Sphere B is the image of sphere A after dilation by a scale factor of 44. If the volume of sphere A is 50 m^3
3
, find the volume of sphere B, the image.

Answer:

7.6

Step-by-step explanation:

We want to find the distance between (0,6) and (-3,-1)

We can find the distance between any two points using the distance formula

Distance between two points =

[tex] \sqrt{(x2 - x1)^{2} +(y2 - y1) {}^{2} } [/tex]

Where the values of x and y are derived from the the two points. (x1,y1) and (x2,y2)

Here the two points are (0,6) and (-3,-1)

So we have (x1,y1) = (0,6) so x1 = 0 and y1 = 6

And we have (x2,y2) = (-3,1) so x2 = -3 and y2 = -1

Now we plug in the values of x and y into the formula and evaluate to get the distance.

Again recall distance = √(x2-x1)²+(y2-y1)²

==> plug in x2 = -3 , x1 = 0, y2 = -1 and y1 = 6

Distance = √(-3-0)²+(-1-6)

==> evaluate operations inside of parenthesis

Distance = √(-3)²+(-7)²

==> evaluate all exponents

Distance = √9+49

==> and 9 and 49

Distance = √58 = 7.6 (rounded)

Answer:

  walk area = 125.6 m²

Step-by-step explanation:

You are asked for the area of a sidewalk of given width that is around a circle of given radius. The pattern you're asked to fill in would have you compute the area of the inner circle, and of the outer circle, then find the difference between the areas.

__

The formula for the area of a circle is ...

  A = πr²

The radius is shown as 11 m, so its area is ...

  A = π(11 m)² = 121π m² = 379.94 m²

The radius is shown as 9 m, so its area is ...

  A = π(9 m)² = 81π m² = 254.34 m²

The difference between the two areas is ...

  walk area = big circle area - small circle area

  walk area = 379.94 m² -254.34 m² = 125.6 m²

_____

Additional comment

The area can also be computed by multiplying the centerline length of the sidewalk by its width. The center of the walk is (9+11)/2 = 10 m from the centers of the circles, so the circumference (centerline length) is

  C = 2πr = 2(3.14)(10 m) = 62.8 m

The width of the sidewalk is 11 -9 = 2 meters, so its area is ...

  (2 m)(62.8 m) = 125.6 m² . . . . sidewalk area

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's simplify ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 10x + 25 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 5x - 5x + 25 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{} (x- 5) - 5(x - 5) } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ (x- 5) (x - 5) } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ (x- 5) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: (x- 5) [/tex]

value x lies between :

[tex]\qquad \sf  \dashrightarrow \: - 5 \leqslant x \leqslant 5[/tex]

if the value of x is taken -5

[tex]\qquad \sf  \dashrightarrow \: - 5 - 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 10[/tex]

if value of x is taken as 5

[tex]\qquad \sf  \dashrightarrow \:5 - 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:0[/tex]

So, the possible values of the required expression lies between ~

[tex]\qquad \sf  \dashrightarrow \: - 10 \leqslant \sqrt{ {x}^{2} - 10x + 25 } < 0[/tex]

I hope you understood the whole procedure. let me know if you have any doubts in given steps ~

Step-by-step explanation:

[tex]1.a + 27 = 90 \: \: (complementary \: angles = 90) \\ a = 90 - 27 \\ a = 63degrees \\ 2. \: x + 101 + 109 + 90= 360 \: (revolution \: angles = 360) \\ x = 360 - (101) - (109) - (90) \\ x = 60degrees \\ 3. \: a + 85 = 180 \: (angles \: on \: str \: line = 180) \\ a = 180 - 85 \\ a = 95degrees \\ b = 85 \: (vertically \: opp \: angle) \\ c = 95 \: (vertically \: opp \: angle)[/tex]

Answer:

Answer: B) 6.5

Step-by-step explanation:

   We will use the Pythagorean theorem to solve. The "c" variable is the hypotenuse and the other variables are the legs.

a² + b² = c²

3.6² + b² = 7.4²

12.96 + b² = 54.76

b² = 41.8

b = [tex]\sqrt{41.8}[/tex]

b ≈ 6.5

     The length of the missing side is about B) 6.5.

Answer:

B)6.5

Step-by-step explanation:

H²=P²+B²

7.4²=3.6²+B²

B=√41.8

B=6.465≈ 6.5

[tex]\text{Given that,} ~ p(x) = x^2 -5~ \text{and}~ h(x) = \sqrt{x+5}\\\\(p\circ h)(x)\\\\=p(h(x))\\\\=p\left( \sqrt{x+5} \right)\\\\=\left( \sqrt{x+5} \right)^2 -5\\\\=x +5-5\\\\=x[/tex]

Answer:

  D.  1/4

Step-by-step explanation:

You want to know the probability Marcy will miss a free throw, given that she makes 15 of 20.

We assume Marcy's record at practice is typical of her performance. It tells us that she makes 15/20 = 3/4 of the free throws she takes. That means she misses 1 -3/4 = 1/4 of the free throws.

The probability she will miss her free throw is 1/4.

__

Additional comment

Many assumptions are involved in this calculation. One of them is that her next throw is unaffected by her last throw. It is a rare player for whom that is the case.

<95141404393>

Using the given box and whisker plot, it is found that the mean most likely exceeds the median for Elaine, hence option B is correct.

A box and whisker plot shows three things:

In this problem:

The mean most likely exceeds the median for Elaine, hence option B is correct.

More can be learned about box and whisker plots at https://brainly.com/question/27743205

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Answer:

x = 48

Step-by-step explanation:

5x + 12 = 6x - 36 ( subtract 6x from both sides )

- x + 12 = - 36 ( subtract 12 from both sides )

- x = - 48 ( multiply both sides by - 1 )

x = 48

Step-by-step explanation:

5x + 12 = 6x - 36

5x + 12 - 6x = - 36

- x = - 36 - 12

- x = - 48

Now change the sign of both side of the equation...

x = - ( - 48)

x = 48...

Answer:

31.2%

Step-by-step explanation:

75000+35000 = 110000

160000 - 110000 = 50000

50000 ÷ 160000 = 0.312

0.312 x 100 = 31.2 %

Answer:

[tex]\sqrt{241}[/tex]

Step-by-step explanation:

3+1=4

7+8=15

4^2=16

15^2=225

16+225=241

[tex]\sqrt{241}[/tex]

[tex]|-24 \div 2^2|\\\\\\=\left|-24 \times \dfrac 1{2^2} \right|\\\\\\=\left|-\dfrac{24}4\right|\\ \\\\=|-6|\\\\\\=6[/tex]

The values of x in f(x) = 3|x - 2| + 6 when f(x) = 18 are 6 and -2

The function is given as:

f(x) = 3|x - 2| + 6

The value of f(x) is

f(x) = 18

So, we have:

3|x - 2| + 6 = 18

Subtract 6 from both sides

3|x - 2| = 12

Divide both sides by 3

|x - 2| = 4

Remove the absolute bracket

x - 2 = 4 or x - 2 = -4

Add 2 to both sides

x = 6 or x = -2

Hence, the values of x are 6 and -2

Read more about absolute values at:

https://brainly.com/question/729268

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Answer:

14

Step-by-step explanation:

Given:

A student earned a grade of 70% on a math test that had 20 problems.

To Find:

How many problems on this test did the student answer correctly? ( round to the nearest whole number)

Solve:

When I solve these question I have a formula.

Which is

Number of question correctly ÷ Total × 100

Thus,

1/20 × 100 = 5%

2/20 × 100 = 10%

3/20 × 100 = 15%

4/20 × 100 = 20%

5/20 × 100 = 25%

6/20 × 100 = 30%

7/20 × 100 = 35%

8/20 × 100 = 40%

9/20 × 100 = 45%

10/20 × 100 = 50%

11/20 × 100 = 55%

12/20 × 100 = 60%

13/20 × 100 = 65%

14/20 × 100 = 70%

15/20 × 100 = 75%

16/20 × 100 = 80%

17/20 × 100 = 85%

18/20 × 100 = 90%

19/20 × 100 = 95%

20/20 × 100 = 100%

As you can see that 14/20 × 100 = 70%

Hence, the student answer 14 question correct.

Kavinsky

Answer:

Step-by-step explanation:

We know that:

We also know:

Here are the answers verified:

The correct option is B.

Answer:

Step-by-step explanation:

I would just like to explain how this works with a visual (please enjoy my drawing <3 haha)

With my drawing we know that the bird is 150 feet above sea level, and the fish is 100 feet below sea level.

From the bird to the water it is 150 feet, from water to fish is 100 feet

From the bird to the fish it is 150 feet + 100 feet

so we know from the bird (150 feet above sea level) to the fish(100 feet below sea level).

Answer:

C

Step-by-step explanation:

  x = 7 cos (2pi/3)            y =  7 sin (2pi/3)

  x = -7/2                          y = 7 sqrt(3) /2

Answer:

The solution is in the image

Answer:

y = (-2/3)x + 4

Step-by-step explanation:

the equation of a line is given by the formula y = mx + b where m is the slope and b is the y intercept.

so,

y = (-2/3)x + b

to find b we plug in the values of x and y given by the point (-6,8)

8 = 4 + b

b = 4

so y = (-2/3)x + 4

Answer:

Infinitely many solutions

Step-by-step explanation:

Equations can either have no solutions, one solution, or infinitely many solutions.

Examples:

Given: 3(2x − 4) = 2(3x − 6)

Distribute:

3(2x − 4) = 2(3x − 6)

3(2x) + 3(−4) = 2(3x) + 2(−6)

6x − 12 = 6x − 12

As both sides of the equation are identical, this equation has an infinite number of solutions.

Learn more here:

https://brainly.com/question/25326244

Answer:

9

Step-by-step explanation:

Do the powers

Then the bracket

Then x or ÷

And then + or -

Answer:

A

Step-by-step explanation:

You have to simplify the brackets in turn.

3 times x^3- 7x+1 = 3x^3- 21x+ 3

then do 3 times x + 4= 3x + 12

you then add them all together, if they have a power add them, if they just have an x add them, and if they are just a number add them.

So it goes to 3x^3- 24x - 9,

this is because 3x^3 cant be added/ subtracted by anything, -24x is made from -21x- 3x, and -9 is made from 3 - + 12, so this means 3 - 12 = -9.

I hope this helps, have a lovely day.

Step-by-step explanation:

it's either 3 or 2 probably

The cylinder is a three-dimensional shape and it has a radius, diameter and a height

Assume the square has the following dimensions:

Base dimensions = x

Height = h

Assume the cylinder has the following dimensions:

Radius  = r

Height = h

When the square is drilled out, the lateral surface area would be:

Lateral Area = Cylinder - Square

This gives

[tex]Lateral = 2\pi rh - 4xh[/tex]

Factor out 2h

[tex]Lateral = 2h( \pi h - 2x)[/tex]

Using the same dimensions in (a), we have:

Total surface Area = Cylinder - Square

This gives

[tex]Area = 2\pi r(r +h) - 2(2x^2 - xh)[/tex]

Factor out 2

[tex]Area = 2[\pi r(r +h) - (2x^2 - xh)][/tex]

Using the same dimensions in (a), we have:

Base area = Cylinder - Square

So, we have:

[tex]Base = \pi r^2 - x^2[/tex]

Using the same dimensions in (a), we have:

Volume = Cylinder - Square

So, we have:

[tex]Volume = \pi r^2h - x^2h[/tex]

Factor out h

[tex]Volume = h(\pi r^2 - x^2)[/tex]

Read more about cylinder at:

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Answer:

  No

Step-by-step explanation:

An exponent signifies the number of times the base is a factor in the product. When products involving the same base are multiplied, the total number of factors is the sum of the number in each of those products.

__

  [tex]5^2=5\cdot5\\\\5^9=5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\\\\5^2\cdot5^9=(5\cdot5)\cdot(5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5)=5^{11}[/tex]

The base of the exponent in the product is the value that is a repeated factor. It is 5, not (5·5).

Your friend is not correct.

__

The general rule for exponents is ...

  (a^b)(a^c) = a^(b+c)

Answer:

Step-by-step explanation:

Area of rectangle is  b*h

so

a = (x-3)(x+7)

75 = (x-3)(x+7)

75 = x²+4x-21

0 = x²+4x-96

(x+12)(x-8)=0

x = -12, or x = 8

Answer:

Doing something despite difficulty or delay in achieving success.

Step-by-step explanation:

Answer:

continued effort to do or achieve something despite difficulties, failure, or opposition

Step-by-step explanation:

Answer:

Width = 9ft.

Length=22ft.

Step-by-step explanation: