A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius of the cone?

Answers

Answer 1

Cylinder Volume = PI * radius^2 * height
Cylinder Volume = 3.14159 * 1 * 21
Cylinder Volume = 65.97 cc

Volume Cone = [PI * radius^2 * height] / 3
radius^2 = 3 * 65.97 / (3.14159 * 7)
radius^2 = 9
radius = 3 centimeters

Answer 2

The radius of the cone is 3 cm.

Related Questions

Use the number line to find the ratio BG/AD Simplify the ratio.

Answers

The simplified ratio of BG/AD is 10/7.

The simplified ratio is 10/7

Randy bought a zero coupon bond and a TIPS 5 years ago for $2,500 each. Both had 10 years to maturity. The TIPS's coupon was 2% while the zero coupon bond will be redeemed for $3,000. What should the maximum real value of his bonds be if he tries to sell them today? Select the best answer from the choices provided. $250 $750 $5,250 $5,750

Answers

So, we have that the final value of the zero coupon bond after ten years will be 3000$. The TIPS mature after 10 years, but the interest will be calculated only for 5 years. Each year of interest, the TIPS gains 2%*2500=2*25=50$. Hence the TIPS gains 50$ for each year of interest. Since the interest is not compounding, it will gain 5*50=250$ in value. Hence its total value after ten years is 2500+250=2750$. The total maximum value of the two assets combined is 3000+2750=5750$ and it is attained after 10 years. If one things that money is more important now than in 10 years, the assets could be sold at a lower price; nonetheless their max value never exceeds choice d)=5.750$

(2)
For this problem I did 2.5/8 = 1.5/4.8, then I cross multiplied and got 12=12 so I would assume that the polygons are infact similar? It must be B or C based on this, but I am pretty confused about the whole ratio part.

Answers

You are correct in saying that the figures are similar; however, the ratio you picked is incorrect. The ratio is 8:4.8 which represents the ratio of JK to PQ

Notice how JK and PQ are the first two letters of JKML and PQRS respectively. So they correspond to one another. Furthermore, notice that 8/4.8 = 1.667 approximately. Also, KM/QR = 2.5/1.5 = 1.667 approximately as well. KM and QR are the two middle letters of JKML and PQRS respectively. The fact we get 1.667 approximately both times, and because of the congruent angles, proves the figures to be similar.

In short, the actual answer is choice B

For polygons to be similar, they must have the same angles and the ratio of the lengths of the corresponding sides must be the same.

First you should rotate the second polygon 90 degrees clockwise (so angle S is on the left) to make it easier to visualize corresponding sides. Now with the shapes in the same orientation, it seems they could be similar. But we have to verify their angles and lengths.

If the two polygons are similar, then the similarity statement might be JKML~PQRS. Notice the order the angles are listed are the same for both shapes (e.g. top left angle is listed first for both shapes). That being said, you could also have written a similarity statement LMKJ ~ SRQP, or another combination of letters with corresponding angles listed in the same order.

First let's check the corresponding sides.
The ratio between corresponding sides JK and PQ is JK/PQ = 8/4.8 = 1.667
The ratio between corresponding sides JL and PS JL/PS = 2.5/1.5 = 1.667
LM/SR and KM/QR also equal 1.667.
Corresponding sides are proportional. We are halfway there.

Now let's check angles. Angle J equals 115 degrees, and its corresponding angle P also equals 115 degrees, so Angle J = Angle P.

The other angles are also similar. Quick proof here: draw a diagonal from angle L to K and from S to Q to split the shape to two triangles. The left triangles are similar by SAS similarity and the right triangles are congruent by SSS similarity. Similar triangles have the same angles, so the two entire polygons have the same angles.

Since the polygons JKML and PQRS have the proportional lengths and same angles, they are similar polygons.

Now, the second part in the answer choices is the ratio between JKML and PQRS. In our example of JK and PQ we found the ratio to be JK/PQ = 8/4.8 = 1.667, and every corresopnding side to also be 1.667. So the entire polygon ratio of JKML to PQRS has the ratio 8/4.8.

While in europe, if you drive 107 km per day, how much money would you spend on gas in one week if gas costs 1.10 euros per liter and your car's gas mileage is 42.0 mi/gal ? assume that 1euro=1.26dollars?

Answers

Answer:

The money spend on gas in one week = 46.13 Euro

The money spend on gas in one week = $58.12

Step-by-step explanation:

1 week = 7 days

You drive 107 km per day.

Kilometer driven for 7 days = 7 *107 = 749 kilometers.

Now let's convert kilometers to miles.

1 mile = 1.60934 kilometers

We have to divide 749 km by 1.60934.

So, 749 km = 465.41 miles.

Car mileage is 42 miles / gallon.

We need to find the number of gallons of gas needed to travel 465.41 miles.

So, we have to divide 465.41 miles by 42.

The number of gallons of gasoline needed = [tex]\frac{465.41}{42} = 11.08 gallons[/tex]

cost of 1 .10 Euros per liter.

Now we have to convert 11.08 gallons to liters.

1 gallon = 3.78541 liters.

So we have to multiply 11.08 by 3.78541

11.08 gallons = 41.94 liters.

Now to find the cost, we need to multiply 41.94 liters by 1.10 Euro.

The money spend on gas in one week = 46.13 Euro

To convert the cost in dollars.

1 euro = 1.26

We need to multiply 46.13 by 1.26

The money spend on gas in one week = $58.12

Three couples go to the movies and sit in six consecutive seats. if the couples must sit together, in how many ways can they be seated

Answers

Since each couple must sit together, let's think of each couple as a single unit. That gives us three ways to arrange three units. It helps to draw a diagram. We can see that each coupe can sit in three distinct ways. [tex](3)(3)=9[/tex].

9

Given f(x)=5x^2−2x and g(x)=3x ^2+x−4 .

Answers

add both together by combing like terms to get 8x^2-x-4

The addition of the two functions f(x) and g(x) is 8x² − x − 4. Then the correct option is C.

What is a function?

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The functions are given below.

[tex]\rm f(x)=5x^2-2x \\\\g(x)=3x ^2+x-4[/tex]

The addition of the functions is given as

f(x) + g(x) = 5x² − 2x + 3x² + x − 4

f(x) + g(x) = 8x² − x − 4

More about the function link is given below.

https://brainly.com/question/5245372

A 45° sector in a circle has an area of 13.75π cm².

What is the area of the circle?

Use 3.14 for pi.

Enter your answer as a decimal in the box.

Answers

As the circle is divided into sectors, first we need to find out how many sectors are in the circle, considering one sector = 45°:

Number of sectors in a circle = 360°/45° = 8

Now multiply this number to 13.75[tex] \pi [/tex] to get the area of the circle.

[tex] \pi [/tex] = 3.14

Area of the circle = 8 * 13.75 * 3.14 = 345.4 [tex]c m^{3} [/tex]

Ans: 345.4 [tex]c m^{3} [/tex]
-i

Answer:

345.4

Step-by-step explanation:

I took the test

What is the probability that the card is either a face card or a spade?

Answers

50% is what I believe it is. Please mark MOST brianlest.

A cruise ship travels 1900 miles per trip. There are a total of 4 stops the ship makes, and the distance to the first stop is 460 miles. If the variable d stands for the distance left to travel after the first stop, which of the following units could apply to this variable?
A. ships
B. days
C. stops
D. miles

Answers

I believe the answer is D. miles just seems to sound the best to me.

I think the answer is D

The explicit rule for a sequence is

an=17−5n .

What is the recursive rule for the sequence?

can you explain also

Answers

The general form of an explicit rule for an arithmetic sequence is
[tex]a_n=a_1+d(n-1)[/tex], where a₁ is the first term of the sequence and d is the common difference. Since we have [tex]a_n=17-5n[/tex], we know that n is multiplied by 5. That means that d must be 5, since that is the only thing that n gets multiplied in our general form. This gives us:
[tex]a_n=a_1+5(n-1) \\ \\a_n=a_1+5*n-5*1 \\ \\a_n=a_1+5n-5[/tex]
We know that we add something to 5n and then subtract 5 to get 17. Cancelling this process, we can add 5 to 17 to get 22. This gives us
[tex]a_n=22+5(n-1)[/tex]
We know that our first term, a₁, is 22 and our common difference, d, is 5.
The general form of a recursive formula for an arithmetic sequence is
[tex]a_n=a_n_-_1+d[/tex], where d is the common difference and [tex]a_n_-_1[/tex] is the previous term. We know that d is 5, so our recursive formula is
[tex]a_n=a_n_-_1+5[/tex]

If l = 65 cm and j = 33 cm, what is the length of k?

Answers

Answer:

The answer is 56 inches on Study Island.

Step-by-step explanation:

Thomas is saving pennies in a jar. The first day he saves 3 pennies, the second day 12 pennies, the third day 48 pennies, and so on. How many pennies does Thomas have on the eighth day?

Answers

It looks to me as if the amount of pennies is increasing times four. So I think you just keep multiplying by four until you reach the eighth day?

Moving a figure around a fixed point in the plane is called making a ___.

Answers

Answer:

Rotation.

Step-by-step explanation:

There are three rigid motions (which do not change the shape and size of the figures): rotation, translation and reflection.

You make a rotation of a figure when you turn it about a fixed point (which can be inside, on an edge or outside the figure) and it is measured in degrees. The rotation can be clockwise or counterclockwise.

Answer:

The answer is Reflection

The home that you are interested in purchasing is listed at $135,000. In order to get financing, you have to place a 15% down payment. From the given information, determine the amount of the down payment. a. $2,025 c. $114,750 b. $135,000 d. $20,250

Answers

135,000x15%=20,250 D. 20,250.

Answer:

its D

Step-by-step explanation:

Which of the following data sets represents a positive correlation?

A
B
C

Answers

B as you can see the points go upwards as they go across :) Hope this helps!

B)
It is B) because the y-value is increasing as the x-value is increasing.

Find the distance between the points given.

(-3, -6) and (3, 2)

4
10
√52

Answers

The answer is the square root of 52. I used to the distance formula to solve it.

What is the question

Answers

To solve for this problem, we need to combine like-terms. Let's list our current variables:
2x - 2y - 5y + 5z - 2x - y + 3z; now, we need to list like-terms together and simplify.
2x - 2x; 0
2y - y; -3y
5z + 3z; 8z

Now, let's put this into an expression;
-3y + 8z.

From our answer choices in the image above, the last option "D.) -3y + 8z" is the correct answer.

I hope this helps!

Find the area of the shaded region?

Answers

10 x 12 = 120
3 x4 = 12
4x 1 = 4
120 - 12 = 108
108-4 = 104 square feet

Which of the following statements is always true?

A: All rational numbers are whole numbers.

B: All real numbers are rational numbers.

C: All irrational numbers are real numbers.

D: All square roots are irrational numbers.

Answers

Hi!

The correct answer is B: All real numbers are rational numbers.

Hope this helps!

Answer:

Step-by-step explanation:

took the test got it right

Please Hurry, I really need help! A cylinder has a height of 6" and the circumference of its base is 16π".

Find the volume of the cylinder. (P.S There is no picture of the cylinder)

96π cubic inches
192π cubic inches
384π cubic inches

Answers

Volume is pi*r^2*h
Circumference is 2*pi*r
16pi=2pir
r=8
v=pi*8^2*6
v=384pi cubic inches

Hey!

Height of cylinder = 6 inch
Circumference of base = 16 π inch

Volume of cylinder = πr^2h

Radius =?
Circumference of circle = 2πr

2πr= 16π
2r= 16
r= 16/2
r= 8 inch

Volume= π×8×8×6
Volume= 384π cubic inches

Hope it helps...!!!

HELP! This circle graph shows the results of a survey that asked people to identify their favorite type of music. What percent of people chose rock or country as their favorite type of music? 9% 35% 45% 55%

A circle graph with 5 sections. The first section is labeled Rock 27 percent. The second section is labeled Hip Hop 28 percent. The third section is labeled Jazz 19 percent. The fourth section is labeled Country 18 percent. The fifth section is labeled Other 14 percent.

Answers

45 percent because you and the 18 percent country and then the 27 percent rock together

The percentage that choose rock or country is 45%

From the circle graph, we have the following parameters:

Rock = 27%.

Hip Hop = 28%

Jazz = 19%.

Country = 18%

Other = 14%

The percentage that choose rock or country is then calculated as:

Rock or Country = 27% + 18%

Rock or Country = 45%

Hence, the percentage that choose rock or country is 45%

Answers

In the sample has a mean of m=90 and each score in the sample is multiply by 5 and you want to calculate the mean for the new distribution, you only have to multiply the mean (m=90) by 5.

Then:

m= 90x5
m=450

Therefore, the answer is: The mean for the new distribution is 450 (m=450).

Final answer:

When each score in a sample is multiplied by a constant, the mean of the new distribution will also be multiplied by that constant, resulting in a new mean value of 450.

Explanation:

The mean of a sample is a measure of the average value of the data points in that sample.

When each score in a sample is multiplied by a constant, like 5 in this case, the resulting mean of the new distribution will also be multiplied by that constant.

In this scenario, since each score is multiplied by 5, the mean of the new distribution will be 5 times the original mean, giving a new mean of 450.

The simplest form of square root of eighty can be written as a times square root of b, where a

Answers

sqrt(80 ) = sqrt (16 * 5) = 4 sqrt(5)
a = 4
b = 5 I'm guessing.

What is the following quotient? sqrt 120 / sqrt 30

Answers

are you asking the square root after you divide
cuz if so when you divide 120/30 you get 4 and the square root of 4 is 2

Answer:

[tex]2[/tex]

Step-by-step explanation:

we have

[tex]\frac{\sqrt{120}}{\sqrt{30}}[/tex]

we know that

[tex]\frac{\sqrt{120}}{\sqrt{30}}=\sqrt{\frac{120}{30}}=\sqrt{4} =2[/tex]

What is the greatest common factor of the polynomial's terms? 14a3b4−7ab7+21a2b

Answers

The Answer is 7(ab).

I did the quiz.

Answer: 7ab

Step-by-step explanation:

The given polynomial : [tex]14a^3b^4-7ab^7+21a^2b[/tex]

The terms of the above polynomial can be written as :

[tex]14a^3b^4=(7\times2)a^{2+1}b^{3+1}=(7\times2)a^2(a)b^3b\\\\-7ab^7=-7ab^{6+1}=-7ab^6(b)\\\\21a^2b=(7\times3)a^{1+1}b=(7\times3)a(a)b[/tex]

Now, we can see that the greatest common factor of the polynomial's terms= [tex]7ab[/tex]

please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

We can solve this question with an equation. Knowing that the numbers in the sequence are EVEN, we know that they are two apart. So...

x + (x+2) + (x + 4) + (x + 6) + (x + 8) = 310

Combine like terms and you'll get this:

5x + 20 = 310

Using subtraction of equality:

5x = 290

Using division of equality:

x = 58

NOW, the question isn't asking for the value of x but the value of the 3rd number in the sequence. Go back to the original equation and plug in x to the 3rd number.

the 3rd number = x + 4 = 58 + 4 = 62

Voila! Hope this helps!

The sum of 4 interior angles of a pentagon is 402. Find the measure of the fifth interior angle.

108
62
138
42

Answers

complete interior angle = 540

5th angle = 540 - 402 = 138

your answer is 138 because u have to divide the 4th interior by the fith and plug in 458

Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm, is a right triangle?

Answers

Answer:

Let first side= 5 cm

second side= 12 cm

third side = 13 cm

To prove this triangle to be right angle triangle, we need to prove Pythagoras Theorem

[tex]5^{2}[/tex]=25

[tex]12^{2}[/tex]=144

[tex]13^{2}[/tex]=169

169= 25+144

169=169

According to Pythagoras theorem ,

[tex]p^{2}[/tex]+[tex]b^{2}[/tex]=[tex]h^{2}[/tex]

since, it follows Pythagoras theorem,

Hence, it is a Right angle Triangle

HELP!!!!!!!!!!!!!
To solve the equation 3x−2=4x−1 , Veronica graphs the functions f(x)=3x−2 and g(x)=4x−1

on the same set of coordinate axes.

Which statement describes the solution of the equation 3x−2=4x−1?

(A) The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.

(B) The solution of the equation cannot be found graphically. Veronica should solve the equation algebraically.

(C) The solution of the equation is the y-coordinate of the ordered pair where the graphs of the two functions intersect.

(D) The solution of the equation is the y-intercept of the linear equations.

Answers

we have that

f(x)=3x-2

g(x)=4x-1

3x-2=4x-1-------------> 4x-3x=-2+1--- > x=-1

find the value of f(x) or g(x) for x=-1

f(x)=3x-2 -------> f(-1)=3*(-1)-2 ------> f(-1)=-5

the solution is the point (-1,-5)

using a graph tool

see the attached figure

the answer is

case (A) The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.

Angle 2 and angle 3 are vertical angles. true or false

Answers

Answer: If you don't know the answer don't put one down but i do believe the answer is false.

Step-by-step explanation:

Final answer:

The statement 'Angle 2 and Angle 3 are vertical angles' can be true depending on their position, as vertical angles are those directly opposite from each other at the intersection of two lines.

Explanation:

The question is asking about vertical angles. Vertical angles are pairs of non-adjacent angles formed when two lines intersect. This means they are the angles that are directly opposite from each other where the two lines intersect. So if Angle 2 and Angle 3 are directly opposite each other at the point where two lines cross, then they are indeed vertical angles. So, the statement 'Angle 2 and Angle 3 are vertical angles' can be true depending on their placed positions.

Learn more about vertical angles here:

https://brainly.com/question/24460838

#SPJ2

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