Suppose that 15 inches of wire costs 60 cents.
At the same rate, how many inches of wire can be bought for 48 cents?

Answer:

Jill gets €18 Gary gets €45.

Step-by-step explanation:

First you add the two numbers of the ratio together. 2+5=7. Then you divide the constant, 63, by the total of the ratio, 7. 63/7=9. Then you multiply each number of the ratio by the quotient. 2 x 9= 18. 5 x 9= 45.

Answer:

a=w/9F

Step-by-step explanation:

First multiply 9a to F to have 2 equations equal each other. Divide 9aF by 9F to get a on it’s own.

Steps clear down below

Using the midpoint method, the price elasticity of demand is approximately -0.67.

To calculate the price elasticity of demand using the midpoint method, we'll use the following formula:

Price Elasticity of Demand (Ed) = (% change in quantity demanded) / (% change in price)

First, let's find the percentage changes:

% change in quantity demanded = ((New Quantity Demanded - Old Quantity Demanded) / Midpoint of Quantities) * 100
= ((80 - 100) / ((100 + 80) / 2)) * 100
= (-20 / 90) * 100
= -22.22%

% change in price = ((New Price - Old Price) / Midpoint of Prices) * 100
= ((7 - 5) / ((5 + 7) / 2)) * 100
= (2 / 6) * 100
= 33.33%

Now, let's plug the values into the formula:

Ed = (-22.22% / 33.33%)
= -0.67

So, the price elasticity of demand is approximately -0.67.

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Answer:

x -2x and the y is -2y

Step-by-step explanation:

The population in 2007 will be 873.

We know that in 1995 the population in a town was 60.

Each year, it increases by 25%, then the population function as a function of x, the time in years, is:

P(x) = 60*(1 + 0.25)^x

The population in 2007 is what we get if we evaluate the function in x = 12 (12 yearsafter 1995) the population will be:

P(12) = 60*(1 + 0.25)^12 = 873

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If Paul has 10 sockets, he would have 61 wrenches based on the expression.

Let's represent the number of sockets by the variable 's'.

We are given that the number of wrenches is eleven more than five times the number of sockets.

To write an expression for the number of wrenches, we can use this information.

The number of wrenches can be calculated by multiplying the number of sockets by five and then adding eleven to the result.

So the expression for the number of wrenches is:

Number of wrenches = 5s + 11

In this expression, '5s' represents five times the number of sockets because we multiply the number of sockets (s) by five.

Then we add eleven to account for the fact that the number of wrenches is eleven more than five times the number of sockets.

For example, if we assume Paul has 10 sockets (s = 10), we can substitute this value into the expression:

Number of wrenches = 5(10) + 11

= 50 + 11

= 61

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PART A:

In the expression -7 - (-9), we can combine both negative signals and create a positive signal, so the expression will be -7 + 9.

That means in the number line we start at the number -7 and go 9 units to the right.

So Karissa is not correct, because she said a different starting point and a different direction to add the 9 units.

PART B:

Let's solve the equation:

We can see that the equation is not true, since the final statement is false. So Hugo is not correct, because the final values of each side of the equation didn't match.

Answer:

Example: Suppose you give $100 to a bank which pays you 10% compound interest at the end of every year. After one year you will have $100 + 10% = $110, and after two years you will have $110 + 10% = $121.

compound interest image

Problem:

If you deposit $4500 into an account paying 7% annual interest compounded semi anualy , how much money will be in the account after 9 years?

Result:

The amount is $8358.7 and the interest is $3858.7.

Explanation:

STEP 1: To find amount we use formula:

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

In this example we have

After plugging the given information we have

STEP 2: To find interest we use formula , since 8358.7  P =  we have:

3858.7

Step-by-step explanation:

Answer: 40

Step-by-step explanation: Subtract 16 from 36 and you get 20. It says half so you multiply by 2 and get 40.

The equation of the tangent line to the curve y = −3x²/2x³ at the point (1, 2) is y = −x + 3.

The first step is to find the derivative of the curve. The derivative of y = −3x²/2x³ is y' = −3(1 + x²)/2x⁴.

The next step is to evaluate the derivative at the point (1, 2). The value of y' at (1, 2) is −3(1 + 1)/2(1)⁴ = −3/2.

The final step is to use the point-slope form of linear equations to find the equation of the tangent line. The point-slope form of linear equations is y - y1 = m(x - x1), where (x1, y1) is the point of tangency and m is the slope of the tangent line.

In this case, (x1, y1) = (1, 2) and m = −3/2. Substituting these values into the point-slope form of linear equations, we get y - 2 = −3/2(x - 1). Simplifying this equation, we get y = −x + 3.

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CI = 6.76 ± 1.96 × (2.67/√50)
CI = 6.76 ± 0.96
Therefore, the 95% confidence interval for the population means rating for Miami is: (5.80, 7.72)

We can be 95% confident that the true mean rating for Miami International Airport falls within this interval.
To develop a 95% confidence interval for the population means rating for Miami International Airport, we need to follow these steps:

1. Calculate the sample mean (x) by adding up all the ratings and dividing by the sample size (n=50).
2. Calculate the sample standard deviation (s).
3. Use a t-distribution to find the t-score for a 95% confidence interval with (n-1) degrees of freedom.
4. Calculate the margin of error (ME) using the t-score, standard deviation, and sample size.
5. Add and subtract the margin of error from the sample mean to find the lower and upper limits of the confidence interval.

To calculate the 95% confidence interval, we need to use the formula:
CI = x ± Z' (s/√n)
Where:
x = sample mean
Z' = z-score for the desired confidence level (in this case, 95%, so

Z' = 1.96)
s = sample standard deviation
n = sample size

Step 1: Calculate the sample mean (x)
Sum of ratings = 346
Sample size (n) = 50
x = 346/50 = 6.92

Step 2: Calculate the sample standard deviation (s)
Variance = [(Sum of (rating - x)^2) / (n-1)] = 88.48
Standard deviation (s) = √(88.48) = 9.41

Step 3: Find the t-score
For a 95% confidence interval with 49 (n-1) degrees of freedom, the t-score is approximately 2.01.

Step 4: Calculate the margin of error (ME)
ME = t-score × (s / √n) = 2.01 × (9.41 / √50) = 2.01 × 1.33 = 2.67

Step 5: Find the confidence interval
Lower limit: x - ME = 6.92 - 2.67 = 5.80
Upper limit: x + ME = 6.92 + 2.67 = 7.72

Thus, the 95% confidence interval for the population mean rating for Miami International Airport is approximately

(5.80, 7.72)

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The regular price of the book bag was $38.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the regular price of the bag. After applying the coupon:

Price = x - 5

After the discount:

23.10 = (x - 5) -  30% of (x - 5)

23.10 = (x - 5) - (0.3x  - 1.5)

0.7x - 3.5 = 23.10

x = 38

The regular price of the book bag was $38.

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Point A is inefficient.

Point B is efficient

Point C is efficient.

Pont D is unattainable.

Pont E is unattainable.

Point F is inefficient.

The Production possibilities frontiers is a curve that shows the various combination of two goods a company can produce when all its resources are fully utilised.

Point outside the curve or to the right of the curve means that the production level is not attainable given the level of resources. Points inside the production possibilities frontier means that the nations resources are not being fully utilised. Points on the curve are efficient and attainable.

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Step-by-step explanation:

5 times 7 times 7 since there are two sevens that means both sides are the same and thar means it is a square and that the other sides are the same makeing it so Q=5

Answer:

-18

Step-by-step explanation:

9/4 x -8/1

-72/4

-18

Based on the information given, Colin woke up to a temperature of 4°F.

The correct answer is B) 4°F.

When Colin went to bed, the temperature outside was -4°F.

The following morning, the temperature rose by 8 degrees.

To determine the temperature when Colin woke up, we need to add the temperature increase to the initial temperature.

Starting with -4°F, we add 8 degrees to account for the rise in temperature.

Mathematically, we can express this as -4 + 8 = 4°F.

Therefore, the temperature when Colin woke up was 4°F.

To elaborate further, a rise in temperature indicates an increase in heat energy. In this scenario, the temperature rose by 8 degrees.

This could be due to various factors such as solar radiation, weather patterns, or a change in atmospheric conditions.

It's important to note that temperature is typically measured using the Fahrenheit or Celsius scale.

In this case, we are using the Fahrenheit scale. Fahrenheit is commonly used in the United States, while Celsius is more widely used internationally.

Therefore, based on the information given, Colin woke up to a temperature of 4°F.

This means that it was 4 degrees Fahrenheit outside when he woke up, indicating a notable increase from the initial -4°F temperature.

In conclusion, the correct answer is B) 4°F.

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The complete question may be like: Colin went to bed when the temperature outside was -4°F. The following morning, the temperature rose by 8 degrees. What was the temperature when Colin woke up?

A) -4°F

B) 4°F

C) -12°F

D) 4°C.

The probability that monofilament cables will be discovered during the next ten years and that both discoveries will occur within the next twenty years are, respectively, 0.811 and 0.833.

X = time taken to discover Negative gravity

Y = time taken to discover Monofilament Cables

X follow exponential distribution with mean = 10

Y follow exponential distribution with mean = 6

a)P(Y < y) = 1- e^(-y/mean)

 P(Y < 10)

= 1 - e^(-10/6)

= 0.8111

The probability monofilament cables will be discovered within the next 10 years is 0.8111

b)P(X <20 ,Y < 20)= P(X < 20)P(Y < 20)

= (1 - e^(-20/10)) (1 - e^(-20/6))

= 0.8338

The probability both discoveries will take place within the next 20 years

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The three angle bisector of a triangle intersect at a single point that point of concurrency of the angle of bisectors is called the incenter.

Given:

the 3 angle bisectors of a triangle intersect.

when three angle bisector of a triangle intersect then that point of concurrency is called incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Incenter formula:

= (ax1+bx2+x3 / a+b+c  , ay1+by2+y3 / a+b+c).

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Answer:

Yes

Step-by-step explanation:

10/5=2

4/2=2

The ratios are equal

Answer: Yes

Step-by-step explanation:

10:5 and 4:2 round to 2:1 respectively, which are equivalent.

Hence, the inequaliy is of the form

\(|x-7| < 20\)

What is the inequality?

An inequality is said to be sharp if it cannot be relaxed and still be valid in general.

Here given that,

A number is less than \(20\)units away from \(7\) on the number line.

it is of the form

\(|x-7| < 7\)

\(x-7 > 20\\x > 20+7\\x > 27\)

or

\(x-7 < -20\\x < -20+7\\x < -13\\x > 13\)

Draw the graph

Hence, the inequaliy is of the form

\(|x-7| < 20\)

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An equation that describes this function in slope-intercept form is y = -6x - 1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-7 - 5)/(1 + 1)

Slope (m) = -12/2

Slope (m) = -6

At data point (-1, 5) and a slope of -6, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -6(x + 1)

y - 5 = -6x - 6

y = -6x - 1

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9514 1404 393

Answer:

  Object 1 is the heaviest object.

Step-by-step explanation:

The first column of the table tells you ...

  Object 1 is heavier than the 10 kg weight

The second column of the table tells you ...

  Object 2 weighs 10 kg

The third column of the table tells you ...

  Object 3 is lighter than the 10 kg weight

Then the relative weights are ...

  Object 1 > Object 2 > Object 3

That is, Object 1 is the heaviest object.

Answer:

Object 1 is the Heaveyist!!!!

Step-by-step explanation:

3-column table with 2 rows titled effects of each object. The first row has entries Object 1, Object 2, Object 3. The second row has entries the balance tips toward the object, the balance remains balanced, the balance tips toward the weight.

Which statement is best supported by the information in the chart?

Object 1 is the heaviest object.----------!!!!!!!!!!!!!!!!!!!!!ΨΩΩΣΡξβνζ

Object 3 is heavier than Object 1.

The weight is heavier than Object 2.

The weight is the heaviest object.

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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Answer:

1) x= - 8

2) x = 10

3) x= 5/7

Answer:

D

Step-by-step explanation:

Since the point C is (-4,-4) on quadrant 3 it will aways be a negative and a negative so it being dilated would be point (-8,-8)

Answer:

.41 cents

Step-by-step explanation:

divide it by 6

Answer:

I think it is $0.41

Answer:

r1/r2 = 2ω2/ω1

Step-by-step explanation:

The velocity of each pulley is expressed as v = ωr where;

v is the linear velocity of the pulley

ω is the angular velocity of the pulley

r is the radius of the pulley.

For the two pulleys, the velocity I'd both pulleys are the same.

v1 = v2

v1 is the linear velocity of first pulley

v2 is the linear velocity of the second pulley.

v1 = ω1r1

v2 = 2ω2(r2)

r1 and r2 is the radius of pulley 1 and pulley 2 respectively.

Since v1 = v2

ω1r1 = 2ω2(r2)

Divide both sides by r2

ω1r1/r2 = 2ω2(r2)/r2

ω1r1/r2 = 2ω2

Divide both sides by ω1

ω1r1/r2/ω1= 2ω2/ω1

r1/r2 = 2ω2/ω1

The Wronskian of y1 = e^(3x) and y2 = e^(-7x) on the interval (-∞, ∞) is W(y1, y2) = 10.

To find the Wronskian of y1 = e^(3x) and y2 = e^(-7x), we can use the formula for calculating the Wronskian of two functions. Let's denote the Wronskian as W(y1, y2).

The formula for calculating the Wronskian of two functions y1(x) and y2(x) is given by:

W(y1, y2) = y1(x) * y2'(x) - y1'(x) * y2(x)

Let's calculate the derivatives of y1 and y2:

y1(x) = e^(3x)

y1'(x) = 3e^(3x)

y2(x) = e^(-7x)

y2'(x) = -7e^(-7x)

Now, substitute these values into the Wronskian formula:

W(y1, y2) = e^(3x) * (-7e^(-7x)) - (3e^(3x)) * e^(-7x)

= -7e^(3x - 7x) - 3e^(3x - 7x)

= -7e^(-4x) - 3e^(-4x)

= (-7 - 3)e^(-4x)

= -10e^(-4x)

So, the Wronskian of y1 = e^(3x) and y2 = e^(-7x) is W(y1, y2) = -10e^(-4x).

Note that the order of the functions matters in the Wronskian calculation. If we were to reverse the order and calculate W(y2, y1), the result would be the negative of the previous Wronskian:

W(y2, y1) = -W(y1, y2) = 10e^(-4x).

Since the Wronskian is a constant value regardless of the interval (-∞, ∞) in this case, we can evaluate it at any point. For simplicity, let's evaluate it at x = 0:

W(y1, y2) = 10e^(0)

= 10

Therefore, the Wronskian of y1 = e^(3x) and y2 = e^(-7x) on the interval (-∞, ∞) is W(y1, y2) = 10.

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To find the fifth value when the mean of five values is given, we can use the formula for the mean:

mean = (sum of all values) / (number of values)

In this case, the mean is given as 9.4 and four of the values are provided as 7, 11, 6, and 14. We can substitute these values into the formula and solve for the sum of all values:

9.4 = (7 + 11 + 6 + 14 + x) / 5

To isolate x, we can multiply both sides of the equation by 5 and then subtract the sum of the known values:

9.4 * 5 = 7 + 11 + 6 + 14 + x - (7 + 11 + 6 + 14)

47 = 27 + x

Finally, we can solve for x by subtracting 27 from both sides of the equation:

x = 47 - 27

x = 20

Therefore, the fifth value is 20.

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