n a circle, a 180 degree sector has area 162\pi in Superscript 2. What is the radius of the circle?
Answers
The radius of the circle is 10 inches.
Area of a sector.A sector is a part of a given circle which is made from two radii and an arc. It's area can be determined by;
area of a sector = θ/360*πr^2
where θ is the measure of its central angle, and r is its radius.
Then from the given question, we have;
area of a sector = θ/360*πr^2
162 = 180/360 *3.14*r^2
= 1.57r^2
r^2 = 162/1.57
= 103.1847
So that;
r = (103.1847)^1/2
= 10.16
The radius of the circle is approximately 10 inches.
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Related Questions
Select all of the linear transformations from ℝ3 to ℝ3 that are invertible. There may be more than one correct answer.
A. Identity transformation (i.e. T(v⃗ )=v⃗ for all v⃗ )
B. Projection onto the xz-plane
C. Reflection in the y-axis
D. Rotation about the x-axis
E. Dilation by a factor of 6
F. Projection onto the z-axis
Answers
Identity transformation
Rotation about the x-axis
Rotation about the y-axis by π will be the correct answer
What is invertible linear transformation ?
Let W and V both have the same finite dimension and be vector spaces over the field F. A linear transformation, T:V→W, shall exist.
If S(T(x))=x for all x∈V, then T is said to be invertible by a linear transformation S:W→V. The opposite of T is known as S. S, to put it simply, reverses all changes T makes to an input x.
In fact, based on the presumptions made at the outset, T is only invertible if it is bijective. Here, we provide evidence that bijectivity necessitates invertibility. As an exercise, try going the other way.
Assume T is a bijective. Consequently, there exists a single vector in W called yx such that T(x)=yx for each x∈V. S:W→V is defined as follows: for every y∈W, Give x∈V a value such that y=yx. The choice is distinct because T is injective, and such an x occurs since T is surjective. As a result, S(T(x))=x and S is a well-defined function from W to V. S still needs to be demonstrated to be a linear transformation.
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Complete the steps to solve the equation 4e2 + 2x = x − 3 by graphing.
Answers
Hi,
Complete the steps to solve the equation 4e2 + 2x = x − 3 by graphing.
The equation 4e2 + 2x = x - 3 has
x-3
x -coordinates
has no solution
The displacement vector of a particle is given by r=(4.0+2.5t2)x^+(5/t)y^ 1) Find the AVERAGE VELOCITY during the interval t=1 s to t=10 s.(10 points) 2) What is the INSTANTANEOUS Velocity when t=0.5 s ? What angle does the Velocity vector make to the positive x-axis? (10 points) 3) A ball with velocity at 5 m/s, begins to roll DOWN from the top of a 10-meterIong ramp inclined at 33 degrees. Find the acceleration DOWN the ramp, and the final velocity once it reaches the bottom.
Answers
1) Average velocity = (254x + 0.5y - 6.5x - 5y) / 9s.
2) Instantaneous velocity at t=0.5s: v = 2.5x - 20y, angle with positive x-axis ≈ -80.54 degrees.
3) Acceleration = 5.25\(m/s^2\), final velocity = 10.27 m/s.
1) The average velocity during the interval t=1s to t=10s can be found by calculating the displacement over that time interval and dividing it by the duration. The displacement is given by r(10s) - r(1s):
\(r(10s) = (4.0 + 2.5(10^2))x + (5/10)y = 254x + 0.5y\)
\(r(1s) = (4.0 + 2.5(1^2))x + (5/1)y = 6.5x + 5y\)
Average velocity = (r(10s) - r(1s)) / (10s - 1s) = (254x + 0.5y - 6.5x - 5y) / 9s
2) The instantaneous velocity at t=0.5s can be found by taking the derivative of the displacement vector with respect to time and evaluating it at t=0.5s:
\(v(t) = d(r(t))/dt = (d(4.0 + 2.5t^2)/dt)x + (d(5/t)/dt)y\)
\(= (5t)x - (5/t^2)y\)
\(v(0.5s) = (5(0.5))x - (5/(0.5)^2)y = 2.5x - 20y\)
The angle that the velocity vector makes with the positive x-axis can be found using the arctan function:
θ = arctan(vy/vx) = arctan((-20)/(2.5)) = arctan(-8) ≈ -80.54 degrees
3) The acceleration down the ramp can be determined using the formula:
\(a = g sin(θ) = 9.8 m/s^2 * sin(33 degrees) ≈ 5.25 m/s^2\)
The final velocity once it reaches the bottom of the ramp can be found using the equation of motion:
\(v^2 = u^2 + 2as\)
Assuming the ball starts from rest (u = 0), the final velocity is given by:
v = sqrt(2as) = sqrt(2 * 5.25 * 10) ≈ 10.27 m/s
Therefore, the acceleration down the ramp is approximately 5.25 m/s^2 and the final velocity at the bottom is approximately 10.27 m/s.
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list the two types of sampling procedures group of answer choices causation and exact sampling precise and imprecise sampling probability and nonprobability sampling statistical and linear sampling large and small size sampling
Answers
The correct answer is Probability and non probability sampling procedure.
There are two distinct exits from sampling procedures.
There are two types of sampling: probability sampling and non-probability sampling.
In probability sampling each population has equal and independent chance to comes in the study . There are various types of probability samplings technique exists . These are simple random sampling , stratified random sampling, cluster sampling , systematic random sampling etc.
In non probability sampling the samples are selected on the basis of personal biasness, judgments and preferences. Judgemental sampling , quota sampling, dimensional sampling etc comes under this type of sampling procedure.
So here the correct answer is
Option -E- Probability and non probability sampling procedure.
Except it all other options are wrong.
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Which of the following are assumptions underlying the simple linear regression model y = Bo B1x e? Check all that apply The variance of the error term e varies for differing values of x. The error term is a random variable with an expected value of zero. The error term is normally distributed. The error term E follows a chi-square distribution.
Answers
The error term is a random variable with an expected value of zero.2. The error term is normally distributed
The assumptions underlying the simple linear regression model `y = Bo + B1x + e` are: 1.
The variance of the error term e is constant across all values of x.Thus, the assumptions that are underlying the simple linear regression model `y = Bo + B1x + e` are the second and the third options, which are "The error term is normally distributed." and "The variance of the error term e is constant across all values of x." respectively.
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What happens to momentum when objects stick together.
Answers
Multiply:3/10 * 7/2
Answers
In order to multiply two fractions, we can follow the steps below:
0. find the product between the two numerators; ,(3 * 7 = 21)
,1. find the product between the two denominators; ,(10 * 2 = 20)
,2. the product of the two fractions will be the result of step 1 (the numerator of the final result), divided by the result of step 2 (the denominator of the final result):
\(\frac{3}{10}\cdot\frac{7}{2}=\frac{3\cdot7}{10\cdot2}=\frac{21}{20}\)Therefore, the answer is:
\(\frac{21}{20}\)Which could be the first step in solving the equation represented by the model below?
X X X x
II
O Add 4 negative unit tiles to both sides.
O Add 4 negative unit tiles to the left side, and add 6 negative unit tiles to the right side.
O Add 4 positive unit tiles to both sides.
O Add 6 negative unit tiles to the left side, and add 4 negative unit tiles to the right side.
Answers
O Add 6 negative unit tiles to the left side, and add 4 negative unit tiles to the right side.
a circle with radius 2 is translated 5 units. what is the perimeter of the region swept out by the circle?
Answers
The perimeter of the region swept out by a circle with radius 2, when translated 5 units, remains the same at 4π or approximately 12.57 units.
When a circle is translated, its center is moved without changing its shape or size. In this case, the circle with a radius of 2 is translated 5 units. Since the translation is in a straight line, the shape swept out by the circle is a larger circle with the same radius.
The perimeter of a circle is given by the formula:P = 2πr
where P is the perimeter and r is the radius.
For the original circle with a radius of 2, the perimeter is:
P1 = 2π(2) = 4π
For the translated circle with the same radius, the perimeter is also:
P2 = 2π(2) = 4π
Therefore, the perimeter of the region swept out by the circle is the same as the perimeter of the original circle, which is 4π or approximately 12.57 units.
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If a pair of jeans coast $14. 99 in 1973 when the CPI was 135, what would the price of jeans have been in 1995 if the CPI was 305
Answers
If the CPI was 305 in 1995, the price of jeans that cost $14.99 in 1973 would be approximately $47.05 in 1995 after adjusting for inflation.
To find the price of jeans in 1995, we first need to adjust the 1973 price for inflation using the Consumer Price Index (CPI). CPI measures the average change in prices of goods and services over time, so it can help us compare prices from different years.
First, we need to calculate the inflation rate between 1973 and 1995. We can do this by dividing the CPI in 1995 (305) by the CPI in 1973 (135):
Inflation rate = (305 / 135) * 100% = 226.67%
This means that prices in 1995 were about 2.27 times higher than in 1973. Now, we can apply this inflation rate to the price of jeans in 1973:
Price in 1995 = Price in 1973 * (1 + inflation rate)
Price in 1995 = $14.99 * (1 + 2.2667) = $47.05
Therefore, if the CPI was 305 in 1995, the price of jeans that cost $14.99 in 1973 would be approximately $47.05 in 1995 after adjusting for inflation. This calculation helps to compare the cost of goods across different time periods by taking inflation into account, thus giving a better understanding of the changes in purchasing power over time.
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use the graph to find f(x) = -3
Answers
Answer:
D. -3
Step-by-step explanation:
For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation.
A.-12 + 4 – 4/3 +4/9 – 4/27 +4/81 - … = -12/(1+1/3)
B.∑ (1/3)^n = 6*1/3^6(1/3^11-1)/(1/3-1)
Answers
a. The exact value of the sum of -12 + 4 – 4/3 +4/9 – 4/27 +4/81 - … = -12/(1+1/3) is 12/7.
b.The exact value of the sum of∑ (1/3)ⁿ = 6*1/3⁶(1/3¹¹-1)/(1/3-1) is 3/2.
A.-12 + 4 – 4/3 +4/9 – 4/27 +4/81 - …
This is an infinite geometric series with first term a = -12 and common ratio r = 4/(-3). The sum of an infinite geometric series is given by:
S = a / (1 - r)
Substituting the values of a and r, we get:
S = (-12) / [1 - (4/(-3))]
Simplify the denominator by multiplying both numerator and denominator by (-3):
S = (-12) / [-3 - 4]
S = (-12) / (-7)
S = 12/7
Therefore, the exact value of the sum is 12/7.
B. 6*1/3⁶(1/3¹¹-1)/(1/3-1)
This is a geometric series with first term a = 1 and common ratio r = 1/3. The sum of a geometric series with n terms is given by:
S = a (1 - rⁿ) / (1 - r)
As n approaches infinity, rⁿ approaches zero and the sum converges to:
S = a / (1 - r)
Substituting the values of a and r, we get:
S = 1 / (1 - 1/3)
S = 3/2
Therefore, an expression that gives the exact value of the sum is 3/2.
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Can anyone help me please
Answers
Answer:
a. 41.5
b, 26.5
Step-by-step explanation:
a.
2x + 6 = 180
2x = 172
x = 86
b.
2x+ 90 +26+11 = 180
2x+127 = 180
2x = 53
x = 26.5
Answer:
a) x = 9 b) x = 10
Step-by-step explanation:
a)
6² + (x - 1)² = (x + 1)²
36 + x² - 2x + 1 = x² + 2x + 1
36 = 4x
x = 9
b)
x² + (x + 14)² = 26²
x² + x² + 28x + 196 = 676
2x² + 28x = 480
2x² + 28x - 480 = 0
x² + 14x - 240 = 0
(x + 24)(x - 10) = 0
x = -24 or 10
Mrs. Austin has 10 students in her class. She asked them whether they like football (F) or basketball (B). Sarah, Allen, kara, Todd said football. Joseph, Lydia, Matt said basketball. Caleb and Britney said they like both. Ethan said he didn't like either. 1. Define the universal set. 2. Define the two subsets.
Answers
1.The universal set is defined as {Sarah, Allen, Kara, Todd, Joseph, Lydia, Matt, Caleb, Britney, Ethan}.
2.Caleb and Britney are included in both subsets since they like both football and basketball.
1. The universal set (U) consists of all the students in Mrs. Austin's class. In this case, U = {Sarah, Allen, Kara, Todd, Joseph, Lydia, Matt, Caleb, Britney, Ethan}.
2. The two subsets are:
a) The set of students who like football (F) = {Sarah, Allen, Kara, Todd, Caleb, Britney}
b) The set of students who like basketball (B) = {Joseph, Lydia, Matt, Caleb, Britney}
Caleb and Britney are included in both subsets since they like both football and basketball.
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a deck of playing cards has 52 cards of which 12 are face cards what are the odds the top 3 are face cards
Answers
In a deck of playing cards has 52 cards of which 12 are face cards, The odds are 33 / 3315 or 0.01 that the top 3 are face cards.
The total number of cards was 52, and there were 12 face cards.
Probability equals the number of possible outcomes divided by the total number of possibilities.
The first attempt had a probability of 12/52,
the second attempt had a probability of 11/51,
and the third attempt had a probability of 10/50.
Therefore, the probability that each of the three cards are face cards is equal to 12 / 52 × 11 / 51 × 10 / 50 = 1320 / 132600 = 132 / 13260 = 33 / 3315
the probability that all three are face cards = 0.00995475113 ≈ 0.01
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Marsha recorded the time it took six children of different ages to run one lap around the track using the line of best fit, which is the closest to the length of time it should take marsha’s 8 year old son to run one lap?
A. 168
B. 176
C. 182
D. 190
Answers
Based on the information provided, we need to find the closest length of time it should take Marsha's 8-year-old son to run one lap around the track.
To do this, we can use the line of best fit, which is a line that represents the trend or pattern in the data.
Since the line of best fit is not given, we need to estimate the time based on the given options. We can do this by considering the ages of the children and their corresponding times.
If the line of best fit indicates that older children take longer to run a lap, then it is reasonable to assume that Marsha's 8-year-old son would take less time compared to the older children.
Now, let's analyze the given options:
A. 168
B. 176
C. 182
D. 190
Since the 8-year-old son is younger than the children in the data set, it is reasonable to assume that his time would be less than the average of the given times.
Based on this analysis, the closest option to the length of time it should take Marsha's 8-year-old son to run one lap is the option with the lowest time. Therefore, the answer would be A. 168.
The closest length of time it should take Marsha's 8-year-old son to run one lap around the track is 168.
To find the closest length of time it should take Marsha's 8-year-old son to run one lap, we can use the line of best fit. The line of best fit is a line that represents the trend or pattern in the data. However, since the line of best fit is not given, we need to estimate the time based on the given options.
To make an estimate, we can consider the ages of the children and their corresponding times. If the line of best fit indicates that older children take longer to run a lap, it is reasonable to assume that Marsha's 8-year-old son would take less time compared to the older children.
Now let's analyze the given options: 168, 176, 182, and 190. Since the 8-year-old son is younger than the children in the data set, it is reasonable to assume that his time would be less than the average of the given times.
Based on this analysis, the closest option to the length of time it should take Marsha's 8-year-old son to run one lap is the option with the lowest time, which is 168.
In conclusion, the closest length of time it should take Marsha's 8-year-old son to run one lap around the track is 168. The closest length of time it should take Marsha's 8-year-old son to run one lap around the track is 168.
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Find the value of x and y.
Answers
Answer:
x and y are both 45
Step-by-step explanation:
Answer:
x = 3√2 ≈ 4.243y = 3√2 ≈ 4.243Step-by-step explanation:
Given an isosceles right triangle with hypotenuse length 6, you want the lengths of the two legs of the triangle.
Isosceles right triangleThe ratios of side lengths in an isosceles right triangle are ...
1 : 1 : √2 = x : y : 6
Multiplying by 6/√2 = 3√2, the side length ratios are ...
x : y : 6 = 3√2 : 3√2 : 6
The values of x and y are 3√2 ≈ 4.243.
Find the volume of the figure. Use 3.14 for pi
Answers
Answer:
13
Step-by-step explanation:
Simplify the following functions using the Karnaugh Map method and obtain all possible minimized forms of the function. I Function 1 - Minimized SOP form (6 possible functions) F(a,b,e,d)=2m(0,1,3,4,6,7,8,9,11,12, 13, 14, 15) Function 2 - Minimized POS form (3 possible functions) F(a,b,c,d,e)=2m (4,5,8,9,12,13,18,20,21,22,25,28,30,31) Submit the following: 1. All grouped and labelled K-Maps of Function 1 2. All minimized SOP forms of Function 1 3. All grouped and labelled K-Maps of Function 2 4. All minimized POS forms of Function 2
Answers
However, I can explain the process of simplifying the given functions using the Karnaugh Map (K-Map) method and provide you with the minimized SOP and POS forms.
1. For Function 1, we have the following grouped and labeled K-Maps:
- K-Map for variables a, b, and e (4x4 grid)
- K-Map for variable d (2x2 grid)
2. To obtain the minimized SOP forms of Function 1, we need to analyze the grouped cells in the K-Maps and write the corresponding Boolean expressions. By applying the K-Map method, we can obtain six possible minimized SOP forms for Function 1.
3. For Function 2, we have the following grouped and labeled K-Maps:
- K-Map for variables a, b, c, and e (4x4 grid)
- K-Map for variable d (2x2 grid)
4. To obtain the minimized POS forms of Function 2, we need to analyze the grouped cells in the K-Maps and write the corresponding Boolean expressions. By applying the K-Map method, we can obtain three possible minimized POS forms for Function 2.
Please note that the specific expressions and grouped cells for each function can be obtained by visually examining the K-Maps. It would be best to refer to a resource that allows you to draw and label the K-Maps to get the accurate results for Function 1 and Function 2.
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Miyoko's goal is to earn more than this week. She earns for every day she works as a cryptographer, and
earns for every day she works as a geologist.
Write an inequality that represents the number of days Miyoko should work as a cryptographer and as a
geologist to achieve her goal.
Answers
Answer:
$250*C + $180*G = $950
Step-by-step explanation:
Solving for G, it is G = (950 - 250C)/180
Solving for C, it is C = (950 - 180G)/250
Max can travel 100 miles in 2 hours. At this rate, how many hours will it take him to travel 650 miles?
Answers
650miles in x hrs
If you think of it 650/100 = 6.5
So the distance is 6.5 times
So the time is 6.5 times 2hrs
=13 hrs total
Name the intersection of lines n and m.
Answers
intersection of lines n and m is D
From a pack of cards with two jokers, one card is drawn out. Find the probability of:
(i) getting a joker.
(ii) getting a face card (J, Q and K are
called face cards).
(iii) getting a red ace.
Answers
Answer: 1/28, 3/14, 1/28
Step-by-step explanation: There are two Jokers in the deck. This is 2/56 chance, which is reduced to 1/28. There are 12 face cards: 4 Kings, 4 Queens, and 4 Jacks. This is 12/56, which reduces to 3/14. There are two red aces: The Ace of Diamonds and the Ace of Hearts. This is a s2/56 chance, which reduces to 1/28 chance.
The chemical element einsteinium -253 naturally loses its mass over time . A sample of einsteinium-253 had an initial mass of 320 grams when we measured it
Answers
If there are infinite numbers of solutions of the two equations : x+4y=7 , 3X+ky = 21, then k =
Answers
Answer:
k = 12
Step-by-step explanation:
x + 4y = 7 ---------- (1)
3x + Ky = 21 -------- (2)
from equation 1
x = 7 - 4y
put the value of x in equation 2
3x + Ky = 21
3( 7 - 4y) + Ky = 21
21 - 12y + Ky = 21
Ky = 21 - 21 + 12y
Ky = 12y
divide both sides by y
k = 12
The value of the term k is equal to 12
We are given that there are infinite numbers of solutions of the two equations :
x + 4y = 7 ---------- (1)
3x + Ky = 21 -------- (2)
Then from equation 1
x = 7 - 4y
put the value of x in equation 2
3x + Ky = 21
3( 7 - 4y) + Ky = 21
21 - 12y + Ky = 21
Ky = 21 - 21 + 12y
Ky = 12y
Then divide both sides by y
k = 12
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If you want to buy an item in a store that costs $24 and is on sale for 30% off, then how much would the item actually cost you after the discount? Round to the nearest cent.
Answers
Answer: $16.80
Step-by-step explanation:
First you need to find 30% of 24. You can do this by doing .30*24. Then you get 7.2. Now you know what 30% of 24 is, so you subtract it from 24 since it is a discount. So -> 24 - 7.2 = $16.80.
Hope this helped!
Write the Taylor series for f(x)=e^x about x=−2 as ∑n=0[infinity] cn(x+2)^n.
Find the first five coefficients.
Answers
The first five coefficients, we have: f(x) = e⁻² + e⁻²(x + 2) + (e⁻²/2)(x + 2)² + (e⁻²/6)(x + 2)³ + (e⁻²/24)(x + 2)⁴ + ..
To find the Taylor series for the function f(x) = eˣ about x = -2, we can use the general formula for the Taylor series expansion:
f(x) = ∑n=0^∞ c_n(x - a)ⁿ
where c_n represents the nth coefficient, (x - a)^n is the term raised to the nth power, and a is the point about which we are expanding the series.
In this case, we want to find the Taylor series for f(x) = eˣ about x = -2. So, a = -2.
To find the coefficients c_n, we can use the formula:
c_n = (1/n!) * fⁿᵃ
where f^(n)(a) denotes the nth derivative of f evaluated at x = a.
Let's find the first five coefficients:
Step 1: Find f(x) and its derivatives:
f(x) = eˣ
f'(x) = eˣ
f''(x) = eˣ
f'''(x) = eˣ
f''''(x) = eˣ
Step 2: Evaluate the derivatives at x = -2:
f(-2) = e⁻²
f'(-2) = e⁻²
f''(-2) = e⁻²
f'''(-2) = e⁻²
f''''(-2) = e⁻²
Step 3: Calculate the coefficients:
c_0 = f(-2)/0! = e⁻²/1 = e⁻²
c_1 = f'(-2)/1! = e⁻²/1 = e⁻²
c_2 = f''(-2)/2! = e⁻²/2 = e⁻²/2
c_3 = f'''(-2)/3! = e⁻²/6 = e⁻²/6
c_4 = f''''(-2)/4! = e⁻²/24 = e⁻²/24
Therefore, the first five coefficients for the Taylor series expansion of f(x) = eˣ about x = -2 are:
c_0 = e⁻²
c_1 = e⁻²
c_2 = e⁻²/2
c_3 = e⁻²/6
c_4 = e⁻²/24
The Taylor series for f(x) = e^x about x = -2 can be written as:
f(x) = ∑n=0^∞ c_n(x + 2)ⁿ
Substituting the first five coefficients, we have: f(x) = e⁻² + e⁻²(x + 2) + (e⁻²/2)(x + 2)² + (e⁻²/6)(x + 2)³ + (e⁻²/24)(x + 2)⁴ + ..
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which expression is equivalent to 7(6m - 7) + 9?
- 42 + 2
- -7(6m + 7) + 9
- 7 (-7 + 6m) + 9
- -40m + 42
Answers
Answer:
\(7( - 7 + 6m) + 9\)
cual es el 75% de 160¿
What is 75% of 160¿
Answers
Answer:
120
Step-by-step explanation:
calculator
help asap!!!!!!!!!!!!!!
Answers
Answer:
\(2x + 2 = 5x - 4 \\ 2x - 5x = - 4 - 2 \\ - 3x = - 6 \\ x = \frac{ - 6}{ - 3} \\ x = 2\)