Therefore , the solution of the given problem of area comes out to be
r = 8.
Define area.The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.
Here,
A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as
Sector Size/Sector Area = Circle Area/360
16 ft2/90 = n/360
(360) (16 ft2)/90 = n
(4)(16 ft2) = n
The total size of the circle is n = 64 ft2.
Since Area of a Circle equals r2,
∏r2 = 64
r2 = 64/∏
r = √(64/∏)
We multiply by / to get by rationalizing the denominator.
r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of
r = √(64∏)/∏
r = 8
Therefore , the solution of the given problem of area comes out to be
r = 8.
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Geometry The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.
Answer:
shaded area = 2x² + 6x + 17
If these are squares, what is the "x + 3"?
Step-by-step explanation:
shaded area = (x + 4)² - (x - 1)² = x² + 8x + 16 + x² - 2x + 1 = 2x² + 6x + 17
what is 7 divided by 9102
Answer:
[tex] = 9102 \div 7 \\ = 1300.29 \\ [/tex]
Hurricane Irma knocked a tree down and destroyed a 45 degree section of your
circular fence that has a radius of 22 feet. If you want to replace the fence, how
long would you need the replacement section to be?h
Consider parallelogram ABCD with vertices A(-6,6), B(0,10), C(2,4), D(-4,0). Classify the parallelogram and select all that apply
ABCD is a square
ABCD is a rectangle
ABCD is a rhombus
ABCD is none of the above
9514 1404 393
Answer:
D. none of the above
Step-by-step explanation:
The sides are different lengths and not at right angles, so the figure is not a rhombus or a rectangle. It is "none of the above."
__
Counting grid squares in the attached figure, we see that one side is the diagonal of a 2×3 rectangle, and the adjacent side is the diagonal of a 1×3 rectangle. This tells you two things: (a) the sides are different length, (b) they are not at right angles to each other. (If the sides were perpendicular, the slopes of the segments would be opposite reciprocals.)
PLEASE HELP 30 POINTS
The answer is No!! I hope this helps, have a wonderful day!
Answer:
A) yes, both functions are inverses of each other.
[tex]---------[/tex]
[tex]hope ~ it ~ helps\\\\have ~ a ~ great ~day!![/tex]
Find the surface area of this box in square inches.
Use the formula : SA= 2lw + 2lh + 2w
L = 18 in
w = 20 in
h = 16 in
Find the surface area of the box.
Use the Formula: SA=2lw+2lh+2wh
L= 10.5 in
W= 15.5 in
H= 20 in
Step-by-step explanation:
1.
Given that,
L = 18 in , w = 20 in , h = 16 in
The surface area of the box is given by :
SA= 2lw + 2lh + 2wh
Put all the values,
SA= 2lw + 2lh + 2wh
= 2(lw+lh+wh)
= 2(18(20)+18(16)+20(16))
= 2 (968)
= 1936 in²
2.
L= 10.5 in , W= 15.5 in , H= 20 in
The surface area of the box is given by :
SA= 2lw + 2lh + 2wh
Put all the values,
SA= 2lw + 2lh + 2wh
= 2(lw+lh+wh)
= 2(10.5(15.5)+10.5(20)+15.5(20))
= 2 (682.75)
= 1365.5 in²
Hence, this is the required solution.
If p is true and q is true, then ^p — ^ ~ q is true.
Answer:
okey???????????????????????? p and q is true got it.
Answer:
wat?
Step-by-step explanation:
solve the following equation n-31/105>1
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{n - \dfrac{31}{105}>1}[/tex]
[tex]\large\textsf{First you have to SIMPLIFY EACH SIDES of the INEQUALITY}[/tex]
[tex]\mathsf{n + (-\dfrac{31}{105})>1}[/tex]
[tex]\large\textsf{Second ADD }\mathsf{\dfrac{31}{105}}\large\textsf{ to BOTH of your SIDES}[/tex]
[tex]\mathsf{n - \dfrac{31}{105}+\dfrac{31}{105}> 1 +\dfrac{31}{105}}[/tex]
[tex]\large\textsf{CANCEL out: }\mathsf{-\dfrac{31}{105}+\dfrac{31}{105}}\large\textsf{ because that gives the value of 0}[/tex]
[tex]\large\textsf{KEEP: }\mathsf{1+\dfrac{31}{105}}\large\textsf{ because it helps what is being COMPARED to the n value}[/tex]
[tex]\large\textsf{Simplify above (}\mathsf{1+\dfrac{31}{105}}\large\textsf{) and you should have your result to this question}[/tex]
[tex]\mathsf{1+\dfrac{31}{105}=\bf \dfrac{136}{105}}[/tex]
[tex]\boxed{\mathsf{Answer: \bf n> \dfrac{136}{105\ }\boxed{\large\textsf{ it is an \bf O P E N E D circle shaded to the right}}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?
(b) What is the probability that the mean return will be less than 8%?
Answer:
a) 0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.
b) 0.4129 = 41.29% probability that the mean return will be less than 8%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean 8.7% and standard deviation 20.2%.
This means that [tex]\mu = 8.7, \sigma = 20.2[/tex]
40 years:
This means that [tex]n = 40, s = \frac{20.2}{\sqrt{40}}[/tex]
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?
This is 1 subtracted by the pvalue of Z when X = 13. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{13 - 8.7}{\frac{20.2}{\sqrt{40}}}[/tex]
[tex]Z = 1.35[/tex]
[tex]Z = 1.35[/tex] has a pvalue of 0.9115
1 - 0.9115 = 0.0885
0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.
(b) What is the probability that the mean return will be less than 8%?
This is the pvalue of Z when X = 8. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8 - 8.7}{\frac{20.2}{\sqrt{40}}}[/tex]
[tex]Z = -0.22[/tex]
[tex]Z = -0.22[/tex] has a pvalue of 0.4129
0.4129 = 41.29% probability that the mean return will be less than 8%
In November, the Sport Shop sold
74 pairs of snow skis and 3 pairs of water
skis. Each month the shop sold 11 more
pairs of water skis and 6 fewer pairs of
snow skis than the previous month,
When was the first month the shop sold
more water skis than snow skis?
Answer:
March is the first month
Step-by-step explanation:
If we make a graph. We can see that the quantity of sold water skis overpasses the quantity of snow skis in the month of March.
A bag contains 9 tiles, each with a different number from 1 - 9. You chose a tile without looking, put it aside, choose a second tile without looking, put it aside, then choose a third tile without looking. What is the probability that you choose tiles with the numbers 1, 2, and 3 in that order?
Someone pls explain this. I know the answer is 1/504 but how do you get there?
The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation and is equal to 1/504.
What are permutations?Permutations refer to the arrangements of objects in certain order or way.
The number of alternative arrangements in a set can be calculated mathematically using a permutation where the order of the configurations is important.
The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation.
The probability is obtained as 1 / ₉P₃
where;
₉P₃ = 9! / (9 - 3)!
₉P₃ = 9! / 6!
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
6! = 6 * 5 * 4 * 3 * 2 * 1
₉P₃ = 504
Hence, the probability = 1/504
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the distance around a square room measures 101 feet 7 inches. Estimate the length of each side of the room
Answer:
304.75 inches
Step-by-step explanation:
Total distance = 101 feet 7 inches
Recall :
1 Feet = 12 inches
Total distance in inches = (101 * 12) + 7 = 1219 inches
Perimeter of square = 1219
Sides of a square are always equal
Number of sides = 4
Hence, length of each side = 1219 inches / 4 = 304.75 inches
During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes. Based on this relative frequency, how many pars or better could he be expected to make on the remaining 150 holes? Round to the nearest whole number if necessary.
70 pars or better
60 pars or better
65 pars or better
53 pars or better
Dirk will make 70 pars or better.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes.
Out of 90 holes, Dirk made par or better on 42 holes.
At this rate, Out of 1 hole, Dirk made par or better on (42/90) holes.
Then, Out of 150 holes, Dirk will make par or better on -
(42/90 x 150) holes
(42/90 x 150)
70
Therefore, Dirk will make 70 pars or better.
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In Satoru's hometown, the highest temperature ever recorded is 111°F.
Convert this temperature to Celsius. Round to the nearest tenth of a
degree. F= _C + 32
5
Answer:
Step-by-step explanation:
F=9/5C+32 should be F = (9/5)C + 32
We are given 111 degrees F and want the same temperature in degrees Celcius.
In F = (9/5)C + 32 multiply all three terms by 5:
5F = 9C + 160, which can be solved for C:
5F - 160 = 9C
Let F = 111. Then 555 - 160 = 9C, or
395 = 9C
Dividing both sides by 9, we get C = 395/9 = 43 8/9 degrees C
What's the area of the square?
Answer: 18
Step-by-step explanation:
you just times the 4 1/2 4 times
Help!!!!!!!!!!!!!!!!!!!!!!
Answer:
Method 1 = 8.75
method 2 = 12.16
Hope this helped gll
Step-by-step explanation:
If hari buys 20biscuits for Rs 200 and sells it for Rs 100 find the loss
Answer:
hdvbn
Step-by-step explanation:
nfshvjjnmmnjjmbm
Hey need some help, pretty desperate so please help thank you <3
Answer:
Hello!
answer x = 46
z = 24
y = 14
6x2x(x−3) x (x−3)10(x+2)
The product of given numbers is 60x³(x−3)²(x+2)
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra,
Multiply the numbers:
6x²x(x−3) * (x−3)10(x+2)
Multiply 6 and 10
60x²x(x−3) (x−3)(x+2)
Multiply x terms
60x³(x−3) (x−3)(x+2)
Multiply (x-3) terms
60x³(x−3)²(x+2)
So, the product of given numbers is 60x³(x−3)²(x+2)
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Pls help me I beg u I need help with the red ones
Answer:
see below
Step-by-step explanation:
You want the ingredient quantities for several different multiples of the basic recipe.
Table ValuesTo fill the table, consider what the column heading is as a multiple of the recipe for 12 people. Use that multiplier for the rest of the numbers in the column.
[tex]\begin{array}{ccccc}\text{12 people}&\times2&\times3&\times\dfrac{1}{3}&\times\dfrac{1}{2\vphantom{g_g}}\\\cline{1-5}1\text{ cup}&2&3&\dfrac{1\vphantom{b^b}}{3\vphantom{g_g}}&\dfrac{1}{2}\\3\text{ cups}&6&9&1&1\dfrac{1}{2}\\2\text{ cups}&4&6&\dfrac{2}{3\vphantom{_g}}&1\\\dfrac{1}{2}\text{ cup}&1&1\dfrac{1}{2}&\dfrac{1}{6}&\dfrac{1\vphantom{^b}}{4\vphantom{_g}}\\1\dfrac{\vphantom{^b}1}{3}&2\dfrac{2}{3}&4&\dfrac{4}{9}&\dfrac{2}{3}\end{array}[/tex]
PLEASE HELP THIS IS VERY IMPORTANT I WILL GIVE U BRAINLIEST AND 5 STAR AND THANKS
Answer:
it wont let me put any numbers down, it keeps saying they're improper
Step-by-step explanation:
3. Mia has read 27 pages out of an 80 page book. What percent of the pages has she read?
Answer: She has read 33.75% of the pages.
Explanation: You can divide 27 by 80 to get the answer :)
Given that MTW = CAD, which segments are corresponding parts of the congruent triangles?
Answer: MW = CD
Explanation: It would be this way because if you wrote the triangles out, MW would be in the same place as CD, making them corresponding.
The following segments are corresponding parts of the congruent triangles.
segment MT ≅ segment CA
segment TW ≅ segment AD
segment MW ≅ segment CD
What are congruent triangles?Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal. They are of the same shape and size.
Given that
Triangle MTW = Triangle CAD
If two triangles are congruent then the corresponding sides and corresponding angles are congruent.
∴ segment MT ≅ segment CA
{corresponding parts of the congruent triangles}
segment TW ≅ segment AD
{corresponding parts of the congruent triangles}
segment MW ≅ segment CD
{corresponding parts of the congruent triangles}
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Which of the following is a line in the drawing?
Answer:
JN
Step-by-step explanation:
It is the only segment that does not have a bend.
Please someone help me
Answer:
6,9 and 3 times respectively
HELP PLSSSSSSSS I'M LOST PLSSSSSSSSSSSSSSSSSS
Answer:
1. 1/4 or 25/100, .25 and 25%
2. 1/10 or 1/100, .10 and 10%
Step-by-step explanation:
25 cubes out of 100 is 25/100
Simplify to 1/4
if its 25 cubes out of 100 its gonna fill up 25% or .25 of the whole thing
10 cubes out of 100 is 10/100
then simplify to 1/10
other two are obvious lol
Ifn(r'ns')+ n(r'ns)=3 n(r n s) = 4 & n(s'nr)= 7 find n(u).
Answer:
14
Step-by-step explanation:
You want to know the size of the universal set if ...
n(r'∩s') +n(r'∩s) = 3n(r∩s) = 4n(s'∩r) = 7UniverseThe given sets are mutually exclusive and exhaustive, so the sum of their sizes is the size of the universal set:
n(u) = 3 + 4 + 7
n(u) = 14
__
Additional comment
(r'∩s') ∪ (r'∩s) = r'∩(s' ∪ s) = r' . . . . n(r') = 3
(r∩s) ∪ (r∩s') = r∩(s ∪ s') = r . . . . . . n(r) = 4 +7 = 11
Then r' ∪ r = u, the universal set. . . . . n(u) = 3 +11 = 14
The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests, and then load passengers. Cabs arrive at the hotel every 8 minutes; if a taxi drives by the hotel and the line is full, it must drive on. Hotel guests require a taxi every 5 minutes, on average. It takes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel(exponentially distributed).
1. What is the average time a cab must wait for a fare?
2. What is the probability that the line will be full when a cab drives by, causing it to drive on?
Answer:
The appropriate solution is:
(1) 22.81 minutes
(2) 0.171
Step-by-step explanation:
According to the question, the values will be:
The service rate of guess will be:
= [tex]5+3.5[/tex]
= [tex]8.5 \ minutes[/tex]
The mean arrival rate will be:
[tex]\lambda =\frac{60}{5}[/tex]
[tex]=7.5 \ cabs/hr[/tex]
The mean service rate will be:
[tex]\mu= 7.05 \ cabs/hr[/tex]
(1)
The average time a cab must wait will be:
⇒ [tex]W_q=22.95-\frac{1}{7.05}[/tex]
⇒ [tex]=\frac{161.798-1}{7.05}[/tex]
⇒ [tex]=\frac{160.798}{7.05}[/tex]
⇒ [tex]=22.81 \ minutes[/tex]
(2)
The required probability will be:
⇒ [tex]P(X\geq 6)=\frac{1-2.115}{1-7.5}[/tex]
⇒ [tex]=\frac{-1.1115}{-6.5}[/tex]
⇒ [tex]=0.171[/tex]
PLS I NEED HELP ASAP!!!!
Answer:
Step-by-step explanation:
180 - ( 37+67) = 180 - 104
= 76°
Paulo’s grandfather gave him a collection of 20 coins. Each month Paulo adds 4 coins to his collection. Which inequality can be used to find m, the number of months after starting his collection when Paulo will have more than 50 coins in his collection?
Answer:
[tex]4m+20>50[/tex]
Step-by-step explanation:
Let m represent the amount of months that has passed.
Paulo started out with 20 coins.
Each month, he adds four more coins to his collection.
Therefore, the amount of coins added after m months will be given by 4m.
So, the amount of coins Paulo has total after m months can be given by:
[tex]4m+20[/tex]
We want to know when Paulo will have "more than" 50 coins in his collection. Therefore, we will use the "greater than" sign. Thus, our inequality will be:
[tex]4m+20>50[/tex]