Explain how to do function operation and function composition. Use the following functions to complete f(x) + g(x), g(x) - f(x), f(x) - g(x), g(f(x)) and f(g(x)). Explain why you don’t need to do both f(x) + g(x) and g(x) + f(x). f(x) = 2x - 1 and g(x) = x^2 - 9x - 4

The information that can be missing from the dot plot is the scale and data points.

Elias dot plot may not have a distinct scale on the axes, which makes it challenging to identify the precise values or quantities being displayed. This is based on the fundamental idea of a dot plot. A scale offers the required context for correctly analysing the data by, among other things, specifying the measurement intervals or units that were employed.

Furthermore, certain data points, such as the number of tropical fish in each tank or the exact values being displayed, may be absent from the dot plot. It would be difficult to evaluate the dot plot or make inferences from it without the actual data points. Overall, it is impossible to pinpoint exactly what information may be lacking without further detailed details concerning Elias' dot plot.

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Answer:

• 32 inches by 40 inches

Step-by-step explanation:

4:1 means that 4 inches on the actual painting, is 1 inch on the scaled painting.

4:1

8 by 10 inches

8 x 4 = 32 inches

10 x 4 = 40 inches

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32 inches by 40 inches,

just answering to help the other dude the brainliest

We can estimate that the underlying normal distribution from which the data was generated has a mean of 3 and a standard deviation of 1.

To estimate the mean and standard deviation of the underlying normal distribution from the given data using the probability plot method, we need to first create a probability plot of the data.

After creating the probability plot, we can visually inspect it to see if the data points fall on a straight line. If the data points fall on a straight line, then we can assume that the data is normally distributed. We can then use the slope of the line to estimate the standard deviation and the intercept of the line to estimate the mean.

Using the given data, we can create a probability plot as follows:

- First, we need to order the data from smallest to largest:
-3.58 -1.83 0.27 1.23 1.25 1.36 2.33 2.49 2.88 3.04 3.19 3.67 3.73 4.33 4.38 4.72 4.99 5.40 5.52 7.42

- Next, we need to calculate the percentiles for each data point:
0.5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 99.5%

- We can then plot the percentiles on the y-axis and the ordered data on the x-axis.

After creating the probability plot, we can see that the data points fall approximately on a straight line. This suggests that the data is normally distributed. We can then estimate the mean and standard deviation of the underlying normal distribution as follows:

- The slope of the line is approximately 1, which suggests that the standard deviation of the underlying normal distribution is approximately 1.
- The intercept of the line is approximately 3, which suggests that the mean of the underlying normal distribution is approximately 3.

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To copy segment AB, D, The distance between points A and B needs to be identified for the construction.

A segment is a section of a line that is bounded by two unique ends and contains every point on the line between them. A segment is designated after its endpoints, therefore segment AB refers to the section of the line connecting points A and B.

To copy segment AB can be accomplished by utilizing a measuring instrument such as a ruler or tape measure to determine the distance between the two spots. Once the distance is determined, a new point that is the same distance away from point A as point B can be produced.

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The hypothesis test is:
H0: p = 0.224 (the percentage of children who develop asthma is the same in the other country)
Ha: p < 0.224 (the percentage of children who develop asthma is lower in the other country)

The sample proportion is:
p = 71/342 = 0.2076

The standard error is:
SE = sqrt[(0.224)(1-0.224)/342] = 0.0225

The test statistic is:
z = (0.2076 - 0.224) / 0.0225 = -0.7467

The p-value for this one-tailed test is:
p-value = P(z < -0.7467) = 0.2254

Therefore, the test statistic, z = -0.7467 and the p-value = 0.2254.
In this hypothesis test, we are comparing the proportion of children with asthma in another country to the proportion in the US (22.4%). Let's set up our null and alternative hypotheses:

H0: p = 0.224 (proportion of children with asthma in the other country is the same as in the US)
Ha: p < 0.224 (proportion of children with asthma in the other country is lower than in the US)

Now, we can calculate the test statistic (z) and p-value using the provided data:

n = 342 (sample size)
x = 71 (number of children with asthma)
p-hat = x/n = 71/342 = 0.2076 (sample proportion)

We also need the standard error (SE) for the sample proportion:
SE = sqrt((p0 * (1 - p0)) / n) = sqrt((0.224 * (1 - 0.224)) / 342) = 0.0260

Now, calculate the z-score:
z = (p-hat - p0) / SE = (0.2076 - 0.224) / 0.0260 = -0.6285 (rounded to four decimal places)

Next, find the p-value by looking up the z-score in a standard normal table or using a calculator:
p-value = P(Z < -0.6285) ≈ 0.2647 (rounded to four decimal places)

So, the test statistic z = -0.6285, and the p-value = 0.2647.

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Answer:

Step-by-step explanation:

To calculate how much Gloria will pay over 30 years for her $70,000 mortgage at 7.5%, we need to use the formula for a standard mortgage payment, which is:

P = L[c(1 + c)^n]/[(1 + c)^n - 1]

Where:

P = the monthly payment

L = the loan amount

c = the monthly interest rate (annual interest rate divided by 12)

n = the total number of payments (30 years multiplied by 12 months per year)

First, we need to calculate the monthly interest rate:

c = 7.5% / 12 = 0.00625

Next, we need to calculate the total number of payments:

n = 30 years x 12 months per year = 360

Now we can plug in these values to the formula:

P = 70000[0.00625(1 + 0.00625)^360]/[(1 + 0.00625)^360 - 1]

P = $493.95

Therefore, Gloria will pay $493.95 per month for 30 years for her $70,000 mortgage at 7.5%. Over the course of the 30 years, she will pay a total of:

Total Payments = P x n = $493.95 x 360 = $177,822

So, Gloria will pay a total of $177,822 over 30 years for her $70,000 mortgage at 7.5%.

If your data set is left-skewed, then your mean will be less than your median.

In a left-skewed distribution, the tail of the distribution is longer on the left-hand side, which means that there are some extreme low values that pull the mean towards the left. On the other hand, the median is not affected as much by extreme values, since it only depends on the middle value(s) of the data set. Therefore, in a left-skewed distribution, the median is usually greater than the mean.

The margin of error for the confidence interval with a 98% confidence level is 6.912. So, the correct answer is (f) 6.912. To find the margin of error of the confidence interval with a 98% confidence level for the scores of a standardized test, we'll follow these steps:

1. Identify the given values:
  - Population standard deviation (σ) = 12 points
  - Sample size (n) = 20 scores
  - Sample mean (x) = 99 points
  - Confidence level = 98%

2. Determine the appropriate z-score for a 98% confidence level. Since the remaining 2% is split evenly on both tails, we'll look for the z-value corresponding to 0.01 (1% in the tails). From the provided values, z0.01 = 2.576.

3. Calculate the standard error (SE) of the sample mean using the formula:
  SE = σ / √n = 12 / √20 ≈ 2.683

4. Calculate the margin of error (ME) using the formula:
  ME = z-score * SE = 2.576 * 2.683 ≈ 6.912

The margin of error for the confidence interval with a 98% confidence level is 6.912. So, the correct answer is (f) 6.912.

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The margin of error at a 98% confidence level is c) 5.259 points.

To determine the margin of error at a 98% confidence level, we need to calculate the critical value, which corresponds to the confidence level.

In this case, the critical value is 2.326, which can be found in the standard normal distribution table.

Therefore, the margin of error at a 98% confidence level is c) 5.259 points.

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To find the value of x, we need to follow these steps:

1. Calculate the total sum of the ages of the 6 cars.
2. Subtract the sum of the known ages from the total sum.
3. The result will be the value of x.

Step 1: Since the average age of the 6 cars is 7 years, we multiply the average (7) by the number of cars (6) to find the total sum of ages.
Total sum of ages = 7 * 6 = 42 years

Step 2: Subtract the sum of the known ages (6, 14, 5, 1, and 8) from the total sum.
Sum of known ages = 6 + 14 + 5 + 1 + 8 = 34 years
42 (total sum of ages) - 34 (sum of known ages) = 8

Step 3: The result is the value of x.
x = 8

So the value of x is 8.

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The Beck Depression Inventory (BDI) would be an example of a measurement instrument.

A measurement instrument is a tool or technique used to measure or assess a particular variable or construct, in this case, depression. The BDI is a standardized self-report questionnaire that is widely used to assess the severity of depressive symptoms. It consists of 21 questions or items that ask the respondent to rate the intensity of their depressive symptoms on a 4-point scale. The total score on the BDI can be used to classify the severity of depression and guide treatment decisions.

In contrast, a variable is a characteristic or attribute that can take on different values or levels, such as age, gender, or income. Data refers to the collection of measurements or observations obtained from a particular study or investigation. Internal validity is a concept that refers to the extent to which a study is designed and conducted in a way that minimizes the potential for bias or confounding variables.

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The mean exam score of student 2 for all four exams is 87.5.  Based on the information provided, you have a spreadsheet containing the scores of 50 students on 4 different exams. To calculate the mean exam score for Student 2 across all four exams, you need to follow these steps:

1. Locate the scores for Student 2 on all four exams. They should be on the first sheet of the spreadsheet and likely in a row or column corresponding to Student 2.

2. Add the scores of Student 2 for all four exams together. For example, if their scores were 80, 85, 90, and 95, the total would be 80 + 85 + 90 + 95 = 350.

3. To calculate the mean, divide the total score (from step 2) by the number of exams (which is 4 in this case). Using the example scores above, the mean would be 350 / 4 = 87.5.

So, the mean exam score for Student 2 for all four exams is 87.5. Keep in mind that this example assumes hypothetical exam scores; you will need to replace them with the actual scores found in the spreadsheet to obtain the correct mean score for Student 2.

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Answer:

#4 A- Height of trees (needs to be given in digits)

#5 A- 27

#6 D- 10

#7 D

#8 B- 19

#9 C Make a frequency table

Step-by-step explanation:

I'm not too sure, you should ask Brainly too!

From Week 3 to Week 5, Gym A membership increases at a rate of 32 people per week,  and Gym B membership increases at a rate of 34 people per week. So, Gym B is growing faster.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

From Week 3 to Week 5, the change in the input is given as follows:

5 - 3 = 2.

From the table for Gym A and graph for Gym B, the change in the output for each gym is given as follows:

Hence the rates are given as follows:

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Based on the provided informations and given values, the value of k for the given function and domain is calculated to be 11.

To find the value of k for the function G(x) = |5x - 4|, we need to evaluate the function at the endpoints of the given domain and find the maximum value.

The domain of the function is 0 ≤ x ≤ 3, so we need to evaluate the function at x = 0 and x = 3.

When x = 0:

G(0) = |5(0) - 4| = 4

When x = 3:

G(3) = |5(3) - 4| = 11

So, the maximum value of the function occurs at x = 3, and the value is 11.

Since the function is continuous over the given domain, we know that the maximum value occurs either at one of the endpoints or at a critical point in between.

The critical point is where the expression inside the absolute value bars, 5x - 4, equals zero:

5x - 4 = 0

x = 4/5

However, 4/5 is not in the given domain, so the maximum value occurs at x = 3, and the value is 11.

We know that the maximum value of the function is k, so:

k = G(3) = 11

Therefore, the value of k for the given function and domain is 11.

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The option that is a valid claim is:

The number of milk chocolate pieces is between 115 and 120 pieces.

The correct option is the last option.

From the question, we are to determine the valid option about the claim.

From the given information,

A sample of chocolate from the local candy shop contained 17 milk chocolate pieces out of a sample of 50. An entire batch of chocolate contains 350 pieces

To determine the option about the population that is valid claim, we will determine the number of milk chocolate in an entire batch.

We know that

17 are milk chocolate out of a sample of 50.

Let the number of milk chocolate in an entire batch be x.

If there 17 milk chocolate out of 50 samples

Then,

There will be x chocolate out 350 samples

50 × x = 350 × 17

x = (350 × 17)/ 50

x = 119

Thus,

The 119 milk chocolates in an entire batch

The valid claim is:

The number of milk chocolate pieces is between 115 and 120 pieces.

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Answer: independent = p, dependent = c

Step-by-step explanation: the number of copies Tristan makes, or c, depends (is DEPENDENT) on the number of people who plan to attend, which is INDEPENDENT on the amount of copies

the number of copies is a reaction (DEPENDS) on the amount of people, not the other way around.

For a one-tailed test with a 0.05 level of significance, the critical z statistic is 1.645, but the critical t statistic is 1.96. The statement is false.

The statement is incorrect. For a one-tailed test with a 0.05 level of significance, the critical z statistic is indeed 1.645. However, the critical t statistic value depends on the degrees of freedom (df), which is not provided in the statement. The 1.96 value mentioned is actually the critical z statistic for a two-tailed test with a 0.05 level of significance.

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The amount of money saved by Kaitlin is $6.

We have,

Cost of Game= $12

Amount Kaitlin saved= 1/2 of total money

So, She saved

= 12 x 1/2

= 12 x 1/2

= 6 x 1

= $6

Thus, Kaitlin saved $6.

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Using a table or calculator, we find that the area between z = -1.67 and z = -0.33 is approximately 0.3121 or 31.21%. Therefore, approximately 31.21% of plants in this region are between 10 and 14 inches tall.

we will use the concepts of standard, percentage, and deviation. We know that the mean height (µ) of plants is 15 inches and the standard deviation (σ) is 3 inches. We want to find the percentage of plants with heights between 10 and 14 inches.

Step 1: Calculate the z-scores for 10 and 14 inches.
z = (X - µ) / σ

For X = 10 inches:
z1 = (10 - 15) / 3 = -5/3 ≈ -1.67

For X = 14 inches:
z2 = (14 - 15) / 3 = -1/3 ≈ -0.33

Step 2: Find the percentage of plants corresponding to these z-scores using a z-table or calculator.
P(-1.67 < Z < -0.33) = P(Z < -0.33) - P(Z < -1.67)

Using a z-table or calculator, we find:
P(Z < -0.33) ≈ 0.3707
P(Z < -1.67) ≈ 0.0475

Step 3: Calculate the percentage of plants between 10 and 14 inches.
Percentage = (0.3707 - 0.0475) * 100% ≈ 32.32%

Next, we look up the area between these two z-scores in a standard normal distribution table. This area represents the percentage of plants in the region between 10 and 14 inches tall.

As for the bonus, I'm unable to plot a graph here, but you can use graphing software to plot a normal distribution curve with a mean of 15 and a standard deviation of 3. Shade the area between 10 and 14 inches to represent the percentage of plants in this range.

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Answer: I would say B srry if I'm  wrong

Step-by-step explanation:

To find the volume of the prism, we need to multiply the area of the base by the height. The base of the prism is made up of 6 cubes arranged in a rectangle, so its area is:

Base area = length x width Length = 2 cubes = 1 foot Width = 3 cubes = 1.5 feet Base area = 1 x 1.5 = 1.5 square feet

The height of the prism is also equal to one cube, which is 1/2 feet.

Therefore, the volume of the prism can be calculated as follows:

Volume = Base area x Height Volume = (1.5 square feet) x (0.5 feet) Volume = 0.75 cubic feet

John Doe was killed approximately 4.06 hours ago.

To determine the time of death for John Doe, we will use the given formula: [tex]T = T0 + (T1 - T0)(0.97)^t[/tex],[/tex]where T is the body temperature at time t, T0 is the air temperature (74°F), and T1 is the body temperature at the time of death (93°F).

We are trying to find the time (t) when John Doe's body temperature was 98.6°F (normal body temperature). So, we'll set T equal to 98.6°F and solve for t:

[tex]98.6 = 74 + (93 - 74)(0.97)^t[/tex]

To solve for t, follow these steps:

1. Subtract 74 from both sides:
[tex]24.6 = 19(0.97)^t[/tex]

2. Divide by 19:
[tex]1.2947 ≈ (0.97)^t[/tex]

3. Take the natural logarithm of both sides:
ln(1.2947) ≈ [tex]ln((0.97)^t)[/tex]

4. Apply the logarithm power rule:
ln(1.2947) ≈ t * ln(0.97)

5. Divide by ln(0.97):
t ≈ ln(1.2947) / ln(0.97)

6. Calculate t:
t ≈ 4.06

So, John Doe was killed approximately 4.06 hours ago.

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Answer:

The estimated proportion of Americans over 45 who smoke is 0.239 or 239/1000.

Step-by-step explanation:

To estimate the proportion of Americans over 45 who smoke, we need to calculate the fraction of the sample who smoke.

The number of people who don't smoke is 631, so the number of people who smoke is:

830 - 631 = 199

Therefore, the fraction of Americans over 45 who smoke is:

199/830 = 0.239 (rounded to three decimal places)

So, the estimated proportion of Americans over 45 who smoke is 0.239 or 239/1000.

To estimate the proportion of Americans over 45 who smoke, we first need to find the number of people in the sample who do smoke. We can do this by subtracting the number of people who don't smoke from the total sample size:
Therefore, we estimate that approximately 0.240 or 24.0% of Americans over 45 smoke.

Step 1: To estimate the proportion of Americans over 45 who smoke, we first need to find out how many people in the sample do smoke. Since we have a sample of 830 Americans and 631 don't smoke, we can subtract the non-smokers from the total sample to find the number of smokers.

830 (total) - 631 (non-smokers) = 199 (smokers)

Step 2: Now, we can calculate the proportion of smokers in the sample by dividing the number of smokers (199) by the total number of people in the sample (830).

199 (smokers) / 830 (total) = 0.2398 (rounded to four decimal places)

As a fraction, this would be approximately 240/1000, which can be simplified to 12/50.

So, the estimated proportion of Americans over 45 who smoke based on the given data is 0.240 or 12/50.

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To compute px(x), we sum the joint probabilities over all possible values of y:

px(x) = Σp(x,y) for all y

Substituting the given values for p(x,y):

px(x) = Σd/[(n(n+1))/2] for y=1 to x

px(x) = xd/[(n(n+1))/2]

To compute py(y), we sum the joint probabilities over all possible values of x:

py(y) = Σp(x,y) for all x

Substituting the given values for p(x,y):

py(y) = Σd/[(n(n+1))/2] for x=y to n

py(y) = (n-y+1)d/[(n(n+1))/2]

To determine whether x and y are independent, we compare the product of the marginal probabilities to the joint probability:

If px(x)*py(y) = p(x,y), then x and y are independent.

Substituting the computed values for px(x) and py(y):

px(x)*py(y) = [xd/[(n(n+1))/2]]*[(n-y+1)d/[(n(n+1))/2]]

px(x)*py(y) = (xd/n)*(n-y+1)/n

px(x)*py(y) = xd(n-y+1)/n^2

Comparing to the given value for p(x,y):

p(x,y) = d/[(n(n+1))/2]

We see that px(x)*py(y) is not equal to p(x,y) in general. Therefore, x and y are not independent.

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It would take (6π/5) seconds to bend a straight wire into a circle of radius 6 using a machine that bends wire at a rate of 10 unit(s) of curvature per second.

To calculate the time it takes to bend a straight wire into a circle of radius 6 using a machine that bends wire at a rate of 10 unit(s) of curvature per second, we need to find the length of the wire and then divide it by the rate of curvature.

The circumference of a circle with a radius of 6 is 2πr = 2π(6) = 12π. Therefore, the length of the wire that needs to be bent is 2πr = 12π.

Now we can calculate the time it takes to bend the wire by dividing the length by the rate of curvature:

Time = length of wire / rate of curvature = (12π units) / (10 units/second)

Simplifying, we get:

Time = (6π/5) seconds

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Step-by-step explanation:

Volume = area of end   x   height

            = pi r^2   x 8

           = pi  2^2 * 8    = 32 pi  units^3    <====exact answer

Using the relative frequency we can estimate that 1355 people will preffer mustard.

To find this estimation, we need to find the relative frequency of people that preffers mustard.

To get this, take the quotient between the people that preffers mustard (27) and the total number of people surveyed (150)

It gives:

F = 27/150

Now multiply the total number of people in the game by that number:

N = 7,525*27/150 = 1354.5

Rounding we get 1355

So the correct option is the first one.

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Answer:

B

Step-by-step explanation: its 3,010. EZ

True. When the normality assumption is violated and the sample size is small. Transforming the dependent variable using the Box-Cox methodology with the suggested Lambda value can help ensure the normality of the sampling distribution.

Normality refers to the distribution of data being normally distributed, while sample size refers to the number of observations in a sample. Sampling refers to the process of selecting a subset of individuals or data points from a larger population.

A variable is any characteristic or attribute that can be measured or observed. The Lambda value is a parameter in the Box-Cox transformation that determines the type of transformation to be applied to the data.

Thus, When normality is violated and the sample size is too small to ensure the normality of the sampling distributions, one option is to try to transform the dependent variable using the Box-Cox methodology using the suggested Lambda value. This transformation can help stabilize the variance and achieve a more normal distribution, making it more suitable for parametric statistical tests.

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Answer:

The answer is 59 units

Step-by-step explanation:

area of sector =0/360×pir²

A=56/360×22/7×11²

A=149072/2520

A=59units

For a sum of $20709, prize is of either $100 or $25, there will be 15 prizes of $100 and 48 prizes of $25.

Let's assume that x prizes are given for $100 and y prizes are given for $25. Then, we can set up a system of two equations based on the given information,

x + y = 63 (the total number of prizes is 63)

100x + 25y = 2709 (the total value of the prizes is $2709)

We can solve this system of equations by substitution or elimination. Here, we will use the elimination method, multiplying the first equation by 25, we get,

25x + 25y = 1575

75x = 1134

Dividing both sides by 75, we get,

x = 15.12

Since we cannot have a fractional number of prizes, we can round this down to 15 (because it is closer to 15 than to 16).

Substituting x = 15 in the first equation, we get,

15 + y = 63

Solving for y, we get,

y = 48

Therefore, 15 prizes are given for $100 and 48 prizes are given for $25.

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