Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
The formula for the area of a sector can be written as follows:
Area = [tex] \frac{1}{2} [/tex][tex]r^{2} [/tex](R)
In the above formula, “r” represents the radius while “R” represents the radian measure of a sector. The radius is given to us in the image above as 10 inches. However, we still need the radian measure of the two sectors. To find this measure, we can use the following conversion:
1 degree = [tex] \frac{pi}{180} [/tex] radians
Because the two sectors have a given measure of 72 degrees, we need to multiply both sides of the above conversion by 72:
72 degrees = [tex] \frac{72pi}{180} [/tex]
Reduce the fraction on the right side of the equation:
72 degrees = [tex] \frac{2pi}{5} [/tex]
We now have the radian measure of both sectors. Now simply insert this and any other known values into the “area of a sector” formula above:
Area = [tex] \frac{1}{2} [/tex][tex]10^{2} [/tex]([tex] \frac{2pi}{5} [/tex])
Simplify the right side of the equation to get the following answer:
Area = 20 pi
We have now proven that the area of one sector is equal to 20 pi.
If, however, you need the combined area of the two identical sectors, simply multiply the proven area by 2 to get a total area of 40 pi.
I hope this helps!
Answer: 40 pi
Step-by-step explanation:
Related Questions
How many positive integers $N$ from 1 to 5000 satisfy both congruences, $N\equiv 5\pmod{12}$ and $N\equiv 11\pmod{13}$?
Answers
So, we found that [tex]N=5\cdot13+11\cdot12^2=1649[/tex], but the least positive solution is [tex]1649\equiv89\pmod{\underbrace{156}_{12\cdot 13}}[/tex], and in general we can have [tex]N=89+156k[/tex] for any integer [tex]k[/tex].
Now, since [tex]5000=32\cdot156+8[/tex], or [tex]4992=32\cdot156[/tex], we know that there are 32 possible integers [tex]N[/tex] that satisfy the congruences.
Lupe can ride her bike at a rate of 20 mph when there is no wind. On one particular day, she rode 2 miles against the wind and noticed that it took her the same amount of time as it did to ride 3 miles with the wind. How fast was the wind blowing
Answers
40+2w=60-3w
5w=20
w=4mph
The speed of the wind is 4 mph.
Let, the speed of the wind is W mph.
When Lupe rides with the wind, her effective speed is 20 + W mph, and when she rides against the wind, her effective speed is 20 - W mph.
We are given two pieces of information:
Lupe rode 2 miles against the wind, and it took her the same amount of time as riding 3 miles with the wind.
The time taken to cover a distance is equal to the distance divided by the speed.
Using this information, we can set up two equations:
Time taken against the wind = Time taken with the wind
2 / (20 - W) = 3 / (20 + W)
Now, let's solve for W:
2(20 + W) = 3(20 - W)
40 + 2W = 60 - 3W
5W = 20
W = 20 / 5
W = 4 mph
The speed of the wind is 4 mph.
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Jamie mowed 7 lawns. He earned $10, $15, $12, $15, $8, And $15 for six lawns. How much did he earn the seventh time if the mean of the data is 12
Answers
Please answer this question I need it fast:
Together, Mary Sue and Betty have 603 necklaces. Mary Sue has 115 more necklaces than Betty. How many necklaces does Betty have?
Answers
M = necklaces owned by Mary Sue
B = necklaces owned by Betty
You know that:
M + B = 603
M - B = 115
Therefore, when you have the sum and the difference of two numbers, in order to find the biggest number you have to sum the sum and the difference and divide it by 2, and in order to find the smallest number you have to subtract the difference from the sum and divide it by 2:
M = [(M + B) + (M - B)] ÷ 2
= [603 + 115] ÷ 2
= 359
B = [(M + B) - (M - B)] ÷ 2
= [603 - 115] ÷ 2
= 244
Hence, Mary Sue has 359 necklaces and Betty has 244 necklaces.
Answer:
mary sue: 359, betty; 244
Step-by-step explanation:
⇔↓⊕㏒㏑∞
Need help on 1-6 please I need to solve for x and I need to get this done.
Answers
1. Sin = Opposite/Hypotenuse
x = 10*sin(40°) ≈ 6.428
2. Sin = Opposite/Hypotenuse
x = arcsin(7/12) ≈ 35.69°
3. Tan = Opposite/Adjacent
x = 18/tan(52°) ≈ 14.063
4. b^2 = a^2 +c^2 -2ac*cos(B)
B = arccos((a^2 +c^2 -b^2)/(2ac)) = arccos((7^2 +13^2 -8^2)/(2*7*13))
B = arccos(11/13) ≈32.20°
5. Same formula.
x = √(a^2 +c^2 -2ab*cos(B)) = √(157-132cos(42°)) ≈ 7.675
6. The ratio of side lengths is the same as the ratio of the sines of the opposite angles.
6/10 = sin(x)/sin(100°)
x = arcsin((6/10)*sin(100°)) ≈ 36.22°
X is a normally distributed random variable with a mean of 5 and a standard deviation of 2. the probability that x is greater than 10.52 is
Answers
A suitable calculator can help with this.
Final answer:
The probability that X is greater than 10.52 for a normal distribution with a mean of 5 and a standard deviation of 2 is found by calculating the z-score of 10.52. The z-score is 2.76, and the area to the right under the normal curve represents a very small probability, typically less than 0.003.
Explanation:
To find the probability that X is greater than 10.52, when X is a normally distributed random variable with a mean of 5 and a standard deviation of 2, we first need to calculate the z-score for 10.52. Using the formula:
Z = (X - mean) / standard deviation
Substitute the given values into the formula:
Z = (10.52 - 5) / 2 = 5.52 / 2 = 2.76
This z-score tells us how many standard deviations above the mean our value lies. In this case, X = 10.52 is 2.76 standard deviations above the mean.
The probability of X being greater than 10.52 corresponds to the area under the standard normal distribution curve to the right of the z-score 2.76. Using standard normal distribution tables or software, we can find this probability to be very small, typically less than 0.003.
How many different ways are there to choose 10 donuts from 20 varieties if at most 4 chocolate donuts are chosen?
Answers
If instead exactly 3 donuts are chocolate, then you have [tex]19^{17}[/tex] ways of choosing the others.
Continuing the pattern, we see that the total number of ways to choose up to 4 chocolate donuts is given by
[tex]\displaystyle\sum_{c=0}^419^{20-c}=19^{20}\sum_{c=0}^419^{-c}[/tex]
which comes out to be
39 678 289 291 775 535 447 366 041
Q9 Q4.) Write the augmented matrix for the system of equations to the right.
Answers
the first equation is x-y +8z = 7
so the first row in the matrix would be 1 ( there is 1x) -1 ( there is 1 negative y) 8 ( there are 8 z's) and then the answer is 7
then follow this step for the other 2 equations
see attached picture for answer:
(08.06 MC) Carly and Janiya put some money into their money boxes every week. The amounts of money (y), in dollars, in their money boxes after certain amounts of time (x), in weeks, are shown by the equations below: Carly y = 60x + 40 Janiya y = 50x + 80 After how many weeks will Carly and Janiya have the same amount of money in their money boxes and what will that amount be? (1 point) 5 weeks, $280 5 weeks, $340 4 weeks, $280 4 weeks, $340
Answers
y = 60x + 40
y = 50x + 80
Equaling both equations we have:
60x + 40 = 50x + 80
From here, we clear the value of x:
60x - 50x = 80 - 40
10x = 40
x = 40/10
x = 4 weeks
Substituting x = 4 in any of the equations we have:
y = 60 (4) + 40
y = 240 + 40
y = 280 $
Answer:
$ 280 4 weeks
Answer:
$ 280 4 weeks
Step-by-step explanation:
There is 3\8 of a pizza in one box and 1/8 of a pizza in another box. How much altogether
Answers
3/8 + 1/8 = 4/8
4/8 = 1/2
There is 1/2 of a pizza left
Hope this helps!
Hope this helps!
Find the missing numerators in each of the following problems. a. 10⁄15 = ⁄60 b. ⁄108 = 4⁄9 c. 7⁄11 = ⁄121 d. ⁄144 = 2⁄6
Answers
For 10/15 = x / 60
x = (10/15) * (60)
x = 40
For x / 108 = 4/9
x = (4/9) * (108)
x = 48
For 7/11 = x / 121
x = (7/11) * (121)
x = 77
For x / 144 = 2/6
x = (2/6) * (144)
x = 48
Final answer:
The missing numerators are found by creating equivalent fractions. By multiplying both the numerator and the denominator by the same factor that converts the original denominator to the new denominator, we find the missing numbers: 40, 48, 77, and 48 for each problem respectively.
Explanation:
To find the missing numerators, we need to use the concept of equivalent fractions. Equivalent fractions have different numerators and denominators but represent the same value.
a. 10⁄15 = ⁄60
We find the factor that converts 15 to 60, which is 4 (since 15 * 4 = 60), and multiply the numerator by the same factor (10 * 4 = 40). So, the missing numerator is 40.
b. ⁄108 = 4⁄9
To convert 9 into 108, multiply by 12 (since 9 * 12 = 108), and do the same with the numerator (4 * 12 = 48). Hence, the missing numerator is 48.
c. 7⁄11 = ⁄121
11 times 11 equals 121, so we multiply the numerator 7 by 11 as well (7 * 11 = 77), giving us 77 as the missing numerator.
d. ⁄144 = 2⁄6
To get from 6 to 144, multiply by 24 (since 6 * 24 = 144), so multiply the numerator 2 by 24 to get 48 as the missing numerator.
which values of x are solutions of the equation x^3+ x^2-2x=0
Answers
A particular hybrid car travels approximately 204 mi on 4 gal of gas. Find the amount of gas required for a 714-mi trip.
Answers
The car needs 14 gallons of gas for the 714 mile trip.
To determine the amount of gas required for a 714-mile trip, we can set up a proportion based on the given information:
We know that the car travels 204 miles on 4 gallons of gas. We need to find the amount of gas needed for 714 miles. Let the gas required for 714 miles be X gallons
First, let us set up the proportion:
204 mi / 4 gal = 714 mi / X galNext, we solve for x (the amount of gas required for 714 miles):
204 mi × X gal = 714 mi × 4 gal204X = 2856X = 2856 / 204X = 14Therefore, the car requires 14 gallons of gas for a 714-mile trip.
Help!!!!!!!!!!!!!!!!
Answers
∠y + 56 + 51 = 180
To find y, simplify, isolate and simplify again to get y. Remember, what you do to one side, you do to the other.
∠y + 107 = 180
∠y + 107 (-107) = 180 (-107)
∠y = 180 - 107
∠y = 73°
A triangle is = 180°. With this knowledge, you can find ∠x (the last angle).
Plug in 73° for y
y = 73
73 + 72 + x = 180
Simplify.
x + 145 = 180
isolate the x, subtract 145 from both sides
x + 145 (-145) = 180 (-145)
x = 180 - 145
x = 35°
A) 35° is your answer
hope this helps
What is the domain of this function?
{x| x > }
Answers
So the domain would be {x | x ≥ 0}
Hope this helps.
{x | x ≥ 0}
_____
The solid dot at (0, 9) indicates x=0 is part of the domain. The arrow at the right end of the line indicates the domain extends to +∞.
What are the correct coefficients (reading from left to right) when the chemical equation is balanced?__pbr3(l)+__h2o(l)→__h3po3(aq)+__hbr(aq)what are the correct coefficients (reading from left to right) when the chemical equation is balanced?________1, 3, 1, 31, 3, 3, 13, 5, 1, 81, 2, 1, 2?
Answers
1,3,1,3
The correct coefficients (reading from left to right) are chemical equation is balanced as 1PBr₃(l) + 3H₂O(l) → H₃PO₃(aq) + 3HBr(aq). which is the correct answer would be an option (A).
What is the rule of conservation of mass?Mass, according to the rule of conservation of mass, cannot be generated or destroyed. As a result, the mass of products must match the mass of reactants. Each element's atom count must be identical on the reactant and product sides. As a result, chemical equations are balanced.
According to the given question,
We have to substitute the coefficients (reading from left to right) are 1,3,1,3 in the given chemical equation
Thus, the correct coefficients (reading from left to right) are balanced chemical equation as :
⇒ 1PBr₃(l) + 3H₂O(l) → H₃PO₃(aq) + 3HBr(aq).
Hence, the correct answer would be option (A).
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Dan uses a compass to draw an arc from Q, as shown. He wants to construct a line segment through R that makes the same angle with line segment QR as line segment PQ.
first chart
Which figure shows the next step to construct a congruent angle at R?
Charts 2 3 4 & 5
Answers
Answer:
Chart 2.
Step-by-step explanation:
In the figure Dan has constructed an angle at point Q.He wants to cinstruct an angle ar point R which is congruent to angle made at point Q.To construct the angle at point R Dan needs to draw an arc at point R .He will put the compass on point R and draw an arc .This is shown in the figure 2.
The figure is added below.
Charles owed $390 to his friend. On the first day Charles paid his friend $12. Each following week the amount Charles paid his friend increased by the same amount. After 10 payments, Charles had paid back the full amount. By how much did each payment increase?
Answers
Amount owe=$390
Payment=$10
Number of payments=10
thus using the formula:
A=P(1+r)^n
plugging the values we get:
390=10(1+r)^10
solving for r we get
39=(1+r)^10
r=0.4425
thus the amount increased by 44.25%
sandra has 5 toy cars .Each toy car has a mass of 8 grams .what is the total mass of all 5 cars?
Answers
Final answer:
The total mass of Sandra's 5 toy cars is calculated by multiplying the mass of one toy car (8 grams) by the total number of cars, resulting in a total mass of 40 grams.
Explanation:
The question requires us to calculate the total mass of Sandra's toy cars. Since each toy car has a mass of 8 grams, we can find the total mass by multiplying the mass of one car by the number of cars, which is 5 in this case. Therefore, the calculation we need to perform is 8 grams times 5, which will give us the total mass of all the toy cars combined.
To solve: 8 grams/car × 5 cars = 40 grams.
Thus, the total mass of all 5 toy cars that Sandra has would be 40 grams.
Translate the given statement into an algebraic inequality or compound inequality: The IRS says you are in a certain tax bracket if your taxable income, i, is over $24,500, but not over $59,725.
Answers
This means, the taxable income can be more than $ 24,500 but less than or equal to $ 59,725.
If i represents this taxable income, we can write the inequality as:
$ 24,500 < i ≤ $ 59,725
Answer:
C. your welcome
2-2*3+3. What is the correct answer
Answers
________________________________________________________
Note:
_________________________________________________________
2 - 2 * 3 + 3 =
2 - (2 * 3) + 3 =
(2 - 6) + 3 =
-4 + 3 = -1 .
_____________________________________________________
The correct answer is: " -1 " .
_____________________________________________________
Kayla bought 9/4 pounds of apples. What is that weight as a mixed number?
Answers
A church has 10 bells in its bell tower. before each church service 3 bells are rung in sequence. no bell is rung more than once. how many sequences are there?
Answers
Answer:
720
Step-by-step explanation:
Given : A church has 10 bells in its bell tower.
Before each church service 3 bells are rung in sequence.
To Find: How many sequences are there?
Solution:
Since we are given that 3 bells are rung in sequence. no bell is rung more than once.
So, we will use permutation.
Formula :[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
Since A church has 10 bells in its bell tower.
So, n =10
We are also given that Before each church service 3 bells are rung in sequence . So, r =3
So, the number of possible sequence = [tex]^{10}P_3[/tex]
= [tex]\frac{10!}{(10-3)!}[/tex]
= [tex]\frac{10!}{(7)!}[/tex]
= [tex]\frac{10 \times 9 \times 8 \times 7!}{(7)!}[/tex]
= [tex]10 \times 9 \times 8[/tex]
= [tex]720[/tex]
Hence there are 720 sequences.
There are 120 different sequences in which the 3 bells can be rung in sequence before each church service without any bell being rung more than once.
To find the number of sequences in which the 3 bells can be rung in sequence out of 10 bells without any bell being rung more than once, you can use the concept of combinations.
The number of ways to choose 3 distinct bells out of 10 is given by the binomial coefficient "10 choose 3," which is denoted as C(10, 3) and calculated as follows:
C(10, 3) = 10! / (3!(10 - 3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
So, there are 120 different sequences in which the 3 bells can be rung in sequence before each church service without any bell being rung more than once.
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Q7 Q26.) Find the quotient of the complex numbers and leave your answer in polar form.
Answers
(Where [tex]\text{cis}(\theta) = \cos(\theta) + i\sin(\theta)[/tex])
Then [tex]\dfrac{c_1}{c_2} = \dfrac{r_1}{r_2}\text{cis}(\theta_1-\theta_2)[/tex]
So then for your problem, that would be
[tex]\dfrac{z_1}{z_2} = \dfrac37\text{cis}\left(\dfrac\pi8-\dfrac\pi9\right)=\boxed{\dfrac37\text{cis}\left(\dfrac\pi{72}\right)}[/tex]
So that would be [tex]\boxed{\dfrac37\left(\cos\left(\dfrac\pi{72}\right)+i\sin\left(\dfrac\pi{72}\right)\right)}[/tex]
Hope this helps.
Explain why a square is always a rectangle but a rectangle is not always a square.
Answers
therefore, because a square has 4 straight sides with 4 right angles, it is a rectangle.
and a rectangle can have unequal adjacent sides, so it is not always a square
Kim spun the spinner 75 times and got a three 30 times. What is the experimental probability?
Answers
So 30 / 75 = 0.4 = 40%
Hope this helps.
A triangular traffic island has a base half as long as its height. The island has an area of 25 m2 . Find the base and the height.
Answers
Isabel created the tree diagram to represent the different ways she could order a salad at her favorite restaurant.
According to the diagram, how many combinations of lettuce type, dressing, and topping are possible?
Answers
Answer: Option B
(B) 12
Step-by-step explanation:
Tim answered all the questions on his math test but got 101010 answers wrong. He received 444 points for every correct answer, and there was no penalty for wrong answers. His score was 767676 points.
Write an equation to determine the total number of questions (q)(q)left parenthesis, q, right parenthesis on Tim's math test.
Find the total number of questions on his math test.
questions
Answers
4(q -10) = 76 . . . . . Tim got 4 points for every right answer, for a score of 76. He answered correctly 10 fewer questions than were on the test.
b)
q = 10 +76/4
q = 29
The total number of questions on Tim's math test was 29.
Answers:
Equation: [tex]q=\frac{76}{4} +10[/tex]
Questions: [tex]29[/tex]
Also, the verified Tutor above is in fact correct, but this answer is way more simple and easier to understand, thank you for your time :D
Explanation:
First, we need to find out the questions, even though the first question is, "What is the equation?". So, to the find the answer to how many questions there are in total we need to grab the total points "[tex]76[/tex]" and divide that by "[tex]4[/tex]" because that'll tell us how many questions that he answered correct. Especially since the "[tex]10[/tex]" questions he got wrong didn't affect his points.
So [tex]\frac{76}{4} =19[/tex]. Now we must add 10 to 19. [tex]10+19=29[/tex]. And so [tex]29[/tex] is the total amount of questions. Now we must write down how we found out. We found out by dividing [tex]76[/tex] and [tex]4[/tex], then we added [tex]10[/tex]!
Conclusion:
As simple as that, we found out how many questions there were in total and how we found out! Thank you for sticking with me♥!
if I have 300 apples and eat 123 how many do I have left?
Answers
You have 177 apples left.
You will have 177 apples left.