The length of the arc on a circle with radius 10 cm intercepted by a 20° angle is,
Lenght of arc = 3.48 cm
We have to given that,
In a circle,
Radius = 10 cm
And, Angle = 20 degree
Since, We know that,
Lenght of arc = 2πr (θ/360)
Where, θ is central angle and r is radius.
Substitute all the values,
Lenght of arc = 2πr (θ/360)
Lenght of arc = 2 x 3.14 x 10 (20/360)
Lenght of arc = 3.48 cm
Therefore, the length of the arc on a circle with radius 10 cm intercepted by a 20° angle is,
Lenght of arc = 3.48 cm
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2.75603957 rounded to 2 decimal places
What is the line of symmetry for the parabola whose equation is y = x2 + 10x + 25?
A-x = -5
B-x = 5
C-x = -10
Answer:
x = -5
Step-by-step explanation:
Please write this as y = x^2 + 10x + 25. Here the coefficients are {1, 10, 25}.
The equation of the axis of symmetry is x = -b/[2a], which here is
x = -10 / [2*1] = -5
If Tony wants to add a 22% tip to his $35 charge from the barbershop, how much should he add?
Answer:
Tony should add $7.70
Step-by-step explanation:
22% = 0.22
0.22 x $35 = $7.70
Consider a sample with data values of 6, 17, 14, 7, and 16. Compute the variance. (to 1 decimal) Compute the standard deviation.
The standard deviation of the sample data is 4.6 and the variance is 21.2.
To compute the variance, follow these steps:
1. Calculate the mean (average) of the data values. In this case, (6 + 17 + 14 + 7 + 16) / 5 = 12.
2. Subtract the mean from each data value and square the result. For each value: (6 - 12)² = 36, (17 - 12)² = 25, (14 - 12)² = 4, (7 - 12)² = 25, and (16 - 12)² = 16.
3. Calculate the sum of all the squared differences: 36 + 25 + 4 + 25 + 16 = 106.
4. Divide the sum by the number of data values (5) to get the variance: 106 / 5 = 21.2 (rounded to 1 decimal place).
To compute the standard deviation, take the square root of the variance.
Standard deviation = √(21.2) = 4.6
Variance measures how much the data values differ from the mean, while the standard deviation represents the average amount of deviation from the mean. In this sample, the variance is 21.2 and the standard deviation is 4.6. These metrics help quantify the spread and variability of the data set.
Therefore the standard deviation of the sample data is 4.6.
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What is the value of C?
Answer:
2
Step-by-step explanation:
What’s 1/5 divided by 1/12?
PLEASE HELP ASAP
Find the surface area and volume of the cylinder below:
Answer:
Surface Area: 848.23
Volume: 1727.88
Step-by-step explanation:
I know dis im in 8th grade iz ez!
QUESTION 1
1.1 Find the sum:
1.1.1 2+6+(-7) + 10 =
1.1.2 (-49) + (15) + (-10) =
Answer:
1.is 11
2. is-44
Step-by-step explanation:
1) 2+6-7+10
= 11
2) -49+15-10
= -44
Please Help — Neil is going to a bookstore 45 miles away. The bridge was closed on the way back, so
he had to take an alternate route and had to drive 15 mph slower, which make the trip
back take 7 minutes longer. How fast was he going on the way to the bookstore??
OMG HELP PLS IM PANICKING OMG OMG I GOT A F IN MATH AND I ONLY HAVE 1 DAY TO CHANGE MY GRADE BECAUSE TOMORROW IS THE FINAL REPORT CARD RESULTS AND I DONT WANNA FAIL PLS HELP-
AND CAN ANYONE PLS DRAW ME THE ANSWERS I CANT UNDERSTAND ANYTHING PLS I BEG U ILL GIVE U BRAINLEST
Answer:
The 2/5th’s bucket is the answer to question one.
for the second one, draw a square or rectangle and divide one of them by 5 (draw 4 lines in it) and fill in two of those lines.
the second fraction, draw another rectangle and draw 3 lines on the inside of it, filling in 3. (you’re creating a visual representation of the fractions. you can also look up ‘3/4 picture’ and ‘2/5 picture’ and copy off the internet.
Step-by-step explanation:
He points (2, -3) and (2,5) represent the locaons of two towns on a coordinate grid, where 1 unit is equal to 1 mile. What is the distance, in miles, between the two towns?
Answer:
Distance between the points is 8 miles.
Step-by-step explanation:
Distance between tow points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by,
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between the given points (2, -3) and (2, 5) will be,
Distance = [tex]\sqrt{(2-2)^2+(-3-5)^2}[/tex]
= 8 units
Since, 1 unit = 1 mile
Therefore, distance between these points will be 8 miles.
OK a quarter steam covers a 100' square feet how many courts should you buy to stay in the wheelchair ramp
Answer:
He should buy about 2 quart of stain
Step-by-step explanation:
Find the diagram attached
First we need to find the area of the given ramp
The ramp consists of two identical triangles, a larger and small rectangles
Since area of triangle = 1/2 * base * height
Area of the identical triangles = 1/2 * 25ft * 25/12 ft (Note that 1ft = 12in)
Area of the 2 identical triangles = 2* 625/24ft² = 625/12 ft²
Area of the large rectangle = Length * Width
Area of the large rectangle = 25 1/12 * 5
Area of the large rectangle = 301/12 * 5
Area of the large rectangle = 1505/12 ft²
Area of the small rectangle = 25/12 * 5
Area of the small rectangle = 125/12 ft²
Area of the figure = 625/12 + 1505/12 + 125/12
Area of the figure = (625+1505+125)/12
Area of the figure = 2255/12
Area of the figure = 187.917
Area of the figure = 187.917ft²
Since a quarter steam covers a 100' square fee, then;
1 quarter = 100ft²
x = 187.917ft²
Cross multiply
100 * x = 187.917
100x =187.917
x = 187.917/100
x = 1.87917
x ≈ 2
Hence he should buy about 2 quart of stain
find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3e−x, y = 3, x = 2; about y = 6 v =
The volume (v) of the solid obtained by rotating the region about y = 6 is approximately 339.02 cubic units.
To find the volume of the solid obtained by rotating the region bounded by the curves y = 3e^(-x), y = 3, and x = 2 about the line y = 6, we can use the method of cylindrical shells.
First, let's plot the curves and the line of rotation to visualize the region:
|
| y = 3e^(-x)
| _______
|__________| y = 3
| |
| |___ x = 2
|
y=6|_____________________
We can see that the line y = 6 is above the region bounded by the curves. To find the volume, we will integrate the circumference of each cylindrical shell multiplied by its height.
The height of each cylindrical shell is given by the difference between the line y = 6 and the curve y = 3e^(-x), which is 6 - 3e^(-x).
The radius of each cylindrical shell is given by the distance from the line y = 6 to the x-axis, which is 6 - 0 = 6.
The differential volume element is given by dV = 2πrh dx, where r is the radius and h is the height.
Therefore, the volume of the solid can be obtained by integrating this expression over the range of x from 0 to 2:
V = ∫[0,2] 2π(6 - 3e^(-x))(6) dx
Simplifying the expression:
V = 12π ∫[0,2] (6 - 3e^(-x)) dx
V = 12π ∫[0,2] (6 - 3e^(-x)) dx
V = 12π [6x + 3e^(-x)] evaluated from 0 to 2
V = 12π [(12 + 3e^(-2)) - (0 + 3e^(-0))]
V = 12π (12 + 3e^(-2) - 3)
V = 12π (9 + 3e^(-2))
V ≈ 339.02 cubic units
Therefore, the volume (v) of the solid obtained by rotating the region about y = 6 is approximately 339.02 cubic units.
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Suppose the price of a bond is given by the following
function:
23.751-1+i-20i+5001+i-20=547.50
Use linear interpolation to approximate the value of
i:
The approximate value of i using linear interpolation is i ≈ 0.010526.
To approximate the value of i using linear interpolation, we need two data points on either side of the desired value of i. In the given equation, we have the following data points:
When i = 0, the price of the bond is 547.50.
When i = 0.01, the price of the bond is 23.751 - 1(0.01) - 20(0.01) + 500 / (1 + 0.01 - 20) = 442.24.
Since the desired value of i lies between 0 and 0.01, we can use linear interpolation to approximate it.
Linear interpolation assumes a linear relationship between two data points and estimates the value based on the proportionate distance between those points.
Let's denote the desired value of i as [tex]i_d[/tex]. We can set up the following equation to find [tex]i_d[/tex]:
[tex](i_d - 0) / (0.01 - 0) = (547.50 - 442.24) / (0.01 - 0)[/tex]
Simplifying the equation:
[tex](i_d - 0) / 0.01 = (547.50 - 442.24) / 0.01i_d / 0.01 = 105.26 / 0.01i_d = 105.26[/tex]
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What is the mean? 2, 4, 7, 5, 8, 10
Remember- add all the
numbers, and then divide by the total
amount of numbers
6
9
5
36
Answer:
6
Step-by-step explanation:
2+4+7+5+8+10
=36÷6
=6
Eileen jogs every day. Last month, she jogged 6.5 hours for a total of 37.05 miles. At this speed, if Eileen runs 31.5 hours, how far can she run? (what equation would I use?)
I hope this helped
Step-by-step explanation:
First: 37.05 miles / 6.5 hours = 5.7
Next: 5.7 miles per hour
Third: 31.5 hours times 5.7 miles= 179.55 miles
Lastly: 179.55 miles for 31.5 hours
12/5 divided by 21/10
PLEASE HELP!
Write down the Equation of the following lines:
1)parallel to y=2x-1 and passing through (1, 8)
Answer:
y=2x+6
Step-by-step explanation:
We use this following formula to find the equation:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
Now, we substitute the values in [tex]y_{1}[/tex] and [tex]x_{1}[/tex] :
[tex]y-8=2(x-1)[/tex]
Distribute the 2 inside the parentheses:
[tex]y-8=2x-2[/tex]
Now add 8 to both sides:
[tex]y=2x+6[/tex] is your answer.
Step-by-step explanation:
y=mx+b
m=slope
b=y-intercept
y=2x-1
2=slope
-1=y intercept
NOTE: parallel lines have the same slope
and we put the point (1,8) into y=mx+b with (x,y)
8=1m+b
now we put in 2 for the slope
8=1(2)+b
6=b
2=m
now insert that back into y=mx+b
y=2x+6
and that is the line that is parallel to y=2x-1 and passes through (1,8)
Hope that helps :)
X and Y are two continuous random variables whose joint pdf f(x, y) = kr² over the region 0≤x≤1 and 0 ≤ y ≤ 1, and zero elsewhere. Calculate the covariance Cov(X,Y).
The covariance Cov(X, Y) can be calculated for the given joint probability density function (pdf) f(x, y) = kr² over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1.
To calculate the covariance Cov(X, Y), we need to determine the joint probability density function (pdf) of X and Y and apply the formula for covariance.
First, we need to find the constant k by integrating the joint pdf over its entire range to ensure it integrates to 1 (since it represents a probability density function).
The integral of f(x, y) over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is given by:
∫∫ f(x, y) dy dx = ∫∫ kr² dy dx.
Integrating with respect to y first, we get:
∫[0,1] ∫[0,1] kr² dy dx = k∫[0,1] r² [y=0 to y=1] dx
= k∫[0,1] r² dx
= k[r²x] [x=0 to x=1]
= k(r² - 0)
= kr².
Since the integral of the joint pdf over its entire range equals 1, we have kr² = 1, which implies k = 1/r².
Now, we can calculate the covariance Cov(X, Y) using the formula:
Cov(X, Y) = E[XY] - E[X]E[Y],
where E denotes the expected value.
Since X and Y are continuous random variables with a uniform distribution over the range [0,1], we have E[X] = E[Y] = 1/2.
To calculate E[XY], we integrate the product XY over the range [0,1] for both x and y:
E[XY] = ∫∫ xy f(x, y) dy dx
= ∫∫ xy kr² dy dx
= k∫∫ xyr² dy dx
= k∫[0,1] ∫[0,1] xyr² dy dx.
Integrating with respect to y first, we get:
E[XY] = k∫[0,1] ∫[0,1] xyr² dy dx
= k∫[0,1] [(1/2)xr² [y=0 to y=1]] dx
= k∫[0,1] (1/2)xr² dx
= (k/2)∫[0,1] xr² dx
= (k/2)[(1/3)x³r² [x=0 to x=1]]
= (k/2)(1/3)r²
= (1/2)(1/3)r²
= 1/6r².
Finally, we can calculate the covariance:
Cov(X,Y) = E[XY] - E[X]E[Y]
= 1/6r² - (1/2)(1/2)
= 1/6r² - 1/4.
Therefore, the covariance Cov(X, Y) for the given joint pdf f(x, y) = kr² over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is 1/6r² - 1/4.
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Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m3 (the article "Counting at Low Concentrations: The Statistical Challenges of Verifying Ballast Water Discharge Standards"† considers using the Poisson process for this purpose).
For what amount of discharge would the probability of containing at least 1 organism be 0.993? (Round your answer to two decimal places.)
The amount of discharge for which the probability of containing at least 1 organism is 0.993 is approximately 0.14 m³.
To find the amount of discharge for which the probability of containing at least 1 organism is 0.993, we can use the Poisson distribution formula. The Poisson distribution describes the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence.
In this case, the concentration of organisms in the ballast water is given as 10 organisms/m³. Let's denote λ as the average rate of occurrence, which is equal to the concentration in this case, λ = 10 organisms/m³.
The Poisson distribution formula is:
P(X ≥ k) = 1 - P(X < k) = 1 - e^(-λ) * (λ^0/0! + λ^1/1! + λ^2/2! + ... + λ^(k-1)/(k-1)!)
We want to find the amount of discharge (let's call it x) for which P(X ≥ 1) = 0.993. Plugging in the values into the formula, we have:
0.993 = 1 - e^(-10) * (10^0/0! + 10^1/1!)
Simplifying the equation, we have:
0.993 = 1 - e^(-10) * (1 + 10)
Now we can solve for e^(-10) using logarithms:
e^(-10) = 1 - 0.993 / (1 + 10)
e^(-10) ≈ 0.0045
Substituting this back into the equation, we have:
0.993 = 1 - 0.0045 * (1 + 10)
Simplifying further, we get:
0.993 = 1 - 0.0045 * 11
Now, let's solve for the discharge amount x:
0.993 = 1 - 0.0495x
0.0495x = 1 - 0.993
0.0495x ≈ 0.007
x ≈ 0.007 / 0.0495
x ≈ 0.14 m³
Therefore, the amount of discharge for which the probability of containing at least 1 organism is 0.993 is approximately 0.14 m³.
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Student Council is selling T-shirts to raise money for new volleyball equipment. There is a fixed cost of
$200 for producing the T-shirts, plus a variable cost of $5 per T-shirt made. Council has decided to sell
the T-shirts for $8 each.
A. Write an equation to represent the total cost, C, as a function of the number, n, of T-shirts
produced.
B. Write an equation to represent the revenue, R, as a function of the number, n, of T-shirts
produced
C. Profit, P, is the difference between revenue (R(n)) and expenses (C(n)). Develop an algebraic
function to model the profit.
D. How many T-shirts does the Student Council have to sell to "break even," make a $0 profit?
Answer:
It is A
Write an equation to represent the total cost, C, as a function of the number, n, of T-shirts
produced.
Step-by-step explanation:
:)
A bicycle has a listed price of $615.98 before tax. If the sales tax rate is 9.75%, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.
An auto maker estimates that the mean gas mileage of its sports utility vehicle is at least 20 miles per gallon. A random sample of 36 such vehicles had a mean of 18 miles per gallon and a standard deviation of 5 miles per gallon. At α = .01 can you reject the auto maker's claim?
Answer:
Yes, we reject the auto maker's claim.
Step-by-step explanation:
H0 : μ ≥ 20
H1 : μ < 20
Sample mean, xbar = 18 ;
Sample size, n = 36
Standard deviation, s = 5
At α = 0.01
The test statistic :
(xbar - μ) ÷ s /sqrt(n)
(18 - 20) ÷ 5/sqrt(36)
-2 /0.8333333
= - 2.4
Pvalue from test statistic : Pvalue = 0.00819
Pvalue < α
0.00819 < 0.01
Hence, we reject the Null
19.
20
Z
45°
y у
60°
63
2 =
I NEED HELP WITH NUMBER 19 PLEASE HELP!
z=90degrees
Y=135degrees
Find the mean of the following probability distribution? Round your answer to one decimal. P(2) 0 0.0017 1 0.3421 2 0.065 3 0.4106 4 0.1806 mean = ___
The mean of the given probability distribution is 3.4.
To find the mean of a probability distribution, we multiply each value of x by its corresponding probability and then sum them up. Using the provided data:
P(2) 0
P(1) 0.0017
P(2) 0.3421
P(3) 0.065
P(4) 0.4106
P(5) 0.1806
mean = 2(0) + 1(0.0017) + 2(0.3421) + 3(0.065) + 4(0.4106) + 5(0.1806)
= 0 + 0.0017 + 0.6842 + 0.195 + 1.6424 + 0.903
= 3.4263
Therefore, the mean of the given probability distribution is approximately 3.4 (rounded to one decimal place).
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convert the angle 0=17 pie/18 radians to degrees
Answer:
it would be 170°
Step-by-step explanation:
( 17 πover 18 ) ⋅ 180 ° over π
17over18 ⋅ 180
then you cancel the common factors
17 ⋅ 10 mulitply those two and end up with
170°
PLEASE HELP ME OUT! QUICK POINTS FOR YOU!
All information needed can be found in the image below
Thank you in advance.
Answer:
5π
Step-by-step explanation:
just need to find half of the circumference
In a certain raffle, you buy 2 tickets. 50 tickets are sold altogether. 7 prizes will be awarded. Find the probability that you win 0 prizes.
0.16
0.04
0.26
0.74
The probability of winning 0 prizes in the raffle is 0.74. The last option.
ProbabilityTo find the probability of winning 0 prizes in the raffle, we need to calculate the probability of not winning any prize.
First, let's calculate the probability of winning a prize with a single ticket. Since there are 7 prizes and a total of 50 tickets sold, the probability of winning a prize with one ticket is 7/50.
To calculate the probability of not winning a prize with one ticket, we subtract the probability of winning a prize from 1:
1 - (7/50) = 43/50.
Since you bought two tickets, the probability of not winning any prize with both tickets is the probability of not winning a prize with one ticket multiplied by itself:
(43/50) * (43/50) = 1849/2500.
Therefore, the probability of winning 0 prizes in the raffle is 1849/2500, which is approximately equal to 0.7396 or 0.74 when rounded to two decimal places.
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Events A and B are such that P() = 0.55 and P( ∪ ) = 0.75. Given that A and B are independent and non-mutually exclusive, determine P().
Given that A and B are independent and non-mutually exclusive. The answer is: P(A or B) = 0.52.
we haveP(A and B) = P(A) * P(B)P(A ∪ B) = P(A) + P(B) - P(A and B)
Also, given that P(A) = 0.55 and P(A ∪ B) = 0.75, we can find P(B)
as follows:0.75 = P(A) + P(B) - P(A and B)0.75 = 0.55 + P(B) - P(A and B)0.75 - 0.55 = P(B) - P(A and B)0.2 = P(B) - P(A) * P(B) [Using P(A and B) = P(A) * P(B)]0.2 = P(B)(1 - P(A)) [Taking out P(B) as a common factor]0.2 = P(B)(1 - 0.55) [Substituting the value of P(A)]0.2 = 0.45P(B) [Simplifying]P(B) = 0.2/0.45 = 4/9Now, we can find P(A or B) as follows:P(A or B) = P(A) + P(B) - P(A and B)P(A or B) = 0.55 + 4/9 - (0.55 * 4/9) [Substituting the values of P(A), P(B), and P(A and B)]P(A or B) = 1.16/2.25 [Simplifying]P(A or B) = 0.52
Therefore, the answer is: P(A or B) = 0.52.
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For independent and non-mutually exclusive A and B, the value of P(A ∪ B) is 0.64.
Events A and B are such that P(A) = 0.55 and P(A ∪ B) = 0.75.
A and B are independent and non-mutually exclusive.
To find out the probability of B, we can use the formula:
P(B) = P(A ∪ B) - P(A)
As we have already been given the value of P(A) and P(A ∪ B), so we can easily find the value of P(B)
P(B) = P(A ∪ B) - P(A)
P(B) = 0.75 - 0.55
P(B) = 0.2
Now, to find P(A ∩ B), we can use the formula:
P(A ∩ B) = P(A) × P(B)
As we have been given that A and B are independent events.
Hence, we can say that:
P(A ∩ B) = P(A) × P(B) = 0.55 × 0.2
P(A ∩ B) = 0.11
Now, we can use the formula of addition of probabilities to find P(A ∪ B):
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
P(A ∪ B) = 0.55 + 0.2 - 0.11
P(A ∪ B) = 0.64
Therefore, the value of P(A ∪ B) is 0.64.
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what is the equation of a parabola with the given vertex and focus ?
vertex(-2,5)focus(-2,6)
14.what is the center and radius of a circle with the given equation?
x^2+y^2-4x+10y=7
The equation of a parabola with vertex (h, k) and focus (h, k + p) is given by the equation (x - h)^2 = 4p(y - k). In this case, the vertex is (-2, 5) and the focus is (-2, 6). Since the x-coordinate of both the vertex and focus is the same, we can conclude that the parabola opens either upward or downward. The equation of the parabola is then (x + 2)^2 = 4p(y - 5).
The given equation x^2 + y^2 - 4x + 10y = 7 can be rewritten as (x^2 - 4x) + (y^2 + 10y) = 7. To complete the square, we need to add and subtract terms to both sides of the equation to create perfect square trinomials. By adding (4/2)^2 = 4 to the x terms and (10/2)^2 = 25 to the y terms, we have (x^2 - 4x + 4) + (y^2 + 10y + 25) = 7 + 4 + 25, which simplifies to (x - 2)^2 + (y + 5)^2 = 36. Comparing this equation to the standard form of a circle (x - h)^2 + (y - k)^2 = r^2, we can identify the center of the circle as (2, -5) and the radius as the square root of 36, which is 6. Therefore, the center and radius of the circle are (2, -5) and 6, respectively.
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