Calculate the next term in the arithmetic sequence that
increases by 21, if the current term is 55.
What is the next term if the first two terms of a
Fibonacci sequence are 2, 25?
Find the 72th term o

The expression which uses the commutative property to make it easier to evaluate (-3/4)x1/5x(-16) is (-3/4)x(-16)x1/5) which is therefore denoted as option A.

This states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.

In the expression (-3/4)x1/5x(-16) , there is the need to arrange them so as to make it easier for them to be reduced to their lowest factor which is why -16 was put close to the  (-3/4).

(-3/4)x(-16)x1/5 = 12 × 1/5 =  12/5

This is therefore the reason why option A was chosen as the correct choice.

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The speaker has a volume of about 34.67 cubic inches.

V = (1/3) * 13 * 8

= 104/3

≈ 34.67 cubic inches

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.

Volume is sometimes referred to as capacity. The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Many forms have various volumes. The several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.

From the question:

The following formula can be used to determine a pyramid's volume:

V = base area * height * (1/3)

Since the speaker in this instance is shaped like a triangular pyramid, we can use the base area of 13 square inches and the height of 8 inches to calculate the volume.

When the values are added to the formula, we obtain:

V = (1/3) * 13 * 8

= 104/3

≈ 34.67 cubic inches

Hence, the speaker's volume is roughly 34.67 cubic inches.

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To estimate the average height of black spruce trees in a 1,000 ha plot with 99% confidence that the estimate is within 0.5 m, you need a sample size of at least 19. This is based on the standard deviation of tree heights in a nearby location of 1.10 m as determined in a study conducted last year.

To estimate the average height of black spruce trees in a 1,000 ha plot with 99% confidence that the estimate is within 0.5 m, we can use the formula for sample size calculation:

n = (z² × σ²) / E²

Where:

n = sample size

z = z-score for the desired confidence level (99% confidence level corresponds to a z-score of 2.576)

σ = standard deviation (1.10 m)

E = margin of error (0.5 m)

Plugging in the values into the formula, we get:

n = (2.576² × 1.10²) / 0.5²n = 18.15.

Therefore, the sample size must be at least 19 black spruce trees to have 99% confidence that the estimate is within 0.5 m.

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Answer:

a = 1

Step-by-step explanation:

6a + 5a + 1 = 12

Subtract one to both side leaving a by itself.

6a + 5a = 12 - 1

Now simply by add or subtracting, multiply or dividing.

11a = 11

Divide 11 to both side leaving a = ?

a = 1

Answer:

a= 1

Step-by-step explanation:

6a + 5a + 1 = 12

(-1) + 6a + 5a +1 = 12 -1

6a + 5a = 11

11a = 11

11a/11 = 11/11

a= 1

The height of the cone is approximately 28.867 units and the radius is approximately 21.65 units.

Let's denote the height of the cone as "h" and the radius as "r".

From the problem statement, we know that:

r = (3/4)h ...(1) (given)

The surface area of the cone is given as 3750 square units. The formula for the surface area of a cone is:

Surface Area of Cone = πr(r + l),

where "l" is the slant height of the cone. Since the slant height is not given in the problem, we need to express "l" in terms of "r" and "h" using the Pythagorean theorem:

l² = r² + h²

l² = (3/4)² h² + h²

l² = (9/16)h² + h²

l² = (25/16)h²

l = (5/4)h

Substituting this expression for "l" and the expression for "r" from equation (1) into the surface area formula, we get:

3750 = πr(r + l)

3750 = π[(3/4)h] [(3/4)h + (5/4)h]

3750 = π (9/16 + 15/16) h²

3750 = π (24/16) h²

3750 = (3/2) π h²

h² = (2500/3π)

h ≈ 28.867

Substituting this value of "h" into equation (1), we get:

r = (3/4)h

r ≈ 21.65

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Answer: Radius 37.5    &      height 50

Step-by-step explanation: correct in edmuntum/plato

Answer:

The lateral area of the prism is 190 square inches and the total surface area is 358 square inches.

Step-by-step explanation:

To find the lateral area and total surface area of a rectangular prism, we need to use the following formulas:

Lateral Area = perimeter of the base x height

Total Surface Area = 2 x base area + lateral area

Where the base area is simply the product of the length and width of the rectangular prism.

Let's apply these formulas to the rectangular prism with dimensions 12in x 7in x 5in:

Lateral Area:

To find the perimeter of the base, we add up the lengths of all four sides of the rectangle:

Perimeter of the base = 2(length + width) = 2(12in + 7in) = 2(19in) = 38in

Now, we multiply the perimeter of the base by the height of the prism:

Lateral Area = 38in x 5in = 190in^2

Therefore, the lateral area of the rectangular prism is 190 square inches.

Total Surface Area:

To find the base area, we simply multiply the length and width of the rectangular prism:

Base Area = length x width = 12in x 7in = 84in^2

Now, we can use the formula for total surface area:

Total Surface Area = 2 x base area + lateral area

Total Surface Area = 2(84in^2) + 190in^2

Total Surface Area = 168in^2 + 190in^2

Total Surface Area = 358in^2

Therefore, the total surface area of the rectangular prism is 358 square inches.

So the lateral area of the prism is 190 square inches and the total surface area is 358 square inches.

The polynomial function P(x) with a quadratic function zero of 3-4i and an additional zero is P(x) = (x2 - 6x + 25)(x - additional zero).

A polynomial function, P(x), is a function that can be written in the form P(x) = anxn + an-1xn-1 + ... + a1x + a0, where n is a non-negative integer and an, an-1, ..., a1, a0 are real numbers. A quadratic function is a polynomial function of degree 2, which means it can be written in the form P(x) = ax2 + bx + c.

If a polynomial function has a zero of 3-4i, then it must also have a zero of 3+4i, since complex zeros always come in conjugate pairs. This means that the polynomial function must have factors of (x - (3-4i)) and (x - (3+4i)). Multiplying these two factors together gives us (x - 3 + 4i)(x - 3 - 4i) = x2 - 6x + 25.

If the polynomial function also has an additional zero, then it must have a factor of (x - additional zero). Multiplying this factor with the previous one gives us P(x) = (x2 - 6x + 25)(x - additional zero).

So, the polynomial function P(x) with a quadratic function zero of 3-4i and an additional zero is P(x) = (x2 - 6x + 25)(x - additional zero).

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The leading coefficient of the given polynomial 4x^(6)+3x^(5)+x^(4)+5 is 4.

A polynomial is an expression of the form anxn + an-1xn-1 + ... + a1x + a0, where an, an-1, ..., a1, and a0 are constants and x is a variable.

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In the given polynomial, the term with the highest degree is 4x^(6), so the leading coefficient is 4.

Therefore, the leading coefficient of the given polynomial 4x^(6)+3x^(5)+x^(4)+5 is 4.

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Approximately 11,800 of the 16,000 voters would be expected to vote against the bond issue.

Data in math is information that can be quantified and organized. It can include numeric values, words, dates, and other types of data. Data is used to analyze relationships and make predictions. Data can be used to create charts, graphs, and tables that display trends, patterns, and relationships. Data can also be used to inform decisions and help solve problems.

Based on the collected data, it is likely that the bond issue will pass. Out of the three samples, only one showed a majority of people against the bond issue, and the other two samples showed a majority of people in favor. This indicates that there is a strong likelihood of the bond issue passing. I am confident in this assessment because the samples are representative of the same population, and there is a clear majority of people in favor of the bond issue.

Using the mean of the samples, approximately 11,800 of the 16,000 voters would be expected to vote against the bond issue.

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Answer:

The formula for the length of an arc of a circle is given by:

length of arc = (central angle/360) x 2πr

where r is the radius of the circle and the central angle is measured in degrees.

In this problem, we know the length of arc RV is 3π/2 units and the radius of circle M is 6 units. Therefore, we can solve for the central angle using the formula above:

3π/2 = (central angle/360) x 2π(6)

3π/2 = (central angle/180) x π x 6

3/2 = (central angle/180) x 6

central angle = (3/2) x (180/6) = 45 degrees

So the approximate measure of angle RMV is 45 degrees, which corresponds to option B.

