Jennifer had 7/8 of her pan of macoroni and chese left after supper. The next day she split what was left evenly between her five kids. What fraction of the total pan did each of them get

The expression that represents the area of the parking lot is (5 - 7) * (3 + 4).

The length of the parking lot can be represented as (5 - 7), which simplifies to -2. The width of the parking lot can be represented as (3 + 4), which simplifies to 7. To find the area of a rectangle, we multiply the length by the width.

Therefore, the expression that represents the area of the parking lot is (-2) * 7. Multiplying -2 by 7 gives us -14. So, the area of the parking lot is -14 square units.

However, it is important to note that negative areas do not have practical meaning in this context, as areas are typically positive values. Therefore, the area of the parking lot would be considered 14 square units.

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The new total bill including the tip of 15% is $59.01.

To find the amount of the tip, we can multiply the total bill by the percentage as a decimal:

tip = 0.15 * $51.31 = $7.70

To find the new total including the tip, we can add the tip to the original bill:

new total = $51.31 + $7.70 = $59.01

So the new total, including a 15% tip, will be $59.01.

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The price of one teddy bear is $7 and the price of one doll is $14.

Let's use matrices to solve this system of equations:

First, we need to define the variables:

x = price of one teddy bear

y = price of one doll

Then we can write the system of equations:

14x + 3y = 158

8x + 12y = 296

system of matix:

| 14   3 |   | x |   | 158 |

|  8  12 | * | y | = | 296 |

To solve for x and y, we can use matrix multiplication and inversion:

| x |   | 12  -3 |   | 158 |   |  99 |

| y | = | -8  14 | * | 296 | = | -14 |

So, x = $7 and y = $14. Therefore, the price of one teddy bear is $7 and the price of one doll is $14.

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There are 30 slices in total, so our denominator would be 30.

Now we simply have to add 4, 7 and 5. The answer to this would be 16.

So the amount of cake eaten in total is 16/30.

If your assignment is for improper fractions, I'm guessing the answer would be 16/3 instead.

Answer:

  1 37/60 cakes

Step-by-step explanation:

You want the total cake eaten if 4 of 8 slices, 7 of 10 slices, and 5 of 12 slices were eaten.

The sum of the three fractions is ...

  4/8 +7/10 +5/12

  = 5/10 +7/10 +5/12 . . . . . . . 4/8 = 1/2 = 5/10

  = 12/10 +5/12

  = 6/5 +5/12

  = (6·12 +5·5)/(5·12) = 97/60 = 1 37/60

The total amount of cake that was eaten was equivalent to 1 37/60 cakes.

__

Additional comment

Your calculator can relieve the tedium of this calculation.

Area of sector NPQ ≈ 127.23 square units

To find the area of the sector NPQ, we first need to find the measure of the central angle that defines the sector. We know that the measure of the angle NPQ is 104 degrees, but we need to find the measure of the central angle that includes this arc.

Since NP is a radius of the circle, we know that triangle NQP is an isosceles triangle, with angles NQP and PNQ each measuring (180 - 104)/2 = 38 degrees. Therefore, the measure of the central angle that includes arc NPQ is 2 * 38 + 104 = 180 degrees.

The area of the sector NPQ is then a fraction of the total area of the circle, where the fraction is equal to the ratio of the central angle to the total angle around the circle. Since the total angle around a circle is 360 degrees, the fraction of the circle's area covered by the sector is:

180 degrees / 360 degrees = 1/2

Therefore, the area of the sector NPQ is equal to half the area of the circle with radius 9 units:

Area of sector NPQ = (1/2) * π * 9^2 = 40.5π

Rounding to the nearest hundredth, the area of the sector NPQ is approximately:

Area of sector NPQ ≈ 127.23 square units

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The probability that Carmen's total wait time over the course of 60 days is less than 5.5 hours is approximately 0.0746.

The total wait time over 60 days will have a mean of 360 minutes (6 minutes per day x 60 days) and a variance of 720 minutes (12 minutes per day x 60 days). Since the wait times are uniformly distributed, the total wait time over 60 days will follow a normal distribution.

To find the probability that the total wait time over 60 days is less than 5.5 hours, we need to standardize the value using the z-score formula:

z = (x - μ) / σ

where x is the total wait time in minutes, μ is the mean total wait time in minutes, and σ is the standard deviation of the total wait time in minutes.

Substituting the values, we get:

z = (330 - 360) / sqrt(720) = -1.4434

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.4434 is 0.0746.

Therefore, the probability that Carmen's total wait time over the course of 60 days is less than 5.5 hours is approximately 0.0746.

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The probability of the spinner not landing on red and then landing on red is 7/64.

The probability chance that the spinner will not land on red then land on red is calculated as follows;

The probability of the spinner not landing on red is 1 - 1/8 = 7/8.

To find the probability that the spinner will not land on red and then land on red, we multiply the probabilities:

(7/8) x (1/8) = 7/64

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The mass of the original sample was approximately 1592.5 grams.

The half-life of an element is the time it takes for half of a given sample of that element to decay.

Let's assume that the original mass of the sample was x grams.

After the first half-life of 8 years, the mass of the sample would be x/2 grams.

After the second half-life (16 years total), the mass would be x/4 grams.

After the third half-life (24 years total), the mass would be x/8 grams.

We can continue this pattern until we get to 100 years (which is 12.5 half-lives):

Mass after 100 years = x/2^12.5

We also know from the problem that the mass after 100 years is 10 grams:

x/2^12.5 = 10

Solving for x:

x = 10 x 2^12.5

x ≈ 1592.5 grams

Therefore, the mass of the original sample was approximately 1592.5 grams.

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Answer:5

Step-by-step explanation:
4780/25=191.2
You don't want an odd amount of castings in different piles.
191*25=4755
4780-4755=5









I think i read the question wrong. Sorry if i did

When separating 4,780 castings into 25 piles, there will be 5 castings left over.

A fraction is a numerical expression representing a part of a whole. It consists of a numerator (the top number) that indicates how many parts are considered, and a denominator (the bottom number) that shows the total number of equal parts in the whole. Fractions are typically expressed as a/b, where "a" is the numerator and "b" is the denominator. They are used in various mathematical operations, including addition, subtraction, multiplication, and division, and in real-life scenarios involving proportions and portions.

In order to determine the number of castings left over when separating 4,780 castings into 25 piles, we can use division. Divide 4,780 by 25 to find the number of castings in each pile.

The quotient is 191.2. Since we can't have a fraction of a casting, we round down to 191.

To find the number of castings left over, subtract the total number of castings in the piles from the original total. 4,780 - (191 x 25)

= 4,780 - 4,775

= 5

Therefore, when you complete the job, you will have 5 castings left over.

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The expectation of the product of two discrete random variables x and y is given by E(xy) = ∑(x∑(yP(x,y))) where P(x,y) is the joint probability distribution of x and y.

To find the expectation of the product of two random variables, we need to use the formula:

E(XY) = ΣΣ(xy)p(x,y)

where p(x,y) is the joint probability mass function of X and Y.

So, for the given joint distribution of X and Y, we have:

E(XY) = ΣΣ(xy)p(x,y)

We need to sum this over all possible values of X and Y. If the joint distribution is given in a table or a function form, we can simply plug in the values of X and Y and calculate the sum.

However, without any specific information about the joint distribution of X and Y, it is impossible to calculate the expectation of X times Y. We would need to know either the joint probability mass function or the joint probability density function of X and Y.

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Answer:

740

Step-by-step explanation:

37 times 20

Answer:

740 miles

Step-by-step explanation:

37 miles in 1 day

So we need to multiply 37*20 to find the number of miles for 20 days

So, he travels 740 miles

To optimize the company's inventory costs, we need to determine the optimal order quantities for both tablets and laptops.

