Find the following measure for this figure.
Area of circle =
6 square units
12 square units
36 square units
Answers
Answer: Last option.
Step-by-step explanation:
The formula for calculate the area of the circle is the shown below:
[tex]A_c=r^2\pi[/tex]
Where r is the radius of the circle.
As you can see in the figure attached, the radius of the circle is 6 units, then:
[tex]r=6units[/tex]
Therefore, when you substitute the value of the radius into the formula shown above, you obtain the following result:
[tex]A_c=(6\ units)^2\pi[/tex]
[tex]A_c=36\pi\ units^2[/tex]
Answer:
The correct answer is 36π square units
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where r - radius of circle
From the figure we can see a circle with radius 5 units
To find the area of circle
Area = πr² = π * 6² = 36π square units
Area of given circle = 36π square units
Therefore the correct answer is 36π square units
Related Questions
Let p(x)=909+50e−x .
What is p(5) ?
Answers
Answer:
The answer is 9.6
hope this helps!
Which of the following are equivalent to the function y=3cosx + 2?
Check all that apply
Note: The ones I highlighted in blue are the answers I've chosen
Answers
Answer:
your choices are correct
Step-by-step explanation:
sin(x +π/2) is a translation of the sine function to the left by π/2 units, which makes it look exactly like the cosine function that you want.
cos(-x) is the same as cos(x), since the cosine function is an even function.
___
sin(x -π/2) will look like -cos(x), not what you want.
The third choice is a reflection across the x-axis of the function you started with. It is not equivalent.
(9CQ) Find the distance from the balloon to the soccer fields.
Answers
Answer:
The distance from the balloon to the soccer fields = 3.6 miles ⇒ answer (b)
Step-by-step explanation:
* Let the hot air balloon at point A , the soccer fields
at point B and the football field at point C
∵ The measure of the angle of depression to the
soccer fields is 20° 15'
∴ The measure of angle B = 20° 15'
∵ The measure of the angle of depression to the
football field is 62° 30'
∴ The measure of angle C = 62° 30'
∵ The sum of measures of the interior angles of any triangle = 180°
∴ The measure of angle A = 180 - (20° 15' + 62° 30') = 97° 15'
* The distance between the balloon and the soccer field
is represented by the side AB of triangle ABC
- Use the sin Rule to find the length of side AB
∵ a/sin(A) = b/sin(B) = c/sin(C)
- a is the side opposite to angle A, b is the side opposite
to angle B and c is the side opposite to angle C
∵ AB = c ⇒ opposite to angle C
∵ The distance between the two fields = 4 miles
∴ BC = 4 miles
∵ BC = a ⇒ opposite to angle A
∴ 4/sin(97° 15') = c/sin(62° 30')
∴ c = (4 × sin(62° 30')) ÷ sin(97° 15')
∴ c = 3.6 miles
∴ The distance from the balloon to the soccer fields = 3.6 miles
answer (b)
Susan has $800 in a savings account that earns 6% annually. If the interest is not compounded, how much interest will she earn in 5 years?
Answers
$240
800x.06= 48
48x5=240
If aₙ = 3(3)ⁿ⁻1 , what is S₃?
Answers
Answer:
S3 = 39
Step-by-step explanation:
* an = 3(3)^(n-1) is a geometric sequence
* The general rule of the geometric sequence is:
an = a(r)^(n-1)
Where:
a is the first term
r is the common difference between each consecutive terms
n is the position of the term in the sequence
The rules means:
- a1 = a , a2 = ar , a3 = ar² , a4 = ar³ , ........................
∵ an = 3(3)^(n-1)
∴ a = 3 and r = 3
∴ a1 = 3
∴ a2 = 3(3) = 9
∴ a3 = 3(3)² = 27
* S3 = a1 + a2 + a3
∴ S3 = 3 + 9 + 27 = 39
Note:
We can use the rule of the sum:
Sn = a(1 - r^n)/(1 - r)
S3 = 3(1 - 3³)/1 - 3 = 3(1 - 27)/-2 = 3(-26)/-2 =3(13) = 39
Answer:
The correct answer is S₃ = 39
Step-by-step explanation:
It is given that,
aₙ = 3(3)ⁿ⁻¹
To find a₁
a₁ = 3(3)¹⁻¹ = 3(3)°
= 3 * 1 = 3
To find a₂
a₂ = 3(3)²⁻¹ = 3(3)¹
= 3 * 3 = 9
To find a₃
a₃ = 3(3)³⁻¹ = 3(3)²
= 3 * 9 = 27
To find the value of S₃
S₃ = a₁ + a₂ + a₃
= 3 + 9 + 27 = 39
Therefore the correct answer is S₃ = 39
Pumping stations deliver oil at the rate modeled by the function D, given by d of t equals the quotient of 5 times t and the quantity 1 plus 3 times t with t measure in hours and and D(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 4-hour period from t = 0 to t = 4? Give 3 decimal places.
Answers
The pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.
Explanation:To find the amount of oil delivered by the pumping stations during the 4-hour period from t = 0 to t = 4, we need to evaluate the definite integral of the function D(t) over that interval. The function D(t) is given by D(t) = 5t / (1 + 3t). We can find the integral of this function using the substitution method. Let u = 1 + 3t, then du = 3dt. Rearranging this equation, we have dt = du / 3.
Substituting this in the integral, we get:
∫ D(t) dt = ∫ (5t / u) * (1/3) du = (5/3) * ∫ (t / u) du
Integrating the above expression, we get:
∫ D(t) dt = (5/3) * ∫ (t / u) du = (5/3) * ∫ (t / (1 + 3t)) du
To evaluate this integral, we can use the natural logarithm function. We know that ∫ (1/u) du = ln|u| + C, where C is the constant of integration. Substituting back for u, we have:
(5/3) * ∫ (t / (1 + 3t)) du = (5/3) * ∫ (t / u) du = (5/3) * ln|1 + 3t| + C
Now, we can use the definite integral to find the amount of oil delivered during the 4-hour period:
∫04 D(t) dt = (5/3) * ∫04 (t / (1 + 3t)) dt = (5/3) * [ln|1 + 3(4)| - ln|1 + 3(0)|] = (5/3) * [ln|13| - ln|1|] = (5/3) * ln|13| = 8.188
Therefore, the pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.
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in each family of function,the____function is the most basic function in the family
A.linear
B.quadratic
C.simple
D.parent
Answers
Answer: Your answer is option D. In each family of function,the Parent function is the most basic function in the family
The family function has same highest degree, same shape for graph and consequently.
The correct option is D.
Given:
Identify the function is the most basic function in the family.
Below are the few example of family function.
[tex]y=x^2[/tex]
[tex]y=3x^2[/tex]
The graph for the both the function has same highest degree, same shape for graph and consequently. The parent function is the simplest from a family of function.
Thus, the correct option is D.
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The ABC Book club charges a $40 monthly fee, plus $2 per book read in that month. The Easy Book Club charges a $35 monthly fee, plus $3 per book read in that month. For each club, how many books must be read in 1 month for the total charges from each club to be equal?
Answers
Answer:
5 books must be read in 1 month for the total charges from each club to be equal.
Step-by-step explanation:
Monthly Charges of ABC club = 40$
Per book read charges of ABC club = 2$
amount of book read = x
Total charges of ABC club = 40 + 2x
Monthly Charges of Easy book club = 40$
Per book read charges of Easy Book club = 3$
Total charges of Easy book club = 35 + 3x
To calculate how many books must be read in 1 month for the total charges from each club to be equal,
Total charges of ABC club = Total charges of Easy book club
40 + 2x = 35 + 3x
40 - 35 = 3x -2x
5 = x
x = 5
Therefore, 5 books must be read in 1 month for the total charges from each club to be equal.
HELP WORTH 99 POINTS IM SO CONFUSED.
A. At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle (blue) with a radius of 11 m. The inner edge if the sidewalk is a circle (orange) with a radius of 9 m. Find the approximate area of the larger circle (blue)
B. Find the approximate area of the smaller circle (orange)
C. Find the approximate area of the sidewalk (shaded region between the blue and orange circles.)
Use 3.14 for pi. Show your work!
(use 3.14 pi on all three problems!)
Answers
Answer:
Area of Large Circle = 380.13
Area of Small Circle = 254.47
Area of Sidewalk = 125.66
Step-by-step explanation:
The side walk is just subtracting the smaller number from the bigger one.
The area is just Pi*r^2
Answer:
A 379.94 m^2
B 254.34 m^2
C 125.6 m^2
Step-by-step explanation:
A Area of a circle is given by
A = pi r^2
We know the radius is 11
A = pi 11^2
A = 3.14 (121)
A = 379.94 m^2
B The Area of the orange circle
A = pi r^2
The radius is 9 m
A = pi 9^2
A = 3.14 (81)
A = 254.34 m^2
C The Area between the circles is the difference between the large circle and the small circle
Ablue-Aorange
379.94-254.34
125.6 m^2
When two six-sided dice are rolled what is the probability that the product of their scores will be greater than six?
Answers
Answer: [tex]\bold{\dfrac{11}{18}}[/tex]
Step-by-step explanation:
Think of the products row by row:
11 12 13 14 15 16 - 0 products greater than 6
21 22 23 24 25 26 - 3 products greater than 6
31 32 33 34 35 36 - 4 products greater than 6
41 42 43 44 45 46 - 5 products greater than 6
51 52 53 54 55 56 - 5 products greater than 6
61 62 63 64 65 66 - 5 products greater than 6
[tex]\dfrac{\text{number greater than 6}}{\text{total possible outcomes}}=\dfrac{22}{36}=\dfrac{11}{18}\ when\ reduced[/tex]
Answer:
11/18.
Step by.step explanation:
There are 36 possible outcomes when 2 dice are rolled.
Outcomes for a product greater than six are:
2,4 2,5 2,6 3,3 3,4 3,5 3,6 4,2 4,3 4,4 4,5 4,6 5.2 ......5.6 , 6.2 .......6.6.
= 22 ways.
required Probability is 22/36 = 11/18 (answer).
The scatterplot shows the number of home runs Mario hits during his first four seasons on the company softball team. If his output continues to follow the linear model, approximately how many home runs will Mario hit during his ninth season?
A. 30 home runs
B. 35 home runs
C. 45 home runs
D. 50 home runs
Answers
Answer:
i think its B on edge
A window is in the shape of a rectangle with a base of 4 ft and a height of 5 ft. The window has a colored glass in the shape of a kite. Use the grid to identify the area of the colored glass.
Answers
Answer:
A = 10 ft²Step-by-step explanation:
Look at the picture.
A₁ = 2 · 2 = 4
A₂ = 2 · 3 = 6
The area of a rhombus:
A = A₁ + A₂ ⇒ A = 4 + 6 = 10
You can use the formula of an area of a rhombus:
[tex]A=\dfrac{d_1d_2}{2}[/tex]
d₁ = 4, d₂ = 5
Substitute:
[tex]A=\dfrac{(4)(5)}{2}=(2)(5)=10[/tex]
Answer:
10 ft²
Step-by-step explanation:
A = 1/2 (d1) (d2)
A = 1/2 (4) (5)
1/2 x 20
=10 ft²
Line AD is a tangent to circle B at point C and m
What is the measure of
(The answer is 90 but how do you get this answer?)
Answers
BCA is 90 degrees, because a tangent line is perpendicular to the raduis line BC.
Final answer:
The measure of angle M is 90 degrees.
Explanation:
The measure of angle M is 90 degrees. To understand why, we can use the fact that a line tangent to a circle is perpendicular to the radius drawn to the point of tangency. In this case, line AD is tangent to circle B at point C, so we can draw line AC, which is the radius of the circle, and find the measure of angle M by finding the complement of the angle formed by lines AD and AC. Since the complement of a 90-degree angle is 90 degrees, the measure of angle M is 90 degrees.
20 POINTS
Which equation does the graph below represent?
y = 1/4x
y = 4x
y = -1/4x
y = −4x
Answers
Answer:
Step-by-step explanation:
Line passes through (0,0) and (-1,4) .
Slope = -4
Equation of line is : y - 0 = - 4(x - 0)
y = - 4x
The area of a right triangle is 30 ft2. The base of the triangle is 12 ft. What is the length of the hypotenuse?
Please show your work, and don't forget to label your answer!! Thank you!
Answers
➷ The formula for a right triangle is:
(b x h) / 2
We know this:
(12 x n) / 2 = 30
Multiply both sides by 2:
12 x n = 60
Divide both sides by 12:
n = 5
Now we know the height is 5
We can now use Pythagoras' theorem to calculate the hypotenuse:
c^2 = 5^2 + 12^2
c^2 = 169
Square root it:
c = 13
The hypotenuse is 13 ft
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
The formula for working out the area of a triangle:
(b x h) / 2
[tex](12*h)/2=30\\(*2)\\12*h=60h\\h=5[/tex]
Pythagoras' theorem to calculate the hypotenuse:
c² = 5² + 12²
c² = 169
c = 13
The hypotenuse is 13 ft
Step-by-step explanation:
email received a $50 gift card for his birthday.after buying some clothes,he had$16 left on the card.how much did he spend on the clothes?
A. 16-c=50
B. 50-c=16
C. 16c=50
D. c=16+50
Answers
50 - c = 16
Subtract 16 from both sides.
34 - c = 0
Add c on both sides.
34 = c
So, they spent $34 on clothes.
Please consider marking this answer as Brainliest to help me advance.
The correct equation to find out how much was spent on the clothes is 50 - c = 16. Solving this, we find that c, the cost of the clothes, is $34.
The student initially had a $50 gift card and after purchasing some clothes, they were left with $16 on the card. To find out how much was spent on clothes, we need to subtract the remaining amount on the card from the initial amount. The correct equation to represent this situation is:
B. 50 - c = 16
We can then solve for c, which represents the cost of the clothes:
50 - 16 = c
34 = c
So, the amount spent on clothes is $34.
Rewrite this sum of two logarithms as a single logarithm.
Answers
Answer:
log9(11x)
Step-by-step explanation:
log9(11) + log9(x)
We know that loga(b) + loga(c) = loga(b*c)
log9(11*x)
log9(11x)
Final answer:
To rewrite a sum of two logarithms as a single logarithm, combine them using the property that the log of a product equals the sum of the logs. For example, log a + log b becomes log (ab).
Explanation:
To rewrite the sum of two logarithms as a single logarithm, we use the relevant log properties. One of the most important properties of exponents is that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers, which is log xy = log x + log y. Conversely, the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers. So, if you have two logarithms of the same base you're adding, like log a + log b, you can combine them into a single log by multiplying the two arguments to get log (a*b).
An example using numbers could look like this:
log₂(3) + log₂(5) = log₂(3*5) = log₂(15)
Therefore, the sum of two logarithms, log a + log b, can be rewritten as log (ab), which expresses the multiplication of a and b within a single logarithm.
Solve for x
(3/4)x-(7/3)=-2x+(5/3)
Answers
Answer:
your answer is x=16/11
explanation:
solve for x by simplifying both sides of the equation then isolation the variable.
exact form: 16/11
decimal form: 1.45
mixed number form: 1 5/11
hope this helps
~~bangtanboys7
Answer: [tex]x=\frac{16}{11}[/tex]
Step-by-step explanation:
To solve the equation shown in the problem you must:
- Add the like terms, as following:
[tex]\frac{3}{4}x+2x=\frac{5}{3}+\frac{7}{3}\\ \frac{11}{4}x=4[/tex]
- Multiply both sides by 4.
- Divide both sides of the equation by 11.
Therefore, the result is:
[tex](4)\frac{11}{4}x=4(4)\\11x=16\\x=\frac{16}{11}[/tex]
Please help if you can!
Answers
the answer is A :)))))))))))))))))
Answer:
I am pretty sure it is Rhombus or a sideway rectangle but since they dont say more than givin I would say Rhombus
Step-by-step explanation:
The cost of fabric (y) is directly proportional to he length is yards (x). If 5 yards of fabric cost $14, which equation models this situation?
Answers
Answer:
5x = 14
Step-by-step explanation:
If 5 yards of fabric is $14 you need an equation that would solve how much 1 yard of fabric costs. You can say 5x = 14 or x = 2.8 which means that one yard of fabric (1x or just x) is $2.80.
Answer: [tex]y==\frac{14}{5}x[/tex]
Step-by-step explanation:
By definition, we know that Direct proportion equation has the following form:
[tex]y=kx[/tex]
Where k is the constant of proportionality.
Then, If 5 yards of fabric cost $14, you can calculate k as following:
[tex]14=k(5)\\k=\frac{14}{5}[/tex]
Therefore substituting the value of k into the first equation, you obtain the following equation:
[tex]y==\frac{14}{5}x[/tex]
Which of the following is a disadvantage to purchasing points
A.they lower monthly payments
B.closing costs are increased
C.An immediate tax break is received
D.the interest rate is lowered for the life of the loan
Apex Answers
Answers
Answer:
B - closing costs are increased
Step-by-step explanation:
All of the other options are advantages to purchasing points. You want lower monthly payments (a), a tax break (c), and lower interest rate (d)
Answer:
The correct answer is option B.closing costs are increased.
Step-by-step explanation:
Mortgage points or discount points refers to the fees paid directly to the lender during closing in exchange for a reduced interest rate.
In this way the buyer buys down the rate, that helps in reducing his monthly mortgage payments.
So, option A, C and D are the advantages of purchasing discount points.
The speed limit on a higway is 70 miles per hour/ About how fast is this in miles per minute?
Answers
Answer:
1 mile a minute.
Step-by-step explanation:
At Bud's company, bowling balls are shaped as a sphere with a diameter of 8 inches. If a store receives a shipment of 14 bowling balls, what is the total volume of the balls? 937.81 cubic inches B. 3,751.3 cubic inches C. 267.95 cubic inches D. 30,009.98 cubic inches
Answers
Answer I think it is c I hope that right I am sorry for late responds
Danielle bought a dress that was on sale at the clothing store. After taking 40% off the original price of the dress, Danielle paid $39.15, not including tax. What was the original price of the dress, to the nearest cent?
Answers
Answer:
Original price of the dress was $97.88
Step-by-step explanation:
40/100=39.15/d
0.4d=39.15
0.4d=39.15
d=39.15/0.4
d=97.88
The original price of the dress is $97.875.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Danielle paid $39.15.
But Danielle paid after 40% off.
So, the price before discount
40% of x = 39.15
x= 3915/40
x= $97.875
Hence, the original price is $97.875.
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Factor. 49x^2−36y^2
Enter your answer in the boxes.
Answers
[tex]\\Rewrite \ in \ form.\\\\(7x)^2 - (6y)^2\\\\\\\\Use \ difference \ of \ squares \ rule.\\\\(7x + 6y) (7x - 6y)\\\\\\Therefore, \ you \ get \fbox{(7x+6y)&(7x-6y)}.[/tex]
The weather reporter says that there is a 14% chance that it will rain tomorrow. What is the probability that it will not rain
Answers
Since an 100% chance is all possibilities, then it must add up to 100. If we take away that 14 from 100 by subtracting, you just get 86. Therefore, there is an 86% chance that it will not rain tomorrow.
Which ordered pair is the solution set for the system of equations below? 2x + y = 18 x – y = –6
Answers
Answer:
(4,10) is the solution
Step-by-step explanation:
2x + y = 18
x – y = –6
Using elimination
2x + y = 18
x – y = –6
----------------------
3x = 12
Dividing each side by 3
3x/3 = 12/3
x =4
Now we can find y
2x+y = 18
2(4) +y =18
8+y = 18
Subtracting 8 from each side
8-8+y = 18-8
y=10
(4,10) is the solution
Please help me out! :)
Answers
-x -x
2x-11=23
+11 +11
2x=34
x=17
3(17)-11 17+23
=40 =40
explanation ;
you would equal them because they are congruent . & you substitute x for 17 in each equation to find out the degrees of both of the angles :)
A pile of 10 000 sheets of paper is 85 cm thick what is the thickness of 1 sheet of paper
Answers
Answer:
0.0085 centimeters.
Step-by-step explanation:
85/10000 is equal to 0.0085 centimeters, which is absurdly thin for anything, really.
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 136 lb and a standard deviation of 28.5 lb. a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 191 lb. The probability is approximately nothing. (Round to four decimal places as needed.) b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 130 lb and 191 lb. The probability is approximately nothing. (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? A. Part (a) because the seat performance for a sample of pilots is more important. B. Part (b) because the seat performance for a sample of pilots is more important. C. Part (b) because the seat performance for a single pilot is more important. D. Part (a) because the seat performance for a single pilot is more important.
Answers
Answer:
A) 0.5564; B) 0.8962; C) Choice D. Part (a) because the seat performance for a single pilot is more important.
Step-by-step explanation:
For part A,
We will find the z score for each value and then subtract the probabilities for each to give us the area between them. We use the z score for an individual value:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Our first X is 130 and our second X is 191. Our mean, μ, is 136 and our standard deviation, σ, is 28.5:
[tex]z=\frac{130-136}{28.5}=\frac{-6}{28.5}\approx -0.21\\\\z=\frac{191-136}{28.5}=\frac{55}{28.5}\approx 1.93[/tex]
Using a z table, we can see that the area under the curve to the left of z = -0.21 is 0.4168; the area under the curve to the left of z = 1.93 is 0.9732. This means the area between them is
0.9732-0.4168 = 0.5564.
For part B,
We will find the z score for each value again and subtract them; however, since we have a sample we will use the z score for the mean of a sample:
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
Our first X-bar is 130 and our second is 191; our mean is still 136; our standard deviation is still 28.5; and our sample size, n, is 36:
[tex]z=\frac{130-136}{28.5\div \sqrt{36}}=\frac{-6}{28.5\div 6}\approx -1.26\\\\z=\frac{191-136}{28.5\div \sqrt{36}}=\frac{55}{28.5\div 6}\approx 11.58[/tex]
The area under the curve to the left of -1.26 is 0.1038; the area under the curve to the left of 11.58 is 1.00:
1.00-0.1038 = 0.8962
For part C,
We want the probability that each individual pilot will be safe in these seats, so the value in part A is more important.
The probability that a randomly selected pilot's weight is between 130 lb and 191 lb is approximately 0.558 or 55.8%. The probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb is approximately 0.1056 or 10.56%. When redesigning the ejection seat, the probability from part (a) is more relevant.
Explanation:To find the probability that a randomly selected pilot's weight is between 130 lb and 191 lb, we need to calculate the z-scores for both weights and find the area under the curve between those two z-scores. First, we calculate the z-score for 130 lb using the formula z = (x - μ) / σ, where x is the weight of 130 lb, μ is the mean weight of 136 lb, and σ is the standard deviation of 28.5 lb. Solving for z, we get z = (130 - 136) / 28.5 = -0.21. Using a z-table or calculator, we find that the area to the left of -0.21 is approximately 0.415. Next, we calculate the z-score for 191 lb using the same formula, z = (191 - 136) / 28.5 = 1.93. Again using a z-table or calculator, we find that the area to the left of 1.93 is approximately 0.973. To find the area between the z-scores, we subtract the smaller area from the larger area: 0.973 - 0.415 = 0.558. Therefore, the probability that a randomly selected pilot's weight is between 130 lb and 191 lb is approximately 0.558 or 55.8%.
To find the probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb, we need to use the Central Limit Theorem. The sample mean follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the mean is still 136 lb and the standard deviation is 28.5 lb divided by the square root of 36, which is 4.75 lb. We can now calculate the z-scores for 130 lb and 191 lb using the same formula, z = (x - μ) / σ. The z-score for 130 lb is (130 - 136) / 4.75 = -1.26, and the z-score for 191 lb is (191 - 136) / 4.75 = 11.58. However, since the z-score for 191 lb is beyond the range of the standard normal distribution table, we can approximate it as 4. This means that we need to find the area under the curve to the left of -1.26 and subtract the area to the left of -4. Using a z-table or calculator, we find that the area to the left of -1.26 is approximately 0.1056, and the area to the left of -4 is approximately 0.000032. Subtracting the smaller area from the larger area, we get 0.1056 - 0.000032 = 0.1056. Therefore, the probability that the mean weight of 36 randomly selected pilots is between 130 lb and 191 lb is approximately 0.1056 or 10.56%.
When redesigning the ejection seat, the probability from part (a) is more relevant. This is because part (a) calculates the probability of a single pilot's weight falling within the given range, while part (b) calculates the probability of the mean weight of a sample of pilots falling within the given range. The ejection seat should be designed to accommodate the weight range of individual pilots, rather than the mean weight of a sample of pilots.
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