The volume of a cone is 400π cm3. The height of the cone is 12 cm.

What is the length of the radius of the cone?

if the CD matures on her 14th birthday, that means 8 years after she got it, since she got it in her 6th birthday, so

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &8 \end{cases} \\\\\\ A=6000\left(1+\frac{0.07}{2}\right)^{2\cdot 8}\implies A=6000(1.035)^{16}\implies A\approx 10403.92[/tex]

Answer: [tex]56.25\pi[/tex]

Step-by-step explanation:

The circumference of a circle can be found using [tex]d\pi[/tex], where d is the diameter. In this case, we can clearly see the diameter is 15.

Next, we must find the radius as the formula for the area of a circle is [tex]\pi r^2[/tex]

The radius is half of the diameter. [tex]\frac{15}{2} =7.5[/tex]

Now sub in this value for the formula of the area of a circle

[tex]\pi r^2\\\\\pi (7.5)^2\\\\56.25\pi[/tex]

Answer:

56.25[tex]\pi[/tex]

Step-by-step explanation:

circumference=2[tex]\pi r[/tex]

15[tex]\pi[/tex]=2[tex]\pi r[/tex]

r=7.5

Area=[tex]\pi r^{2}[/tex]

       =[tex]\pi * 7.5^{2}[/tex]

       = 56.25[tex]\pi[/tex]

Answer:

1/5

Step-by-step explanation:

Answer:

75 ft³ for K12

Answer:

Why is it so important to know the area of wrapping paper it's just paper?

But anyways the answer is b 521 cm

Step-by-step explanation:

Answer:

b= -1/2

Step-by-step explanation:

-2/4 is simplified to -1/2 as the y-intercept

y= -4x - 1/2

Answer: = 3 seconds

Step-by-step explanation: combine the like terms Hope it helps !!

To simplify: 8s - 11s + 6s. Simplify the like terms by combining them

Simplifying 8s - 11s + 6s will give 3s.

Given,

8s - 11s + 6s

Now,

Expression : 8s-11s+6s

To simplify the expression combine like terms. So, all the terms consists of variable s.

Combine all terms having same sign,

So,

Firstly apply addition

8s + 6s

= 14s

Now,

Apply subtraction,

14s - 11s

= 3s

Therefore the simplified version is 3s.

Know more about expressions,

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The red figure is the original and the green the dilation. We know this because the dilated points are marked with '.

Therefore, we can see that the dilation is a reduction of the original figure. The figure got smaller in size after the dilation.

To find the scale factor, we'll need to look at a few of the points before and after the dilation.

A = (-4, 4)

A' = (-2, 2)

C = (0, 4)

C' = (0, 2)

---The scale factor will be the same on all the points, which is why I have selected only 2 sets of points to look at.

Now, we can figure out the scale factor by thinking about how -4 got to -2, how 4 got to 2. In this case, it is simply dividing by 2. The scale factor must be in multiplication, so we cannot use division in reporting the scale factor, it must be a fraction.

2 / 4 = 1 / 2

The scale factor, therefore, is 1/2.

Hope this helps!

Answer:

a) A reduction.

b) 0.5 or 1/2

Step-by-step explanation:

a) The new points are indicated by the ' next to the letters. By observing the graph, we can see that new points have lessened, and therefore shrank the dialtion, so it is a reduction.

b) On each point, it is reducted by 0.5.

Point A went down from 4 to 2, which is half of 4.

Point B went down from -2 to -1, which is half of -2.

Point C went down from 4 to 2, which is half of 4.

Point D went down from 8 to 4, which is half of 8.

hope this helps!

The expression that best represents the value of pi is 53/d.

Pi can be described as the ratio of the circumference of a circle to its diameter. The circumference of the patio is the distance round the patio. The formula that can be used to represent the circumference of the patio is πD

53 = πD

π = 53/d

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Multiply the price of each by the quantity purchased, add those together, then multiy the total by the sales tax.

Total = 1.05(3.99p + 2.50b)

Explanation:

8 people picked comedy out of 14+8+2+4 = 28 people total.

8/28 = (4*2)/(4*7) = 2/7 is the probability of randomly selecting someone who picked comedy as their favorite.

Answer:

Not entirely sure but im sure its no. 2

Step-by-step explanation:

Answer:

I think it's 2

Step-by-step explanation:

The height of the pole from the ground is 19.60 feet round to the nearest hundredth.

To find the lenght of longest side in right angle triangle, the Pythagoras theorem is used.

According to this theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.

A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole.

A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h.  Thus, the length of side of h by the Pythagoras theorem can be given as,

[tex]h^2=22^2-10^2\\h=\sqrt{484-100}\\h=\sqrt{384}\\h=19.60\rm\; ft[/tex]

Thus, the height of the pole from the ground is 19.60 feet round to the nearest hundredth.

Learn more about the Pythagoras theorem here;

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Answer:

  27 units

Step-by-step explanation:

A midpoint divides a line segment into two congruent parts. K being the midpoint of segment JL means ...

  JK = KL

  8x +11 = 14x -1 . . . . . substitute given expressions

  12 = 6x . . . . . . . . add 1 -8x

  2 = x . . . . . . . . divide by 6

Then the length of JK is ...

  8x +11 = 8(2) +11 = 27

JK is 27 units long.

_____

Additional comment

KL = JK = 27 units

JL = 2(27 units) = 54 units

Answer:

First Blank: “controlled” Second Blank: "a Different" Third Blank: "the same" Last Blank: "Height of the ramp"

Step-by-step explanation:

Answer:

x is what????

Step-by-step explanation:

Answer:

dimensions are 51x91

Step-by-step explanation:

Assuming that the gym is rectangular in shape, then...

l*w=4641

and 2l+2w=284

We have two variables and two equations so to solve this we plug one equation into another.

Solve for one variable:

l*w=4641

w=4641/l

Plug into the other equation...

2l+2(4641/l)=284

Solve

l*(2l+9282/l)=284

2l^2+9282=284l

2l^2-284l+9282=0

Factor the trinomial:

2(l−51)(l−91)=0

l−51=0 or l−91=0(Set factors equal to 0)

l=51 or l=91

now, lets plug it into one of the equations to find w

51*w=4641

w=91, l=51

or...

91*w=4641

w=51, l=91

Answer:

91 ft × 51 ft

Step-by-step explanation:

while the other answer is basically correct, it makes a to at the beginning of the calculation (but the continues correctly).

and it assumes you can find the right factoring of the expression.

so, I will show you here how to generally solve this, even if you cannot find the right factorization :

l×w = 4,641 ft²

w = 4641/l

2l + 2w = 284

2l + 2(4641/l) = 284

2l + 9282/l = 284

2l² + 9282 = 284l

2l² - 284l + 9282 = 0

to make things easier let's divide everything by 2

l² - 142l + 4641 = 0

the general solution to a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = l

a = 1

b = -142

c = 4641

l = (142 ± sqrt((-142)² - 4×1×4641))/(2×1) =

= (142 ± sqrt(20,164 - 18,564))/2 =

= (142 ± sqrt(1600))/2 = (142 ± 40)/2 = 71 ± 20

l1 = 71 + 20 = 91

l2 = 71 - 20 = 51

w1 = 4641/91 = 51

w2 = 4641/51 = 91

so, they are interchangeable (it does not matter which we call length and which width).

the dimensions are 91 ft × 51 ft

Answer:

[tex]\frac{8}{32}[/tex]

Step-by-step explanation:

2×4=8

Caron are a total of 8 slices.

8×4=32

There were 32 slices between all 4 pizzas.

Answer:

3000

because you need to dived it

Answer:

5n=c

Step-by-step explanation:

the equation 5n=c can represent the total cost Hong would have paid for the notebooks because given that each notebook costs $5, you would multiply 5 by the number of notebooks (n) that Hong would be purchasing, which would bring you to the cost (c) of the notebooks all together

sorry for the delay. hope this helps

To change a decimal to a percentage, all that we have to do is multiply the decimal by 100 (or move the decimal point to the right two places).

1.276 x 100 = 127.6

Percentage: 127.6%

Hope this helps!

Answer:

y= |x-3|+ |x+2|-|x-5|; x<-2

y=-2

Answer:

the figure is a rectangle with a side of trapezium

according to my calculation the answer is

196m²

Area of trapezium =½(10+8)×4=36

Area of rectangle =10×16=160

add=160+36

Answer:

The circumference (C) of a circle is found by the equation C = 2*[tex]\pi[/tex]*radius

There is a second relationship between [tex]\pi[/tex] and circles.  That of the area (A) of the circle which is found by the formula A = [tex]\pi*radius^{2}[/tex]

Step-by-step explanation:

Answer:

This question is asking for you to determine if the tables represent linear functions, functions in y=mx+b form, and to find the equation for the line.

If something is a linear function, each of the input values will have it's own corresponding y value, therefore c cannot be linear, as -1 and 1 both have 10 as the output.

I hope this helps, but if you need more clarification, please tell me in the comments!

Explanation:

You can use the definition of similarity to show that corresponding sides are proportional. You cannot prove anything about the proportionality of non-corresponding sides.

1. BD║CE . . . . given

2. ∠A≅∠A . . . . reflexive property of congruence

3. ∠ABD≅∠ACE . . . . corresponding angles theorem

4. ΔABD ~ ΔACE . . . . AA similarity postulate

5. BD/CE = AD/AE . . . . definition of similarity

_____

Additional comment

Length DE is related to BC in the same way that AD is related to AB. There is no way to prove the ratio you show in your problem statement. You can show that ...

  DE/AE = (CE -BD)/CE = 1 -(BD/CE) . . . . the difference is proportional to the corresponding longer side

Answer:

yes, it is

Step-by-step explanation:

10 = 4(2) + 2

10 = 8 +2

10 = 10

10  = 2 + 8

10 = 10

Answer:

The answer is yes

*View the attached graph to check your answer graphically.*

Step-by-step explanation:

y = 4x + 2

y = x + 8

For this problem, I will be using substitution, since the second equation is already in the slope-intercept form.

First, I will substitute the second equation, for y, in the first equation:

y = 4x + 2

y = x + 8

x + 8 = 4x + 2

Next, subtract 4x from both sides to isolate x:

x + 8 = 4x + 2

-4x      -4x

-3x + 8 = 2

Then, subtract 8 from both sides:

-3x + 8 = 2

     - 8    - 8

-3x = -6

Now, divide both sides by -3:

-3x = -6

/-3    /-3

x = 2

Now, we find the value of y by substituting 2 for x:

y = 4x + 2

y = 4(2) + 2

y = 8 + 2

y = 10

(x, y) ==> (2, 10)

Therefore, yes (2,10) is a solution to this system of equations.

*View the attached graph to check your answer graphically.*

Hope this helps!

Using an exponential function, it is found that the amounts deposited at the end of each month are given by:

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, we have that A(0) = 100, r = 0.1, hence the equation for the amount deposited after t months is:

[tex]A(t) = 100(1.1)^t[/tex]

Then, for each of the first four months:

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