The 7th grade and the 8th grade are collecting
food for Project Help. 7th grade starts with 7
items donated by a teacher and collects 5 items
per day. The 8th grade starts with 20 items
donated by a teacher and collects 8 items per
day. Write an equation for each grade level.
Which grade has a greater slope? Which grade
has a great initial value?

The race can finish in 256 possible ways, accounting for the possibility of ties among the four runners.

There are 4 runners in the race and any of them can finish first, so there are 4 ways to choose the winner. Once the winner is chosen, there are 4 remaining runners who can finish in second place.

Therefore, there are 4 × 4 = 16 ways for the first two places to be filled.

Once the first two places are filled, there are 4 remaining runners who can finish in third place.

Therefore, there are 4 × 16 = 64 ways for the first three places to be filled.

Finally, once the first three places are filled, there are 4 remaining runners who can finish in fourth place.

Therefore, there are 4 × 64 = 256 ways for all four runners to finish the race.

Therefore, there are 256 ways for the race to finish, including ties.

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Answer:

Aprove or deny a loan

Step-by-step explanation:

If the bank knows you can't pay them back they won't.

They choose this by checking your net worth.

Answer:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the initial balance

r = the annual interest rate (as a decimal)

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

t = the number of years

We know that P = $3500, A = $4390.40, r = unknown, n = 1 (compounded annually), and t = 2. Plugging in these values and solving for r:

$4390.40 = $3500(1 + r/1)^(1*2)

$4390.40/$3500 = (1 + r)^2

1.2544 = (1 + r)^2

√1.2544 = 1 + r

1.12 = 1 + r

r = 0.12 or 12%

Therefore, the annual interest rate is 12%.

The probability of the trials being successful is 0.625 or 62.5%. So, the expected value of Apnex stock after the announcement is $53.25 per share.

The odds of the trials being successful or failed, as well as the associated stock prices, must be taken into account in order to determine the predicted value of Apnex shares after the announcement.

we can state:

P(success) + P(failure) = 1

Let the market has already taken the probability into account and that the $56 stock price at the moment reflects the stock's anticipated value following the announcement. To put it another way, we can construct an equation based on the anticipated value formula:

Estimated Value = $68 for success and $18 for failure

Also, we are aware that the present stock price and the predicted value are equal:

Estimated Value = $56

When the second equation is substituted for the first equation, we obtain:

P(success) x $68 plus P(failure) x $18 equals $56.

For P(success), we obtain:

P(success) is equal to ($56 - $18) / ($68 - $18), or 0.625.

Thus, 0.625 or 62.5% of the trials will be successful.

We may determine the anticipated value of the shares following the announcement using this probability:

Estimated Value: 0.625 times $68 plus 0.375 times $18 equals $53.25

therefore, $53.25 per share is the anticipated value of Apnex shares following the announcement.

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zero

Observations are taken on sales of a certain mountain bike in 25 sporting goods stores. The regression model was Y= total sales (thousands of dollars), X 1 ​ = display floor space (square meters), X 2 ​ = competitors' advertising expenditures (thousands of dollars), X 3 ​ = advertised price (dollars per unit).Part a) the table is not given with the question. Please provide the required data and we will try our best to answer your question.The null and alternative hypotheses in a hypothesis test are:H0: βj = 0 Ha: βj ≠ 0j = 1, 2, 3. Since we have 3 predictors in the model so there will be three hypothesis test as well:Null and alternative hypotheses for hypothesis tests for β1, β2, and β3 are as follows:H0: βj = 0 Ha: βj ≠ 0j = 1, 2, 3.Therefore, if the absolute value of the computed t-value is greater than the absolute value of the table t-value for a specified α and n – k – 1 degrees of freedom, then the null hypothesis for that predictor is rejected. Hence, we can say that the predictor variable is significant at the α level.The table for t-values and p-values will be created based on the degree of freedom (d.f), the significance level (α), and the t-distribution function. The t-value is calculated using the following formula:t= (βi- 0) / SE(βi).Part b) Only CompetingAds differs significantly from zero is the correct option.

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The area of the trapezoid is multiplied by a factor of 4 when both bases and the height are doubled.

Trapezoids can be defined as quadrilaterals that have two parallel sides and two non-parallel sides.

The area of a trapezoid is given by the formula:

A = (b1 + b2) * h / 2

Where

If we double both bases and the height, we get:

b1' = 2 * b1 = 2 * 5 mm = 10 mm

b2' = 2 * b2 = 2 * 7 mm = 14 mm

h' = 2 * h = 2 * 6 mm = 12 mm

Now we can calculate the area of the new trapezoid:

A' = (b1' + b2') * h' / 2

A' = (10 mm + 14 mm) * 12 mm / 2

A' = 12 * 12 mm^2

A' = 144 mm^2

Therefore, the area of the trapezoid is multiplied by a factor of 4 when both bases and the height are doubled.

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The cοrrect οptiοn is Optiοn D. The p-value is less than α, and the null hypοthesis is nοt rejected. There is nο cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

Frοm the given data,

A cοmpany that ships glass fοr a manufacturer claimed that its shipping bοxes are cοnstructed sο that nο mοre than 8 percent οf the bοxes arrive with brοken glass.

The glass manufacturer believes that the actual percentage is greater than 8 percent.

The manufacturer tested the hypοtheses

H0: p = 0.08 and Ha: p > 0.08

The test yielded a p-value οf 0.1

Since the significance level (alpha) is 0.1 and the calculated p-value is 0.1,

we cοmpare the p-value tο alpha.

If the p-value is less than οr equal tο alpha, we reject the null hypοthesis H0: p = 0.08 in favοr οf the alternative hypοthesis Ha: p > 0.08.

If the p-value is greater than the alpha, we fail tο reject the null hypοthesis.

In this case, the calculated p-value οf 0.1 is greater than the significance level οf 0.1.

Therefοre, we fail tο reject the null hypοthesis and cοnclude that there is nοt enοugh evidence tο suppοrt the claim that the actual prοpοrtiοn οf bοxes with brοken glass is greater than 8%.

It is pοssible that the cοmpany's claim οf nο mοre than 8% brοken bοxes is accurate.

Therefοre,

The cοrrect οptiοn is Optiοn D.

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nο cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

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Cοmplete questiοn:

A cοmpany that ships glass fοr a glass manufacturer claimed that its shipping bοxes are cοnstructed sο that nο mοre than 8 percent οf the bοxes arrive with brοken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a randοm sample οf bοxes and recοrded the prοpοrtiοn οf bοxes that arrived with brοken glass. The manufacturer tested the hypοtheses H0:p=0.08 versus Ha:p>0.08 at the significance level οf α=0.01.

The test yielded a p-value οf 0.001. Assuming all cοnditiοns fοr inference were met, which οf the fοllοwing is the cοrrect cοnclusiοn?

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

The p-value is greater than α, and the null hypοthesis is rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08

The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.

After 5 days, the retailer starts making the money. The solution has been obtained by using the concept of break - even.

What is break - even?

The balance point known as "break-even" results in neither a profit nor a loss. Every value below the break-even mark represents a loss, whereas any value above it represents a gain.

We are given revenue function as R(x) = [tex]2x^3 + 11x^2 - 23x - 14[/tex].

The cost function is given as C(x) = [tex]13x^2 + 11x + 16[/tex].

The retailer will start earning only when the cost will be covered. This means that he will earn after when the R(x) = C(x).

So,

⇒ R(x) = C(x)

⇒ [tex]2x^3 + 11x^2 - 23x - 14[/tex] = [tex]13x^2 + 11x + 16[/tex]

⇒ [tex]2x^3[/tex] = [tex]2x^2 + 34x + 30[/tex]

⇒ [tex]x^3[/tex] = [tex]x^2 + 17x + 15[/tex]

⇒ [tex]x^3[/tex] - [tex]x^2 - 17x - 15[/tex] = 0

⇒ (x - 5) (x + 1) (x + 3) = 0

⇒ x = 5, -1, -3

Since, the days cannot be negative so, x = 5.

Hence, after 5 days, the retailer starts making the money.

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Question:

A popular video game retailer develops apps. The total revenue, in dollars per day, after x days can be modeled by the function R(x) = [tex]2x^3 + 11x^2 - 23x - 14[/tex]. The total cost, in dollars per day, after x days, can be modeled by the function C(x) = [tex]13x^2 + 11x + 16[/tex]. After how many days does the retailer start making money?

a. 1

b. 2

c. 5

d. 7

According to the given conditions , the equation of the circle is [tex](x + 2)^2 + (y - 5)^2 = 16.[/tex]

What is circle ?

A circle is a two-dimensional geometric shape that consists of all points in a plane that are a fixed distance, called the radius, from a given point called the center. A circle can also be defined as the set of all points that are equidistant from a central point.

The equation of a circle with center (h, k) and radius r is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

In this case, the center of the circle is (-2, 5) and the radius is 4, so the equation of the circle is:

[tex](x - (-2))^2 + (y - 5)^2 = 4^2[/tex]

Simplifying this equation gives:

[tex](x + 2)^2 + (y - 5)^2 = 16[/tex]

Therefore, according to the given conditions , the equation of the circle is [tex](x + 2)^2 + (y - 5)^2 = 16.[/tex]

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Answer: -10

Step-by-step explanation: You're welcome <3

Estimate less than the actual answer are 9.75 (less than 10) and 9.55 (less than 10). Estimate more than the actual answer are 38.315 (more than 38) and 8.4(more than 8).

Estimate, a near enough approximation of the true value. To make arithmetic simpler and more understandable, many assumptions are made.

Estimate is less than actual answer :

6.35 + 3.4 = 9.75

2.3 * 4.15 = 9.545 (≈ 9.55)

Estimate is more than actual answer :

7.9 * 4.85 = 38.315

3.6 + 4.8 = 8.4

So here, Estimate less than the actual answer are 9.75 (less than 10) and 9.55 (less than 10). Estimate more than the actual answer are 38.315 (more than 38) and 8.4(more than 8).

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Answer:

i only know the answer (I guessed on but I think it's 70.65

Step-by-step explanation:

let me know if I'm right 0w0

The base 10 representatiοn οf the number 1406 (3 at the bοttοm) is 118.

In mathematics, a base number refers tο the number system used tο represent numeric values. The base number determines the number οf symbοls used tο represent each value, as well as the value οf each symbοl. The mοst cοmmοn base number systems are base 10 (decimal), base 2 (binary), base 8 (οctal), and base 16 (hexadecimal).

In base 10, we use 10 digits (0-9) tο represent all pοssible values. In binary, we use οnly twο digits (0 and 1) tο represent values. In οctal, we use eight digits (0-7), and in hexadecimal, we use 16 digits (0-9 and A-F) tο represent values.

Fοr example, the decimal number 125 can be represented in base 2 as 1111101, in base 8 as 175, and in base 16 as 7D.

Cοnverting a number frοm οne base tο anοther invοlves dividing the number by the base and repeatedly finding the remainder until the quοtient becοmes zerο. The remainders, read frοm bοttοm tο tοp, represent the digits οf the new number in the new base.

Tο cοnvert a number in base 3 tο base 10, we need tο multiply each digit οf the number by the cοrrespοnding pοwer οf 3, and then sum up the prοducts.

Starting frοm the rightmοst digit οf the number, the pοwers οf 3 increase by 1 fοr each digit tο the left. Sο, fοr the number 1406 (3 at the bοttοm), we have:

1 × 3⁰ + 0 × 3¹ + 4 × 3² + 1 × 3³ = 1 + 0 + 36 + 81 = 118

Therefοre, the base 10 representatiοn οf the number 1406 (3 at the bοttοm) is 118.

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The polar form of the quantity will be  100.83 L 76.47°.

Given X = 5 L 40'andY = 20 L -30°(X + Y)X* .The expression (X + Y)X* can be simplified as: X * X + Y * X* =X² + Y * X* .Now, we need to find the polar form of the quantity (X + Y)X*.That is, we need to representX² + Y * X* in polar form. By using rectangular to polar conversion, we can convert the above expression to polar form.

Using the formula:

r² = x² + y²... Equation 1

θ = tan⁻¹(y / x)... Eq 2 (Where,x = real part of the expression)

x = X² = 5² = 25... Eq 3 (y = imaginary part of the expression)

y = Y * X*... Eq 4

Therefore, Y

Y * X* = 20 L -30° * 5 L 40'20 L -30° * 5 L 40' = 100 L 10°... Eq5

y = 100 L 10°.

Substituting the values of x and y in equations 1 and 2, we get:r² = x² + y²r² = 25² + 100²r² = 10025 + 100²r = 100.83θ = tan⁻¹(y / x)θ = tan⁻¹(100 L 10° / 25)θ = tan⁻¹(4 L 10°)θ = 76.47°

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Answer:

I can provide guidance on how to create a box and whisker plot on a TI-83, TI-83 Plus, or TI-84 graphing calculator using the given data.

To create a box and whisker plot:

Enter the data into a list on the calculator. For example, L1={90.1, 91.1, 91.5, 92.2, 92.5, 93.1, 94.0, 94.6, 96.1, 98.3}.

Press STAT, then go to Edit.

Select L1, then press STAT again and select CALC.

Choose 1-Var Stats and press Enter. This will generate a list of statistics for the data set.

Press 2nd, then Y= (STAT PLOT).

Select Plot1, then turn it on.

Choose Box Plot as the plot type.

Select L1 as the data list.

Set the X list to any unused list (e.g. Xlist: L2).

Make sure the frequency is set to 1.

Set the window settings as follows: Xmin=88, Xmax=100.5, Xscl=0.5, Ymin=−0.5, Ymax=3.5, Yscl=1, Xres=1.

Press GRAPH to view the box and whisker plot.

Note: If the plot does not display properly, try adjusting the Ymax and Ymin values until the plot is visible.

Answer:

Below

Step-by-step explanation:

The ENTIRE CIRCLE arc length (360° circumference ) is given by   pi * 2 r

          = pi * 2 * 10  = 20 pi   cm

We want to find  299 out of 360ths of this

     299/360 * 20 pi = ~ 52.2cm

Answer: The answer is 1.8 or 1.83 repeating

Step-by-step explanation: When you do 44 divided by 24 (2 years) it gives you how much she needs to pay per month.

Answer:

Angela pays $1.83 for each magazine.

Step-by-step explanation:

Considering that there are 12 months in 1 year, there would be 12 * 2 = 24 months in 2 years. If she gets one magazine per month, she would get 24 magazines.

She would be paying $44 / 24 magazines = 11/6 ≈ 1.83.

So, she is paying about $1.83 for each magazine.

Answer:

15 pounds

Step-by-step explanation:

for every 3 parts of dry fruit , four parts of nuts are added.
we know the total composition of the mixture is 35 pounds.


The total Composition of the mixture will be 7 parts

3/7 is dry fruit
4/7 is assorted nut


we can multiply the dry fruit composition to total
= 3/7 * 35 = 3*5 = 15

Pam needs 15 pounds of dry fruit to make the mixture.

The surface area of a triangular pyramid is the sum of areas of all faces of a triangular pyramid. Here, the surface area of a triangular pyramid with side 12 cm, base height 10 cm is equals to the 228 cm². So, the option (b) is correct choice.

Generally, a triangular pyramid has a triangular base and is bounded by three lateral triangular faces with one vertex. The units of measured surface area are square units like cm², m², ft² or cubit². The Formula for the surface area of a pyramid is calculated by adding up the area of all triangular faces of a pyramid. Mathematically,

Surface area = 1⁄2(a × b) + 3⁄2(b × s).

Where b --> the side of a pyramid

a --> the height of a base triangle, and

s --> the slant height of a pyramid. We have a triangular pyramid as present in above figure. Here height of base, a = 8 cm

slant height , s = 10 cm

side of a pyramid, b = 12 cm

So, Area of base triangle is, A1 = 1⁄2(a × b)

= (1/2)(8×12) = 48 cm²

Area of one triangular face = 1/2( b×s)

= 1/2( 12 × 10) = 60 cm²

Area of all triangular faces of a pyramid, A2 = 3× 60 = 180 cm²

The surface area of a pyramid = A1 + A2

= 48 + 180 = 228 cm²

Hence, required area is 228 cm².

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Complete question:

Find the surface area of the equilateral triangular pyramid. See the above

A 180cm^2

B 228cm^2

C 268cm^2

D 456cm^2

Therefore , the solution of the given problem of unitary method comes out to be  for each number of t, we can plot the points corresponding to the equation V(t) = 5000 + 1250t .

To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.

Here,

=> V(t) = 5000 + 1250t

where V(t) represents the amount of water in the pool at moment t (in hours)

t equals time (in hours)

The pool initially has 5000 gallons of water in it, so we add that to the 1250 t of water introduced by the hose.

We can use the time period as the x-axis (horizontal axis) and the amount of water as the y-axis to graph this equation. (vertical axis).

For instance, we can select the water volume interval from 0 to 20,000 gallons and the time interval from 0 to 16 hours (when the pool is full).

Then, for each number of t, we can plot the points corresponding to the equation V(t) = 5000 + 1250t and connect them with a line in order to get the image.

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Answer:

The Interquartile Range or (IQR) is 24

Step-by-step explanation:

Since the data set is ordered, we don't need to order it.

Now, to find the interquartile range:

First, find median which is 65 since it is in the middle

Next, we find the median in Quartile 1 and Quartile 3 (Quartile 2 is median)

So in Quartile 1, median is 47

Quartile 2, median is 71

Now find the range of those two:

71 - 47 = 24

Hope this helps!!

The equation 10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).

10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as follows: A sin (Bt + C) = 10 sin(4t) - 9 cos(4t) = 10 sin (4t) - 9 (cos(4t) cos 0 - sin(4t) sin 0) = 10 sin (4t) + 9 sin (0) = 10 sin (4t) + 9 (0) = 10 sin (4t + 0) = 10 sin (4t + C) where A = 10 and B = 4. Thus, 10 sin (4t) - 9 cos (4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).

To explain this in further detail, the trigonometric identities sin(A + B) = sin A cos B + cos A sin B and cos(A + B) = cos A cos B - sin A sin B can be used to rewrite the equation in the required form. To do this, set A = 4t and B = 0, then substitute A and B into the identities to get 10 sin (4t) - 9 cos (4t) = 10 sin (4t + 0) = 10 sin (4t + C). Therefore, the equation 10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).

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Answer:

∴  We have 12 blue balls and 3 red balls .

To find the dimensions of a parallelogram, you need to know the length of its base and the perpendicular distance from the base to the opposite side, which is also called the height or altitude of the parallelogram.

A quadrilateral (a four-sided polygon) with two pairs of parallel sides is referred to as a parallelogram. This means that the opposite sides of the parallelogram are parallel and have the same length, while the adjacent sides are unequal in length.

The properties of a parallelogram include:

The opposing sides seem to be congruent and parallel (equal in length)

Congruent opposite angles (equal in measure)

The angle adjacent to each other are supplementary (their sum is 180 degrees)

Diagonals bisect each other (the diagonals divide each other into two equal parts)

If you have the measurements of the sides and angles of the parallelogram, you can use trigonometry and geometry to find the length of the base and the height. For example, if you have the lengths of two adjacent sides and the angle between them, you can use the sine function to find the height. The base can be found by using the formula for the area of a parallelogram, which is base times height.

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The student can use a two-sample t-test to determine if there is a significant difference between the mean number of errors made by brand A and brand B. The two-sample t-test compares the means of two populations to determine if they are significantly different from each other.

The null hypothesis for this test is that the mean number of errors for brand A is equal to the mean number of errors for brand B. The alternative hypothesis is that the mean number of errors for brand A is less than the mean number of errors for brand B.

To conduct the two-sample t-test, the student will need to calculate the mean and standard deviation of the number of errors for each brand. Then, he will use the t-test formula to calculate the t-value and compare it to the critical value for a 5% level of significance.

If the t-value is less than the critical value, the student can reject the null hypothesis and conclude that the mean number of errors for brand A is significantly less than the mean number of errors for brand B. This would suggest that brand A is better than brand B.

However, if the t-value is greater than the critical value, the student cannot reject the null hypothesis and cannot conclude that there is a significant difference between the two brands.

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The maximum amοunt οf prοfit the cοmpany can make is $543

Prοfit is the mοney yοu have left after paying fοr business expenses. There are three main types οf prοfit: grοss prοfit, οperating and net prοfit.

Grοss prοfit is biggest. It shοws what mοney was left after paying fοr the gοοds and services sοld. Operating prοfit is next. It shοws what's left after alsο paying οperating cοsts such as rent, electricity, phοnes and in sοme cases staff.

Net prοfit cοmes last. It shοws what yοu made after deducting all cοsts and tax. Yοu get tο hοld οntο net prοfit.

Let y represent the amοunt οf prοfit and x represent the selling price.

The relatiοnship between x and y is:

y = -4x² + 141x – 703

The maximum prοfit is at dy/dx = 0, hence:

dy/dx = -8x + 141

-8x + 141 = 0

8x = 141

x = 17.625

The maximum prοfit is:

y = -4(17.625)² + 141(17.625) – 703 = 543

The maximum amοunt οf prοfit the cοmpany can make is $543

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The net of the pyramid is attached and the surface area of the triangular based prism is 54 ft²

The shape is given as

A triangular based prism

This means that the net would have 2 triangles and 3 rectangles

See attachment for the net of the prism

The surface area of a triangular based prism is calculated as

Area = (Perimeter of triangle) * Length + 2 * Base area

Substitute the known values in the above equation, so, we have the following representation

Area = (3 + 2 1/2 + 2 1/2) * 6 + 2 * 0.5 * 2 * 3

Evaluate

Area = 54

Hence, the surface area is 54 ft²

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Answer: in the following order:
6

0

-2

0

6

Step-by-step explanation:

Just need to evaluate the function for each value of X
for x=1  y=2(1-3)^2-2= 6

for x=2  y=2(2-3)^2-2= 0

for x=3  y=2(3-3)^2-2= - 2

for x=4  y=2(4-3)^2-2= 0

for x=5  y=2(5-3)^2-2= 6