What is the volume of the cone?

What is the volume of the cylinder?

What is the volume of the sphere?

At the craft store discussed above, the clay cone is $12, the clay cylinder is $30, and the clay sphere is $28. Which is the best buy? Explain.

Hint: Which shapes gives you more clay for less money?

Answer:

[tex]\boxed{f[ g(3) ] = 673}[/tex]

Step-by-step explanation:

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

[tex]f(g(3))[/tex]

[tex]f(5(3)-2)[/tex]

[tex]f(15-2)[/tex]

[tex]f(13)[/tex]

[tex]f(13)=4(13)^2 -3[/tex]

[tex]f(13)=4(169) -3[/tex]

[tex]f(13)=676-3[/tex]

[tex]f(13)=673[/tex]

Answer:

f[g(3)] = 673

Step-by-step explanation:

I took the test

Answer:

Construction II

Step-by-step explanation:

Construct 3 perpendicular bisectors of the triangles sides; where they intersect is the point of concurrency. The distance from the point of concurrency to one of the vertices is the radius.

Answer: 5.79

36

16 cost

Step-by-step explanation:

Answer:  $1,077.50   or   $1,078.06 (see below)

Step-by-step explanation:

Since the interest is applied after 1 year and the debt was repaid in 8 months, no interest was accrued on the $2,550 loan.

Thus, the price of the tv is: $2,550 - $1,422.50 = $1,077.50

Note: If interest is charged for the 8 months (3/4 of a year), then the interest added to the loan amount is: 0.75(3/4) = $0.56

⇒ the the price of the tv is: $1,077.50 + $0.56 = $1,078.06

To find Angle A we use cosine

cos ∅ = adjacent / hypotenuse

From the question

The adjacent is 17

The hypotenuse is 38

So we have

cos A = 17/38

A = cos-¹ 17/38

A = 63.4

To find Angle C we use sine

sin ∅ = opposite / hypotenuse

From the question

The opposite is 17

The hypotenuse is 38

So we have

sin C = 17/38

C = sin-¹ 17/38

C = 26.57

Hope this helps you

I also got the answer 64/49.

:D

The fraction  [tex](\frac{7}{8})^{-2}[/tex] without an exponent can be written as  [tex]\frac{64}{49}[/tex].

To rewrite the fraction [tex](\frac{7}{8})^{-2}[/tex] without an exponent, we can apply the rule of reciprocals.

Reciprocal of a fraction a/b is given by b/a.

So, taking the reciprocal of  [tex](\frac{7}{8})^{-2}[/tex] , we get:

[tex](\frac{7}{8})^{-2}[/tex]  =[tex](\frac{8}{7})^{2}[/tex]

Now let us simplify the numerator and denominator:

[tex]=\frac{8\times 8}{7 \times 7}[/tex]

[tex]=\frac{64}{49}[/tex]

Therefore,  [tex](\frac{7}{8})^{-2}[/tex] can be rewritten as [tex]\frac{64}{49}[/tex].

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Answer:

y=-3x-10

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 85% pure fruit juice?

Answer: Let x be the number of pints of the first fruit juice (i.e 65%) and y be the number of pints of the second fruit juice (i.e 90%).

Since the total number of pints to make the 85% pure fruit juice is 80, it can be represented using the equation:

x + y = 80                              .                  .                 .    1)

Also, x pints of the first juice = 0.65x, y pints of the second juice = 0.9y and 80 pints of the mixture to be produced = 80(0.85) = 68. Therefore:

0.65x + 0.9y = 68               .                 .                  .        2)

We have to solve equation 1 and 2 simultaneously, first multiply equation 1 by 0.65 to get equation 3:

0.65x + 0.65y = 52            .                  .               .        3)

Subtract equation 3 from 2 and solve for y:

0.25y = 16

y = 16/0.25 = 64

y = 64 pints

Put y = 64 in equation 1:

x + 64 = 80

x = 80 - 64 = 16

x = 16 pints

Therefore 16 pints of the 65% pure fruit juice, and 64 pints of the 90% pure fruit juice is required to make 80 pints of 80% fruit juice.

Answer:

Afful is 21 and Naomi is 13.

Step-by-step explanation:

Let [tex]A[/tex] represent the age of Afful and [tex]N[/tex] represent the age of Naomi.

The sum of their ages is 34. In other words:

[tex]A+N=34[/tex]

In 5 years time, Afful will be two times the age of Naomi now. In other words:

[tex]A+5=2N[/tex]

Solve for the system. Substitute.

[tex]A+N=34\\A=34-N\\34-N+5=2N\\39=3N\\N=13\\\\A=34-N\\A=34-(13)\\A=21[/tex]

Afful is currently 21 and Noami is currently 13.

Answer:

Naomi=x

Afful=2x

In 5 years time= +5

So Naomi=x+5

and and Afful=2x+5

=x+5+2x+5=34

=3x+10=34

Subtract 10 on both sides

3x=24

Divide 3 on both sides

X=8

Check:

X=8

Naomi=16

In 5 years

=16+5=21

Naomi=8+5=13

13+21=34

Hope this helps

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

The perimeter = 2*length + 2 * width.

As the ratio is 3:2 the fraction 3 / (3 +2)  is used to find the length:

The measure of the 2 lengths = 3/ (3+2)  * 60

= 3/5 * 60

= 36 cm

So the measure of the length = 18 cm

So the measure of  the width = (60 - 36) / 2

= 24/2

= 12 cm.

Answer:

B. Te procedure for constructing the confidence interval is robust. The larger the sample size, the more resistance the mean. Therefore, the confidence interval is more robust.

Step-by-step explanation:

Misentered data illustrates the concept that if the sample size is larger it will be more resistance to mean. This means confidence interval is more robust. In statistics, robust is a modification of confidence interval. It refers to strength of statistical model. Robust statistics is resistant to errors in statistical model.

Answer:

Number of ways to chose bracelet = 2 ways

Step-by-step explanation:

Given:

Total number of bracelet = 3

Y is chosen first

Find:

Number of ways to chose bracelet

Computation:

Y is chosen first so remain number of bracelet is 2

So,

Number of ways to chose bracelet = !2

Number of ways to chose bracelet = 2 × 1

Number of ways to chose bracelet = 2 ways

Answer:

The correct option is;

More people prefer a beach vacation and a ski vacation than an adventure vacation

Step-by-step explanation:

From the data in the sample;

Table of values,                       Sample

Vacation,                               A                 B

Adventure,                            6                  1

Beach,                                   5                  6

Cruise,                                   70                72

Ski,                                         19                 21

Total,                                   100                 100

Therefore, we have that each member made or selected only on vaction option which gives;

The number of members that prefer a beach vacation and a ski vacation are;

Sample A  = 5 + 19 = 24 members

Sample B =  6 + 21 = 27 members

The number of members that prefer an adventure vacation are;

Sample A  = 6 members

Sample B =  1 members

Which shows that more people prefer a beach vacation and a ski vacation than an adventure vacation.

Answer:

The correct option is;

More people prefer a beach vacation and a ski vacation than an adventure vacation

Step-by-step explanation:

I just did the quiz .

Answer:

the angle will be 144

Step-by-step explanation:

All sides are the same length (congruent) and all interior angles are the same size (congruent).

To find the measure of the angles, you need to divide 1440 by  10 which = 144

If you are solving for the central angle then divide 360 by 10 which = 36

Answer:

b

Step-by-step explanation:

The sum appears to be

[tex]\displaystyle\sum_{n=0}^\infty(2n+1)x^n[/tex]

I'll assume you want to find out what function this sum converges to.

Let

[tex]f(x)=\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]

with -1 < x < 1. Differentiating gives

[tex]f'(x)=\dfrac1{(1-x)^2}=\displaystyle\sum_{n=0}^\infty nx^{n-1}=\sum_{n=1}^\infty nx^{n-1}=\sum_{n=0}^\infty(n+1)x^n[/tex]

So we have

[tex]\displaystyle\sum_{n=0}^\infty(2n+1)x^n=f'(x)+xf'(x)[/tex]

[tex]\displaystyle\sum_{n=0}^\infty(2n+1)x^n=\frac{1+x}{(1-x)^2}[/tex]

Answer:

90 ft²

Step-by-step explanation:

Given the sides of similar figures in the ratio a : b, then

ratio of areas = a² : b²

Here ratio of sides = 1 : 3 , thus

ratio of areas = 1² : 3² = 1 : 9

That is the surface area of the new solid is 9 times the first

SA = 9 × 10 = 90 ft²

The total surface area of the new solid in square feet is 90 square feet

Let the solid be a cube.

The surface area of a cube = 6L²

L is the length o the cube;

If the surface area of a solid is 10 square feet, then;

10 = 6L²

L² = 10/6

L = √10/6

If the dimensions of a similar solid are  three times as great as the first, then;

New length Ln = 3√10/6

Total surface area of the new solid = 6Ln²

Total surface area of the new solid = 6(3√10/6)²

Total surface area of the new solid = 6(9*10/6)

Total surface area of the new solid = 6(90/6)

Total surface area of the new solid = 90 square feet

This shows that the total surface area of the new solid in square feet is 90 square feet

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Answer:

1/x^12

Step-by-step explanation:

X^-12....simply move x^-12 to the other side of the division and change the sign of the exponent.

The simplified form of the expression x Superscript negative 12 is 1/ x¹².

The rule of the exponent is defined as the simplified form of the exponents

where a is the base and b and n are the exponent.

Here given in the question is the expression that x superscript negative 12.

As we now superscript is to write the number in exponent position.

here -12 is written in the superscript of x.

then the mathematical expression will be converted as

x superscript negative 12 = x⁻¹²

As we know from the rule of exponent that a⁻ⁿ = 1/aⁿ where a is the base and n is the exponent.

x⁻¹² can be rewritten as x⁻¹² = 1/ x¹²

Therefore the simplified form of the expression x Superscript negative 12 is 1/ x¹².

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Answer:

ANSWER LINK

Answer:

B

Step-by-step explanation:

sqrt30 -6^2 doesn't work

2.5 sqrt18 and 5 do work

Answer:

Part A:

[tex]\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807[/tex]

Part B:

The closure property describes cases when mathematical operations are CLOSED. It means that if you apply certain mathematical operations in a polynomial it will still be a polynomial. Polynomials are closed for sum, subtraction, and multiplication.

It means:

[tex]\text{Sum of polynomials } \Rightarrow \text{ It will always be a polynomial}[/tex]  

[tex]\text{Subtraction of polynomials } \Rightarrow \text{ It will always be a polynomial}[/tex]  

[tex]\text{Multiplication of polynomials } \Rightarrow \text{ It will always be a polynomial}[/tex]  

But when it is about division:

[tex]\text{Division of polynomials } \Rightarrow \text{ It will not always/sometimes be a polynomial}[/tex]  

Example of subtraction of polynomials:

[tex](2x^2+2x+3) - (x^2+5x+2)[/tex]

[tex]x^2-3x+1[/tex]

Step-by-step explanation:

First, it is very important to define what is a polynomial in standard form:

It is when the terms are ordered from the highest degree to the lowest degree.

Therefore I can give:

[tex]x^5-5x^4+3x^3-3x^2+7x+20[/tex]

but,

[tex]x^5+3x^3-3x^2+7x+20-5x^4[/tex] is not in standard form.

For this question, I can simply give the answer: [tex]x^5-5x^4+3x^3-3x^2+7x+20[/tex] and it is correct.

But I will create a fifth-degree polynomial using this formula

[tex]$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$[/tex]

Also, note that

[tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]

For [tex]a=x \text{ and } b=7[/tex]

[tex]$\left(x + 7\right)^{5}=\sum_{k=0}^{5} \binom{5}{k} \left(x\right)^{5-k} \left(7\right)^k$[/tex]

[tex]\text{Solving for } k \text{ values: } 0, 1, 2, 3, 4 \text{ and } 5[/tex]

Sorry but I will not type every step for each value of [tex]k[/tex]

The first one is enough.

For [tex]k=0[/tex]

[tex]$\binom{5}{0} \left(x\right)^{5-0} \left(7\right)^{0}=\frac{5!}{(5-0)! 0!}\left(x\right)^{5} \left(7\right)^{0}=\frac{5!}{5!} \cdot x^5= x^{5}$[/tex]

Doing that for [tex]k[/tex] values:

[tex]\left(x + 7\right)^{5}=x^{5} + 35 x^{4} + 490 x^{3} + 3430 x^{2} + 12005 x + 16807[/tex]

Answer:

Ty for the free pointsd!

Step-by-step explanation:

Answer:

Angle x is 75 degrees because 180-105 = 75  so the angle next to 105 is the alternate exterior angle to angle x which means they are equal

Step-by-step explanation:

Answer:

a) 75 deg

b) see below

Step-by-step explanation:

a)

x + 105 = 180

x = 75

b) <x and <ABF are supplementary since they are a linear pair, so

x + m<ABF = 180

Since lines AD and EH are parallel, corresponding angles ABF and EFG are congruent.

m<ABF = m<EFG

x + m<EFG = 180

x + 105 = 180

x = 75

Answer:

A = 9x² + 48x + 65

Step-by-step explanation:

Area of a Square Formula: A = lw

Since a square's length is equal to its width, we simply plug it into the formula:

A = (3x + 8)(3x + 8)

Then we simply use FOIL to expand the distribution)

First - 3x(3x) = 9x²

Outside - 8(3x) = 24x

Inside - 8(3x) = 24x

Last - 8(8) = 64

Lastly, we combine like terms

9x² + 24x + 24x + 64

9x² + 48x + 64

Answer:

Step-by-step explanation:

Any time you have compounding more than once a year (which is annually), unless we are talking about compounding continuously, you will use the formula

[tex]A(t)=P(1+\frac{r}{n})^{(n)(t)}[/tex]

Here's what we have:

The amount after a certain time that she has in the bank is 4672.12; that's A(t).

The interest rate in decimal form is .18; that's r.

The number of times the interest compounds is 12; that's n

and the time that the money is invested is 3.5 years; that's t.

Filling all that into the formula:

[tex]4672.12=P(1+\frac{.18}{12})^{(12)(3.5)}[/tex] Simplifying it down a bit:

[tex]4672.12=P(1.015)^{42}[/tex] Raise 1.015 to the 42nd power to get

4672.12 = P(1.868847115) and divide to get P alone:

P = 2500.00

She invested $2500.00 initially.

Answer:

8

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (- 4, 6 ), thus

y = a(x + 4)² + 6

To find a substitute (- 3, 14) into the equation

14 = a(- 3 + 4)² + 6 ( subtract 6 from both sides )

8 = a

Thus the coefficient of the x² term is a = 8

Answer:

6

Step-by-step explanation:

3(4-2)

PEMDAS says parentheses first

3 ( 2)

Then multiply

6

Answer:

Step-by-step explanation:

3(4 - 2)

Solve the terms in the bracket first

That's

4 - 2 = 2

So we have

3( 2) = 6

Hope this helps you

Answer:

A

Step-by-step explanation:

The rhombus cuts the shorter side of the rectangle in half so it's equal to 5

we use pythagoras

[tex]13^{2} = 5^2+x^2\\x^2= 169-25\\x^2= 144\\x=12[/tex]

so the larger side is 2x=24

so the area is 24*10=140cm^2

Answer:

Step-by-step explanation:

A radius to the tangent point always forms a right angle with the tangent.

m∠OAB = m∠OCB = 90°

[tex]m\angle AOC=\stackrel{\big{\frown}}{ADC}=96^o[/tex]

The sum of the angles in the quadrilateral is 360°, so:

x = 360° - 2•90° - 96° = 84°

Answer:

[tex](2x+3)(2x+3)[/tex]

Step-by-step explanation:

The given expression is

[tex]4x^2+12x+9[/tex]

Here, a=4, b=12, c=9.

Step 1: Multiply [tex]a\cdot c=4\cdot 9=36[/tex]

Step 2: Find the factors of ac that add to b.[tex]6\cdot 6=36[/tex] and [tex]6+6=12=b[/tex] So, two factors of ac are 6 and 6.

Step 3:[tex]4x^2+6x+6x+9[/tex]

Step 4:[tex](4x^2+6x)+(6x+9)[/tex]

Step 5:[tex]2x(2x+3)+3(2x+3)[/tex]

Step 6:[tex](2x+3)(2x+3)[/tex]

Therefore, the required factor form is [tex](2x+3)(2x+3)[/tex]. It can also written as [tex](2x+3)^2[/tex].

Answer:

-0.743

Step-by-step explanation:

just plug it into a calculator

Answer:

it is also -sin(48)

Step-by-step explanation: