What is the length of the arc on a circle with radius 10 cm intercepted by a 20° angle? Use 3.14 for π. Round the answer to the hundredths place. Enter your answer in the box. cm
a. 3.14 cm
b. 6.28 cm
c. 12.57 cm
d. 25.13 cm

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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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

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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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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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.

Answer:

5π

Step-by-step explanation:

just need to find half of the circumference

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

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

Answer:

Tony should add $7.70

Step-by-step explanation:

22% = 0.22

0.22 x $35 = $7.70

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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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:

:)

Answer:

6

Step-by-step explanation:

2+4+7+5+8+10

=36÷6

=6

Answer:

2

Step-by-step explanation:

Answer:

Surface Area: 848.23

Volume: 1727.88

Step-by-step explanation:

I know dis im in 8th grade iz ez!

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:

The probability of winning 0 prizes in the raffle is 0.74. The last option.

To 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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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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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°

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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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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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 :)

z=90degrees

Y=135degrees

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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Answer:

1.is 11

2. is-44

Step-by-step explanation:

1) 2+6-7+10

= 11

2) -49+15-10

= -44

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