Look at this set of 5 numbers:
32 52 29 32 25

Which value would change the most if the number 80 replaced the number 25 in the set?

Answer:$8.99

Step-by-step explanation:

The ratio of the areas of the bases of the two similar prisms is approximately 26 to 1.

What is the scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Let h1 and h2 be the heights of the two similar prisms, and let A1 and A2 be the areas of their respective bases.

Also, let k be the scale factor that relates the smaller prism to the larger prism.

a. We know that the volumes of the two similar prisms are proportional to the cubes of their corresponding side lengths, so we have:

(kh1)³ / (kh2)³ = 135 / 5000

Simplifying this expression, we get:

h1³ / h2³ = 135 / 5000

Taking the cube root of both sides, we get:

[tex]h1 / h2 = (135 / 5000)^{(1/3)}[/tex]

Using a calculator, we find:

h1 / h2 ≈ 0.405

Therefore, the ratio of the heights of the two similar prisms is approximately 0.405 to 1.

b. The ratio of the areas of the bases of two similar prisms is equal to the square of the scale factor. That is:

A1 / A2 = k²

To find the scale factor k, we can use the fact that the volumes of the two prisms are proportional to k³. Therefore:

k³ = 5000 / 135

k ≈ 5.091

Using this value of k, we get:

A1 / A2 = k² = (5.091)² ≈ 26

Therefore, the ratio of the areas of the bases of the two similar prisms is approximately 26 to 1.

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Here the  p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level that the valve performs above specifications.

We have to evaluate null and alternative hypotheses for the scenario .

In this scenario, the null hypothesis is

H0: μ = 5.8

here

μ = true mean pressure produced by the valve.

Now for the alternative hypothesis is

HA: μ > 5.8

here

μ = true mean pressure produced by the valve.

Therefore to  determine if there is sufficient observation at the 0.05 level that the valve performs above specifications,

Here we can utilize a one-tailed z-test with

α = 0.05

Then,  test statistic can be evaluated as

z = (X' - μ) / (σ / √n)

where:

X' = sample mean

μ = hypothesized value concerning the population mean

σ = population standard deviation

n = sample size

Substituting in our values, we get:

z = (5.9 - 5.8) / (1 / √130) = 1.8856



Now utilizing a z-table  we can evaluate that the p-value associated with this test statistic is approximately 0.0292.

Since this p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level that the valve performs above specifications.

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For the mean weight five boxes of cookies, the p-value is equals to 0.04189. If p-value is 0.233 > α, the conclusion is that mean weight of cookies is equals to 16.

We have total five boxes of cookies. Let population of weights is normally distributed, 15.91, 14.07 , 14.88, 16.07, 14.79. Use t.test to determine the p value and hypothesis testing for mean weight of product ( cookies). Let null and alternative hypothesis be defined as

[tex]H_0 : \mu = 16[/tex]

[tex]H_a : \mu<16[/tex]

degree of freedom, df = n - 1 = 5

Using the t-test formula, t value= -2.291,

Using t distribution table and the value p-value for t = -2.2907 and 4 degree of freedom is 0.04189. Hence, required value is 0.04189.

b) Now, p-value = 0.233 for mean weight varied from the specified value of 16.

Level of significance, [tex]\alpha[/tex] = 0.05

As we see p-value = 0.233 > 0.05 ( α), so, this is a significant region and null hypothesis can't be rejected. There is no enough evidence to conclude that the mean weight is actually less than 16 ounces.

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Complete question:

Following are the weights of 5 boxes of cookies, each of which is labeled as containing 16 ounces. Assume that the population of weights is normally distributed, 15.91, 14.07 , 14.88, 16.07, 14.79 . A quality control inspector wants to know whether the mean weight is actually less than 16 ounces. Compute the P-value of the test. Write down your P-value. Also, if he obtained a p-value of 0.233. which conclusion is appropriate?

The time it will take to fill the pool at the given rate would be = 8 mins.

To calculate the volume of the cylindrical swimming pool the formula for the volume of the cylinder should be used which is = πr²h

where r = 5ft

h = 8ft

volume = π×5×5×8 = 200πft³

If 25πft³ = 1 minute

200πft³ = X

Make X the subject of formula;

X = 200/25 = 8mins

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Answer:

  see attached

Step-by-step explanation:

You want a clock face with an angle of 240° between the hour and minute hands.

There are 22 possible locations for the minute hand such that the long arc between the hour and minute hands is 240°. The two of these that do not involve fractions of a second are 4:00 and 8:00.

The next occurrence will be 21 minutes 49 1/11 seconds later. And the one after that will be 43 minutes 38 2/11 seconds later, or 1 hour 5 minutes and 27 3/11 seconds after the first occurrence of the pair.

A clock face illustrating 8:00 is attached. You may need to scale it to your desired radius.

You can set your compass to 2" and draw the clock face circle. The points for 12 and 8 can be located by using the 10:00 position as the center of arcs with the same radius. Where those arcs intersect the original circle are the locations of 12 and 8.

An equation in slope-intercept form for the line shown in the given graph is equal to y = -5x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 20)/(0 + 3)

Slope (m) = -15/3

Slope (m) = -5.

At data point (0, 5) and a slope of -5, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -5(x - 0)

y - 5 = -5x

y = -5x + 5

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The correct expressions that give the new acreage are A and C.

A. 0.89y represents the remaining 89% of the original acreage after the sale.

C. y-0.11y represents the original acreage minus the 11% that was sold.

It should be noted that to find the new acreage using the first expression (A), we can simply multiply the original acreage by 0.89:

New acreage = 0.89y

To find the new acreage using the second expression (C), we can subtract 0.11 times the original acreage from the original acreage:

New acreage = y - 0.11y

New acreage = 0.89y

Both expressions give the same result, which is the new acreage after the sale.

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A farmer recently sold a large plot of land. The sale decreased his total acreage by 11%. Let y be the original acreage. Find two equivalent expressions that will give the new acreage. Use pencil and paper. Use the expressions to describe two ways to find the new acreage.

Which two expressions will give the new acreage?

A. 0.89y

OB. 0.11y

C. y-0.11y

D. 11y

OE. y-11y

OF. 0.89y-0.11y

Answer:

C. -1.7

Step-by-step explanation:

-4.2 - x = -2 2/4

-2 2/4 = -10/4 = -2.5

-4.2 - x = -2.5

-x = 1.7

x = -1.7

So, the answer is C. -1.7

Answer:

127. my answer needs to be 20+ character sooooooooooooo

A study has a 2 Ã 2 Ã 3 within-groups factorial design. This example has a total of _12_ cell(s). Researchers would need to investigate _three__ main effect(s), _Three two-way interactions __ two-way interaction(s), and _ One three-way interaction__ three-way interaction(s) in this study.

a 2 x 2 x 3 within-groups factorial design, you have:
A total of 2 x 2 x 3 = 12 cells
Three main effects to investigate (one for each factor)
Three two-way interactions to investigate (AxB, AxC, and BxC)
4. One three-way interaction to investigate (AxBxC)
So, in this study, there are 12 cells, researchers would need to investigate 3 main effects, 3 two-way interactions, and 1 three-way interaction.

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The area under the X2 curve with 5 degrees of freedom to the right of 1.61, 9.24 and 15.09 is 0.078, 0.0001 and 0 respectively.

Area is a two-dimensional measure of a surface, such as a length multiplied by a width. It is used to measure the size of a space, such as a room, or a piece of land. Area can also be used to measure the size of a shape, such as a circle or a square. Area is usually measured in units such as square meters (m2) or square feet (ft2).

(a)1.61

The area under the X2 curve with 5 degrees of freedom to the right of 1.61 can be calculated using the following formula:

Area = 1 - Φ(x; df)

Where Φ(x; df) is the cumulative distribution function of the chi-square distribution, and df stands for the degrees of freedom.

For df = 5, Φ(1.61; 5) = 0.922.

Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 1.61 is equal to 1 - 0.922 = 0.078.

(b) 9.24

For df = 5, Φ(9.24; 5) = 0.9999.

Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 9.24 is equal to 1 - 0.9999 = 0.0001.

(c) 15.09

For df = 5, Φ(15.09; 5) = 1.

Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 15.09 is equal to 1 - 1 = 0.

In conclusion, the area under the X2 curve with 5 degrees of freedom to the right of 1.61, 9.24 and 15.09 is 0.078, 0.0001 and 0 respectively.

Complete questions as follows-

find the area under the x2 -curve with 5 degrees of freedom to the right of (a) 1.61 (b) 9.24 (c) 15.09.

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The solution to the given problem of the triangle comes out to be AC are 20 units long.

If a polygon contains at least one more segment, it is a hexagon. It is a simple rectangle in shape. Anything identical to a standard triangle form can only be distinguished from it by edges across A and B. Euclidean geometry does not completely describe the cube, despite the fact that its edges are all collinear. A triangle is formed by a circle with five sides and three angles.

Here,

If DE is the midpoint of triangle ABC, DE is parallel to AC and has a length of 50% of AC.

Let's use "x" units to represent the length of AC.

Given the information, DE equals 10 units, or 50 percent of AC's length. So that we may create the equation:

=>  DE = AC/2

When we enter DE's value as 10 units, we get:

=> 10 = x/2

To separate x, we multiply both sides of the equation by 2 and obtain:

=> 2 * 10 = x

=> x = 20

Therefore, AC is 20 units long.

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Answer:

---------------------

Perimeter is the sum of side lengths.

Given sides:

Find the perimeter by adding up side lengths:

2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.

To determine whether it would be unlikely to get a box with 31 red pencils based on the Mean Absolute Deviation (MAD) for the given data set, we first need to calculate the MAD.

Step 1: Calculate the mean of the data set

The given data set is: 22, 28, 30, 28, 35, 30, 28

The mean is calculated by adding up all the numbers and dividing by the total number of values:

Mean = (22 + 28 + 30 + 28 + 35 + 30 + 28) / 7 = 201 / 7 = 28.71 (rounded to two decimal places)

Step 2: Calculate the absolute deviations

The absolute deviation for each data point is calculated by finding the absolute difference between the data point and the mean:

|22 - 28.71| = 6.71

|28 - 28.71| = 0.71

|30 - 28.71| = 1.29

|28 - 28.71| = 0.71

|35 - 28.71| = 6.29

|30 - 28.71| = 1.29

|28 - 28.71| = 0.71

Step 3: Calculate the MAD

The MAD is the mean of the absolute deviations:

MAD = (6.71 + 0.71 + 1.29 + 0.71 + 6.29 + 1.29 + 0.71) / 7 = 17.71 / 7 = 2.53 (rounded to two decimal places)

Now, to determine whether it would be unlikely to get a box with 31 red pencils, we can compare 31 with the MAD. If the difference between 31 and the mean (28.71) is greater than the MAD (2.53), then it would be unlikely.

Difference = 31 - 28.71 = 2.29

Since 2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.

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Annette surveyed a total of 480 people.

Let x be the total number of people Annette surveyed. According to the problem, 37.5% of the people surveyed do not want a new mall, and this amounts to 180 people. We can set up the equation:

0.375 * x = 180

Now, let's solve for x:

x = 180 / 0.375

x = 480

Selina will get £153.78 of interest by the end of 3 years.

To calculate the total amount of interest Selina will get by the end of 3 years, we need to use the compound interest formula:

A = P[tex](1 + r/n)^{(nt)}[/tex]

where:

A = the amount of money at the end of the time period

P = the principal amount (the amount initially invested)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

In this case, we have:

P = £2000 (the amount initially invested)

r = 2.5% per annum = 0.025 (as a decimal)

n = 1 (the interest is compounded annually)

t = 3 (the time period is 3 years)

So, plugging in the values into the formula, we get:

A = 2000[tex](1 + 0.025/1)^{(1×3)}[/tex]

= 2000[tex](1.025)^{3}[/tex]

= 2000(1.07689)

= £2,153.78 (rounded to the nearest penny)

To find the total amount of interest Selina will get, we need to subtract the principal amount from the final amount:

Total interest = £2,153.78 - £2,000

= £153.78

Therefore, Selina will get £153.78 of interest by the end of 3 years.

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BMED is a trapezoid and OD is equals to BD/2. Proof of these is given below.

It should be noted that to prove that BMED is a trapezoid, we need to show that either BM || ED or BM || DE. We will show that BM || DE.

Since O is the midpoint of AM, we have OA = OM, and thus triangle ODM is isosceles. Therefore, OD = DM.

Also, since E is the midpoint of DC, we have DE || AB (because AB is also a mid-segment of triangle ADC). Therefore, angle ADE = angle ABC.

Using the fact that angles in a triangle add up to 180 degrees, we have:

angle EDC + angle ADE + angle CED = 180 degrees

Substituting angle ADE = angle ABC, we get:

angle EDC + angle ABC + angle CED = 180 degrees

But angle CED = angle BCD (because they are alternate interior angles formed by transversal BD cutting parallel lines DC and AB). Therefore:

angle EDC + angle ABC + angle BCD = 180 degrees

This means that angles BCD, ABC, and EDC are all on the same line, and thus angle BCD + angle ABC = 180 degrees.

Now, using the fact that angles in a triangle add up to 180 degrees, we have:

angle BAC + angle ABC + angle ACB = 180 degrees

Substituting angle BCD + angle ABC = 180 degrees, we get:

angle BAC + angle BCD + angle ACB = 180 degrees

Since triangle BCD is isosceles (because BD is an angle bisector), we have angle BCD = angle CBD. Therefore:

angle BAC + angle CBD + angle ACB = 180 degrees

But angle ACD = angle ACB + angle CBD, so:

angle BAC + angle ACD = 180 degrees

This means that triangle ABC is similar to triangle ACD.

Now, since BM is a median of triangle ABC, we have:

BM = 1/2 AC

But triangle ADC is similar to triangle ABC, so:

AC = 2 AD

Therefore:

BM = AC/2 = AD

So we have BM || DE, and BM = DE, which means that BMED is a trapezoid.

2. To prove that D is the midpoint of AE, we will use the fact that BMED is a trapezoid. Since BM || DE, we have:

BD/DM = BE/EM

But DM = OD (since triangle ODM is isosceles) and EM = DC/2 = AC/4 (since E is the midpoint of DC and AC is a mid-segment of triangle ADC).

Therefore:

BD/OD = BE/(AC/4)

But we also have:

BE = BD + DE = BD + BM = 2BD

Substituting this into the previous equation, we get:

BD/OD = 2BD/(AC/4)

Simplifying:

BD/OD = 8BD/AC

This means that:

OD = AC/8

But we also know that AC = 2AD, so:

OD = AD/4

Since O is the midpoint of AM, we also have:

OD = OM = AM/2

Therefore:

AD/4 = AM/2

This means that:

AD = 2AM/4 = AM/2 = OD

So D is the midpoint of AE, and CD = 2AD.

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In a triangle ABC. [AM] is the median relative to [BC] and O is the midpoint of [AM]. (BO) cuts [AC] at D. Let E be the midpoint of [DC]. 1) Prove that BMED is a trapezoid. 2) Prove that D is the midpoint of [AE); deduce that CD = 2AD. 3) Prove that OD == BD.

Answer:

Step-by-step explanation:

a coordinate plane has given a coordinate to each an every point we draw on that. So when we have to find the radius of this circle , we have to find a pair of coordinates.

So I am taking these coordinates; (0,3) and (0,7)

So the radius = 7-3= 4 units

The water property that explains why the air temperature significantly changed but the water temperature stayed relatively the same is the property of specific heat.

Water's high specific heat capacity allows it to absorb and retain heat energy without much change in temperature, explaining why its temperature did not shift despite significant changes in the air temperature. Air has low specific heat capacity, while water has high.

Therefore, This caused the stream water temperature to remain stable despite environmental changes. Air temps change quickly due to its lower heat capacity.

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12) There were about 557 principals in attendance. 13) Option A: The college will have about 480 students who prefer cookies. 14) Option C: bar graph, title favorite sport and the x axis labeled sport and the y axis.

The relationship between two quantities that are measured on the same scale and in the same units is known as a percentage. The relative size or magnitude of one thing in comparison to another is represented by proportions, which are frequently stated as ratios, fractions, or percentages. For instance, if there are 8 girls and 12 boys in a class, the girl-to-boy ratio is 8:12, or 2:3, which indicates that there are 3 guys for every 2 girls. Statistics, geometry, and physics are just a few of the mathematical and scientific disciplines that use proportions. Proportions are frequently used in statistics to describe the distribution of a population or a sample.

12) For the number of principals in conference we set up a proportionality with total people as follows:

We know that, 52 principals out of 70 people thus:

52/70 = x/750

Now,

x = (52/70) * 750

x = 557.14

Hence, we can predict that there were about 557 principals in attendance at the conference.

13) Given that, out of 225 students 27 prefer cookies thus,

27/225 = 0.12

That is 12% students like cookies.

Now, for the total number of students we have:

0.12 * 4000 = 480

Thus, option A: The college will have about 480 students who prefer cookies.

14) For the collected data the best representation is option C: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.

15) For the given description of the line plot the median is:

For Bus 47 = 16

For Bus 18 = 13

The faster bus is Bus 47, with a median of 16.

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2 ¼ hours + 1 ½ hours = 3 ¾ hours

Jordan studied for his science test for 3 ¾ hours this weekend.

Science is a systematic process that produces knowledge in the form of testable predictions and universe-related explanations that can be organized and placed into order.

In general, science entails an effort to learn about universal truths or how fundamental laws work. Learning about the components of the universe and how they operate right now, in the past, and perhaps in the future is done through science.

Although science is intricate and multifaceted, its most significant traits are simple: Learning understanding what is in the natural world, how it functions, and how it came to be the way it is through science.

2 ¼ hours + 1 ½ hours = 3 ¾ hours

Jordan studied for his science exam for 3 ¾ hours this weekend.

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Jordan spent a total of 3 hours and 45 minutes studying for his science test this weekend.

what is arithmetic sequence.

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

Jordan studied for 2 ¼ hours on Saturday and 1 ½ hours on Sunday for his science test. To find the total number of hours he studied, we can add these two amounts.

2 ¼ hours is the same as 2 + ¼ hours, or 2 hours and 15 minutes.

So, we have:

2 hours and 15 minutes (Saturday) + 1 hour and 30 minutes (Sunday)

To add these two amounts, we can first add the hours and then add the minutes separately.

2 hours + 1 hour = 3 hours

15 minutes + 30 minutes = 45 minutes

Therefore, Jordan spent a total of 3 hours and 45 minutes studying for his science test this weekend.

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The surface area of the cylinder to the nearest tenth is 82.2 in²

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

The surface area of cylinder is expressed as;

A = 2πr(r+h) . Where r is the radius and h is the height of the cylinder.

A = 2 × 3.14 × 1.7( 1.7+6)

= 10.68× 7.7

= 82.2 in²( nearest tenth)

Therefore the surface area of the cylinder is 82.2

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Answer:

Step-by-step explanation:

To find x and the degree measure of each angle, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

(a) Writing an equation to find x, we have:

mZH + m<1 + m<J = 180

(2x - 3) + (5x + 7) + x = 180 (substituting given angle measures)

8x + 4 = 180 (combining like terms)

8x = 176

x = 22

Therefore, x = 22 is the solution to the equation.

(b) To find the degree measure of each angle, we can substitute x = 22 into the given expressions:

mZH = 2x - 3 = 2(22) - 3 = 41 degrees

m<1 = 5x + 7 = 5(22) + 7 = 117 degrees

m<J = x = 22 degrees

Therefore, the degree measures of the angles are mZH = 41 degrees, m<1 = 117 degrees, and m<J = 22 degrees.

Answer: a) x=23. b) x=12

Step-by-step explanation:

a) Alternate angles are equal
b) corresponding angles add to 180 degrees

Answer:

Prove the following identitics: tan 0 + cot 0 = I/(sin 0 cos 0) 0 + tan 0 sec 0 = cosec 0 'sec? 0. 18 cosec = cosec? 0 = tan? 0 cot2 19 sec? 0 sin ' 0 =cos? 0 'sin? 20 cos4 (sec 0 + tan 0) (sec 0 _ tan 0) = 1 2 sin? 0 = cOs? 0 _ 'sin? 0. 22 2 cos? 0_I=1 23 sec? 0 + cosec 0 = sec? 0 cosec? sin? , COs? 24 sec" 0 cosec" 0 = cos 0 sin" 0 25 =I tan 0 + 1 cot? 0 +4 26 (sec? 0 1) (cosec? 0 1) = [ 27 ((sec? 0 _0)+ V(cosec" 0 _ !) = sec € cosec 0 28 (sec? tan? 0) + V(cosec? 0 ~ cot? 0) = 2 cos? 0 29 =1 sin sec? 0 _ 1 sec 0 cosec 0 tan 0 + cot 0 30 tan 0 cot 0 sec 0 + cosec 0 cos 0 sin 0 31 =l V( + tan? 0) V( + cot? 0) Eliminate 0 from the following equations: 32 x = 4 cos 0, y = b sin 0. 33 x = 4 cot 0,y = b cosec 0. 34 x=a tan 0,y =b cos 0. 35 x = ] sin 0, y = [ + cos 0, 36 x =a sec 0,y = b +c cos 0. 37 x=a cosec 0, y = b sec 0. 38 X=l+ tan 0,y = cos 0. 39 x=sin 0 + cos 0,y = sin 0 40 cos X = sCc 0 + tan 0, y = sCc 0 ~ tan 0.

5/3 is greater than 1 (it's 1.67), and the product will be located on a number line to the right of 2/3. As a result, "The product will be located to the right because is greater than 1." is correct.

The area model, linear model, and set model are the three major types of fraction models. Evidence demonstrates that allowing pupils to deal with all three models is critical for establishing a conceptual knowledge of fractions.

The student is utilizing the model to calculate the product of 5/2 and 2/3, or (5/2) x (2/3).

To multiply fractions, simply multiply their numerators and then their denominators. So:

(5/2) x (2/3) = (5 x 2) / (2 x 3) = 10/6 = 5/3

Because 5/3 is greater than 1 (it's 1.67), the product will be located on a number line to the right of 2/3. As a result, "The product will be located to the right because is greater than 1." is correct.

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Complete question: