Consider the line 3x+8y=−1 Find the equation of the line that is perpendicular to this line and passes through the point (5,−1). Find the equation of the line that is parallel to this line and passes through the point (5,−1).

The average velocity of Gwen over the time interval 0 < t is zero. We need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer.

Given that Gwen runs back and forth along a straight track and her velocity, in feet per second, is modeled by the function v(t) during the time interval 0 < t < 45 seconds; We are to determine the first time at which Gwen changes direction and find her average velocity over the time interval 0 < t.Firstly, we know that velocity is a vector quantity and has both magnitude and direction.

Since she is running back and forth along a straight track, her displacement at any given time t is given by the function s(t), which is the integral of her velocity function v(t).That is, s(t) = ∫v(t)dtWe can find the displacement by taking the definite integral of v(t) from 0 to t. Since Gwen is running back and forth, her displacement will be zero at the times when she changes direction.

Therefore, we need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer. Therefore,t = 45n/πwhere n is an integer. Since we are looking for the first time at which Gwen changes direction, we need to take the smallest positive value of n, which is n = 1.

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Answer:

Step-by-step explanation:

6x-y=-5

-6x+y=5

Adding the 2 equations we have:

0 + 0 = 0

0 = 0

This means there are infinite solutions

- the equations are identical.

System B

x+3y=13

-x+3y=5

Adding:

6y = 18

y = 3.

x = 13 - 3(3) = 4.

The system has a unique solution

(x. y) = (4, 3).

Answer:

1.1667

Step-by-step explanation:

Brainliest please!

probability for X<=20 is 1

the probability is the department of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The chance of an event is a number between 0 and 1, in which, roughly speaking, zero indicates the impossibility of the event and 1 shows certainty.

probability = the number of ways of attaining success. the total number of possible results. For instance, the chance of flipping a coin and its being heads is ½, due to the fact there may be 1 way of getting a head and the total number of possible outcomes is two (a head or tail).

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We can find the corresponding density function f(x) by taking the derivative of the cumulative distribution function (CDF) F(x)\(= P[X\leq x]\). The density function is equal to the negative of the derivative of P[X > x] with respect to x.

We know that the probability of X is greater than some value x can be expressed as P[X > x] = 1 - F(x). Rearranging this equation, we get F(x) = 1 - P[X > x].

Since the CDF is defined as the integral of the density function over the range of X, we can differentiate F(x) with respect to x to get the density function:
\(f(x)=\frac{d}{dx}F(x) =\frac{d}{dx}  (1 - P[X > x])\)
\(= -\frac{d}{dx} P[X > x]\)

Therefore, to find the density function given P[X > x] for all x, we simply need to take the derivative of 1 - P[X > x] with respect to x, which is equal to the negative of the derivative of P[X > x] with respect to x.

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The volume of B is given as follows:

468.75 m³.

The volume of B is obtained applying the proportions in the context of the problem.

The ratio between the side lengths is given as follows:

Figure A/Figure B = 2/5

As the side lengths are given in units, and the volume is given in cubic units, the ratio of the volumes is given as follows:

Va/Vb = (2/5)³

Va/Vb = 8/125.

Then the volume of B is obtained as follows:

30/Vb = 8/125

8Vb = 30 x 125

Vb = 30 x 125/8

Vb = 468.75 m³.

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The standard deviation measures the spread of data points around the mean. It considers all data points, not just the farthest or nearest ones. A higher standard deviation indicates a greater spread.

The standard deviation is a statistical measure that tells us how much the data points in a set vary from the mean. It provides information about the spread or dispersion of the data. To calculate the standard deviation, we take the square root of the variance, which is the average of the squared differences between each data point and the mean.

By considering all data points, the standard deviation provides a comprehensive measure of how spread out the data is. Therefore, the statement "The difference between the mean and the data point farthest from the mean" is incorrect, as the standard deviation does not focus on just one data point.

The statement "The difference between the mean and the data point nearest to the mean" is also incorrect because the standard deviation takes into account the entire data set. The statement "The difference between the mean and the median" is incorrect as well, as the standard deviation is not specifically related to the median.

Hence, the correct answer is "None of the above."

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A sample in which every possible combination of items in the population has an equal chance of constituting the sample is a random sample, option a.

A random sample is a type of sample in which every possible combination of items in the population has an equal chance of constituting the sample. This means that each individual or group in the population has an equal opportunity to be selected for the sample.

A combination is a group of items that can be selected from a larger set, while a population is the entire set of individuals or groups that are being studied. A representative sample is one that accurately reflects the characteristics of the population being studied, while a judgment sample is one that is chosen based on the researcher's judgment or expertise.

So, the correct option is a. random sample.

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The expected recorded score in a grade book is the total amount of points earned on both parts of the assignment. This is written as e(x+y), where e stands for expected, x is the points earned on part 1, and y is the points earned on part 2. Therefore, the expected recorded score is the sum of the points earned on both parts, e(x+y).

e(x+y)

e = expected

x = points earned on part 1

y = points earned on part 2

So, the expected recorded score is the total of points earned on both parts: e(x+y).

The expected recorded score in a grade book is the total amount of points earned on both parts of the assignment. This is written as e(x+y), where e stands for expected, x is the points earned on part 1, and y is the points earned on part 2. Therefore, the expected recorded score is the sum of the points earned on both parts, e(x+y). This formula is useful for quickly calculating the total score of an assignment, allowing the grade book to be updated quickly and accurately.

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The system of inequalities that is represented by the graph is given as follows:

The system of linear inequalities is defined with linear functions, which have the slope-intercept format given as follows:

y = mx + b.

In which the parameters are given as follows:

For the upper bound of the inequality, we have that the linear function:

Then the upper bound of the inequality has the definition given by:

y ≤ -x + 1.

For the lower bound of the inequality, we have that the linear function:

Hence the lower bound of the inequality has the definition given by:

y ≥ -0.75x + 0.5.

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Answer:

2875

Step-by-step explanation:

Answer:

I think 141 is the answer

The probability that the athlete has actually been using the prohibited drug given that they tested positive is approximately 0.5789 or 57.89%.

To solve this problem, we can use Bayes' theorem, which relates the conditional probabilities of two events.

Let A be the event that the athlete has been using the prohibited drug, and let B be the event that the athlete tests positive.

We want to find the probability of A given B, which we can write as P(A | B).

Using Bayes' theorem, we have:

P(A | B) = P(B | A) * \(\frac{P(A) }{P(B)}\)

where P(B | A) is the probability of testing positive given that the athlete has been using the prohibited drug, P(A) is the prior probability of the athlete using the prohibited drug, and P(B) is the overall probability of testing positive, which can be calculated using the law of total probability:

P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)

where P(B | not A) is the probability of testing positive given that the athlete has not been using the prohibited drug, and P(not A) is the complement of P(A), i.e., the probability that the athlete has not been using the prohibited drug.

Using the given information, we can plug in the values:

P(B | A) = 1 - 0.12 = 0.88 (probability of testing positive given the athlete is using the drug)

P(A) = 0.05 (prior probability of the athlete using the drug)

P(B | not A) = 0.04 (probability of testing positive given the athlete is not using the drug)

P(not A) = 1 - P(A) = 0.95 (probability that the athlete is not using the drug)

Then, we can calculate P(B) as:

P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)

= 0.88 * 0.05 + 0.04 * 0.95

= 0.076

Finally, we can calculate P(A | B) as:

P(A | B) = P(B | A) * \(\frac{P(A) }{ P(B)}\)

= 0.88 * \(\frac{0.05 }{ 0.076}\)

= 0.5789

Therefore, the probability that the athlete has actually been using the prohibited drug given that they tested positive is approximately 0.5789 or 57.89%.

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Answer:

c(12 + 9 + 6)

12(2.25c)

Step-by-step explanation:

12c + 12 (3/4c) + 12 (1/2c)

12(1c) + 12(3/4c) + 12 (1/2c)

12(c + 3/4c + 1/2c)

12(2 1/4c)

12(2.25c)

Or

12c + 12 (3/4c) + 12 (1/2c)

12c + 9c + 6c

c(12 + 9 + 6)

There are 2 tablespoons in an ounce. So for 2 ounces, you will need 4 tablespoons, for 4 ounces 8 tablespoons, and so on.

A tablespoon is a unit of volume measurement in United States, and some other countries. It is equal to approximately 15 milliliters (0.51 fluid ounces). One tablespoon can be further divided into three teaspoons, meaning that one tablespoon is equal to three teaspoons.

In the United States, one tablespoon is equal to 0.5 ounce, which is equal to 14.3 grams. This is slightly different in the UK, where one tablespoon is equal to 0.6 ounces (which is equal to 17.7 grams). To convert tablespoons to ounces, you can use the following formula is 1 tablespoon = 0.5 ounces.

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Answer:

-7 The root of -14 is -7

Answer:

angle 8 and angle 5

Step-by-step explanation:

The height of the cone is 4cm

The parameters given in the question are

volume= 36

radius= 3

The formula for calculating the height of a cone is

height= 3(v/πr²)

= 3(36/3.14×3²)

= 3(36/28.26)

= 3(1.273)

= 3.8

⇒4

Hence the height of the cone is 4 cm

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The average rate of change between the interval x = 0.5 to x = 3.5 is: 5.

x = 3.5 represents 3.5 hours after noon.

Given an interval of x = a to x = b, the average rate of change over the given interval of a function can be calculated using the formula below:

\(\frac{f(b) - f(a)}{b - a}\)

Given table representing the function as shown in the image attached below, let's determine the average rate of change for x = 0.5 to x = 3.5.

a = 0.5

f(a) = 47 (from the table, when x = 0.5, y = 47)

b = 3.5

f(b) = 62 (from the table, when x = 3.5, y = 62)

Plug the values into \(\frac{f(b) - f(a)}{b - a}\)

Average rate of change = \(\frac{62 - 47}{3.5 - 0.5} = \frac{15}{3} = 5\)

Average rate of change = 5

x = 3.5 represents 3.5 hours after noon.

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Answer:

P(9,-6), L(3,1)

Step-by-step explanation:

P(4+5,-6)= (9,-6)

L(-2+5, 1)= (3,1)

Answer:

P'(9,-6),L'(3,1)

Step-by-step explanation:

(x,y)→(x+5,y). P'(4,-6)→(4+5,-6)=(9,-6). L'(-2,1)→(-2+5,1)=(3,1).

Answer:

30 + 25 + (4x + 25) = 180

55 + (4x + 25) = 180

-55                    -55

4x + 25 = 125

-25 -25

4x = 100

Divide by 4 on both sides

X = 25

Now we just replace the x with 25

4 x 25 = 100, 100 + 25 = 125 degrees is the missing angle of y

The proportion of cats in the sample suffers from separation anxiety is 33%

Given 432 cats, a sample of 42 cats is taken.

Out of these 42, cats 14 are suffering from separation anxiety.

The proportion of cats suffering from separation anxiety is: 14/42

The percentage of Cats suffering from separation anxiety is:\(\frac{14}{42}*100\)%

This is equal to 33%, rounding off to the nearest percentage value.

Therefore, The proportion of cats in the sample who suffers from separation anxiety is 33%.

The sample proportion (p^hat) describes the proportion of people in a sample who have a particular attribute or trait. Divide the number of persons (or items) who have the characteristic of interest by the total number of people (or items) in the sample to get the sample proportion.

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The proportion of cats in the sample suffers from separation anxiety is 33%

Given 432 cats, a sample of 42 cats is taken.

Out of these 42, cats 14 are suffering from separation anxiety.

The proportion of cats suffering from separation anxiety is: 14/42

The percentage of Cats suffering from separation anxiety is:(14/42)*100%

This is equal to 33%, rounding off to the nearest percentage value.

Therefore, The proportion of cats in the sample who suffers from separation anxiety is 33%.

The sample proportion (p^hat) describes the proportion of people in a sample who have a particular attribute or trait. Divide the number of persons (or items) who have the characteristic of interest by the total number of people (or items) in the sample to get the sample proportion.

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Answer:

21

Step-by-step explanation:

21 + 21 = 42

42 + 12 = 54

so 21 is your answer

Answer:

21.

Step-by-step explanation:

For questions like this, it's easiest to work your way backwards from the answer to get the original number.

In this case, you subtract 12 from 54, which gives you 42 (54-12=41)

Then, you divide by 2, the opposite of "doubling". 42 ÷ 2 = 21.

Since there are no other operations, your original number is 21.

To confirm, just go through the problem again starting with 21 and seeing if you get to 54.

21, doubled (42), add 12 = 54.

Answer:-1/12

Step-by-step explanation:

16x=64x+4

16x-64x-4

-48x=4

x=4/-48

Ans:-1/12

Answer:

\(\huge\boxed{\sf x = -1/12}\)

Step-by-step explanation:

\(\sf 16x = 64x+4\\\\Subtract \ 64x \ to \ both \ sides\\\\16x-64x=4\\\\-48x = 4\\\\Divide \ -48 \ to \ both \ sides\\\\x= 4 / -48\\\\x = - 1 / 12\\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

y=-11

Step-by-step explanation:

Step 1: Subtract 12 from both sides.

2y+12−12=−10−12

2y=−22

Step 2: Divide both sides by 2.

2y/2=-22/2

And would get you y=-11

x=-2 that is the answer