Let's start by finding the optimal order quantity for tablets:

Total cost (TC) = ordering cost + holding cost

Ordering cost = (demand rate/order quantity) x ordering cost per shipment

Holding cost = (order quantity/2) x unit cost x holding cost rate

We can set these two costs equal to each other and solve for the optimal order quantity (Q):

(demand rate/Q) x ordering cost per shipment = (Q/2) x unit cost x holding cost rate

Solving for Q, we get:

Q = sqrt((2 x demand rate x ordering cost per shipment)/(unit cost x holding cost rate))

Plugging in the values given in the problem, we get:

Q = sqrt((2 x 10000 x 10000)/(100 x 0.25)) = 2000

Therefore, the optimal order quantity for tablets is 2000 units per shipment.

Next, let's find the optimal order quantity for laptops:

Following the same procedure as for tablets, we get:

Q = sqrt((2 x 4000 x 10000)/(400 x 0.25)) = 2000

Therefore, the optimal order quantity for laptops is also 2000 units per shipment.

In summary, the company should place orders of 2000 units each for both tablets and laptops to minimize its inventory costs.

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the value of the line integral ∫_C 2y dx + 2x dy along the straight line path from (4,3) to (9,6) is 84.

To evaluate the line integral ∫_C 2y dx + 2x dy along the straight line path from (4,3) to (9,6), follow these steps:
Step:1. Parametrize the straight line path: Define a vector-valued function r(t) = (1-t)(4,3) + t(9,6) = (4+5t, 3+3t), where 0 ≤ t ≤ 1. Step:2. Calculate the derivatives: dr/dt = (5,3). Step:3. Substitute the parametric equations into the line integral: 2(3+3t)(5) + 2(4+5t)(3). Step:4. Calculate the line integral: ∫(30+30t + 24+30t) dt, where the integration is from 0 to 1. Step:5. Combine the terms and integrate: ∫(54+60t) dt from 0 to 1 = [54t + 30t^2] from 0 to 1.
Step:6. Evaluate the integral at the limits: (54(1) + 30(1)^2) - (54(0) + 30(0)^2) = 54 + 30 = 84.

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To find the critical points of f(x) = x - 18x² + 96x, we need to find the values of x where f'(x) = 0.

f'(x) = 1 - 36x + 96

Setting f'(x) = 0, we get:

-36x + 97 = 0

x = 97/36

So the critical point is (97/36, f(97/36)).

To use the Second Derivative Test, we need to find f''(x):

f''(x) = -36

At the critical point x = 97/36, f''(97/36) = -36 < 0.

Since f''(97/36) is negative, the Second Derivative Test tells us that the critical point corresponds to a local maximum.

Therefore, the critical point (97/36, f(97/36)) is a local maximum.
To find the critical points of the function f(x) = x - 18x² + 96x, we first need to find its first derivative, f'(x), and then set it to zero to find the critical points.

1. Find the first derivative, f'(x):
f'(x) = d/dx (x - 18x² + 96x) = 1 - 36x + 96

2. Set f'(x) to zero and solve for x:
0 = 1 - 36x + 96
36x = 95
x = 95/36

Now, let's use the Second Derivative Test to determine if this critical point corresponds to a local minimum or maximum.

3. Find the second derivative, f''(x):
f''(x) = d/dx (1 - 36x + 96) = -36

4. Evaluate f''(x) at the critical point x = 95/36:
f''(95/36) = -36

Since f''(95/36) is negative, the Second Derivative Test tells us that the critical point x = 95/36 corresponds to a local maximum.

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To evaluate the integral ∫√5+x/5-x dx, we first need to simplify the integrand. We can do this by multiplying the numerator and denominator of the fraction by the conjugate of the denominator, which is 5+x. This gives us:

∫√(5+x)(5+x)/(5-x)(5+x) dx

Simplifying further, we get:

∫(5+x)/(√(5-x)(5+x)) dx

We can now make a substitution by letting u = 5-x. This gives us du = -dx, and we can substitute these values into the integral to get:

-∫(4-u)/(√u(9-u)) du

To simplify this expression, we can use partial fraction decomposition to break it up into simpler integrals. We can write:

(4-u)/(√u(9-u)) = A/√u + B/√(9-u)

Multiplying both sides by √u(9-u), we get:

4-u = A√(9-u) + B√u

Squaring both sides and simplifying, we get:

16 - 8u + u^2 = 9A^2 - 18AB + 9B^2

From this equation, we can solve for A and B to get:

A = -B/3
B = 2√2/3

Substituting these values back into the partial fraction decomposition, we get:

(4-u)/(√u(9-u)) = -√(9-u)/3√u + 2√2/3√(9-u)

We can now substitute this expression back into the integral to get:

-∫(-√(9-x)/3√x + 2√2/3√(9-x)) dx

This integral can be evaluated using standard integral formulas, and we get:

(2/3)√(5+x)(9-x) - (2/9)√(5+x)^3 + C

where C is the constant of integration.

In summary, to evaluate the integral ∫√5+x/5-x dx, we simplified the integrand by multiplying the numerator and denominator by the conjugate of the denominator, made a substitution to simplify the expression further, used partial fraction decomposition to break it up into simpler integrals, and evaluated the integral using standard integral formulas. The final answer is (2/3)√(5+x)(9-x) - (2/9)√(5+x)^3 + C.

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the volume of the basketball is approximately 490 cubic inches. we can get this answer by using volume formula of volume

what is approximately ?

"Approximately" means almost, but not exactly. It is used to indicate that a value or quantity is very close to the true or exact value, but there may be a small difference or error. In mathematical terms, an approximate value is an estimate or a rounded value that is used

In the given question,

To find the volume of the basketball, we first need to find its radius.

Circumference of a sphere = 2πr

29.516 = 2 * 3.14 * r

r = 29.516 / (2 * 3.14) ≈ 4.7 inches (rounded to one decimal place)

Now, we can use the formula for the volume of a sphere:

Volume of sphere = (4/3) * π * r^3

Volume of basketball = (4/3) * 3.14 * (4.7)^3

Volume of basketball ≈ 490 cubic inches (rounded to the nearest whole number)

Therefore, the volume of the basketball is approximately 490 cubic inches..

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Answer:

Step-by-step explanation:

To understand the relationship between -41/2 and its opposite position in relation to zero on a number line, let's first plot them on the number line.

We start by marking the position of zero at the center of the number line, and then we can represent -41/2 and its opposite position by moving to the left and right of zero respectively.

When we move 41/2 units to the left of zero on the number line, we reach the point -41/2. This means that -41/2 is located to the left of zero on the number line.

On the other hand, the opposite position of -41/2 is obtained by moving the same distance (41/2 units) to the right of zero. This position is represented by the point 41/2 on the number line.

Therefore, we can see that -41/2 and its opposite position (41/2) are equidistant from zero on the number line, with zero located exactly halfway between them. In other words, -41/2 and 41/2 are located at equal distances from zero but in opposite directions. This relationship is often referred to as the symmetry property of the number line.

This will ensure that his check register accurately reflects his current account balance and transaction history.

This table represents Rico's check register, and on August 15th, he made a transfer of $30.00 from his savings account into his checking account.

To record this transaction on his check register, Rico should enter it as a deposit in his checking account column, and also include a note indicating that the deposit was a transfer from his savings account.

This will ensure that his check register accurately reflects his current account balance and transaction history.

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Answer:

D

Step-by-step explanation:

25x+75=750

25x=675

x=27

we can't go over this amount, but we can have 27 employees, so it will be equal as well.

x<27 and x=27

A) The acute angles equivalent to 70 degrees, 110 degrees, and 250 degrees are all 20 degrees.

B) The characteristics of a reference angle is acute and positive.

C) Because reference angle only depends on quadrant.

A. Three different angles which could have a reference angle of 20 degrees are 70 degrees, 110 degrees, and 250 degrees. To arrive at this answer, we need to subtract 20 degrees from 90 degrees, which gives us 70 degrees. To find the other two angles, we add 180 degrees to 70 degrees, which gives us 250 degrees, and we subtract 180 degrees from 110 degrees, which gives us 290 degrees. However, since we're looking for angles with a reference angle of 20 degrees, we have to find the acute angle between 0 and 90 degrees that is equivalent to these angles. So, we subtract 90 degrees from 250 degrees, which gives us 160 degrees, and we subtract 90 degrees from 290 degrees, which gives us 200 degrees. The acute angles equivalent to 70 degrees, 110 degrees, and 250 degrees are all 20 degrees.

B. The characteristics of a reference angle are that it is always an acute angle, it is the smallest angle between the terminal side of the given angle and the x-axis, and it is always positive.

C. Angles can have different measurements but still have the exact same reference angle because the reference angle only depends on the quadrant in which the terminal side of the angle lies. For example, an angle of 50 degrees and an angle of 310 degrees are both in the fourth quadrant and therefore have the same reference angle of 40 degrees. Similarly, an angle of 100 degrees and an angle of 260 degrees are both in the third quadrant and therefore have the same reference angle of 10 degrees.

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A sample size of 9604 is needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, with a 95% confidence level and a margin of error of 0.01.

To find the sample size needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, we can use the following formula:

n = [Z^2 * p * (1 - p)] / E^2

where:

Z is the z-score associated with the desired confidence level (95%), which is 1.96
p is the estimated proportion of students who earn a bachelor's degree in four years or less (since we don't have any prior knowledge, we can use 0.5 as a conservative estimate)
E is the margin of error, which is 0.01
Plugging in the values, we get:

n = [(1.96)^2 * 0.5 * (1 - 0.5)] / (0.01)^2
n = 9604

Therefore, a sample size of 9604 is needed to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less, with a 95% confidence level and a margin of error of 0.01.

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The remaining distance after 33 minutes of driving = 58.8 miles.

Here, the slope of a linear function the remaining distance to drive (in miles) is -0.85

For this situation, we can write a linear equation as,

remaining distance = (slope)(drive time) + (intercept)

remaining distance = -0.85(drive time) + (intercept)      

y =  -0.85x + c        ..........(1)

where y represents the remaining distance

x is the drive time

and c is the y-intercept

Here, Laura has 52 miles remaining after 41 minutes of driving.

i.e., x = 41 and y = 52

Substitute these values in equation (1)

52 =  -0.85(41) + c    

c = 52 + 34.85

c = 86.85

So, equation (1) becomes,

y =  -0.85x + 86.85

Now, we need to find the remaining distance after 33 minutes of driving.

i.e., the value of y for x = 33

y =  -0.85(33) + 86.85

y =  -28.05 + 86.85        

y = 58.8

This is the remaining distance 58.8 miles.

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Step 1: Answer

The point (2, 8) is the point (x1, y1) identified from the equation y - 8 = 3(x - 2).

Step 2: Explanation

The equation y - 8 = 3(x - 2) is in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope of the line. In this case, the slope of the line is 3, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.

Comparing the given equation with the point-slope form, we can see that x1 = 2 and y1 = 8. Therefore, the point (2, 8) is the point identified from the equation.

The expression of the width of the rectangle is 2x¹²y⁸z¹¹/3.

Given that the area of a rectangle is 72x¹³y⁹z¹⁶ sq. yds and the length of the rectangle is 3x9y4z⁵, we need to find the width,

Using these expressions, we have,

Area = length × width

72x¹³y⁹z¹⁶ / 3x9y4z⁵ = width

Width = 72x¹³/3x × y⁹/9y × z¹⁶/4z⁵

Width = 24x¹²y⁸z¹¹/36 = 2x¹²y⁸z¹¹/3

Hence the expression of the width of the rectangle is 2x¹²y⁸z¹¹/3.

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The absolute maximum value is 20/17, which occurs at x = 5, and the absolute minimum value is 4/5, which occurs at x = 1.

To find the absolute maximum and minimum values of the function f(x) = 8x/(6x + 4) on the interval (1, 5), we need to find the critical points of the function within the interval and evaluate the function at those points, as well as at the endpoints of the interval.

First, let's find the derivative of the function:

f(x) = 8x/(6x + 4)

f'(x) = [8(6x + 4) - 8x(6)] / (6x + 4)^2

f'(x) = [8(2)] / (6x + 4)^2

f'(x) = 16 / (6x + 4)^2

The critical points occur when f'(x) = 0 or is undefined. However, since f'(x) is always positive on the interval (1, 5), there are no critical points within the interval.

Next, let's evaluate the function at the endpoints of the interval:

f(1) = 8(1)/(6(1) + 4) = 8/10 = 4/5

f(5) = 8(5)/(6(5) + 4) = 40/34 = 20/17

Finally, we need to determine which of these values is the absolute maximum and which is the absolute minimum.

Since f(x) is always positive on the interval (1, 5), the function can never be less than 0. Therefore, the absolute minimum value is the smallest value of f(x) on the interval, which occurs at x = 5, where f(5) = 20/17.

To find the absolute maximum value, we compare the values of f(1), f(5), and the maximum value of f(x) as x approaches the endpoints of the interval. We can use the fact that the function is continuous on the closed interval [1, 5] to find the maximum value.

As x approaches 1, we have:

f(x) = 8x/(6x + 4) → 8/10 = 4/5

As x approaches 5, we have:

f(x) = 8x/(6x + 4) → 40/34 = 20/17

Therefore, the absolute maximum value is 20/17, which occurs at x = 5, and the absolute minimum value is 4/5, which occurs at x = 1.

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The two aircraft are 128.535 far away.

What is the distance formula?

The d-distance between two places is calculated using the distance formula. The Euclidean distance formula is another name for the formula used to calculate the separation between two points on a two-dimensional plane.

Here, we have

Given: Two radars A and B are 80km apart and B is due to the east of A. One aircraft is on a bearing of 030 degrees from A and 346 degrees from B. A second aircraft is on a bearing 325 degrees from A and 293 degrees from B.

Calculating the Slope of AC,  tan60° = 1.732

Calculating the Slope of BC, tan104° = -4.011

Calculating the Slope of AD, tan125° = -1.482

Calculating the Slope of BD, tan157° = -0.424

When pointing C intercepts:

y₁ = 1.732x₁....(1)

y₁ = -4.011(x₁-80)....(2)

Solving equation(1) and(2) , we get

x₁ = 55.873

y₁ = 96.772

When point D intercepts:

y₂ = -1.428x₂....(3)

y₂ = 0.424(x₂-80)....(4)

Solving equations (3) and (4), we get

x₂ = 18.315

y₂  = -26.154

Calculating distance by applying the distance formula:

D = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

D = [tex]\sqrt{(-26.154-96.772)^2+(18.315-55.873)^2}[/tex]

D = [tex]\sqrt{4986.9019+1410.6033}[/tex]

D = 128.535

Hence, the two aircraft are 128.535 far away.

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Becky is currently 38 years old and Joey is currently 18 years old.

Let's start by assigning variables to their ages. Let Joey's age be "J" and Becky's age be "B".

From the first piece of information, we know that Joey is 20 years younger than Becky. This can be expressed as:

J = B - 20

Now, let's use the second piece of information. In two years, Becky will be twice as old as Joey. So, we can set up an equation:

B + 2 = 2(J + 2)

We add 2 to Becky's age because in two years she will be that much older. On the right side, we add 2 to Joey's age because he will also be two years older. Then we multiply Joey's age by 2 because Becky will be twice his age.

Now, we can substitute the first equation into the second equation:

B + 2 = 2((B - 20) + 2)

Simplifying the right side:

B + 2 = 2B - 36

Add 36 to both sides:

B + 38 = 2B

Subtract B from both sides:

38 = B

So, Becky is currently 38 years old. Using the first equation, we can find Joey's age:

J = B - 20
J = 38 - 20
J = 18

So, Joey is currently 18 years old.

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