Dominic says the approximate volume
of the sphere below is 85.33 cm3.
Find the correct approximate volume,
using 3.14 for p. Round to the nearest
hundredth. What was Dominic’s
likely error? (The radius is 4.)

Answer:  Refer to the screenshot below

I've filled in the boxes with the proper answers

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Explanation for problem 1

In line 1, I used the distributive rule a*(b+c) = a*b+a*c. On the left side the 3(n+2) becomes 3n+6. On the right side, the 9(6-n) becomes 54-9n

On the next line, I added 9n to both sides. The 3n on the left side updates to 3n+9n = 12n.

For the third line, I subtracted 6 from both sides. Then the last line involves dividing both sides by 12 to fully isolate n. To confirm the solution n = 4, plug it back into the original equation. You should get the same thing on both sides after simplifying.

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Explanation for problem 2

The steps here are similar as problem 1, but this time we're involving fractions. Unfortunately, these steps don't involve clearing out the fractions which is often a handy trick to use.

We use the distributive rule on line 1

For line 2, we subtract 2m/9 from both sides. Think of 2m/3 as 6m/9 to help combine the fractions. The denominators must be the same for you to be able to add or subtract fractions.

For line 3, we subtract 4/3 from both sides. Think of 4/3 as 12/9.

The last step is to multiply both sides by 9/4, which is the reciprocal of 4/9. Your teacher made a typo on the right hand side of the last line. It should read [tex]\frac{4}{9}m[/tex] and not [tex]\frac{2}{9}m[/tex]. Refer to the previous line.

Answer: d.

2x + x = 180: 60°and 120°

Step-by-step explanation:

Let x= one of the supplements.  (smaller)

As per given , measure of second angle = 2x

We know that,

The sum of two supplements = 180 degrees

Then,

smaller angle + larger angle =180°

i.e. x+2x = 180°

3x= 180°

x=60°

then, 2x = 2 (60°) = 120°

hence, the correct option is d.

2x + x = 180: 60°and 120°

Answer:

5/8

that's mah answer tht is correct

Answer:

18.57 centimeters

Answer:

2/3

Step-by-step explanation:

Answer:

76

Step-by-step explanation:

so the sequence(pattern) is it increases by 5

there are 2 ways to solve this promblem

one count on your toes and hands by 5 starting at one until u get to 10 fingers and 5 toes. soon the promblems will get harder and you cant do that

other way multiply 5 by 15 and add it to 1

t( 15 ) = t( 1 ) + [ 14 × ( Constant value ) ]

________________________________

t( 1 ) = 1

&

Constant value = t( 2 ) - t( 1 ) = t( 3 ) - t( 2 )

Constant value = 6 - 1

Constant value = 5

________________________________

Thus :

t ( 15 ) = 1 + [ 14 × 5 ]

t( 15 ) = 1 + 70

t( 15 ) = 71

Answer:

The mode is the number that appears the most in a data set, therefore the mode is $4 since it is the only number appearing twice

Answer:

4

Step-by-step explanation:

Answer:

b=27,-13

▩▩▩▩▩▩▩▩

Steps:

|b-7|=20

Activate the law of absolute values

b - 7 = -20 or b-7=20

b = 27 or b = -13

Answer:

[tex]b = 27[/tex]

Step-by-step explanation:

[tex]20 = |b - 7| [/tex]

[tex]b - 7 = 20[/tex]

[tex]b = 20 + 7[/tex]

[tex]b = 27[/tex]

Given:

The graph of a function.

To find:

The average rate of change of h over the interval [tex]5\leq t\leq 9[/tex].

Solution:

The average rate of change of a function f(x) over the interval [a,b] is:

[tex]m=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

So, the average rate of change of h over the interval [tex]5\leq t\leq 9[/tex] is:

[tex]m=\dfrac{h(9)-h(5)}{9-5}[/tex]

From the given graph it is clear that [tex]h(9)=7,h(5)=3[/tex]. Substituting these values, we get

[tex]m=\dfrac{7-3}{9-5}[/tex]

[tex]m=\dfrac{4}{4}[/tex]

[tex]m=1[/tex]

Therefore, the average rate of change of h over the interval [tex]5\leq t\leq 9[/tex] is 1.

Answer:

1036

Step-by-step explanation:

Answer:

1036

Step-by-step explanation:

298 + 738 = ?

→ 298 + 738

→ 1036

Answer: 42

Step-by-step explanation:

Given

An Umbrella manufacturer has [tex]1584\ \text{Umbrellas}[/tex]

One case will hold [tex]38[/tex] Umbrellas

Number of cases required to hold all the Umbrellas are

[tex]\Rightarrow n=\dfrac{1584}{38}\\\\\Rightarrow n=41.68\approx 42[/tex]

Thus, 42 packs are required to hold all the Umbrellas

Angle D = ABC arc / 2

x + 100 = ABC arc / 2

ABC arc = 2 × ( x + 100 )

ABC arc = 2x + 200 ( ♡ )

_________________________________

Angle B = ADC arc / 2

3x = ADC arc / 2

ADC arc = 2 × 3x

ADC arc = 6x ( ☆ )

_________________________________

ABC arc + ADC arc = 360

( ♡ ) , ( ☆ ) :

( 2x + 200 ) + ( 6x ) = 360

8x + 200 = 360

8x = 360 - 200

8x = 160

x = 160/8

x = 20

____________________________

Thus :

Angle A = 5(20) - 3 = 97 degrees

Angle B = 3(20) = 60 degrees

Angle D = 20 + 100 = 120 degrees

____________________________

Sum of the interior angles of any four-sides figures are equal 360 degrees ,

Thus :

Angle A+Angle B+Angle C+Angle D = 360

97 + 60 + Angle C + 120 = 360

Angle C + 120 + 157 = 360

Angle C + 277 = 360

Angle C = 360 - 270 - 7

Angle C = 90 - 7

Angle C = 83 degrees

Answer:

y = 2x + 3

Step-by-step explanation:

The slope can be found by taking two points, for instance: (0,3) and (3,9) which lie on the graph.  Find the slope between the two, remember rise over run:

(9-3)/(3-0) = 6/3 = 2

The y-intercept is (0,3)

So b in the y= mx + b equation is 3.

m is the slope, so it is 2.

y = 2x + 3

Answer:

y- intercept = - 1

Step-by-step explanation:

To find the y- intercept , let x = 0 in the equation and evaluate for y

y = 3(0)² + 2(0) - 1 = 0 + 0 - 1 = - 1

y- intercept = - 1 or (0, - 1) in coordinate form

Answer:

Plug x=0 into the equation and solve the resulting equation

The y-intercept:

3x^2 + 2x - 1

3(0)^2 + 2x(0)- 1

0+0-1

-1

y=−1 is intercept for y  

(0,−1)

Step-by-step explanation:

Hi there!

[tex]\large\boxed{-n^2 + 4n}[/tex]

Begin by evaluating f - g:

4n - 5 - (n² - 5)

Simplify:

4n - 5 - n² + 5  = 4n - n²

Or it can be written as -n² + 4n to match the first answer choice.

Answer:

its 6 square units

Step-by-step explanation:

count how many boxes the that contain blue and devide by 2

Answer:

6

Step-by-step explanation:

There are 3 parts to each side. All three of them are the same so we only have to find the area of one different parts

Area of One Side

Triangle

The side of a square is 1 square unit.

each leg of the triangle is 1 unit

The area of 1 triangle = 1/2 * 1 * 1 = 1/2

Area of 1 side

There are 3 equal parts (3 triangles) that make up a side.

Area of the three triangles = 3 * 1/2 = 3/2 = 1.5

Area of all 4 sides

4 * 1.5 = 6

The area of the blue colored figure is 6 units.

Given:

Consider the given expression is:

[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]

By using the quotient property of exponents, we get

[tex]=x^{4-2}y^{-4-(-2)}z^{-2-4}[/tex]              [tex]\left[\because \dfrac{a^m}{a^n}=a^{m-n}\right][/tex]

[tex]=x^{2}y^{-4+2}z^{-6}[/tex]

[tex]=x^{2}y^{-2}z^{-6}[/tex]

By using negative exponent property, we get

[tex]=\dfrac{x^{2}}{y^{2}z^{6}}[/tex]           [tex]\left[\because a^{-n}=\dfrac{1}{a^n}\right][/tex]

The simplified form of the given expression is [tex]\dfrac{x^{2}}{y^{2}z^{6}}[/tex].

Therefore, the correct option is B.

Answer:

1. x = 10

2. x = 9

Step-by-step explanation:

131231231212312312312312312312312313131231231231231312312312

123123211231312132

Answer: 120 cubed inches

Step-by-step explanation:

First, multiply them all together. 6x10x2 = 120 cubed inches

Answer:

[tex]x = 1\frac{4}{5}[/tex]

Step-by-step explanation:

Factor and set each factor equal to zero.

Answer:

Step-by-step explanation:

30x-45=5x

30x-5x=45

25x=45

x=45/25

x=9/5

Answer:

[tex](a)\ y = 2x +8[/tex]

[tex](b)\ y = 0[/tex]

[tex](c)\ y = -5[/tex]

Step-by-step explanation:

Given

[tex]y = x^2[/tex]

First, graph [tex]y = x^2[/tex] (See attachment)

We are not limited to any particular linear equation; as long as we meet the required condition

Solving (a): Equation of a line that intersects [tex]y = x^2[/tex] at two points

Select any two points on opposite sides of the curve

The selected points are:

[tex](x_1,y_1) = (-2,4)[/tex]

[tex](x_2,y_2) = (4,16)[/tex]

Calculate slope (m)

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

[tex]m = \frac{16 - 4}{4 - -2}[/tex]

[tex]m = \frac{12}{6}[/tex]

[tex]m = 2[/tex]

The equation is then calculated using:

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

This gives:

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

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

Open bracket

[tex]y = 2x +4 + 4[/tex]

[tex]y = 2x +8[/tex]

Solving (b): Equation of a line that intersects [tex]y = x^2[/tex] at one point

A good illustration of this is x-axis

Because it intersects with the line at just one point, which is origin (0,0).

The equation of line at this point is:

[tex]y = 0[/tex]

Solving (c): Equation of a line that does not intersect [tex]y = x^2[/tex]

Here, we make use of any horizontal line below the x-axis

Select any two horizontal points below the x-axis

[tex](x_1,y_1) = (-5,-5)[/tex]

[tex](x_2,y_2) = (5,-5)[/tex]

Calculate slope

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

[tex]m = \frac{0}{10}[/tex]

[tex]m = 0[/tex]

The equation is then calculated using:

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

[tex]y = 0(x - -5) + (-5)[/tex]

[tex]y = 0-5[/tex]

[tex]y = -5[/tex]

Answer:

Hello! answer:

rectangle a: 8

rectangle b: 24

figure: 32

Step-by-step explanation:

Hello I'll show a demonstration, with a picture and explanation. Ok so as shown in the picture i circled the base and height those are basically what you have to multiply to find the area.

we are given the height for rectangle a but not the base so we have to find it we know the base at the bottom for the whole thing is 5 and the base for B is. 3 so we can just subtract 3 from 5 to find A's base so... 5 - 3 = 2

now we have everything we need to find the area so....

4 × 2 = 8 so rectangle a is 8

3 × 8 = 24 so rectangle b is 24

then for the whole figure we can just add those two up for the entire area so...

24 + 8 = 32 therefore the figures area is 32 Hope that helps!

Answer:

Step-by-step explanation:

rotten oranges=10/100*20

200/100

2 dozen

good oranges=total dozen-rotten oranges

20-2

18 d0zen were good oranges.

Answer:

Flexibility: Stretching

Endurance: Being able to dance for periods of time

Answer:

56.549 cm   (choice 1)

Step-by-step explanation:

If the area of the square if 36 cm, then each side is 6 cm.

That means the diameter for each semi circle is also 6 cm.

Formula for a semi circle is 1/2(πr²)

We need the radius, which is half the diameter. So the radius is 6÷2= 3

Now plug in to the formula.

A= 1/2(π3²)

A= 14.137 (nearest hundredths)

Now multiply that by 4, because there are 4 semi circles

4(14.137)= 56.549 cm (nearest hundredths)