 = 2 · (n² + 3 · n - 54) = 2 · (n + 9) · (n - 6)

Case 16

5 · n² + 10 · n + 20 = 5 · (n² + 2 · n + 4) = 5 · (n + 2)²

Case 17

2 · k² + 22 · k + 60 = 2 · (k² + 11 · k + 30) = 2 · (k + 5) · (k + 6)

Case 18

a² - a - 90 = (a - 10) · (a + 9)

Case 19

p² + 11 · p + 10 = (p + 10) · (p + 1)

Case 20

5 · v² - 30 · v + 40 = 5 · (v² - 6 · v + 8) = 5 · (v - 2) · (v - 4)

Case 21

2 · p² + 2 · p - 4 = 2 · (p² + p - 2) = 2 · (p + 2) · (p - 1)

Case 22

4 · v² - 4 · v - 8 = 4 · (v² - v - 2) = 4 · (v - 2) · (v + 1)

Case 23

x² - 15 · x + 50 = (x - 10) · (x - 15)

Case 24

v² - 7 · v + 10 = (v - 5) · (v - 2)

Case 25

p² + 3 · p - 18 = (p + 6) · (p - 3)

Case 26

6 · v² + 66 · v + 60 = 6 · (v² + 11 · v + 10) = 6 · (v + 10) · (v + 1)

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The expression of sine function of sinâ1(â3/2) is undefined. The value of cosâ1(1/2) = π/3 radians.

The expression sinâ1(â3/2), since the sine function is only defined for angles between -π/2 and π/2, we cannot find an angle with a sine of -â3/2. Therefore, the expression is undefined.

The expression cosâ1(1/2), Since the cosine function is positive for angles between 0 and π, we know that the angle we are looking for is in the first or fourth quadrant.

To find the angle, we can use the inverse cosine function, which gives us the angle whose cosine is equal to the given value. Therefore, we have

cosθ = 1/2

Taking the inverse cosine of both sides, we get

θ = cos⁻¹(1/2)

Using the unit circle or trigonometric identities, we can find that cos⁻¹(1/2) = π/3 or 2π/3. Since the cosine function is positive in the first quadrant and negative in the fourth quadrant, we choose the solution in the first quadrant, which is θ = π/3.

Therefore, cosâ1(1/2) = π/3 radians.

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