Find the area of a circle with a radius of 9. Leave the answer in terms of π.

radius= 8 m

the volume of the sphere

[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]

[tex]v = \frac{4}{3} \times \pi \times {8}^{3} [/tex]

[tex]v = 2144.66058 \: {m}^{3} [/tex]

[tex]v = 2144.7 \: {m}^{3} [/tex]

therefore, the volume of the given sphere is 2144.7 cubic meters.

[tex]\large\boxed{Formula: V= \frac{4}{3}\pi {r}^{3}}[/tex]

In this question the radius is given so we'll simply have to substitute the values and solve.

Let's solve!

Substitute the values according to the formula.

[tex]V= \frac{4}{3}\times\pi\times{8}^{3}[/tex]

Calculator value:

[tex]V= 2144.660585 \: {m}^{3}[/tex]

Now, we'll have to round off to the nearest tenth.

The value in hundredths place is greater than 5 so, we will have to round up which means, we'll have to add 1 to the tenths place.

Final answer:

[tex]\large\boxed{V= 2144.7 \: {m}^{3}}[/tex]

Hence, the volume of the given sphere is 2144.7 cubic meters.

Answer:

12x < 200

Step-by-step explanation:

12 - x ≥ 4

-x  ≥  -8

x ≤ 8

12 is not a solution to this one.

x + 4 ≤ 12

x  ≤  8.

12 is not a solution to this one.

12 x < 200

x < 200/12

x <  16 2/3

12 is a solution.

Answer:

Step-by-step explanation:

Answer: Okay, I believe it is mean and 4inches

Step-by-step explanation:

If you add altogether, it is 40 and of course divide by 10 (the number of data) it’s 4

Answer: HCF=130

Step-by-step explanation:

The histogram shows that the majority of Omar's Final Fitness Team had weight loss between 30 to 49 kg, with only a few members achieving higher weight loss of 60 to 69 kg.

To create a histogram from the given data, follow these steps:

Step 1: Determine the range of the data (largest value - smallest value): Range = 90 - 31 = 59

Step 2: Choose a number of classes for the histogram. A convenient number of classes is usually between 5 and 15. For this data set, we can choose 6 classes.

Step 3: Determine the width of each class by dividing the range by the number of classes:

Class width = Range / Number of classes

Class width = 59 / 6 = 9.83

Round the class width up to 10 to make it a convenient number.

Therefore, the class width is 10.

Step 4: Determine the lower limit of the first class. Choose a value that is equal to or less than the smallest data point.

Lower limit of first class = 30

Step 5: Create the frequency distribution table by counting how many data points are in each class:

| Class Interval | Frequency |

|:----:|:----:|

| 30 - 39 | 2 |

| 40 - 49 | 2 |

| 50 - 59 | 0 |

| 60 - 69 | 2 |

| 70 - 79 | 1 |

| 80 - 89 | 1 |

Step 6: Draw the histogram. On a horizontal axis, mark the class intervals. On the vertical axis, mark the frequency for each class. Draw vertical bars to represent the frequency in each class. Make the bars touch each other so that it shows a continuous distribution.

Here's the histogram of the given data:

```

           Frequency

           |

           |    x

           |    x

   --------|----|----|----|----|---|---

          30   40  50   60   70  80  90

          |        Class intervals       |

```

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Answer:

In 15 years the final balance will be $632.15

Step-by-step explanation:

The final balance would be $632.15 and the total compound interest would be $332.15. If you have trouble with these kind of questions in the future I suggest using a compound interest calculator that can be found online :)

Answer:

(Choice B) Add the equations

Step-by-step explanation:

The equations that were given are:

[tex]5x + 3y = 9 \\ 4x - 3y = 9[/tex]

If we add the equequatiothen the y variable would be eliminated:

[tex] +3y + (-3y) = 0[/tex]

Answer:

We can tell by looking at the graph that it is a positive slope, so we can eliminate answers b and d.

It is rise over run. from a point, it goes up 4, and over 1.

4/1

which would be 4. The answer is C! Hope this helps!

Step-by-step explanation:

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

Let's consider two points on the line and calculate its Slope ~

Slope (m) of a line is :

[tex]\qquad \sf  \dashrightarrow \: m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex]\qquad \sf  \dashrightarrow \:m = \dfrac{2 - 1}{8 - 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \:m = \dfrac{1}{4} [/tex]

Answer:

h(x + 2) = x² + 2x

Step-by-step explanation:

The base function is :

⇒ h(t) = t² -- 2t

⇒ h(t) = t (t - 2)

Substitute x + 2 in place of t :

⇒ h(x + 2) = (x + 2) (x + 2 - 2)

⇒ h(x + 2) = (x + 2)(x)

⇒ h(x + 2) = x² + 2x

[tex]h(t) = t^2 -2t\\\\h(x+2) = (x+2)^2 - 2(x+2)\\\\~~~~~~~~~~~~=x^2 +4x + 4 -2x -4\\\\~~~~~~~~~~~~=x^2 +2x[/tex]

Answer: 48 feet

Step-by-step explanation:

Answer:

12 feet

Step-by-step explanation:

Containers are generally in the shape of a rectangular prism.

Formula

Step-by-step explanation:

the slope of f(x) = 1

for every increase of x by 1 also y increases by 1.

the slow of g(x) = -2

for every increase of x by one y decreases by 2.

so, we see, as

g(x) = k × f(x)

k = g(x) / f(x) = slope g / slope f = -2/1 = -2

why ? because both functions are linear functions (lines).

they look like

y = ax + b

with a being the slope of the line.

so, when multiplied by k, this is kax + kb, and we see k as factor already in the slope of the line itself.

Answer:

88km

Step-by-step explanation:

If a car travels 40 km in 1 hour, then that same car would travel 40*2.2 km in 2.2 hours.

So, the car travelled 88km in 2.2 hours

Remember that speed is a rate!

Answer:

speed=distance/travel time

distance=2*40+60*3=80+180=260 km

travel time=2+3=5 hrs

Average speed during entire journey=260/5=52 km/h

Answer:

I would be a right angle or 90°

Explanation:

If a square is cut out of the paper, every corner of a square is a right angle, so there's your answer.

hope i helped :)

Answer:

  y = 3x -4

Step-by-step explanation:

The two pairs of x and y values are used to find the slope of the line. That and one of the pairs is used to find the y-intercept. These values are put into the slope-intercept equation to give the equation of the line through the two points.

__

Each (x, y) pair represents a point on a graph. The slope-intercept equation for a line relates all the (x, y) pairs that lie on the line. That equation is ...

  y = mx +b . . . . . . where m is the slope, and b is the y-intercept

The slope is the "steepness" of the line. It is positive when the line goes up to the right, and negative when the line goes down to the right. It is 0 for a horizontal line.

The slope is found from (x, y) pairs using the formula ...

  m = (y2 -y1)/(x2 -x1) . . . . . . where (x1, y1) and (x2, y2) refer to different pairs

  m = (8 -(-1))/(4 -1) = 9/3 = 3 . . . . using the (x, y) values from the table

The y-intercept (b) is the y-value where the line crosses the y-axis. It can be found by rearranging the slope-intercept equation shown above:

  b = y - mx . . . . . . . for a line with slope m and a point (x, y) on the line

Using the first point listed in the table with the value of m we just found, we see that b is ...

  b = -1 - 3(1) = -4 . . . . . . for (x, y) = (1, -1) and m = 3

Now that we have found m=3 and b=-4 for the points in the table, we can put these values in the slope-intercept equation:

  y = mx +b

  y = 3x -4 . . . . . equation of the relationship in the table

The solution to the system of equation is (4.75, -11)

3.2x + 0.5y = 4.2

-1.6x -0.5y = 3.4

3.2x + 0.5y = 4.2

-1.6x -0.5y = 3.4

add equation(i) to equation(ii)

Therefore,

1.6x = 7.6

divide both sides by 1.6

x = 7.6 / 1.6

x = 4.75

Therefore,

3.2(4.75) + 0.5y = 4.2

0.5y = 4.2 - 15.2

0.5y = -11

y = - 11 / 0.5

y = - 22

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Answer:

The solution is x=4.75  and   y = -22

Step-by-step explanation:

To find the solution to the system of equations, we will follow the steps below:

3.2x + 0.5y = 4.2 --------------------------------------------------------------------------(1)

-1.6x -0.5y = 3.4 ----------------------------------------------------------------------------(2)

add equation (1) and equation (2)

1.6x =7.6

Divide both-side of the equation by 1.6 to get the value of x

1.6x /1.6 =7.6/1.6

x =4.75

substitute x = 4.75 into equation (1) and solve for y

3.2(4.75) + 0.5y = 4.2

15.2 + 0.5y = 4.2

subtract 15.2 from both-side of the equation

15.2 - 15.2 + 0.5y = 4.2-15.2

0.5y = -11

Divide both-side of the equation by 0.5

0.5y/0.5 = -11/0.5

y = -22

The solution is x=4.75  and   y = -22

The range of f as shown in the graph is -6 ≤ f(x) ≤ 5. The correct option is A. -6 ≤ f(x) ≤ 5

From the question, we are to determine the range of f.

The range of a function is the set of its possible output values.

The graph of the function, f, is shown in the diagram.

From the graph,

The minimum value of f on the x-axis is -6. That is, f(x) ≥ -6

and

The maximum value of f on the x-axis is 5. That is, f(x) ≤ 5

Combining the two expressions, we get

f(x) ≥ -6 and f(x) ≤ 5

That is,

-6 ≤ f(x) and f(x) ≤ 5

∴ -6 ≤ f(x) ≤ 5

Hence, the range of f as shown in the graph is -6 ≤ f(x) ≤ 5. The correct option is A. -6 ≤ f(x) ≤ 5

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If A and B are independent variables, P(A and B) =0.12. Therefore, option B is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

Given that, p(a)=0.60 and p(b)=0.20.

If A and B are independent variables,

P(A and B) =P(P∩B)= P(A) × P(B)

Here, P(P∩B)=0.60×0.20

= 0.12

Therefore, option B is the correct answer.

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Answer:  The correct option is (A) (2, -2).

Step-by-step explanation:  Given that rectangle with vertices at K, L, M and N is graphed on the coordinate plane as shown in the figure.The figure is rotated 360° counterclockwise using the origin as the center of rotation.

We are to find the location of the image of point K after the rotation.

We know that

a rotation of 360° in counterclockwise direction about the origin map a point to itself. That is, the co-ordinates of the image point will be same as the original one.

From the figure, we see that the co-ordinates of point K are (2, -2).

Therefore, after rotation of 360° counterclockwise using the origin as the center of rotation,

the co-ordinates of the image of point K will also be (2, -2).

Thus, the location of the image of point K is (2, -2).

Option (A) is CORRECT.

Answer:

A

Step-by-step explanation:

Answer:

D is not true.

Step-by-step explanation:

[tex] |4.5| = 4.5[/tex]

[tex] | - 45| = 45[/tex]

[tex]4.5 \leqslant 45[/tex]

Answer:

The solution is in the image

Answer:

If yo translate ABC down 5 units and to the right 2 units, it coincides with GHI.

Step-by-step explanation:

You just have to follow the directions

Answer:

,

Step-by-step explanation:

answer. is in the image

Total pounds of yogurt they buy (as a mixed number) : [tex]1\dfrac{5}{16}[/tex]

Mass is one of the principal quantities, which is related to the matter in the object  

The main mass unit consists of 7 units of other than other units of mass such as quintals, tons, pounds, ounces:  

Kilogram, kg  

Hectogram, hg  

Decagram, dag  

gram, g  

Decigram, dg  

centigram, cg  

milligrams, mg  

Each unit descends then multiplied by 10, and if one unit increases then divided by 10  

Fraction numbers are known as numerator and denominator

On a number line, fractions are expressed in points that lie between two integers

The general form of fractions is

[tex]\dfrac{a}{b}[/tex]

Mixed fractions consist of integers and ordinary fractions

A mixed number is a combination of a whole number and a fraction

Sara has 14 ounces of vanilla yogurt

Her father's yogurt weighs half of much, so her fathers have yogurt :

= 0.5 x 14 ounces

= 7 ounces

Total ounces of yogurt they buy

= 14 + 7 = 21 ounces

for 1 ounces (oz) the conversion = 0.0625 pounds(lbs)

So for 21 ounces there will be

= 21 x 0.0625

= 1.3125 pounds

if we express as a mixed number , it will be :

[tex]=\dfrac{13125}{10000}[/tex]

[tex]=1\dfrac{5}{16}[/tex]

Hence Total pounds of yogurt they buy (as a mixed number) : [tex]1\dfrac{5}{16}[/tex]

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