a local mechanic keeps track of the number of customers each day, x, and the revenue for that day, y. he hired a data analyst to make a model for the data. the analyst gave him the table below that shows the number of customers and the predicted revenue. suppose the mechanic had a day with 10 customers and a revenue of $1243. what is the residual? x y^ 5 620 6 702 7 784 8 866 9 948 10 1030 11 1112 12 1194 13 1276

[tex]\cos(35^o )=\cfrac{\stackrel{adjacent}{y}}{\underset{hypotenuse}{22}} \implies 22\cos(35^o)=y \implies 18.0\approx y[/tex]

Step-by-step explanation:

to find to multiply it 3 times

V=length x width x height

V=25in x 25in x 25in

V=15,625 cubic inches

Answer:

[tex]V = 15,625 in^3[/tex]

Step-by-step explanation:

The formula for the area of a square is if x is the length of a side

V = x^3

V =25^3

V = 25 · 25 · 25

V = 625 ·25

V = 15,625 in^3

Answer: 25

Step-by-step explanation:

You have 2  secants, i have attached an image that may help with the rules for secants

Multiply short length * full = other short length* full

What is the short length, 3

Full length of that line is x.

3x=5(10+5) simplify

3x=75

x=25

Answer:

Step-by-step explanation:

The inverse of the function f(x) = x³ + 1 is f⁻¹(x) = ∛(x - 1).

Given the function in the question;

f(x)  = x³ + 1

To determine the inverse of the function  f(x) = x³ + 1,

we can follow these steps:

Step 1: Replace f(x) with y

y = x³ + 1

Step 2: Solve for x in terms of y

y = x³ + 1

y - 1 = x³

x = ∛(y - 1)

Step 3: Replace x with f⁻¹(x) to get the inverse function

f⁻¹(x) = ∛(x - 1)

Therefore, the inverse of is f⁻¹(x) = ∛(x - 1).

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The amount of servings are in 16.8 grams of the snack is: 5 servings

Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.

We are told that:

Serving Size for a snack = 3¹/₅ grams = 16/5 grams

In 16.8 grams, we can write as 168/10 or 84/5

Thus:

The amount of servings are in 16.8 grams of the snack is:

84/5 ÷ 16/5

= 84/5 * 5/16

= 84/16

= 21/4

= 5.25

Approximately 5 servings

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The solution to the linear equation graph problems are:

a) 20 months

b) 7 pounds

c) 27 pounds

d) Rate of change of weight per month

e) Weight of the infant at birth

The general form of the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

a) The corresponding age at which the infant weighed 11 pounds from the graph is: 20 months

b) The infants weight at birth is the age at 0 years which in this case is 7 pounds

c) Paul's function is given as:

y = ⁵/₄x + 7

Thus, at 16 months, the weight is:

y = ⁵/₄(16) + 7

y = 27 pounds

d) What the number 5/4 represents in the model is the rate of change of weight per month.

e) The number 7 in part c denotes the weight at birth.

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Answer:

To solve this problem, we can use the cumulative distribution function (CDF) of the normal distribution.Given:

Mean (μ) = 133 lb

Standard Deviation (σ) = 6.4 lb

Weight (X) = 126.6 lb

We can use the formula for the standard normal distribution to calculate the z-score:

z = (X - μ) / σ

Plugging in the values, we get:z = (126.6 - 133) / 6.4 = -0.984375

Now, we can use a standard normal distribution table or a calculator with a built-in normal distribution function to find the cumulative probability (P) associated with the z-score of -0.984375.

Using a standard normal distribution table, we find that the cumulative probability for a z-score of -0.984375 is approximately 0.1611.

So, approximately 16.11% of the registered female Great Danes in the United States weigh less than 126.6 lbs.

Step-by-step explanation:

The required decimal form of two hundred five thousandths is 0.205.

When we write a decimal number, each digit represents a different power of 10, with the digit to the left of the decimal point representing the one place, and the digits to the right of the decimal point representing fractions of a whole.

So, to represent two hundred five thousandths in decimal form, we need to write 2 in the thousandth place, which is three digits to the right of the decimal point. This gives us the number 0.205.

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Answer:

Step-by-step explanation:

10

Tukey's procedure to investigate significant differences between brands is x3. and x5.

x4. and x5.

To use Tukey's procedure to investigate significant differences between brands, we need to calculate the value of W and compare it with the critical value from the Studentized Range Distribution.

The formula for W is:

W = q(α, 5, 15) * √(MSE/4)

where q(α, 5, 15) is the critical value from the Studentized Range Distribution with α = 0.05, k = 5 (number of brands), and df = 15 (total degrees of freedom). Using a table or calculator, we find:

q(0.05, 5, 15) = 3.07

Plugging in the given values, we get:

W = 3.07 * √(450.8/4) ≈ 17.99

Since the computed value of F was found to be significant at level α = 0.05, we can conclude that there are significant differences between at least some of the brands. To determine which brands differ significantly from one another, we can use the formula:

|xi. - xj.| ≥ W / √(2MSE/4)

where xi. and xj. are the sample averages for any two brands i and j. If this inequality is satisfied, then we can say that the two brands differ significantly from one another.

Calculating the absolute differences between all pairs of sample averages and comparing them with the right-hand side of the inequality above, we get:

|462.0 - 502.8| = 40.8 ≥ 8.99 → Significant

|462.0 - 427.5| = 34.5 < 8.99 → Not significant

|462.0 - 469.3| = 7.3 < 8.99 → Not significant

|462.0 - 532.1| = 70.1 ≥ 8.99 → Significant

|502.8 - 427.5| = 75.3 ≥ 8.99 → Significant

|502.8 - 469.3| = 33.5 < 8.99 → Not significant

|502.8 - 532.1| = 29.3 < 8.99 → Not significant

|427.5 - 469.3| = 41.8 ≥ 8.99 → Significant

|427.5 - 532.1| = 104.6 ≥ 8.99 → Significant

|469.3 - 532.1| = 62.8 ≥ 8.99 → Significant

Using the critical value W, we can conclude that brands 1, 2, 4, and 5 differ significantly from one another. Therefore, the correct answer is:

x1. and x2.

x1. and x5.

x2. and x3.

x3. and x4.

x3. and x5.

x4. and x5.

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The surface area of the rectangular prism is 160 square meters

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

5 m by 10 m by 2 m

The surface area of the rectangular prism is calculated as

Area = 2 * (5 * 10 + 5 *2 + 10 * 2)

Evaluate

Area = 160

Hence, teh area is 160 square meters

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In this hypothetical two-way layout, we are studying the effects of two drugs A and B on remaining life. The drugs are each taken in quantities of 0g, 1g or 2g, resulting in a total of 9 possible treatment combinations.

Our outcome of interest is years of remaining life. To analyze this data, we would likely use a two-way ANOVA to assess the main effects of each drug and the interaction effect between the two drugs. This analysis would allow us to determine if there is a significant difference in remaining life between the different drug doses and if the effect of one drug is influenced by the dose of the other drug.

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The negation of "p and q" is "not p or not q", which means that "p and q" is false if either "p" or "q" is false.

To negate a conjunction, which is a statement of the form "p and q", we need to negate each of the component statements and change "and" to "or". The negation of "p and q" is "not p or not q", which means that "p and q" is false if either "p" or "q" is false.

For example, if we have the statement "John will go to the beach and he will go to the park", we can negate it by saying "It is not the case that John will go to the beach and he will go to the park", which can be written symbolically as "not (John will go to the beach and he will go to the park)". Using the rule for negating a conjunction, we can rewrite this statement as "John will not go to the beach or he will not go to the park".

Note that this is different from the negation of a disjunction, which is a statement of the form "p or q". The negation of "p or q" is "not p and not q", which means that "p or q" is false if both "p" and "q" are false.

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The range of the graphed function is  y  ≤ 1, or written in interval form, it is:

(-∞, 1]

The range is the set of the possible outputs of the function, so we need to look at the vertical axis (also called the y-axis).

Here we can see that we have the maximum at y = 1, and then the function goes down. (We can assume it will go to negative infinity, this is beacuse we can see arrow points at the ends, which means that the function keeps going downwards)

Then the range is:

y  ≤ 1

Or (-∞, 1] in interval form.

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"If one were testing whether a particular sample was drawn from a population with a particular mean and the standard deviation of the entire population was known, one would use the Z-test to statistically answer the question". Option A is correct.

In statistical hypothesis testing, when the standard deviation of the entire population is known and you want to determine if a particular sample was drawn from a population with a specific mean, the appropriate test to use is the Z-test.

The Z-test is used when the population standard deviation is known and the sample size is large enough to satisfy the assumptions of normality. It compares the observed sample mean to the hypothesized population mean and determines the likelihood of obtaining such a sample mean if the population mean is actually equal to the hypothesized value.

By calculating the Z-score and comparing it to the critical value, you can make a statistical inference about whether the sample is likely to have been drawn from the specified population.

Option A holds true.

The complete question:

If one were testing whether a particular sample was drawn from a population with a particular mean and the standard deviation of the entire population was known, one would use the ______test to statistically answer the question.

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The requried features of the given function has been shown below.

The function f(x) = -(1/3)^x +5 has the following features:

Domain: The domain of the function is all real numbers.

Range: The range of the function is y ≤ 5. In other words, the function has a maximum value of 5, which is approached but never reached as x approaches negative infinity.

x-intercept: The x-intercept is where the graph of the function intersects the x-axis. The x-intercept is approximately -3.96.

y-intercept: The y-intercept is where the graph of the function intersects the y-axis. The y-intercept is (0, 4).

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a. To compare these two estimates of variance, we calculate the F statistic as Var1/Var2 with 2 and 3 degrees of freedom (why 3 df is because we have 3 levels). b. We reject the null hypothesis that the variances are equal and conclude that they are significantly different. c. It does not necessarily mean that the means of the data are significantly different.

a. To test the effects of radiation on the growth of tardigrades, we experimented with 3 levels of radiation: 1, 2, and 3. For each level, we had a sample size of 2 and calculated the mean and variance. The mean and variance for each level are as follows:
Level 3 (highest radiation): Mean = 83.74, Variance = 14
Level 2 (medium level): Mean = 65.83, Variance = 16
Level 1 (lowest radiation): Mean = 56.76, Variance = 23
If the means are the same, each mean has the same mean and variance of sigma2/2, we can build 2 estimates of variance. The first estimate (Var1) is calculated using the formula: Var1 = 2 * (sum(meaning - meant)²) / 2, where meant is the overall mean of the data. The second estimate (Var2) is a pooled estimate of variance, which can be calculated using the formula taught in class (lecture 18).
b. We can test if the 2 estimates of variance are the same by comparing the F statistic we calculated in part a to the critical F value from the F distribution table with 2 and 3 degrees of freedom at a given significance level (e.g. 0.05). If the calculated F statistic is greater than the critical F value, we reject the null hypothesis that the variances are equal and conclude that they are significantly different.
c. If Var1>>Var2, it means that there is a larger variation within each level of radiation compared to the variation across all levels. This could be due to experimental error or other factors that are not related to radiation. It does not necessarily mean that the means of the data are significantly different.

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Answer:

$96.25

Step-by-step explanation:

$77 x 25% = $19.25

$77 + $19.25 = $96.25

a. A function that represents the balance (in dollars) or the future value of the savings account after t years is C. s(t) = 6,000(1 + 0.045/12)^12t.

b) The balance (future value) of the account after 6 years, to the nearest cent, is $7,855.82.

The future value can be computed using the FV formula or function below:

s(t) = 6,000(1 + 0.045/12)^12t

s(t) = 6,000(1 + 0.045/12)^12(6)

= $7,855.8186

= $7,855.82

This future value can also be computed using an online finance calculator as follows:

N (# of periods) = 72 months (6 years x 12)

I/Y (Interest per year) = 4.5%

PV (Present Value) = $6,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $7,855.82

Total Interest = $1,855.82

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Answer:

Step-by-step explanation:

If each side of a small cube is 1/3 cm, then one side of a big cube is 2/3.

Area of cube: x^3

2/3 * 2/3 * 2/3 = 8/27

The answer is A. Please make me brainliest!

There is a very low probability of fewer than 100 insects surviving in the rose garden.

Given that the insecticide is advertised as being 99% effective, it means that 1% of the insects are not affected by the insecticide. Therefore, the probability of an insect surviving the insecticide is 0.01.

Let's assume that the number of surviving insects, X, follows a binomial distribution with parameters n = 2000 and p = 0.01. We want to find the probability that fewer than 100 insects survive, i.e., P(X < 100).

Since the number of trials is large (n = 2000) and the probability of success is small (p = 0.01), we can approximate the binomial distribution with a Poisson distribution with parameter λ = np = 2000*0.01 = 20.

Using the Poisson distribution, we can calculate the probability of fewer than 100 insects surviving as:

P(X < 100) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 99)
          = e^(-20) * (20^0/0!) + e^(-20) * (20^1/1!) + e^(-20) * (20^2/2!) + ... + e^(-20) * (20^99/99!)

We can use a calculator or a software program to calculate this sum, which gives us an approximation of 0.0000386 or 0.00386%.

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Based on the random sample, there is not enough evidence to conclude that more than 65% of all adults in the US use television as one of their main sources of news.

To answer your question, we will perform a hypothesis test using the given information.
Step 1: State the hypotheses.
H0 (null hypothesis): p = 0.65 (65% of all adults in the US use television as one of their main sources for news)
Ha (alternative hypothesis): p > 0.65 (more than 65% of all adults in the US use television as one of their main sources for news)
Step 2: Determine the sample proportion (p-hat) and sample size (n).
p-hat = 0.66 (66% from the random sample of 1500 adults)
n = 1500
Step 3: Calculate the test statistic (z) using the formula:
z = (p-hat - p) / sqrt[(p * (1-p)) / n]
z = (0.66 - 0.65) / sqrt[(0.65 * (1-0.65)) / 1500]
z = 0.01 / 0.013 (given Sâ¢Eâ¢=â0.013)
z ≈ 0.77
Step 4: Find the p-value corresponding to the test statistic.
Using a z-table or calculator, we find the p-value for z = 0.77 is approximately 0.2206. Since this is a one-tailed test, we will use this p-value directly.
Step 5: Compare the p-value to the significance level (α) and make a decision.
Assuming a common significance level (α) of 0.05, our p-value (0.2206) is greater than α. Therefore, we fail to reject the null hypothesis (H0).

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Answer:

The answer to your problem is, D. (x,y) → (x - 2, y +3)

Step-by-step explanation:

We can see that the vector that translates JKLM to J'K'L'M' is given by the difference between the coordinates of J and J', and the difference between the coordinates of K and K'.

The differences can be called, "a" and "b", respectively. Then we can write:

a = J' - J = (-1) - 0 = -1

b = K' - K = 3 - (-1) = 4

Which can conclude to the mapping formula expressed by the vector that translates JKLM to J'K'L'M' is:

(X,Y) → (X - 1, Y + 4)

Thus the answer to your problem is, D. (x,y) → (x - 2, y +3)

Answer: 41 degrees

Step-by-step explanation:

118 + 21 = 139

180 - 139 = 41

1. (1/64)^–⅚ = 32 True

2. √12 - 2/5 × √75 = 4√3 = False

3. √9a + √98b -a+√2b = 2a+10√b = 0 =True

4. 1/(√5-√6)² = 11-2√30/241 = False

1. (1/64)^–⅚ = 32

write in exponential form

2⁵ = 2⁵, hence, true

2. √12 - 2/5 × √75 = 4√3

Simplify the expressions

2√3-2√3 = 4√3

Eliminate the opposites

0 = 4√3

The statement is false

3. √9a + √98b -a+√2b = 2a+10√b = False

Evaluate

3a + √98b-a + √2b = 2a+10√b

Collect like terms

2a + √98b+ √2b = 2a+10√b

Cancel equal terms

98b+ √2b = 10√b Simplify the equation

98b+28b+2b = 100b

Collect like terms

128b = 100b

Move the variable to the left

128b 100b = 0

28b = 0

Divide both sides

b = 0

4. 1/(√5-√6)² = 11-2√30/241 = False

The approximate value of 1 / (√5-√6)² is 21.95445 and the approximate value of 11-2√30/ 241 is 0.000188999, meaning 1/(√5-√6)² ≠ 11-2√30/241

1/(√5-√6)² = 11-2√30/241, so equality is false

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There are 210 different selections of 4 books that can be made from 10 different books with no restriction. There are 28 different selections of 4 books that can be made from 10 different books if two particular books are always selected. There are 70 different selections of 4 books that can be made from 10 different books if two particular books are never selected.

(i) If there is no restriction, then we can choose any combination of 4 books from the 10 different books. This is a combination problem, and the formula for combinations is:

n C r = n! / r!(n-r)!

where n is the total number of items to choose from, and r is the number of items we want to choose.

So, in this case, we have n = 10 and r = 4. Plugging these values into the formula, we get:

10 C 4 = 10! / 4!(10-4)! = 210


(ii) If two particular books are always selected, then we only need to choose the remaining 2 books from the remaining 8 books. We can do this using the same combination formula, but with different values of n and r:

n = 8 (since we only have 8 books to choose from)
r = 2 (since we want to choose 2 books)

Plugging these values into the formula, we get:

8 C 2 = 8! / 2!(8-2)! = 28


(iii) If two particular books are never selected, then we need to choose 4 books from the remaining 8 books. Again, we can use the same combination formula:

n = 8
r = 4

Plugging these values into the formula, we get:

8 C 4 = 8! / 4!(8-4)! = 70

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The false statement is option d. The mean of a standard normal distribution is zero, but the mean of any normal distribution can vary and is not always zero.

The number of calls coming in to an office follows a Poisson distribution with a mean of 5 calls per hour. To find the probability of exactly 7 calls within the next hour, we can use the formula for the Poisson probability:

P(X = k) = (e^(-λ) * (λ^k)) / k!

Where λ is the mean (5 calls per hour), k is the number of calls we're interested in (7), and e is the base of the natural logarithm (approximately 2.71828).

P(7 calls) = (e^(-5) * (5^7)) / 7! ≈ 0.104

So the probability of exactly 7 calls within the next hour is 0.104 (option b).

For the false statement among the given options:

a. Using the normal curve, the P(Z < 1.28) is approximately 0.9
b. Using the standard normal curve, the area between z=0 and z = 3.50 is about 0.50
c. In the normal distribution, the total area under the curve is equal to one (1)
d. The mean of any normal distribution is always zero

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If a researcher has access to a list of all pilots who are members of the Air Line Pilots Association and she wishes to conduct a study, she can use this list as the frame for selecting a random sample of pilots. By doing so, she can ensure that the sample is representative of the larger population of pilots who are members of the association.  

Suppose a researcher wants to conduct a study on pilots who are members of the Air Line Pilots Association. The researcher has access to a list of all these pilots, which serves as the frame for the study. In order to randomly select a sample of pilots, the researcher can follow these steps:

1. Assign a unique number to each pilot on the list.
2. Determine the sample size required for the study based on the research objectives.
3. Use a random number generator or a random sampling technique (e.g., simple random sampling) to select the desired number of pilots from the list.
4. Once the sample has been chosen, the researcher can proceed with the study by contacting the selected pilot members and collecting the necessary data.

This method ensures that the sample is representative of the entire population of pilots in the Air Line Pilots Association and helps maintain the validity of the research findings.  This is important because it allows her to draw conclusions about the population based on the sample data. The sample should be selected in a random and unbiased manner to ensure that it is a true representation of the population. The researcher can then use the data collected from the sample to make inferences about the population of pilots who are members of the Air Line Pilots Association.

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