NEED HELP NOW PLS WILL GIVE BRAINLIEST

NEED HELP NOW PLS WILL GIVE BRAINLIEST

Answers

Answer 1

The missing leg has a length of 15.371.

How to find the missing leg of a right triangle

In this problem we find the representation of a right triangle and the measures of the hypotenuse and an angle adjacent to a leg, whose length must be found by following trigonometric function:

cos 36° = y / 19

Where y is the missing length.

Then, we compute the length of the leg by algebra properties:

y = 19 · cos 36°

y = 15.371

The length of the missing leg is equal to 15.371.

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Related Questions

the town mouse and the country mouse

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1. The characters in "The Town Mouse and the Country Mouse" are two mice who are cousins. The town mouse is described as elegant, refined, and sophisticated, while the country mouse is simple and unsophisticated.

2. The main idea of the story is that one should be content with their simple life rather than crave for a luxurious life full of dangers and uncertainties.

What is The Town Mouse and The Country Mouse?

"The Town Mouse and the Country Mouse" is a fable, a short story that teaches a moral or lesson. It tells the story of two cousins, a town mouse and a country mouse, who visit each other's homes and experience each other's way of life. The town mouse lives in luxury and eats rich food, but is always in danger from the cat, while the country mouse lives a simple life but is safe and content.

3. The sequence of events in the story is as follows:

The country mouse invites the town mouse to visit him in the countryside.The town mouse accepts the invitation and visits the country mouse.The country mouse serves the town mouse simple food, which the town mouse finds unappetizing.The town mouse invites the country mouse to visit him in the town.The country mouse accepts the invitation and visits the town.The town mouse serves the country mouse luxurious food, but they both get scared and run away when the cat appears.The country mouse returns to his simple life, realizing that it's better to be safe and content than to live in luxury but in constant danger.

4. Important details in the story include the description of the town and country mice, the differences in their lifestyles, and their reactions to each other's homes. These details are important because they emphasize the theme of the story, which is that it's better to be content with one's simple life than to crave for a luxurious but dangerous life.

5. I think "The Town Mouse and the Country Mouse" is a great story because it teaches an important lesson in a fun and engaging way. The characters are well-developed, and the plot is entertaining, making it easy for readers to understand the message.

6. One question I have about the writing is whether the author intended the story to be a commentary on social class and wealth.

7. A fable is a short story that teaches a moral or lesson. Fables usually feature animals or other non-human characters that can talk and behave like humans.

8. The moral of "The Town Mouse and the Country Mouse" is that it's better to be content with a simple life than to crave for luxury and danger. The story shows that the country mouse is happier and safer in his simple life than the town mouse, who is always in danger despite his luxurious lifestyle. This lesson teaches readers to be satisfied with what they have rather than always craving for more.

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town mouse and country mouse are cousins, the town mouse is working hard, (keep up the good work bud,) and the city mouse is relaxing, one day, town mouse was invited to city mouse’s city, they were relaxing, and then, a dog almost killed the mouses.

Find the measures of angle and B. Round to the nearest degree.

Answers

The measure of angle A and angle B are 30° and 60° respectively.

What is the measure of angle A and angle B?

The figure in the image is a right-triangle.

To find the measure of angle A and angle B, we use the trigonometric ratio.

Solving for the measure of angle A:

sinθ = opposite / hypotenuse

opposite of angle A = 8

hypotenuse = 16

Plug in the values

sinθ = 8/16

sinθ = 1/2

θ = sin⁻¹( 1/2 )

θ = 30°

Solving for angle B

cosB = adjacent / Hypotenuse

adjeacent of angle B = 8

Hypotenuse = 16

Plug in the given values

cosB = 8/16

cosB = 1/2

B = cos⁻¹( 1/2 )

B = 60°

Therefore angle A is 30 degrees and angle B is 60 degree.

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7. Suppose that there is a rumour going around
your school that next year all weekends will
be extended to three days. Initially, on day 0,
five students know the rumour. Suppose that
each person who knows the rumour tells two
more students the day after they hear about
it. Also assume that no-one hears the rumour
more than once.
a) How many people will learn about the
rumour
i) on day 1?
ii) on day 2?

Answers

On day 1, each of the 5 people tells 2 more people, so 5 x 2 = 10 people now know the rumor, including the original 5.

a) How many people will learn about the rumour

i) on day 1?

a) Let's first consider how the number of people who know the rumor grows each day:

On day 0, 5 people know the rumor.

On day 1, each of the 5 people tells 2 more people, so 5 x 2 = 10 people now know the rumor, including the original 5.

On day 2, each of the 10 people tells 2 more people, so 10 x 2 = 20 people now know the rumor, including the original 5 and the 10 from day 1.

i) Therefore, on day 1, a total of 10 people will know the rumor.

ii) On day 2, a total of 20 people will know the rumor.

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What is the value of the expression 8w−4j2 when w=0. 25 and j=0. 5?

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The value of the expression 8w - 4j² when w = 0.25 and j = 0.5 is 1.

The expression 8w - 4j² is a combination of variables, w and j, and a constant, 8 and 4. In order to evaluate the expression when w = 0.25 and j = 0.5, we substitute these values for w and j in the expression and perform the necessary calculations.

First, we substitute w = 0.25 and j = 0.5 in the expression:

8(0.25) - 4(0.5)²

Next, we simplify the expression by performing the calculations in the parentheses first. Since 0.5² = 0.25, we can simplify 4(0.5)² to 4(0.25) = 1. We can then simplify 8(0.25) - 4(0.5)² to:

= 2 - 1

= 1

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The given question is incomplete, the complete question is:

What is the value of the expression 8w−4j² when w=0. 25 and j=0. 5?

Briana Ralph is married and claims 2 allowances. Her gross weekly salary is $450. Each week she pays federal, Social Security, and Medicare taxes, $21.20
for medical insurance, and $5.00 for the credit union. What is her net pay?

Answers

Answer:

423.8

Step-by-step explanation:

you have to add the taxes and insurance together then subtract it by the gross salary and then you get your answer brainly please

Maureen bought 3/4 of a pound of small binder clips and 3/4 of a pound of jumbo binder clips. How much did she spend

Answers

If Alice has $50 and spends 4/5 of her money, she spends $40.

A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. Fractions are commonly represented using two numbers separated by a horizontal line, where the top number is called the numerator and the bottom number is called the denominator.

Alice spends 4/5 of her money, which is equivalent to 0.8 of her money.

To find out how much Alice spends, we can multiply her total money ($50) by 0.8

= $50 x 0.8

Multiply the numbers

= $40

Therefore, Alice spends $40.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Alice has $50 and spends 4/5 of her money. How much does Alice spend?

PLEASE HELP AND SHOW YOUR WORK . I WILL MARK YOU BRAINLIEST IF YOU EXPLAIN.

Answers

The approximation of √300 to the nearest integer is 17

What is an integer?

An integer is a whole number that can be positive or negative or zero. Examples of integers are 0, -5, 10, 15, 1000. e.t.c. Decimal numbers are not integers.

Since the value of √300 can not give a whole number because 300 is not a perfect square. This means that the answer given will not be an integer. Therefore saying that we should approximate to integer means approximation to whole number.

√ 300 = 17.32. Therefore the approximation of the value of √300 to the nearest integer = 17.

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Which table represents a function?

Answers

Answer:

Table 4 represents a function because each x-value corresponds to exactly one y-value.

School: Date Assignment: Directions: Solve the following equation. Write the complete solutions on a 1 whole sheet of paper. 1) y + 6 = 20 2) x-12 = 18 3) c + 15 = 25 4) 5y-2 = 18 5)3 + 2x = 17 6) 5x (12 + 5) = 85 7) 96-4b = 28 8) 5h + (-55) = 20 9)-12 + y + (-25) = 45 10) y-(-18) = 14 +11​

Answers

You seem to have made a typo.

Answer:

y = 14

x = 30

c = 10

y = 4

x = 7

x = 3

b = 17

h = 15

y = 82

y = 32

This is not an equation and cannot be solved.

