Jim was thinking of a number. Jim doubles it, then adds 19 to get an answer of 70.1. What was the original number?

Answer:

60[tex]\pi[/tex] m³

Step-by-step explanation:

Use the cone volume formula, V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

If the diameter is 12 m, the radius will be 6 m.

Plug in the height and radius into the formula, and solve:

V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

V = [tex]\pi[/tex](6²)[tex]\frac{5}{y}[/tex]

V = [tex]\pi[/tex](36)[tex]\frac{5}{3}[/tex]

V = 60[tex]\pi[/tex]

So, the volume of the cone is 60[tex]\pi[/tex] m³

Answer:

Elisa y Romina comieron 5/16 de la pizza completa cada una.

Step-by-step explanation:

Dado que Elisa y Romina tienen 5/8 de pizza y decidieron dividírsela en partes iguales, para determinar qué parte de la pizza completa le tocó a cada una se debe realizar el siguiente calculo:

(5/2) / 8 = X

2.5 / 8 = X

0.3125 = X

0.3125 = 5/16

Por lo tanto, Elisa y Romina comieron 5/16 de la pizza completa cada una.

Answer:

See Below.

Step-by-step explanation:

Problem 1)

We want to verify that:

[tex]\displaystyle \left(\cos(x)\right)\left(\cot(x)\right)=\csc(x)-\sin(x)[/tex]

Note that cot(x) = cos(x) / sin(x). Hence:

[tex]\displaystyle \left(\cos(x)\right)\left(\frac{\cos(x)}{\sin(x)}\right)=\csc(x)-\sin(x)[/tex]

Multiply:

[tex]\displaystyle \frac{\cos^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]

Recall that Pythagorean Identity: sin²(x) + cos²(x) = 1 or cos²(x) = 1 - sin²(x). Substitute:

[tex]\displaystyle \frac{1-\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]

Split:

[tex]\displaystyle \frac{1}{\sin(x)}-\frac{\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]

Simplify:

[tex]\csc(x)-\sin(x)=\csc(x)-\sin(x)[/tex]

Problem 2)

We want to verify that:

[tex]\displaystyle (\csc(x)-\cot(x))^2=\frac{1-\cos(x)}{1+\cos(x)}[/tex]

Square:

[tex]\displaystyle \csc^2(x)-2\csc(x)\cot(x)+\cot^2(x)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]

Convert csc(x) to 1 / sin(x) and cot(x) to cos(x) / sin(x). Thus:

[tex]\displaystyle \frac{1}{\sin^2(x)}-\frac{2\cos(x)}{\sin^2(x)}+\frac{\cos^2(x)}{\sin^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]

Factor out the sin²(x) from the denominator:

[tex]\displaystyle \frac{1}{\sin^2(x)}\left(1-2\cos(x)+\cos^2(x)\right)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]

Factor (perfect square trinomial):

[tex]\displaystyle \frac{1}{\sin^2(x)}\left((\cos(x)-1)^2\right)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]

Using the Pythagorean Identity, we know that sin²(x) = 1 - cos²(x). Hence:

[tex]\displaystyle \frac{(\cos(x)-1)^2}{1-\cos^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]

Factor (difference of two squares):

[tex]\displaystyle \frac{(\cos(x)-1)^2}{(1-\cos(x))(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]

Factor out a negative from the first factor in the denominator:

[tex]\displaystyle \frac{(\cos(x)-1)^2}{-(\cos(x)-1)(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]

Cancel:

[tex]\displaystyle \frac{\cos(x)-1}{-(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]

Distribute the negative into the numerator. Therefore:

[tex]\displaystyle \frac{1-\cos(x)}{1+\cos(x)}=\displaystyle \frac{1-\cos(x)}{1+\cos(x)}[/tex]

Answer:

do you have an attatchment or guide i can use to answer this?

Step-by-step explanation:

Transposing a,

[tex]d + a = h \\ a = h - d[/tex]

Answer:

$14.43¢

Step-by-step explanation:

We are given; [tex]1\frac{2}{5}[/tex] pounds, 1 pound = $4.20 and [tex]2\frac{1}{4}[/tex] pounds,1 pound = $3.80 that Andrea bought.

Now we need to find her total cost. To do that, we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert [tex]1\frac{2}{5}[/tex] to a decimal. It is 1.4. Now we can set up a graph.

Avocados

[tex]\frac{4.2}{1}=\frac{x}{1.4}[/tex]

Switch sides

[tex]\frac{x}{1.4}=\frac{4.2}{1}[/tex]

Apply rule: [tex]\frac{a}{1}=a[/tex]

[tex]\frac{x}{1.4}=4.2[/tex]

Multiply both sides by 1.4

[tex]\frac{1.4x}{1.4}=4.2\cdot \:1.4[/tex]

Simplify

[tex]x=5.88[/tex]

So, her cost for avocados is $5.88¢

Now we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert [tex]2\frac{1}{4}[/tex] to a decimal. It is 2.25. Now we can set up a graph.

Asparagus

[tex]\frac{3.8}{1}=\frac{x}{2.25}[/tex]

Switch sides

[tex]\frac{x}{2.25}=\frac{3.8}{1}[/tex]

Apply rule : [tex]\frac{a}{1}=a[/tex]

[tex]\frac{x}{2.25}=3.8[/tex]

Multiply both sides by 2.25

[tex]\frac{2.25x}{2.25}=3.8\cdot \:2.25[/tex]

Simplify

[tex]x=8.55[/tex]

So, her cost for asparagus is $8.55¢

Total cost

Now that we have found out how much both of the fruits Andrea bought costs, we need to sum it up (meaning add it) to find the total cost:

$5.88¢ + 8.55¢ =

5.88 + 8.55 = 14.43

Therefore, Andrea's total cost of the fruits is $14.43¢

Answer:

f(g(x)) = 8x² + 18x - 8

Step-by-step explanation:

Substitute x = g(x) into f(x) , that is

f(g(x))

= f(- 2x - 1)

= 2(- 2x - 1)² - 5(- 2x - 1) - 15

= 2(4x² + 4x + 1) + 10x + 5 - 15

= 8x² + 8x + 2 + 10x - 10

= 8x² + 18x - 8

Answer:

42y-30

Step-by-step explanation:

here you go

Answer:

when a is negative, the parabola opens downward

Step-by-step explanation:

5 marbles.

We first need to find how many marbles we have in total.

8 marbles * 5 boys = 40 marbles.

These 40 marbles will now be divided by 8, since we are taking the total amount of marbles we have and separating them into 8 different piles.

40/8 = 5

There will be 5 marbles in each heap.

Answer:

Alright so youd havee to right the terms in order which should be easy then your done! Hope this helped!

Step-by-step explanation:

Step-by-step explanation:

Therefore the third side should be less than 12+15 = 27cm

And also the third side cannot be less than the difference of the two sides

Therefore, the third has to be more than 15-12 = 3cm

Thus, the third side could be the length more than 3cm and less than 27cm.

Answer:

y(t) = 720e^0.3466t

y = 2036.6288

Step-by-step explanation:

The exponential relation :

y = Ae^kt

A = initial value ; y = final value ; r ; k = exponential rate, t = time

At t = 0

y = 720e^0 ; y = 720

At t = 2 ; y = 720e^2k

1440 = 720e^2k

1440/720 = e^2k

2 = e^2k

Take the In of both sides

0.6931471 = 2k

k = 0.6931471 / 2

k = 0.3466

Hence, equation becomes :

y = 720e^0.3466t

After 3 hours ;

t = 3

y = 720e^0.3466*3

y = 720e^1.0398

y = 720 * 2.8286512

y = 2036.6288

Answer:

The answer is 12 feet. .

Step-by-step explanation:

You have to multiply 3/4 or 0.75 by the number of tiles. So you would go, 0.75 x 10 and then 0.75 x 6 and add the answers together.

Answer:

For the first one its: Volume = 402.12in³

For the second one its: Volume = 201.0619 in³

Step-by-step explanation:

For the first one work:

Volume = 3.1416 x 42 x 8

= 3.1416 x 16 x 8

For the second one work:

Volume = 3.1416 x 42 x 4

= 3.1416 x 16 x 4

Answer:

the formula is : V=πr2h

the volume of the first cylinder is 402.12cm³ and the second is 201.06cm³ (these answers are rounded to two decimal places)

Step-by-step explanation:

Volume is pi times the radius squared (which is 4 in both these cylinders) times the height of the cylinder which is 8 in the first cynlinder and 4 in the second.

Answer:

The value of P(B) = 0.5

Step-by-step explanation:

Given:

Value of P(A and B) = 0.20

Value of P(A|B) = 0.40

Find:

The value of P(B)

Computation:

P(A and B) = P(A|B) x P(B)

By putting value of P(A and B)  and P(A|B)

⇒ 0.20 = 0.40 x P(B)

⇒ The value of P(B) = 0.20 / 0.40

⇒ The value of P(B) = 20 / 40

⇒ The value of P(B) = 1 / 2

The value of P(B) = 0.5

Answer:

2 1/3 and 1 1/6

Step-by-step explanation:

opposite pairs of triangles are congruent.

Answer:

Opposite pair of triangles are congruent

Step-by-step explanation:

Because in parallelogram

So.opposite pair of triangles are congruent

Answer:5.7

Step-by-step explanation:

Answer:

The answer would be exactly 250 messages.

0.50 × x = $125

125÷ 0.50=250

Hope this helps!

Answer:

942 6/7 cm²

Step-by-step explanation:

Since O = Center of bigger circle, OA = Radius of bigger circle.

∴ Area of smaller circle - Area of bigger circle = Area of shaded part.

∴ Area of smaller circle = 22/7 × 10²

                                       = 22/7 × 100

                                       = 2200/7

                                       = 314 2/7 cm²

∴ Area of bigger circle = 22/7 × 20 ²

                                      = 22/7 × 400

                                      = 1257  1/7 cm²

∴ Area of shaded part = 1257 1/7 - 314 2/7

                                     =  942 6/7 cm²

Answer:

true

Step-by-step explanation:

Answer:

false because 140.23 is not less then 140.203

Answer:

the answer interm of pie will be 18π

Step-by-step explanation:

circumference of circle is given as πD where D is the diameter , we have been given diameter as 18 , hence c=πD will be 18π

Answer:

I think A or D but i'm stuck on D

Step-by-step explanation:

Answer:

D because if you multiply all the other brands to get a 100oz they are more expensive/ high than D.

Answer:

when u distribute a number you are basically giving the number off and multiplying other factors by that number

Step-by-step explanation:

3(x+4) ( distribute the 3 ) so u would multiply the 3 by both factors ( the x and the 4) getting 3x+12

Answer:  2 heads

Step-by-step explanation:

First, write the experimental probability as a fraction in simplest form.

P(heads)

=

heads

total

=

heads

heads+tails

=

4

4+2

=

4

6

=

2

3

The experimental probability is

2

3

.

We can predict the outcome of the second set of trials by assuming that the ratio will be the same as in the first set of trials. Write a proportion by setting the two ratios equal to each other, then solve.

2

3

=

n

3

2

3

(33)

=

n

3

(33) Multiply both sides by (33)

23

= 3n Simplify

6

= 3n Simplify

2

= n Divide both sides by 3

Based on experimental probability, Latrell should expect 2 of the next 3 flips to come up heads.

Questions

answered

16

Time

elapsed

00 22 05

HR MIN SEC

SmartScore out of 100

44

Need a break?

Answer:

It's C :D

Step-by-step explanation: