A single 6-sided dice is being rolled. What is the probability of rolling a 5 or an odd number?

Answers

Answer 1

S = sample space
S = set of all possible outcomes
S = {1,2,3,4,5,6}

E = event space
E = set of items we want to happen (rolling a 5, or rolling an odd number)
E = {1, 3, 5}
note: the event of "rolling a 5" is a subset of "rolling an odd number" because 5 is odd

n(S) = number of items in the sample space
n(S) = 6

n(E) = number of items in event space
n(E) = 3

Divide the values to get the probability
P(E) = n(E)/n(S)
P(E) = 3/6
P(E) = 1/2
P(E) = 0.50
P(E) = 50%

The answer in fraction form is 1/2
The answer in decimal form is 0.50
The answer as a percentage is 50%
These three values all represent the same idea, just written in different forms.

note: writing "P(E)" means "the probability of event E occurring", which I've defined as the event space above

Related Questions

Britany sends between 10 and 20 text messages per day. Each text message costs $0.80. Suppose Britany's cellular bill spans a period of 8 weeks. Which is a reasonable amount that she would spend on text messages on one cellular bill

Answers

well if its between 10 & 20 take the median which is 15 and multiple it by the about of days which is 56 and you get 840 dollars

At the school book sale, Michael bought 3 books for $6. Darnell bought 5 books for $10. Are these rates proportional?

Answers

Michael:
3 books = $6
1 book = $6 ÷ 3 = $2

Darnell:
5 books = $10
1 book = $10 ÷ 5 = $2

Both Michael and Darnell bought their book at $2/book. The rates are proportional.

Answer Yes, the rate of proportional.

3 for $6 = 6/3 = $2/book
-------------↑-----------------
Michael
_____________________________________________________________

5 for $10 = 10/5 = $2/book
---------------↑-------------------
Darnell
_____________________________________________________________

Yes,they can form a proportion because they are equal

Hope this helps :)

The graph of which function has a minimum located at (4, –3)?

f(x) = x2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = x2 – 4x + 5
f(x) = 2x2 – 16x + 35

Answers

[tex]f(x)=ax^2+bx+c[/tex]

The graph of this function has minimum if a > 0.

Minimum is in point (h; k) where:

[tex]h=\dfrac{-b}{2a};\ k=f(h)[/tex]

[tex]minimum(4;-3)\to h=4;\ k=-3[/tex]

[tex]f(x)=x^2+4x-11;\ a=1 > 0;\ b = 4\\\\h=\dfrac{-4}{2\cdot1}=-2\neq4[/tex]

[tex]f(x)=-2x2+16x-35;\ a=-2 < 0[/tex]

[tex]f(x)=x^2-4x+5;\ a=1 > 0;\ b=-4\\\\h=\dfrac{-(-4)}{2\cdot1}=\dfrac{4}{2}=2\neq4[/tex]

[tex]f(x)=2x^2-16x+35;\ a=2 > 0;\ b=-16\\\\h=\dfrac{-(-16)}{2\cdot2}=\dfrac{16}{4}=4\\\\k=f(4)=2\cdot4^2-16\cdot4+35=2\cdot16-64+35=32-64+35=3\neq-3[/tex]

Answer: Any graph of this functions hasn't a minimum located at (4; -3).

If the coordinates of minimum are (4; 3),
then your answer is f(x) = 2x² - 16x + 35

Answer:

f(x) = 1/2x^2 – 4x + 5 (the third option)

Step-by-step explanation:

On ed :)

The graph models the daily high temperature, H(t), in Santiago, Chile, t days after the hottest day of the year. What does the point (0,29) represent?

Answers

Final answer:

The point (0,29) on the graph models the daily high temperature in Santiago, Chile on the hottest day of the year, where '0' represents that hottest day and '29' is the high temperature on that day.

Explanation:

The point (0,29) on the graph represents the weather condition in Santiago, Chile on the hottest day of the year. Here, '0' in the pair represents the day which is essentially the hottest day and '29' is the high temperature on that day. It depicts that on this specific day, the highest temperature was 29. The graph is an example of a time series graph, where the changing patterns or trends are displayed over a certain period of time - in this case, the temperature changes across the days following the hottest day of the year.

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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

T.A.=

Answers

Answer: Total area of the given prism is (104 + 16√13) Square inches.

Step-by-step explanation:

By the given diagram,

In the right triangular prism,

The sides of the base ( right triangle ) are 4 inches and 6 inches,

We have to finds : T.A. ( the total area of the prism )

Thus, the total base area of the prism = 2 × ( Area of triangle having base 4 inches and height 6 inches )

= 2× ( 1/2 × 4 × 6 )

= 4 × 6

= 24 square inches,

Let the hypotenuse of the triangles having sides 4 and 6 is x inches, ( shown in the diagram )

Thus, by the given diagram,

[tex]x^2 =4^2+6^2[/tex]

[tex]x^2 = 16 + 36[/tex]

[tex]x^2 = 52[/tex]

[tex]x=2\sqrt{13}[/tex]

Now, the total lateral area of the prism,

= 8×2√13 + 8×4 + 8×6

= 16√13 + 32 + 48

= (16√13 + 80) square inches,

Since, the total area of the given prism (T.A.) = Total base area of the prism(B.A.) + Total lateral area ( L.A.)

= 24 + 16√13 + 80

= (104 + 16√13) Square inches.

Line Q is represented by the following equation: 2x + y = 11

Which equation completes the system that is satisfied by the solution (3, 5)? (4 points)

x + 2y = 15

x + y = 15

x + y = 8

x − y = 2

Answers

The answer is x + y = 8

The coordinates are (3,5) where 3 is the x coordinate and 5 is the y coordinate.

If you substitute (3,5) into x + y = 8

you'll get get

3 + 5 = 8 which is true

Answer:

the Answer is x + y = 8 because 3 + 5= 8

Step-by-step explanation:

What is the volume of a cylindrical bucket that is 35 cm tall and has a base with a diameter of 21 cm? Use pi= 22/7 and round your answer to the nearest tenth of a cubic centimeter.

Answers

Hello!

Formula for the volume of a cylinder: [tex]V = \pi r^{2}h [/tex]

Plug in the values and solve[tex] 12,127.5 = \frac{22}{7} * 10.5^2 * 35 [/tex]

The answer is 12,127.5. Hope I helped!

Answer: 12,127.5

Step-by-step explanation:EDGE2021

Calculus question... I need help understanding thanks.
Calculate Гx^3dx

Answers

Apply the power rule:

[tex]\displaystyle\int x^3\,\mathrm dx=\dfrac{x^4}4+C[/tex]

which holds since

[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac{x^4}4+C\right]=\dfrac{4x^3}4+0=x^3[/tex]

please help with math? will give branliest!!
2. A wildlife refuge in South America has howler monkeys and spider monkeys. A biologist working there randomly selected eight adults of each type of monkey, weighed them, and recorded their weights in pounds.
howler monkey: {15, 16, 17, 17, 17, 17, 18, 19}
spider monkey: {12, 13, 13, 14, 14, 14, 16, 16}
(a) Calculate the median each type of monkey.
(b) Calculate the mean for each type of monkey.
(c) Calculate the MAD for each type of monkey.
(d) Calculate the means-to-MAD ratio for the two types of monkeys.
(e) What inference can be made about the weight of both types of monkeys? Explain.
Answer:

Answers

howler 17 17 0.75
spider 14 14 1

The median of howler monkey is, 17

And, Median of spider monkey is, 14

The mean for the howler monkeys is 17 and the MAD is 0.8571.

The mean for the spider monkeys is 14 and the MAD is 1.1429.

The means-to-MAD ratio is 2.6249.

This means that on average, the number of mean absolute deviations that separate the means is 2.6. This means they are different.

Find the median of data set as;

For howler monkey;

There are 8 number of howler monkey.

Hence, Median is,

= (8/2 + 1)

= 5 th term

= 17

For spider monkey;

There are 8 number of spider monkey.

Hence, Median is,

= (8/2 + 1)

= 5 th term

= 14

To find the mean of the howler monkeys, add all of the data values and divide by 7:

= (15+16+17+17+17+17+18+19)/7

= 119/7

= 17

To find the MAD, subtract each data point from the mean; take the absolute deviation; then average these together:

= (|15-17|+|16-17|+|17-17|+|17-17|+|17-17|+|17-17|+|18-17|+|19-17|)/7

= (2+1+0+0+0+0+1+2)/7

= 6/7

= 0.8571

And, Repeating these processes for the spider monkeys:

Mean:

(12+13+13+14+14+14+16+16)/7

= 98/7

= 14

And, MAD:

= (|12-14|+|13-14|+|13-14|+|14-14|+|14-14|+|14-14|+|16-14|+|16-14|)/7

=(2+1+1+0+0+0+2+2)/7

= 8/7

= 1.1429

To find the means-to-MAD ratio, find the difference in the means and divide it by the larger MAD:

17-14=3;

Hence, We get;

3/1.1429 = 2.6249

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Please help!!!!!!!!!!!!!!

Answers

Pay attention here because I'm adding an extra letter to our circle to help keep track of the values in our formula. OUTSIDE of the intercepted arc I'm adding the point E. So the major arc is arc BEG and the minor arc is arc BG. The formula then for us is ∠[tex]BFG= \frac{1}{2}(arcBEG-arcBG) [/tex]. We just don't have values for the arcs yet. If the measure of the central angle is 4x+238, then the measure of arcBG is also 4x+238. Around the outside of the circle is 360°. So we will use it in an expression. ArcBEG=360-(4x+238). Fitting that into our formula we have [tex]2x+146= \frac{1}{2}[(360-4x-238)-(4x+238)] [/tex]. Doing all the simplifying inside there we have [tex]2x+146= \frac{1}{2}(122-4x-4x-238) [/tex] and [tex]2x+146= \frac{1}{2}(-8x-116) [/tex]. Multiply both sides by 2 to get rid of the fraction: 4x+292=-8x-116. Combine like terms to get 12x = -408 and divide to solve for x. x = -34. Fourth choice down from the top.

4 students ran for class president. In the elction, Mario got 40% of the votes. Jazmyne got 35% of the votes, Arturo got 10%,and Rachel got 60 votes. How many students voted?

Answers

Rachel = 100% - 35% - 40% - 10% = 15%

15% = 60 votes

1% = 60 ÷ 15 = 4 votes

100% = 4 x 100 = 400 votes

Answer: 400 students voted

The length of a rectangular field is represented by the expression 14x-3x^2+2yThe width of the field is represented by the expression 5x-7x^2+7y How much greater is the length of the field than the width?

Answers

[tex](14x-3x^2+2y)-(5x-7x^2+7y)\\\\=14x-3x^2+2y-5x+7x^2-7y\\\\=-3x^2+7x^2+14x-5x+2y-7y\\\\=4x^2+9x-5y[/tex]

#2 The lunch choices last Friday were mushroom or pepperoni pizza. The cafeteria made 57 mushroom pizzas and 38 pepperoni pizzas. What percentage of the pizzas were mushroom pizzas?

Answers

60% of the pizzas were mushroom pizzas.
To find this, you add up 57 and 38 to find the total number of pizzas, then divide 57 (number of mushroom pizzas) by 95 (the total). This will give you 0.6, which you miltiply to get a percent. Thus getting 60% as the final answer.

I hope this helps!

To find the percentage of pizzas that were mushroom pizzas, you must divide the number of mushroom pizzas by the total number of pizzas. To find the total number of pizzas, we must add the number of mushroom and pepperoni pizzas together.

57 + 38 = 95

Next, we can complete our division.

57/95 = 0.6

Finally, we should multiply by 100. This is because to convert a decimal to a percentage, we must move the decimal point two places to the right so that this value is out of 100 total percent.

0.6 * 100 = 60%

Therefore, 60% of the total pizzas are mushroom.

Hope this helps!

The width of a rectangle is 5 inches less than twice the length. The area of the rectangle is 700 square inches. What is the length of the rectangle?

Answers

To calculate the length of the rectangle we let the length be x in, let width be
(2x-5) inches
The area will be given by:
A=length×width
A=x(2x-5)
but
A=700 in²
thus
700=x(2x-5)
700=2x²-5x
this can be written in quadratic form as:
2x²-5x-700=0
solving the quadratic we get:
x=20 or x=-35/2
since the length cannot be negative then:
x=20 in
thus the width will be:
2*20-5
=40-5=35 inches

A system of equations consists of two lines. One line passes through (-1, 3) and (0, 1). The other line passes through (1, 4) and (0, 2). Determine of the system has no solution, one solution, or an infinite number of solutions.

Answers

The equation of the line in its generic form is:
y = mx + b
Where,
m = (y2-y1) / (x2-x1)

For (-1, 3) and (0, 1):
We look for the value of m:
m = (1-3) / (0 - (- 1))
m = (- 2) / (0 + 1)
m = -2
We look for the value of b:
1 = m (0) + b
b = 1
The line is:
y = -2x + 1

For (1, 4) and (0, 2):
We look for the value of m:
m = (2-4) / (0-1)
m = (- 2) / (- 1)
m = 2
We look for the value of b:
2 = m (0) + b
b = 2
The line is:
y = 2x + 2

The system of equations is:
y = -2x + 1
y = 2x + 2

Answer:
the system has one solution

What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 120? A. 720 B. 900 C. 1080 D. 180 E. 360 F. 540

Answers

Sum of the measures of the interior angles of a regular polygon is 180°, using properties of interior and exterior angle and regular polygon.

What is a regular polygon?

A regular polygon is a n-sided polygon in which all sides are of same length and are symmetrically placed about the center.

Properties of interior and exterior angles:

1. The sum of adjacent interior and exterior angle for a polygon is 180°.

2. The sum of exterior angles of a polygon is always equal to 360°.

Here,

Let's consider number of exterior angle=x

given that: each exterior angle measures 120°.

Now, using 2nd property,

x*120 = 180

x = 3

So, total number of exterior angles are = 3

Using 1st property,

each interior angle measures = 180 - 120

= 60°

And total number of interior angle = total number of exterior angle

= 3

So, the sum of interior angles = 3*60

= 180° .

Hence, we reached our answer.

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Mike has attempted 84 free throws. Of those attempted, 63 have gone in the basket. Based on this rate, what is the probability that Mike's next free throw attempt will go in the basket?

Answers

Final answer:

The probability that Mike's next free throw attempt will go in the basket is 75%.

Explanation:

To find the probability that Mike's next free throw attempt will go in the basket, we can use the ratio of successful attempts to total attempts. In this case, Mike has made 63 out of 84 attempts. So the probability can be calculated as:

Probability = Number of successful attempts / Total number of attempts

Probability = 63 / 84

Probability = 0.75

Therefore, the probability that Mike's next free throw attempt will go in the basket is 0.75 or 75%.

Write the equation of the line going through the point (4,6) that is perpendicular to the lie 3x+6y=12

Answers

3x + 6y = 12
6y = - 3x + 12
y = - 1/2x + 2

Since your slope is - 1/2, we take the opposite reciprocal to find the perpendicular slope. Your perpendicular slope is 2.

y = 2x + b

Plug in the point to solve for b and get your final line.

6 = 2(4) + b
6 = 8 + b
6 - 8 = b
- 2 = b

y = 2x - 2 is your perpendicular line

Hal’s sporting Goods had a 1 day sale. The original price of a mountain bike we 325. In a sale it was 276.25. What is the percent decrease for this sale?

Answers

Well, the decrease of the amount would be $48.75 then you would divide this by how the original price which is $325, so the answer would be about 6% decrease.

Decrease = 325 - 276.25 = $48.75

Percentage decrease = 48.75/325 x 100 = 15%

Answer: 15%

a cooking show currently has about 223,00 regular viewers. The number of regular viewers has been decreasing at a rate of 4.7% per year. Which is the best prediction for the number of regular viewers the show will have in 6 years?
35,420
37,167
104,810
167,056

Answers

The best prediction for the number of regular spectators that the program will have in 6 years is obtained with the following formula:
Pf = Po×(1-b) ^ t
Where:
Pf = final population
Po = initial population
b = decrease rate
t = timpo in years
So:
Pf = 223.00×(1-0.047) ^ 6
Pf = 167,056
The answer is the last option.

What Is the Measure of Y

41

49

51

61

Answers

The answer is:  " 41 " .
_____________________________________________________
→  " y = 41 " .
_____________________________________________________
Explanation:
______________________________________________________

From the "image attached", note that:

"139" and "y" ; together; form a "straight line" ;

→ that is: "139" and "y" are supplementary ;

and by definition; "supplementary angles" add up to " 180 degrees" ;
______________________________________________________

  → y + 139 = 180 ; Solve for "y" ;

Subtract " 139 " from each side of the equation;
to isolate "y" on one side of the equation; & to solve for "y" ;

→ y + 139 − 139 = 180 − 139 ;

to get:

→ y = 41 degrees:
_____________________________________________________
The answer is: " 41 " .
_____________________________________________________
→ " y = 41 " .
_____________________________________________________

Answer:

ITS A.) 41

Step-by-step explanation:

Write the equation of a line that is parallel to y=-0.75x and that passes through the point (8,0)

Please help

Answers

Answer:

The equation of the line that is parallel to the given is equal to the expressions below:

[tex]\displaystyle \boxed{ y = -0.75(x - 8) \text{ or } y = -0.75x + 6 }[/tex]

General Formulas and Concepts:
Algebra I

Slope-Intercept Form: y = mx + b

m - slopeb - y-intercept

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinatey₁ - y coordinatem - slope

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyley = - 0.75x \\\text{Point } (8, 0) \\[/tex]

Step 2: Find Equation

Recall that a parallel line has the same slope as the one that is given. Therefore, we can define the slope of our parallel line to be m = -0.75:

[Point-Slope Form] Substitute in variables:
[tex]\displaystyle y - 0 = -0.75(x - 8)[/tex]Simplify:
[tex]\displaystyle \boxed{ y = -0.75(x - 8) }[/tex]

We can rewrite this form into slope-intercept form as well by expanding:

[tex]\displaystyle y = -0.75(x - 8) \rightarrow \boxed{ y = -0.75x + 6 }[/tex]

∴ we have found the equation of a line that is parallel to the given information.

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Topic: Algebra I

Answer:

what the guy above said

Step-by-step explanation:

Shelly is installing a fence around the edge of her property. Her property measures 41 meters by 35 meters. What is the perimeter of Shelly's property?
A.142 m
B.152 m
C.1,420 m
D.1,435 m

Answers

It is D, Hope this helps!

The perimeter of Shelly's property is 152 meter.

Option (B) is correct.

It is required to find the perimeter.

What is rectangle?

A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square. A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.

Given that:

The Shelly's property is in the shape of rectangle.

Length of property=41 meter

Breadth of property=35 meter

Perimeter of rectangle=2(Length+ Breadth)

Perimeter of rectangle=2(41+ 35)

Perimeter of rectangle=2*76

Perimeter of rectangle=152 meter

Therefore, the perimeter of Shelly's property is 152 meter.

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( Please help me, the year is ending and I'm almost at a failing grade): ) An athlete is running along a circular path that has a diameter of 250 yards. The arc traveled by the athlete is 120 degrees. Using 3.14 for (symbol that looks like two Ts that are connected), how many yards did the athlete run? Round the answer to the nearest yard.

Answers

For this case the arc length is given by:
S = R * theta
Where,
R: radius of the circle
Theta: central angle
Substituting values we have:
S = (250/2) * (120) * (3.14 / 180)
S = 261.6666667 yards
Round to the nearest yard:
S = 262 yards
Answer:
the athlete ran:
S = 262 yards

To find the distance an athlete ran on a circular path with a diameter of 250 yards and an arc length of 120 degrees, calculate the arc length using the radius and angle in radians. The athlete ran approximately 262 yards.

To find the distance the athlete ran around a circular path with a given arc length of 120 degrees and a diameter of 250 yards, first, determine the radius of the circle:

Radius (r) = Diameter / 2 = 250 yards / 2 = 125 yards

Convert 120 degrees to radians: 120 degrees × π / 180 = 2π / 3 radians

Calculate the arc length using the formula: Arc Length = Radius × Angle in radians = 125 yards × 2π / 3 = 250π / 3 ≈ 261.8 yards

Therefore, the athlete ran approximately 262 yards.

Bernice estimated that 69% of 242 is 168. Is her estimate reasonable?

Answers

Her estimate is not reasonable.

Since she estimated 69%, you could do either of these options. You could...
A. Divide 242 (or .5) to show how much half off would be, then compare her estimate with half of 242 (121). OR...
B. Simply divide 242 by 69% (.69) and compaor her estimate to the exact amount (166.98).

I hope this helps!

Answer:

D Yes, because her calculation should be 70% of 240.

Step-by-step explanation:

Let A = {the whole numbers} and B = {the integers}. Find A ∩ B.
0
the integers
the whole numbers
the real numbers

Answers

The correct answer is THE WHOLE NUMBERS.
Whole numbers refers to numbers starting from zero to any number, but they do not include negative numbers, fractions and decimals. Integers refers to whole numbers but they also include negative number. The intersection between the two refers to the numbers that are common to the the two of them. Thus, in this case the common numbers are the whole numbers, because whole numbers exist in the two groups.

The answer is WHOLE NUMBERS.

A trait has two alleles, and their frequencies are represented by p and q. if p = 0.90, what is q?

Answers

The sum of the frequency is equal to 1.
Therefore, we have the following equation:
p + q = 1
Substituting values we have:
0.90 + q = 1
Clearing the value of q we have:
q = 1 - 0.90
q = 0.10
Answer:
The value of q is given by:
q = 0.10

If f(x)=2x+1 and g(x)=x^2-7, find (f+g)(x)

A. x^2=2x-6
B. 2x^2-15
C. x^2+2x+8
D. 2x^3-6

Answers

f(x)=2x+1 and g(x)=x^2-7
(f+g)(x) = 2x + 1 + x^2 - 7
(f+g)(x) = x^2 + 2x - 6

answer
x^2 + 2x - 6

Answer: The correct option is (A) [tex]x^2+2x-6.[/tex]

Step-by-step explanation: We are given the following two functions :

[tex]f(x)=2x+1,\\\\g(x)=x^2-7.[/tex]

We are to find the value of [tex](f+g)(x).[/tex]

We know that

for any two functions p(x) and q(x), we have

[tex](p+q)(x)=p(x)+q(x).[/tex]

Therefore, we get

[tex](f+g)(x)\\\\=f(x)+g(x)\\\\=(2x+1)+(x^2-7)\\\\=2x+1+x^2-7\\\\=x^2+2x-6.[/tex]

Thus, option (A) is CORRECT.

A survey was conducted that asked 1011 people how many books they had read in the past year. results indicated that x overbarequals14.8 books and sequals16.6 books. construct a 90% confidence interval for the mean number of books people read. interpret the interval

Answers

Since we do not know the population standard deviation, we will use the t-distribution to construct the 90% confidence interval of the mean number of books people read. The value of [tex]t_{\frac{\alpha }{2}}[/tex] with 1010 degrees of freedom and with alpha equals to 0.10 is 1.64

First, we need to solve for the margin of error, E.
[tex]E=t_{\frac{\alpha }{2}}\cdot \frac{s}{\sqrt{n}}=1.64\cdot \frac{16.6}{\sqrt{1011}}=0.86[/tex]

The lower bound of the confidence interval is
[tex]LB=\overline{x}-E=14.8-0.86=13.94[/tex]

The upper bound of the confidence interval is
[tex]LB=\overline{x}+E=14.8+0.86=15.66[/tex]

Therefore, the 90% confidence interval is (13.94, 15.66).

We are 90% confident that the interval from 13.94 books to 15.66 books does contain the true value of the population mean number of books people read.

What size does the radius of a sphere need to be for its volume to be larger than its surface area? HINT! It is less than 10. HINT! It is NOT a whole number. If you can show me a whole number for a radius where the surface area and volume are equal, then any radius bigger than that will have a larger volume.

To get full points you will need to SHOW me formulas for surface area of a sphere, volume of a sphere, and calculations on how you found your answer.
Question 1 options:
The formula for the surface area of a sphere is 4 x pi x radius^2
The formula for the volume of a sphere is 4/3 x pi x radius^3.

Answers

we know that
volume of a sphere=(4/3)*pi*r³----> (r/3)*(4*pi*r²)
and
surface area of sphere=4*pi*r²
so
the volume of a sphere=(r/3)*surface area of sphere
therefore
if r=3
volume of a sphere=(3/3)*surface area of sphere
volume of a sphere=surface area of sphere

if r> 3
the term (r/3) is > 0
so
volume of a sphere > surface area of sphere

if r<3
the term (r/3) is < 0
so
volume of a sphere < surface area of sphere

examples
1) for radius r=3 units
volume of a sphere=(4/3)*pi*3³----> 113.04 unit³
surface area=4*pi*3²----> 113.04 units²
volume is equal to surface area

2) for radius r=10 units
volume of a sphere=(4/3)*pi*10³----> 4186.67 unit³
surface area=4*pi*10²----> 1256 units²
volume is > surface area

3) for radius r=2 units
volume of a sphere=(4/3)*pi*2³----> 33.49 unit³
surface area=4*pi*2²----> 50.24 units²
volume is < surface area

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