10. (02.03)
Below are the steps to solve an equations
Step 1: IX - 4l+ 1 = 8
Step 2: IX - 4l = 8 - 1
Step 3: IX - 4l = 7
Which of the following is a correct next step to solve the equation? (1 point)
X-4 = -7
x+4=-7
x + 4 = 7
-x-4= 7

It will takes 15 weeks before Jeremy and Katie have the same amount of money saved up.

Define Expression

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given,

Jeremy has balance in his savings account = $120

Each week Jeremy adds amount to his account = $14

Katie has balance in her savings account = $180

Each week Katie adds amount to her account = $10

Let, x = number of weeks

At the end of each week Jeremy has = 120 + 14x

At the end of each week Katie has = 180 + 10x

As we want to have same amount in both the account for that just equate the values of each week of Jeremy and Katie.

120 + 14x = 180 + 10x

14x - 10x = 180 - 120

4x = 60

x = 15

Hence, it will takes 15 weeks before Jeremy and Katie have the same amount of money saved up.

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The system random sampling involves the introduction of a sampling interval during the sampling process. Hence, the use of a fixed interval is more likely to miss the potential defect noticed based on the sampling interval selected.

Therefore, with simple random sampling, Sergio stands a better chance of capturing the defect better than using systematic random sampling

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Answer:

If the defect is in every other cake, a systematic random sample could miss it completely depending on what Sergio chooses for kkk.

Step-by-step explanation:

got right on kahn

Answer:

yes i think so but im not sure

Answer:

a- about 3$

b-about 8$

c-about .04

Step-by-step explanation:

a-100.8/35=2.88

2.88 is around 3

b-49.2/6=8.2

8.2 is close to 8

c-.78/20=.039

.039 is the nearest to .04

The type of variable required is Qualitative with two possible outcomes.

An estimate level of uncertainty is expressed by a range of values known as a confidence interval.

Keeping in mind, the z-score and other data's decimal places should be preserved when generating the confidence interval upper and lower bounds. The responses will be accurate and round-off errors will be prevented.

Also, the confidence interval boundaries are expressed in percentages. The maximum value of 0.8740, for instance, is 87.4% in decimal notation.

Make sure to specify the confidence level, the percentage of the population that the confidence interval actually captures, and the bounds expressed in percentages when expressing the meaning of the confidence interval.

Hence, the type of variable required to construct a confidence interval for a population​ proportion is Qualitative with 2 possible outcomes.

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To find the average value of the function f(x, y) = 8x + 5y over the given triangle, we need to calculate the double integral of f(x, y) over the region and then divide it by the area of the triangle.

The vertices of the triangle are (0, 0), (2, 0), and (0, 7). We can set up the integral as follows:

∬R f(x, y) dA = ∫₀² ∫₀ᵧ (8x + 5y) dy dx

Integrating with respect to y first, the inner integral becomes:

∫₀ᵧ (8x + 5y) dy = 8xy + (5y²/2) |₀ᵧ = 8xᵧ + (5ᵧ²/2)

Now integrating with respect to x, the outer integral becomes:

∫₀² (8xᵧ + (5ᵧ²/2)) dx = (4x²ᵧ + (5ᵧ²x)/2) |₀² = (8ᵧ + 10ᵧ² + 20ᵧ)

To find the area of the triangle, we can use the formula for the area of a triangle: A = (1/2) * base * height.

The base of the triangle is 2 and the height is 7.

A = (1/2) * 2 * 7 = 7

Finally, to find the average value, we divide the double integral by the area of the triangle:

Average value = (8ᵧ + 10ᵧ² + 20ᵧ) / 7

Simplifying this expression gives:

Average value = (8 + 10ᵧ + 20ᵧ) / 7 = (8 + 10(7) + 20(7)) / 7 = 142/7 = 20 2/7

Therefore, the correct answer is not listed among the options provided.

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The statement provided is actually the opposite of the correct definitions.

In database terminology, a field refers to a single piece of information that is stored in a database table. A field can contain a variety of data types such as text, numbers, dates, and so on. For example, in a database table of customer information, there might be fields for the customer's name, address, phone number, and email.

A record, on the other hand, is a complete set of information about an entity in a database. A record consists of a collection of fields that are all related to each other. For example, in the customer information table mentioned above, a single record might represent a specific customer, and would contain all the fields related to that customer (name, address, phone number, email, etc.).

So to summarize, a field is a single piece of information within a record, while a record is a collection of related fields that together represent a complete set of information about an entity in a database.

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Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

Mode and mean

Step-by-step explanation:

The measure of central tendency that can be determined by just looking at the  box plot is : MEDIAN but the other measures of central tendencies. that cannot be determined  accurately by just looking at the box plot . are MODE  and MEAN

This simply because of how a box plot is created ( it makes it easier to determine the median value other than other central tendencies )

Answer: Infinitely many

Step-by-step explanation:

Let the value of \(\frac{x}{y}\) be \(k\), where \(k\) is an integer. Then, \(x=ky\).

\(\implies \frac{x+1}{y+1}=\frac{ky+1}{y+1}=\frac{k(y+1)}{y+1}+\frac{1-k}{y+1}=k+\frac{1-k}{y+1}\)

This means we need \(\frac{1-k}{y+1}\) to be an integer. If we let this fraction equal \(n\), then:

\(\frac{1-k}{y+1}=n \implies 1-k=ny+1 \implies y=\frac{-k}{n}\)

From this, we see that there are infinitely many pairs.

The runner's rate in miles per hour is D * 4/3 miles per hour.

Distance is a measure of the physical space between two objects or points. It is the length of the shortest path between two points in space. Distance can be measured in different units, such as meters, kilometers, miles, feet, or inches, depending on the scale of the objects or the purpose of the measurement.

In geometry, the distance between two points in a Euclidean space can be calculated using the Pythagorean theorem or the distance formula. The distance formula is expressed as:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where d is the distance between two points (x1, y1) and (x2, y2) in a two-dimensional plane. This formula can be extended to three dimensions by adding a third term to the equation.

Distance can also be calculated using other methods, such as GPS (Global Positioning System) or by measuring the time it takes for an object to travel from one point to another, using the speed of light or sound.

In everyday life, distance is a fundamental concept used in various contexts, such as navigation, transportation, sports, and communication. It plays a significant role in determining the time and effort required to travel between two points and is often used as a basis for making decisions.

We can use the formula:

rate = distance / time

where distance is the distance traveled by the runner and time is the time taken to travel that distance.

Given that the runner travels 2/3 of the marathon distance in 10 minutes, we can find the total distance of the marathon by dividing the distance traveled by 2/3:

total distance = distance traveled / (2/3) = distance traveled * 3/2

Let's denote the total distance of the marathon as D. Then:

D = distance traveled * 3/2

distance traveled = D * 2/3

We know that the time taken to travel 2/3 of the distance is 10 minutes. Let's convert this to hours:

10 minutes = 10/60 hours = 1/6 hours

Now we can calculate the runner's rate:

rate = distance / time = (D * 2/3) / (1/6) = (D * 4/3) / 1 = D * 4/3

So the runner's rate in miles per hour is D * 4/3 miles per hour.

Note that we don't have a specific value for the total distance D of the marathon, so we cannot give a numerical answer. We can only express the runner's rate in terms of D as:

runner's rate = D * 4/3 miles per hour

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(\sqrt(q^3))/(\sqrt[4]{q}) simplifies to q^(5/4).

We can simplify the expression (\sqrt(q^3))/(\sqrt[4]{q}) using the property of radicals that states:

√(a^n) = a^(n/2)

and

√m = a^(1/m)

Using these properties, we have:

(\sqrt(q^3))/(\sqrt[4]{q}) = q^(3/2) * q^(-1/4)

= q^(3/2 - 1/4)

= q^(5/4)

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Answer:

c

Step-by-step explanation:

I think

The distance of 40 lb will be 5ft, according to the question.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have the given information:

The fulcrum be located from the 40 lb.

The weight of bar is 9ft long.

Now, we will calculate the distance,

40x = 50(x-1)

40x = 50x - 50

40x - 50x = -50

-10x = -50

x = 5

Therefore, the required answer is 5ft.

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Answer:

3 out of 4 I think

Step-by-step explanation:

because the total amount is 4 so there's a 3/4 chance youll get less than 4

Answer:

Simplify the following algebraic expressions.

- 6x + 5 + 12x -6

2(x - 9) + 6(-x + 2) + 4x

3x2 + 12 + 9x - 20 + 6x2 - x

(x + 2)(x + 4) + (x + 5)(-x - 1)

1.2(x - 9) - 2.3(x + 4)

(x2y)(xy2)

(-x2y2)(xy2)

Solution

Group like terms and simplify.

- 6x + 5 + 12x -6 = (- 6x + 12x) + (5 - by

Solution

Use rules of exponential to simplify the numerator first.

(a b2)(a3 b) / (a2 b3) = (a4 b3) / (a2 b3)

Rewrite as follows.

(a4 / a2) (b3 / b3)

Use rule of quotient of exponentials to simplify.

= a2

Rewrite as follows.

(21 x5) / (3 x4) = (21 / 3)(x5 / x4)

Simplify.

= 7 x

(6 x4)(4 y2) / [ (3 x2)(16 y) ]

Multiply terms in numerator and denominator and simplify.

(6 x4)(4 y2) / [ (3 x2)(16 y) ] = (24 x4 y2) / (48 x2 y)

Rewrite as follows.

= (24 / 48)(x4 / x2)(y2 / y)

Simplify.

= (1 / 2) x2 y

Factor 4 out in the numerator.

(4x - 12) / 4 = 4(x - 3) / 4

Simplify.

= x - 3

Factor -5 out in the numerator.

(-5x - 10) / (x + 2) = - 5 (x + 2) / (x + 2)

Simplify.

= - 5

Factor numerator and denominator as follows.

(x2 - 4x - 12) / (x2 - 2x - 24) = [(x - 6)(x + 2)] / [(x - 6)(x + 4)]

Simplify.

= (x + 2) / (x + 4) , for all x not equal to 6

Solve for x the following linear equations.

2x = 6

6x - 8 = 4x + 4

4(x - 2) = 2(x + 3) + 7

0.1 x - 1.6 = 0.2 x + 2.3

- x / 5 = 2

(x - 4) / (- 6) = 3

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

x / 5 + (x - 1) / 3 = 1/5

Solution

Divide both sides of the equation by 2 and simplify.

2x / 2 = 6 / 2

x = 3

Add 8 to both sides and group like terms.

6x - 8 + 8 = 4x + 4 + 8

6x = 4x + 12

Add - 4x to both sides and group like terms.

6x - 4x = 4x + 12 - 4x

2x = 12

Divide both sides by 2 and simplify.

x = 6

Expand brackets.

4x - 8 = 2x + 6 + 7

Add 8 to both sides and group like terms.

4x - 8 + 8 = 2x + 6 + 7 + 8

4x = 2x + 21

Add - 2x to both sides and group like terms.

4x - 2x = 2x + 21 - 2x

2x = 21

Divide both sides by 2.

x = 21 / 2

Add 1.6 to both sides and simplify.

0.1 x - 1.6 = 0.2 x + 2.3

0.1 x - 1.6 + 1.6 = 0.2 x + 2.3 + 1.6

0.1 x = 0.2 x + 3.9

Add - 0.2 x to both sides and simplify.

0.1 x - 0.2 x = 0.2 x + 3.9 - 0.2 x

- 0.1 x = 3.9

Divide both sides by - 0.1 and simplify.

x = - 39

Multiply both sides by - 5 and simplify.

- 5(- x / 5) = - 5(2

What is the y intercept of the line - 4 x + 6 y = - 12?

Solution

Set x = 0 in the equation and solve for y.

- 4 (0) + 6 y = - 12

6 y = - 12

y = - 2

y intercept: (0 , - 2)

What is the x intercept of the line - 3 x + y = 3?

Solution

Set y = 0 in the equation and solve for x.

- 3 x + 0 = 3

x = -1

x intercept: (-1 , 0)

What is point of intersection of the lines x - y = 3 and - 5 x - 2 y = - 22?

Solution

A point of intersection of two lines is solution to the equations of both lines. To find the point of intersection of the two lines, we need to solve the system of equations x - y = 3 and -5 x - 2 y = -22 simultaneously. Equation x - y = 3 can be solved for x to give

x = 3 + y

Substitute x by 3 + y in the equation - 5 x - 2 y = -22 and solve for y

-5 (3 + y) - 2 y = - 22

-15 - 5 y - 2 y = - 22

-7 y = - 22 + 15

-7 y = - 7

y = 1

Substitute x by 3 + y in the equation -5 x - 2 y = - 22 and solve for y

x = 3 + y = 3 + 1 = 4

Point of intersection: (4 , 1)

For what value of the constant k does the line - 4 x + k y = 2 pass through the point (2,-3)?

Solution

For the line to pass through the point (2,-3), the ordered pair (2,-3) must be a solution to the equation of the line. We substitute x by 2 abd y by - 3 in the equation.

- 4(2) + k(-3) = 2

Solve the for k to obtain

k = - 10 / 3

What is the slope of the line with equation y - 4 = 10?

Solution

Write the given equation in slope intercept form y = m x + b and identify the slope m.

y = 14

It is a horizontal line and therefore the slope is equal to 0.

What is the slope of the line with equation 2 x = -8?

Solution

The above equation may be written as

x = - 4

It is a vertical line and therefore the slope is undefined.

Find the x and y intercepts of the line with equation x = - 3?

Solution

The above is a vertical line with x intercept only given by

(-3 , 0)

Find the x and y intercepts of the line with equation 3 y - 6 = 3?

Solution

The given equation may be written as

y = 3

The above is a horizontal line with y intercept only given by

(0 , 3)

What is the slope of a line parallel to the x axis?

Solution

A line parallel to the x axis is a horizontal line and its slope is equal to 0.

What is the slope of a line perpendicular to the x axis?

Solution

A line perpendicular to the x axis is a vertical line and its slope is undefined

Step-by-step explanation:

y = -22 and solve for y

-5 (3 + y) - 2 y = - 22

-15 - 5 y - 2 y = - 22

-7 y = - 22 + 15

-7 y = - 7

y = 1

Answer:

18/60 or 3/10

Step-by-step explanation:

10+8+42=60

10+8=18

=18/60

or

18/6=3

60/6=10

=3/10

Answer:

482 km

63.94 degrees

Step-by-step explanation:

to solve this question we will use the cosine rule. For starters, draw your diagram. From point A, up north is 500km and 060 from there, another 300. If you join the point from the road junction back to the starting point, yoou have a triangle.

Cosine rule states that

C = \(\sqrt{A^{2} + B^{2} -2AB cos(c) }\)

where both A and B are the given distances, 500 and 300 respectively, C is the 3rd distance we're looking for and c is the given angle, 060

solving now, we have

C = \(\sqrt{500^{2} + 300^{2} -2 * 500 * 300 cos(60) }\)

C = \(\sqrt{250000 + 90000 - [215000 cos(60) }]\)

C = \(\sqrt{340000 - [215000 * 0.5 }]\)

C = \(\sqrt{340000 - [107500 }]\)

C =\(\sqrt{232500}\)

C = 482 km

The bearing can be gotten by using the Sine Rule.

\(\frac{sina}{A}\) = \(\frac{sinc}{C}\)

sina/500 = sin60/482

482 sina = 500 sin60

sina = \(\frac{500 sin60}{482}\)

sina = 0.8983

a = sin^-1(0.8983)

a = 63.94 degrees

Answer:X=-13

Step-by-step explanation:

The value of r in the equation r(61/2)=5(61/2)-3.5 is 4.88.

Given an equation r(61/2)=5(61/2)-3.5.

We are required to find the value of r in the equation.

Equation is like a relationship between two or more variable that are expressed in equal to form. The equation of two variables look like ax+by=c. It may be a linear equation, quadratic equation, cubic equation and many more depending on the powers of the variable present in that equation.

In our equation the variable is r.

The equation is given as:

r(61/2)=5(61/2)-3.5

r(61/2)=305/2-3.5

r(61/2)=(305-7)/2

r(61/2)=298/2

r=(298*2)/(2*61)

r=596/122

r=4.88

Hence the value of r in the equation r(61/2)=5(61/2)-3.5 is 4.88.

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The function that represents the same relationship is \(y = 3.75 * (0.8)^x.\)

From the table, we can observe that as the value of x increases by 1, the corresponding value of y decreases by a constant factor. This indicates an exponential relationship between x and y.

To determine the function that represents this relationship, we can use the general form of an exponential function, \(Y=a * (b)^x,\) where a and b are constants.

By examining the given data points, we can see that when x = 0, y = 3. Therefore, the value of a in the exponential function is 3. Additionally, when x increases by 1, y decreases by a factor of 0.8. This implies that the base of the exponential function is 0.8.

Combining these observations, we can express the relationship between x and y as \(y = 3 * (0.8)^x.\) This function accurately models the data in the table, as the values of y decrease exponentially as x increases.

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The whole number for the value (x + 21) is 41.

All integers starting from 0 are called whole numbers. The opposite of their corresponding positive numbers, the negative numbers are additive. The blackboard bold math Z or boldface Z is a common way to represent the set of integers in mathematical terminology.

given,

       x = 20

then by putting the value of x = 20 in

       (x + 21)°      we get,

     = (20 + 21)°

     = 41°

Hence, the whole number of (x + 21) is 41

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The portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.

To calculate the portfolio weights for stock A and stock B, we need to determine the total value of the portfolio and the proportion of each stock's value within that total.

The total value of the portfolio can be calculated as follows:

Total value = (Number of shares of stock A × Price per share of stock A) + (Number of shares of stock B × Price per share of stock B)

Total value = (135 × $84) + (110 × $82)

Total value = $11,340 + $9,020

Total value = $20,360

Now, we can calculate the portfolio weights for each stock:

Weight of stock A = (Value of stock A ÷ Total value) × 100%

Weight of stock A = (($84 × 135) ÷ $20,360) × 100%

Weight of stock A = $11,340 ÷ $20,360

Weight of stock A ≈ 0.5569 or 55.69%

Weight of stock B = (Value of stock B ÷ Total value) × 100%

Weight of stock B = (($82 × 110) ÷ $20,360) × 100%

Weight of stock B = $9,020 ÷ $20,360

Weight of stock B ≈ 0.4431 or 44.31%

Therefore, the portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.

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The amount and interest after 2 years will be $3788.58 and $88.58, respectively.

Given that:

Investment, P = $3,700

Rate, r = 1.19

Time, n = 2 years

The amount is calculated as,

A = P(1 + r)ⁿ

A = $3700 (1 + 0.0119)²

A = $3700 x 1.0239

A = $3788.58

The amount of interest is calculated as,

I = A - P

I = $3788.58 - $3700

I = $88.58

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The length of the dinosaur bones in millimetres is 220 mm

Length is a measure of how long an object is or the distance between two points. Therefore, the length of the dinosaur bones was given as 22 centimetres.

The length should be converted from centimetres to millimetres as follows:

1 cm = 10 mm

22 cm = ?

cross multiply

length of the dinosaur bones  = 22 × 10

length of the dinosaur bones  = 220 mm

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The probability that exactly one of the bridges will collapse in the next year in Dystopia county is 0.2988 (rounded to four decimal places).

To calculate the probability of exactly one bridge collapsing, we need to consider the probabilities of each bridge collapsing and not collapsing. Let E, Y, and A represent the events of the Elder, Younger, and Ancient bridges collapsing, respectively.

The probability of exactly one bridge collapsing can be found by considering three cases:

Only the Elder bridge collapses: P(E) * P(Y') * P(A') = 0.18 * (1 - 0.06) * (1 - 0.28) = 0.18 * 0.94 * 0.72.

Only the Younger bridge collapses: P(Y) * P(E') * P(A') = 0.06 * (1 - 0.18) * (1 - 0.28) = 0.06 * 0.82 * 0.72.

Only the Ancient bridge collapses: P(A) * P(E') * P(Y') = 0.28 * (1 - 0.18) * (1 - 0.06) = 0.28 * 0.82 * 0.94.

Summing up the probabilities from these three cases gives the total probability of exactly one bridge collapsing: 0.18 * 0.94 * 0.72 + 0.06 * 0.82 * 0.72 + 0.28 * 0.82 * 0.94 ≈ 0.2988.

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B. (b+3c)+(b+3c)

C. 2(b)+2(3c)

Step by Step instruction :)))

we have

2 (b+3c)

Distribute the number 2

2(b+3c) = 26 + 2(3c) = 26 + 6c

Verify each case

Case A) 3(b+2c)

distribute the number 3

3(b + 2c) = 36 + 3(2c) = 36 + 6c

3b + 6c is NOT equal to 2b + 6c

therefore

Choice A is not equivalent to the given expression

Case B) (b+3c)+(b+3c)

Combine like terms

b + 3c) + (b + 3c) = (b + b) = 3c + 3c = 26 + 6c

2b + 6c = 26 + 6c

therefore

Choice B is equivalent to the given expression

Case C) 2(b)+2(3c)

Multiply both terms by 2

2(b) + 2(3c) = 2b + 6c

2b + 6c = 26 + 6c

therefore

Choice C is equivalent to the given expression

♡Hope it helps♡

Answer:

B. (b+3c)+(b+3c)

C. 2(b)+2(3c)

Step by Step instructions:

we have

2 (b+3c)

Distribute the number 2

2(b+3c) = 26 + 2(3c) = 26 + 6c

Verify each case

Case A) 3(b+2c)

distribute the number 3

3(b + 2c) = 36 + 3(2c) = 36 + 6c

3b + 6c is NOT equal to 2b + 6c

therefore

Choice A is not equivalent to the given expression

Case B) (b+3c)+(b+3c)

Combine like terms

b + 3c) + (b + 3c) = (b + b) = 3c + 3c = 26 + 6c

2b + 6c = 26 + 6c

therefore

Choice B is equivalent to the given expression

Case C) 2(b)+2(3c)

Multiply both terms by 2

2(b) + 2(3c) = 2b + 6c

2b + 6c = 26 + 6c

therefore

Choice C is equivalent to the given expression

The correct answer is Men continue to earn more than women.

The average yearly wages of men and women are different from one another. Men make more money than women do.

What is the annual salary?

Annual earnings may also be referred to as annual income or yearly income. It displays a person's earnings over a specific time period.

The yearly earning of a person or a corporation is calculated by dividing the monthly earnings by the number of months in a year.

Men continue to earn more than women under the situation mentioned above, hence their wages are higher. The red line is always above the blue line.

As a result, choice A is accurate which is men continue to earn more than women.

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Answer: C. women's earnings have increased in relation to men's earnings

Step-by-step explanation:

The chart shows that