PLS HELP ME!!!! use the properties of exponents to simplify the expression

Answer:

[tex]36\pi {a}^{3} [/tex]

Step-by-step explanation:

Volume = [tex] \frac{4}{3} \times \pi \times (r)^{3} [/tex]

[tex] \frac{4}{3} \times \pi \times {3a}^{3} [/tex]

[tex] \frac{4\pi}{3} \times {3}^{3} [/tex]

[tex] \frac{4\pi}{3} \times 27[/tex]

[tex] \frac{4\pi}{3} \times (3(9))[/tex]

[tex]4\pi \times 9[/tex]

[tex]36\pi {a}^{3} [/tex]

Answer:

Correct me if I'm wrong but I'm sure it's -12

Step-by-step explanation:

34+30= 64

64-76= -12

Answer:

650

Step-by-step explanation:

There are  [tex]55[/tex] ways of these integers be selected to give a sum.

Given that:

It has [tex]12[/tex] consecutive integers .

Now,

Definition of consecutive integers :

" Consecutive integers are the integers that follow in the fixed sequence .

Consecutive integers is represented by  [tex]n,n+1,n+2,n+3,....[/tex] where [tex]n[/tex] is an integer."

By given :

we have [tex]12[/tex] consecutive integers .

Thus,[tex]n=1[/tex] and substitute the equation is,

[tex]1,(n+1),(1+2),(1+3),(1+4),(1+5),(1+6),(1+7),(1+8),(1+9),(1+10),(1+11)\\\\\implies 1,2,3,4,5,6,7,8,9,10,11,12[/tex]

Now,

Split all the integers into 4 equal parts,

Part 1:  Those integers are divisible by [tex]4[/tex] and the remainder be 0.

Then,  

   [tex]a=0(mod 4)[/tex]

Part 2:  Those integer producing the remainder [tex]1[/tex] when it is divisible by [tex]4[/tex].

Then,

   [tex]a=1(mod 4)[/tex]

Part 3:  Those integer producing the remainder [tex]2[/tex]  when it is divisible by[tex]4[/tex].

Then,

    [tex]a=2(mod 4)[/tex]

Part 4: Those integer producing the remainder [tex]3[/tex]  when it is divisible by[tex]4[/tex].

Then,

   [tex]a=3(mod4)[/tex]

Since, three of these integers be selected to give a sum which divides by [tex]4[/tex] is,

In any 12 consecutive integers there are [tex]12\div4[/tex]

i.e. exactly 3 numbers of each category of mod4 namely ,

[tex]0(mod4), 1(mod4), 2(mod4), 3(mod4)[/tex]

Thus, the  total combinations of above [tex]5[/tex] categories of sets of [tex]3[/tex] integers are

                 [tex]3C_1=3(1)=3[/tex]

            [tex]3C_1*3C_2=3(1)*3=9[/tex]

           [tex]3C_1*3C_1*3C_1=3*3*3=27[/tex]

           [tex]3C2 * 3C1 = 3*3 = 9[/tex]

           [tex]3C1 * 3C2 = 3*3 = 9[/tex]

Thus, sum of the total ways be [tex]12[/tex] consecutive integers of three integers is divisible by 4 is,

       [tex]3+9+27+9+9=55[/tex]

Hence, it has [tex]55[/tex] ways.

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Multiply the amount of paint started with by the amount used:

2/3 x 1/2 = (2 x 1) / (3 x 2) = 2/6 = 1/3

There is 1/3 liter left

Answer:

7 x 1/10 = 7/10

Step-by-step explanation:

There are 7 "bumps" on the number line, and each "bump" moves the line 1/10.

This can also be modeled as

1/10 + 1/10 + 1/10 +1/10 +1/10 +1/10 +1/10 = 7/10

Answer:

J and K are supplementary

Step-by-step explanation:

Given

The attached image

Required

The true statement

From the attached image, it is hard to determine the values of angles I and L as there are no enough information to determine their values.

However, J and K can be worked easily.

From the image

[tex]J = 65^o[/tex] --- vertically opposite angles

And:

[tex]K + 65^o = 180^o[/tex] ---- angle on a straight line

Substitute: [tex]J = 65^o[/tex]

[tex]K + J = 180^o[/tex]

When two angles add up to 180, the angles are supplementary.

Hence, (c) is correct

I can't understand tell me in english

Answer:

A rational number is one that may be represented in the manner p/q.

245/1000 = 0.245

Step-by-step explanation:

[tex]x = - 2 \: then \: g( - 2) = 0 \\ x = 4 \: then \: g(4) = - 4.[/tex]

Hence, The values of the function when x = -2 is g(x) = 0 and x = 4 is

g(x) = - 4.

A composite function is created when one function is substituted into another function.

Given

Composite Function g

g(x) = 6,   -8 ≤ x ≤ -2

g(x) = 0,   -2 ≤ x ≤ 4

g(x) = -4,   4 ≤ x ≤ 10

The values of the function when x = -2

x is between -2 and 4

g(x) = 0, -2 ≤ x ≤ 4

Thus, The values of the function when x = -2 is g(x) = 0

The values of the function when x = 4

x is between 4 and 10

g(x) = -4, 4 ≤ x ≤ 10

Thus, The values of the function when x = 4 is g(x) = - 4

Hence, The values of the function when x = -2 is g(x) = 0 and x = 4 is

g(x) = - 4.

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the answer is in the picture

Answer:

Joey will use 6 bowls.

Step-by-step explanation:

We have to divide to solve.

What is [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{9}[/tex] ?

When you divide fractions you just multiply by the reciprocal (the fraction flipped.)

[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{9}[/tex] = [tex]\frac{2}{3}[/tex] × [tex]\frac{9}{1}[/tex]

[tex]\frac{2}{3}[/tex] × [tex]\frac{9}{1}[/tex] = [tex]\frac{18}{3}[/tex]

[tex]\frac{18}{3}[/tex] = 6

Joey will use 6 bowls.

Answer:

D. The coefficient of determination is the ratio of the explained variation to the total variation.

C. The coefficient of determination is the percent of variation of y that is explained by the relationship between x and y

Step-by-step explanation:

The Coefficient of determination is the ratio of the explained variation in y to the total variation in y.

Coefficient of determination, r² ;

r² = explained variation / total variation

The coefficient of determination is the proportion of variation in y (predicted value) which is due to the regression line ; Hence, it is the percent of variation of y that is explained by the relationship between x and y.

Answer:

[tex]Area = 130977cm^2[/tex]

Step-by-step explanation:

Given

[tex]W=840[/tex]

[tex]U = 350[/tex]

[tex]\angle V = 63^o[/tex]

Required

The area

The area is calculated as:

[tex]Area = \frac{1}{2}UW\sin(V)[/tex]

So, we have:

[tex]Area = \frac{1}{2}*350*840*\sin(63^o)[/tex]

[tex]Area = \frac{1}{2}*350*840*0.8910[/tex]

[tex]Area = 130977cm^2[/tex]

9514 1404 393

Answer:

  x ∈ {π/18, 5π/18, 13π/18, 17π/18, 25π/18, 29π/18}

Step-by-step explanation:

Using the trig identity ...

  cos(2x) = 1 -2sin²(x)

we can rewrite the equation as ...

  (1 -2sin²(3x)) -5sin(3x) +2 = 0

  2sin²(3x) +5sin(3x) -3 = 0 . . . . . standard form

  (sin(3x) +3)(2sin(3x) -1) = 0 . . . . factored form

There are no real values of x that will make the first factor zero. The second factor is zero when ...

  sin(3x) = 1/2

  3x = arcsin(1/2) +2nπ   or   (2n+1)π -arcsin(1/2)

  x = 1/3(π/6 +2nπ)   or   1/3((2n +1)π -π/6)

  x = (12n+1)π/18  or  (12n+5)π/18

  x ∈ {π/18, 5π/18, 13π/18, 17π/18, 25π/18, 29π/18}

Answer: 28

Step-by-step explanation: ADB = 1/2 ACB

Answer:

3

Step-by-step explanation:

I think its 3 because when we add 2 to x the graphic must be continue two step to right

Answer:

Six at top, ten at second, twenty-seven at third, and four at bottom.

Answer:

The answer is below

Step-by-step explanation:

a) the volume of the pit = length * width * depth = 9 dm * 6 dm * 7 dm = 378 dm³

Hence to fil the pit, 378 dm³ of sand is needed.

b) Volume of the room = length * width * height = 2.3 m * 0.59 m * 3.74 m = 5.08 m³

The cabinet would occupy 5.08 m³ of space.

c) volume = length * width * height

210 dm³ = 3.5 dm * 6 dm * width

width = 210 dm³ / (3.5 dm * 6 dm) = 10 dm

d) Volume of the room = length * width * height = 15 m * 15 m * 15 m = 3375 m³

The stockroom has a space of 3375 m³

e) volume = length * width * height = 5 dm * 5 dm * 5 dm = 125 dm³

The container has a space of 125 dm³

f) volume = length * width * height = 41 cm * 13 cm * 24 cm = 12792  cm³

The box has a space of 12792  cm³

g) volume of prism = length * width * height

72 m³ = 4 m * 3 m * length

length = 72 m³ / (4 m * 3 m) = 6 m

h) volume = length * width * height = 8 cm * 8 cm * 8 cm = 512 cm³

The figure has a volume of 512 cm³

i) volume = length * width * height = 5 ft * 2 ft * 3 ft = 30 ft³

The cabinet has a space of 30 ft³

Answer:

(1,4) , (3,12) , (5,20)

Step-by-step explanation:

You should put the first number in X and find the second number from equation.

Answer:

[tex]F = k\frac{m_1m_2}{r^2}[/tex]

Step-by-step explanation:

Direct proportional:

Multiplication

Inverse proportional:

Division

The gravitational attraction F between two objects of masses m1 and m2 is jointly proportional to the masses

This means that:

[tex]F = k\frac{m_1m_2}{}[/tex]

Inversely proportional to the square of the distance r between the objects.

Denominator is [tex]r^2[/tex]. Thus:

[tex]F = k\frac{m_1m_2}{r^2}[/tex]

Answer:

Step-by-step explanation:

I=∫e^2x dx

put 2x=t

2dx=dt

dx=dt/2

I=1/2∫e^t dt

=1/2 e^t+c

=1/2 e^{2x}+c

Answer:  y = 57°;

               Angle Values: 66° and 114°.

Step-by-step explanation:

The sum of the corresponding angles is 180°.

y + 9 + 2y = 180

3y = 180 - 9

3y = 171

y = 57

Angle Values:

57° + 9° = 66°

57° · 2 = 114°

Answer:

Step-by-step explanation:

We need to first find out how much 400% of 170 is and then add that increase to the original 170 people.

4(170) = 680 and

680 + 170 = 850 people after 3 years.

Answer:

14

Step-by-step explanation:

Simply take the square root of 196.

Hope that this helps!

Answer:

The side length is 14 m

Step-by-step explanation:

The formula for the area of a square is A = s^2, where s represents the length of one side.

If A = s^2  =  196m^2, we find the side length by taking the square root of both sides:  

s = √(196 m^2) = 14 m

The side length is 14 m

Answer:

Step-by-step explanation: