Answer:
0.083 is the required probability.
Step-by-step explanation:
We are given the following in the question:
Probability of captain hitting pirate's ship =
[tex]P(A) = \dfrac{1}{2}[/tex]
Probability of pirate hitting the captain's ship =
[tex]P(B) = \dfrac{1}{6}[/tex]
Probability that both the pirate and the Captain hit each other's ships:
[tex]P(A\cap B) = P(A)\times P(B)[/tex]
Putting values, we get,
[tex]P(A\cap B) =\dfrac{1}{2}\times \dfrac{1}{6} = \dfrac{1}{12} \\\\P(A\cap B) = 0 .083[/tex]
0.083 is the probability that both the pirate and the Captain hit each other's ships.
40 POINTS PLEASE HELP
Explain how solve 4^(x + 3) = 7 using the change of base formula log^ b y= log y/ log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.
Answer:
-1.596
Step-by-step explanation:
4^(x + 3) = 7
log4 both sides
log4[4^(x + 3)] = log4(7)
(x + 3) × log4(4) = lg7/lg4
x + 3 = 1.403677461
x = -1.596322539
3. Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped
with side lengths of 10 inches, and the hole had side lengths of 4 inches, how much wood was
left after the hole was cut out?
Answer:
it would be 40 inche and there be not that much for the hole to left
Answer:
840 cubic squares
Step-by-step explanation:
I believe the answer is A can someone confirm please and thank you, I cant get this answer wrong.
Answer:
A is correct.
Step-by-step explanation:
HELP!!!!for the given situation identify the independent and dependent variables and then find a reasonable domain and range of values. Listed below will be four statements that relate to the given situation. She’s the statement that would have to be false given the situation and it’s parameters.
Jimmy earns eight dollars an hour at his job. He can work up to 40 hours per week
here are the statements
1)The range will be from zero to $400
2) there a dependent variable will be the amount of money he earns
3) The independent variable will be the number of hours he works
4) The domain will be from 0 to 40 hours
Answer:
1
Step-by-step explanation:
he cant earn 400 dollars because 8*40 is 320. if he cant work more than eight hours, theres no possible way he can earn 400 dollars ('least in a math equation).
Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of water remaining. The tank initially contains 350 liters and 20 liters leak out during the first day. When will the tank be half empty? How much water will there be after 4 days?
To solve the problem, use the concept of differential equations and solve for the rate of water leakage. Then, find the time at which the tank will be half empty and the volume of water after 4 days.
Explanation:To solve this problem, we can use the concept of differential equations. Let's denote the volume of water in the tank at any time t as V(t). We are given that the rate at which water leaks is proportional to the square root of the remaining volume, so we can write the differential equation:
dV/dt = k * sqrt(V)
Where k is the proportionality constant. We also know that during the first day, 20 liters leak out, so we can find k:
dV/dt = k * sqrt(350) = -20
Now, we can solve this differential equation to find the time at which the tank will be half empty, and the volume of water after 4 days.
Learn more about differential equations here:https://brainly.com/question/33814182
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The tank will be half empty (175 liters remaining) after approximately 3.6 days, and there will be about 135 liters of water remaining after 4 days. The problem involves solving differential equations relating to the leak rate being proportional to the square root of the remaining volume.
This problem involves solving a differential equation based on the rate at which water leaks out of a cylindrical tank. The leak rate is proportional to the square root of the volume of water remaining in the tank.
Differential Equation and Initial Conditions
Given:
Initial volume: 350 liters (V0)20 liters leak out in the first dayRate of leakage, dV/dt = -k√VWhere k is a constant. To find k, we use the initial conditions:
At t = 1 day,
V = 350 - 20
= 330 liters.
We integrate the differential equation:∫dV/√V = [tex]-k\int_{V_0(350)}^{V(330)} dt \quad \text{from} \quad t=0 \quad \text{to} \quad t=1[/tex]
Solving, we get:[tex]2\sqrt{V}\Bigg|_{350}^{330} = -kt\Bigg|_{0}^{1}[/tex]
2(√330 - √350) = -k(1)
Solving for k, we get:k ≈ 2(√350 - √330)
Finding When the Tank is Half Empty
Half of the initial volume is 350/2 = 175 liters.
We need to find t when V = 175.
Integrating the differential equation again:[tex]2\left(\sqrt{V}\Bigg|_{350}^{175}\right)[/tex] = -kt
2(√350 - √175) = kt
Substituting k, we get t ≈ 3.6 days.
Volume After 4 Days
We use our k value and solve for V when t = 4:[tex]2\left(\sqrt{V}\Bigg|_{350}^{V}\right)[/tex] = -k(4)
2√V = 2√350 - 4k
Solving for V, we find V ≈ 135 liters.PJ11
At the city museum, child admission is $5.70 and adult admission is $9.50. on Friday, 155 tickets were sold for a total sales of $1255.90. how many child tickets were sold that day?
i love brainless tttree
Answer: 57 child tickets were sold that day.
Step-by-step explanation:
Let x represent the number of child tickets that were sold.
Let y represent the number of adult tickets that were sold.
on Friday, 155 tickets were sold. It means that
x + y = 155
At the city museum, child admission is $5.70 and adult admission is $9.50. The ticket sales totaled $1255.90 on that day. It means that
5.7x + 9.5y = 1255.9- - - - - - - - - 1
Substituting x = 155 - y into equation 1, it becomes
5.7(155 - y) + 9.5y = 1255.9
883.5 - 5.7y + 9.5y = 1255.9
- 5.7y + 9.5y = 1255.9 - 883.5
3.8y = 372.4
y = 372.4/3.8
y = 98
x = 155 - y = 155 - 98
x = 57
A cylinder has a radius of 5 cm and a height of 16 cm. Another cylinder is four times as tall but has the same radius. How does the volume of the second cylinder compare to that of the first?
Answer:
The answer to your question is 4 times bigger.
Step-by-step explanation:
Data
radius = 5 cm
height = 16 cm
Cylinder 2, 4 times taller the radius is the same
Process
1.- Calculate the volume of the first cylinder
Volume 1 = πr²h
-Substitution
Volume = π(5)²(16)
-Simplification
Volume = 400π cm³
2.- Calculate the volume of the second cylinder
height = 4(16)
= 64
-Substitution
Volume = π(5)²(64)
-Simplification
Volume 2 = 1600π cm³
3.- Find the relationship between the volume
Volume 2 / volume 1 = 1600π / 400π
= 4
4.- The second cylinder is 4 times bigger than the first cylinder
Plz help ->
Find the arithmetic and the geometric means of
5 and 125
1 and 9
4 and 9
Answer: ok so for 5 and 125 it is 65 and 25
for 1 and 9 it is 5 and 3 and for 4 and 9 it is 13/2 and 6
How many solutions does this system have?
2x-4y=8
x+y=7
The system has ______
solution(s)
Answer:
The solution for the system is the pair (6,1).
Step-by-step explanation:
The system has two equations and two variables, therefore i has only one solution. To solve it we will multiply the second equation by "-2". So we have:
2x-4y = 8
x + y = 7 *(-2)
2x - 4y = 8
-2x -2y = -14
We now sum boh equations:
2x -2x -4y -2y = 8 -14
-6y = -6
y = -6/-6 = 1
2x - 4(1) = 8
2x - 4 = 8
2x = 8 + 4
2x = 12
x = 12/2 = 6
The solution is the pair (6,1).
Answer:
The system has 2 solution .
Step-by-step explanation:
The equation is a simultaneous equation
2x - 4y=8 ............(i)
x + y=7................(ii)
make x the subject of the formula in equation (ii)
x = 7 - y
Substitute the value of x in equation(i)
2(7 - y) - 4y = 8
14 - 2y - 4y = 8
14 - 6y = 8
-6y = 8 - 14
-6y = -6
divide both sides by -6
y = 1
insert the value of in equation (ii)
x + y = 7
x + 1 = 7
x = 7 - 1
x = 6
The system has 2 solution .
Shane is measuring a shelf. It is 24 inches long. He measures again to find the number of feet. Will the length of the shelf be less than, greater than, or the same length in feet?
Answer:
Same length
24 ÷ 2=12
There is 12 inches in a foot
1 + 1= 2 ft
24 inches = 2 feet
Answer:
The length of the shelf will be less than 24 in feet. It will be 2 feet long.
Step-by-step explanation:
Inches are a smaller unit than feet, meaning that when something is measured in inches, the numerical amount of inches will be higher than the numerical amount of feet. The ratio is 12 inches to 1 foot, meaning that even though the length may be the exact same, inches represents the length with a higher numerical value and feet represent the length with a lower numerical value.
There are 10 millimeters in 1 centimeter.Convert 27 centimeters to millimeters.
A. 2.7
B. 27
C. 270
D. 2700
Answer:
C. 270
Step-by-step explanation:
If there are 10 millimeters in 1 centimeter, that means there is 10 times the number of millimeters in a centimeter. So, we would multiply 27 centimeters by 10 to find the number of millimeters.
A baseball stadium holds 15,002 seats. The lower level has 50 fewer than three times as many seats as the upper
level. The middle level has 40 more than twice as many seats as the upper level.
x+ (2x + 40) + (3x - 50) = 15,002
Answer:
Upper level = 2502 seats
Middle level = 5044 seats
Lower level = 7456 seats
Step-by-step explanation: given that
A baseball stadium holds 15,002 seats.
Let the Upper, middle and lower levels be represented as U, M and L respectively. And x = number of seat at the upper level
The lower level has 50 fewer than three times as many seats as the upper. That is
L = 3x - 50 .... (1)
The middle level has 40 more than twice as many seats as the upper level. That is
M = 2x + 40
Where L = x
x+ (2x + 40) + (3x - 50) = 15,002
You solved for x and found out the upper level has 2,502 seats . How many seats are in the lower level and how many seats are in the middle ?
That is x = 2502
Substitute x into equation 1
L = 3(2502) - 50
L = 7456 seats
Substitutes x into equation 2
M = 2(2502) + 40
M = 5044 seats
Which ratio is also equal to StartFraction R T Over R X EndFraction and StartFraction R S Over R Y EndFraction? StartFraction X Y Over T S EndFraction StartFraction S Y Over R Y EndFraction StartFraction R X Over X T EndFraction StartFraction S T Over Y X EndFraction
Answer:
△RST ~ △RYX by the SSS similarity theorem. Which ratio is also equal to RT/RX and RS/RY ?
A.XY/TS
B.SY/RY
C.RX/XT
D.ST/YX
Step-by-step explanation:
Check attachment for solution
Answer:
D
Step-by-step explanation:
A grocery store has a small bag of apples for $5 and a large bag for $8. If you bought 6 bags and spent $45, how many of each size of bags did you buy?
Answer:
1 small bags and 5 large bags
Step-by-step explanation:
In this case we can solve it using a 2x2 system of equations, like this:
let x: number of small bag
let y: number of large bag
So:
5 * x + 8 * y = 45
x + y = 6 => x = 6 - y
Replacing, we are left with that:
5 * ( 6 - y) + 8 * y = 45
30 - 5 * y + 8 * y = 45
- 5 * y + 8 * y = 45 - 30
3 * y = 15
y = 15/3
y = 5
Now to calculate x:
x = 6 - 5
x = 1
this means that 1 small bag and 5 large bags
Answer:
he bought 1 bag of small apple and 5 bags of Large apple
Step-by-step explanation: given that A small bag of apples = $5 and
A large bag = $8.
If you bought 6 bags and spent $45,
Let number of small apple be S
And large Apple be L
L + S = 6 ....... (1) ×8
8L + 5S = 45 .......(2)
Solve equation 1 and 2 simultaneously
8L + 8S = 48
8L + 5S = 45
Eliminate L
3S = 3
S = 1
Substitute S in equation 1
L = 6 - 1 = 5
Therefore, he bought 1 bag of small apple and 5 bags of Large apple
For what value of X is expression
2x-1/x
[tex]2x - 1 \div x[/tex]
Steps to simplify:
2x - 1 / x
~Convert to fraction
2xx/x - 1/x
~Combine the fractions
2xx-1/x
~Simplify
2x²-1/x
Best of Luck!
What is the value of 3/7 times 0.1 divided by 5/21
Answer:
0.18
Step-by-step explanation:
Answer:
9/50
Step-by-step explanation:
0.1 is the equivalent of 1/10
You multiply:
[tex]\frac{3}{7} *\frac{1}{10}[/tex]
= [tex]\frac{3}{70}[/tex]
[tex]\frac{3}{70}[/tex]÷[tex]\frac{5}{21}[/tex] is the equivalent of
[tex]\frac{3}{70}* \frac{21}{5}[/tex]
which equals [tex]\frac{63}{350}[/tex], or [tex]\frac{9}{50}[/tex] simplified (divide both sides by 7)
Which graph represents this system? y = 2 x + 1. y = negative 4 x + 7. On a coordinate plane, a line goes through (0, 7) and (1, 3) and another goes through (1, 3) and (2, 5). On a coordinate plane, a line goes through (negative 4, 0) and (0, 7) and another line goes through (negative 4, 3) and (0, 1). On a coordinate plane, a line goes through (0, negative 4) and (1, 3) and another goes through (0, 2) and (1, 3). On a coordinate plane, a line goes through (0, 7) and (8, 5) and another line goes through (0, 1) and (8, 5).
Answer:
It is the first choice. (A)
Step-by-step explanation:
Red line: y = 2x + 1
Blue line: y = -4x + 7
find the diameter of a circle with an area of 90.25 pi square meters
Answer:
19 meters
Step-by-step explanation:
The area of a circle is given as [tex]90.25\pi[/tex]
-A circle's area is calculated using the formula:
[tex]A=\pi r^2, r=0.5D, D=Diameter[/tex]
#We substitute for area in the equation and solve for D;
[tex]A=\pi (0.5D)^2\\\\90.25\pi=\pi (0.5D)^2\\\\\sqrt{90.25}=0.5D\\\\D=19[/tex]
Hence, the circle's diameter is 19 meters
Diameter of a circle = 19 meters
Circle :
Circle is a rounded figure that consists of points that are equidistance from the center
Area of a circle :Area of a circle is the area enclosed by the circle . The distance between the center to the circumference of circle is the radius.
Diameter is a straight line from one end of circle to the other end and it passes through the center of the circle
Given that area of the circle is 90.25 pi square meters
Area of the circle formula is
[tex]Area = \pi r^2\\90.25\pi =\pi r^2\\divide \; both \; sides \; by \; pi\\90.25=r^2\\take \; square \; root \; on \; both \; sides\\r=\sqrt{90.25}\\ r=9.5[/tex]
diameter of the circle = 2 times of the radius
Diameter = 2 times 9.5=19 meters
Diameter of a circle = 19 meters
Learn more information about 'Circle' here :
brainly.com/question/23984227
A yearbook company was investigating whether there is a significant difference between two states in the percents of high school students who order yearbooks. From a random sample of 150 students selected from one state, 70 had ordered a yearbook. From a random sample of 100 students selected from the other state, 65 had ordered a yearbook. Which of the following is the most appropriate method for analyzing the results?
A. A one-sample zz-test for a sample proportion
B. A one-sample zz-test for a population proportion
C. A two-sample zz-test for a difference in sample proportions
D. A two-sample zz-test for a difference in population proportions
E. A two-sample zz-test for a population proportion
Answer:
Null hypothesis: [tex] p_1 = p_2[/tex]
Alternative hypothesis: [tex] p_1 \neq p_2 [/tex]
So we need to conduct a:
D. A two-sample z-test for a difference in population proportions
Because the idea is to check if the population proportions in the states are similar or not.
Step-by-step explanation:
For this case they are trying two proof if there is a significant difference between two states in the percents of high school students who order yearbooks, and we chan check this with the difference of proportions.
Lets say that [tex]p_1,p_2[/tex] are the two proportions of interest and we want to check the following hypothesis:
We have the following info given:
[tex]\hat p_1 = \frac{70}{150}= 0.47[/tex] proportion of students that had ordered a yearbook from one state
[tex]\hat p_2= \frac{65}{100}= 0.65[/tex] proportion of students that had ordered a yearbook from another state
[tex]n_1 = 150[/tex] sample size from one state
[tex]n_2=100[/tex] sample size from another state
Null hypothesis: [tex] p_1 = p_2[/tex]
Alternative hypothesis: [tex] p_1 \neq p_2 [/tex]
So we need to conduct a:
D. A two-sample z-test for a difference in population proportions
Because the idea is to check if the population proportions in the states are similar or not.
A zoo keeper published the following stem-and-leaf plot showing the number of lizard at each major zoo in the country. How many zoos have exactly 42 lizards
This question is incomplete because it lacks the diagram showing the leaf and stem plots
Find attached to this answer the diagram showing the Stem and leaf plots
Answer:
Only one Zoo has exactly 42 lizards
Step-by-step explanation:
If you check out the attached diagram , you will observe that there is a separation using a vertical line
In the diagram also we have been provided with a key which was explained as :
2|0 = 20 lizards
On the left hand side, we have number ranging from 0 - 6 arranged in a vertical form. On the right hand side we almost have numbers that are arranged in front of each number horizontally
Let me further explain the attached diagram
It is important to note that the numbers arranged vertically on the left are in the units of tens. Hence, using the given key :2l0
0|
1|
2| 0 6 8 8 8
This means , we have 20 lizards in one zoo, 26 lizards in one zoo, 28 lizards in 3 zoos
3| 0 2 6 6 7 8
30 lizards in one zoo, 32 lizards in one zoo, 36 lizards in 2 zoos , 37 lizards in one zoo and 38 lizards in one zoo
4| 1 2 6 6
We have 41 lizards in one zoo, 42 lizards in one zoo, and 46 lizards in two zoos
5l
6|
Based on the explanation given above, we can see that only one Zoo has exactly 42 lizards
Answer:20
Step-by-step explanation:
KHAN
PLZ HELP ME
I appreciate any help, especially if you can show me how you got the answer
Answer:
C
Step-by-step explanation:
Since this is an indererminate form, use L'Hopital
d(sint)/dt = cos(t)
d[ln(2e^t) - 1] = (2e^t)/[2e^t - 1]
As t --> 0,
cos(0) = 1
(2e^t)/[2e^t - 1] = 2
1/2 is the limit
The city limits of Las Pythagoras form a perfect shape of an isosceles right triangle whose legs are both 25 kilometers long. The population in Las Pythagoras is 100,000,000 people. What is the population density of Las Pythagoras?
Answer:
320,000 people / km²
Step-by-step explanation:
We need to find the area of the city first.
The area of a triangle is: [tex]A=\frac{1}{2} bh[/tex], where b is the base and h is the height.
Here, both b and h are the legs of the right triangle and they're equal to 25 km. So:
[tex]A=\frac{1}{2} bh[/tex]
[tex]A=\frac{1}{2} *25*25=312.5[/tex] km²
Population density is simply (population) ÷ (area). Here, the population is 100,000,000 people and the area is 312.5 km², so:
100,000,000 ÷ 312.5 = 320,000 people / km²
Answer:
320,000 people per km²
Step-by-step explanation:
Since two angles are equal, their opposite lengths are also equal
Assuming it's a right ankle triangle,
Area = ½ × 25 × 25 = 312.5 km²
Population density:
100,000,000/312.5
320,000
Find the area of the rectangle below.
(3x + 4) feet
(x + 3) feet
Answer:
Area= (3x+4)×(x+3)
Step-by-step explanation:
(3x^2+10x+12)feet
Answer:
3x² + 13x + 12 ft²
Step-by-step explanation:
To work out the area of a rectangle you have to multiply the length and width together. In this case the length is 3x + 4 and the width is x + 3
So
( 3x + 4 ) × ( x + 3 )
Remember FOIL when expanding brackets
F = First two so 3x × x = 3x²
O = Outer two so 3x × 3 = 9x
I = Inner two so 4 × x = 4x
L = Last two so 4 × 3 = 12
but we aren't finished
3x² + 9x + 4x + 12 = 3x² + 13x + 12
Don't forget unit! ft²
Write the number 6 x 10-5 in standard form.
Answer:
Step-by-step explanation:
[tex]6*10^{-5}= \frac{6}{100000}\\\\=0.00006[/tex]
Hello so I need help with my math since that's not my best subject and I'm also squarely brained so can I get some help
Answer:
212
Step-by-step explanation:
47 goes into 99 2 times
Bring down the 5
47 goes into 56 1 time
Bring the 9
47 goes into 94 2 times
18. A coin is flipped eight times where each flip comes up either heads or tails. Howmany possible outcomesa) are there in total?b) contains exactly three heads?c) contains at least three heads?d) contains the same number of heads and tail
Answer:
16
Step-by-step explanation:
a coin is 2 sided thus has 2 out comes so doing it 8 times = 16 outcomes
Mohamed and Li Jing were asked to find an explicit formula for the sequence -5\,,-25\,,-125\,,-625,...−5,−25,−125,−625,...Minus, 5, comma, minus, 25, comma, minus, 125, comma, minus, 625, comma, point, point, point. Mohamed said the formula is g(n)=-5\cdot5^{\large{n}}g(n)=−5⋅5 n g, left parenthesis, n, right parenthesis, equals, minus, 5, dot, 5, start superscript, n, end superscript, and Li Jing said the formula is g(n)=-5\cdot5^{\large{n-1}}g(n)=−5⋅5 n−1 g, left parenthesis, n, right parenthesis, equals, minus, 5, dot, 5, start superscript, n, minus, 1, end superscript. Which one of them is right? Choose 1 answer: Choose 1 answer:
Answer:
Li Jing
Step-by-step explanation:
Given the sequence:
-5,-25,-125,-625,...
Mohamed's Formula is given as: [tex]g(n)=-5\cdot5^{\large{n}}[/tex]
Using Mohamed's formula:
[tex]When\: n=1,g(n)=-5\cdot5^{\large{n}}=-5\cdot5^{1}=-25\\When\: n=2,g(n)=-5\cdot5^{\large{n}}=-5\cdot5^{2}=-125\\[/tex]
Li Jing's Formula is given as: [tex]g(n)=-5\cdot5^{\large{n-1}}[/tex]
Using Mohamed's formula:
[tex]When\: n=1,g(n)=-5\cdot5^{\large{n-1}}=-5\cdot5^{1-1}=-5\\When\: n=2,g(n)=-5\cdot5^{\large{n-1}}=-5\cdot5^{\large{2-1}}=-25\\[/tex]
We can see that Li Jing's Formula produces the gien sequence.
Li Jing is Right.
Answer:
Only Li Jing
Step-by-step explanation:
This is because the formula −5 * 5 is worng as the first term is reapeated again so it is Li Jing
What is the solution to -5m = -40?
Answer:
m=8
Step-by-step explanation:
-40 divided by -5
Your answer is 8
Answer:
8m would be the answer
Step-by-step explanation:
-5m/-5 = -40/5 = positive 8
Periodically a bottling company gets complaints that their bottles are not holding enough liquid. To test this claim the bottling company randomly samples 70 bottles and finds the average amount of liquid held by the bottles is 9.896 ounces with a standard deviation of .46 ounce. Suppose the p-value of this test is .054. State the proper conclusion.
Answer:
The null hypothesis was not rejected at 1% and 5% level of significance, but was rejected at 10% level of significance.
Step-by-step explanation:
The complaints made by the customers of a bottling company is that their bottles are not holding enough liquid.
The company wants to test the claim.
Let the mean amount of liquid that the bottles are said to hold be, μ₀.
The hypothesis for this test can be defined as follows:
H₀: The mean amount of liquid that the bottles can hold is μ₀, i.e. μ = μ₀.
Hₐ: The mean amount of liquid that the bottles can hold is less than μ₀, i.e. μ < μ₀.
The p-value of the test is, p = 0.054.
Decision rule:
The null hypothesis will be rejected if the p-value of the test is less than the significance level. And vice-versa.
Assume that the significance level of the test is, α = 0.01.The p-value = 0.054 > α = 0.01.
The null hypothesis was failed to be rejected at 1% level of
significance. Concluding that the mean amount of liquid that the
bottles can hold is μ₀.
Assume that the significance level of the test is, α = 0.05.The p-value = 0.054 > α = 0.05.
The null hypothesis was failed to be rejected at 5% level of
significance. Concluding that the mean amount of liquid that the
bottles can hold is μ₀.
Assume that the significance level of the test is, α = 0.10.The p-value = 0.054 < α = 0.10.
The null hypothesis will be rejected at 10% level of
significance. Concluding that the mean amount of liquid that the
bottles can hold is less than μ₀.
Ariel and her family are going to order one large circular pizza that has a diameter of 20 inches and one small circular pizza that has a diameter of 12 inches. Which measurement is closest to the difference between the area of the large pizza and the area of the small pizza in square inches? *
5 points
804 in. squared
427 in. squared
314 in. squared
201 in. squared
To calculate the difference in area between two circular pizzas, first compute the area of each using the formula A = πr². After finding the areas, subtract the smaller area from the larger one to find the difference. The result is approximately 201 square inches.
Explanation:The question involves calculating the area of two circles and finding the difference between the two. First, we need to find the radius of each pizza. Since the diameter is twice the radius, the large pizza has a radius of 10 inches (20 inches divided by 2), and the small pizza has a radius of 6 inches (12 inches divided by 2). The area of a circle is calculated using the formula A = πr², where π is approximately 3.14159, and r is the radius.
The area of the large pizza is A = π(10 inches)² = π * 100 inches² = 314.16 inches² (rounded to two decimal places). The area of the small pizza is A = π(6 inches)² = π * 36 inches² = 113.10 inches² (rounded to two decimal places). To find the difference, we subtract the area of the small pizza from the area of the large pizza, which gives us 314.16 inches² - 113.10 inches² = 201.06 inches², which is closest to 201 inches².