The volume of the packing material that luke will need is: 11 cubic feet
How to find the volume of the box?The formula for the volume of a box is expressed as:
V = length * width * height
Now, we are given:
Area of base = 15 square feet
height = 3 feet
Thus:
Volume of box = 15 * 3 = 45 cubic feet
If he is going to ship a toy that is 34 cubic feet, then it means that:
Volume of packing material Luke needs = 45 - 34 = 11 cubic feet
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The equations for two savings accounts for the same Initial amount of $1125 and an interest rate of 1.875% accrued differently are shown in the table. Savings Account A A = 21.09t + 1125 Savings Account B JAN 1 A = 1125 1+ (1. 0.01875 2 2t Complete the statement. After 9 years, savings account [DROP DOWN 1] will have more money because it is modeled by [DROP DOWN 2] where the investment [DROP DOWN 3].
Savings Account B will have more money after 9 years because it is modeled by the exponential equation, and the investment grows exponentially with time
We have,
To determine which savings account has more money after 9 years, we can evaluate the amount of money in each account using the given equations.
For Savings Account A, the equation is:
A = 21.09t + 1125
Substituting t = 9 (since we're interested in the amount after 9 years), we get:
A = 21.09(9) + 1125 = 1300.81
So, after 9 years, Savings Account A will have $1300.81.
For Savings Account B, the equation is:
A = 1125(1 + 0.01875/2)^(2t)
Substituting t = 9, we get:
A = 1125(1 + 0.01875/2)^(2(9)) = 1318.98
So, after 9 years, Savings Account B will have $1318.98.
Therefore,
Savings Account B will have more money after 9 years because it is modeled by the exponential equation, and the investment grows exponentially with time
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Help me please! if a conditional statement is written in the form “If p then q”, how is the converse of the conditional statement is written?
A) If not q then p
B) If q then p
C) If not p then q
D) If not p then not q
The converse statement is of the conditional “If p then q” is the one in option B.
if q then p.
How can we identify the converse statement?For two given propositions p and q, a conditional statement is written as:
"if p, then q"
So, if the proposition p is true, also is the proposition q.
The converse statement just changes the order of the two propositions ( if the proposition q is true, also is the proposition p), then here start with q and end with p, so the converse statement is:
if q then p.
The correct option is B.
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2×2 pleaseeee hellppppppp
i am need of help so very badly
100 points for the answer
4
add 2 and 2 together and you get 4.
Answer:
4
Step-by-step explanation:
2x2 is the same as 2+2, so 2+2 is 4.
1. Define, compare and contrast common stock and preferred stock.
2. Define, compare and contrast dividends and dividends in arrears.
3. Define, compare and contrast bond premium and discount.
4. What are the 3 main fee structures of mutual funds?
5. What is NAV and how is it calculated?
Common Stock:
- Represents ownership in a company and a claim on a portion of the company's assets and earnings.- Has voting rights, allowing shareholders to participate in corporate decision-making.- Dividends are not guaranteed and can fluctuate.- In the event of liquidation, common stockholders are paid after preferred stockholders.Preferred Stock:
- Represents partial ownership in a company but typically does not carry voting rights.- Typically has a fixed dividend rate, which is paid before dividends to common stockholders.- In the event of liquidation, preferred stockholders have priority over common stockholders.- Can be converted to common stock or have a callable feature, allowing the company to redeem shares at a predetermined price.Comparison:
- Common stockholders have voting rights, while preferred stockholders generally do not.- Preferred stock usually has a fixed dividend rate, while common stock dividends can fluctuate.- Preferred stockholders have priority in receiving dividends and in the event of liquidation.2. Dividends vs Dividends in Arrears:Dividends:
- Payments made by a corporation to its shareholders, usually in the form of cash or additional shares.- Typically paid from a company's profits or retained earnings.- Can be regular (e.g., quarterly) or special (one-time) dividends.Dividends in Arrears:
- Unpaid dividends owed to preferred stockholders.- Occur when a company does not pay the full dividend amount it has committed to for preferred stockholders.- Must be paid before any dividends can be paid to common stockholders.Comparison:
- Dividends are regular or special payments to shareholders, while dividends in arrears are unpaid dividends owed to preferred stockholders.- Dividends in arrears must be paid before any dividends can be paid to common stockholders.3. Bond Premium vs Bond Discount:Bond Premium:
- Occurs when a bond's market price is higher than its face value.- Usually results from a decrease in market interest rates, making the bond's fixed interest payments more attractive to investors.- Bond premium is amortized over the life of the bond, reducing the bond's book value.Bond Discount:
- Occurs when a bond's market price is lower than its face value.- Usually results from an increase in market interest rates, making the bond's fixed interest payments less attractive to investors.- Bond discount is amortized over the life of the bond, increasing the bond's book value.Comparison:
- A bond premium represents a bond selling for more than its face value, while a bond discount represents a bond selling for less than its face value.- Bond premiums typically occur when market interest rates decrease, while bond discounts occur when market interest rates increase.4. 3 Main Fee Structures of Mutual Funds:1. Sales Loads: Fees paid when buying or selling shares of a mutual fund. They can be front-end loads (charged when buying shares) or back-end loads (charged when selling shares).
2. Expense Ratio: The annual fee that covers the fund's operating expenses, including management fees, administrative fees, and other costs. It is expressed as a percentage of the fund's average net assets.
3. 12b-1 Fees: Annual fees charged by some mutual funds to cover marketing and distribution expenses. These fees are included in the fund's expense ratio.
5. NAV (Net Asset Value):- NAV represents the per-share value of a mutual fund, calculated by dividing the fund's total net assets by the number of outstanding shares.- Total net assets are calculated by subtracting the fund's liabilities from its total assets.- NAV is typically calculated at the end of each trading day and is the price at which investors can buy or sell shares of the mutual fund.Need answer ASAP What is the circumference of the circle
Answer:
157.08 in.
Step-by-step explanation:
C=2πr=2·π·25≈157.07963
Answer:
A
Step-by-step explanation:
look at pic below.
Here are steps to find the circumference of a circle with a radius of 25 inches:
1. Recall the formula for the circumference of a circle:
C = 2πr
2. Substitute the value of the radius into the formula:
C = 2π(25)
3. Simplify the expression by multiplying 2π by 25:
C = 50π
4. Use the approximate value of π, which is 3.14, to get a numerical answer:
C ≈ 50(3.14)
5. Calculate the product:
C ≈ 157
Therefore, the circumference of a circle with a radius of 25 inches is approximately 157 inches.
Which of the following is not a money market mutual fund?(1 point)
Responses
a pension fund that tracks growth stocks
a fund with a minimum investment that tracks the value of cash
a fund that tracks the S&P 500
a fund that tracks commodities such as gold and silver
Answer:
Step-by-step explanation:
1. $4,076.92
2. Assets = Liabilities + Equity
3. They can be used to make online purchases.
4. by using an emergency fund for this unplanned expense
5. a fund with a minimum investment that tracks the value of cash (This question)
6. 1930s
7. Banks because they are highly regulated by the government, so the loan terms will not be predatory.
8. their vacation cabin
9. You should shop around for the best overall deal.
10. If you use a credit card, it is easy to run up huge debts.
11. They are tied directly to your bank account.
12. preventative care
13. $100,000 per person bodily injury, $300,000 per incident for bodily injury, $50,000 for property damage
14. how long the coverage lasts, how much the premium costs, and the cash value
15. 1-year renewable group term life
16. Identity thieves can intercept unencrypted data being sent to Wi-Fi hot spots.
17. Wells Fargo employees were opening unauthorized deposit and credit accounts for its customers.
18. 2 year in state community college degree
19. tuition assistance
20. -a sundae, -movie tickets
Explanation: All of these answers are correct!
Personal Finance Semester Exam
5/11/2023
7cos^2 -26 = -20sin -7
The only solution to the equation is cos(x) = 5/7.
We have,
cos²(x) + sin²(x) = 1:
Substituting.
7cos²(x) - 26 = 7(1 - sin²(x)) - 26
= 7 - 7sin²(x) - 26
= -19 - 7sin²(x)
Now,
-19 - 7sin²(x) = -20sin(x) - 7
We can simplify this equation by moving all the terms to one side:
7sin^2(x) - 20sin(x) - 12 = 0
We can solve this quadratic equation using the quadratic formula:
sin(x) = [20 ± √(20² - 4(7)(-12))] / (2(7))
sin(x) = [20 ± √(784)] / 14
sin(x) = (10 ± 28) / 14
sin(x) = 2/7 or sin(x) = -2.
However, we should check whether each solution is valid by substituting it back into the original equation and ensuring that both sides are equal.
So,
If sin(x) = 2/7,
7cos²(x) - 26 = -20 (2/7) - 7
7cos²(x) = -10/7
But since cos²(x) is always non-negative, there is no real solution to this equation.
If sin(x) = -2,
7cos²(x) - 26 = -20 (-2) - 7
7cos²(x) = 25
Taking the square root of both sides, we get:
cos(x) = ±5/7
The two solutions to the original equation are:
sin(x) = -2 and cos(x) = 5/7
or
sin(x) = -2 and cos(x) = -5/7
However, we should note that there is no real number whose sine is equal to -2, so there is no real solution to the equation.
Therefore, the only solution is:
cos(x) = 5/7
Thus,
The only solution is cos(x) = 5/7.
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pls complete a and b!
a. The error is that the two factors should be 5s and 3s-7s²+1
b. The student out to multiply the two factors if the product will be 15s²-35s³+5s
What is factorization?Factorization or factoring consists of writing a number or another mathematical object as a product of several factors.
For example, if we are given an expression , 2x +6. The expression consist of two terms and the common factor between them is 2 . Therefore we bring the 2 out . i.e 2( x+3). This means the two factors are 2 and x+3
Similarly , 15s²-35s³+5s can be factorized by bring out the common factors between the three terms
= 5s( 3s-7s²+1)
This means that the student omitted +1 and she ought to have cross checked by multiplying the two factors back if the product will be the polynomial.
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is this a rigid motion
The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.
The transformation for this problem has the rule defined as follows:
(x,y) -> (x + 2, -y).
The transformations are defined as follows:
x -> x + 2 is a translation right two units.y -> -y is a reflection over the x-axis.Neither transformation is a dilation, hence it is a rigid motion.
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12. You start the day left with 3 assignments due tomorrow. Your work load seems to double every period!
That means you would have how many assignments due tomorrow by 1st period? 4th period? 8th period?
Write an equation for this scenario & answer all questions.
The equation for the scenario of the work load doubling every period would be Assignments due = 3 x 2^(number of periods)
The assignments due would be:
1 st period - 6 assignments 4 th period - 48 assignments 8th period - 768 assignments How to find the assignments due ?Assignments start at 3 assignments and then double per period so the best equation is:
Assignments due = 3 x 2^(number of periods)
After 1 period:
Assignments due = 3 x 2^(number of periods)
= 3 x 2
= 6 assignments
After 4 periods:
= 4 x 2⁴
= 48 assignments
After 8 periods:
= 4 x 2 ⁸
= 768 assignments
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Ethan's class is handing out balloon arrangements consisting of 4 balloons each. Each balloon has an equally likely chance of being red, blue, or yellow. Ethan created a spinner to simulate this probability. Here is Ethan's data from 30 trials of 4 spins on the spinner (r = red, b = blue, y = yellow):
ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr
According to this data, what is the experimental probability that an arrangement will contain at least one yellow balloon?
0.75
0.23
0.767
0.233
The experimental probability that an arrangement will contain at least one yellow balloon is 0.767. Then the correct option is C.
Given that:
Each balloon arrangement in Ethan's class has four balloons in it. The likelihood of each balloon being red, blue, or yellow is equal. To represent this possibility, Ethan made a spinner.
ybrr, bybb, rbbb, rrry, rbbb, rryy, yybb, ryry, ryyr, rbyr, ryyr, rryy, rrrr, yrby, bbyy, byyr, byyr, byyb, rbby, ybry, rryy, rbrr, rybb, bbbr, rrbr, ybry, ryrr, rryb, rrrb, rryr
The experimental probability that an arrangement will contain at least one yellow balloon is calculated as,
P = 23 / 30
P = 0.767
Thus, the correct option is C.
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This data gives the length of the radius, in feet, of several circles.
Length (ft): 12, 316, 12, 12, 38, 38, 316, 12, 316, 716
Create a line plot to display this data.
To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
Radius of Circles
1/16
1/8
3/16
1/4
5/16
3/8
7/16
1/2
Length (ft)
0
1
2
3
4
5
6
7
8
9
10
Answer: on 1 = 0
on 2 = 0
on 3 = 3
on 4 = 0
on 5 = 0
on 6 = 2
on 7 = 1
on 8 = 4
Step-by-step explanation:
As the first, second, fourth and fifth do not have any numbers we will skip to the next number on the number line.
1/16 = 0
1/8 = 0
3/16 = 3
1/4 = 0
5/16 = 0
3/8 = 2
7/16 = 1
1/2 = 4
Devon bought a tie. The tie cost $22.50 before tax. After tax, Devon spent $24.30. What was the percent of sales tax
8% will be the value of sales tax that has been charged on a tie will be.
The tie cost is $22.50
The cost after the tax is $24.30.
The change in the cost will be:
= cost after-tax - cost before tax
=24.30-22.50
=1.8
The percentage change will be
Next, assemble a ratio of the sales tax to the pre-tax cost of the tie.
=Sales tax/Pre-tax value
= (1.8/22.50)*100
=8%
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Find the arc
length of AB.
3 cm
P 64°
A
B
PLEASE SHOW WORK!
The measure of the arc length AB is 16π/15 centimeters.
Since,
An arc length is simply the distance between two points along a section of a curve.
We know that;
The arc length is expressed as:
s = 2πr × (θ/360°)
Where s is the arc length, r is the radius, θ is the angle and π is constant pi.
Given that:
Radius r = 3cm
Angle θ = 64 degree
Arc length s = ?
Now, Plug the values into the above formula
s = 2πr × (θ/360°)
s = 2 × π × 3cm × ( 64°/360°)
s = 16π/15 cm
Therefore, the arc length is 16π/15 cm.
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Which shows the correct first step to solving the system of equations in the most efficient manner?
3x+2y-17
x+4y=19
O x=-4y+19
-2y+17
3
O x-
O4y=-x+19
Oy=-3x+17
Answer:
(a) x = -4y +19
Step-by-step explanation:
You want to know a good first step for solving the system of equations in an efficient manner.
3x +2y = 17x +4y = 19SubstitutionOne way to solve these equations is by substitution. To do that, we typically write an expression for one of the variables in terms of the other. It is efficient to choose a variable that already has a coefficient of 1.
Here, a useful first step is to solve the second equation for x:
x = -4y +19
__
Additional comment
Then the solution proceeds with substitution for x:
3(-4y +19) +2y = 17
-10y +57 = 17
-10y = -40
y = 4
x = -4(4) +19 = 3
The solution is (x, y) = (3, 4).
Another reasonable first step is to subtract the second equation from twice the first:
2(3x +2y) -(x +4y) = 2(17) -(19)
5x = 15
x = 3
3 +4y = 19 . . . . . . substitute for x in the second equation
y = (19 -3)/4 = 4
The "addition" or "elimination" method shown second is also shown using 5 steps, but these are generally more complicated steps than the ones shown for the "substitution" solution. It appears the substitution solution probably is "the most efficient" in this case.
Fast will give Brainliest.
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over y = −2.
N′(−3, 2), M′(0, 1), O′(−5, 3)
N′(−5, 0), M′(−2, −1), O′(−3, 1)
N′(−5, 1), M′(−2, 0), O′(−3, 2)
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Answer:
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Step-by-step explanation:
To reflect a point over a line, we can use the following steps:
Find the distance between the point and the line.
Construct a perpendicular line from the point to the given line.
Extend this perpendicular line to the same distance on the other side of the given line.
The intersection of the extended perpendicular line with the given line is the reflected point.
Alternatively, we can use the fact that reflecting a point over a line is equivalent to reflecting the coordinates of the point across the line. In this case, we are reflecting over the line y = -2, so we can simply negate the y-coordinate of each point to find its reflection.
Using this method, the reflected vertices are:
N'(-5, -4)
M'(-2, -3)
O'(-3, -1)
′(Therefore, the correct answer is option D: N−5, −6), M′(−2, −5), O′(−3,-7)
The table of values below represent an exponential function. Find the constant ratio of successive y-values. x y -2 5 -1 7.5 0 11.25 1 16.875 2 25.3125 a. 5 c. 1.5 b. 1.33 d. 0.5
Answer: 1.5
Step-by-step explanation:
To find the constant ratio of successive y-values, we need to divide each y-value by the previous one.
For example, to find the ratio between the second and first y-values:
7.5 ÷ 5 = 1.5
Similarly, we can find the other ratios:
11.25 ÷ 7.5 = 1.5
16.875 ÷ 11.25 = 1.5
25.3125 ÷ 16.875 = 1.5
Since all the ratios are the same, we can conclude that the constant ratio of successive y-values is 1.5.
Therefore, the answer is c. 1.5.
at age 25 , someone sets up an ira (individual retirement account) with an apr of 6%. at the end of each month he deposits $85 in the account. how much will the ira contain when he retired at age 65? compare that amount to the total deposits made over the time period.
Answer: This is what the balance in the IRA should be after 40 years.
Total deposits should be =$75 x 40 years x 12 months =$36,000
$196,861 - $36,000 =$160,861 was interest earned over 40-year period.
P.S. Do the math in the above formula and you should get the same answer that I got!!.
Guest Oct 19, 2017
Step-by-step explanation: im sure thats the answer
The coordinates of ΔRGB are R(‒3, 2), G(3, 4) and B(1, 1). Under a series of transformations, the resulting figure ΔUNA has the following coordinates: U(2, ‒3), N(‒4, ‒3) and A(‒1, ‒1).
Which statement is not true?
RB has the same length as UA.
GB is congruent to AN.
The measure of ∠R is the same as ∠N.
The original triangle ΔRGB is congruent to ΔUNA.
The statement that is not true is (c) The measure of ∠R is the same as ∠N.
We have,
From the question, we have the following parameters that can be used in our computation:
The coordinates of ΔRGB are R(‒3, 2), G(3, 4) and B(1, 1).
The coordinates of ΔUNA are U(2, ‒3), N(‒4, ‒3) and A(‒1, ‒1).
Looking at the above coordinates, we can see that the transformation rule is (x, y) = (-x, -y)
This is a rigid transformation
And so, the side lengths and the corresponding angle measures are equal
However, angles R and N are not corresponding angles
So, the false statement is (c) The measure of ∠R is the same as ∠N.
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if P = (4,2), Find: Rx=3 (P). Pls help!!
The coordinates of the reflected point P' will be (4, -3).
When a point is reflected over the x-axis, its y-coordinate changes sign.
In this case, the point P has coordinates (4,3).
To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.
So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.
Therefore, the coordinates of the reflected point P will be (4, -3).
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Answer:
Step-by-step explanation:
Question 6
A square is placed within a rectangle. Find the area of the shaded region.
Select one:
O
✪
✪
O
559 ft²
640 ft²
721 ft²
604 ft²
32 ft
19A
9 ft
20 ft
The area of the shaded region is 559 ft².
How to find the area of the shaded region?In order to find the area of the shaded region, we will subtract the area of the square from the area of the rectangle. That is:
area of the shaded region = area of rectangle - area of square
area of the shaded region = (32 * 20) - (9 * 9)
area of the shaded region = 640 - 81
area of the shaded region = 559 ft²
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Complete Question
See attached image
f(1)=0
f(n)=f(n−1)+2
Answer: f(n) = 2n - 2
Therefore, we can use this formula to find the value of f(n) for any positive integer n.
Step-by-step explanation: Using the given recursive formula:
f(1) = 0
f(n) = f(n-1) + 2
We can find the values of f(n) for different values of n:
f(1) = 0
f(2) = f(1) + 2 = 0 + 2 = 2
f(3) = f(2) + 2 = 2 + 2 = 4
f(4) = f(3) + 2 = 4 + 2 = 6
f(5) = f(4) + 2 = 6 + 2 = 8
And so on.
We can see that each term in the sequence is 2 more than the previous term. So, we can write the general formula for f(n) as:
f(n) = 2n - 2
Therefore, we can use this formula to find the value of f(n) for any positive integer n.
Complete the ratio table
Answer: do u need help
Step-by-step explanation: ask a teacher dont cheat
find the area of two rectangles that make a patio
Answer:
Step-by-step explanation:
picture?
6ft=____yd
Remember to convert to a larger unit divide
Answer:
2 yards
Step-by-step explanation:
2 yards equals 6 feet because 2x3=6 or 72 inches because 6x12 equals 72. 1 yard is equal to 3 feet.
Hawa models a can of ground coffee as a right cylinder. She measures its radius as
3/4 in and its volume as 8 cubic inches. Find the height of the can in inches. Round your answer to the nearest tenth if necessary
Answer: The height is 4.5 in
Step-by-step explanation:
We can use the given formula for volume, transform it to solve for height (h), and then substitute our given values to solve.
Given formula:
[tex]\displaystyle V=\pi r^2h[/tex]
Transformed to solve for height:
[tex]\displaystyle h=\frac{V}{\pi r^2}[/tex]
Substitute given points:
[tex]\displaystyle h=\frac{(8\; \text{cubic inches})}{\pi (0.75\; \text{inches})^2}[/tex]
Square:
[tex]\displaystyle h=\frac{(8\; \text{cubic inches})}{\pi (0.5625)}[/tex]
Multiply:
[tex]\displaystyle h=\frac{8}{1.767146}[/tex]
Divide:
[tex]\displaystyle h=4.527[/tex]
Round to the nearest tenth:
[tex]\displaystyle h=4.5[/tex]
Amelie travelled to her friend's house and her journey is shown on the distance-time graph below. She travelled the final 4 hours of her journey at a constant speed of 60 km/h. Work out the value of d. Distance travelled (km) 270- 0 3 Time (hours) -
The total distance traveled by Amelia to her friend's house is d = 510 miles
Given data ,
Let the distance traveled by Amelia to her friend's house be d
Now , the speed of the final 4 hours of her journey = 60 km/hr
So , the distance traveled in the final 4 hours = 4 x 60 = 240 km
And , the initial distance traveled = 270 km
So , from the graph
The total distance d = 270 + 240
d = 510 miles
Hence , the distance traveled by Amelia = 510 miles
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A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
PLS HELP! TEST REVIEW AND I DONT UNDERSTAND
(a) Volume of the cylinder is 153 cm³
(b) Volume of the cone is 51 cm³
(c) Volume of the cone = 1/3 × Volume of the cylinder
Calculating the volume of a cylinder and a coneFrom the question, we are to determine the volume of the cylinder and the volume of the cone
The volume of a cylinder can be calculated by using the formula,
V = πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
A = πr² = 17 cm²
A is the area of the base
h = 9 cm
Thus,
V = 17 cm² × 9 cm
V = 153 cm³
Therefore,
Volume of the cylinder is 153 cm³
(b)
For the volume of the cone
V = 1/3 πr²h
Substitute the given parameters
V = 1/3 × 17 cm² × 9 cm
V = 17 cm² × 3 cm
V = 51 cm³
Hence,
Volume of the cone is 51 cm³
(c)
Volume of the cone = 1/3 × Volume of the cylinder
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Solid metal support poles in the form of right cylinders are made out of metal with a density of 5.4 g/cm^3. This metal can be purchased for $0.71 per kilogram. Calculate the cost of a utility pole with a radius of 17.8 cm and a height of 700 cm. Round your answer to the nearest cent. (Note: the diagram is not drawn to scale)
The cost of the utility pole with a radius of 17.8 cm and a height of 700 cm is; $3774.4
How to determine the volume?From the information given, we have the following parameters;
Density = 5.4 g/cm³
Mass = Ikg = 0.71 kg
Cost per mass = $0. 51
Let's determine the volume of this cylinder:
Volume = mass / density
Substitute the values
Volume = 0.71 /5.4
Volume = 0.131 cm³
Thus, 0.131 cm³ costs $0.71
For the utility pole;
Volume = 2 πr²h
Where:
r is 17.8cm
height is 700cm
Volume = 3. 142 × 17.8 × 17.8 × 700
Volume = 696414.32 cm³
If 0.131 cm³ costs $0.71
Then 696414.32 cm³ will cost:
= 696414.32 × 0.71/ 0.131
= 3774.4
Thus, the cost of a utility pole is $3774.4
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