Explanation:

To solve each equation, we need to isolate the variable (the letter that we are solving for) on one side of the equation. To do this, we perform the same operation on both sides of the equation until the variable is alone on one side. Here are the steps for each equation:

y + 6 = 20

Subtract 6 from both sides: y = 14

x-12 = 18

Add 12 to both sides: x = 30

c + 15 = 25

Subtract 15 from both sides: c = 10

5y-2 = 18

Add 2 to both sides: 5y = 20

Divide both sides by 5: y = 4

3 + 2x = 17

Subtract 3 from both sides: 2x = 14

Divide both sides by 2: x = 7

5x (12 + 5) = 85

Simplify the left side: 5x (17) = 85

Divide both sides by 85: x = 3

96-4b = 28

Subtract 96 from both sides: -4b = -68

Divide both sides by -4: b = 17

5h + (-55) = 20

Add 55 to both sides: 5h = 75

Divide both sides by 5: h = 15

-12 + y + (-25) = 45

Add 12 and 25 to both sides: y = 82

y-(-18) = 14

Simplify the left side: y + 18 = 14

Subtract 18 from both sides: y = -4

This is not an equation and cannot be solved.

a researcher wishes to see if the average number of sick days a worker takes per year is greater than 5. a random sample of 28 workers at a large department store had a mean of . the standard deviation of the population is . is there enough evidence to support the researcher's claim at ? assume that the variable is normally distributed. use the -value method with tables.

Answers

The p-value is greater than 0.05, the researcher would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the average number of sick days taken per year by workers is greater than 5.

It appears that some values are missing in your question, specifically the sample mean and the population standard deviation.

Without these values, I cannot provide a complete answer to your question.

A general idea of how to approach this type of hypothesis test.

To test whether the average number of sick days a worker takes per year is greater than 5, the researcher would need to set up the following hypotheses:

Null hypothesis (H0):

The average number of sick days taken per year by workers is equal to or less than 5.

Alternative hypothesis (Ha):

The average number of sick days taken per year by workers is greater than 5.

The next step would be to collect a random sample of workers and calculate their sample mean and sample standard deviation.

Based on these values, the researcher would then calculate the t-value using the formula:

t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size))

The hypothesized population mean in this case is 5, the sample size is 28, and the sample mean and sample standard deviation would be substituted in.

Once the t-value is calculated, the researcher would then use a t-distribution table to find the corresponding p-value based on the degrees of freedom (sample size minus 1) and the level of significance (0.05).

If the p-value is less than 0.05, the researcher would reject the null hypothesis and conclude that there is enough evidence to support the claim that the average number of sick days taken per year by workers is greater than 5.

The specific critical t-value would be based on the degrees of freedom and level of significance.

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what does it mean to be 90% confident in this problem? use the definition of confidence level. there is a 90% chance that the confidence interval contains the population mean 90% of all simple random samples of size 8 from this population will result in confidence intervals that contain the population mean the confidence interval contains 90% of all samples

Answers

Being 90% confident in a problem means that there is a 90% chance that the confidence interval calculated from a sample contains the true population mean.

In other words, if we take 100 different samples of the same size from the population and calculate a confidence interval for each sample, then we can expect that 90 of those intervals will contain the true population mean.

This is the definition of a confidence level. Therefore, we can say that there is a 90% chance that the confidence interval we have calculated includes the true population mean.

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Simplify. 6 5/8- 2 1/2

Answers

To simplify the expression 6 5/8 - 2 1/2, we need to first convert the mixed numbers to improper fractions and then find a common denominator to subtract them.

6 5/8 = (8 × 6 + 5) / 8 = 53 / 8
2 1/2 = (2 × 2 + 1) / 2 = 5 / 2

Now we find a common denominator, which is 8 × 2 = 16.

53 / 8 - 5 / 2 = (53 × 2 - 5 × 8) / (8 × 2) = (106 - 40) / 16 = 66 / 16

The fraction 66 / 16 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2.

66 / 16 = (2 × 33) / (2 × 8) = 33 / 8

Therefore, 6 5/8 - 2 1/2 = 33 / 8, or in mixed number form, 4 1/8.

What’s the IQR for 5,10,8,5,9,4,10,7,5

Answers

Answer: 4.5

The interquartile range IQR is the range in values from the first quartile Q1 to the third quartile Q3. Find the IQR by subtracting Q1 from Q3.

in order to determine whether or not there is a significant difference between the hourly wages of two companies, two independent random samples were selected and the following statistics were calculated. company a company b sample size 80 60 sample mean $6.75 $6.25 population standard deviation $1.00 $0.95 refer to exhibit 10-8. the value of the test statistic is . a. 3.01 b. 1.645 c. 2.75 d. .098

Answers

The value of the test statistic is approximately 2.84. Its significance can't be determined.

To determine whether or not there is a significant difference between the hourly wages of two companies, we need to conduct a hypothesis test.

The null hypothesis states that there is no significant difference between the hourly wages of the two companies, while the alternative hypothesis states that there is a significant difference.

The test statistic for this hypothesis test is calculated using the formula:

[tex]t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^(1/2)[/tex]

where x1, x2 are the sample means for companies A and B, s1 and s2 are the sample standard deviations for companies A and B, and n1 and n2 are the sample sizes for companies A and B.

Plugging in given values, we get:

[tex]t = (6.75 - 6.25) / [(1^2/80) + (0.95^2/60)]^(1/2)[/tex]

t = 0.5 / 0.1759

t = 2.8437

Without knowing the significance level or the degrees of freedom, we cannot determine whether or not the test statistic is statistically significant.

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The value of the test statistic is 2.75.

To determine the test statistic for comparing the hourly wages of two companies, the researcher would need to conduct a two-sample t-test with equal variances.

The formula for the test statistic is:

[tex]t = (\bar x1 - \barx2) / [s_p \times \sqrt(1/n1 + 1/n2)][/tex]

where:

[tex]\bar x1[/tex] and[tex]\bar x2[/tex] are the sample means for Company A and Company B, respectively

[tex]s_p[/tex] is the pooled standard deviation of the two samples, calculated as:

[tex]s_p = sqrt [((n1 - 1) \times s1^2 + (n2 - 1) \times s2^2) / (n1 + n2 - 2)][/tex]

n1 and n2 are the sample sizes for Company A and Company B, respectively

s1 and s2 are the sample standard deviations for Company A and Company B, respectively.

Plugging in the given values, we get:

[tex]t = (6.75 - 6.25) / [\sqrt(((80-1)\times 1^2 + (60-1)\times 0.95^2)/(80+60-2)) \times \sqrt(1/80 + 1/60)][/tex]

[tex]t = 2.75[/tex]

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marvin company sells pens ($6) and flashlights ($10). if total sales were $624 and customers bought 7 times as many pens as flashlights, what would be the number of pens sold?

Answers

If total sales were $624 and customers bought 7 times as many pens as flashlights, then the number of pens sold is 84.

Let's start by assigning variables to represent the unknown quantities.

Let x be the number of flashlights sold.

Then, since "customers bought 7 times as many pens as flashlights," the number of pens sold would be 7x.

The total sales can be expressed as the sum of the sales of each item:

10x (sales from flashlights) + 6(7x) (sales from pens) = 624

Simplifying this equation

10x + 42x = 624

52x = 624

x = 12

So, the number of flashlights sold is 12.

And the number of pens sold would be 7x = 7(12) = 84.

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What is -7(7-2p)=-22+5p

Answers

To solve the equation -7(7-2p)=-22+5p, you can start by distributing the -7 on the left-hand side of the equation:

-7(7-2p) = -49 + 14p

Substituting this expression into the original equation gives:

-49 + 14p = -22 + 5p

Next, you can simplify by moving all the terms with p to one side of the equation, and the constant terms to the other side. Adding 49 to both sides gives:

14p = 27 + 5p

Subtracting 5p from both sides gives:

9p = 27

Finally, you can solve for p by dividing both sides by 9:

p = 3

Therefore, the solution to the equation -7(7-2p)=-22+5p is p = 3.

Step-by-step explanation:

-49+14p=-22+5p

-49+22=5p-14p

-27=-9p

p=3

A right triangle has a side length of 10,6 and x. Find x if it is one of the legs show your work

Answers

Answer:

The missing side of the right triangle is 8, and it is one of the legs.

Step-by-step explanation:

Step 1: Write down the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In equation form, it looks like this:

a^2 + b^2 = c^2

where a and b are the lengths of the legs (the shorter sides) and c is the length of the hypotenuse.

Step 2: Identify which sides are the legs and which is the hypotenuse.

In our triangle, we are given the lengths of two sides, 10 and 6. We don't know which one is the hypotenuse and which one is a leg. However, we can use the fact that the hypotenuse is always the longest side to figure it out. Since 10 is longer than 6, we know that 10 is the hypotenuse.

Step 3: Apply the Pythagorean theorem to find x.

Now that we know which side is the hypotenuse, we can use the Pythagorean theorem to find x. We substitute the values we know into the formula and solve for x:

a^2 + b^2 = c^2

6^2 + x^2 = 10^2

36 + x^2 = 100

x^2 = 100 - 36

x^2 = 64

x = √64

x = ±8

Step 4: Choose the positive value of x.

Since x represents a length of a side of a triangle, it must be a positive value. Therefore, x = 8.

Step 5: Verify that the answer is correct.

We can check that our answer is correct by substituting x = 8 into the Pythagorean theorem and seeing if it holds true:

6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

A point that moves on a coordinate line is said to be in simple _________ ___________ if its distance d from the origin at time t is given by either d = a sin ωt or d = a cos ωt.

Answers

A point that moves on a coordinate line is said to be in simple harmonic motion if its distance d from the origin at time

t  is given by either d = a sin ωt or d = a cos ωt.

Simple harmonic motion, or SHM for short, is a particular kind of periodic motion of a body that results from a dynamic

equilibrium between an inertial force that is proportional to the body's acceleration away from the static equilibrium

position and a restoring force on the moving object that is directly proportional to the size of the object's displacement

and acts towards the object's equilibrium position. If friction or any other energy dissipation is not present, it leads to an

oscillation that is represented by a sinusoid and that lasts indefinitely.

The oscillation of a mass on a spring when it is subject to the linear elastic restoring force specified by Hooke's law is a

good example of simple harmonic motion, which may be used as a mathematical model for many different motions.

The motion has a single resonant frequency and is sinusoidal in time. Simple harmonic motion can be used to simulate

a variety of other phenomena, such as the motion of a simple pendulum, though it is only a good approximation when

the angle of the swing is small; for more information, see small-angle approximation. In order for the model to be

accurate, the net force acting on the object at the end of the pendulum must be proportional to the displacement.

Molecular vibration can also be modelled using straightforward harmonic motion.

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To decrease by 19% what is the decimal multiplier

Answers

Answer:

0.81

Step-by-step explanation:

[tex]\frac{100-19}{100} =0.81[/tex]

Find the missing measures in each diagram.

Answers

Answer:

X = 65°

Y = 75°

Z = 65°

Step-by-step explanation:

Hello!

Angle Y and the angle measuring 75 degrees are corresponding angles, and corresponding angles are congruent to each other in degree measure.

There is also another set of corresponding angles, and those are Angle Z and Angle X.

Since Angle Y and 75° are corresponding, we can state that Angle Y is also 75°. We can now find Angle Z by subtracting 40° and 75° from 180°. This is because the sum of angles in a triangle is 180°.

Angle Z:180° - 40° - 75°180°-115°65°

The measure of Angle Z is 65°. We know that Z and X are corresponding, so X is also 65°.

the physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. the distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 4. using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 42 and 50?

Answers

Thus, the approximate percentage of lightbulb replacement requests numbering between 42 and 50 is 34%.

Explain about the bell-shaped curve:

A bell curve is a form of graph that is used to show how a collection of selected values are distributed; it often has a peak at the centre that tends to be normal, with low and high extremes tapering out rather symmetrically on either side.

Given that:

Mean = 42 with standard deviation of 4.

Now,

If mean = 42,

1 standard deviation (+1σ) above that mean = 42 + 4  =48

1 standard deviation (-1σ) below that mean = 42 - 4 = 38

By the empirical rule  68-95-99.7 rule:

68% of the given normal distribution data lies between -1σ and +1σ:  That is between 38 - 48  requests.

And,

In the range 42 - 50  requests (between that mean and +1σ) is half of the given 68% : 68/2 = 34%

Thus, the approximate percentage of lightbulb replacement requests numbering between 42 and 50 is 34%.

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Correct question:

the physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. the distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 4. using the empirical rule  68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 50?

11. three players on a baseball team are only permitted to pitch. the remaining 12 players are multitalented and can play any of the 8 remaining positions. how many baseball teams of nine can be formed?

Answers

There are 302,702,400 possible baseball teams of nine that can be formed with three designated pitchers and 12 multitalented players who can play any of the remaining positions.

Since three players are designated as pitchers, we need to choose three players out of the total 15 players on the team. This can be done in C(15, 3) ways, where C(n, r) represents the number of combinations of r objects selected from a set of n objects.

For the remaining six positions, any of the 12 multitalented players can be assigned to any of the positions, which means that there are 12 choices for the first position, 11 choices for the second position, and so on, down to 7 choices for the sixth position.

Therefore, the total number of baseball teams of nine that can be formed is:

C(15, 3) x 12 x 11 x 10 x 9 x 8 x 7

which simplifies to:

(15 x 14 x 13 / 3 x 2 x 1) x (12 x 11 x 10 x 9 x 8 x 7)

= 455 x 665,280

= 302,702,400

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Describe the association for the following graph. Be sure to talk about the variable association (direction), linear association, and specialty (outliers and clusters).

Answers

The graph is a positive association

The graphs shows a linear relationship

There is outliers in coordinate (3, 105) and clusters from domain value of 8

What is variable association

Variable association refers to the relationship between two variables, and it can be either positive or negative. A positive association means that as one variable increases, the other variable tends to increase as well, while a negative association means that as one variable increases, the other variable tends to decrease.

Linear association specifically refers to the relationship between two variables that can be best represented by a straight line. This means that as one variable increases or decreases, the other variable changes proportionally.

Specialty in statistics can refer to two different concepts: outliers and clusters.

Outliers are data points that are significantly different from the other data points in a dataset. These points can have a large effect on statistical analysis and can distort results, so they are often removed or treated separately.

Clusters refer to groups of data points that are close together in a dataset. These clusters can indicate that there are subpopulations within the dataset or that there is a relationship between the variables being studied. Clusters can also be used to identify patterns or trends in the data.

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which measure of variation is affected most by a few extreme scores? which measure of variation is affected most by a few extreme scores? standard deviation mode range median mean

Answers

Standard deviation and median are less affected by extreme scores, while mode is not affected at all since it represents the most frequently occurring value.

The measure of variation affected most by a few extreme scores is the range, as it considers only the difference between the highest and lowest values in a dataset. However, the mean can also be influenced by extreme scores, causing it to deviate from the central tendency. Standard deviation and median are less affected by extreme scores, while the mode is not affected at all since it represents the most frequently occurring value.

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The measure of variation affected most by a few extreme scores is the range. The range is the difference between the

highest and lowest values in a data set. Extreme scores significantly increase the range, making it a sensitive measure

of variation.

The measure of variation that is affected most by a few extreme scores is the standard deviation.

The reason for this is that the standard deviation is calculated by taking the square root of the sum of squared

deviations from the mean, and the squared deviations from the mean are particularly sensitive to extreme scores.

On the other hand, the mode, range, median, and mean are less affected by a few extreme scores.

The mode is simply the most frequently occurring value in a dataset and is not affected by extreme scores.

The range is the difference between the highest and lowest values in a dataset and can be affected by extreme scores, but only to a limited extent.

The median is the middle value in a dataset, and it is also not affected by extreme scores unless they are extreme

enough to change the position of the middle value.

The mean is the average value in a dataset, and while it can be influenced by extreme scores, its effect is typically less

pronounced than on the standard deviation.

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let x1, x2, and x3 be independent normally distributed random variables with means, 4, 8, and 12, respectively, and standard deviations of 2, 3, and 4, respectively. a. what is the distribution of x1 x2? b. find the probability that x1 x2 is greater than 16. c. what is the distribution of 3x1 2x2 x3?

Answers

a. The distribution of x1 x2 is z1z2 ~ Cauchy(0,1). (b) The probability that x1 x2 is greater than 16 is 0.1056. (c) The distribution of 3x1 + 2x2 + x3, is given as N(38, 29).

What is cumulative distribution function?

A probability density function (PDF) expresses the likelihood that a continuous random variable will take a specified value or fall within a predetermined range of values. It is a derivative of the cumulative distribution function (CDF), which is the likelihood that a random variable will have a value that is less than or equal to a certain value.

The CDF is a function that converts every potential value of the random variable to a probability between 0 and 1, and it is defined for both discrete and continuous random variables.

a. Covert the x1 and x3 into standard normal variables by subtracting their means and dividing by their standard deviations:

z1 = (x1 - 4) / 2 ~ N(0,1)

z2 = (x2 - 8) / 3 ~ N(0,1)

The product is thus:

z1z2 ~ Cauchy(0,1)

b. The probability that x1 x2 is greater than 16:

Y / z1 ~ Cauchy(0,1)

Now,

z1 = Y / (z1z2) ~ Cauchy(0,1)

Here, the probability that x1 x2 > 16 is:

P(x1 x2 > 16) = P(Y / z1 > 16 / z1) = P(z1 < -Y / 16) + P(z1 > Y / 16)

= 2 * P(z1 < -Y / 16)

Substituting the value of z1 and Y we have:

P(x1 x2 > 16) = 2 * P(z1 < -16z1z2 / (9)) = 2 * Φ(-16z2 / 3) ≈ 0.1056

Hence, the probability that x1 x2 is greater than 16 is 0.1056.

c) The distribution of 3x1 + 2x2 + x3, is given as:

[tex]3x1 + 2x2 + x3 \~ N(34 + 28 + 12, 3^22^2 + 2^23^2 + 4^2) = N(38, 29)[/tex]

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# 15) A boat is heading towards a lighthouse, where Jeriel is watching from a vertical distance of
113 feet above the water. Jeriel measures an angle of depression to the boat at point A to be
8°. At some later time, Jeriel takes another measurement and finds the angle of depression to
the boat (now at point B) to be 52°. Find the distance from point A to point B. Round your
answer to the nearest tenth of a foot if necessary.

Answers

the distance between point A and point B is approximately 777.9 feet.

what is  distance ?

Distance is a numerical measurement of how far apart two objects or points are from each other. It is a fundamental concept in mathematics and physics, and it can be defined in different ways depending on the context.

In the given question,

Let's denote the distance between Jeriel and point A as x, and the distance between Jeriel and point B as y. We want to find the distance between point A and point B, which we can call d.

From the first measurement, we can draw a right triangle with one leg of length x, another leg of length 113, and an acute angle of 8 degrees. The angle opposite the leg of length 113 is 90 degrees minus 8 degrees, or 82 degrees. We can use tangent to find x:

tan(8) = 113/x

x = 113/tan(8)

x =802.5

From the second measurement, we can draw another right triangle with one leg of length y, another leg of length 113, and an acute angle of 52 degrees. The angle opposite the leg of length 113 is 90 degrees minus 52 degrees, or 38 degrees. We can use tangent to find y:

tan(52) = 113/y

y = 113/tan(52)

y =72.4

Now we can use the Law of Cosines to find d:

d² = x² + y² - 2xy cos(130)

where 130 degrees is the angle between the sides of length x and y. We can simplify this equation and substitute the values we found for x and y:

d² = (802.5)² + (72.4)² - 2(802.5)(72.4) cos(130)

d =777.9

Therefore, the distance between point A and point B is approximately 777.9 feet.

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Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. −9. 5 − (−8) − 6. 5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain. Then, show your work, and represent the answer as a single rational number

Answers

The value of the expression as a single rational number is -8.

Kent was likely referring to the idea that subtracting a negative number is the same as adding a positive number. Specifically, to subtract a negative number, we can add the opposite of that number (i.e., the positive version of that number). In this case, we can rewrite the expression as:

= -9.5 - (-8) - 6.5

= -9.5 + 8 - 6.5      (replacing -(-8) with its positive equivalent 8)

= (-9.5 - 6.5) + 8    (grouping like terms)

= -16 + 8                (simplifying)

= -8

Therefore, the value of the expression is -8, which is a single rational number.

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Teachers at Arcadia Elementary School asked students to name their favorite desserts.

Ice cream
1
3
Frozen yogurt
2
9
Cookies
1
9
Candy
1
9
Pudding
1
9
Brownies
1
9
Favorite desserts


If there were 99 students voting, how many of them named brownies as their favorite dessert?

Answers

Out of 99 students, 11 of them named brownies as their favorite dessert.

What is proportion?

A proportion is a statement that two ratios are equal. In other words, when two ratios have the same relationship between their corresponding values, they are said to be in proportion. Proportions are commonly used in mathematics to solve problems involving equivalent ratios and to scale quantities up or down. They can also be used to represent real-world situations, such as calculating the ratio of ingredients in a recipe or determining the scale of a map.

According to the chart, 1 out of 9 students named brownies as their favorite dessert.

To find the actual number of students who named brownies, you can set up a proportion,

1/9 = x/99

Where x represents the number of students who named brownies.

To solve for x, you can cross-multiply,

9x = 1 × 99

Simplifying,

9x = 99

x = 11

Therefore, out of 99 students, 11 of them named brownies as their favorite dessert.

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Correct question is "Teachers at Arcadia Elementary School asked students to name their favorite desserts.

Ice cream -1/3

Frozen yogurt - 2/9

Cookies - 1/9

Candy - 1/9

Pudding - 1/9

Brownies - 1/9

If there were 99 students voting, how many of them named brownies as their favorite dessert?"

Consider the equation 2/3×(p-q)=1
Which one of these can be the values of p and q

Answers

The values which satisfy the given equation 2/3×(p-q)=1 is given by option b.  p= 5/2 , q= 1.

Equation is equal to,

2/3×(p-q)=1

Simplifying the equation multiply both the sides by 3/2we get,

2/3 × (p-q) = 1

⇒2/3 × (p-q) × 3/2 = 1 × 3/2

⇒ (p-q) = 3/2

Now check all the values of p and q which satisfy this equation,

p = 3/2, q = 1

⇒ (p-q) = (3/2 - 1)

⇒ (p-q) = 1/2

It is not equal to 3/2,

So option a) is not a solution.

p = 5/2, q = 1

⇒ (p-q) = (5/2 - 1)

⇒ (p-q) = 3/2

It is equals to 3/2.

So option b) is a solution.

p = 3/2, q = 5/2

⇒ (p-q) = (3/2 - 5/2)

⇒ (p-q)  = -1

It is not equal to 3/2,

So option c) is not a solution.

p = 1, q = 1/2

⇒(p-q) = (1 - 1/2)

⇒(p-q) = 1/2

It is not equal to 3/2,

So option d) is not a solution.

Therefore, the only values that satisfies the equation 2/3 × (p-q) = 1 is option b) p= 5/2 , q= 1.

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The above question is incomplete , the complete question is:

Consider the equation 2/3 × (p-q) = 1. Which of these can be the values of p and q?

a) p = 3/2, q= 1

b) p= 5/2 , q= 1

c) p= 3/2 , q= 5/2

d) p= 1, q= 1/2

It costs $50 every two days to rent a bike. The amount y is proportional to the number x of days the bike is rented. a. Find the rate of change (slope) in simplest form. b. Write an equation that represents the situation. c. How many dollars will you pay for renting the bike 6 days?

Answers

Therefore , the solution of the given problem of equation comes out to be the cost of renting the bike for six days is $150.

What is equation?

Variable words are frequently used in complex algorithms to show consistency between two competing arguments. Academic expressions called equations are used to show the equality of various academic figures. Think on the details connected to those x + 7 proposals. In contrast to another method that involved splitting 12 identical components into two halves, elevating in this case yields b + 7 while building y + 7 and integrating.

Here,

The amount y changes in relation to how many days x the bike is rented; this is known as the rate of change (slope).

The rate of change (slope) is $50 every two days, or $25 per day, because renting a bike costs $50 every two days.

b. The scenario is represented by the equation

=> y = 25x.

c. You can enter x = 6 into the equation to get the price for renting the bike for six days:

=> y = 25(6)

=>  y = 150

Therefore, the cost of renting the bike for six days is $150.

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