Determine whether the sequence converges or diverges. If it converges, give the limit.

60, -10, 5/3, -5/18


Diverges


Converges; 11100 (this is definitely the wrong answer.)


Converges; 72


Converges; 0

Answer:

B

Step-by-step explanation:

We are given:

[tex]y=4x[/tex]

[tex]2x^2-y=0[/tex]

We are going to put 4x in place of the second y since the first y equaled it:

[tex]2x^2-4x=0[/tex]

So we can factored this equation:

[tex]2x(x-2)=0[/tex]

This implies 2x=0 or x-2=0.

2x=0

Divide both sides by 2:

x=0

x-2=0

Add 2 on both sides:

x=2

If x=0 and y=4x, then y=4(0)=0 so we have (0,0) is an intersection.

If x=2 and y=4x, then y=4(2)=8 so we have (2,8) is an intersection.

Answer:

the answer to the problem given is b

There are 216 different meals available when you select an appetizer, an entrée, and a dessert from the restaurant's menu.

Given that there are 6 choices for the appetizer, 12 choices for the entrée, and 3 choices for the dessert.

Total number of choices:

6 (choices for appetizer) × 12 (choices for entrée) × 3 (choices for dessert) = 216 different meals

Therefore, there are 216 different meals available when you select an appetizer, an entrée, and a dessert from the restaurant's menu.

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There are 216 possible meals. This answer is obtained by applying the counting principle in mathematics, which multiplies together the choices for each part of the meal (appetizer, entrée, dessert).

This problem regards the counting principle in mathematics, which is a way of finding the total number of possible outcomes for a series of events. In this case, the events are choosing an appetizer, entrée, and dessert. The counting principle tells us that we can find the total number of possible meals by multiplying together the number of choices for each part of the meal.

Thus, we can solve this problem as follows:

By the counting principle, we multiply these together to get the total number of possible meals: 6 * 12 * 3 = 216 meals.

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Answer:

(x - 2)²/2² + (y + 1)²/3² = 1 ⇒ The bold values and signs are the answers

Step-by-step explanation:

* Lets revise the equation of the ellipse  

- The standard form of the equation of an ellipse with center (h , k)  

 and major axis parallel to x-axis is (x - h)²/a² + (y - k)²/b² = 1  

- The coordinates of the vertices are (h ± a , k)

- To change the form of the equation of the ellipse to standard form we

 will using the completing square

∵ The equation of the ellipse is 9x² + 4y² - 36x + 8y + 4 = 0

- Lets collect x in bracket and y in bracket

∴ (9x² - 36x) + (4y² + 8y) + 4 = 0

- We will take a common factor 9 from the bracket of x and 4 from the

 bracket of y

∴ 9(x² - 4x) + 4(y² + 2y) + 4 = 0

- Lets make 9(x² - 4x) a completing square

∵ √x² = x ⇒ the 1st term in the bracket

∵ 4x ÷ 2 = 2x ⇒ the product of the 1st and 2nd terms

∵ 2x ÷ x = 2 ⇒ the 2nd term in the bracket

∴ The bracket is (x - 2)²

∵ (x - 2)² = x² - 4x + 4 ⇒ we will add 4 in the bracket and subtract 4

  out the bracket

∴ 9[(x² - 4x + 4) - 4] = 9[(x - 2)² - 4]

- Lets make 4(y² + 2y) a completing square

∵ √y² = y ⇒ the 1st term in the bracket

∵ 2y ÷ 2 = y ⇒ the product of the 1st and 2nd terms

∵ y ÷ y = 1 ⇒ the 2nd term in the bracket

∴ The bracket is (y + 1)²

∵ (y + 1)² = y² - 2y + 1 ⇒ we will add 1 in the bracket and subtract 1

  out the bracket

∴ 4[(y² + 2y + 1) - 1] = 4[(y + 1)² - 1]

- Lets write the equation with the completing square

∴ 9[(x - 2)² - 4] + 4[(y + 1)² - 1] + 4 = 0 ⇒ simplify

∴ 9(x -2)² - 36 + 4(y + 1)² - 4 + 4 = 0 ⇒ add the numerical terms

∴ 9(x - 2)² + 4(y + 1)² - 36 = 0 ⇒ add 36 to both sides

∴ 9(x - 2)² + 4(y + 1)² = 36 ⇒ divide both sides by 36

∴ (x - 2)²/4 + (y + 1)²/9 = 1

∵ 4 = 2² and 9 = 3²

∴ (x - 2)²/2² + (y + 1)²/3² = 1

* The standard form of the equation of the ellipse is

  (x - 2)²/2² + (y + 1)²/3² = 1

Answer: (x - 2)²/2² + (y + 1)²/3² = 1

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

2/5 = 40%

40% of 8 Carrots = 3.2

3 Carrots on Platter

5 Carrots in Plastic Bag

Answer:

12 carrots

Step-by-step explanation:

To get the answer, you need to multiply and divide.

x ÷ 3 · 2 = 8

Now, we need to do the equation backwards to find x.

8 ÷ 2 · 3 = 4 · 3 = 12 carrots

Answer:

3

Step-by-step explanation:

The points they have in bold is probably a hint to the problem.

The points they have in bold are (1,2) on curve g which means g(1)=2

and (3,2) on curve f which means f(3)=2.

g(x)=f(kx)

We know g(1)=2 so if we replace the x's with 1, we get:

g(1)=f(k*1)

g(1)=f(k)

2=f(k).

Now we just need to solve f(k)=2 for k.

We know the point (3,2) is on f so f(3)=2.

If you compare:

f(k)=2

and

f(3)=2

then you should see that k=3.

Answer:

[tex]4x^{3}+8x^{2} +4x+3[/tex]

Step-by-step explanation:

Hello

To simplify the polynomial we must eliminate the parentheses

by definition

[tex]ax^{n}*bx^{m} =abx^{n+m}[/tex]

[tex](2x-1)(2x^{2} +5x+3)+(3x+6)\\(4x^{3} +10x^{2} +6x-2x^{2} -5x-3)+(3x+6)\\\\We\ add\ the\ similar\ terms\\\\(4x^{3}+8x^{2} +x-3)+(3x+6)\\\\4x^{3}+8x^{2} +4x+3[/tex]

I hope it helps

Have a great day

Answer:

Its A

Step-by-step explanation:

Just took it.

Answer:

Nelson burned the most calories per hour

Explanation:

To solve this question, we will get the amount calories burned by each in one hour and then compare the two values

To do this, we will divide the total amount of calories burned by the total time

1- For Sabra:

We are given that she burnt 845 calories in [tex]3\frac{1}{25}[/tex] (which is equivalent to 3.25) hours

Therefore:

Calories burnt in an hour = [tex]\frac{845}{3.25}=260[/tex] calories/hour

2- For Nelson:

We are given that he burnt 1435 calories in [tex]4\frac{7}{8}[/tex] (which is equivalent to 4.875) hours

Therefore:

Calories burnt in an hour = [tex]\frac{1435}{4.875}=294.36[/tex] calories/hour

3- Comparing the two values:

From the above calculations, we can deduce that Nelson burned the most calories per hour

Hope this helps :)

Answer:

Nelson burned more cal/hr than Sabra at a rate of 294.36 cal/hr.

Step-by-step explanation:

To find out how many calories per hour each person burned, divide the amount of calories they burned by the amount of hours they spent exercising.

Sabra: 845 cal / 3.25 hr = 260 cal/hr

Nelson: 1435 cal / 4.875 hr = 294.36 cal/hr

260 < 294.36, so Nelson burned more calories/hour than Sabra.

Answer:

[tex]5-10i[/tex]

Step-by-step explanation:

we know that

To subtract two complex number, subtract the real parts and subtract the imaginary parts

so

[tex](a+bi)-(c+di)=(a-c)+(b-d)i[/tex]

we have

[tex](7-4i)-(2+6i)[/tex]

so

[tex](7-4i)-(2+6i)=(7-2)+(-4-6)i=5-10i[/tex]

Answer:  ordinal

Step-by-step explanation:

There are 4 levels of measurements scales :-

1. Nominal scale : It is used when we categorize the data on the basis of the characteristic such as Religion, Gender , etc.

2. Ordinal scale : It is used when we can order attributes according to their ranks. For example : First > Second > Third and so on.

3. Interval scale : It provides the characteristic of the difference between any two categories. For example : Fahrenheit scale to measure temperature.

4. Ratio scale : It has all the qualities of nominal, ordinal, and interval measures and in addition a "true zero" point. For example : Age.

From the above definitions , A level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes are ordinal measures.

Answer:

  240

Step-by-step explanation:

The x^k term will be ...

  (6Ck)(x^k)(4^(6-k))

For k=4, this is ...

  (6C4)(x^4)(4^2) = 15·16·x^4 = 240x^4

The coefficient of x^4 is 240.

_____

nCk = n!/(k!(n-k)!)

The length of the shortest ladder that will reach from the ground over the fence to the wall of the building is:

                              16.65 ft.

Let L denote the total length of the ladder.

In right angled triangle i.e. ΔAGB we have:

[tex]L^2=h^2+(x+4)^2[/tex]

( Since by using Pythagorean Theorem)

Also, triangle ΔAGB and ΔCDB are similar.

Hence, the ratio of the corresponding sides are equal.

Hence, we have:

[tex]\dfrac{h}{8}=\dfrac{x+4}{x}[/tex]

i.e.

[tex]h=\dfrac{8(x+4)}{x}[/tex]

Hence, on putting the value of h in equation (1) we get:

[tex]L^2=(\dfrac{8(x+4)}{x})^2+(x+4)^2\\\\i.e.\\\\L^2=\dfrac{64(x+4)^2}{x^2}+(x+4)^2\\\\i.e.\\\\L^2=(x+4)^2[\dfrac{64}{x^2}+1]----------(2)[/tex]

Now, we need to minimize L.

Hence, we use the method of differentiation.

We differentiate with respect to x as follows:

[tex]2L\dfrac{dL}{dx}=2(x+4)[\dfrac{64}{x^2}+1]+(x+4)^2\times \dfrac{-128}{x^3}\\\\i.e.\\\\2L\dfrac{dL}{dx}=2(x+4)[\dfrac{64}{x^2}+1+(x+4)\times \dfrac{-64}{x^3}]\\\\\\i.e.\\\\\\2L\dfrac{dL}{dx}=2(x+4)[\dfrac{64}{x^2}+1-\dfrac{64}{x^2}-\dfrac{256}{x^3}]\\\\\\i.e.\\\\\\2L\dfrac{dL}{dx}=2(x+4)[1-\dfrac{256}{x^3}][/tex]

when the derivative is zero we have:

[tex]2(x+4)[1-\dfrac{256}{x^3}]=0\\\\i.e.\\\\x=-4\ and\ x=\sqrt[3]{256}[/tex]

But x can't be negative.

Hence, we have:

[tex]x=\sqrt[3]{256}[/tex]

Now, on putting this value of x in equation (2) and solving the equation we have:

[tex]L^2=277.14767[/tex]

Hence,

[tex]L=16.6477\ ft.[/tex]

which on rounding to two decimal places is:

[tex]L=16.65\ ft.[/tex]

Using the Pythagorean theorem, the length of the shortest ladder that will reach from the ground over the 8 ft fence to the wall of the building 4 ft away is approximately 8.94 ft.

This problem is an example of a right triangle problem in trigonometry. The fence and the ground form the two legs of a right triangle and the ladder forms the hypotenuse. The 8ft fence is perpendicular to the 4ft distance from the building, forming a 90-degree angle.

To find the length of the shortest ladder from the ground over the fence to the wall of the building, we need to use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the formula is h² = a² + b², where h is the length of the ladder (hypotenuse), 'a' is the height of the fence (8 ft), and 'b' is the distance from the fence to the building (4 ft).

Therefore, the length of the shortest ladder can be solved as follows:
h² = 8² + 4² = 64 + 16 = 80
By taking the square root of both sides, we find that h (the length of the ladder) is approximately 8.94 ft, rounded to two decimal places.

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Answer:

A = 196 pi m^2

Step-by-step explanation:

The area of a circle is given by

A = pi * r^2

The radius is 14

A = pi *14^2

A = 196 pi m^2

Answer:

196π m2

Step-by-step explanation:

The change in the X values is in multiples of 2.

The change in the h(x) values need to be: -0.3 x 2 = -0.6

Now find the h(x) values that have a difference of -0.6

A negative value is a decrease.

2 to 4 is an increase.

4 to 6 is an increase.

6 to 8 is an increase.

8 to 10 is an increase.

10 to 12 = 20-19.8 = 0.2

12 to 14 = 19.8 - 19.2 = 0.6

The two columns are 12 and 14

Answer:

Let μ1 and μ2 represent the mean number of days with symptoms of a diaper rash when diapers were changed every three hours and two hours, respectively.

Let μd be the mean of the differences in the  number of days with symptoms of a diaper rash.

The null hypothesis and alternative hypotheses are two mutually exclusive things about any population. The null hypothesis is that, which is to be actually tested but an alternative hypothesis gives an alternative to the null hypothesis.

Here the appropriate null and alternative hypotheses will be :

H0: μd=0  (null)

Ha: μd>0 (alternative)

This given study is a matched pair design study, so we are using  μd : the mean of the differences.

Also, here we are testing if the number of diaper rashes are more when they are changed every 3 hours than 2 hours. This is why we chose the above hypothesis H0: μd = 0 and Ha: μd > 0.

Answer:

Let μ1 and μ2 represent the mean number of days with symptoms of a diaper rash when diapers were changed every three hours and two hours, respectively.

Let μd be the mean of the differences in the number of days with symptoms of a diaper rash.

The null hypothesis and alternative hypotheses are two mutually exclusive things about any population. The null hypothesis is that, which is to be actually tested but an alternative hypothesis gives an alternative to the null hypothesis.

Here the appropriate null and alternative hypotheses will be :

H0: μd=0 (null)

Ha: μd>0 (alternative)

This given study is a matched pair design study, so we are using μd : the mean of the differences.

Also, here we are testing if the number of diaper rashes are more when they are changed every 3 hours than 2 hours. This is why we chose the above hypothesis H0: μd = 0 and Ha: μd > 0.

Answer:

  B.  x ≈ 13/8

Step-by-step explanation:

We assume that one iteration consists of determining the midpoint of the interval known to contain the root.

The graph shows the functions intersect between x=1 and x=2, hence our first guess is x = 3/2.

Evaluation of the difference between the left side expression and the right side expression for x = 3/2 shows that difference to be negative, so we can narrow the interval to (3/2, 2). Our 2nd guess is the midpoint of this interval, so is x = 7/4.

Evaluation of the difference between the left side expression and the right side expression for x = 3/4 shows that difference to be positive, so we can narrow the interval to (3/2, 7/4). Our 3rd guess is the midpoint of this interval, so is x = 13/8.

_____

The sign of the difference at this value of x is still negative, so the next guess would be 27/16. It is a little hard to tell what the question means by "3 iterations." Evaluating the function for x=13/8 will be the third evaluation, so the determination that x=27/16 will be the next guess might be considered to be the result of the 3rd iteration.

Answer:

B. x=13/8

Step-by-step explanation:

#platofam

Answer:

95%

Step-by-step explanation:

For a given sample data, the width of the confidence interval would vary directly with the confidence level i.e. more the confidence level,  wider will be the confidence interval.

This is because the critical value associated with the confidence level(e.g z value) becomes larger as the confidence level is increased which results in an increased interval.

The confidence interval for a population proportion is given by the formula:

[tex]p \pm z\sqrt{\frac{pq}{n} }[/tex]

So, for a fixed value of p,q and n, the larger the value of z the wider will be the confidence interval.

Hence 95% confidence interval will be wider than 80% confidence interval.

The 95% confidence interval is wider than the 80% confidence interval because it includes a larger area under the curve of a normal distribution, offering a higher level of confidence the true population parameter falls within this range.

In statistical analysis, especially for polls like the one mentioned about favorite pies, the confidence interval plays a significant role in interpreting the reliability of the results. The 95% confidence interval is wider than the 80% confidence interval. This is because a higher confidence level, in this case 95%, means we are more sure that the actual population parameter lies within the interval, but in order to gain this certainty, the interval necessarily needs to be wider.

This can also be understood in the context of a normal distribution. For a 95% confidence interval, we are including a larger area under the curve of the distribution, thus the interval has to be wider than the one for the 80% confidence interval, which covers a smaller area.

It's important to note, however, that a wider confidence interval doesn't necessarily imply better predictability. It simply means there's a higher level of confidence that the true population parameter falls within the specified range.

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Answer:

15 degrees

Step-by-step explanation:

Draw a horizontal segment approximately 4 inches long. Label the right endpoint A and the left endpoint C. Label the length of AC 4.2 meters. That is the horizontal distance between the eye and the blackboard.

At the right endpoint, A, draw a vertical segment going up, approximately 1 inch tall. Label the upper point E, for eye. Label segment EA 1 meter since the eye is 1 meter above ground.

At the left endpoint of the horizontal segment, point C, draw a vertical segment going up approximately 2 inches. Label the upper point B for blackboard. Connect points E and B. Draw one more segment. From point E, draw a horizontal segment to the left until it intersects the vertical segment BC. Label the point of intersection D.

The angle of elevation you want is angle BED.

The length of segment BC is 2.1 meters. The length of segment CD is 1 meter. That means that the length of segment BD is 1.1 meters.

To find the measure of angle BED, we can use the opposite leg and the adjacent leg and the inverse tangent function.

BD = 1.1 m

DE = 4.2 m

tan <BED = opp/adj

tan <BED = 1.1/4.2

m<BED = tan^-1 (1.1/4.2)

m<BED = 15

Answer: 15 degrees

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The angle of elevation is 15°.

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

Given that Tony's seat in the classroom, his eyes are 1.0 m above ground. On the wall 4.2 m away, he can see the top of a blackboard that is 2.1 m above ground. Therefore, The angle of elevation,

tan(x) = (2.1 - 1.0)/4.2

x = tan⁻¹ (1.1/4.2)

x = 14.68° ≈ 15°

Hence, the angle of elevation is 15°.

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Let [tex]x[/tex] be the number of liters of the 10% solution she needs to use. She'd end up with a 6% solution with a volume of [tex]9+x[/tex] liters. The starting solution contains 0.04*9 = 0.36 liter of salt. Each liter of the 10% solution contributes 0.1 liter of salt, so that

[tex]0.36+0.1x=0.06(9+x)[/tex]

Solve for [tex]x[/tex]:

[tex]0.36+0.1x=0.54+0.06x[/tex]

[tex]0.04x=0.18[/tex]

[tex]x=4.5[/tex]

so Mayra needs to add 4.5 liters of the 10% solution.

The dollars worth of zinc which is contained in hair cut in the United States every year is:

                         $ 2,220,000

The total kilograms of hair that are  cut in the United States are: 25,000,000 kg

Also, the amount of zinc present in 1kg of hair is: 0.0002 kg

Hence, the amount of zinc present in 25,000,000 kg of hair is:

25,000,000×0.0002=5,000 kg

Also, cost of 1 kg of zinc= $ 444

Hence, cost of 5,000 kg of zinc will be: 5,000×444

Hence, cost of 5,000 kg of zinc=$  2,220,000

Answer:

20,000

Step-by-step explanation:

25,000,000 * 0.0002 =5,000

5,000 * 4 = 20,000

Answer:

  f(x) appears to be match the trig function sin(x)

Step-by-step explanation:

The function is an odd function that is periodic with a period of 2π. It is symmetrical about either of ±π/2. It matches sin(x) in every detail shown.

Answer:

  L = 720 cm² ; S = 1239.6 cm²

Step-by-step explanation:

The area of a hexagon is given by the formula ...

  A = (3/2)√3·s²

where s is the side length. Then the area of the two hexagonal bases will be ...

  base area = 3√3·(10 cm)² ≈ 519.6 cm²

__

The lateral area is the product of the perimeter of the base and the height of the prism:

  L = 6×(10 cm)×(12 cm)

  L = 720 cm²

The totals surface area is the sum of lateral area and base area:

  S = L + base area = (720 +519.6) cm²

  S = 1239.6 cm²

Answer:

L = 720 cm2 ; S = 1239.6 cm2

Step-by-step explanation:

Got lucky ('<')

Answer:

-7 is real and complex

Step-by-step explanation:

Every number is complex.

Complex numbers are in the form of a+bi where a and b are real numbers.

Pure imaginary are complex numbers with a being 0.

Real numbers are complex number with b being 0.

-7 is a real number and a complex number.

(It doesn't have an imaginary part)

-7 is a real and complex number.

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Answer:

B.  2cos3θsinθ.

Step-by-step explanation:

Use the identity

sin x - sin y   = 2 [cos(x + y)/2]sin [x - y)/2].

So we have:

sin4θ - sin2θ = 2 cos (4θ+2θ)/2 sin (4θ-2θ)/2

= 2cos3θsinθ.

Answer:

  D.  -1.8

Step-by-step explanation:

A graphing calculator can show you this easily, as can any calculator or spreadsheet that helps you evaluate the functions at different values of x.

The graphs cross at approximately x = -1.8.

Answer:

Step-by-step explanation:

d

Answer:

5/7

Step-by-step explanation:

We need the Pythagorean Theorem here.

If you have a right triangle, you can use the equation a^2+b^2=c^2 where a and b are legs and c is the hypotenuse.

Plug in your information.

(3/7)^2+(4/7)^2=c^2

Simplify what you can.

9/49+16/49=c^2

25/49=c^2

Square root both sides.

5/7=c

Answer:

5/7.

Step-by-step explanation:

Let the hypotenuse = h , then:

h^2 = (3/7)^2 +(4/7)^2    ( By the Pythagoras Theorem).

h^2 = 9/49 + 16/49

h^2 = 25/49

h =  5/7.

Answer:

  D.)  f(x) = 197(1.03)^(7x); grows at a rate of approximately 3% daily

Step-by-step explanation:

The growth equation can be written in terms of a rate compounded 7 times per week:

  f(x) = 197×1.25^x = 197×(1.25^(1/7))^(7x)

  f(x) ≈ 197×1.0324^(7x) . . . . x represents weeks, a daily growth factor is shown

The daily growth rate as a percentage is the difference between the daily growth factor and 1, expressed as a percentage:

  (1.0324 -1) × 100% = 3.24%

The best match is choice D:

  f(x) ≈ 197(1.03^(7x)); grows approximately 3% daily

The correct answer to this question is D

Answer:

a = sqrt( 3x+1)

Step-by-step explanation:

f(x) = sqrt(x-1)

g(x) = 3x+2

(f°g)(x) means replace g(x) in f(x) every place you see an x

(f°g)(x) = sqrt( g(x) -1)

          = sqrt( 3x+2 -1)

     Simplifying

          =sqrt( 3x+1)

Answer:

  8.3 cm

Step-by-step explanation:

The product of lengths to the near and far point of intersection with the circle is the same in all cases:

  (7 cm)(7 cm) = (y)(11 cm +y) = (4 cm)(4 cm +x)

Since we're only interested in x, we can divide by 4 and subtract 4:

  49 cm² = (4 cm)(4 cm +x)

  (49/4) cm = 4 cm +x . . . . . . divide by 4 cm

  8.25 cm = x . . . . . . . . . . . . . subtract 4 cm

To the nearest tenth, x = 8.3 cm.

_____

For a tangent segment, the two points of intersection with the circle are the same point, so the product of lengths is the square of the length.

___

The angles depend on the size of the circle, which is not given.

Let the width = X, then the length would be 5x ( 5 times as long as the width).

The perimeter is adding the 4 sides.

x + x + 5x + 5x = 70

Combine the like terms:

12x = 70

Divide both sides by 12:

x = 70/12

x = 5.83

The width = 5.83 cm.

The length = 5 x 5.83 = 29.15

Now round each length to the nearest tenth:

5.8 and 29.2 cm.

The answer is d.