Sebastian is 12 34 years old. camden is 1 38 years older than sebastian and jane is 1 15 years older than camden. how old is jane?

The compensating variation is $13.52.

The compensating variation is the amount of money that Greg would need to be compensated for a price increase in order to maintain his original level of utility. In this case, Greg's utility function is u = x^0.38x^0.962. His income is $83.00, and he faces these prices: (P1, P2) = (4.00, 1.00). If the price of x increases by $1.00, then the new prices are (P1, P2) = (5.00, 1.00).

To calculate the compensating variation, we can use the following formula:

CV = u(x1, x2) - u(x1', x2')

where u(x1, x2) is Greg's original level of utility, u(x1', x2') is Greg's new level of utility after the price increase, and CV is the compensating variation.

We can find u(x1, x2) using the following steps:

Set x1 = 83 / 4 = 20.75.

Set x2 = 83 - 20.75 = 62.25.

Substitute x1 and x2 into the utility function to get u(x1, x2) = 22.13.

We can find u(x1', x2') using the following steps:

Set x1' = 83 / 5 = 16.60.

Set x2' = 83 - 16.60 = 66.40.

Substitute x1' and x2' into the utility function to get u(x1', x2') = 21.62.

Therefore, the compensating variation is CV = 22.13 - 21.62 = $1.51.

To two decimal places, the compensating variation is $13.52.

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\(format \: \: y = mx + c\)

\(m = \frac{5 - 0}{10 - 0} = \frac{5}{10} = \frac{1}{2} \)

\(c = 0 \: since \: the \: line \: passes \: through \: the \: origin \\ \)

\((d) \: \: \: y = \frac{x}{2} \)

Answer:

for y=x-1 y=-1 and for y=x2 y=0

Step-by-step explanation:

to find the y intercept substitute x=0 so you have your answer y=-1 and y=0  

A person must score at least 129.24 to be in the top 10%.

Using the z-table, find the z-score that corresponds to the 90% probability.

probability = 0.90

z-score = 1.2825

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

The z-score can be calculated using the formula below.

z-score = (x – μ) / σ

where x = individual data value

μ = mean

σ = standard deviation

Plug in the values and find the score to be in the top 10%, x.

z-score = (x – μ) / σ

1.2825 = (x – 110) / 15

x – 110 = 19.2377

x = 129.24

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Step-by-step explanation:

I think it is $4,821 because that is what I got as an answer. I hope this helped!

Using synthetic division, we can divide the polynomial x³ + 7x² - 12x + 14 by the divisor 1. Performing the synthetic division, we obtain a quotient of x² + 6x - 6 and a remainder of 8.

To divide the polynomial x³ + 7x² - 12x + 14 by the divisor 1 using synthetic division, we set up the synthetic division table as follows:

1  |   1   7  -12   14

We begin by bringing down the coefficient of the first term, which is 1, and place it on the line below the division bar. Then we multiply the divisor, 1, by the value we brought down and write the result under the next coefficient. Adding the values in the second row, we obtain the new value. We continue this process for each term until we reach the last term.

1  |   1   7  -12   14

 1   8  -4     10

The values in the last row represent the coefficients of the quotient polynomial. Therefore, the quotient is x² + 6x - 6. The remainder, which is the last value in the last row, is 10. Since the divisor is 1, the remainder does not affect the quotient. Hence, the result of the division is x² + 6x - 6 with a remainder of 10.

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Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Answer:

y+2=1/2(x+3)

Why?

Point slope form is written as (y-y1) = m(x-x1) with y1 being the value of y at a certain point, x1 being the value of x at a certain point, and m being slope. y1 and x1 are given to us by the point (-3, -2) letting us know that y1=-2 and x1=-3. The only thing left to find is slope. Parallel lines have the same slope. If the line we are trying to find is parallel to the one given in the question, we just need to find the slope of the equation given. That equation is given in slope-intercept form which is y = mx + b. m is still slope so we can see that the slope is 1/2. Now we can plug m, x1 and y1 into the point slope form equation to get y + 2 = 1/2(x + 3)

Thus, the Fourier series of the given function simplifies to Sf(t) = π/4.

To determine the Fourier series of the 2π-periodic function f(t) = |t|, we need to find the coefficients of the trigonometric terms in its Fourier series representation.

The Fourier series representation of f(t) can be written as:

f(t) = a₀ + Σ(aₙcos(nt) + bₙsin(nt))

where a₀, aₙ, and bₙ are the Fourier coefficients to be determined.To find these coefficients, we will calculate the integrals involving f(t) multiplied by the trigonometric functions:

₀ = (1/2π) ∫[π,-π] |t| dt

To find the integral of |t| over the interval [-π, π], we split the integral into two parts:

₀ = (1/2π) ∫[0,π] t dt + (1/2π) ∫[-π,0] -t dt

= (1/2π) ([(t²/2)] from 0 to π + [(-t²/2)] from -π to 0)

= (1/2π) ([(π²/2) - (0)] + [(0) - (π²/2)])

= (1/2π) (π² - π²/2)

= (1/2π) (π²/2)

= π/4

Next, we calculate the coefficients for the sine terms:

= (1/π) ∫[π,-π] |t|sin(nt) dt

Since the function |t| is symmetric around the y-axis, the integral of |t| multiplied by an odd function (such as sin(nt)) over a symmetric interval is zero. Therefore, bₙ = 0 for all n.

Finally, we calculate the coefficients for the cosine terms:

aₙ = (1/π) ∫[π,-π] |t|cos(nt) dt

We can split the integral into two parts similar to before:

= (1/π) ∫[0,π] t cos(nt) dt + (1/π) ∫[-π,0] -t cos(nt) dt

the integrals, we have:

aₙ = (1/π) ([(t/n)sin(nt)] from 0 to π + [(t/n)sin(nt)] from -π to 0)

= (1/π) ([(π/n)sin(nπ) - (0)] + [(0) - (-π/n)sin(-nπ)])

= (1/π) ([(π/n)sin(nπ)] - [(π/n)sin(nπ)])

= 0

Therefore, aₙ = 0 for all n.

In summary, the Fourier series representation Sf(t) of the function f(t) = |t| is:

Sf(t) = a₀ + Σ(aₙcos(nt) + bₙsin(nt))

= (π/4) + 0

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Answer- √ 26

Explanation:

Use the distance formula:  

√ ( y 2 − y 1 )²  +  ( x 2 − x 1 ) ²

Plug in your values:

√ ( − 5−   ( − 4 )  )²  +  ( 2 −  ( − 3 ) )²

Simplify:

√ ( − 1 )²  +  ( 5 )²

Simplify:  

√ 1 + 25

Simplify:

√ 26

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

Anyways bye!

The optimal solution is x = 70,000 and The maximum value of z is 7600.

To solve the given linear programming problem, we can use the simplex method.

Here's the problem statement:

Objective function: Maximize z = 0.07x + 0.09y

Subject to:

1. x + y = 100,000

2. x - 2y >= 0

3. y <= 30,000

4. x >= 0 5. y >= 0

First, convert inequality constraints to equations by introducing slack variables:

2. x - 2y + s1 = 0

3. y + s2 = 30,000

Now, we have a system of equations:

1. x + y = 100,000

2. x - 2y + s1 = 0

3. y + s2 = 30,000 4. x ≥ 0 5. y ≥ 0 6. s1 ≥ 0 7. s2 ≥ 0

Solve the system of equations using the simplex method.

The optimal solution is x = 70,000, y = 30,000, which gives the maximum value of z = 0.07 × 70,000 + 0.09 × 30,000 = 4,900 + 2,700 = 7,600.

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Answer:

3.17

Step-by-step explanation:

2.5/1.5 = 1.66667, 1.66667 (it goes on infinitely 1.6666 etc.)

1.66667 x 1.9 = 3.166666654, and when rounded to nearest tenth it is 3.17

Answer:

10 inches

Step-by-step explanation:

radius = 5 inches

Diameter = radius x 2 = 5 x 2 = 10 inches

Complete question:

The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 70% pure fruit juice?

Answer:

Juice A = 15

Juice B = 35

Step-by-step explanation:

Given the following:

Juice A:

Let juice A = a

35% pure fruit juice

Juice B:

Let juice B = b

85% pure fruit juice

We need to make 50 pints of juice from both: that is ;

a + b = 50 -------(1)

In terms of pure fruit:

a = 0.35 ; b = 0.85 ;

Our mixed fruit juice from a and b should be 70% pure fruit = 0.7

Mathematically,

0.35a + 0.85b = 50(0.7)

0.35a + 0.85b = 35 -------(2)

Multiply (2) by 100

35a + 85b = 3500 --------(3)

We can then solve the simultaneous equation:

a + b = 50 -------(1)

35a + 85b = 3500 --------(3)

Multiply (1) by 35

35a + 35b = 1750 -----(4)

35a + 85b = 3500 ---(5)

Subtract (5) from (4)

-50b = -1750

b = 35

Substitute b = 35 into (2)

0.35a + 0.85(35) = 35

0.35a + 29.75 = 35

0.35a = 35 -29.75

0.35a = 5.25

a = 5.25/0.35

a = 15

Juice A = 15

Juice B = 35

Answer:

hello! :) have a good day!

W = 9

The band boosters had custom t-shirts made for homecoming and need to sell a certain number of shirts to cover their expenses. An equation, 10x = 25.90 + 8.15x, can be used to determine the number of shirts they need to sell to break even.

Let's break down the given information and formulate an equation to represent the situation.

The band boosters paid a setup fee of $25.90 and an additional cost of $8.15 per shirt to have the custom t-shirts made. They plan to sell each shirt for $10.

Let's represent the number of shirts they need to sell as 'x'. The cost to produce 'x' shirts would be the sum of the setup fee and the cost per shirt multiplied by the number of shirts:

Cost to produce 'x' shirts = Setup fee + (Cost per shirt × Number of shirts)

Using the given values, the equation becomes:

Cost to produce 'x' shirts = $25.90 + ($8.15 × x)

To break even, the revenue from selling the shirts should equal the cost to produce them. The revenue can be calculated by multiplying the selling price per shirt ($10) by the number of shirts sold:

Revenue from selling 'x' shirts = Selling price per shirt × Number of shirts sold

The equation representing the situation can be written as:

$10x = $25.90 + ($8.15 × x)

Simplifying the equation, we have:

10x = 25.90 + 8.15x

Now we have the equation that represents the situation.

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Based on the information, thee mast was 31 meters tall before it broke.

In order to solve this, we can use the Pythagorean Theorem.

We can set up the following equation:

(24 meters)² = (7 meters)² + (height of top of mast)²

Solve for the height of the top of the mast:

576 = 49 + (height of top of mast)²

527 = (height of top of mast)²

Take the square root of both sides:

23 = height of top of mast

Therefore, the mast was 31 meters tall before it broke.

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The new points after the translation are (1, 0) and (1, 4)

A translation of 3 units to the right and 2 units down, applied to a general point (x, y), gives:

(x + 3, y - 2)

Here we know that one line passes through the points (-4, 2) and (-4, 6). (so this is a vertical line)

If we apply the translation, we will get:

(-4 + 3, 2 - 2) = (1, 0)

(-4 + 3, 6 - 2) = (1, 4)

These are the new points of the line.

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Answer: 57 apples

Step-by-step explanation:

A dozen = 12

5 dozen = 5 × 12

= 60

Percentage of good apples= 100% - 5%

= 95%

Total of good apples = 95% × 60

= 57

The coordinates of the rectangle are (3,-3), (3, -7), (7, -7) and (7, -3).

We also know that the distance between the left and right sides of the rectangle is 4 (since the x-coordinate of the right side is 7 and the x-coordinate of the left side is 3). So we have the equation:

4x = 16

Solving for x, we get x = 4. This means that the length of the top and bottom sides of the rectangle is 4 units. The height of the rectangle is 16/4 = 4 units.

Now that we know the length and height of the rectangle, we can draw it on the coordinate plane.

The left side starts at (3, -3) and ends at (3, -7). The right side starts at (7, -3) and ends at (7, -7).

The top side starts at (3, -3) and ends at (7, -3). The bottom side starts at (3, -7) and ends at (7, -7).

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Answer:

The correct answer is D. 3 of the students volunteered at least 40 hours, whereas 6 of the students volunteered between 10 and 20 hours.

Answer:

option D

Step-by-step explanation:

by unplotting the stem and leaf plot we have the following data:

10, 12, 13, 14, 17, 18

21, 22, 25, 25, 26, 28

30, 33, 34, 34, 34

41, 42, 42

option A is incorrect, as

number of students volunteered more than 30 hours = 7

number of students volunteered fewer than 30 hours = 12

option B is incorrect, as

most common number of hours volunteered is 34

option C is incorrect as well

option D is correct as

students who volunteered between 9 and 20 hours = 6

students who volunteered more than 40 hours = 3

Answer:

Can you please show more context.

Step-by-step explanation:

I'm assuming that we're looking for the angle of that symbol.

\( {cos}^{ - 1} = \frac{adj}{hyp} = \frac{4.4}{11} \)

\( = 66.42182152 \: degrees\)

round as you wish.

Answer:

C

Step-by-step explanation:

x - 3 < -9

simplifies to x < -6, which is to the left with an open circle

x + 5> 12

simplifies to x > 7, which is to the right a closed circle

Given:

Arc(AB) = 78 degrees

Measure of angle CMD = 106 degrees

To find:

The measure of arc CD.

Solution:

Secant intersection theorem: If two secant of a circle intersect each other inside the circle, then the intersection angle is the average of intercepted arcs.

Using secant intersection theorem, we get

\(m\angle CMD=\dfrac{1}{2}(Arc(AB)+Arc(CD))\)

\(106^\circ=\dfrac{1}{2}(78^\circ+Arc(CD))\)

Multiply both sides by 2.

\(212^\circ=78^\circ+Arc(CD)\)

\(212^\circ-78^\circ=Arc(CD)\)

\(134^\circ=Arc(CD)\)

Therefore, the measure of arc CD is 134 degrees and the correct option is C.

Answer:

B.

I hope it will be useful.

Answer:

option A is correct

let p =x

x2 = 64

p2=8*8=64

Step-by-step explanation:

hope my answer is helpful to you

Answer: One Half

Step-by-step explanation: 3 is half of 6 and  I took the test ;)

Answer:

Express each number in scientific notation.

1) 0.0056 = 5.6 × 10^-3

3) 4,085 = 4.085 × 10³

5) 0.000796 = 7.96 × 10^-4

Standard and Scientific Notations

50,413 = 5.0413 × 10^4

11 = 1.1 × 10^1

11 = 1.1 × 10^1

2) 24,010 = 2.401 × 10^4

4) 0.017 = 1.7 × 10^-2

6) 952 = 9.52 × 10^2

8) 0.004 = 4 × 10^-3

Answer: 496 square units.

Step-by-step explanation:

trust me