The scale factor between two similar cones with surface areas of 20 ft² and 125 ft² is found by taking the square root of the ratio of the surface areas, which is [tex]\frac{1}{6.25}[/tex], resulting in a scale factor of B. [tex]\frac{2}{5}[/tex].
The question is asking about the scale factor between two similar cones with given surface areas. In the case of similar figures, the ratio of their surface areas is equal to the square of the scale factor. To find the scale factor, we take the square root of the ratio of the surface areas.
First, find the ratio of the surface areas: surface area of smaller cone : surface area of larger cone = [tex]\frac{20 ft^2}{125 ft^2}[/tex] = [tex]\frac{1}{6.25}[/tex].
Then, we take the square root of the ratio to find the scale factor: [tex]\sqrt{ (\frac{1}{6.25})}[/tex] = [tex]\frac{1}{2.5}[/tex], which simplifies to [tex]\frac{2}{5}[/tex]. Therefore, the scale factor is [tex]\frac{2}{5}[/tex], making option B the correct answer.
To find the scale factor between two similar cones, you can use the ratio of their corresponding lengths.
The surface area of a cone is proportional to the square of its height.
Let's denote the scale factor as kk. If A1A1 and A2A2 are the surface areas of the first and second cone respectively, then:
A1/A2=(k/1)^2
Given A1=20 ft^2 and A2=125 ft^2, we have:
20/125=(k/1)^2
Solving for k:
k= √ 20/125=√ 4/25=2/5=52
So, the correct answer is B. 2/5
complete question;
The surface areas of two similar cones are 20 ft^2 and 125 ft^2. What is the scale factor?
A. 1/5
B. 2/5
C. 3/5
D. 4/5
How much money must be deposited today to become $1300 in 20 years at 7.5% compounded continuously?
Find the equation of the line whose x-intercept is 8 and y-intercept is -2. write the equation in slope-intercept form.
The equation of the straight line whose x - intercept = 8 and
y - intercept = - 2 is y = x/4 - 2.
What is the slope intercept form of a straight line?
The slope - intercept form of a straight line is -
y = mx + c
Given is the equation of the line whose x-intercept is 8 and y-intercept is -2.
The given intercepts are -
x - intercept = 8
y - intercept = - 2
Then, the coordinates of the points through which the line passes are -
(0, -2) and (8, 0)
The slope of this line will be -
m = 0 - (- 2)/8 - 0
m = 2/8
m = 1/4
So the equation of the straight line will be -
y = x/4 - 2
Therefore, the equation of the straight line whose x - intercept = 8 and
y - intercept = - 2 is y = x/4 - 2.
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The volume of a cone is 88π cubic feet. Its height is 8 feet. Fatima is finding the radius of the cone. Her work is shown below.
Step 1: 88π = 1/3 πr² (8)
Step 2: 88π = 8/3 πr²
Step 3: 8/3 (88) = r²
Step 4: 234.7 = r²
Step 5: 15.3 =r
What is Fatima's error?
- In step 4, Fatima did not find the correct value of 8/3 (88).
- In step 2, Fatima should not have multiplied 1/3 and 8.
- In step 3, Fatima did not multiply 88 by the reciprocal of 8/3
- In step 1, Fatima did not substitute the correct value for the height in the formula.
Answer:
step 3
Step-by-step explanation:
took test
The larger square has area of 400 square inches. the areas of the two squares have a ratio of 1:4. what is the side lengh of the smaller square?
Final answer:
To find the side length of the smaller square, we take the square root of the larger square's area (400 sq inches) to get 20 inches, then halve it to align with the 1:2 scale factor of the sides for a correct length of 10 inches.
Explanation:
To solve this problem, we first acknowledge that the ratio of the areas of the two squares is 1:4. Since area is a function of the side length squared, we look for a scale factor of the side length that when squared will give us this ratio. In this case, the scale factor is 1:2, meaning the side length of the smaller square is half that of the larger square.
The area of the larger square is given as 400 square inches. To find the side length, we take the square root of the area, which is 20 inches. Therefore, the side length of the smaller square is half of this, which is 10 inches. However, given that the statement seems to expect an 8-inch side for the larger square, there might be a misunderstanding in the problem, assuming that area scales directly with side length rather than its square. Nonetheless, based on area and scale factor, the correct side length is 10 inches.
How do you simplify x^2+y^2?
If I’m 17 1/2 do I still have to wait a year to get my provisional license after I get my permit in Florida
What are the zeros of f(x) = x2 + 3x – 10?
A. x = –5 and x = 2
B. x = 5 and x = 2
C. x = –5 and x = –2
D. x = 5 and x = –2
One maid can clean the house in 3 hours. Another maid can do the job in 6 hours. How long will it take them to do the job working together?
The number of hours if they worked the job together will be 2 hours.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
One maid can clean the house in 3 hours. Another maid can do the job in 6 hours.
We know that work and time are inversely proportional to each other.
Let T be the total time taken. Then the equation will be
1/T = 1/3 + 1/6
1/T = (2 + 1) / 6
1/T = 3 / 6
T = 6 / 3
T = 2
The number of hours if they worked the job together will be 2 hours.
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I WILL MARK BRAINIEST 25 POINTS Find the area of trapezoid BCDE.
A) 12 5/8 in2
B) 13 7/8 in2
C) 16 1/8 in2
D) 18 5/6 in2
PLEASE HELP ME!!!! Thank you
I have milk that contains 1 percent fat and milk that contains 4 percent fat. a customer wants a double latte made with 1/3 of a pint of 2 percent milk. how much of each type of milk should i use ?
The double lathe milk with 2 percent fat concentration, is made by
considering the concentration and amount of each constituent.
The amount of each type of milk to be used in the [tex]\dfrac{1}{3}[/tex] pint of double lathe
are;
[tex]\dfrac{2}{9}[/tex] pint of the 1 percent fat milk and [tex]\dfrac{1}{9}[/tex] pint of the 4 percent fat milk.Reasons:
Let x represent the amount of the milk that contains 1 percent fat in the
volume of the 2 percent fat milk.
Therefore, we have;
The amount of the 4 percent fat milk to be used = [tex]\dfrac{1}{3} - x[/tex]
[tex]Amount \ of \ fat = \dfrac{1}{100} \times x + \dfrac{4}{100} \times \left (\dfrac{1}{3} - x\right) = \dfrac{2}{100} \times \dfrac{1}{3} = \dfrac{2}{300}[/tex]
[tex]\dfrac{1}{100} \times x + \dfrac{4}{100} \times \left (\dfrac{1}{3} - x\right) = \dfrac{4 - 9 \cdot x}{300} = \dfrac{2}{300}[/tex]
Therefore;
4 - 9·x = 2
4 - 2 = 9·x
[tex]x = \dfrac{2}{9}[/tex]
The amount of the 1 percent fat milk to be used for the double lathe, x = [tex]\dfrac{2}{9}[/tex]
of a pint.
The amount of the 4 percent fat milk to be used for the double lathe = [tex]\dfrac{1}{3} - x[/tex]
Therefore;
The mount of the 4 percent fat milk = [tex]\dfrac{1}{3} - \dfrac{2}{9} =\dfrac{1}{9}[/tex]
The amount of the 4 percent fat milk to be used for the double lathe = [tex]\dfrac{1}{9}[/tex]
pint.
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A museum opened at 8:00am.In the first hour 350 people purchased admission tickets.In the second hour 20% more people purchased admission tickets than in the first hour.Each admission ticket cost 17.50. What was the total amount of money paid for all the tickets purchased in the first two hours?
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Solve the triangle: α = 58°, a = 9, b = 15.
Subtract 8 + 7i from 4 − 16i. -4 − 23i 4 − 23i 4 + 9i 4 − 11i
Answer:
-4-23i
Step-by-step explanation:
Above answer didn't quite understand what the question was asking. It's asking to SUBTRACT 8+7i from 4-16i. So it would be written like this:
(4-16i) - (8+7i).
Simplify it from there and you'd get -4-23i
To subtract 8 + 7i from 4 - 16i, subtract the real parts and the imaginary parts separately, resulting in -4 - 23i.
Explanation:To subtract 8 + 7i from 4 − 16i, you treat the real and imaginary parts separately.
Subtract the real parts: 4 − 8 = −4.
Subtract the imaginary parts: (−16i) − (7i) = −16i − 7i = −23i.
Combine the results to get the final answer: −4 − 23i.
Therefore, subtracting 8 + 7i from 4 − 16i gives −4 − 23i.
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Find the quotient. 6^8/6^6
How do I do this ??
A jar contains nickels and pennies there are 56 coins in the jar in all the total value of he coins is $1.52 how many pennies are in the jar
In an origami class, the instructor tells the students to cut a square that has an area of 24 square inches. Kevin cuts a square with a side length of 4.80 inches. Which statement is true?
Answer:
The side length of the square Kevin cuts is slightly less than the length the instructor required
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Damien bowled 5 games, His scores were:
82, 83, 65, 84, 76.
What is Damien's mean bowling score?
Please hurry! On a time limit!
To find Damien's mean bowling score, we add up his scores and divide by the number of games played. The mean bowling score is 78.
Explanation:To calculate Damien's mean bowling score, we need to find the sum of all his scores and divide it by the total number of games played. Damien's scores are 82, 83, 65, 84, and 76.
Adding these scores together we get: 82 + 83 + 65 + 84 + 76 = 390.
Then, divide the sum by the total number of games played: 390 ÷ 5 = 78.
Therefore, Damien's mean bowling score is 78.
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The mean percentage of a population of people eating out at least once a week is 57% with a standard deviation of 3.5%. assume that a sample size of 40 people was surveyed from the population an infinite number of times. 95% of the sample mean occurs between % and %. nextreset
solve for y. triangle PQR is congruent to triangle DEF, PQ= 15, QR= 10, RP=8, and EF = 6y +4
Elizabeth brought a box of donuts to share. there are two-dozen (24) donuts in the box, all identical in size, shape, and color. six are jelly-filled, 6 are lemon-filled, and 12 are custard-filled. you randomly select one donut, eat it, and select another donut. find the probability of selecting two custard-filled donuts in a row.
if you enjoy math and science, the career cluster that might be best for you is
Information Technology and Engineering
Step-by-step explanation:Mathematics is also a branch of Science. A person who is good in mathematics can take the analytical view of anything and convert ideas into practical form by using mathematical models. There are a lot of applications that can be used for converting analog models into digital models by using mathematics. So all of these models require mathematical backgrounds and engineers are the people who bring ideas to reality. The same is applied on IT field too.
someone help me, please :)
Given the two expressions shown below:
A. \sqrt{3} +\sqrt{2}
B. \sqrt{3} +\sqrt{6}
Which statement best describes the two expressions?
Both are rational.
Both are irrational.
A is rational, but B is irrational.
A is irrational, but B is rational.
In which situation would a savings account be the best investment to earn interest?
saving for retirement in 20 years
saving to buy a new car in three years
saving to buy a new house in seven years
saving to easily access the money when needed
Saving to easily access the money when needed is the situation would a savings account be the best investment to earn interest
What is Investment?Investment is traditionally defined as the commitment of resources to achieve later benefits
An investment can be regarded as asset or item that is been gotten so as to generate income or appreciation.
It should be noted that appreciation serves as increase in the value of an asset over time.
To earn interest, it will be best to use savings account so that there could be easy access to the money when needed.
Hence, saving to easily access the money when needed is the situation would a savings account be the best investment to earn interest
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Eliminate the parameter.
x = one divided by two t, y = 3t^3 - 1
Answer choices:
y = three divided by eight t^3 - 1
y = 24x^3 - 1
y = 6x^3 - 1
y = 24x - 1
What is the y-value of sin(x) when x = -90°?
What will it cost to tile a rectangular floor measuring 231 feet by by 37 feet if the tile costs $ 14 per square foot?
The total cost to tile a rectangular floor measuring 231 feet by 37 feet, with tile costing $14 per square foot, will be $119,658.
Explanation:To find the cost of tiling a rectangular floor, first, calculate the area of the floor which is the length times the width. In this case, the rectangle is 231 feet by 37 feet so its area is 231 x 37 = 8,547 square feet.
With the tile costing $14 per square foot, the total cost will be the area of the floor times the cost per square foot. This can be calculated by multiplying 8,547 square feet x $14 per square foot = $119,658.
Therefore, the total cost to tile the rectangular floor will be $119,658.
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A rectangular garden measures 40 yards by 35 yards. a lawn of uniform width surrounds the garden and has an area of 316 square yards. find the width of the lawn that surrounds the garden.
The width of the lawn surrounding the garden is 2 yards.
Let's denote the width of the lawn as "w" yards.
The dimensions of the garden are 40 yards by 35 yards. Including the lawn, the dimensions become:
Length: 40 + 2w yards
Width: 35 + 2w yards
The area of the rectangle including the garden and the lawn is:
(40 + 2w) × (35 + 2w) square yards
The area of the garden itself is:
40 × 35 = 1400 square yards
The area of the lawn alone is:
Total area - Area of the garden = 316 square yards
Therefore:
(40 + 2w) × (35 + 2w) - 1400 = 316
Expand the left side of the equation:
= (40 + 2w)(35 + 2w)
= 40 × 35 + 40 × 2w + 35 × 2w + 2w × 2w
= 1400 + 80w + 70w + 4w²
= 1400 + 150w + 4w²
Set up the equation:
= 1400 + 150w + 4w² - 1400 = 316
= 150w + 4w² = 316
Rearranging the equation:
4w² + 150w - 316 = 0
Solve this quadratic equation using the quadratic formula:
w = (-b ± √(b² - 4ac)) / 2a
Here, a = 4, b = 150, and c = -316
Calculate the discriminant:
= b² - 4ac
= 150² - 4 × 4 × (-316)
= 22500 + 5056
= 27556
√27556 ≈ 166
Therefore:
w = (-150 ± 166) / 8
This gives two potential solutions:
w = (16 / 8) = 2
w = (-316 / 8) (not valid as width cannot be negative)