A fruit basket contains 12 apples and 7 pears. How many pears do you need to add to the basket to make the ratio of apples to pears as 2:3?

So, the area of triangle DEF is 312.5 square feet, using the scale factor of 5/2.

the context of mathematics and geometry, dilation is a transformation that changes the size of an object. It is a type of transformation that scales an object by a certain factor, without changing its shape or orientation.

In other words, dilation involves multiplying the coordinates of a geometric figure by a fixed constant, which results in an enlarged or reduced version of the original figure. The constant is known as the dilation factor or the scale factor, and it can be any real number greater than zero.

For example, if we dilate a circle by a scale factor of 2, every point on the circle will be moved twice as far away from the center, resulting in a new circle with a diameter twice as large as the original.

Let's start by using the formula for the perimeter of a triangle:

[tex]Perimeter of triangle ABC = AB + BC + AC = 65.5 feet[/tex]

We can also use Heron's formula to find the area of triangle ABC:

[tex]Area of triangle ABC = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]

where s is the semi perimeter of the triangle:

[tex]s = (AB + BC + AC) / 2[/tex]

We can use these equations to solve for the side lengths of triangle ABC:

[tex]AB + BC + AC = 65.5[/tex]

[tex]s = (AB + BC + AC) / 2[/tex]

[tex]25 = \sqrt(s(s-AB)(s-BC)(s-AC))[/tex]

Solving for AB, BC, and AC gives us:

AB = 15

BC = 20

AC = 30.5

Now, let's dilate triangle ABC by a factor of 5/2 to create triangle DEF. This means that each side of triangle ABC will be multiplied by 5/2 to get the corresponding side length of triangle DEF.

DE = AB * (5/2) = 37.5

EF = BC * (5/2) = 50

DF = AC * (5/2) = 76.25

Now we can use Heron's formula again to find the area of triangle DEF:

s = (DE + EF + DF) / 2 = 81.875

Area of triangle DEF = sqrt(s(s-DE) (s-EF) (s-DF)) = 312.5 square feet

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If the the a is greater than 1, compared to the parent function the C. Stretched vertically.

The equation y = ax^2 + c represents a quadratic function where "a" is the coefficient of the x^2 term and "c" is a constant term. The parent function of this quadratic function is y = x^2.

If the equation of a quadratic function is given in the form y = ax^2 + c and "a" is greater than 1, then the graph of the function will be stretched vertically and the vertex will be shifted up or down depending on the value of "c".

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After calculation we get

11) d. m/JML = 90 degrees, a. m/GMH = 45 degrees, b. mLH = 90 degrees, c. m/LKH = 45 degrees

12) a. AGKH is an isosceles triangle, b. Another triangle formed by two radii is an equilateral triangle.

13) a. m/GKH = 33.4 degrees, c. m/KHJ = 33.4 degrees, e. mJL66.8 degrees, b. m/KGH = 66.8 degrees, d. m/JKL = 113.2 degrees

A quadrilateral is a geometric shape with four straight sides and four angles. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and kites.

According to the given information:

a. Since m/LGH and m/GHJ are both 45°, GH is a bisector of ∠JGL. Therefore, m/GMH = 90° - 45° = 45°.

b. Since GH is a bisector of ∠JGL, m/LGH = m/HGL = 45°. Also, since LH is a straight line, m/LGH + mLH + m/HGL = 180°. Thus, mLH = 90° - 45° = 45°.

c. Since GH is a bisector of ∠LJK, m/GHK = m/JHK = 45°. Also, since LK is a straight line, m/LKH + m/JHK + m/LJK = 180°. Thus, m/LKH = m/LJK = (180° - 2*45°)/2 = 45°.

d. Since GH is a bisector of ∠JGL and JML is a straight line, m/JML = m/JGH + m/HGL = 45° + 45° = 90°.

a. AGKH is a quadrilateral with two sides that are radii of the circle. Since all radii of a circle are equal, AGKH is a kite. Furthermore, since the two radii AG and KH are perpendicular to each other, AGKH is also a rectangle.

b. Another triangle formed by two radii is AKJ, where AK and AJ are radii of the circle and KJ is a chord.

a. Since GH is a diameter of the circle and GKH is a right triangle with ∠GHK = 90°, m/GKH = 180° - 90° = 90°.

b. Since GH is a diameter of the circle and KJ is a chord, m/KGH = m/KJ = 1/2 * m/KHJ = 1/2 * (180° - 113.2°) = 33.4°.

c. Since GH is a diameter of the circle and KHJ is a right triangle with ∠KHJ = 90°, m/KHJ = 180° - m/GKH = 180° - 90° = 90°.

d. Since GH is a diameter of the circle and JKL is a right triangle with ∠JKL = 90°, m/JKL = 180° - m/KJ - m/JKH = 180° - 33.4° - 45° = 101.6°.

e. Since JL is a chord of the circle and ∠JGL is an inscribed angle that intercepts it, m/JGL = 1/2 * m/JL = 1/2 * (180° - m/JKL) = 1/2 * (180° - 101.6°) = 39.2°. Also, since GH is a diameter of the circle and GJL is a right triangle with ∠GJL = 90°, m/GJL = 90° - m/GHL = 90° - 45° = 45°. Therefore, m/JLH = m/JGL - m/GLH = 39.2° - 45° = -5.8°. Note that the negative value indicates that ∠JLH is a reflex angle.

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The domain restrictions on the function [tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex] are the x values -9, 0, 3, 4 and 9

From the question, we have the following function that can be used in our computation:

[tex]\left f(x\right)=-\frac{3x}{81\:-\:x^2}\:\cdot \frac{81\:-\:x^2}{2x^2-6x}\:\div \frac{x^2+2x-6x}{3x^2-30x+63}[/tex]

Next, we set the denominator to 0 and solve for x

So, we have

81 - x²: x = ±9

2x² - 6x: x = 0 and x = 3

x² + 2x - 6x: x = 0 and x = 4

Hence, the domain restrictions are the x values -9, 0, 3, 4 and 9

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Answer:

B) 352

Step-by-step explanation:

45% = 0.45

640 x 0.45= 288

288 is how many students walked to school

So to find how many took the bus to school

640- 288= 352

Answer:

The coins are picked without replacement.

The probability of picking at least one Canadian quarter is 1 minus the probability of picking 6 U.S. quarters:

[tex]1 - ( \frac{41}{50} )( \frac{40}{49} )( \frac{39}{48} )( \frac{38}{47} )( \frac{37}{46} )( \frac{36}{45} ) [/tex]

[tex] = 1 - .28296 = .71704[/tex]

So the probability of picking at least one Canadian quarter is about 71.7%.

Answer: 36

Step-by-step explanation:

F(4)=9 is the value for this function.

A function that is defined by numerous smaller functions across various time intervals is known as a piecewise function. The domain of a function is the sum of all the smaller domains, and each sub-function has its own formula and domain. The input value and the function that establishes that interval determine the function's output.

The typical functional notation, which represents the body of a function as an array of functions and related subdomains, can be used to define piecewise functions. Together, these subdomains must encompass the entire domain; frequently, it is also necessary for them to be pairwise disjoint, or constitute a partition of the domain.

x=4 is bigger than or equal to 0 because it.

we use the third function definition

F(x)=x+5.

Therefore, F(4)=4+5=9.

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Since -4 is less than or equal to -2, we use the first part of the definition of f(x) which is f(x) = x + 4 if x ≤ -2. Therefore,

f(-4) = (-4) + 4 = 0.

So, the answer is D. 0.

Step-by-step explanation:

x = the number

1/4 * x = 1/8   <====given,     Multiply both sides of the equation by 4

4  * 1/4   x = 4 * 1/ 8

x = 4/8 = 1/2

Step-by-step explanation:

Let the given number Be X  

SO given thatone fourth of X is one eighth

x/4 = 1/8

x  = 1/2

x = 0.5

Therefore, the volume of the prism is 60 cubic feet.

Volume is the amount of space occupied by a three-dimensional object or the capacity of an object. It is typically measured in cubic units such as cubic meters, cubic feet, or cubic centimeters. The formula for finding the volume of a solid object depends on its shape. In general, the volume of a shape can be found by dividing it into smaller, more easily measured shapes and adding up their volumes. This is known as the method of integration in calculus, and it is used to find the volumes of irregularly shaped objects or fluids. Understanding the concept of volume is important in many fields, such as architecture, engineering, physics, and chemistry. In these fields, volume is used to determine the capacity of containers, the displacement of fluids, and the amount of materials needed for a construction project.

Here,

The volume of a prism is given by the formula:

V = Bh

where B is the area of the base and h is the height of the prism.

Substituting the given values:

V = (20 ft)(3 ft)

V = 60 cubic feet

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Answer:

B is the answer

Step-by-step explanation:

The expression that is not equal to the others is B [[2/−5]] The other expressions are A −[[2/5]], C [[−2/5]], and D [[2/5]].

Answer: y=2

Step-by-step explanation:

We're given x=1 so we can plug this in 3x - y =1 and isolate to solve for y.

[tex]3(1)-y=1\\3-y=1\\-y=-2\\y=2[/tex]

For all x, P(x) (using universal quantifier ∀) and  It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:

1. For all x in S, P(x) (using universal quantifier ∀)

2. It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)

If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:

For all x, P(x) (using universal quantifier ∀)

It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:

For all x in S, P(x) (using universal quantifier ∀)

It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)

If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:

1. For all x, P(x) (using universal quantifier ∀)

2. It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)

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The range of the 98% confidence interval for the percentage of faulty components that differ between machines A and B is about between -0.2448 and 0.1305. (rounded to 4 decimal places).

Given:

Sample proportion from machine A ([tex]p_1[/tex]) = 5/35 = 0.14285714285714285

Sample proportion from machine B ([tex]p_2[/tex]) = 7/35 = 0.2

Sample size from machine A ([tex]n_1[/tex]) = 35

Sample size from machine B ([tex]n_2[/tex]) = 35

Standard error (SE) = [tex]\sqrt{ [(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)}[/tex]

= [tex]\sqrt{[0.14285714285714285 * (1 - 0.14285714285714285) / 35] + [0.2 * (1 - 0.2) / 35] }[/tex]

= 0.07058061453775912 (rounded to 11 decimal places)

Margin of error (ME) = Critical value * Standard error

= 2.660 * 0.07058061453775912 (using z-score for a 98% confidence level)

= 0.18765117789861733 (rounded to 11 decimal places)

Confidence interval (CI) = Sample statistic ± Margin of error

= [tex](p_1 - p_2) \pm ME[/tex]

= (0.14285714285714285 - 0.2) ± 0.18765117789861733

= -0.05714285714285715 ± 0.18765117789861733

The 98% confidence interval for the difference in proportions of defective parts between machine A and machine B is approximately -0.2448 to 0.1305 (rounded to 4 decimal places).

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So, multiple choice algebra questions. the correct answer would be option D: [tex]3x^7 - 6x^6 - 11x^4 + 4x^5 - 4x^2[/tex].

To simplify the given expression [tex](3x^4+4x^2) (x^3-2x^2-1)[/tex], we can use the distributive property of multiplication to multiply each term of the first expression by each term of the second expression. This gives us:

[tex](3x^4+4x^2) (x^3-2x^2-1) \\= 3x^4(x^3) + 3x^4(-2x^2) + 3x^4(-1) + 4x^2(x^3) - 4x^2(2x^2) - 4x^2(1)[/tex]

Simplifying each term, we get:

[tex]= 3x^7 - 6x^6 - 3x^4 + 4x^5 - 8x^4 - 4x^2[/tex]

So, the correct answer would be option D: [tex]3x^7 - 6x^6 - 11x^4 + 4x^5 - 4x^2.[/tex]

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Answer:

step by step explanation:

All you have to do is expand and reduce the expressions

then evaluate -2 being a root of the expressions

To do that you need to substitute -2 into the simplified expressions

if the result comes as zero then f(-2) is factor of f(x) according to the factor theorem.

Example 1.

simplify (-5x-2)(7x-4)-2x+3

if you substitute f(x) as f(-2)

then substitute x with -2

when you simply and evaluate the expression you will get that the expression is equal to -137

which means -2 isn't a root since the expression must be equal to 0

-2 is not a root

do the same for the other expressions

The independent variable x represents the number of hours since the snow began to fall while the dependent variable is total amount of snow on Samir's lawn after x hours because the total amount of snow on Samir's lawn depends on the number of hours the snow fell.

The function M(6) refers to the amount of snow on Samir's Lawn after 6 hours

An independent variable is defined as the variable that causes a change.

However, a dependent variable is defined as the variable that occurs as a result or effect of a change.

The independent variable x represents the number of hours since the snow began to fall while the dependent variable is total amount of snow on Samir's lawn after x hours because the  total amount of snow on Samir's lawn depends on the number of hours the snow fell.

The function M(6) refers to the amount of snow on Samir's Lawn after 6 hours

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In linear equation, 44%  of the shoppers have an e-mail account and 56%  of the shoppers do not have computer access at home.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Total number of the shoppers who were surveyed = 150

a). Number of shoppers who have an e-mail account = Shoppers who have email accounts and computer access at home + Shoppers who have email accounts but no computer access at home

= 44 + 22

= 66

Percentage of the shoppers having an e-mail account = 66/150 * 100

                                                                        = 44%

b). Total number of shoppers who do not have computer access at home

= 7 + 77

=  84

Percentage of the shoppers having computer access at home

                                             = 84/150  * 100   =  56%

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If three points that are provided are not collinear then the only possible polygon that can be formed by connecting these points would be a triangle.

A polygon is a closed two-dimensional shape made up of straight line segments called sides. It is formed by connecting three or more points (vertices) in a specific order. The sides of a polygon do not intersect, and each vertex is connected to exactly two sides. The region enclosed by the sides of a polygon is called its interior, while the points outside the polygon but on the same plane are called its exterior.

If three points are provided and they are not collinear (i.e., they do not lie on the same straight line), then the only possible polygon that can be formed by connecting these points would be a triangle(refer image attached). A triangle is a polygon with three sides and three angles.

The specific type of triangle (e.g., equilateral, scalene, isosceles) would depend on the lengths of the sides and the measure of the angles formed by connecting these points in a specific order. Different orders of connecting the points may result in different types of triangles.

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After 5 half-lives, only 3.9 g of the original 155 g of radioactive isotope will remain.

Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be represented in a variety of forms, such as the natural numbers, real numbers, and complex numbers. Numbers can be used to describe physical quantities, such as volume, mass, and time, as well as abstract quantities, such as sets, functions, and abstract objects. Numbers are also used to represent concepts such as truth, beauty, and goodness.

To calculate this, we can use the formula:
Final Mass = Initial Mass * (1/2)Number of Half Lives

In this case, the Initial Mass is 155 g, and the Number of Half Lives is 5. Therefore, the equation to use is:
Final Mass = 155 g * (1/2)⁵

Plugging the numbers into the equation, we get:
Final Mass = 155 g * (1/2)⁵
Final Mass = 155 g * (1/32)
Final Mass = 3.9 g

Therefore, after 5 half-lives, only 3.9 g of the original 155 g of radioactive isotope will remain. This is due to the fact that the half-life of a radioactive isotope is the amount of time it takes for the isotope to be reduced to half its original mass. As the number of half-lives increases, the amount of the isotope left decreases exponentially.

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The length of XY uisng the midpoint theorem is 40 units

The midpoint theorem states that if a line segment is drawn connecting the midpoints of two sides of a triangle, then that line segment is parallel to the third side of the triangle, and its length is half the length of the third side.

In this case, we have a triangle XYZ, and points A, B, C are the midpoints of sides XY, YZ, and ZX respectively.

By the midpoint theorem, we know that AB is parallel to ZX and has a length of half of ZX.

Similarly, BC is parallel to XY and has a length of half of XY, and AC is parallel to YZ and has a length of half of YZ.

We are given that BC has a length of 20, and we want to find the length of XY.

Using the midpoint theorem, we know that

XY is twice the length of BC

So

XY = 2 * BC = 2 * 20 = 40.

Therefore, the length XY is 40 units

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As a result, the vertex form of the f(x) equation is: [tex]f(x) = -(x - 5)^2 + 2[/tex]which is equivalent to choice (b).

A quadratic function is a sort of second-degree polynomial equation, meaning it has at least two squared element. A quadratic equation's generic form is: [tex]ax^2 + bx + c = 0[/tex] where the variable x and the constants a, b, and c. If the coefficient a were zero, the expression would be linear rather than quadratic. Several ways to solve a quadratic equation, including factoring, squaring the square, and utilising the quadratic formula. The negative numbers or roots of the quadratic equation are the values of x which it make the equation true and are the solutions to the quadratic equation.

given

The factored form of the quadratic function f(x), which has roots of 3 and 7, is as follows:

f(x) = a(x - 3)(x - 7) (x - 7) where "a" stands for a fixed coefficient.

We can utilise the point (1, 12) through which the function passes to determine the value of "a"

12 = a(1 - 3) (1 - 3)(1 - 7)

12 = -24a

a = -1/2

Inputting the value of "a" into the factored form yields the following results:

[tex]f(x) = -1/2(x - 3)(x - 7) (x - 7)[/tex]

By extending this phrase, we get:

[tex]f(x) = -1/2(x^2 - 10x + 21)[/tex]

We need to finish the square before we can transform this into vertex form. To achieve this, add and remove the square of the coefficient of x's half:

[tex]f(x) = -1/2(x^2 - 10x + 25 - 4)[/tex]

If we condense this phrase, we get:

[tex]f(x) = -1/2[(x - 5)^2 - 4][/tex]

As a result, the vertex form of the f(x) equation is: [tex]f(x) = -(x - 5)^2 + 2[/tex]which is equivalent to choice (b).

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Answer:

d. x > 2 or x < -2

Step-by-step explanation:

Domain describes the range of x-values in a function.

Domain

The domain of a graph is all of the x-values covered by the function. The domain does not reflect the y-values of a function. This means that answers A and B are automatically wrong.

By looking at the graph, we can tell that there is a gap where some x-values are not covered. This gap is known as a discontinuity. The discontinuity begins at -2 and ends at 2. All of the x-values in the discontinuity are not a part of the domain, and any parts of the graph that are continuous, are included in the domain. The graph is continuous at all points greater than 2 and less than -2, so all of those values are included in the domain. Now, we just need to find out if the endpoints are included in the domain.

Included Values

We know that the domain includes all x-values greater than 2 and less than -2, but we need to know if the domain includes 2 and -2. On a graph, included values will be shown as a closed circle and non-included values will be shown as an open circle. By looking at the graph, we can tell that 2 is not included but -2 is. This means that the domain is x > 2 or x < -2 because the domain does not include x = 2.

There are 250 students in the sixth grade.

First, let's define some variables:

The total number of sixth-grade students is called "x."

The number of students who purchased their lunches will be referred to as "p."

The number of students who brought their lunch from home will be referred to as "h."

We know that from the problem statement that

p + h = x (since all students either purchased their lunch or brought their lunch from home)

p = 0.24x (since 24% of the students purchased their lunch)

h = 190 (since 190 students brought their lunch from home)

We can use these equations to solve for x:

p + h = x

0.24x + 190 = x (substituting in the value of p and h from the other equations)

0.76x = 190 (subtracting 0.24x from both sides)

x = 250 (dividing both sides by 0.76)

Therefore, there are 250 students in the sixth grade.

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The numbers in each cell represent the frequency of people who chose that combination of gender and movie type.

What is the frequency?

The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.

To construct a two-way frequency table for the data, we need to organize the responses by gender and movie type. The table is in the attached image.

The rows represent the gender of the moviegoers, and the columns represent the movie type.

The numbers in each cell represent the frequency of moviegoers who chose that combination of gender and movie type.

For example, there are 12 men who chose Drama as their favorite movie type, and there are 13 women who chose Action as their favorite movie type.

The total number of moviegoers who chose Drama is 22, and the total number who chose Action is 27. The total number of moviegoers is 49.

Hence, The numbers in each cell represent the frequency of people who chose that combination of gender and movie type. For example, 12 men chose Drama as their favorite movie type.

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The principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.

To calculate the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59%, we first need to calculate the amount of interest that has accrued over the 51 months.

Using the formula:

Interest = Principal x Rate x Time

where Principal = $10,000,

Rate = 12.59% per year,

Time = 51/12 years (since the interest is compounded monthly):

Interest = $10,000 x 0.1259 x (51/12)

= $5,307.13

So the total amount owed after 51 months would be:

Total amount owed = Principal + Interest

= $10,000 + $5,307.13

= $15,307.13

Therefore, the principal when making the first payment 51 months later on a private student loan with a principal of $10,000 and a rate of 12.59% would be $15,307.13.

As for recent examples of community change that involves a clash between different cultures that helped disadvantaged communities and the populations, one example is the Black Lives Matter movement, which has brought attention to systemic racism and police brutality in the United States.  Another example is the #MeToo movement, which has raised awareness about sexual harassment and assault and has led to changes in workplace policies and cultural attitudes toward these issues.

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Answer:

b)

Step-by-step explanation: