Find the volume of a
cone with a base radius of 5 yd and a height of 7 yd.
Write the exact volume in terms of Tt, and be sure to include the correct unit in your answer.

Answer:

Lisa played 4.35 hours over the weekend :)

Step-by-step explanation:

Answer:

0.625

Step-by-step explanation:

5/8th simplified is just 5 divided by 8

5/8 = 0.625

hope this helps!

Turn to decimals

Done!

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{f(x)}{y}~~ = ~~5+2x\implies \stackrel{quick~switcheroo}{x~~ = ~~5+2y}\implies x-5=2y\implies \boxed{\cfrac{x-5}{2}~~ = ~~\stackrel{f^{-1}(x)}{y}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(x)}{y}~~ = ~~4-\sqrt{2x-3}\implies \stackrel{quick~switcheroo}{x~~ = ~~4-\sqrt{2y-3}}\implies x+\sqrt{2y-3}=4 \\\\\\ \sqrt{2y-3}=4-x\implies \stackrel{\textit{squaring both sides}}{2y-3=(4-x)^2} \\\\\\ 2y=(4-x)^2+3\implies \boxed{\stackrel{f^{-1}(x)}{y}~~ = ~~\cfrac{(4-x)^2 +3}{2}}[/tex]

Next three terms after 27 are 36, 45 and 54.

Answer:

Step-by-step explanation:

unknown length=√(13²-12²)=√(169-144)=√25=5

B

yes

Answer:

x = 6

Step-by-step explanation:

As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.

For small values of x, we have that f(x) < g(x). For example:

f(1) = 1/2 * 2 = 1

g(1) = 5*1 + 2 = 7

f(2) = 1/2 * 4 = 2

g(2) = 5*2 + 4 = 14

So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.

For x = 5, we have:

f(5) = 1/2 * 32 = 16

g(5) = 5*5 + 4 = 29

For x = 6, we have:

f(6) = 1/2 * 64 = 32

g(6) = 5*6 + 4 = 34

For x = 7, we have:

f(7) = 1/2 * 128 = 64

g(7) = 5*7 + 4 = 39

So the largest integer value of x for f(x) ≤ g(x) is x = 6.

Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).

Answer:

  x = 6

Step-by-step explanation:

We assume your functions are ...

In general, mixed polynomial and exponential functions have no algebraic solution. That means we need to solve f(x) = g(x) using a table of values, or by graphing.

__

Attached is a graphical solution. It shows the largest value of x for which f(x) = g(x) is x=6.

Check: f(6) = 1/2(2^6) = 32 = g(6) = 5(6) +2

__

Additional comment

We can start with f(x) = g(x) and subtract g(x) from both sides of the equation. This gives ...

  f(x) -g(x) = 0

Many graphing calculators readily identify the zeros of a function or expression. We have used that fact to find the two values of x where these functions are equal: ≈0.32 and 6.

For x>6, the exponential function increases without bound, so the graphs never cross again. Likewise, for x < -0.32, the linear function decreases without bound, so the graphs never cross again.

The lower value of x where the graphs cross is an irrational number near −0.319886722135.

Work Shown:

q = 1 - p

q = 1 - 0.5

q = 0.5

Answer:

  A.  x= 5, y = 4

Step-by-step explanation:

The attachment shows a graphing calculator solution to this system of equations.

  (x, y) = (5, 4) . . . . . one solution

Answer:

39364

Step-by-step explanation:

You can simplify the equation to make 4(1+3+9...) The nth term is therefore [tex]3^{n-1}[/tex] so u can substitute that into the equation so 4([tex]3^{n-1}+ 3^{n} + 3^{n+1}[/tex]..). This would simplify to 4([tex]3^0 +3+3^2[/tex]+[tex]3^3+3^4+3^5+3^6+3^7+3^8[/tex]). By simplifying this, you can make it so 4([tex]2^2+6^2+18^2+42^2+81^2[/tex]) = 4(4+36+324+2916+6561) =39364

A. The rolls of groovy wallpaper is needed to cover the apartment bedroom. 9 rolls

B.The cost to re-wallpaper the apartment room $143.10

Based on the question, we have to assume there are no windows and no doors in that bedroom... to calculate how much less wallpaper we really need, and we cover completely from the floor to the ceiling.

A. If one rolls covers 50 sq ft, how many rolls do we need?

First, let's calculate the perimeter of that room, which is 16'x10'.

P = 16 + 10 + 16 + 10 = 52 feet of perimeter.

Now, the walls are 8 feet high... so, let's see just how big is the area to cover.

A = 52 feet * 8 feet = 416 sq feet to cover all walls.

Since we know each roll covers 50 sq ft, we will need:

416 / 50 = 8.32 rolls.

When talking about quantity you need to buy or to fill something, you always have to round up to the next unit.  Because you usually can't buy a portion of a unit and if you round it down, you'll miss material to cover your walls.

So, we will need 9 rolls.

B. Total cost, based on $15.90 per roll.

We already know we need 9 rolls... so how much will it cost us?

C = 9 * $15.90 = $143.10

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Answer:

1/2

Step-by-step explanation:

because Mackenzie chose two candles and we are to find the probility that he selects a polka dot candle

Answer:

Step-by-step explanation:

The values of CotD and SinC from the information given in the task content are; 15/8 and 15/17 respectively.

It follows from the task content that the right triangle has tanC = 15/8 and cosD=15/17.

On this note, it follows from Pythagoras theorem that the other value are as follows;

Hence, it follows that the values of cotD and sinC are; 15/8 and 15/17 respectively.

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Step-by-step explanation:

f(x) = y= -x²-x+6

When y is max, f'(x) = 0

f'(x) = -2x-1

Equating to 0,

-2x-1= 0

x= -1/2

Put the value of x in f(x)

y = -(-1/2)² -(-1/2) +6

= -1/4+1/2+6

= 6+1/2

y= 13/2

Answer:

2

Step-by-step explanation:

The point being shown is 4,2 so the constant of proportinality is just a simple multiplication problem 2x2=4 so 2 is the answer.

a numerical expression is a mathematical statement involving only numbers and one or more operation symbols. and a algebraic expession is an expressions that includes at least one variable and at least one operation. Order of operation goes (), exponent, divison, multiplication, addtion and subratcion

Answer:

  a +7d = 11

Step-by-step explanation:

The sum of an arithmetic series is given by the formula ...

  Sn = (n/2)(2·a1 +d(n -1))

where n is the number of terms, a1 is the first term, and d is the common difference.

__

Here, you are given n=15, S = 165, a1=a, and asked to find a relation for 'a' and 'd'. Substituting the known values, we have ...

  165 = (15/2)(2a +d(14))

  11 = a +7d . . . . . . . . simplify and divide by 15

We have found the relation to be ...

  a +7d = 11 . . . . . as required

Step-by-step explanation:

In an interdependent world, nations tend to cooperate more with each other. Some even argue that big wars are less likely to happen because countries need each other. The downside is that nations tend to have less autonomy when it comes to making major decisions.

The vertex of the given function [tex]f(x)= -4(x-2)^2+100[/tex] is (2, -25). the y-intercept is (0,-21). the x-intercept are (-3,0) and (7,0).

The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.

The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis,

where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.

We have the function,

[tex]f(x)= -4(x-2)^2+100[/tex]

On simplifying, we get,

[tex]f(x)= x^2 - 4x -21\\\\f(x) = (x+3)(x-7)[/tex]

Now, the factors of the given functions are (x+3) and (x - 7).

We have,an intercept form of the function is .

[tex]f(x) = (x+3)(x-7)[/tex]

Now, we know that,

Value of x-coordinate of the vertex is -b/2a

= 4 / 2

= 2

x = 2

Then,

[tex]f(2)= 2^2 - 4(2) -21\\\\f(2)= -25[/tex]

So, the vertex of the function is (2, -25).

Further, we know that 'the y-intercept of a function is the point where the function crosses the y-axis'.

So, when x=0, we have,  i.e. f(0) = -21

Thus, the y-intercept is (0,-21)

Also, 'the x-intercept of a function is the point where the function crosses x-axis'.

Then, for f(x)=0, we have  i.e.  i.e. x= -3 and x= 7

Thus, the x-intercept are (-3,0) and (7,0).

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Answer:

97 degrees

Step-by-step explanation:

supplementary angles are 2 angles that add up to 180 degrees

so

180- 83 = 97

[tex]\boxed{\sf 97~degrees}\boxed{explanation~below}[/tex]

         [tex]\sf 180 - 83 = 97deg.[/tex]

The data set which contains an outlier from the given answer choices is; Choice D; {16, 42, 45, 45, 46, 48}.

An outlier in a set of data values is a data value which differs significantly from other data points and hence, tends to affect the mean of such set of data values significantly.

On this note, choice D is the set of data values which contains an outlier.

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Answer:

11) 49 in.²

13) 4.515 m²

Step-by-step explanation:

11) area of square = (side)²

area = (7 in.)² = 7 in. × 7 in. = 49 in.²

13) area of triangle = base × height/2

area = 4.3 m × 2.1 m / 2 = 4.515 m²

Step-by-step explanation:

"properly" is very vague.

as your can imagine, particularly in math, where many things are commutative or have other degrees of freedom what do when in what sequence, you will find particularly for the little techniques many different approaches. and most of them are correct.

particularly today I keep scratching my head about what i think is immensely complicated but teachers swear they are helping the students.

anyway, this is how I do divisions by using an example :

73496 ÷ 17

the "window" I use to look at the first number is a long as the second number. in this case 2 digits.

step 1a :

as mentioned, we look at the 2 left most digits (73) and see how often 17 fits inside that as a whole :

73 ÷ 17 = 4

4×17 = 68, so we have a remainder of 73-68 = 5.

I write it like this :

73|496 ÷ 17 = 4

05 (4×7 = 28 and 5 is then 33, carry over 3,

4×1 = 4 plus carry 3 = 7, 0 difference)

step 1b :

pull the next position down

734|96 ÷ 17 = 4

054

step 2a :

we look at the bottom number and divide this by 17.

54 ÷ 17 = 3 and a remainder of 3.

734|96 ÷ 17 = 43

054

03 (3×7 = 21 and 3 is then 24, carry over 2,

3×1 = 3 plus carry 2 = 5, 0 difference)

step 2b :

pull the next position down

7349|6 ÷ 17 = 43

054

039

step 3a :

we look at the bottom number and divide this by 17.

39 ÷ 17 = 2 and a remainder of 5.

734|96 ÷ 17 = 432

054

039

05 (2×7 = 14 and 5 is then 19, carry over 1,

2×1 = 2 plus carry 1 = 3, 0 difference)

step 3b :

pull the next position down

73496| ÷ 17 = 432

054

039

056

step 4a :

we look at the bottom number and divide this by 17.

56 ÷ 17 = 3 and a remainder of 5.

73496| ÷ 17 = 4323

054

039

056

05 (3×7 = 21 and 5 is then 26, carry over 2,

3×1 = 3 plus carry 2 = 5, 0 difference)

step 4b :

pull the next position down. but we have reached the last position before the decimal point. from that moment on we create result numbers after the decimal point.

and because the left number did not have any explicit digits after the decimal point, all the numbers we are pulling down now are 0.

73496.0| ÷ 17 = 4323.

054

039

056

050

step 5a :

we look at the bottom number and divide this by 17.

50 ÷ 17 = 2 and a remainder of 16.

73496.0| ÷ 17 = 4323.2

054

039

056

050

16 (2×7 = 14 and 6 is then 20, carry over 2,

2×1 = 2 plus carry 2 = 4, 1 difference)

step 5b :

pull the next position down. because the left number did not have any explicit digits after the decimal point, all the numbers we are pulling down now are 0.

73496.00| ÷ 17 = 4323.2

054

039

056

050

160

step 6a :

we look at the bottom number and divide this by 17.

160 ÷ 17 = 9 and a remainder of 7.

73496.00| ÷ 17 = 4323.29

054

039

056

050

160

07 (2×7 = 14 and 6 is then 20, carry over 2,

2×1 = 2 plus carry 2 = 4, 1 difference)

step 6b :

pull the next position down. because the left number did not have any explicit digits after the decimal point, all the numbers we are pulling down now are 0.

73496.000| ÷ 17 = 4323.29

054

039

056

050

160

070

step 7a :

we look at the bottom number and divide this by 17.

70 ÷ 17 = 4 and a remainder of 2.

73496.00| ÷ 17 = 4323.294

054

039

056

050

160

070

02 (4×7 = 28 and 2 is then 30, carry over 3,

4×1 = 4 plus carry 3 = 7, 0 difference)

step 7b :

pull the next position down. because the left number did not have any explicit digits after the decimal point, all the numbers we are pulling down now are 0.

73496.0000| ÷ 17 = 4323.294

054

039

056

050

160

070

020

and so on ...

Answer:

$2.4

Step-by-step explanation:

85.9-55=30.9

30.9-30=0.9

0.9+1.5=2.4

Answer:

A

Step-by-step explanation:

10-7= 7-4= 3

That's it!

Answer:

$39.13

Step-by-step explanation:

559 x 7 is 3913 divided by 100 since its a percent is 39.13

The required amount paid for tax is obtained as $39.13.

In order to calculate the percent value take the ratio of the tax amount to the amount of the goods and then multiply it by 100.

The tax value is often written in terms of percent.

The price of laptop is given as $559.

And, the percent value of sales tax is 7%.

The amount of tax can be calculated as follows,

7% × Price of laptop

= 7% × 559

= 7/100 × 559

= $39.13

Hence, the amount paid by Dwade for the sales tax is $39.13.

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Answer:

X= -6 & x= 14

Step-by-step explanation:

The factors are -14 and 6, these numbers are multiplied to get -84 and added to get -8.

Therefore the new equation is:

x^2 -14x +6x -84 = 0

factorize: x (x -14) 6 (x - 14)

So: (x+6) (x-14) = 0

x = -6 and 14