A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of `pi`.)
A.
452.16 cm3
B.
840.54 cm3
C.
1,055.04 cm3
D.
1,456.96 cm3

Answer:

True for all b

Interval notation; (-∞, ∞)

Step-by-step explanation:

We have been given the following inequality;

26+6b>2(3b+4)

The first step is to open the brackets on the right hand side;

26+6b>6b+8

26-8>6b-6b

18>0

Since 18 is actually greater than 0, the solution set to the inequality is;

True for all b.

Here the answer is in this picture

Answer:

1. Ratio is 1 : 3

Step-by-step explanation:

1. The average salary for a professional baseball player in the United States can be approximated by = [tex]283(1.2)^{t}[/tex]

Where t = 0 represents the year 1984.

Salary in year 1988 = [tex]283(1.2)^{4}[/tex]  [t = 4 years]

Salary in year 1994 = [tex]283(1.2)^{10}[/tex] [t = 10 years]

Ratio of the average salary in 1988 to the average salary in 1994 = [tex]\frac{283(1.2)^{4}}{283(1.2)^{10}}=\frac{(1.2)^{4}}{(1.2)^{10}}[/tex]

= [tex]\frac{1}{(1.2)^{10-4}}=\frac{1}{(1.2)^{6}}[/tex]

= [tex]\frac{1}{3}[/tex]

2. Corrected form

[tex]\frac{x^{-9} }{x^{-3}}[/tex]

= [tex]x^{-9+3}[/tex][since [tex]\frac{a^{1}}{a^{1}}=a^{1-1}=a^{0}=1[/tex]]

= [tex]x^{-6}[/tex]

= [tex]\frac{1}{x^{6}}[/tex]  [ since [tex]\frac{1}{a^{1}}=a^{-1}[/tex] ]

Now we can compare the corrections and errors in the highlighted form.

Expression needs correction

[tex]\frac{x^{-9} }{x^{-3}}[/tex]

= [tex]x^{-9-3}[/tex]

=  [tex]x^{-12}[/tex]

= [tex]\frac{1}{x^{-12}}[/tex]

If you mean -10.0 - (-2.3) then the answer is -7.7

Final answer:

To subtract -10.0 - (-2.3), you change the subtraction of the negative number to addition and calculate -10.0 + 2.3, resulting in -7.7.

Explanation:

Subtracting a negative number from another negative number is equivalent to adding the absolute value of the number being subtracted. To solve the given problem, we can visualize it as negative 10.0 plus 2.3.

The subtraction of two negative numbers can be transformed into an addition problem by remembering that subtracting a negative is the same as adding a positive. Here is how you would calculate it step-by-step:

Start with the first number: -10.0.

Change the subtraction to addition because subtracting a negative is like adding a positive.

Add the absolute value of the second number: +2.3.

Combine both numbers: -10.0 + 2.3 = -7.7.

So, negative 10.0 minus (negative 2.3) equals -7.7.

Answer:

x =34

Step-by-step explanation:

The sum of the angles of a triangle add to 180

The two angles in the middle are vertical angles to they are both 56 degrees

56+x+90 = 180

Combine like terms

146 +x = 180

Subtract 146 from each side

146-146 +x = 180-146

x = 34

ANSWER

[tex]x \: < \: - 8[/tex]

EXPLANATION

The given inequality is

[tex]3 - (2x - 5) \: < \: - 4(x + 2)[/tex]

Expand:

[tex]3 - 2x + 5 \: < \: - 4x - 8[/tex]

Group similar terms, to obtain:

[tex] - 2x + 4x\: < \: - 8 - 5 - 3[/tex]

Combine similar terms:

[tex]2x\: < \: - 16[/tex]

Divide both sides by 2 to get,

[tex]x \: < \: - 8[/tex]

Answer:

The baton will not fit in the rectangular box

Step-by-step explanation:

step 1

Find the diagonal of the base of the  rectangular base and then compare with the length of the baton

Applying the Pythagoras Theorem

Let

x ----> the length of the diagonal base of rectangular box

we know that

[tex]x^{2}=13^{2}+35^{2} \\ \\x^{2} =1,394\\ \\x= 37.3\ in[/tex]

[tex]38\ in > 37.3\ in[/tex]

therefore

The baton will not fit in the rectangular box

Answer:

Step-by-step explanation:

f(x) + n - translation n units up

f(x) - n - translation n units down

f(x + n) - translation n units to the left

f(x - n) - translation n units to the right

===========================================

g(x) = 21

translation 7 units down: g(x) - 7 = 21 - 7 = 14

Moving a graph or function vertically down is as simple as subtracting the number of units you wish to move from the original function. The function g(x) = 21 moved 7 units down resulting in h(x) = 14.

A vertical translation in a graph is a shift in the graph either up or down along the y-axis. In the case of the function g(x) = 21, which is a horizontal line at y = 21, a vertical translation 7 units down would yield the new function h(x) = 21 - 7 = 14. Therefore, the equation that represents this translation is h(x) = 14.

https://brainly.com/question/12463306

#SPJ3

Answer:

[tex]LW=17.5\ units[/tex]

Step-by-step explanation:

we know that

In the right triangle LAY

Find the measure of side LY applying the Pythagoras Theorem

[tex]LY^{2} =3.5^{2}+ 7.0^{2} \\ \\ LY^{2} =61.25\\ \\ LY=\sqrt{61.25}\ units[/tex]

Find the cosine of angle ALY

[tex]cos(<ALY)=\frac{LA}{LY}[/tex]

[tex]cos(<ALY)=\frac{3.5}{\sqrt{61.25}}[/tex] -----> equation A

In the right triangle LWY

[tex]cos(<ALY)=\frac{LY}{LW}[/tex]

[tex]cos(<ALY)=\frac{\sqrt{61.25}}{LW}[/tex] -----> equation B

equate equation A and equation B and solve for LW

[tex]\frac{3.5}{\sqrt{61.25}}=\frac{\sqrt{61.25}}{LW}[/tex]

[tex]LW=(\sqrt{61.25})(\sqrt{61.25})/3.5[/tex]

[tex]LW=17.5\ units[/tex]

Answer:

There

Step-by-step explanation:

Answer:

The angles are 65° and 115°

Step-by-step explanation:

Let

x,y ----> the two side interior angles of two parallel lines

we know that

x+y=180° ----> equation A

x-y=50° ----> equation B

Adds equation A and equation B

x+x=180°-50°

2x=130°

x=65°

Find the value of y

x+y=180° -----> 65°+y=180° ----> y=180°-65°=115°

therefore

The angles are 65° and 115°

Answer:

the answer is c

Step-by-step explanation:

Answer:

Between A and B : Decreasing

Between B and C : Increasing

Between C and D : Decreasing

Between D and E : Constant

Step-by-step explanation:

If graph goes downward between two points then it indicates function is decreasing.

If graph goes upward between two points then it indicates function is increasing.

If graph goes parallel to the x-axis between two points then it indicates function is constant.

Then final answer is given by:

Between A and B : Decreasing

Between B and C : Increasing

Between C and D : Decreasing

Between D and E : Constant

Answer:

X=57/37 , X=1.540

Answer:

Step-by-step explanation:

Euler's formula is

V - E + F = 2

Givens

V = 15

E = 15

F = ?

Solution

15 - 15 + F = 2

F = 2

I'm not sure this makes sense, but it is what the formula gives you.

The student can calculate the number of edges in a polyhedron by using Euler's formula for polyhedra. Given the number of faces and vertices, both being 15, we solve for edges and find that the polyhedron would have 28 edges.

The student wants to calculate the missing number of edges in a geometrical shape given the number of faces and vertices. This can be solved in mathematics using Euler's formula for polyhedra which is Faces + Vertices - Edges = 2. In the current situation, where the shape has 15 faces and 15 vertices, you can solve for edges. Inserting these values into Euler's equation yields: 15 (faces) + 15 (vertices) - Edges = 2. As a result, Edges = 15 + 15 - 2 = 28 edges.

https://brainly.com/question/34369062

#SPJ12

ANSWER

B.[tex] (x + 6)^{4} [/tex]

EXPLANATION

The given functions are:

f(x)=x+6

and

[tex]g(x)= {x}^{4} [/tex]

We want to find

[tex]g(f(x)) = g(x + 6)[/tex]

This is the composition of functions, where one function becomes the input of the second function.

We plug in x+6 into the expression for g(x) to obtain,

[tex]g(f(x)) = (x + 6)^{4} [/tex]

The correct answer is B.

43/60 would be the probability

The required estimation is [tex]P(A)=\frac{43}{60}[/tex]

Important information:

Number of observation=60

Number of expected outcomes =43

Probability: Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed between zero and one. So, the formula probability is,

P(A)=Expected observation/number of observations

Now, substituting the given values into the above formula we get,

[tex]P(A)=\frac{43}{60}[/tex]

Learn more about the topic probability:

https://brainly.com/question/14642847

Answer:

-2040

Step-by-step explanation:

[tex]S_n=a_1\dfrac{r^n-1}{r-1} \qquad\text{for first term $a_1$ and common ratio r}\\\\S_8=-8\dfrac{2^8-1}{2-1}=-2040[/tex]

The sum of the first 8 terms is -2040.

Answer:

B. the 15,559 residents

Step-by-step explanation:

I just took the final exam

ANSWER

[tex]x = 11[/tex]

EXPLANATION

According to the exterior angle theorem, the sum of remote interior angles equal an exterior angle.

This implies that,

[tex](7x + 7) \degree + 66 \degree =(1 2x + 18) \degree[/tex]

We group the similar terms to get:

[tex]7 + 66 - 18 = 12x - 7x[/tex]

[tex]55= 5x[/tex]

Divide both sides by 5.

[tex]x = \frac{55}{5} [/tex]

[tex]x = 11[/tex]

Answer:

I did this test. The answer to this question is c.multiply each side by 4

Step-by-step explanation:

Answer:

(5,-6)

Step-by-step explanation:

When you write the equation of a circle in the form

[tex](x-x_0)^2+(y-y_0)^2=r^2[/tex]

Then the center of the circle will be [tex](x_0,y_0)[/tex] and the radius will be [tex]r[/tex].

Answer:  The center of the given circle is (5, -6).

Step-by-step explanation:  We are given to find the center of the circle represented by the following equation :

[tex](x-5)^2+(y+6)^2-4^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the STANDARD equation of a circle with center (h, k) and radius r units is given by

[tex](x-h)^2+(y-k)^2=r^2.[/tex]

From equation (i), we have

[tex](x-5)^2+(y+6)^2=4^2\\\\\Rightarrow (x-5)^2+(y-(-6))^2=4^2.[/tex]

Comparing with the standard form, we get that the center of the given circle is (h, k) = (5, -6).

Thus, the center of the given circle is (5, -6).

Answer:

No answer

Step-by-step explanation:

I don't think this equation has an answer.

Normally, you'd try to combine like terms

3 3/4 = 2 + 3/4

3 3/4 = 2 3/4

3 and 3/4 is not equal to 2 and 3/4.

So, I believe this equation has no answer

Answer: $1,950 explanation: 1500 x 0.05 =75 75 x 6 years = 450. 1500+450=1950

assuming simple interest.

[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &6 \end{cases} \\\\\\ A=1500[1+(0.05)(6)]\implies A=1500(1.3)\implies A=1950[/tex]

Answer:

n > 2

Step-by-step explanation:

-10 − -3n > -4

-10 + 3n > -4

3n > 6

n > 2

Check our answer: if n = 3:

-10 − -3(3)

-10 − -9

-10 + 9

-1

-1 > -4

-10 - (-3n) > -4 ---> -10 + 3n > -4

^^^^ -3n became positive because a negative times a negative gives a positive

Step 1: Combine like terms

normal numbers go with normal numbers. This would be -10 and -4. To get -10 to the right side of the inequality you must add 10 to both sides

(-10 + 10) + 3n > (-4 + 10)

(0) + 3n > 6

3n > 6

Step 2: Isolate n by dividing 3 to both sides of the inequality

[tex]\frac{3n}{3} > \frac{6}{3}[/tex]

n > 2

Hope this helped!

on the twelfth day because 3-6-9-12 and 12

Billy will have both swimming and piano lessons on the same day every 12th day.

To determine when Billy will have both swimming and piano lessons on the same day, we need to find the least common multiple (LCM) of the two schedules. Billy has swimming lessons every 3rd day and piano lessons every 12th day.

The LCM of 3 and 12 is the smallest number that both 3 and 12 can divide into without leaving a remainder. The prime factorization of 12 is [tex](2^2 \times 3\))[/tex], and the prime factorization of 3 is simply 3 . To find the LCM, we take the highest powers of all prime factors that appear in the factorization of both numbers:

For 3: [tex]\(3^1\)[/tex]

For 12: [tex]\(2^2 \times 3^1\)[/tex]

The LCM is [tex]\(2^2 \times 3^1 = 4 \times 3 = 12\)[/tex].

Since the LCM of 3 and 12 is 12, Billy will have both lessons on the same day every 12th day. This is because every 12th day is a day when both his 3-day swimming lesson cycle and his 12-day piano lesson cycle align.

Answer:

x-1

Step-by-step explanation:

(3)(2)+5x-(5)(2)-4x+5-2

=6+5x-10-4x+5-2

=x-1

Answer:

-2x2+x+3

Step-by-step explanation:

you have to combine like terms

-5x2+ 3x2= -2x2

5x-(-4x)= x

5-2=3

-2x2+x+3

Answer:

It's B. 1/6^9

Step-by-step explanation:

It is simplified to 6^-9 which is equal to 1/6^9.

Answer:

2 cake donuts

Step-by-step explanation:

This is a question on probability, which means that we can find:

# of wanted outcomes/total outcomes.

Wanted outcomes: Vicky ate 3 cake donuts, so our value is 3.

Total outcomes: Vickey ate 3 + 4 + 8 = 15 donuts, so our value is 15.

Plug in: 3/15

Simplify: 1/5

So 1/5 of donuts Vicky eats will probably be cake donuts.

1/5 * 10 = 2

Answer:

No, The answer should be 240

Step-by-step explanation: