How many cups of flour are needed if we increase the recipe by 50%?
2c. divided 100%= x c. divided by 150%

The rate at which the distance between the man and the plane is increasing when the plane passes over the radio tower is approximately 519.92 ft/sec.

Let's denote the distance between the man and the plane as x and the time elapsed since the plane passes over the radio tower as t. We are given that the plane is flying horizontally away from the man, so the height of the plane remains constant at 5000 ft.

We can set up a proportion based on the similar triangles formed by the man, the plane, and the tower:

x / 12000 = 5000 / t

Cross-multiplying, we have:

xt = 12000 * 5000

xt = 60,000,000

Now, we can differentiate both sides of the equation with respect to time t:

d(xt)/dt = d(60,000,000)/dt

dx/dt * t + x * dt/dt = 0

dx/dt * t + x * 1 = 0

dx/dt = -x/t

We are given that the plane is flying at a rate of 520 ft/sec, so dx/dt = 520 ft/sec.

At the moment the plane passes over the radio tower, the distance x is 12000 ft. We can substitute these values into the equation to find the rate at which the distance between the man and the plane is increasing:

520 = -12000 / t

Solving for t:

t = -12000 / 520 = -23.08 sec (approximately)

Since time cannot be negative, we discard the negative value and take the positive value of t.

Now, we can substitute the value of t into the equation to find dx/dt:

dx/dt = -x / t = -12000 / (-23.08) = 519.92 ft/sec (approximately)

Therefore, the rate at which the distance between the man and the plane is increasing when the plane passes over the radio tower is approximately 519.92 ft/sec.

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Answer:

Are you asking how much per $ gigabyte, if so, it's $24.79

Step-by-step explanation:

Answer: 48 = 2x + 4

Step-by-step explanation:

x = number of students Bill gave bouncy balls to

The + 4 is there because he had 4 remaining bouncy balls.

48 is what it equals because that is his total number of bouncy balls that he won.

Hope this helps!

The numbers differing by 42 whose product is as small as possible are (- 21 + √(441 + p)) and (- 21 - √(441 + p)).

Let us suppose the numbers to be x and y.

As per the given information, we can write;

xy = p ---- (1)

We have to find two numbers differing by 42 whose product is as small as possible.

If two numbers are differing by 42; then we can say

x - y = 42 ---- (2)

From equation (2), we can say

x = y + 42

Now, substitute the value of x in equation (1), we get;

xy = p(y + 42)y² + 42y - p

= 0

Solving this quadratic equation, we will get;

∆ = 1764 + 4p

∴ y = (- 42 ± √(1764 + 4p)) / 2

Now, to find the minimum value of xy, we need to find the value of y that makes xy minimum.

Therefore, the two numbers that make xy as small as possible are;

y = (- 42 + √(1764 + 4p)) / 2

and

x = y + 42

So, the two numbers are;

y = (- 42 + √(1764 + 4p)) / 2

and

x = y + 42

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Answer:

[tex]y=-3x[/tex]

Step-by-step explanation:

We want to write the equation for a line that has a slope of -3 and passes through (-1, 3).

So, we can use the point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope and (x₁, y₁) is a point.

Let's let (-1, 3) be (x₁, y₁) and let's substitute -3 for m. This yields:

[tex]y-3=-3(x-(-1))[/tex]

Simplify:

[tex]y-3=-3(x+1)[/tex]

Distribute on the right:

[tex]y-3=-3x-3[/tex]

Add 3 to both sides. So, our equation is:

[tex]y=-3x[/tex]

And we're done!

1. The monthly payment of the 5-year loan is approximately $2,225.77.

2. The equivalent uniform annual cost for the tractor is approximately $5,572.50.

1. To calculate the monthly payment of a loan, we can use the formula for an amortizing loan. The formula is:

PMT = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

PMT = Monthly payment

P = Principal amount (loan amount)

r = Monthly interest rate (annual interest rate divided by 12)

n = Total number of payments (number of years multiplied by 12)

In this case, the principal amount (P) is $100,000, the annual interest rate is 12%, and the loan duration is 5 years.

r = 12% / 12 = 1% per month

n = 5 years * 12 months/year = 60 months

PMT = 100,000 * (0.01 * (1 + 0.01)^60) / ((1 + 0.01)^60 - 1)

PMT ≈ $2,225.77

Therefore, the monthly payment of the 5-year loan is approximately $2,225.77.

2. To calculate the equivalent uniform annual cost, we need to consider the initial cost of the tractor, salvage value, maintenance costs, and the interest rate.

The equivalent uniform annual cost (EUAC) can be calculated using the formula:

EUAC = (Initial cost - Salvage value) + (Annual maintenance cost * Present worth factor)

The present worth factor can be calculated using the formula:

Present worth factor = (1 - (1 + r)^-n) / r

Where:

r = Interest rate (10%)

n = Number of years (10 years)

EUAC = ($7,500 - $5,000) + ($500 * ((1 - (1 + 0.10)^-10) / 0.10))

EUAC = $2,500 + ($500 * ((1 - 0.3855) / 0.10))

EUAC ≈ $2,500 + ($500 * 6.145)

EUAC ≈ $2,500 + $3,072.50

EUAC ≈ $5,572.50

Therefore, the equivalent uniform annual cost for the tractor is approximately $5,572.50.

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Answer:

False

Step-by-step explanation:

These two rectangles are not similar because the corresponding sides can’t be written in proportion to each other.

View this :

I think this is your answer.

Answer:

x = -2

Step-by-step explanation:

Step 1: Write equation

5(x + 6) + 11 = 25 - 3x

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

5(-2 + 6) + 11 = 25 - 3(-2)

5(4) + 11 = 25 + 6

20 + 11 = 25 + 6

31 = 31

Answer:

x=-8

Step-by-step explanation:

5x+30+11=

5x +41= 25-3x

5x+ 41-25= 25-25-3x

5x+16=3x

5x-5x= 3x-5x

16=-2x

16/-2=x

-8=x

The correct option is c.) swimsuit sales throughout the year; sunscreen sales throughout the year.

Correlation coefficient is a measure of the strength and direction of a relationship between two variables. The correlation coefficient varies from -1 to +1. A correlation of -1 means that a negative association between two variables is perfect, while a correlation of +1 means that there is a positive association between two variables that is perfect. The closer the correlation coefficient is to 0, the weaker the association between two variables is. A correlation coefficient of 0 means that there is no relationship between two variables.From the given options, the data set that is most likely to have a negative association and a correlation coefficient between 0 and -1 is (c) swimsuit sales throughout the year and sunscreen sales throughout the year.The reason behind this is that when it's summer or a hot season, people tend to buy more swimsuits than sunscreen. And when it's winter or a cold season, people tend to buy more sunscreen than swimsuits. Hence, the correlation coefficient between swimsuit sales throughout the year and sunscreen sales throughout the year is most likely to be between 0 and -1 because there is an inverse relationship between these two variables.

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Answer:Steepness of Appalachian Trail; John’s Speed while hiking the Appalachian Trail

Step-by-step explanation:

Answer: 0.616

Step-by-step explanation:

Adds up

Answer:

1 1/2

Step-by-step explanation:

12 divided by 8 = 1.5

Answer:

18

Step-by-step explanation:

first convert 12 ft to in. there are 12 inches in 1 ft so 12*12=144

then dived 144/8=18

Answer:

...

let me c

Step-by-step explanation:

Answers:

It's the last one in the chart

(-3-2i -2(24)=8      -51-6i)

Answer:

Step-by-step explanation:

We are told that  Jeanette uses 18 square inches of paper for each card, for us to get the number of square inches she will need to make 150 cards, we will use the equality operation;

18 in² = 1 card

x in² = 150 cards

cross multiply

x * 1 = 18*150

x = 2700 in²

Convert 2700 in² to feet²

Since 1in² = 0.00694444ft²

2700in² = x

cross multiply

x = 2700 * 0.00694444

x = 18.749988ft²

Hence she will] need 18.749988ft²  to make 150 cards

The area of the training field is 6621 square meters.

1. Determine the area of the rectangle:

  Area of a rectangle = length × width

  Area of the rectangle = 87 m × 54 m = 4698 square meters

2. Determine the area of one semicircle:

  The radius of the semicircle is half the width of the rectangle, which is 54 m / 2 = 27 m.

  Area of a semicircle = (π × radius²) / 2

  Area of the semicircle = (π × 27 m × 27 m) / 2 = 729π square meters

3. Determine the combined area of two semicircles:

  Since there are two semicircles, the combined area is 2 times the area of one semicircle.

  Combined area of the two semicircles = 2 × 729π square meters = 1458π square meters

4. Determine the area of the training field:

  Area of the training field = Area of the rectangle + Combined area of two semicircles

  Area of the training field = 4698 square meters + 1458π square meters

5. Approximate the value of π:

  π is an irrational number, but we can use an approximation of π as 3.14 for calculation purposes.

6. Substitute the value of π and calculate the final area:

  Area of the training field ≈ 4698 square meters + 1458 × 3.14 square meters

  Area of the training field ≈ 4698 square meters + 4579.32 square meters

  Area of the training field ≈ 6621.32 square meters

Therefore, the area of the training field is approximately 6621 square meters.

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The probable question may be:

A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 87 m long and 54 m wide. find the area of the training field.

Answer:

frequency

Step-by-step explanation:

frequency is the amount of waves in a certain period of time

The light wave is how fast it goes up and down wavelength will be "frequency"

 The separation between such a wave motion's crests and troughs would be known as the wavelength of a particular light.

The frequency of a repeated event would be its number of instances per unit of time. Frequency in the context of light would be the count of wavelength repetitions per second.

Therefore, the light wave is how fast it goes up and down wavelength will be "frequency"

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the answer is in the photo

Answer:

Domain {-1, 2, 8}

Range {3}

Step-by-step explanation:

This relation is displayed as a mapping diagram.

The inputs (domain) are in the left circle and the outputs (range) are in the right circle.

The domain is {-1, 2, 8}. They are on the left side of the two circles.

The range is {3}. It is on the right side of the two circles.

Hope this helps.

Answer:

3 blue fish

Step-by-step explanation:

3/5 = 60%, 3-1=2, 3 blue fish, 2 red fish

The number of blue fish in the aquarium is given as 5.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

Given that,

The percent of blue fish in the aquarium is 60%.

Suppose the number of blue fish is x.

Then the number of red fish is x - 1.

As per the question the following equation can be formed  for the given case,

60% of (2x -1) = x

=> 60/100(2x - 1) = x

=> 120x - 100 = 100x

=> 120x - 100x = 100

=> 20x = 100

=> x = 5

Hence, the number of blue fish in the aquarium is 5.

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Answer:

[tex]y = - \frac{1}{4} x + 6 \frac{1}{2} [/tex]

Step-by-step explanation:

[tex](6 - ( - 2 \times \frac{1}{4} )) = 6 \frac{1}{2} [/tex]

The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.

To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16.  We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.

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The expected number of attempts at taking out gloves individually from the drawer till you find both sides (left hand and right hand) of gloves is n.

To find the expected number of attempts at taking out gloves individually from the drawer till you find both sides (left hand and right hand) of gloves we can use the principle of geometric distribution. The geometric distribution is a probability distribution that represents the number of trials required to obtain the first success in repeated Bernoulli trials where each trial has a constant probability of success.To find the expected number of attempts at taking out gloves individually from the drawer till you find both sides (left hand and right hand) of gloves we have to first determine the probability of finding the first glove. Since the drawer has an infinite number of gloves, the probability of finding a left glove or a right glove is 1/2. Thus, the probability of finding the first glove is 1. Now, we have to find the probability of finding the matching glove of the first glove. The probability of this is 1/n, where n is the total number of gloves in the drawer. Thus, the probability of finding both the left glove and the right glove is given by the product of the probability of finding the first glove and the probability of finding the matching glove. This is given by 1 x 1/n or 1/n. Therefore, the expected number of attempts at taking out gloves individually from the drawer till you find both sides (left hand and right hand) of gloves is given by the formula E(X) = 1/p, where p is the probability of finding both the left glove and the right glove. Thus, E(X) = 1/(1/n) = n.

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Answer:3x+y=23

Step-by-step explanation:

Answer:

x=-1/3y+23/3

Step-by-step explanation:

Let's solve for x.

y−2=−3(x−7)

Step 1: Flip the equation.

−3x+21=y−2

Step 2: Add -21 to both sides.

−3x+21+−21=y−2+−21

−3x=y−23

Step 3: Divide both sides by -3.

−3x/-3=y-23/-3

x=-1/3y+23/3

Answer:

because both result in the equation 10x=1000

Step-by-step explanation:

beacuse of cross multiplication, your gonna find that they are the same

Answer:

D

Step-by-step explanation:

Answer:

i dont understand what you're trying to say but 16 * 25 = 400

The criminal will go down the rope safely if his acceleration is less than 9.81 m/s^2.

To get down safely without breaking the rope, a criminal who wants to escape from the third storey window of a jail, by going down a rope to the road below and has a mass of 75 kg while the rope can only support 65 kg without breaking can use the following method :Step-by-step explanation:

Calculate the acceleration produced by the criminal and find the maximum tension the rope can withstand.

According to Newton's second law, F = ma .Frictional force (f) acts upward and it opposes the weight of the criminal. Therefore, F = mg - f. If the criminal is accelerating downwards at a constant rate, a, the tension in the rope (T) is given by T = m(g - a).

If a is positive, then the tension in the rope is greater than mg and the rope breaks.

If a is negative, then the tension in the rope is less than mg and the rope is safe.

Let's assume that the tension in the rope is just equal to the breaking point.

Then:65*9.81 = 75* a + 65 *9.81a = 6.74 m/s^2

The criminal will go down the rope safely if his acceleration is less than 9.81 m/s^2.

This means that he should create additional friction by wrapping the rope around his legs, to increase the force of friction acting upwards. By doing this, he will decrease the net force acting downwards and thus reduce his acceleration.

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Answer:

21 boys

its simple math

Answer:

14 boys

Step-by-step explanation:

In order for the answer to be 14, you need to know the times tables of 5 and 7. 5 times 7 is 35, and 2 times 7 is 14. Your answer is 14.

Answer:

....................... What's the question?

Answer:

A: 25

B: 800

C: 2,400

Step-by-step explanation:

Hopes this helps. :) ( Unless you have already solved ) Just have a good day.

Answer:

A: 25

B: 800

C: 2,400

Step-by-step explanation: