Two machines, X and Y, produce earbuds. Let X represent the diameter of an earbud produced by machine X, and let
Y represent the diameter of an earbud produced by machine Y. X has a mean of 14 mm with a standard deviation of
0.6 mm, and Y has a mean of 15.2 mm with a standard deviation of 0.2 mm. Which answer choice correctly calculates
and interprets the mean of the difference, D = X-Y?
OD=-1.2; earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X
and Y, on average, to be -1.2 mm.
OH = 0.4; earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X and
Y, on average, to be 0.4 mm.
O = 1.2; earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X and
Y, on average, to be 1.2 mm.
OD = 29.2; earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X
and Y, on average, to be 29.2 mm.
Answers
-1.2, earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X
Given that two machines, X and Y, produce earbuds
Let X represent the diameter of an earbud produced by machine X, and
let Y represent the diameter of an earbud produced by machine Y. X has a mean of 14 mm with a standard deviation of 0.6 mm
Y has a mean of 15.2 mm with a standard deviation of 0.2 mm.
The mean of the difference, D = X - Y, can be calculated as:
mean(D) = mean(X) - mean(Y)
= 14 - 15.2
= -1.2
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Related Questions
Julia volunteers at a zoo. She records the number of people in each group of visitors in one day.
Based on Julia's data, if a larger zoo has 600 groups of visitors in a day, how many of them would you expect to be groups of 5 or more?
People in Group 1 2 3 4 5 6 7 8
Frequency
9 52 27 38 16 6 5 7
about
groups
Answers
We would expect 138 groups in the larger zoo to have 5 or more people based on the relative frequency of group sizes in Julia's data.
To determine how many groups of 5 or more people we would expect to see in a larger zoo with 600 groups of visitors in a day, we need to use the relative frequency of each group size in Julia's data.
To calculate the relative frequency of each group size, we need to divide the frequency of each group size by the total number of groups:
Group Size Frequency Relative Frequency
1 9 9/150 = 0.06
2 52 52/150 = 0.35
3 27 27/150 = 0.18
4 38 38/150 = 0.25
5 16 16/150 = 0.11
6 6 6/150 = 0.04
7 5 5/150 = 0.03
8 7 7/150 = 0.05
We can see that the relative frequency of groups with 5 or more people is 0.11 + 0.04 + 0.03 + 0.05 = 0.23. This means that we would expect 23% of the 600 groups in the larger zoo to have 5 or more people.
To calculate the actual number of groups with 5 or more people, we multiply the total number of groups by the relative frequency:
Number of groups with 5 or more people = 600 x 0.23 = 138
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peaceful travel agency offers vacation packages each vacation packages includes a city, and a airline.The agency has 6 cities, and 2 airlines to choose from.how many different vacation packages do they offer
Answers
Solving the given word problem systematically, Serene Travel Organization offers 12 diverse vacation packages.
How to Solve the Problem?To calculate the overall number of distinctive excursion packages that Quiet Travel Organization offers, we ought to duplicate the number of cities by the number of carriers:
Add up to number of get-away bundles = number of cities x number of airlines
Since the agency has 6 cities and 2 aircrafts to select from, we are able substitute those values within the over equation:
Add up to number of get-away bundles = 6 x 2 = 12
In this manner, Serene Travel Organization offers 12 diverse get-away bundles.
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Qd=50-4Px+0.5I+10Py-2Pz
Answers
Answer:
The equation Qd = 50 - 4Px + 0.5I + 10Py - 2Pz represents the demand function for a certain good X, where Qd is the quantity demanded, Px is the price of X, I is the consumer's income, Py is the price of another good Y, and Pz is the price of another good Z.
To solve for the equilibrium price and quantity, we need to find the point where the quantity demanded equals the quantity supplied. However, without information on the supply function or market conditions, we cannot find the equilibrium price and quantity.
We can use the demand equation to determine the effect of changes in the independent variables on the quantity demanded for the good. For example, an increase in the price of X (Px) would lead to a decrease in the quantity demanded (Qd), while an increase in the price of Y (Py) or a decrease in the price of Z (Pz) would lead to an increase in the quantity demanded (Qd). An increase in income (I) would also lead to an increase in the quantity demanded (Qd).
Note that it is important to understand the context and assumptions underlying the demand function in order to make accurate economic predictions or decisions based on it.
Step-by-step explanation:
Suppose it is known that the proportion of students at a local high school that take public transit to school is p = 0.15
Answers
The distribution of the sample is approximately normal with a mean of 0. 15 and a standard deviation of 0. 03852.
How to describe the distribution ?One can utilize the Central Limit Theorem (CLT) for proportions to detail the dispersion of the sample proportion. Explained by the CLT, if the size of the sample is sufficiently significant enough, then the distribution with respect to the sample proportion will be mostly indistinguishable from a typical distribution.
np ≥ 10
n(1-p) ≥ 10
Given that both conditions are fulfilled, we can essentially posit that the said sample proportion distribution is almost normal. In light of this knowledge, it would be pertinent to ascertain the mean (μ) and standard deviation (σ) of the sample proportion distribution.
Mean = p = 0.15
Standard deviation:
= √ ( ( 0.15 x ( 1 - 0. 15 ) ) / 86 )
= 0.03852
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What transformation were used
Answers
Since ΔJKL was transformed to create ΔMNO, the sequence of transformations that were used include the following:
Reflection over the y-axis.
(x, y) → (x, y - 9).
What is a reflection over the y-axis?In Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to the coordinate of the given triangle JKL, we have the following coordinates:
Coordinate J = (3, 7) → Coordinate J' = (-(3), 7) = (-3, 7).
Next, we would apply a vertical translation by shifting triangle J'K'L' down by 9 units to produce ΔMNO;
(x, y) → (x, y - 9).
J' (-3, 7) → (-3, 7 - 9) = M' (-3, -2).
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Find the 13th term of the geometric sequence 4, −8, 16, ...
Answers
Answer:
Step-by-step explanation:
I'm very confused on this question.
Answers
The value of angle x is determined as 107⁰.
What is the x?
The value of angle x is calculated by applying principle of intersecting chord theorem.
The intersecting chord theorem states that half of the difference between the arc of two intersecting chords is equal to the tangent angle.
Based on the angle of intersecting chord theorem, we will have the following equation.
m∠MNP = ¹/₂( arc MLP - arc MP )
x = ¹/₂ [(360 -73) - (73)]
x = ¹/₂ (287 - 73 )
x = ¹/₂ (214)
x = 107⁰
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Ben wants to compare the scores of this year's basketball games to the scores of last year's games. He made the following double stem-and-leaf plot to make
his comparison.
Comparison of
Basketball Scores
Between the Last
Two Years
Last
Year
995
97753
6654
9
Stem
OB. 20
OC 16.
0
1
2
3
4
5
What is the difference between the median score this year and the median score last year?
OA 18
OD. 17
This
Year
999
7889
456778
233
2
Answers
helphelphelphelphelphelphelphelphelphelphelphelphelp
Answers
The volume of the flower vase, can be found to be 2, 199 cm ³.
How to find the volume ?The volume of the flower vase can be found by subtracting the volume of the cone from the volume of the rectangular prism.
Volume of rectangular prism :
= Length x Width x Height
= 20 x 12 x 10
= 2, 400 cm ³
The volume of the cone is:
= π x radius ² x height / 3
= π x 4 ² x 12 / 3
= 201. 06 cm ³
Volume of vase:
= 2, 400 - 201. 06
= 2198.94
= 2, 199 cm ³
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Harold ran 3 miles in 24 minutes. How long would it take him to run 4 miles?
Answers
If you want to know how I got that comment!
Answer:32 minutes
Step-by-step explanation:
He is running at a rate of 1 mile every 8 minutes. 3 miles in 24 minutes and 4 miles in 32 minutes
You skateboards down a ramp. The ramp starts at a height of 10 feet and runs 55 feet along the ground. How steep was the ramp? We are missing a side or and angle? Regular or Inverse Trig?
Answers
The steepness of the ramp is approximately 56 feet.
How to find the steepness of the ramp?You skateboards down a ramp. The ramp starts at a height of 10 feet and runs 55 feet along the ground.
Therefore, let's find how steeped the ramp is.
Hence, using Pythagoras's theorem,
c² = a² + b²
where
a and b are the other legsc is the hypotenuse sideTherefore,
55² + 10² = c²
c² = 3025 + 100
c² = 3125
square root both sides of the equation
c = √3125
c = 55.9016994375
c = 56 feet
Therefore,
steepness of the ramp = 56 feet
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In the first group of 5, average was 6.5. In the second group of 15, the average was 4.5. What was the overall average of the two groups?
Answers
Step-by-step explanation:
First group of five total score = 5 * 6.5 = 32.5
Group of fifteen total score = 15 * 4.5 = 67.5
total score of 20 is 67.5 + 32.5 = 100
Average = 100 /20 = 5.0
In △ABC, AB=6 cm, AC=15 cm, and m∠A=48°.
What is the area of △ABC?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answers
The area of triangle ABC is : 33.44 cm²
What is the Area of a Triangle?The area of a triangle is the region enclosed within the sides of the triangle. The area of a triangle varies from one triangle to another depending on the length of the sides and the internal angles. The area of a triangle is expressed in square units, like, m2, cm2, in2, and so on.
We have the information from the question is:
In triangle ABC :
AB=6 cm,
AC=15 cm, and
m ∠A=48°.
We have to find the area of Triangle ABC
Area of triangle is : 1/2 × bc × (SinA)
Area of Triangle = 1/2 × 6 × 15 × (Sin 48° )
We know the value of Sin 48° is 0.7431
Area of Triangle = (1/2) × 66.88
Area of triangle = 33.44 cm²
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Isosceles triangle LMN is graphed with vertices L(0, 1), M(3, 5), and N(6,1). What is the slope of side LN?
Negative StartFraction 4 over 3 EndFraction.
0
StartFraction 4 Over 3 EndFraction.
3
\
Answers
The y-coordinate of point L is 1, and the y-coordinate of point N is 1, so the difference in y-coordinates is 1 - 1 = 0.
The x-coordinate of point L is 0, and the x-coordinate of point N is 6, so the difference in x-coordinates is 6 - 0 = 6.
Therefore, the slope of side LN is 0/6 = 0.
The correct answer is 0.
Accounting question.help
Answers
The computations of the net profit or loss using the following cost valuation methods are as follows:
FIFO, net profit = $20,000
Weighted Average, net profit = $17,555.54.
What are the inventory cost valuation methods?The inventory cost valuation methods include FIFO (First In, First Out), LIFO (Last In, First Out), WAC (Weighted Average Cost), and Specific Identification.
Under the FIFO basis, the cost of inventory is evaluated based on the assumption that inventory that are first brought in are the first to be sold.
Under the Weighted Average Cost method, the average cost is computed by dividing the total cost of goods available for sale by the number of units.
Other inventory cost valuation methods include LIFO and Specific Identification.
FIFO Basis:Cost of Goods Sold = $80,000 ($10,000 x 3 + $12,000 x 2 + $13,000 x 2)
Sales Revenue = $106,000 ($15,000 x 7)
Overhead = $6,000
Net Profit = $20,000 ($106,000 - $80,000 - $6,000)
Weighted Average Cost Basis:Weighted Average Cost per tractor = $11,777.78 ($106,000 ÷ 9)
Cost of Goods Sold = $82,444.46 ($11,777.78 x 7)
Sales Revenue = $106,000 ($15,000 x 7)
Overhead = $6,000
Net Profit = $17,555.54 ($106,000 - $82,444.46 - $6,000)
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On the first day of school, the eighth graders get to select one of two dances to attend for no cost. They can attend either the Fall Fling or the Spring Social for free.
Of the 144 boys in eighth grade, 82 choose to attend the Fall Fling for free. Of the 156 girls in eighth grade, 75 choose to attend the Spring Social for free.
The president of the eighth grade class constructed the following two-way table to show the numbers of boys and girls that choose each dance. Some of the values and totals are incorrect.
If the following two-way table was constructed from the data, select all the values the president of the eighth grade class has in
the correct spots.
Answers
The two-way table constructed from the data showing the numbers of boys and girls that choose each dance category should look like this:
Boys Girls Total
Fall Fling 82 81 163
Spring Social 62 75 137
Total 144 156 300
What is a two-way table?A two-way table is a data display tool that displays the frequencies for two different categories collected from a single group.
A two-way table use rows to represent one category variable and the columns to represent a second category variable, while the cells display the proportions or frequencies of each row and column combination.
The total number of boys in eighth grade = 144
The number of boys who choose to attend the Fall Fling = 82
Therefore, the number of boys who attend the Spring Social = 62 (144 - 82)
The total number of girls in eighth grade = 156
The number of girls who choose to attend the Spring Social = 75
Therefore, the number of girls who attend the Fall Fling = 81 (156 - 75)
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Answer:
62, 82, 163, 300
Step-by-step explanation:
I got this on study island
If the amount of food available is increased, then the cricket frog population will (increase/decrease/stay the same) over the span of five years.
Answers
Find the range of the following: 20, 3, 95, 54, 71, 66
Answers
Answer:
92.
Step-by-step explanation:
To find the range of the set of numbers 20, 3, 95, 54, 71, 66, we first need to find the difference between the largest and smallest numbers in the set.
Largest number = 95
Smallest number = 3
Range = Largest number - Smallest number
Range = 95 - 3
Range = 92
Therefore, the range of the set of numbers 20, 3, 95, 54, 71, 66 is 92.
Answer:92
Step-by-step explanation: highest-lowest
it helps to put the terms in order first
95-3=92
sage team brought 224 cans they brought 3 times cans as asifs team joes team brought 4 times as asifs team how much cans did joes team bring in
Answers
The number of cans brought by Joes team is J = 299 cans
Given data ,
Let the number of cans brought by Joes team be J
Now , sage team brought 224 cans
And , sage team brought 3 times cans as asifs team
And , joes team brought 4 times as asifs team
On simplifying the equation , we get
Asif's team brought 224/3 = 74.67 (rounded to the nearest whole number) cans.
Joe's team brought 74.67 x 4 = 298.68
So , J = 299 cans
Hence , the equation is solved and J = 299 cans
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If tan A= 28 /45 and cosB= 13 12 and angles A and B are in Quadrant I, find the value of tan(A+B).
Answers
The value of Tan A + B is 6.009.
How to solve for the tangent[tex]sin^2 A + cos^2 A = 1sin^2 A = 1 - cos^2 Asin A = sqrt(1 - cos^2 A)sin A = sqrt(1 - (28/45)^2)sin A = sqrt(1 - 784/2025)sin A = sqrt(1241/2025)cos A = 28/45\geq[/tex]
We have to solve for Tan B
[tex]sin^2 B + cos^2 B = 1sin^2 B = 1 - cos^2 Bsin B = sqrt(1 - cos^2 B)sin B = sqrt(1 - (13/12)^2)sin B = sqrt(55/144)Therefore, tanB = sinB / cosB = (sqrt(55/144)) / (13/12) = (12 sqrt(55)) / 143[/tex]
[tex]tan(A+B) = (3207 \sqrt{55}) + 1804 \sqrt{124})) / (3115 - 207 \sqrt{(341)}[/tex]
= 6.009.
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6) The height h(t) of a projectile is given by
h(t) = −t² + 7t + 9.
Find the time (s) at which the rocket is
20 ft above the ground.
Answers
Answer:
2.38 s
4.62 s
Step-by-step explanation:
The height of a projectile is given by the function:
[tex]h(t) = -t^2 + 7t + 9[/tex]
where:
h(t) is the height of the rocket about the ground (in feet).t is the time (in seconds).To determine the time(s) at which the rocket is 20 ft above the ground, set h(t) = 20 and solve for t.
[tex]-t^2+7t+9=20[/tex]
To solve the equation for t, complete the square.
Subtract 9 from both sides:
[tex]-t^2+7t=11[/tex]
Divide both sides by -1:
[tex]t^2-7t=-11[/tex]
Add the square of half the coefficient of the term with the variable "t" to both sides of the equation:
[tex]t^2-7t+\left(\dfrac{-7}{2}\right)^2=-11+\left(\dfrac{-7}{2}\right)^2[/tex]
Simplify:
[tex]t^2-7t+\dfrac{49}{4}=\dfrac{5}{4}[/tex]
We have now created a perfect square trinomial on the left side of the equation. Factor the perfect square trinomial:
[tex]\left(t-\dfrac{7}{2}\right)^2=\dfrac{5}{4}[/tex]
To solve for t, square root both sides:
[tex]t-\dfrac{7}{2}=\pm \sqrt{\dfrac{5}{4}}[/tex]
[tex]t-\dfrac{7}{2}=\pm\dfrac{\sqrt{5}}{2}[/tex]
Add 7/2 to both sides of the equation:
[tex]t=\dfrac{7}{2}\pm\dfrac{\sqrt{5}}{2}[/tex]
[tex]t=\dfrac{7\pm\sqrt{5}}{2}[/tex]
Therefore, the times at which the rocket is 20 ft above the ground is:
[tex]t=\dfrac{7-\sqrt{5}}{2}=2.38\; \rm s[/tex]
[tex]t=\dfrac{7+\sqrt{5}}{2}=4.62\; \rm s[/tex]
 1.What did Ruskin write about Nocturne in Black and Gold: Falling Rocket?
2. How did Whistler defend his work in court? ( You need to mention the two paintings he brought with him to court.)
3. What was the outcome of the trial?
4. Why do you think the lawsuit was important in the history of art?
Answers
2. Whistler defended his work by claiming that he was not trying to depict a specific subject, but rather the mood and atmosphere of a fireworks display. He also brought two other paintings to court, Nocturne in Blue and Silver: Chelsea and Nocturne in Blue and Gold: Old Battersea Bridge, to demonstrate that his style was consistent across multiple works.
3. The trial ended in Whistler's favor, with the jury ruling that Ruskin's criticisms had not damaged Whistler's reputation or his ability to sell his paintings.
4. The lawsuit was important in the history of art because it raised questions about the nature of art and the role of the artist. Whistler's defense of his work as an expression of mood and atmosphere, rather than a realistic depiction of a specific subject, challenged traditional notions of art and paved the way for new artistic movements such as Impressionism. The trial also highlighted the importance of critical reviews in shaping public perception of art, and the potential for artists to use the legal system to protect their reputations and livelihoods.
Area of a regular polygon work
Answers
Answer:
Step-by-step explanation:
[tex]\frac{x}{18} =cot~30\\x=18cot~30=18 \times \sqrt{3} =18\sqrt{3} \\base=36\sqrt{3} \\area~of~triangle=3\times \frac{1}{2} \times36\sqrt{3} \times 18=972\sqrt{3} \approx 1683.55~mm^2[/tex]
Find the x intercept of the line 1x -2y =23
Answers
Answer: x=23
Step-by-step explanation:
Answer: 23
Step-by-step explanation:
When you have a value on the x-axis, your y=0
plug in y=0 to find your x-intercept
1x-2(0)=23
1x=23
x=23
What are the features of the function f(x)=2log3 (x+7)graphed below?
Answers
The key features of the function f(x) = 2log₃(x+7) graphed below include the following:
The domain of this function is [-7, ∞]The range of this function [-∞, ∞] or all real numbers.x-intercept = (-6, 0).y-intercept = (0, 2log₃(7)).Vertical asymptote is at: x = -7No extreme points.What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.
Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of this logarithmic function shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-7, ∞].
Range = [-∞, ∞].
In conclusion, we can logically deduce that this logarithmic function has a vertical asymptote is at x equal to negative seven.
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Ellen bought a pedometer wristband to track how many steps she takes. Each day she recorded the number of steps in a table. At the end of the week, she found her mean number of steps was 10,000. She made a bar graph to show her daily steps for the week. Which graph could show Ellen’s steps?
THANKS SO MUCH!!!
Answers
Answer:
it is b got it right on my test
Step-by-step explanation:
The required graph that shows Ellen's steps where her mean steps for a week is 10000 is graph 2 where the data are as,
Day 1 = 11000 , Day 2 = 9000, Day 3 = 10000, Day 4 = 12000, Day 5 = 8000, Day 6 ≈ 10000, Day 7 ≈ 10000
Mean of ungrouped data is the average of all the values of the observation in the data set.
Mean = (Summation of all values in data set)/ (Number of observations)
Here there are 7 observations and the mean number of steps is 10000.
For graph 1 the values for each day of the week are as,
Day 1 = 8000 , Day 2 = 9000, Day 3 = 12000, Day 4 = 2000, Day 5 = 6000, Day 6 = 10000, Day 7 = 10000
Thus, the mean number of steps is = (8000+ 9000+ 12000+ 2000+ 6000+ 10000 + 10000) / 7
= 8143 (approximately) ≠ 10000
For graph 2 the values for each day of the week are as,
Day 1 = 11000 , Day 2 = 9000, Day 3 = 10000, Day 4 = 12000, Day 5 = 8000, Day 6 ≈ 10000, Day 7 ≈ 10000
Thus, the mean number of steps is = (11000+ 9000+ 10000+ 12000+ 8000+ 10000 + 10000) / 7
= 10000
For graph 3 the values for each day of the week are as,
Day 1 = 7000 , Day 2 = 14000, Day 3 = 11500, Day 4 = 10000, Day 5 = 4500, Day 6 = 6000, Day 7 = 11000
Thus, the mean number of steps is = (7000+ 14000+ 11500+ 10000+ 4500+ 6000 + 11000) / 7
= 9143 (approximately) ≠ 10000
For graph 4 the values for each day of the week are as,
Day 1 = 8000 , Day 2 = 9000, Day 3 = 9500, Day 4 = 10000, Day 5 = 9000, Day 6 = 7000, Day 7 = 11000
Thus, the mean number of steps is = (8000+ 9000+ 9500+ 10000+ 9000+ 7000 + 11000) / 7
= 9071 (approximately) ≠ 10000
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PLEASE HELP FAST I’M HAVING A LITTE TROUBLE PLEASE GIVE THE RIGHT ANSWER
Answers
Answer:
C) 1/2 and 8
Step-by-step explanation:
-2x + y = 7 Eq. 1
6x + y = 11 Eq. 2
From Eq. 1:
y = 7 + 2x Eq. 3
From Eq. 2:
y = 11 - 6x Eq. 4
Equalyzing Eq. 3 and Eq. 4:
7 + 2x = 11 - 6x
2x + 6x = 11 - 7
8x = 4
x = 4/8
x = 1/2
From Eq. 3:
y = 7 +2* 1/2
y = 7 + 1
y = 8
Check:
From Eq. 2
6x + y = 11
6*1/2 + 8 = 11
3 + 8 = 11
The ratio of alcohol and water in a mixture of 72 units is 2 ratio 1 what is the amount of water that must be added to the mixture in order to make this ratio 1 ratio 2
Answers
The amount of water needed is 72 liters.
Given that, the ratio of the alcohol and water in a mixture of 72 units is 2 ratio 1, we need to find the amount of water that must be added to the mixture in order to make this ratio 1 ratio 2,
So,
The quantity of water in it = 72 / 3 × 1 = 24
New ratio =
48 / 24+x = 1/2
96 = 24+x
x =72
Hence, the amount of water needed is 72 liters.
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I know the answer, but I don't understand how. The answer is 90 degrees
Answers
In the circle the measure of arc YP as per the given measurements is equal to option D. 166°
In the circle,
Measure of arc ST = 70°
Measure of arc RS = 96°
Measure of angle YZP = 128°
Arc formed by vertically opposite angles are equal
This implies,
Measure of arc YT = Measure of arc PR
Measure of arc ST + Measure of arc RS + Measure of arc YT = 180°
⇒70° + 96° + Measure of arc YT = 180°
⇒Measure of arc YT = 180° - 166°
⇒Measure of arc YT = 14°
⇒ Measure of arc PR = 14°
Measure of arc YP = 360° - ( Measure of arc (PR + RS + ST + TY ))
⇒ Measure of arc YP = 360° - ( 14° + 96° + 70° + 14° )
⇒Measure of arc YP = 360° -194°
⇒ Measure of arc YP = 166°
Therefore, the measure of arc YP is equal to option D. 166°
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Please help, I don't know how to do this !
Answers
The lengths of the legs, the circumference and the radius of the circles are;
First part; The diameter = 18 units
The second leg = 9 units
Second part; The circumference = 34·π units
Third part; The radius is r = 36 cm
What is a radius of a circle?The radius of a circle is the distance from the center to the circumference.
First part;
cos(30°) = 9·√3 ÷ The diameter = (√3)/2
The diameter = (9·√3) ÷ ((√3)/2) = 18
The length of the other leg, using the relationship between special triangles is 18/2 = 9
Second part;
The lengths of the legs of the right triangle indicates that we get;
The square of the diameter, D² = 30² + 16² = 1156
The length of the diameter, D = √(1156) = 34
The formula for finding the circumference of a circle, C, based on the diameter can be presented as follows;
C = π × D
Therefore;
The circumference of the circle, C = π × 34
The circumference of the circle = 34·π units
Third part
The length of the 20° arc = 4·π cm
Therefore;
4·π = 2·π·r × 20/360
Where;
r = The radius of the circle
Therefore;
r = (360/20) × 4·π ÷ (2·π) = 36
The radius of the circle, r = 36 cm
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