Consider the rational function 1 -a-12 Instruction: Use the Graphing Strategy Step 1 Analyze f(x).. A). Find the domain of f(x), B). Find the intercepts of f(x). C). Find asymptotes. Step 2. Analyze.f'(x) Determine the intervals where f(x) is increasing, decreasing, and find local maxima and local minima. Step 3 Analyze f'(x) Determine the intervals on which the graph of f(x) is concave upward or concave downward, and find the inflection points. Step 4. Sketch the graph of f(x) using all the steps above.

Answer:

-2

Step-by-step explanation:

From the graph, it appears that (0, 2) and (2, -2) are points on the line.  (Othere points will work, as well; you just need two points.)

Slope = (difference between the y coordinates) / (difference between the x coordinates)

One phrase to remember this is slope = "rise over run"  (vertical change divided by horizontal change from point to point).

Slope = (-2 - 2) / (2 - 0) = -4 / 2 = -2

The slope is -2.

The new coordinates are : N'=(3,-7), O'=(-4,-5), W'=(-1,-1).

If a point \((x,y)\) is rotated \(90\) degrees counterclockwise about the origin, it becomes \((-y,x)\).

Here, \(N=(-7,-3)\). So, \(N'=(3,-7)\)

\(O=(-5,4)\). So, \(O'=(-4,-5)\)

\(W=(-2,1)\). So, \(W'=(-1,-1)\)

So, image after rotation is:  

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Answer:

The new coordinates are

Step-by-step explanation:

N'=(3,-7), O'=(-4,-5), W'=(-1,-2)

Answer:

1.4 people out of 10

Step-by-step explanation:

Just divide it by 10

Answer:

only 4 people

Answer:

100 chocolate bars

Step-by-step explanation:

30 ÷ 3 = 10 so you need to times 10 by 10?

hope that helps!

We can infer from the data set provided that more women than men are interested in basketball.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

From table given in question

Number of males that like basketball = 21

Number of females that like basketball = 29

Percentage of males that like basketball =  (21/50)*100 = 42%

Percentage of females that like basketball =  (29/50)*100 = 58%

So, from above data we can conclude that females like basketball more than that of males.

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The system of linear equations represented in the graph have one solution at (2, −1)

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

The graph (see attachment)

The graph represents two linear functions

The point of intersection of the linear functions represent the solution

In this case, the linear functions intersect at (2, −1)

Hence, it has one solution at (2, −1)

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The inequality that shows the number of gallons of each drink that Harry can buy is 2x + 2.5y ≤ 24.

The number of gallons of iced tea that Harry can buy if he buys 5 gallons of lemonade is 5 gallons of iced tea

The number of gallons of iced tea that can be bought is x so the total price would be:

= 2x

Number of gallons of lemonade is:

= 2.5y

Harry can spend not more than $24.00 which means the total should either be $24 or less:

2x + 2.5y ≤ 24

If Harry buys 5 gallons of lemonade, he would spend:

= 5 x 2.50

= $12.50

The number of gallons of iced tea he can buy is:

= (24 - 12.50) / 2.00

= 5 gallons of iced tea

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a) The (9,009, 10,585) range represents the 99% confidence interval for the mean number of steps taken on an average workday for all New York City employees who wear activity trackers. No, we are unable to determine the likelihood of specific values using the confidence interval. Only inferences about the population mean can be drawn from it.

A 99% confidence interval for the mean needs to be calculated.

Since the population standard deviation is unknown, we must infer it from the sample standard deviation in order to get the critical number using a t-students distribution.

Sample Mean(M) = 9,797

Sample Standard Deviation(s) = 2,313.

Sample Size(N) = 61

When σ is unknown, an estimation of σM is made by dividing s by the square root of N:

S = s/√n

S = 2313/√61

S = 2313/7.8102

S = 296.1512

These sample size's degrees of freedom are:

df = n - 1

df = 61 - 1

df = 60

With 61 degrees of freedom and a 99% confidence interval, the t-value is 2.66.

The Margin of Error calculated as:

MOE = t × S

MOE = 2.66 × 296.1512

MOE = 787.7622

The confidence interval's lower and upper bounds are as follows:

Lower Bound = M - MOE

Lower Bound = 9797 - 787.7622

Lower Bound = 9,009.2378

Lower Bound = 9,009(approx)

Upper Bound = M + MOE

Upper Bound = 9797 + 787.7622

Upper Bound = 10,584.7622

Upper Bound = 10,585(approx)

We have a 95% confidence interval between 9,009 and 10,585 steps as the mean number of steps taken on a normal workday for all New York City employees using activity trackers.

b) The value of 8,500 steps is outside the confidence interval, which indicates that it is a high figure for the average number of steps taken by all New Yorkers using activity trackers.

The confidence interval cannot be used to calculate the likelihood of specific values.

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The complete question is:

Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.

a. Construct and interpret a 99 percent confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.

b. A wellness director at a company in New York City wants to investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on a typical workday. Is it appropriate to use the confidence interval found in part (a) to conduct the investigation.

The distance from home plate to second base is 180 feet, which is double the distance from home plate to first base.

A baseball diamond is a square with four bases, with home plate in the middle. 90 feet separate first base from home plate, and 90 more feet separate first base from second base. Therefore, the total distance from home plate to second base is twice that distance, or 180 feet. The same applies to all of the bases; the distance between them is always 90 feet, so the total distance from home plate to any base is twice that of the distance from home plate to first base. This means that the distance from home plate to second base, third base, and home plate is all 180 feet.

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The the parallelogram is like:

Where h is the height, The area of this parallelogram is calculated as:

A = 24*h

If the Area is equal t 18 square units, the height h is:

18 = 24*h

Solving for h, we get:

18/24 = h

0.75 units = h

Answer: a possible parallelogram's height is 0.75 units

Answer:

49.84

Step-by-step explanation:

Hope it helped!

Answer:

56

Step-by-step explanation:

The triangular prism has 5 sides. We will find the area of each individual side and add them together.

Sides 1 and 2: The triangles

These triangles have base 6 and height 4. Use the area of a triangle formula A=1/2*base*height=1/2*6*4 = 12 to get the area of each one.

Sides 3 and 4: The rectangular sides other than the base

These are rectangles with length 5 and width 2. A = 10.

Side 5: The base

This is a rectangle of length 6 and width 2. A = 12.

Adding it all up:

12+12+10+10+12 = 56.

FMECA is a bottom-up hardware approach to risk assessment. It is an inductive, or data-driven, linking elements of a failure chain as follows: Effect of Failure, Failure Mode, and Causes/Mechanisms. To estimate the reliability of software, most software prediction models use the probability density function to predict "Mean Time To Failure."

FMECA is a systematic and structured analytical methodology used to identify potential failures in a system, equipment, process, or product, and to assess the effect and probability of those failures. FMECA stands for Failure Modes, Effects, and Criticality Analysis. FMECA is similar to FMEA (Failure Modes and Effects Analysis) in that it is used to identify failure modes and assess their risk.

However, FMECA goes beyond FMEA by analyzing the criticality of each failure mode. This makes it an effective tool for identifying the most significant failure modes and prioritizing them for corrective action. A Probability Density Function (PDF) is a function that describes the likelihood of a random variable taking on a particular value.

PDF is used in software prediction models to estimate the reliability of software by predicting "Mean Time To Failure" (MTTF). MTTF is the average time between failures of a system, equipment, process, or product.

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The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.

In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.

CV = (Standard Deviation / Mean) * 100

CV = (5.2 / 340) * 100

CV ≈ 1.53%

Therefore, the correct answer is option B: 1.53%.

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The mean of the number of houses burglarized in this sample is 4.5 based on probability.

The probability of a house in an urban area being burglarized is 15%. This means that out of every 100 houses, 15 will be burglarized.

If 30 houses are randomly selected, we can use the binomial distribution to find the mean number of houses burglarized. The formula for the mean of a binomial distribution is:

Mean = n * p

where n is the number of trials (in this case, 30) and p is the probability of success (in this case, 0.15).

Substituting these values, we get:

Mean = 30 * 0.15
Mean = 4.5

Therefore, the mean number of houses burglarized out of 30 randomly selected houses is 4.5. Note that this is an expected value and may not represent the actual number of houses burglarized in any particular sample of 30 houses.
To find the mean of the number of houses burglarized, we can use the formula:

Mean = (Probability of success) x (Number of trials)

In this case:
- Probability of success (a house being burglarized) is 15%, or 0.15 as a decimal.
- Number of trials (randomly selected houses) is 30.

Using the formula, we get:

Mean = (0.15) x (30) = 4.5

So, the mean of the number of houses burglarized in this sample is 4.5.

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Answer: 150000

Step-by-step explanation:

1. 589 x 219 = 128991

2. 128991 (estimate) = 150000

(a) 95% confidence interval for the difference between female and male times is (11.954, 255.591).

(b) The assumptions and conditions for the two-sample t-test are met, so we can use the results of the test and confidence interval.

a) To construct a 95% confidence interval for the difference between female and male times, we can use a two-sample t-test. Let's denote the mean time for female swimmers as μf and the mean time for male swimmers as μm. We want to test the null hypothesis that there is no difference between the two means (i.e., μf - μm = 0) against the alternative hypothesis that there is a difference (i.e., μf - μm ≠ 0).

The formula for the two-sample t-test is:

t = (Xf - Xm - 0) / [sqrt((s^2f / nf) + (s^2m / nm))]

where Xf and Xm are the sample means for female and male swimmers, sf and sm are the sample standard deviations for female and male swimmers, and nf and nm are the sample sizes for female and male swimmers, respectively.

Using the data from the plots, we get:

Xf = 917.5, sf = 348.0137, nf = 15

Xm = 783.7273, sm = 276.0625, nm = 28

Plugging in these values, we get:

t = (917.5 - 783.7273 - 0) / [sqrt((348.0137^2 / 15) + (276.0625^2 / 28))] = 2.4895

Using a t-distribution with (15+28-2) = 41 degrees of freedom and a 95% confidence level, we can look up the critical t-value from a t-table or use a calculator. The critical t-value is approximately 2.021.

The confidence interval for the difference between female and male times is:

(917.5 - 783.7273) ± (2.021)(sqrt((348.0137^2 / 15) + (276.0625^2 / 28)))

= 133.7727 ± 121.8187

= (11.954, 255.591)

Therefore, we can be 95% confident that the true difference between female and male times is between 11.954 and 255.591 minutes.

b) Assumptions and conditions for the two-sample t-test:

Independence, We assume that the observations for each group are independent of each other.

Normality, We assume that the populations from which the samples were drawn are approximately normally distributed. Since the sample sizes are relatively large (15 and 28), we can rely on the central limit theorem to assume normality.

Equal variances, We assume that the population variances for the female and male swimmers are equal. We can test this assumption using the F-test for equality of variances. The test statistic is,

F = s^2f / s^2m

where s^2f and s^2m are the sample variances for female and male swimmers, respectively. If the p-value for the F-test is less than 0.05, we reject the null hypothesis of equal variances. If not, we can assume equal variances. In this case, the F-test yields a p-value of 0.402, so we can assume equal variances.

Sample size, The sample sizes are both greater than 30, so we can assume that the t-distribution is approximately normal.

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Answer:b

Step-by-step explanation:

Answer:

8x+29

Step-by-step explanation:

open the brackets the collect like terms together

Answer: 9

Step-by-step explanation:

36/4=9

The distribution (or scattering) of IQ scores approximates a bell-shaped curve, also called a normal distribution or Gaussian distribution.

Normal distribution, also known as Gaussian distribution, is a type of probability distribution that is commonly used in statistical analysis. It is a continuous probability distribution with a bell-shaped curve that is symmetrical around the mean, or average, of the data.

The shape of the normal distribution curve is determined by two parameters: the mean and the standard deviation. The mean represents the central tendency of the data, while the standard deviation measures the spread of the data around the mean. The standard deviation also determines the width of the curve. In a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations of the mean, and about 99.7% falls within three standard deviations of the mean.

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Answer:

pi it is irrational because it doesnt stop

Step-by-step explanation:

hope i helped love yall can i get brainliest

Answer: that symbol represents pie which the number is equal to 3.14159

The advantage of using the range as a measure of variability is that it provides an account of the dataset's most extreme values.

The range is calculated by subtracting the minimum value from the maximum value in a dataset. By considering the minimum and maximum values, the range gives us an idea of the spread or dispersion of the data.

It provides information about the dataset's most extreme values, allowing us to understand the range over which the data values vary.

However, it's important to note that the range has limitations as a measure of variability. It only considers the minimum and maximum values and does not take into account the distribution or the values in between.

It does not provide a comprehensive summary of the patterns with which values cluster within the distribution, and it does not capture the shape of the distribution.

Therefore, while the range is a simple and straightforward measure of variability, it may not fully represent the overall characteristics of the dataset.

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Answer:

Solve the equation using the method of completing the square.

Step-by-step explanation:

Answer:

3; 6; 6; 5

Step-by-step explanation:

15 / 5 = 3

18 / 3 = 6

12 / 2 = 6

25 / 5 = 5

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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the answer would be 8. z= 8

Answer:

Z=8

Step-by-step explanation:

I solved it before

Answer:y

y=4x−5

Step-by-step explanation: