help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Help Meeeeeeeeeeeeee Pleaseeeeeeeeeee Rn Rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help Meeeeeeeeeeeeee

Answers

Answer 1

The area of a rectangle is the product of its length and breadth. The maximum area enclosed by the fence is 36800 square meter  and the dimensions of the enclosed area are 115 meter and 320 meter. The width is given as 115 meter.

What is a rectangle?

A rectangle is a type of parallelogram that has equal diagonals.

All the interior angles of a rectangle are equal to the right angle.

The diagonals of a rectangle do not bisect each other.

The dimensions of the given rectangle is (650 - 2x) and x.

Then, the area of the given rectangle is A(x)  = x(650 - 2x)

In order to find the maximum area enclosed take the derivative of A(x) and equate it to zero as follows,

(660 - 2x) - 2x = 0

=> 4x = 660

=> x = 660 / 4

=> x = 115

Now, the maximum area is the value of A(x) at x = 115 as below,

= 115 × (650 - 2×115)

= 115 × 320

= 36800

The dimensions for the maximum area are 115 and (650 - 2 × 115) = 320.

Hence, the largest area enclosed is 36800 square meter and the dimensions of the enclosed area are 115 meter and 320 meter. The width labeled in the figure is given as 115 meter.

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Related Questions

16. Describe, step-by-step how to find the slope of a line through two points.

Answers

Answer:

1. find the 2 points and determine their coordinates.

2. determine the difference in the rise or y-coordinates.

3. determine the difference in the run or x-coordinates.

4. place the rise over the run and divide to find slope

help meeeeeeeeeeeeeee pleaseeeeeee

Answers

Answer: 2.5, 5.4

Step-by-step explanation:

[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]

can you help me on this?

Answers

Answer:

The answer is run because the line is going down.

Step-by-step explanation:

Select the correct answer.
Solve the system of equations.
y=x-5
y=x-5x+3
O A. (4,-3) and (2,-1)
О в.
(4,-1) and (2,-3)
O C.
(-4,-9) and (-2,-7)
O D.
(4,-9) and (2,-7)

Answers

The value of x is -2 and the value of y is -7. The correct option is C.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equations are y = x - 5 and y = 5x + 3. The value of x and y will be calculated by solving the equations,

y=x-5

y=5x+3

x -5 = 5x + 3

-4x = 8

x = -2

The value of y will be calculated as,

y = x - 5

y = -2 - 5

y = -7

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Hello! Having a little trouble on this question, thanks for your help!

Answers

The graph of the function:

[tex]g(x)=ln(4-x)[/tex]

Can be obtained by using the parent function:

[tex]f(x)=ln(x)[/tex]

Whose graph is shown below:

We must first turn x into -x by making a reflection over the y-axis. This way, the function becomes:

[tex]f(-x)=ln(-x)[/tex]

And the graph is:

Finally, we just add 4 to x to translate the graph 4 units to the right to get our desired function:

[tex]g(x)=f(4-x)=ln(4-x)[/tex]

The graph is shifted 4 units to the right as shown:

I need help to find x and could you explain it also please

Answers

X=75
A+B+C=180
So 60+45+75=180

4x+2y=2 and y=-3x+2 slove the system of equations

Answers

The solution of the given system of equations is x =1 and y = -1.

What is a system of equations?

In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

Given is a system of equations; 4x+2y=2 and y=-3x+2

Solving the equation by substitution, we get,

4x+2(-3x+2) = 2

4x-6x-4 = 2

-2x+4 = 2

-2x = -2

x = 1

Put x = 1 in any of the given equation,

y = -3*1+2

y = -3+2

y = -1

Hence, The solution of the given system of equations is x =1 and y = -1.

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Zachary is paying his dad back for the money he borrowed to pay for a car repair. The amount that he owes his dad is shown in the graph

Answers

Answer:

so you need to divide this and turn it into a coefficient for the answer

Step-by-step explanation:

 

Determine the probability of being dealt 4 Aces of cards, from a deck of 52 playing cards, with a replacement.

Answers

Before finding the probability of being dealt 4 Aces of cards, let's find the probability of being dealt an Ace card on each draw.

The probability of getting an specific card from a deck is given by the ratio between the amount of this specific card and the total amount of cards. We have 4 Aces in a deck, and 52 cards, therefore, the probability of getting an Ace is

[tex]\frac{4}{52}=\frac{1}{13}[/tex]

Since the cards are replaced, it is the same probability of getting an Ace on each draw.

Each draw is an independent event, the probability of them happening simultaneously is given by their product. The probability of being dealt 4 Aces of cards with a replacement is

[tex]\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}=\frac{1}{13^4}=\frac{1}{28561}=0.00003501277\ldots[/tex]

Can someone help? :)

Answers

The slope of the given line is 2

What is slope of a line?

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by

m = [tex]tan\theta[/tex]

If the line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]

slope = [tex]\frac{y_2-y_1}{x_2 - x_1}[/tex]

The given line passes through ( 0, 5) and  (-2, 1) .

Slope of the line  =

                               [tex]\frac{1-5}{-2-0}\\\\\frac{-4}{-2}\\\\2[/tex]

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6) How long will it take for an investment to double in value if it earns 4.75% compoundedcontinuously?A) 14.593 yearsB) 15.711 years C) 23.129 years D) 7.296 years

Answers

A quantity that is compounded continuously follows the next equation:

[tex]A=Pe^{rt}[/tex]

Where:

[tex]\begin{gathered} A=\text{ amount in time ''t''} \\ P=\text{ initial amount} \\ r=\text{ rate of interest in decimal form} \\ t=\text{ time} \end{gathered}[/tex]

Now, the interest rate in decimal notation is determined by dividing the percentage by 100:

[tex]r=\frac{4.75}{100}=0.0475[/tex]

Now, we are asked to determine the time required for the quantity to double. Therefore, we need to determine "t" when:

[tex]A=2P[/tex]

Substituting in the formula we get:

[tex]2P=Pe^{rt}[/tex]

Now, we can cancel out the "P":

[tex]2=e^{rt}[/tex]

Now, we solve for "t". First, we take the natural logarithm to both sides:

[tex]ln2=lne^{rt}[/tex]

Now, we use the following property of logarithms:

[tex]lnx{}^y=ylnx[/tex]

Applying the property we get:

[tex]ln2=rtlne[/tex]

We have that:

[tex]lne=1[/tex]

Therefore:

[tex]ln2=rt[/tex]

Now, we divide both sides by "r":

[tex]\frac{ln2}{r}=t[/tex]

Now, we substitute the value of "r":

[tex]\frac{ln2}{0.0475}=t[/tex]

Solving the operations:

[tex]14.593=t[/tex]

Therefore, the right option is A.

To save money for her son's college tuition, Mary invests $98 every month in an annuity that pays 6.1% interest, compounded monthly. Payments will be made at the end of each month. Find the total value of the annuity in 21 years.

Answers

Given

Monthly deposit = $98

Rate = 6.1%

Number of years = 21

Find

Total value of the annuity in 21 years.

Explanation

Total value of annuity is given by

[tex]FV=A[\frac{(1+\frac{r}{m})^{mt}-1}{\frac{r}{m}}][/tex]

where FV is a future value

so ,

[tex]\begin{gathered} FV=98[\frac{(1+\frac{0.061}{12})^{12\times21}-1}{\frac{0.061}{12}}] \\ \\ \end{gathered}[/tex]

now solve this to obtain the future value .

[tex]\begin{gathered} FV=98\times509.227229162 \\ FV=49904.26 \end{gathered}[/tex]

Final Answer

Therefore , the future value is $49904.27

Write the system of linear equations represented by the augmented matrix. (Use variables x, y, and z, if applicable.)1 - 1 21-30 1 -1 50 0 1-5Use back-substitution to solve the system.(x, y, z) =

Answers

The augmented matrix represents the following system of linear equations:

[tex]\begin{gathered} x-y+2z=-3 \\ y-z=5 \\ z=-5 \end{gathered}[/tex]

Use back substitution. It means, use the value of z given in the last equation, to find y in the second equation, and then, use these values to find x in the first equation:

[tex]\begin{gathered} y-z=5 \\ y-(-5)=5 \\ y+5=5 \\ y=5-5 \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} x-y+2z=-3 \\ x-0+2(-5)=-3 \\ x-10=-3 \\ x=-3+10 \\ x=7 \end{gathered}[/tex]

The solution of the system is (x, y, z)=(7, 0, -5)

Subject :- Optional Mathematics
Topic :- Fraction

Answers

The value of x is 0.94 or 3.34 with the functions given.

The function is given as:

f = (x, 4 x - 17)

g = (x, (2 x + 8) / 5)

We get that:

g⁻¹ (x) = (2 x + 8) / 5

f o f (x)

= f (f (x))

= (4x [ 4x - 17] - 17)

= 16 x² - 68 x - 17

ATQ:

16 x² - 68 x - 17 = (2 x + 8) / 5

80 x² - 340 x - 85 = 2 x + 8

80 x² - 342 x - 93 = 0

Solving the equation:

D = b² - 4 ac

D = (-342)² - 4 (80) (-93)

D = 36681

x = (342 ± √36681) / 2(80)

x = (342 ± 191.52) / 160

x = 0.94 or x = 3.34

Therefore, the value of x is 0.94 or 3.34 with the functions given.

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Which figures can have two sides of the same length, but are not parallelograms?quadrilateralrectanglesquareisosceles trapezoid

Answers

A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.

We have special types of quadrilaterals which are,

1) Rectangle

2) Square

3) Rhombus

4) Parallelogram

5) Trapezium

6) Kite

Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms.

An isosceles trapezoid has left and right sides of equal length that join to the base at equal angles.

Below is the diagram of an Isosceles trapezoid

One card is selected at random from a deck of cards. Determine the probability of selecting a card that is less than 5 or a Club. Note that the ace is considered a low card.The probability that the card selected is less than 5 or a club is.(Type an integer or a simplified fraction.)

Answers

The total number of cards in a deck of cards is: 52

The total number of club cards is: 13

The total number of cards that less than 5 is: 8.

The probability of selecting a club card is,

[tex]\begin{gathered} P(Club)=\frac{Total\text{ number of club cards}}{\text{Total number of cards}} \\ =\frac{13}{52} \\ =\frac{1}{4} \end{gathered}[/tex]

The probability of selecting a card that is less than five is,

[tex]\begin{gathered} P(card<5)=\frac{8}{52} \\ =\frac{2}{13} \end{gathered}[/tex]

The total number of club card that is less than 5 is 3.

The probability of selecting a club card and a card that is less than 5 is,

[tex]P\text{ (club and less than 5)}=\frac{3}{52}[/tex]

The probability of selecting a card that is a club or less than 5 is,

[tex]\begin{gathered} P\text{ (Club or less than5)}=P(Club)+P\text{(card less than 5)-P(Club and less than 5)} \\ =\frac{1}{4}+\frac{2}{13}-\frac{3}{52} \\ =\frac{21}{52}-\frac{3}{52} \\ =\frac{9}{26} \end{gathered}[/tex]

Thus, the probability of selecting a club card or card that is less than 5 is 9/26.

Which ordered pair is a solution for this system of linear inequalities?
2x + 3y < 12
3x - 2y ≥ 18

A. (5,0)
B. (3,-1)
C. (-1,3)
D. (4,-9)

Answers

The ordered pair that is a solution for the inequality 2x + 3y < 12 and

3x - 2y ≥ 18 is

D. (4,-9)

How to find the solution

The solution is sought by substituting to each of the pair to the equation and comparing the answers

for  D. (4,-9)

2 * 4 + 3 * -9 < 12

-19 < 12   correct

3x - 2y ≥ 18

3 * 4 - 2 * -9 ≥ 18

30  ≥ 18 correct

This proves that option D is the correct option

trying for A. (5,0)

2 * 5 + 3 * 5 < 12

25 < 12   incorrect

3x - 2y ≥ 18

3 * 5 - 2 * 0 ≥ 18

15  ≥ 18 incorrect

trying for B. (3,-1)

2 * 3 + 3 * -1 < 12

3 < 12   correct

3x - 2y ≥ 18

3 * 3 - 2 * -1 ≥ 18

11  ≥ 18 incorrect

When any part is incorrect the pair is not a solution

trying for C. (-1,3)

2 * -1 + 3 * 3 < 12

7 < 12   correct

3x - 2y ≥ 18

3 * -1 - 2 * 3 ≥ 18

-9  ≥ 18 incorrect

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Lu's deposit includes two checks: $123.45 and $432.90; cash: 3 one-dollar bills, 9 five-dollar bills, 5 ten-dollar bills, 15 quarters, 10 dimes, 18 nickels, and 32 pennies. Find the total deposit.

$556.35

$648.35

$660.32

$721.31

Answers

Answer:

The total deposit is $721.31.

Step-by-step explanation:

i need helppp!!!!!!!!

Answers

Answer:

5

Step-by-step explanation:

y=x+5 cuz it works out for everything

To rent a moving truck for the day, it costs $75 plus $1.50 for each mile, m, driven. Which expression represents the cost, in dollars, to rent the moving truck?

Answers

The expression that represents the total cost of renting a truck and traveling 'n' miles will be 1.50n + 75 = C.

What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

So, the expression to represent the total cost will be:

The truck costs $75.And an extra $1.50 for every mile.

The expression that gives the total cost.

Let, the number of miles are 'n' and the total cost be 'C'.

Now,

1.50n + 75 = C


Therefore, the expression that represents the total cost of renting a truck and traveling 'n' miles will be 1.50n + 75 = C.

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Bill flip a coin and roll a dice independent or dependent

Answers

Dependent Events where what happens depends on what happened before, such as taking cards from a deck makes less cards each time.

Independent Events which we learn about here.

Bill flipping a coin and rolling a dice are independent events. Flipping a coin doesn't depend on rolling a die.

Answer

Independent

Can you please help me out

Answers

ANSWER:

A. 2.2%

STEP-BY-STEP EXPLANATION:

We can calculate the probability using the quotient of the area of the small circle and the area of the entire rectangular sector, like this:

[tex]\begin{gathered} p=\frac{A_c}{A_r} \\ A_c=\pi\cdot r^2 \\ A_r=l\cdot w \end{gathered}[/tex]

In the circle the radius is 6 inches and in the rectangle the length is 84 inches and the width is 60 inches.

Therefore we replace and we have:

[tex]\begin{gathered} A_c=3.14\cdot6^2=113.04 \\ A_r=84\cdot60=5040 \\ p=\frac{113.04}{5040}=0.022=2.2\text{\%} \end{gathered}[/tex]

The first puzzle includes a treasure map. The treasure map is an xy coordinate grid with the origin markingthe center of the room as shown below. Two lines intersect to show the location of the next clue. The linesmust be added to the treasure map.The first line is represented by the equation y = 3x - 16.The graph of the second line passes through the points (1,7) and (4,1).North6s411WestEast112South4. What is the equation of the second line? Show how you found the equation.(Replace this text with your equation)(Replace this text with your work).

Answers

Given

(1,7) and (4,1)

[tex]\begin{gathered} M=\frac{y_2-y_1}{x_2-x_1} \\ M=\text{ }\frac{1-7}{4-1} \\ M=-\frac{6}{3} \\ M=-2 \\ \\ y-y_1=m\mleft(x-x_1\mright) \\ y-7=-2(x-1) \\ y-7=-2x+2 \\ y=-2x+2+7 \\ y=-2x+9 \end{gathered}[/tex]

y=-2x+9

Suppose cone a is similar to cone b and the scale factor between the solids is 3:2, respectively. If the height of cone a is 15 inches, determine the height of cone b.

Answers

The height of cone is 10 inches.

What is cone?
A cone is indeed a three-dimensional geometric shape with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex. A cone is made up of a collection of line segments, half-lines, as well as lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex. The base may only be a circle, any closed one-dimensional figure, any one-dimensional quadratic shape in the plane, or any combination of the above and furthermore all the enclosed points, depending on the author.

What is the formula for finding the height of a cone?

The cone height formula calculates the height of the cone. The height of the cone using cone height formulas are, h = 3V/πr 2 and h = √l2 - r2, where V = Volume of the cone, r = Radius of the cone, and l = Slant height of the cone.

We know that

If two figures are similar, then the ratio of its corresponding sides is proportional

Let x----> the height of cone B

using proportionality

3/2 = 15/x

x = 2 * 15/3

x = 10 inches

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In Mrs. Stone's class, 18 out of 30 student turned in their homework on time. What percent of the class turned their homework in on time?​

Answers

24 percent of kids turned it in

Can anyone help with this? Thanks

Answers

The surface area of the prism is 1440 mm²

Given,

Triangular prism

Height of the prism = 32 mm

Base  of the prism = 24 mm

Length of the prism = 7 mm

We have to find the surface area of the prism;

Surface area, SA = bh + (b₁ + b₂ + b₃) l

Here,

Base, b = 24 mm

Height, h = 32 mm

Length, l = 7 mm

b₁ = 24 mm

b₂ = 32 mm

b₃ = [tex]\sqrt{b_{1} ^{2} + b_{2} ^{2} }[/tex] = [tex]\sqrt{24^{2}+ 32^{2} }[/tex] = [tex]\sqrt{576 + 1024}[/tex] = √1600 = 40 mm

Then,

Surface Area = bh + (b₁ + b₂ + b₃) l

SA = 24 x 32 + (24 + 32 + 40) 7

SA = 768 + 96 x 7

SA = 768 + 672

SA = 1440 mm²

That is,

The surface area of the prism is 1440 mm²

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At a fundraiser hosted by a local restaurant, customers can pay as much or as little as they like for a meal, as long as they pay at least $1. any profits are donated to a local charity. one evening, the mean (average) price paid per customer was $55. one more customer walked in and paid $70 for a meal, bringing the average up to $56. what is the highest possible price that a customer could have paid for their meal that evening? do you think the amounts in your solution are reasonable.


in your solution are reasonable for this situation?

Answers

The highest possible price that a customer could have paid for their meal that evening exists $ 757. Since this is a fundraiser, $ 1 exists probably a very small amount and $757 would be considered a very generous donation for a meal.

How to estimate the highest possible price that a customer could have paid for their meal that evening?

When determining the mean (average) of a group of values, we add up the values in the group and divide that total by the number of values in the group. As a result, the average of the set's values divided by the total number of values is equal to the set's values' sum.

Let n represent how many people were in the store that evening. Thus, a total of 56n was paid that evening by all customers. The bill for the last customer's meal was $70.00. There were (n-1) customers who had already paid a total of (56n-70) dollars before this one arrived. The average cost per customer at that time was $55 dollars.

From the above information, we get

[tex]$\frac{56 n-70}{n-1} &=55 \\[/tex]

simplifying the above equation, we get

56n - 70 = 55(n - 1)

56n - 70 = 55n - 55

n = 15

Since n = 15, it follows that there were 15 customers that evening, and the total amount paid by all customers stood therefore 56 n = 56(15) = 840 dollars.

To estimate the highest possible price that a customer could have paid for their meal that evening, we will assume that 13 of the customers paid the lowest possible price of $ 1. Then the remaining customer would have paid 840 - 13 × 1 - 70 = 757 dollars.

Therefore, the highest possible price that a customer could have paid for their meal that evening exists $ 757.

Since this is a fundraiser, $ 1 exists probably a very small amount and $757 would be considered a very generous donation for a meal.

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Which of the following equations is equivalent to 2/3x- 1/2Y=6
O4x - 3y = 36
2x - y = 36
O 2x - y = 6

Answers

Answer:

4x - 3y = 36

Step-by-step explanation:

⅔x-½y=6

just multiply both sides by the LCM which is 6

6×⅔x-6×½y=6×6

4x-3y=36

A ship travels from Akron (A) on a bearing of 030° to Bellvilie (B),90km away. It then travels to Comptin (C) which is 310 km due east of Akron (A).Draw a diagram showing the movement of the ship indicate:a.)Northb.)the distances travelledc.)the know angles

Answers

Given: The bearing and distance of a ship from Akron(A) through Bellville(B) to Compton(C)

To Determine: The distance travelled and the angles

Solution

The diagram of the journey can be represented as shown below

Let us solve for BC using cosine rule

[tex]\begin{gathered} BC^2=AB^2+AC^2-2(AB)(AC)cosA \\ BC^2=90^2+310^2-2(90)(310)(cos60^0) \\ BC^2=8100+96100-27900 \\ BC^2=76300 \\ BC=\sqrt{76300} \\ BC=276.22km \\ BC\approx276km \end{gathered}[/tex]

The total distance travelled is

[tex]\begin{gathered} Total-distance=AB+BC+AC \\ =90km+276km+310km \\ =676km \end{gathered}[/tex]

Using sine rule, we can determine the measure of angle C

[tex]\begin{gathered} \frac{AB}{sinC}=\frac{BC}{sinA}=\frac{AC}{sinB} \\ \frac{90}{sinC}=\frac{276}{sin60^0}=\frac{310}{sinB} \\ \frac{90}{sinC}=\frac{276}{sin60^0} \\ sinC=\frac{90(sin60^0)}{276} \\ sinC=\frac{155.88}{276} \\ sinC=0.5648 \\ C=sin^{-1}(0.5648) \\ C=34.39^0 \end{gathered}[/tex]

Also know that the sum of angles in a triangle is 180 degree. Therefore

[tex]\begin{gathered} A+B+C=180^0 \\ 60^0+B+34.39^0=180^0 \\ B+94.39^0=180^0 \\ B=180^0-94.39^0 \\ B=85.61^0 \\ B\approx85.6^0 \end{gathered}[/tex]

The bearing of Compton from Bellville(B) is

[tex]Bearing(C-from-B)=90^0+34.39^0=124.39^0\approx124.4^0[/tex]

The bearring of Akron(A) from Compton(C) is

[tex]Bearing(A-from-C)=270^0+34.39^0=304.39^0\approx304.4^0[/tex]

In summary

The total distance travelled is 676km

The bearing of Compton from Bellville is 124.4 degrees, and the bearing of Akron from Compton is 304.4 degrees

A full-grown monarch caterpillar weights 0.75 grams, has a length of 5 centimeters, and is about 2.5 centimeters around. How can the surface area of the caterpillar be estimated?
A ___ can be used to model the surface area of the caterpillar. Based on the model, the caterpillar has an approximate surface area of ___ square centimeters.

The choices for the first blank are:
*rectangular prism
*triangular prism
*sphere
*cylinder

The choices for the second blank are:
*13.5
*6.75
*49.1
*117.8

Answers

A Cylinder can be used to model the surface area of the caterpillar with Surface area of 117.3 cm²

A full-grown monarch caterpillar is of cylinder shape . so , the option 4th is correct for first blank.

Surface area of cylinder is 2πrh + 2πr²

where r is radius of circle and h is height of cylinder

here , length of caterpillar is 5cm and radius is 2.5cm

Surface area = 2πrh + 2πr²

= 2π(5)(2.5) + 2π(2.5)²

= 2π(12.5) + 2π(6.25)

putting π = 3.14

=78.5+39.25

=117.8 cm²

Rewriting the sentence

A cylinder can be used to model the surface area of the caterpillar. Based on the model, the caterpillar has an approximate surface area of 117.8 square centimeters.

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Answer: A Cylinder can be used to model the surface area of the caterpillar with Surface area of 117.8 square centimeters

(if your on PLATO) if not then 117.8

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