What is the volume of the cylinder below? Use the formula V = πr²h​

Answer:

13 2/5

Step-by-step explanation:

a = 2 and b = -3

so the question asks whats.... a^3 - b^3/5

First we plug in the values of a and b

(2)^3 - (-3)^3 /5

Now we solve the ones in paranthesis first

(2)^3 = 8 because 2×2×2 and

-(-3)^3 forget about the - outside the parenthesis so

(-3)^3 = (-27) because (-3)×(-3)×(-3)

now we put it back together

8 -(-27)/5

the two minus become plus so

8 + 27/5

Now we solve it like fractions

8 and 27/5

simplify

13 and 2/5

Hope that helps!

Answer:

45

Step-by-step explanation:

Both angles (2x+45) and x together form a straight angle which measures 180 degrees.

Together should make you think of adding the angle measurements.

So we have that (2x+45)+x should be 180 degrees.

The equation we want to solve is:

(2x+45)+x=180

2x+45+x=180

(2x+x)+45=180

3x+45=180

3x=180-45

3x=135

x=135/3

x=45

Let's confirm that x is 45.

(2x+45) with x=45:

(2*45+45)

(3*45)

135

So (2x+45)+x at x=45 gives us:

135+45

180

Answer has been confirmed.

Answer:

[tex]\boxed{x = 45}[/tex]

Step-by-step explanation:

=> [tex]x+2x+45 = 180[/tex] (Angles on a straight line add up to 180 degrees)

=> [tex]3x+45 = 180[/tex]

Subtracting 45 to both sides

=> 3x = 180-45

=> 3x = 135

Dividing both sides by 3

=> x = 45

Answer:

see explanation

Step-by-step explanation:

differentiate using the power rule.

[tex]\frac{d}{dx}[/tex]( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] , thus

[tex]\frac{d}{dx}[/tex](x² - x + 3 ) = 2x - 1

x = 5 → 2(5) - 1 = 10 - 1 = 9

To find the value of x for minimum , equate [tex]\frac{d}{dx}[/tex] to zero

2x - 1 = 0 , then

2x = 1 and

x = [tex]\frac{1}{2}[/tex]

Please, check the options of the question. The point-slope equation needs the slope, m, in the equation.

Answer:

The point-slope equation of the points (5,2) and (-1,-6) is

[tex] \\ y - 2 = \frac{4}{3}(x-5)[/tex]  or,

[tex] \\ y + 6 = \frac{4}{3}(x+1)[/tex]

which are the same as

[tex] \\ 3y-4x+14 = 0[/tex] , (which is not a point-slope equation, though)

Step-by-step explanation:

The point-slope equation is given by:

[tex] \\ y - y_{1} = m(x - x_{1})[/tex]

Where m is the slope of the line:

[tex] \\ m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

Having the points (5,2) and (-1,-6), then

[tex] \\ m = \frac{-6 - 2}{-1 -5}[/tex]

[tex] \\ m = \frac{-8}{-6}[/tex]

[tex] \\ m = \frac{4}{3}[/tex]

Then, the point-slope equation of the points (5,2) and (-1,-6) is

[tex] \\ y - 2 = \frac{4}{3}(x-5)[/tex] or

[tex] \\ y + 6 = \frac{4}{3}(x+1)[/tex]

The below graph represents both lines (they are the same line).

Answer: C) For every original price, there is exactly one sale price.

For any function, we always have any input go to exactly one output. The original price is the input while the output is the sale price. If we had an original price of say $100, and two sale prices of $90 and $80, then the question would be "which is the true sale price?" and it would be ambiguous. This is one example of how useful it is to have one output for any input. The input in question must be in the domain.

As the table shows, we do not have any repeated original prices leading to different sale prices.

Answer:

C STAY SAFE!!!

Step-by-step explanation:

Ok we know this cant be A the reason is It says tha the original price is increasing so thats FALSE... its trying to trick you so no

The second choice says The sale price is always less than the original price. well take a look at the sale prices are they? Obiously not so False

Ok the third option For every original price, there is exactly one sale price. well this is true ask yourself each it helps.

Last option The sales price is never less than zero. erm   FALSE OBIOUSLY THIS IS TRUE JUST NOT TRUE ITS WRONG        

THE ANSER IS C

Answer:

29 ft x 58 ft

Step-by-step explanation:

Let x be the length of each side perpendicular to the wall, and y be the length of the side parallel to the wall.

The amount of wire available is:

[tex]116 = 2x+y\\y=116-2x[/tex]

The area of the region is:

[tex]A=xy=x(116-2x)\\A(x)=116x-2x^2[/tex]

The value of 'x' for which the derivate of the area function is zero will yield the maximum area:

[tex]A(x)=116x-2x^2\\A'(x) = 116-4x=0\\x=29\ ft[/tex]

The value of y is:

[tex]y=116-2*29\\y=58\ ft[/tex]

The dimensions of the region with the largest area are 29 ft x 58 ft.

Answer:

  SAS Postulate

Step-by-step explanation:

The contributors to the proof are listed in the left column. They consist of a congruent Side, a congruent Angle, and a congruent Side. The SAS Postulate is an appropriate choice.

Answer:

100

Step-by-step explanation:

height = constant/ width

Taking the point (5,20)

where 5 is the width and 20 is the height

20 = constant/ 5

Multiply each side by 5

5*20 = constant

100 = constant

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The given line passes through the points (-4, -3) and (4, 1).

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4, 3)?

a) y - 3 = -2(x + 4)

b) y - 3= - (x + 4)

c) y - 3 = (x + 4)

d) y - 3 = 2(x + 4)

Answer:

The equation of the line that is perpendicular to the given line and passes through the point (-4, 3) is

a) y - 3 = -2(x +4)

Step-by-step explanation:

First of all, we will find the slope of the given line.

We are given that the line passes through the points (-4, -3) and (4, 1)

[tex](x_1, y_1) = (-4,-3) \\\\(x_2, y_2) = (4,1) \\\\[/tex]

The slope of the equation is given by

[tex]$ m_1 = \frac{y_2 - y_1 }{x_2 - x_1} $[/tex]

[tex]m_1 = \frac{1 -(-3) }{4 -(-4)} \\\\m_1 = \frac{1 + 3 }{4 + 4} \\\\m_1 = \frac{4 }{8} \\\\m_1 = \frac{1 }{2} \\\\[/tex]

Recall that the slopes of two perpendicular lines are negative reciprocals of each other.

[tex]$ m_2 = - \frac{1}{m_1} $[/tex]

So the slope of the other line is

[tex]m_2 = - 2[/tex]

Now we can find the equation of the line that is perpendicular to the given line and passes through the point (-4, 3)

The point-slope form is given by,

[tex]y - y_1 = m(x -x_1)[/tex]

Substitute the value of slope and the given point

[tex]y - 3 = -2(x -(-4) \\\\y - 3 = -2(x +4)[/tex]

Therefore, the correct option is (a)

y - 3 = -2(x + 4)

The equation of the line in point-slope form is y - 3 = -2(x + 4)

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the y intercept.

The line passes through the point (-4, -3) and (4, 1). Hence:

Slope = (1 - (-3)) / (4 - (-4)) = 1/2

The slope of the line perpendicular to this line is -2 (-2 *  1/2 = -1).

The line passes through (-4, 3), hence:

y - 3 = -2(x - (-4))

y - 3 = -2(x + 4)

The equation of the line in point-slope form is y - 3 = -2(x + 4)

Find out more on linear equation at: https://brainly.com/question/14323743

Answer:

a. The first six terms are:

-7, -4, -1, 2, 5, 8

b. The first six terms are:

0, 2, 0, 2, 0, 2.

c. The first six terms are:

4, 8, 24, 96, 480, 2880

Step-by-step explanation:

a. an - 3n - 10

For n = 1

a1 = 3(1) - 10

= -7

For n = 2

a2 = 3(2) - 10

= -4

For n = 3

a3 = 3(3) - 10

= -1

For n = 4

a4 = 3(4) - 10

= 2

For n = 5

a5 = 3(5) - 10

= 5

For n = 6

a6 = 3(6) - 10

= 8

The first six terms are:

-7, -4, -1, 2, 5, 8

b. an= (1+(-1)^n)^n

For n = 1

a1 = (1+(-1)^1)^1

= 0

For n = 2

a2 = (1+(-1)^2)^1

= 2

For n = 3

a3 = (1+(-1)^3)^1

= 0

For n = 4

a4 = (1+(-1)^4)^1

= 2

For n = 5

a5 = (1+(-1)^5)^1

= 0

For n = 6

a6 = (1+(-1)^6)^1

= 2

The first six terms are:

0, 2, 0, 2, 0, 2.

c. an= 2n! (2)

For n = 1

a1 = 2(1!)(2)

= 4

For n = 2

a2 = 2(2!)(2)

= 8

For n = 3

a3 = 2(3!)(2)

= 24

For n = 4

a4 = 2(4!)(2)

= 96

For n = 5

a5 = 2(5!)(2)

= 480

For n = 6

a6 = 2(6!)(2)

= 2880

The first six terms are:

4, 8, 24, 96, 480, 2880

Answer:

[tex]\boxed{195}[/tex]

Step-by-step explanation:

The fruit flies grows geometrically.

[tex]125=80k^2[/tex]

Find the value of k.

[tex]\sqrt{\frac{125}{80} } =k[/tex]

[tex]1.25=k[/tex]

[tex]P=80(1.25)^t[/tex]

[tex]t[/tex] is number of days.

[tex]P=80(1.25)^4[/tex]

[tex]P=195[/tex]

Answer:

k = [tex]\frac{980a}{b}[/tex]

Step-by-step explanation:

Fisherman noticed a stretch in the spring = 'b' centimetres

Weight of the fish = a kilograms

If force applied on a spring scale makes a stretch in the spring then Hook's law for the force applied is,

F = kΔx

Where k = spring constant

Δx = stretch in the spring

F = weight applied

F = mg

Here 'm' = mass of the fish

g = gravitational constant

F = a(9.8)

  = 9.8a

Δx = b centimetres = 0.01b meters

Therefore, 9.8a = k(0.01b)

k = [tex]\frac{9.8a}{0.01b}[/tex]

k = [tex]\frac{980a}{b}[/tex]

Therefore, spring constant of the spring will be determined by the expression, k = [tex]\frac{980a}{b}[/tex]

Answer:

The z-score for a sales associate from this store who earns $37,500 is 2

Step-by-step explanation:

From the given information:

mean [tex]\mu[/tex] = 32500

standard deviation = 2500

Sample mean X = 37500

From the given information;

The value for z can be computed as :

[tex]z= \dfrac{X- \mu}{\sigma}[/tex]

[tex]z= \dfrac{37500- 32500}{2500}[/tex]

[tex]z= \dfrac{5000}{2500}[/tex]

z = 2

The z-score for a sales associate from this store who earns $37,500 is 2

Answer:

123 Square Feet. Of Paint. Probably gonna take a little more than a sample-size quart, let me know how it turns out.

Step-by-step explanation:

You would need 11*15=165 square feet of paint. BUT

You need 42 less square feet, because there are 2, 7*3=21 square-foot windows.

165-42

Answer:

20.25 miles

Step-by-step explanation:

If your car travels 27 miles on a full tank of gas, then your car will travel [tex]27\cdot\frac{3}{4}[/tex] miles on [tex]\frac{3}{4}[/tex] tank of gas.

[tex]27 \cdot 0.75 = 20.25[/tex]

I hope this helped!

Answer:

See below.

Step-by-step explanation:

So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.

Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.

Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.

Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:

In other words, we will have:

[tex]f(x)=(x+4)(x-2)^3\cdot n[/tex], where n is some value.

Let's determine n first. We know that f(0)=64, thus:

[tex]f(0)=64=4(-2)^3\cdot n[/tex]

[tex]64=-32n, n=-2[/tex]

Now, let's expand:

Expand:

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

[tex]f(x)=(x^2+2x-8)(x^2-4x+4)(-2)[/tex]

[tex]f(x)=(x^4-4x^3+4x^2+2x^3-8x^2+8x-8x^2+32x-32)(-2)[/tex]

[tex]f(x)=-2x^4+4x^3+24x^2-80x+64[/tex]

This is the simplest it can get.

Answer:

Simply plug in the polynomial into a graphing calc.

Step-by-step explanation:

Answer:

[tex]SA = \pi (6) * 10+\pi ( 6)^2[/tex]

Step-by-step explanation:

The surface area of a cone is given by

[tex]SA = \pi rl +\pi r^2[/tex]

r is the radius and l is the slant height.

The diameter is 12 inches, the radius is 12/2 = 6 inches.

The slant height is 10 inches.

[tex]SA = \pi (6) * 10+\pi ( 6)^2[/tex]

Answer:

SA of cone = [tex](\pi )(6)(8) + (\pi )(6)^2[/tex]

Step-by-step explanation:

Surface Area of cone = [tex]\pi rh+\pi r^2[/tex]

Where r = 6 inches (Diameter = 12 inches) , h = 8 inches (We'll not consider the slant height)

SA of cone = [tex](\pi )(6)(8) + (\pi )(6)^2[/tex]

Answer:

Step-by-step explanation:

Substitute x = 1 and y = 1 to the both inequalities:

[tex]x-8y\leq9\\\\1-8(1)\leq9\\1-8\leq9\\-7\leq9\qquad\bold{TRUE}\\==================\\-7x+5y<4\\\\-7(1)+5(1)<4\\-7+5<4\\-2<4\qquad\bold{TRUE}[/tex]

Answer:

(1,1) does satisfy

x - 8y ≤ 9

- 7x + 5y < 4

Step-by-step explanation:

Well, first we need to plug in (1,1) into,

x - 8y ≤ 9

- 7x + 5y < 4

→ 1 - 8(1) ≤ 9

- 7(1) + 5(1) < 4

1 - 8 ≤ 9

-7 + 5 < 4

-7 ≤ 9

-2 < 4

Thus,

(1,1) does satisfy

x - 8y ≤ 9

- 7x + 5y < 4.

Hope this helps :)

Answer:

This is called an Inductive reasoning.

Step-by-step explanation:

It is a logical process in which a number of premises all believed true combine to come up with specific conclusions. This is a generalisation based on observations.

Hope it helps.

Answer:

5/(1/3)

Step-by-step explanation:

She has 5 granola bars and gives 1/3 of one to each of her friends. To find how many friends she can give it to, divide 5 by 1/3. You would get a total of 15 friends that you can give granola bars to. The question is asking for an expression so the expression would be 5/(1/3) or 5*3

Answer:

1/3 x = 5

x=15

Step-by-step explanation:

You’re multiplying 1/3 times the number of friends (x), and then multiplying both sides by the reciprocal to solve for x

Answer:

x=10/3

Step-by-step explanation:

isolate the variable

Answer:

1. x = 4

2. x = 10/3

Step-by-step explanation:

1. 3x - 5 = 3 + x

3x - x = 3 + 5

2x = 8

x = 4

2. x/2 + 5/9 = 2x/3

(x/2 + 5/9) * 18 = (2x/3) * 18

9x + 10 = 12x

10 = 12x - 9x

10 = 3x

x = 10/3

Answer:

Step-by-step explanation:

Suppose that at time [tex]t_0[/tex] we have x mold cells. We are told that after 12 minutes the amount present is double. That is a [tex]t= t_0+12[/tex] we have 2x cells. Then, at [tex]t = t_0+24[/tex] we have (2x)*2 = 4x. We can continue as follows

[tex]t: t_0+36[/tex] we have (4x)*2 = 8x.

[tex]t: t_0+48[/tex] we have (8x)*2 = 16x

[tex]t: t_0+60[/tex] (one hour later) we have (16x)*2 = 32x.

So after one hour from now we have 32x cells.

The no. of mold cells one hour from now will be 32[tex]x[/tex].

Given,

The number of mold cells doubles every 12 minutes.

Let at time [tex]t[/tex] we have x mold cells.

So, after 12 minutes, the no of molds at[tex],t_{12} =t+12[/tex]  the no. of mold will be[tex]2x.[/tex]

After further 12 minutes at, [tex]t_{24} =t+24[/tex], the no. of mould will be [tex]4x[/tex].

After further 12 minutes at, [tex]t_{36} =t+36[/tex], the no. of mold will be [tex]8x[/tex].

After further 12 minutes at, [tex]t_{48} =t+48[/tex], the no. of mold will be [tex]16x.[/tex]

After further 12 minutes at, [tex]t_{60} =t+60[/tex], the no. of mold will be [tex]32x[/tex].

Hence the no. of mold cells one hour from now will be 32[tex]x[/tex].

For more details follow the link:

https://brainly.com/question/11897796

Answer:

We accept H₀

p-value = 0,1618

Step-by-step explanation:

We are going to solve a one tail proportion-test ( right tail)

We assume Normal distribution

Sample population 1000

Political strategist to test  wants to test:

Null hypothesis                             H₀           p = p₀       or   p = 26 %

Alternate hypothesis                    Hₐ           p > p₀        or  p > 26%

We assume CI  90 % then

α = 10 %     α = 0,1    and  z score for α = 0,1  is critical value

z = 2,32          ( note  2,32 is z score for α = 0,1017 "good approximation")

To compute z(s)

z(s)  =  ( p -p₀ ) / √ p₀q₀/n

z(s)  =  ( 0,29 - 0,26 ) /√ 0,26*0,74/1000

z(s)  = 0,03 / 0,014

z(s) = 2,14

We compare z(s) and z(c)

z(s) < z(c)

2,14 < 2,32

z(s) is in the acceptance region we accept H₀

The p-value for z(s) is from z-table

p-value = 0,1618

Answer:

6/4

Step-by-step explanation:

Answer:

6/4

Step-by-step explanation:

There are 6 brooms to 4 mops.

So you would write it that way as a fraction, but you could also write it like 6:4 or 6 to 4.

Answer:

A and E

Step-by-step explanation:

If the answer was A, it would translate to:

I have done some stuff.

If the answer was D, it would translate to:

I have some stuff.

Both of the sentences are grammatically correct, so A and E are the answers.

Incorrect:

B. - I's do some stuff - doesn't make sense

C. - I's doing some stuff - doesn't make sense

D. - I's did some stuff - doesn't make sense

Answer:

We're solving for CD. If we look at ΔABD we notice that it's a 30-60-90 triangle which has a side length ratio of 1:√3:2 and in this case the 1 is 300 so side BD = 300√3. Similarly, ΔABC is also a 30-60-90 triangle but this time the √3 is 300 so side BC = 100√3. We know that CD = BD - BC using PWP so the answer is 300√3 - 100√3 = 200√3 = 346.4 feet.

Answer: m = - 2200

Step-by-step explanation: Slope of a line is a number which describes the steepness and direction of a linear graph. It is represented by the letter m.

The year a car is bought and its price means:

f(0) = 31,500

Five years later, the price is $20,500, i.e.:

f(5) = 20,500

With these two pairs of value, slope is calculated as:

[tex]m = \frac{y-y_{0}}{x-x_{0}}[/tex]

[tex]m = \frac{20500-31500}{5-0}[/tex]

[tex]m = \frac{- 1100}{5}[/tex]

m = - 2200

The slope of the depreciation line is m = -2200 and it is negative because the line decreases along time.

Answer: x = 40.5

Step-by-step explanation:

Simply divide 27/(2/3) to get 40.5

Hope it helps <3

Answer:

x= 40.5

Step-by-step explanation:

We want to find out what x is. Therefore, we must get x by itself on one side of the equation.

2/3x= 27

2/3 and x are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 2/3.

2/3x / 2/3 = 27/ 2/3

When dividing by a fraction, you can also multiply by the reciprocal of the fraction.

To find the reciprocal, flip the numerator (top number) and denominator( bottom number)

2/3 —> 3/2

Multiply both sides of the equation by 3/2

2/3x *3/2 = 27*3/2

x= 27*3/2

x= 27/1*3/2

x= (27*3)/(1*2)

x= 81/2

x= 40.5

Answer:

-3.5 meters per second

Step-by-step explanation:

Take the distance and divide by the time

-17.5 meters/ 5 seconds

-3.5 meters per second

Answer:

-3.5 m/s

Step-by-step explanation:

Rate of the anchor =  [tex]\frac{distance}{time}[/tex]

[tex]\frac{-17.5}{5}[/tex]

-3.5 meters per second.