Find the length of the third side. If necessary, round to the nearest tenth.
15
25

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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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

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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z=90degrees

Y=135degrees

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 :)

Answer:

1.is 11

2. is-44

Step-by-step explanation:

1) 2+6-7+10

= 11

2) -49+15-10

= -44

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:

y = 36x

Step-by-step explanation:

y varies directly with x ,

that is y [tex]\propto[/tex] x

Let k be constant

=> y = kx

=> 108 = k(3)

=> k = 108/3

=> k = 36

y can be expressed in terms of x as kx or simply 36x . As we found value of constant as 36.

The original equation (10x + 25) / (3x + 12) = 5x / (x + 4) has no valid solutions.

We have,

To determine the number of valid solutions for the equation

(10x + 25) / (3x + 12) = 5x / (x + 4), we need to solve the equation and check if there are any values of x that satisfy the equation while not causing any division by zero.

Let's solve the equation step by step:

(10x + 25) / (3x + 12) = 5x / (x + 4)

Cross-multiply to eliminate the fractions:

(10x + 25)(x + 4) = (3x + 12)(5x)

Expand both sides:

10x² + 40x + 25x + 100 = 15x² + 60x

Combine like terms:

10x² + 65x + 100 = 15x² + 60x

Subtract 10x² + 60x from both sides:

5x² + 5x + 100 = 0

Now we have a quadratic equation.

To solve it, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

For the equation 5x² + 5x + 100 = 0, a = 5, b = 5, and c = 100.

Calculating the discriminant (b² - 4ac):

Discriminant = (5²) - (4 x 5 x 100)

Discriminant = 25 - 2000

Discriminant = -1975

Since the discriminant is negative (-1975), the quadratic equation has no real solutions.

Therefore,

The original equation (10x + 25) / (3x + 12) = 5x / (x + 4) has no valid solutions.

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Answer:

it is 2, 4 and 6

Step-by-step explanation:

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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Answer:

D) -cos(x)

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Hello!

As we can see, our a value, which would be the coefficient of [tex]x[/tex], which determines our slope, is negative, meaning that this whole line is negative.

Furthermore, the correlation can be determined using the r value of the linear regression, which is around -0.9.

If the r value of the linear regression is close to 1 or -1, let's say around |r| > 0.8, then we can consider the regression a strong correlation, meaning that this is a strong negative correlation, which is answer choice A.

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:

:)

Two things that a rigid motion preserves are: length and angle.

The two things that a rigid motion preserves are:

1. Length: A rigid motion preserves the length of objects. This means that the distances between points or the lengths of line segments remain the same after the rigid motion is applied.

For example, if you have a line segment AB of length 5 units, a rigid motion such as translation, rotation, or reflection will not change the length of AB.

2. Angle: A rigid motion preserves angles between lines or line segments. This means that the measure of an angle remains the same after a rigid motion is applied.

For example, if you have an angle ABC with a measure of 60 degrees, a rigid motion will not change the measure of angle ABC.

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70% of the trip length, t, is 35 miles. Find t:

0.70t = 35. Dividing both sides by 0.70, we get:

35

t = ----------- = 50

0.70

The total trip length is 50 miles.

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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Answer:

200 miles

Step-by-step explanation:

Given data

cost of car rental per day= $40

cost per mile= $0.22

We are told that the budget is $84

The expression for the total cost is given as

y= 40+0.22x

where x = the distance travelled

now for y=$84, by substituting we can get x

84=40+0.22x

84-40=0.22x

44=0.22x

divide both sides by 0.22

x= 44/0.22

x=200

Hence the distance that $84 will go is 200 miles

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:

I completely forgot how to do this I'm sorry

Step-by-step explanation:

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°

Answer: G

Step-by-step explanation:

Answer:

Step-by-step explanation:

Edg 2021

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

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

Answer:

see below

Step-by-step explanation:

-2.6

-2.2

-2.193

-2.01

Since they are negatives, the higher number it is, the smaller it actually is.  The smaller the number is, that number will be closer to 0 and will actually be higher than the rest.

Hope this helps! :)