The amount of rope used by Mr.Lucy is given by equation A = 1.28125 feet of rope

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the amount of rope used be represented as A

Now , the equation will be

The total amount of feet of rope Mr.Lucy has = 10 1/4 feet

So , total amount of feet of rope Mr.Lucy has = 10.25 feet

Now , the amount of rope used = ( 1/8 ) of the total amount

On simplifying , we get

The amount of rope used A = ( 1/8 ) x 10.25 feet

The amount of rope used A = ( 41 / 32 ) feet

The amount of rope used A = 1 9/32 feet

The amount of rope used A = 1.28125 feet of rope

Hence , the amount of rope used is A = 1.28125 feet of rope

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The average speed of the boat relative to the water is approximately 17.08 mph.

The average speed of the boat relative to the water can be found by using the formula for distance, speed, and time:

distance = speed × time

We can use this formula to set up two equations, one for the downstream trip and one for the upstream trip:

38 = (s + 6) × t₁

38 = (s - 6) × t₂

We can then use the given information about the total time of the trip to find the values of t₁ and t₂:

4.75 = t₁ + t₂

We can rearrange the first two equations to solve for t₁ and t₂ in terms of s:

t1 = 38/(s + 6)

t2 = 38/(s - 6)

Substituting these values into the third equation and simplifying gives us:

4.75 = 38/(s + 6) + 38/(s - 6)

4.75s² - 57s - 114 = 0

Using the quadratic formula, we can solve for s:

s = (57 ± √(57₂ - 4(4.75)(-114)))/(2(4.75))

s ≈ 17.08 or s ≈ -3.01

Since the speed of the boat cannot be negative, t

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The total surface area of the hollow hemisphere is 1736.4 cm²

The total surface area of a large round bowl (hollow hemisphere) can be calculated by finding the surface area of the outer hemisphere and the surface area of the inner hemisphere and area of the ring and adding them together.

The formula for the surface area of a hemisphere is 2πr^2, where r is the radius of the hemisphere.

The outer radius of the bowl is 12 cm, so the surface area of the outer hemisphere is:

Surface area of outer hemisphere = 2π(12)^2 = 2π(144) = 288π

The inner radius of the bowl is the outer radius minus the thickness, which is 12 - 1 = 11 cm. So the surface area of the inner hemisphere is:

Surface area of inner hemisphere = 2π(11)^2 = 2π(121) = 242π

area of the concentric circle joining the outer surface and inner surface is π(12²-11²)= 23π

The total surface area of the bowl is the sum of the surface area of the outer hemisphere and the surface area of the inner hemisphere:

Total surface area = 288π + 242π + 23π = 553π

So the total surface area of the bowl is 530π cm^2.

then we can use the approximation π ≈ 3.14 to find the total surface area:

Total surface area ≈ 553*(3.14) ≈ 1736.4 cm^2

So the total surface area of the bowl is approximately 1736.4 cm^2.

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In conclusion, the mapping in part B informs us that the two circles are equation congruent, i.e., that their size and shape are the same and that the mapping preserves all of their geometrical characteristics.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The mapping in part B informs us that the points on the two circles correspond exactly to one another. In other words, there is exactly one point on the bigger circle for every point on the smaller circle, and vice versa.

In conclusion, the mapping in part B informs us that the two circles are congruent, i.e., that their size and shape are the same, and that the mapping preserves all of their geometrical characteristics.

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The expression when simplified is (d)

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

Using the above as a guide, we have the following:

The given expression is

3 * Black triangle + 2 * White triangle + 2 * Black square + 1 * White square

This gives

-3x + 2x - 2 + 1

Evaluate the like terms

-x - 1

This means

1 Black triangle and 1 Black square

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We know here that the effect that the circled point will have on the y-intercept is B and that the y-intercept will decrease because the point pulls the least-squares regression line toward it.

In statistics, we know that an intercept is the value of the dependent variable when the independent variable or variables is equal to zero and that it is often represented by the symbol "b" in a linear equation.

We can take an example here:

A simple linear equation has the form y = mx + b, where "y" is the dependent variable, "x" is the independent variable, "m" is the slope of the line, and "b" is the y-intercept. The y-intercept is the point where the line crosses the y-axis so, we can see here that the effect that the circled point will have on the y-intercept is B. The y-intercept will decrease because the point pulls the least-squares regression line toward it.

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The lines IJ and KL are parallel , so the slopes of the lines are equal and the value of b is -4.75

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be I ( -4 , 17 )

Let the second point be J ( 1 , -3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = ( 17 - ( -3 ) ) / ( -4 - 1 )

Slope m₁ = -20/5

Slope m₁ = -4

Now , the lines IJ and KL are parallel , so the slopes are equal

Let the third point be K ( b , 3 )

Let the fourth point be L ( -5 , 4 )

Slope m₂ = ( 4 - 3 ) / ( -5 - b )

Slope m ₂ = 1/ ( -5 - b )

where m₁ = m₂

On simplifying , we get

1/ ( -5 - b ) = -4

Multiply by ( -5 - b ) on both sides , we get

1 = 20 + 4b

Subtracting 20 on both sides , we get

4b = -19

Divide by 4 on both sides , we get

b = -4.75

Therefore , the value of b is -4.75

Hence , the slope of the lines is m = -4

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The book sold 38,100 copies in its first month of release. then approximately 537,324 copies have been sold to date.

What is the percentage?

A percentage is a ratio, fraction, or portion of a whole which is represented as 100.

Let "x" be the total number of copies sold to date.

According to the problem, 38,100 is 7.1% of x, which can be written as:

38,100 = 0.071x

To find x, we can solve for it by dividing both sides of the equation by 0.071:

x = 38,100 / 0.071

x = 537,323.94 (rounded to the nearest whole number)

Therefore, approximately 537,324 copies have been sold to date.

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Step-by-step explanation:

Therefore, the probability of this event is 3/6 or 1/2.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. It is used to quantify the uncertainty or risk associated with a particular event or situation.

given by the question.

Event: Rolling a standard die and landing on either 1, 2, or 3.

A standard die has six faces, numbered from 1 to 6. Rolling the die is a random experiment that can result in any of the six possible outcomes with equal probability. The event described in the statement only includes three of the six possible outcomes, namely 1, 2, and 3

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Answer: 5

Step-by-step explanation:

To solve 4/5x + 3 = 7 for x, we must isolate x on one side of the problem.

To begin, remove 3 from both sides to get:

4/5x = 4

Hence, we can multiply both sides by 5/4 to isolate x:

x = 5

As a result, the answer to the equation 4/5x + 3 = 7 is x = 5.

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The exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.

To find all the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24, we need to find the values of x that make c(x)=0. One way to do this is by using the Rational Root Theorem, which states that if a polynomial has rational zeros, then they must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The factors of the constant term, 24, are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. The factors of the leading coefficient, 3, are ±1 and ±3. Therefore, the possible rational zeros are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24.

Using synthetic division, we can test these possible zeros to see if they are actually zeros of the polynomial. After testing, we find that the zeros are -4, -3/2, 2, and 1.

So, the exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.

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The order of the colors is Red, blue, yellow

Chromatography is a laboratory technique used to separate and analyze mixtures of different compounds based on their physical and chemical properties. It involves passing a mixture through a stationary phase, which may be a solid or a liquid, and a mobile phase, which may be a liquid or a gas.

As the mixture passes through the stationary phase, the different compounds in the mixture interact with the stationary phase to varying degrees, causing them to separate. The mobile phase carries the separated components through the stationary phase, and the separated components are detected and analyzed using a detector, such as a spectrophotometer.

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Answer:

x= 3 or x = -3

Step-by-step explanation:

We can see here that the two values that x can have if 5x² + 41 = 86 is -3 and +3.

To find the values of x that satisfy the equation 5x² + 41 = 86, we can start by isolating the term with the variable on one side of the equation. Here's the step-by-step solution:

Subtract 41 from both sides of the equation:

5x² + 41 - 41 = 86 - 41

5x² = 45

Divide both sides of the equation by 5:

(5x²) / 5 = 45 / 5

x² = 9

Take the square root of both sides of the equation:

√(x²) = √9

x = ±3

Therefore, the equation 5x² + 41 = 86 has two solutions: x = 3 and x = -3.

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The average rate of change for the week is calculated by subtracting the first day's attendance (1,534) from the last day's attendance (2,394) and then dividing by the number of days (7).

Number is an abstract concept used to describe a quantity or amount of something. It is used to measure, count, and label objects, people, places, and other things. Numbers can be used to describe size, shape, location, and many other concepts. They are also used to represent data, money, and other mathematical operations. Numbers are the cornerstone of mathematics, and they are used in a variety of ways in everyday life.

This yields an average rate of change of +77.71 people per day.

This average rate of change is only a good measure for how the number of people changed throughout the week if the number of people changed in a consistent manner. If the attendance was relatively stable from day to day, then the average rate of change would accurately reflect the number of people who attended. However, if the attendance changed drastically from day to day, the average rate of change would not accurately reflect the attendance for the entire week.


Complete questions as follows-
The table shows the number of people, n, who went to see musical , on the duh day of April. What is the average rate of 'change for the number of people from day to day 7? 1,534 2,324 2,418 b. Is the average rate of change a good measure for how the number of people changed throughout the week? Explain your reasoning; ''. ` 2,281 2,350 2,394 1,720 weight (02) 369 Algebra 1".

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The correct answer is c. 7.81.

To find the variance for the distribution of ungrouped data, we need to use the formula:

Variance = (Σ(x^2)f - (Σxf)^2 / n) / n

Where x is the data value, f is the frequency of the data value, and n is the total number of data values.

For the first question:

1. The variance for the following distribution of ungrouped data to its right is:

Dato (x) Frecuencia (f) xf x^2f
3.2 3 9.6 30.72
1.3 4 5.2 6.76
2.4 2 4.8 11.52
Total 9 19.6 49

Variance = (49 - (19.6)^2 / 9) / 9
Variance = (49 - 42.46) / 9
Variance = 0.73

Therefore, the correct answer is a. 0.79.

For the second question:

2. The variance for the following distribution of ungrouped data to its right is:

Edad (x) Frecuencia (f) xf x^2f
6 7 42 252
7 12 84 588
8 10 80 640
9 8 72 648
10 5 50 500
Total 42 328 2628

Variance = (2628 - (328)^2 / 42) / 42
Variance = (2628 - 2570.29) / 42
Variance = 1.38

Therefore, the correct answer is c. 7.81.

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Answer: The function to express the total amount of money Martin will make as a function of the number of calls he makes is:

Total Money = (Number of hours worked x Base pay per hour) + (Bonus pay per hour x Number of bonus calls)

Where:

Number of hours worked = 4

Base pay per hour = $75 / 4 = $18.75 (since he works for 4 hours every day and receives $75)

Bonus pay per hour = ($5.50 x (Number of bonus calls)) / 4 (since he works for 4 hours every day and receives a bonus of $5.50 per call over 35 in one hour, which is equivalent to $5.50 / 4 per call)

Number of bonus calls = (Total calls - (Number of hours worked x Baseline calls per hour))

Using this formula, we can calculate how much money Martin will make for the day if he makes a total of 45 calls every hour:

Number of bonus calls = (45 - (4 x 35)) = 5

Bonus pay per hour = ($5.50 x 5) / 4 = $6.875

Total Money = (4 x $18.75) + (4 x $6.875) = $75 + $27.50 = $102.50

Therefore, if Martin makes a total of 45 calls every hour, he will make $102.50 for the day.

Step-by-step explanation:

When the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours.

What is the linear equation in two variables?

A linear equation in two variables is an equation of the form:

ax + by = c

where x and y are variables, a, b, and c are constants, and a and b are not both zero. The graph of a linear equation in two variables is a straight line, and any point on the line satisfies the equation.

The given equation is:

y = 8x + 57

where y is the quiz score and x is the hours spent on homework.

To find the meaning of the x-value when y = 98, we can substitute y = 98 into the equation and solve for x:

98 = 8x + 57

Subtracting 57 from both sides, we get:

41 = 8x

Dividing both sides by 8, we get:

x = 5.125

when the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours. This suggests that students who spend around 5 hours and 7.5 minutes on homework per week can expect to score around 98 on their weekly quiz.

Therefore, when the quiz score is expected to be 98, the corresponding x-value, which represents the number of hours spent on homework, is approximately 5.125 hours.

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