Zachary measures the area of a glacier at
the start of every year.
2
At the start of this year, the glacier had an
area of exactly 56.20 km². This is 0.2%
less than it was at the start of last year.
Work out what the area of the glacier was
at the start of last year.
2
Give your answer in km² to 2 d.p.

The number of feet that should be on each side of the painting is 4 feet.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Let x be the number of feet on each side of the painting.

The equation to determine the number of feet on each side of the painting would be:

x + 5 + x = 13

So x = (13-5)/2

x = 4

So there should be 4 feet on each side of the painting.

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The length of the rectangle be 12 and Width be 6.

With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Since a rectangle is a two-dimensional form, it has two dimensions: length and width.

A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.

4 sides, 4 corners, and 4 right angles make up the 2D shape of a rectangle. A rectangle's diagonal sides are equal in length, with one pair being longer than the other.

Let the equation be L = 2W and

P = 36 = 2 × ( L + W )

simplifying the equation, we get

⇒ 18 = L + W

⇒ 18 = 2W + W

⇒ 6 = W and L = 2 × W = 2 × 6 = 12

Therefore, the length of the rectangle be 12 and Width be 6.

The complete question is:

The length of a rectangle is twice the width. The perimeter of the rectangle is 36. What is the length and width of the rectangles?

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A histogram of the weights of all 2,000 athletes would be a graph with two normal distributions, one for offense and one for defense.

The offense distribution would have a bell shaped curve centered at 200 pounds, with a range of 150-250 pounds. The defense distribution would have a bell shaped curve centered at 300 pounds, with a range of 250-350 pounds. Each of the distributions would have the same area, representing 1,000 athletes in each group. The total area of the histogram would represent the combined 2,000 athletes with weights ranging from 150-350 pounds. It is important to note that the histogram would not represent the exact weights of the athletes, but rather the relative frequency of each weight.

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The domain is [0,100].[0,100]. The range is [0,1500] [0,1500]

(a) To find the cost of making 25 items substitute

x=25 in the equation

=10+500(25)

=10(25)+500(25)=750

c(x)=10x+500

c(25)=10(25)+500

c(25)=750

the cost of making 25 items is

$750

(b)

Since the maximum cost allowed is

$1500  

10+500≤1500

10x+500≤1500

To solve this inequality

First, subtract 500 from both sides

10≤1000

10x≤1000

Divide both sides by 10

≤100x≤100

This means you can make at most 100 items.

The domain is

[0,100].[0,100].

The range is

[0,1500] [0,1500].

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The value of three subsets is [tex]n(x_{1})=36, n(x_{2})=9, & n\left(x_3\right)=54[/tex].

A set is a collection of objects or elements, grouped in the curly braces, such as {a, b, c, d}. If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.

The elements of sets could be anything such as a group of real numbers, variables, constants, whole numbers, etc. It consists of a null set as well.

If set A has {X, Y} and set B has {X, Y, Z}, then A is the subset of B because elements of A are also present in set B.

Let the number of elements in [tex]$x_2$[/tex] be [tex]$x$[/tex], then

[tex]$$\begin{aligned}& n\left(x_1\right)=4 x \\& n\left(x_2\right)=x \\& n\left(x_3\right)=6 x\end{aligned}$$[/tex]

Given that number of elements in [tex]$x=99$[/tex]

[tex]$$\begin{aligned}\Rightarrow & n\left(x_1\right)+n\left(x_2\right)+n\left(x_3\right)=99 \\\Rightarrow & 4 x+x+6 x=99 \\\Rightarrow & 11 x=99 \\\Rightarrow & x=9 \\\therefore & n\left(x_1\right)=4 x=4 \times 9=36 \\& n\left(x_2\right)=x=9 \\& n\left(x_3\right)=6 x=6 \times 9=54\end{aligned}$$[/tex]

Therefore, the value of  [tex]& n\left(x_3\right)[/tex][tex]=54[/tex].

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Null hypothesis for the investigation Ha=0.38

The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.

This hypothesis is either rejected or not rejected based on the viability of the given population or sample.

In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance.

It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H0.

Here, the hypothesis test formulas are given below for reference.

The formula for the null hypothesis is:

H0:  p = p0

The formula for the alternative hypothesis is:

Ha = p >p0, < p0≠ p0

The formula for the test static is:

[tex]z=\frac{p-p0}{\sqrt{\frac{p0(1-p0)}{n} } }[/tex]

Remember that,  p0 is the null hypothesis and p – hat is the sample proportion.

38 percent of people living in region w have the blood type o positive.

w region

38% - o positive

x region

100 random sample

35 o positive

means 35/ 100*100

35% 0 positive

a hypothesis test to investigate whether the percent of people in region x with o positive blood is different from that of in region w

The formula for the null hypothesis is:

H0:  p = p0 =0.38

Ha = p >p0, < p0≠ p0

Ha=0.38

Null hypothesis for the investigation Ha=0.38

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The coordinate of the circumcentre of ΔABC is (-1, 0.15).

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Triangle ABC.

A = (-5, -4)

B = (3, -4)

C = (-1, 6)

The circumcentre of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect.

Now,

Let the circumcentre be M = (x, y).

The length from each side of the triangle to the circumcentre is equal.

So,

AO² = BO² = CO²

Now,

AO² = BO²

(x + 5)² + (y + 4)² = (x - 3)² + (y + 4)²

x² + 10x + 25 + y² + 8y + 16 = x² - 6x + 9 + y² + 8y + 16

10x + 25 = -6x + 9

16x + 16 = 0

x + 1 = 0

x = -1

BO² = CO²

(x - 3)² + (y + 4)² = (x + 1)² + (y - 6)²

x² - 6x + 9 + y² + 8y + 16 = x² + 2x + 1 + y² - 12y + 36

-6x + 9 + 8y + 16 = 2x + 1 - 12y + 36

20y - 8x + 25 - 36 = 0

20y - 8x - 11 = 0

20y = 11 + 8x

y = (11 + 8x)/20

y = (11 - 8)/20

y = 3/20

y = 0.15

Thus,

Circumcentre M = (-1, 0.15)

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The solution set to inequality - 5 ≤ (1 / 2) · (2 · m + 2) ≤ 14 is equal to - 6 ≤ m ≤ 13. (Correct choice: A)

Herein we find a simultaneous inequality, that is, the combination of two inequalities. We find the following case below by algebra properties:

- 5 ≤ (1 / 2) · (2 · m + 2) ≤ 14

(1 / 2) · (2 · m + 2) ≥ - 5 and (1 / 2) · (2 · m + 2) ≤ 14

Now we proceed to determine the solution set to this inequality by algebra properties:

2 · m + 2 ≥ - 10 and 2 · m + 2 ≤ 28

2 · m ≥ - 12 and 2 · m ≤ 26

m ≥ - 6 and m ≤ 13

- 6 ≤ m ≤ 13

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Answer: The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

So, using the empirical rule, we can say that approximately 99.7% of housing prices in this small town fall within 3 standard deviations of the mean.

To find the range of prices that this corresponds to, we can use the following formula:

(mean - (3 x standard deviation), mean + (3 x standard deviation))

Plugging in the given values:

(157,000 - (3 x 8,000), 157,000 + (3 x 8,000))

(141,000, 173,000)

So, approximately 99.7% of housing prices in this small town are between $141,000 and $173,000.

Step-by-step explanation:

Use 1.75 cups of blue and 1 cup of yellow

What is a mixture?

Mixture can be defined as a substance made by combining two or more different materials in such a way that no chemical reaction occurs. A mixture can usually be separated back into its original components.

The given problem can be placed in the category of ratios and proportions.

There is a ratio of color mixing which contains the proportion of two colors i.e blue and yellow. When we use 2 cups of yellow with 3.5 cups of yellow then we get green color so if we mix half of their amounts then we can get less or simply half amount of color too.

Therefore adding 1 cup of yellow and 1.75 cup of blue will give us small amount in result.

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The area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.

A semicircle is a shape that is half of a circle. It is defined by a center point and a radius, and it is made up of an arc that is 180 degrees of the full circle.

The circumference of a semicircle is given by the formula: C = π * d, where C is the circumference and d is the diameter of the semicircle.

Diameter of the biggest semi-circle = 14cm.

Diameter to two small semi-circles = 3.5cm.

Diameter of other semi-circle = 14 - 2(Diameter to two small semi-circles)

                                                 =14 - 7 cm

                                                = 7cm

Length of boundary = Circumference of bigger semi-circle + Circumference of small semi-circle + 2 ×circumference of the smaller semi-circles

∴Length of boundary= [tex]\pi R+\pi r_{1}+2\pi r_{2}[/tex]

=> Length of boundary=[tex]\pi (R+r_{1})+2\pi r_{2}[/tex]

=> [tex]\frac{22}{7}(7+3.5)+2X\frac{22}{7}X1.75[/tex]

=> 44cm

Area of the biggest semi-circle = [tex]\frac{1}{2}\pi (7)^{2} cm^{2}[/tex]

Area of two small semi-circles = [tex]\pi (1.75)^{2}cm^{2}[/tex]

Area of other semi-circle= [tex]\frac{1}{2}\pi (3.5)^{2}cm^{2}[/tex]

Area of shaded region= π×(24.5−3.0625+12.25)

                                      =π×27.5625 cm^2 =86.59 cm^2

Therefore, the area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.

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Answer:

Is this what youre asking?

Step-by-step explanation:

Price before tax: $ 590.00

+ Sales tax (32.45%): $ 191.46

Total price including tax: $ 781.46

Step-by-step explanation:

To show that the function f(x,y) = 2x^2 − xy is differentiable at any point (a,b), we need to show that the partial derivatives of f with respect to x and y exist and are continuous at that point.

The partial derivative of f with respect to x is:

∂f/∂x = 4x - y

The partial derivative of f with respect to y is:

∂f/∂y = -x

We can see that both of these partial derivatives are continuous functions of x and y and are defined for all (x,y) in the domain of f. Therefore, f is differentiable at any point (a,b).

The derivative of f at (a,b) is the gradient vector of f evaluated at (a,b), which is given by:

Gradient vector of f(a,b) = ∇f(a,b) = ( ∂f/∂x, ∂f/∂y ) = (4a-b, -a)

So the derivative of f at (a, b) is (4a-b, -a).

(a) The number of four-digit numbers with distinct digits in {1, 2, 3, 4, 5, 6} is 6543 = 360.

(b) The number of four-digit numbers in {1, 2, 3, 4, 5, 6} that are even is (3543)/2 = 270.

(c) The number of four-digit numbers in {1, 2, 3, 4, 5, 6} that are even and have distinct digits is (321*1)/2 = 3.

For (a) the total number of four-digit numbers with digits in {1, 2, 3, 4, 5, 6} is 6 options for the first digit, 5 for the second, 4 for the third and 3 for the last one. So, 654*3 = 360.

For (b) since digits in {1, 2, 3, 4, 5, 6} the even digits are 2,4,6. for each of the even digits we have 5 options for the second digit, 4 for the third and 3 for the last one. In total, we have 354*3= 270 even numbers.

For (c) The total number of four-digit numbers with distinct digits that are even is 211 = 2, since there are 2 even digits in {1,2,3,4,5,6} and only one of each can be used. However, this count is double-counting the numbers, so we divide by 2 to get 3.

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Answer:

= -6x + 24

Step-by-step explanation:

6(4-x) = 6*4 + 6*-x

= 24 - 6x

= -6x + 24

The greatest common factor (GCF) of two or more expressions is the largest monomial that divides each expression exactly.

To find the GCF of 36x^2 and 18xy^2, we can factor out the greatest common factor from each expression.

The prime factorization of 36 is 2^2 * 3^2 and of 18 is 2*3^2

The GCF of 36x^2 and 18xy^2 is 18x^2y^2 = 2*3^2 * x^2 * y^2

So, the GCF of 36x^2 and 18xy^2 is 18x^2y^2

Answer:

18xy

Step-by-step explanation:

The number of selections that will contain no defective printers can be found using the nCr formula as well, but with n being the number of non-defective printers (34) and r being the number of items selected (2). So nCr = 34!/(2!(34-2)!) = 34!/(2!32!) = 5,832.

(a) There are 6,632 selections that can be made.

(b) There are 5,832 selections that will contain no defective printers.

(a)The number of selections can be found using the nCr formula: nCr = n!/(r!(n-r)!), where n is the total number of items (42) and r is the number of items selected (2). So nCr = 42!/(2!(42-2)!) = 42!/(2!40!) = 6,632.

(b) The number of selections that will contain no defective printers can be found using the nCr formula as well, but with n being the number of non-defective printers (34) and r being the number of items selected (2). So nCr = 34!/(2!(34-2)!) = 34!/(2!32!) = 5,832.

There are 6,632 selections that can be made when two printers are chosen from a shipment of 42, including 8 that are defective. Out of these selections, 5,832 will contain no defective printers.

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Answer: The slope between two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

We are given that the slope between (8, y) and (14, -13) is -2/3. So we can use this information to set up the equation:

-2/3 = (-13 - y) / (14 - 8)

To find y, we can solve for y:

-2/3 = (-13 - y) / 6

-2 = -13 - y

y = 11

So the value of y is 11.

Step-by-step explanation:

An example of a question that can be solved using the associative method is : (2/5) * (3/4) * (5/6)

One example of a problem involving multiplication of fractions that can be made easier using the associative property is:

(2/5) * (3/4) * (5/6)

Using the associative property of multiplication, we can change the grouping of the fractions to make the problem easier. The associative property states that the way we group the numbers being multiplied does not change the product. For example,

(2/5) * (3/4) * (5/6) = (2/5 * 3/4) * (5/6) = (6/20) * (5/6) = 30/120

This simplification makes it easier to see that the final answer is 1/4.

By using the associative property, we can first multiply (2/5) * (3/4) = (6/20) which is easier to cancel out the common factor and then multiply it with (5/6) = (5/6) * (6/20) = (30/120) = 1/4 which is the final answer

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BFS has an exponential space complexity with respect to d because it stores all the nodes at the same depth level before moving on to the next level

DFS doesn't have an exponential space complexity with respect to d because it only stores the nodes that need to be visited next.

The space complexity of breadth-first search (BFS) is O([tex]b^d[/tex]) and the space complexity of depth-first search (DFS) is O(bd), where b is the maximum branching factor of the search tree and d is the maximum depth of the tree.

The reason for the difference in the space complexities is that BFS uses a queue to store the nodes to be visited, while DFS uses a stack.

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17. The equation can be rewritten as 2x²-8x+1=0.

18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.

17.

The equation can be rewritten as 2x²-8x+1=0.

Vertex:

The vertex is (4, -1). A minimum.

Axis of symmetry:

The axis of symmetry is x = 4.

The parabola opens up.

The graph has 1 solution.

18. How many solutions does the quadratic

have?

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17. The equation can be rewritten as 2x²-8x+1=0. 18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.

17. The equation can be rewritten as 2x²-8x+1=0.

Vertex:

The vertex is (4, -1). A minimum.

Axis of symmetry:

The axis of symmetry is x = 4.

The parabola opens up.

The graph has 1 solution.

18. The coefficient of x, which is -10, is multiplied by two to determine the axis of symmetry, which is x = 5.

This is due to the fact that the axis of symmetry is always located halfway between the two x-intercepts.

The parabola widens, indicating that the vertex is where its maximum is located. The vertex is (5, 6), which is determined by solving for y while changing x = 5 in the equation.

There are two answers to the quadratic equation: x = 4 and x = 6. The equation must be made equal to 0 in order to get the solutions.

Either factoring or applying the quadratic formula can be used to accomplish this.

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The total cost of his groceries in dollars and cents is 91.35 on 8.75% sales tax.

A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.

Sales tax is an indirect fee that is always applied at the point of exchange or purchase and is calculated as a percentage of the item's worth. Retail, manufacturing, wholesale, use, and value-added taxes are the various types of sales taxes (VAT). Note: As of July 1, 2017, the Goods and Services Tax (GST) has taken the place of the Sales Tax.

Sales tax = 8.75%

⇒  8.75/100 × 84

⇒ 7.35

Total price = 7.35 + 84

⇒ $ 91.35

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The percent by mass of a solution is  29.21.

To calculate the percent by mass of a solution, divide the mass of the solute (13.687 grams) by the total mass of the solution (46.833 grams). Then, multiply this value by 100 to get the percent.

% by mass = (mass of solute/total mass of solution) x 100

% by mass = (13.687/46.833) x 100 = 29.21.This calculation can be used to determine the amount of a solute in a given solution. It is important to know the percent by mass of a solution in order to make sure the solution is composed of the desired amount of solute. Knowing the percent by mass can also be used to compare the solutions of different concentrations.

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Answer:

$30

Step-by-step explanation:

1kg= $8

3kg *$8= $24

3/4= 0.75

$8 *0.75= $6

$24+$6= $30

3.75 kg * $8= 30

* = multiply

There are many similarities between Vanguard and Fidelity, but there are also some significant distinctions. Vanguard focuses primarily on long-term, buy-and-hold investing.

Fidelity, on the other hand, caters to investors who prefer a more hands-on approach.

There are more than 8,300 domestic investment-grade bonds held by the Vanguard Total Bond Market ETF.

Therefore, You'll need to study two (or more) sets of statements, keep track of several phone numbers, access a number of websites, and comprehend and keep track of hundreds of different funds.

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There are many similarities between Vanguard and Fidelity, but there are also some significant distinctions. Vanguard focuses primarily on long-term, buy-and-hold investing. Fidelity, on the other hand, caters to investors who prefer a more hands-on approach.

Bonds are issued by borrowers to attract capital from investors ready to extend a loan to them for a specific period of time. When you purchase a bond, you are making a loan to the issuer, which could be a corporate, government, or municipality.

By purchasing a bond, you are effectively lending the issuer money. In exchange, they commit to repay you the face amount of the loan on a particular date and to make periodic interest payments—typically twice a year—along the way. Unlike stocks, which grant you ownership rights, bonds issued by corporations do not.

Therefore, Vanguard's primary investment strategy is long-term buy-and-hold investing. On the other hand, Fidelity caters to investors who favor a more active strategy.

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The cost of each shirt is $6 and the cost of each pant for the given condition is $9.

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

Let us suppose the cost of shirt = x.

Let us suppose the cost of pant = y.

Given that 3 shirts and 3 pants cost $45, this is represented as:

3x + 3y = 45 (equation 1)

1 shirt and 2 pants cost $24, this is represented as:

x + 2y = 24 (equation 2)

Using the elimination method to solve:

Multiply the second equation with 3 and change the signs of all the variables.

(x + 2y = 24) (3)

-3x - 6y = -72 (equation 3)

3x + 3y = 45

Comparing equation 1 and equation 3, the x term is cancelled, and the remaining equation after subtracting both equations is:

- 3y = -27

y = 9

Substitute the value of y in equation 2.

x + 2y = 24

x + 2(9) = 24

x + 18 = 24

x = 24 -18

x = 6

Hence, the cost of each shirt is $6 and the cost of each pant is $9.

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Answer: y = 2-4x

Step-by-step explanation:

The product of the two complex number c₁c₂ is thus 10 + 9i.

Let c₁ = a + ib and c₂ = c + id. Also z₁ represent 2 + 2i and z₂ represent 5 + i. The length of side of the equilateral triangle formed can be obtained by

|z₁ - z₂| = r = √((5 - 2)² + (1 - 2)² = √10

a² + b² - 4a - 4b + 8 = 10

a² + b² - 10a - 2b + 26 = 10

So 6a - 2b = 18 that is 3a - b = 9

Thus b = 3a - 9

Similarly c² + d² - 4c - 4d + 8 = 10

c² + d² - 10c - 2d + 26 = 10

So 3c - d = 9, that is d = 3c - 9

Midpoint of line joining c₁ and c₂ is same as that of z₁ and z₂, so

(c + a)/2 = ( 5 + 2)/ 2 and (d + b)/2 = (1 + 2)/2

So midpoint is 3.5 + 1.5i

Altitude of equilateral triangle of side a is √3a/2

That is √(a - 3.5)² + (b - 1.5)² = √3×√10/2

√(a - 3.5)² + (3a - 9 - 1.5)² = √30 /2

a² - 7a + 12.25 + 9a² - 63a + 110.25 = 30/4

On solving a = (7 ± √3)/ 2

So a = (7 - √3)/ 2, c = (7 + √3)/ 2

b = 3a - 9 = (3 - 3√3)/ 2, d = (3 + 3√3)/2

So c

c₁ = (7 - √3)/2 + i (3 - 3√3)/ 2

c₂ = (7 + √3)/2 + i (3 + 3√3)/ 2

So the product c₁c₂ is

= ((7 - √3)/ 2) * ((7 + √3)/ 2) - ((3 - √3)/ 2) * ((3 + √3)/ 2) + i (((7 - √3)/ 2) * ((3 + √3)/ 2) + ((7 + √3)/ 2) * ((3 - √3)/ 2))

= 10 + 9i

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The equation has a solution of x= 3/4 will be B. 8x = 6

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, the value of x in 3x = 6 will be:

x = 6 / 3

x = 2

The value of x in 8x = 6 will be:

x = 6 / 8

x = 3 / 4

The value of x in 4x = 2 will be:

x = 2/4

x = 1/2

The value of x in 3x = 15 will be:

x = 15 / 3

x = 5

The correct option is B.

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Complete question

Which equation has a solution of x= 3/4?

A. 3x = 6

B. 8x = 6

C. 4x = 2

D. 3x = 15