Answers
Given:
A circle of radius r inscribed in a square.
To find:
The expression for the area of the shaded region.
Solution:
Area of a circle is:
[tex]A_1=\pi r^2[/tex]
Where, r is the radius of the circle.
Area of a square is:
[tex]Area=a^2[/tex]
Where, a is the side of the square.
A circle of radius r inscribed in a square. So, diameter of the circle is equal to the side of the square.
[tex]a=2a[/tex]
So, the area of the square is:
[tex]A_2=(2r)^2[/tex]
[tex]A_2=4r^2[/tex]
Now, the area of the shaded region is the difference between the area of the square and the area of the circle.
[tex]A=A_2-A_1[/tex]
[tex]A=4r^2-\pi r^2[/tex]
[tex]A=4r^2-\pi r^2[/tex]
[tex]A=r^2(4-\pi )[/tex]
Therefore, the correct option is (a).
Related Questions
Please help !!!!!!!!!
Answers
Answer:
5
Step-by-step explanation:
3x -12 = -36
-36 ÷ -3 = 12
-7 + 12 = 5
Answer:
The value of -7 + 3(-12) ÷ (-3) is 5
Step-by-step explanation:
First: -7 + -36 ÷ (-3)
Second: -7 + 12
Third: = 5
Therefore your value of this equation is 5.
your welcome.
The top of a pie container is a circle. The radius of the pie is 8 inches and the radius of the container is 9 inches. What is the difference between the circumference of the container and the circumference of the pie in inches to the nearest tenth?
A 3.1 inches
B 6.3 inches
C 12.6 inches
D 25.1 inches
E 50.2 inches
Answers
Answer:
B
Step-by-step explanation:
2 pi r subtracted by 2 pi r, you get answer
2 x 3.14 ~ 6.28, x 9 ~ 56.54.
2 x 3.14 ~ 6.28, x 8 ~ 50.24
56.54 - 50.24 ~ 6.3
A concrete slab has the dimensions 4 yd by 2 yd by 1.2 yd. What is the volume of 40 of these concrete slabs
Answers
The volume of 40 of the concrete slabs given the dimensions of one concrete slab is 384 yd³.
What is the volume of one concrete slab?The concrete slab has the shape of a rectangular prism. So, the volume of a rectangular prism would be used to determine the volume of the concrete slabs.
Volume of one concrete slab = length x width x height
4 x 2 x 1.2 = 9.6 yd³
Volume of 40 concrete slabs = 40 x 9.6 = 384 yd³
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You know this??????????????
Answers
Answer:
y=x+15
Step-by-step explanation:
Daniel is baking cookies but does not have all of the he needs. The ratio of flour:sugar in his recipe is 3:2cups. If he only has 1.5cups of sugar, how much flour should he use to keep the ratio the same?
Answers
Answer:
Step-by-step explanation:
3:2 = 2.5:1.5
half of 2 is 1 so if you had 1.5 it would only be half. For a better explanation, 1 minute is 60 seconds half of a minute is 30 seconds. if you have 45 seconds it would be 3/4 of a second. this is hard for me to explain so if you need more examples just tell me in the comments.
i hope this helps
have a nice day/night
mark brainliest please:)
Suppose you waited 10 years to invest in the same retirement fund and have the same $400,000 for retirement at the same 8% interest. What amount will you have to deposit each month to match the value of your annuity?
Answers
Answer:
$7,196.42
Step-by-step explanation:
Using the compound interest formula to fins the amount after 10years;
A = P(1+r)^n
Principal P = $400,000
Rate r = 8% = 0.08
Time t = 10 years
Substitute
A = 400,000(1+0.08)^10
A = 400,000(1.08)^10
A = 400,000(2.1589)
A = 863,569.99
A ≈ 863,570
Hence the amount after 10 years is $863,570
Monthly deposit = $863,570/120 (10 years is equivalent to 120months)
Monthly deposit = 7,196.42
Therefore he will have to deposit $7,196.42 into his account monthly
i need help please i’ll give u a brainliest
Answers
Answer:
12
Step-by-step explanation:
c = sqrt(a^2+b^2)
Imput numbers and solve for b!
Find measure of angle A
Answers
Answer:
angel a is 65 degrees
Step-by-step explanation:
40+2x+10=180
40-40+2x+10-10=180-40-10
2x=130
x=65
checking:
65 + 10 + 40 = 75 + 40 = 115
115+65=180
180=180
A booster club sells raffle tickets • Before tickets go on sale to the public, 120 tickets are sold to student athletes. • After tickets go on sale to the public, the tickets sell at a constant rate for a total of 8 hours spread over I days. • At the end of this time, all tickets have been sold. If represents the hours since tickets go on sale to the public and represents the number of raffle tickets sold, which graph best represents the scenario?
Answers
Answer:
The top graph.
Step by step:
Before the tickets go on sale, 120 tickets were already sold.
After that, the tickets sell at a constant rate for a total of 8 hours.
At the end of this time, all the tickets were sold (we have 0 tickets left)
If x (horizontal axis) represents the hours since tickets go on sale, and y (vertical axis) represents the number of raffle tickets sold.
Then, at x = 0, we should already see y = 120
Because we start with 120 tickets sold.
Then, as x increases, the number of tickets sold also should increase, until we get x = 8 hours, where y stops increasing because all tickets are already sold.
Then we should have an increasing line that stops increasing at x = 8 hours.
Then the correct option is the above graph, where we have:
An increasing line.
y = 120 in the vertical axis (y = 120 when x = 0)
A 13 meter ladder is leaning against a wall. It reaches 12 meters up the wall How far is the base of the ladder from the base of the wal
Answers
Answer:
5
Step-by-step explanation:
Pythagorean Theorem. The 13-meter ladder is leaning against a wall, so it's the hypotenuse.
It reaches 12 meters up, so 12 is one leg.
[tex]a^{2} +b^{2}=c^{2}[/tex]
[tex]a^{2}+12^{2}=13^{2}[/tex]
[tex]a^{2}+144=169[/tex]
[tex]a^{2}=25[/tex]
a = 5
do this and thanks for help
Answers
Cubed root 240 = 6.2
So 6.2*3
Maybe
Use pie= 22/7 to approximate the circumference of a circle whose diameter is 28 inches.
Answers
Answer:
88 inches
Step-by-step explanation:
formula for circumference: 2pir or pi*diameter
22/7*28=88
88 inches
What is the volume 9inches 3inches 5inches
Answers
Answer:
135 can i have brain list
Step-by-step explanation:
9X3X5
200% of what number is 350?
Answers
Answer:
The answer is 175
What is 4 minus 3/4
Answers
Hope this helps:)
Use complete sentences to describe the domain of the consine function.
Answers
Answer:
The domain of a function is the set of the possible input values of the function. For example: consider the function f(x) = cos x, the domain of the function is the set of possible values of x.
The cosine function takes x values from all real numbers.
Therefore, the domain of the cosine function is a real numbers.
Step-by-step explanation:
Maurice ran out of gas. The gas tank in his car can hold 13.6 gallons of gas, but the gas cans only hold 3.4 gallons. How many gas cans would he need to fill his tank
Answers
Answer: 4
Step-by-step explanation: 13.6 divided by 3.4 = 136 then divide by 34 you get 34 from 3.4 but divide by 34. Once you divide 136 and 34 you get your answer 4.
find the shaded region of the figure below
Answers
Answer:
-x³ + 3x² - 14x + 12
Step-by-step explanation:
Area of outer rectangle = (x² + 3x - 4) * (2x - 3)
= (x² + 3x - 4) * 2x + (x² + 3x - 4) * (-3)
=x²*2x + 3x *2x - 4*2x + x² *(-3) + 3x *(-3) - 4*(-3)
=2x³ + 6x² - 8x - 3x² - 9x + 12
= 2x³ + 6x² - 3x² - 8x - 9x + 12 {Combine like terms}
= 2x³ + 3x² - 17x + 12
Area of inner rectangle = (x² - 1)* 3x
= x² *3x - 1*3x
= 3x³ - 3x
Area of shaded region = area of outer rectangle - area of inner rectangle
= 2x³ + 3x² - 17x + 12 - (3x³ - 3x)
= 2x³ + 3x² - 17x + 12 -3x³ + 3x
= 2x³ - 3x³ + 3x² - 17x + 3x + 12
= -x³ + 3x² - 14x + 12
There are three candidates for student council secretary: Greg, Brittany, and Eliza. There are also three candidates for treasurer: Trey, Fabian, and Paulina. An experiment using two dice is conducted to simulate the probability of Greg or Fabian being elected. The first die represents the secretary election. The numbers 1 and 2 represent Greg winning, 3 and 4 represent Brittany winning, and 5 and 6 represent Eliza winning. The second die represents the treasurer election. The numbers 1 and 2 represent Trey winning, 3 and 4 represent Fabian winning, and 5 and 6 represent Paulina winning. The experiment was performed eight times, and the results are recorded in the following table.Based on the simulation, what is the probability that Greg or Fabian will win the election?
Answers
Answer:
5/8
Step-by-step explanation:
I have the same problem and this answer was correct.
The table shows the number of games a team won and lost last season with a ratio of win to loss as 3:2. Therefore the tool most appropriate for use is a 5-section spinner with congruent sections, 3 representing a win and 2 representing a loss.
What is ratio?Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.
here, we have,
To calculate a win-to-loss ratio, divide the number of wins by the number of losses.
According to the given data:
Greg is creating a simulation, using previous year’s wins and losses, to foretell the team's conclusion.
Wins in the last season = 24
losses in the last season = 16
Ratio of wins and losses = 24:16 = 3:2
Chances of the team winning out of 5 matches is 3 and losing is 2.
The device which is most suitable for application in a simulation that implements the data is a 5-section spinner with congruent sections, 3 representing a win and 2 representing a loss.
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complete question:
the table shaws the number of games a team won and lost last season. Wins and losses last season number of games wins 24 losses 16 greg has tickets to six of the team’s games this season. He is designing a simulation, using last year’s wins and losses, to predict whether the team will win or lose each of the games he attends. Which tool is most appropriate for use in a simulation that fits the data?
1 a coin with one side representing a win and the other representing a loss
2 a 6-section spinner with congruent sections, 4 representing a win and 2 representing a loss
3 a 5-section spinner with congruent sections, 3 representing a win and 2 4representing a loss an 8-sided die with 5 sides representing a win and 3 sides representing a loss
(a) What was Jennifer’s gross pay for the year?
(b) How much did she pay in federal income tax?
(c) The amount in Box 4 is incorrect. Since Social Security is a 6.2% tax, what dollar amount should have been entered in Box 4?
(d) The amount in Box 6 is incorrect. Since Medicare is a 1.45% tax, what dollar amount should have been entered in Box 6?
(e) How much was Jennifer’s FICA tax (using the corrected values from (c) and (d))?
(f) Jennifer’s taxable income was $32,854. She’s filing her taxes as single. Does she owe the government more money in taxes, or will she receive a refund? How much money will she owe or receive? Explain your thinking process in your own words to earn full credit.
refer to images for help
Answers
B: She paid $3,982.48 in federal income tax.
C:$1,971.24
D:$476.38
E: $2,447.62
F:Jennifer will receive a refund. She will receive $231.48 in her tax refund because her income is $32,854 and she filed for taxes under the status that she is single so she only needs to pay $3,751 in Taxes but she ended up paying $3,982.48 which is $231.48 over how much she should’ve paid.
Jennifer’s gross pay for the year was $32,854. B: She paid $3,982.48 in federal income tax. C:$1,971.24, D:$476.38, E: $2,447.62.
We have given the images
We have to determine the statements a,b,c,d e, and f.
What is the tax?
A tax is a compulsory financial charge or some other type of levy imposed on a taxpayer by a governmental organization in order to fund government spending and various public expenditures.
A: Jennifer’s gross pay for the year was $32,854.
B: She paid $3,982.48 in federal income tax.
C:$1,971.24
D:$476.38
E: $2,447.62
F:Jennifer will receive a refund. She will receive $231.48 in her tax refund because her income is $32,854 and she filed for taxes under the status that she is single so she only needs to pay $3,751 in Taxes but she ended up paying $3,982.48 which is $231.48 over how much she should’ve paid.
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how do you determine a function if a relation is a function
Answers
Answer:
Hello! A function is easily identified when an x value does not have more than 1 y value. a y value can have as many x values to infinity, but x can only have one y.
Example...
x y
3 5
4 5
1 2
at a meeting ,everyone shakes hands exactly once with every other person . if there are 55 handshakes . then what Is the number of people attending
Answers
Every handshake takes 2. If no one shakes hands twice with another, there are 10+1 total people shaking hands (11).
Name them 1 thru 11. Make a line and 11 goes down the line and shakes 10 hands and then leaves. 10 then shakes 9 hands and leaves. 8 then shakes 7 hands and leaves. Etc. 2 shakes hands with 1 and leaves. 1 just leaves.
11— 10 hs
10— 9 hs
9— 8 hs
8— 7 hs
7— 6 hs
6— 5 hs
5— 4 hs
4— 3 hs
3— 2 hs
2— 1 hs
1— leaves
Total handshakes 55, total people 11.
Find the 82nd term of the following sequence.
-32, -27, -22, ....
Answers
CORRECT ANSWER GETS BRAINLIEST
Explain how you would apply exponent rules to evaluate for the value of (x³/x)² if x =1/2?
Answers
Answer:
1/16
Step-by-step explanation:
Picture is attached. The quickest way is to simplify BEFORE plugging in x = 1/2
PLEASE HELP FAST I WIL MARK BRAINLIEST
Answers
Answer: AB = 15 because sides AB and AD are congruent
Step-by-step explanation:
AH PLEASE SOMEONE HELP
Answers
Answer:
Variant b
Step-by-step explanation:
If you multiply it should be a+b but if you divided
A+b-c
A vendor purchase 8 dozen teacups to sell. She packed them into boxes of 4 and each and sold each box for$60. Calculate the amount of the money she earned from the sale of all the teapcups?
Answers
Answer: $1440
Step-by-step explanation:
So if we have 8 dozens that is 8*12=96 teacups
boxes of 4 means 96/4= 24 boxes in total with 4 teacups in each
Since she is being paid 60$ for each of the 24 boxes she makes exactly $1440
Please don't go around not answering others questions. We are all trying to pay it forward and help each other :)
If f(x) = x is changed to g(x) = -f(x + 3) + 2, how is the graph transformed?
Answers
Answer:
f(x) is flipped, and each point is moved 3 units to the left and 2 units up
Step-by-step explanation:
Which way will the parabola open? Explain.
Answers
Explanation:
As value of a changes from positive to negative or from negative to positive, the direction of opening changes. For negative values of a we got negative parabolas that open downward. As the original formula y = x^2 we see that x^2 will always be positive because when you square a number it always gives positive value. Therefore the direction for which it will open, depends on value of a.
Seriously, somebody please help me! I've been asking all day, someone actually help me and not just halfassly answer it for points.
Answers
Answer:
9. A = Length by Width
Length = x
Width = 12x - 6y
A = x(12x - 6y)
A = 12x² - 6xy
10. A = ½bh
h = 2ab
A = ½(b)(2ab)
A = ab²