(3, -4), m= 6 point slope

Answer:

P(X/Y) = 0.4545

Step-by-step explanation:

Let's call X that the transferred ball is black, X' that the transferend ball is white and Y the event that the second ball drawn is black.

The probability that the transferred ball was black given that the second ball drawn was black is equal to:

P(X/Y) = P(X∩Y)/P(Y)

Where P(Y) = P(X∩Y) + P(X'∩Y)

Then, the probability P(X∩Y) that the transferred ball is black and the second ball drawn is black is equal to:

P(X∩Y) = (5/12)*(7/11) = 0.2651

Because the urn A has 12 balls and 5 of them are black, then if the transferred ball is black, the urn B will contain 11 balls and 7 of them will be black balls.

At the same way, the probability P(X'∩Y) that the transferred ball is white and the second ball drawn is black is equal to:

P(X'∩Y) = (7/12)*(6/11) = 0.3181

Because the urn A has 12 balls and 7 of them are white, then if the transferred ball is white, the urn B will contain 11 balls and 6 of them will be black balls.

So, P(Y)  and P(X/Y) are equal to:

P(Y) = 0.2651 + 0.3181

P(Y) = 0.5832

P(X/Y) = 0.2651/0.5832

P(X/Y) = 0.4545

The man's BMI is approximately 22.09 based on his weight of 154 pounds and height of 70 inches.

To calculate the Body Mass Index (BMI) of a person, we use the following formula:

BMI = weight (in kilograms) / height^2 (in meters)

First, we need to convert the weight from pounds to kilograms. Since 1 pound is approximately 0.4536 kilograms, the man's weight of 154 pounds is equal to 69.85 kilograms (rounded to two decimal places).

Next, we need to convert the height from inches to meters. Since 1 inch is equal to 0.0254 meters, the man's height of 70 inches is equal to 1.778 meters (rounded to three decimal places).

Now, we can calculate the BMI using the formula:

BMI = 69.85 kg / (1.778 m)^2

Calculating this expression, we find that the man's BMI is approximately 22.09 (rounded to two decimal places).

In summary, the man's BMI is approximately 22.09 based on his weight of 154 pounds and height of 70 inches.

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The numerical value in this sentence, "the average price of a house in the new subdivision is $257,000" describes a Population Parameter.

A population parameter is a figure that describes a fact about a whole population. In this sentence, we can see that the figure quoted is representative of an entire population. A sample statistic, on the other hand, describes something about a part of a population.

So, for the statement above, we can see that the average price is representative of all the houses in the new subdivision. Thus, the figure is a population parameter.

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Answer:

b. 12

Step-by-step explanation:

Answer:

either a or d because they are both correct.

Step-by-step explanation:

The level of marginal significance inside a statistical hypothesis test, or P-value, represents the likelihood that a particular event will occur.

P-value;

The likelihood of getting a result that is equivalent to or more extreme than what was actually seen, under the null hypothesis, is what is meant by the term "P value." The probability (P) indicator indicates the likelihood that any observed variation between groups is the result of chance.

Here,

The statistical test's extremely low p-value indicates that the null hypothesis must be accepted, and the conclusion that Gilbert is guilty is based on the fact that Gilbert's existence is dependent on the shift deaths.

Relevance of p-value to the trial;

The p-value evaluates the agreement between the trial's actual outcomes and the "pure chance" explanation for them. When the only differences between groups A and C are the result of chance, a p-value of 0.002 favoring group A very extremely seldom occurs.

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The given equation of the circle is:

\( \rm \: x^2 + y^2 = 20\)

We can write this equation in standard form by completing the square:

\( \rm x^2 + y^2 = 20\)

\( \rm x^2 + y^2 - 20 = 0\)

\( \rm (x^2 - 2x + 1) + (y^2 - 20) = 1\)

\( \rm (x - 1)^2 + y^2 = 21\)

Therefore, the center of the circle is (1, 0) and the radius is the square root of 21.

So, adjusted to the greatest tenth, the distance between points R and S is around 4.2 units.

The total movement of something, independent of direction, is its distance. The amount of space that an object has traveled, regardless of where it started or ended, can be referred to as distance. When describing the spacing between two things, distance is frequently utilized. But distance is a mathematical representation of the measurement of a line's category, a line with an identifiable starting - ending point.

The following formula may be used to calculate the separation among points R and S:

d =\(\sqrt{ ((x2 - x1)^2 + (y2 - y1)^2)}\)

where (x1, y1) = (1, 2) and (x2, y2) = (4, 5)

d = \(\sqrt{((4 - 1)^2 + (5 - 2)^2)}\)

d = \(\sqrt{(9 + 9)}\)

d = \(\sqrt{(18)}\)

d ≈ 4.2

So, adjusted to the next tenth, the distance between points R and S is around 4.2 units. The most similar option, B, at 4.6 units, does not provide the right response. The options for the answer don't include the right response.

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Answer:

5, (0, -2)

6, (4, 9)

Step-by-step explanation:

All three components of the fire triangle are usually present whenever and wherever surgery is performed. The fire triangle consists of three elements: fuel, heat, and oxygen.

In the context of surgery, nitrous oxide can be considered as a source of the fuel component of the fire triangle. Nitrous oxide is commonly used as an anesthetic in surgery, and it is highly flammable. It can act as a fuel for fire if it comes into contact with a source of ignition, such as sparks or open flames.

Therefore, it is important for healthcare professionals to be aware of the potential fire hazards associated with the use of nitrous oxide in surgical settings and take appropriate safety precautions to prevent fires.

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The transformation that will produce a figure that is similar but not congruent is given as follows:

A dilation with a scale factor of 2.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor. The resulting image is a larger or smaller version of the original object, depending on whether the scale factor is greater than or less than 1, respectively.

The dilation keeps the figures similar, as the angle measures remain constant, but the figures are not congruent, as they are going to have different side lengths.

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The calculated area of the cross-section is 14 square inches

from the question, we have the following parameters that can be used in our computation:

The prism (see attachment 1)

When a vertical plane intersects the vertex and the shorter edge of the base, the shape formed is a triangle with the following dimensions

Base = 7 inches

Height = 4 inches

See attachment 2

So, we have

Area = 1/2 * 7 * 4

Evaluate

Area = 14

Hence, the area of the cross-section is 14 square inches

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Answer:

y = -2x - 2

Step-by-step explanation:

the equation of a linear graph is y = mx + b

you know the m = -2

so now the equation is y = -2x + b

from here, what you could do to find b is...

plug (-2, 2) into the equation

1) x = -2, y = 2

2) 2 = -2(-2) + b

3) 2 = 4 + b

4) -2 = b

or you can look at the y-intercept which is where the line intersects with the y-axis

it seems to be (0, -2)

so "b" would be equal to -2

this makes the final equation y = -2x + (-2) or y = -2x - 2

Answer:

True

Right angles measure 90° . So each vertical angle = 90° and hence they are equal

Step-by-step explanation:

Answer:

a.) The probability that the chosen candy is red is 53/120.

b.) If the chosen candy is red, the probability that it came from the    second jar is 18/53.

Step-by-step explanation:

(a) To calculate the probability that the chosen candy is red, we need to consider the probabilities from both jars.

Let's define the events:

R1: Candy is red from the first jar.

R2: Candy is red from the second jar.

J1: Jar 1 is selected.

J2: Jar 2 is selected.

Given:

P(R1) = 14 red candies / (14 red candies + 10 green candies) = 14/24 = 7/12

P(R2) = 9 red candies / (9 red candies + 21 green candies) = 9/30 = 3/10

P(J1) = P(J2) = 1/2 (since the jar is selected randomly)

To find the probability that the chosen candy is red (R), we use the law of total probability:

P(R) = P(R|J1) * P(J1) + P(R|J2) * P(J2)

P(R) = P(R1) * P(J1) + P(R2) * P(J2)

= (7/12) * (1/2) + (3/10) * (1/2)

= 7/24 + 3/20

= 35/120 + 18/120

= 53/120

(b) To find the probability that the candy came from the second jar (J2) given that it is red (R), we can use Bayes' theorem:

P(J2|R) = P(R|J2) * P(J2) / P(R)

P(J2|R) = (3/10) * (1/2) / (53/120)

= (3/10) * (1/2) * (120/53)

= 36/106

= 18/53

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Answer:

it will be an even number

The solutions to the given differential equations are:

\(y(t) = (3e^{(-t)} + 10 - 2(e^{(t-3)}))(e^t - e^{(5t)})\)

y(t) = 2t + 4 - 2cos(3t) + sin(3t)

To solve these differential equations using Laplace transforms, follow the standard procedure of taking the Laplace transform of the given equation, solving for the Laplace transform of the unknown function, and then taking the inverse Laplace transform to obtain the solution.

Solve the equation: y" – 6y' + 5y = 3e⁻ˣ; y(0) = 2; y'(0) = 3

Step 1: Taking the Laplace transform of both sides of the equation:

s²Y(s) - sy(0) - y'(0) - 6sY(s) + 6y(0) + 5Y(s) = 3/(s + 1)

Step 2: Simplifying the equation using the initial conditions:

(s² - 6s + 5)Y(s) - 2s - 3 - 12 + 10 = 3/(s + 1)

Step 3: Rearranging the equation to solve for Y(s):

Y(s) = (3/(s + 1) + 15 - 2s - 3)/(s² - 6s + 5)

Step 4: Partial fraction decomposition:

Y(s) = (3/(s + 1) + 10 - 2(s - 3))/(s - 1)(s - 5)

Step 5: Taking the inverse Laplace transform to find y(t):

\(y(t) = (3e^{(-t)} + 10 - 2(e^{(t-3)}))(e^t - e^{(5t)})\)

Solve the equation: y" + 9y = 2x + 4; y(0) = 0; y'(0) = 1

Step 1: Taking the Laplace transform of both sides of the equation:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 2/s² + 4/s

Step 2: Simplifying the equation using the initial conditions:

s²Y(s) - 1 + 9Y(s) = 2/s² + 4/s

Step 3: Rearranging the equation to solve for Y(s):

Y(s) = (2/s² + 4/s + 1)/(s² + 9)

Step 4: Partial fraction decomposition:

Y(s) = (2/s² + 4/s + 1)/(s² + 9)

= 2/s² + 4/s - 2(s/(s² + 9)) + 1/(s² + 9)

Step 5: Taking the inverse Laplace transform to find y(t):

y(t) = 2t + 4 - 2cos(3t) + sin(3t)

Therefore, the solutions to the given differential equations are:

\(y(t) = (3e^{(-t)} + 10 - 2(e^{(t-3)}))(e^t - e^{(5t)})\)

y(t) = 2t + 4 - 2cos(3t) + sin(3t)

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Answer: A. y + 2 = -3(x - 4).

C. y = -3x - 5/3 and E. 3x + y = 7

Step-by-step explanation:

got it correct on edge2020

Check the picture below.

Therefore, the exact cost of producing the 22nd machine is $2,474.80. To find the exact cost of producing the 22nd machine.

We need to substitute x = 22 into the cost function C(x).
Given: C(x) = 1,300 + 60x - 0.3x^2 Substituting x = 22 into the function, we get: C(22) = 1,300 + 60(22) - 0.3(22)^2

Simplifying the equation, we have: C(22) = 1,300 + 1,320 - 0.3(484)

C(22) = 1,300 + 1,320 - 145.2 C(22) = 2,620 - 145.2 C(22) = 2,474.8.

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Answer:

362,880

Step-by-step explanation:

Since there are 9 possible players for the first position, 8 for the 2nd (1 is taken off), 7 for the 3rd, etc. So you would multiply these numbers together. So there are 362,880 different possible batting orders.

Answer:

D

Step-by-step explanation:

She spent $12 and *$ on two separate things, meaning she spent $20 on both.

So, 12 + 8 = 20.

If she started with 25, we subtract 20 from 25 to get how much she has left.

So, 25 - 20 = y.

Therefore, the answer is D.

Answer:

D

Step-by-step explanation:

I agree with the previous answer, it's D.

Sandra spent $12  on apples and $8 on fruit, so you would add.

That's $20, so to find out how much money she has left you do 25 - 20.

Answer:

It will take Scott 221 minutes to run 52 km

Depending on which measure of variability is considered more important, one could argue that either Bus 47 or Bus 14 is the more consistent bus.

In statistics and data analysis, range refers to the difference between the highest and lowest values in a dataset. It is a measure of dispersion or variability, indicating how spread out the data points are. To calculate the range, you simply subtract the lowest value from the highest value.

For example, if you have a dataset of test scores: 65, 72, 80, 85, 92, 98. The highest score is 98, and the lowest score is 65. Therefore, the range of the test scores is 98 - 65 = 33.

While range is a useful and easy-to-calculate measure of variability, it can be sensitive to outliers or extreme values in the dataset. Other measures of dispersion, such as variance or standard deviation, may be more appropriate in some cases.

To determine which bus is the most consistent, we need to compare the measures of variability for the two sets of data, which are the IQR and the range.

The IQR (interquartile range) is the range between the first quartile (Q1) and the third quartile (Q3) and provides a measure of the spread of the middle 50% of the data.

The range is the difference between the maximum and minimum values and provides a measure of the overall spread of the data.

For Bus 47, the IQR is 8 and the range is 24 (28-4).

For Bus 14, the IQR is 6 and the range is 16 (28-12).

Since the IQR for Bus 14 is smaller than the IQR for Bus 47, this suggests that Bus 14 is more consistent in terms of the middle 50% of the data. However, the range for Bus 14 is smaller than the range for Bus 47, suggesting that Bus 47 is more consistent in terms of the overall spread of the data.

Therefore, depending on which measure of variability is considered more important, one could argue that either Bus 47 or Bus 14 is the more consistent bus.

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A. 44

Step-by-step explanation:

An inscribed angle measures the middle of this arc.

The container would hold 2040 cubic feet of shipped goods when it's three-quarters full.

The dimensions of the container are given as 40 ft by 8 ft by 8 ft 6 in. We need to convert the height of 8 ft 6 in to feet by dividing it by 12 since there are 12 inches in a foot:

8 ft 6 in = 8 ft + (6 in / 12) ft

         = 8 ft + 0.5 ft

         = 8.5 ft

Now we can calculate the volume of the container:

Volume = Length × Width × Height

      = 40 ft × 8 ft × 8.5 ft

      = 2720 ft³

To find the volume when the container is three-quarters full, we multiply the total volume by 0.75:

Volume when three-quarters full = 2720 ft³ × 0.75

                              = 2040 ft³

Therefore, the container would hold 2040 cubic feet of shipped goods when it's three-quarters full.

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There is an approximate probability of 0.16807 or 16.807% that Jerry will not wait for more than five minutes throughout the entire week, considering all five days.

To find the probability that Jerry does not wait for more than five minutes all five days this week, we need to calculate the probability for each individual day and then multiply them together since the events are independent.

The probability that Jerry does not have to wait for more than five minutes on any given day is the complement of the probability that he does have to wait for more than five minutes.

Let's denote the probability of waiting for more than five minutes on a given day as p (which is 0.30 in this case).

The probability of not waiting for more than five minutes on a given day is 1 - p.

Therefore, the probability that Jerry does not wait for more than five minutes all five days this week can be calculated as:

(1 - p) * (1 - p) * (1 - p) * (1 - p) * (1 - p)

Plugging in the value of p = 0.30, we have:

(1 - 0.30) * (1 - 0.30) * (1 - 0.30) * (1 - 0.30) * (1 - 0.30)

Simplifying the expression:

0.70 * 0.70 * 0.70 * 0.70 * 0.70

Calculating the result:

0.16807

Therefore, the probability that Jerry does not wait for more than five minutes all five days this week is approximately 0.16807 or 16.807%.

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The total number of ways to make a train consisting of 2 tank cars, 5 boxcars, and 3 flatcars is: 166,320 ways.

To calculate the number of ways to make a train consisting of 2 tank cars, 5 boxcars, and 3 flatcars, we need to use the combination formula.

The number of tank cars, boxcars, and flatcars in the train yard are given as follows:

4 tank cars 12 boxcars 7 flat cars

We need to choose 2 tank cars out of 4, 5 boxcars out of 12, and 3 flatcars out of 7.

The combination formula is given by:

nCr = n! / r! * (n - r)!

where n is the total number of objects,

r is the number of objects being chosen at a time,

and ! represents the factorial of a number.

Substituting the values in the formula:

2 tank cars out of 4:

n1 = 4C2 = 4! / 2! * (4 - 2)! = 6 ways 5 boxcars out of 12:

n2 = 12C5 = 12! / 5! * (12 - 5)! = 792 ways 3 flatcars out of 7:

n3 = 7C3 = 7! / 3! * (7 - 3)! = 35 ways

Therefore, the total number of ways to make a train consisting of 2 tank cars, 5 boxcars, and 3 flatcars is:

n1 x n2 x n3= 6 x 792 x 35= 166,320 ways.

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Answer:

(0, 5)

Step-by-step explanation:

3x + y = 5

Plug x = 0

3*0 + y = 5

0 + y = 5

y = 5

y-intercept = (0, 5)