If you rent a car from Caleb's Cars, you'll pay a $61 fee
and $24 per day. At Vinny's Vehicles, you'll pay a $105 fee and $20 per day. Determine the number of days you can rent a car from either place and pay the same amount. Use substitution or elimination.

Overall, equations provide a mathematical representation and understanding of relationships, while tables present data points in a structured format.

When comparing an equation and a table, you can examine their characteristics, purpose, and the information they provide. Here are some points to consider when making comparisons:

Representation:

An equation represents a mathematical relationship between variables using symbols and mathematical operations. A table presents data or values in a structured format, typically organized into rows and columns.

Communication of Information:

Equations provide a concise and general representation of a relationship, allowing for predictions, calculations, and modeling. Tables present specific data points or values, providing a visual representation of how variables are related or how they change.

Variables:

Equations involve variables, which can be manipulated to explore different scenarios and analyze the relationship between quantities. Tables display specific values or data points for variables, showing how they vary or are related based on the given information.

Visualization:

Equations can express relationships symbolically and provide a mathematical understanding, but they may not offer a visual representation of data. Tables provide a visual representation of data points, allowing for a quick overview and easy comparison of values.

Flexibility:

Equations offer flexibility in terms of adjusting variables and parameters to explore different scenarios and make predictions. Tables can be easily modified or expanded by adding or removing data points to reflect new observations or additional information.

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Answer:

I think it's 6,800 in3 I don't know perfectly whether it is correct answer or not

Answer:

Step-by-step explanation:

Interest be I

\(\\ \rm\rightarrowtail I=\dfrac{PRT}{100}\)

\(\\ \rm\rightarrowtail I=\dfrac{22000(4.85)(15)}{100}\)

\(\\ \rm\rightarrowtail I=680.41\)

Answer:

$9,000 (to the nearest hundred dollars)

Step-by-step explanation:

Loans from banks are usually amortizing loans, which is a type of loan that requires regular monthly payments.

To calculate the regular monthly payment:

\(\sf PMT=\dfrac{P\left(\dfrac{r}{n}\right)}{1-\left(1+\dfrac{r}{n}\right)^{-nt}}\)

where:

Given:

\(\sf PMT=\dfrac{2000\left(\dfrac{0.0485}{12}\right)}{1-\left(1+\dfrac{0.0485}{12}\right)^{-12 \cdot 15}}=172.2604115...\)

Number of months in 15 years = 15 × 12 = 180

⇒ Total payment over the term of the loan = 180 × 172.2604115...

                                                                       = 31006.87406...

Total interest = total payment - principal

                      = 31006.87406... - 22000

                      = 9006.87406...

                      = $9,000 (to the nearest hundred dollars)

Answer:

If function is given by its table representation and you have to determine what type of function it is, you can’t be 100% sure that the given function is linear. Why is that so? Because there are many functions which have the same table representation.

Example: You’re given f(0)=0 and f(1)=1. It can be representation of function f(x)=x, f(x)=x^2, f(x)=x^3 etc. If there are more given datas, maybe you can eliminate some types of functions, but you can’t be sure what type of function it is. :)

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Dennis Wainaina, Student

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a linear function is used to relate to relate an independent variable and a dependent variable by introducing a rate of change(function) of which the independent variable is equated to find the dependent variable for example y=3x hence hence is the dependent variable as it depends on the change of x and 3 is the rate of change which is a constant and is determined by the division of the values of y/x hence to make a table of y over x of which y is determined by the rate of change 3*the independent variable x

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Clyde Maiden

Answered September 17, 2018

Line AB contains points A(4, 5) and B(9, 7). What is the slope of



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Answer:

b

Step-by-step explanation:

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.

In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.

For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

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The correct answer is option C.

If the model improves after adding an interaction, R² should increase and the standard deviation should decrease. Option C is the right answer.

R², also known as the coefficient of determination, is a statistical measure of how well the regression line fits the data points. It indicates the proportion of variance in the dependent variable that can be explained by the independent variables.

The standard deviation is a measure of how spread out the data is in relation to the mean. If the data points are more concentrated around the mean, the standard deviation will be smaller. If the data is more dispersed, the standard deviation will be larger. Interaction terms in regression models explain how the relationship between two independent variables influences the dependent variable.

The inclusion of interaction terms can enhance the model's explanatory power by providing a more accurate depiction of the relationship between the independent and dependent variables. This can result in an increase in R² and a decrease in standard deviation.

So, we can say that if the model improves after adding an interaction, R² should increase and the standard deviation should decrease. Option C is the correct answer.

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Answer:

take out or aluminate i think

Step-by-step explanation:

Answer:

bring the variable to the left side and bring all the remaining values to the right side

Step-by-step explanation:

This company’s revenue function is given by −0.25x³ - 4x² + 1000x + 16,000.

Mathematically, the amount of revenue that's being generated by a company or business organization can be calculated by using the following function (expression):

Revenue = price × demand

R(x) = p(x) × d(x)

The demand (d) for this company’s product at cost (x) is given by this demand function:

d(x) = −0.25x² + 1,000

Also, the price (p) in dollars that this company can charge for its product is given by this price function:

p(x) = x + 16

Substituting the parameters into the revenue function, we have;

Revenue function, R(x) = p(x) × d(x)

Revenue function, R(x) = (−0.25x² + 1,000) × (x + 16)

Revenue function, R(x) = −0.25x³ - 4x² + 1000x + 16,000.

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Complete Question:

Suppose demand, d, for a company's product at cost, x, is predicted by the function, d(x) = −0.25x² + 1,000, and the price, p, that the company can charge for the product is given by p(x) = x + 16. Find the company's revenue function.

Answer:

2.5 60÷24=2.5 so there is ur answer hope it helps

Answer:

yes

Step-by-step explanation:

-34 is an integer and an integer is a rational number

Answer: 9.7 seconds

Step-by-step explanation:

\(16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)

For each given sample result, the p-value and conclusion are as follows:

a. p-value = 0.0067, Conclusion: Reject H0,  b. p-value = 0.0830, Conclusion: Fail to reject H0, c. p-value = 0.0322, Conclusion: Reject H0

d. p-value = 0.6221, Conclusion: Fail to reject H0

The p-value is a measure of the evidence against the null hypothesis (H0). It represents the probability of obtaining a sample result as extreme as or more extreme than the observed result, assuming the null hypothesis is true. A p-value less than the significance level (α) indicates strong evidence against the null hypothesis and suggests that the alternative hypothesis (Ha) may be true.

a. For p = .68, we need to determine the probability of observing a sample proportion as extreme as or less than .68, assuming the null hypothesis is true. By conducting the appropriate statistical test (e.g., using the normal approximation to the binomial distribution), we find the p-value to be 0.0067. Since the p-value is less than α = .05, we reject the null hypothesis and conclude that there is evidence to support the claim that the proportion is less than .75.

b. For p = .72, the p-value represents the probability of observing a sample proportion as extreme as or less than .72. Calculating the p-value using the appropriate statistical test yields 0.0830. Since the p-value is greater than α = .05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the proportion is less than .75.

c. With p = .70, the p-value indicates the probability of observing a sample proportion as extreme as or less than .70. The calculated p-value is 0.0322. As the p-value is less than α = .05, we reject the null hypothesis and conclude that there is evidence to suggest that the proportion is less than .75.

d. For p = .77, the p-value represents the probability of observing a sample proportion as extreme as or greater than .77. After performing the necessary calculations, we find the p-value to be 0.6221. Since the p-value is much greater than α = .05, we fail to reject the null hypothesis. Consequently, we do not have sufficient evidence to conclude that the proportion is less than .75.

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The probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

μρ=ρ

The standard deviation of this sampling distribution of sample proportion is:

σρ=\(\sqrt \frac{p(1-p)}{n}\)

The information provided is:

n = 533

p = 0.09

As the sample size is quite large, i.e. n = 533 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by a Normal distribution.

The mean and standard deviation are:

μρ=ρ=0.09

σρ=\(\sqrt \frac{p(1-p)}{n}\)=\(\sqrt\frac{0.09(1-0.09)}{533}=0.01239\)

Compute the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% as follows:

\(p(p^-p > 0.03)=P(p^ > 0.12) \\=P(z > \frac{0.12-0.9}{0.012}) \\= P(Z > 2.5) \\= 1-P(Z > 2.5) \\ = 1- 0.993 \\ = 0.00621\)

Thus, the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.

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The outcome or result of adding two or more integers is known as the SUM.

The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.

the sum of two or more numbers, magnitudes, quantities, or specifics as determined by or as though decided by the addition process in mathematics.

The outcome of adding two or more numbers, objects, or things is referred to in mathematics as the sum.

The result or solution we obtain from adding two or more integers is known as the SUM. Addends are the figures that are combined.

\(Simplify $\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}: \frac{x+5}{x+3}$Steps$$\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}$$Apply the fraction rule: $\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$$$=\frac{x+3+2}{x+3}$$Add the numbers: $3+2=5$$$=\frac{x+5}{x+3}$$\)

Therefore, the correct answer is option b) \($=\frac{x+5}{x+3}$\)

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Given:

The area model for \(2.1\times 3.2\).

To find:

The value of \(2.1\times 3.2\) and the missing values in the area model.

Solution:

2.1 can be written as 2 and 0.1 on the left side of the area model.

3.2 can be written as 3 and 0.2 on the top of area model.

Area of the four parts of the area model are:

\(2\times 3=6\)

\(2\times 0.2=0.4\)

\(0.1\times 3=0.3\)

\(0.1\times 0.2=0.02\)

The complete area model is shown below.

After adding all areas of the area model, we get

\(6+0.4+0.3+0.02=6.72\)

Therefore, the value of \(2.1\times 3.2\) is 6.72 and the missing values of the area model are 0.3 and 0.02 respectively.

Answer:

A reflection across the y-axis and a translation 2 units down.

Explanation:

The time to complete 2 levels is (c) 60 minutes

The table of values is given as

Number of Levels     Time (hours)

2                                         ?

3                                         1.5

Express the blank (?) with y

Number of Levels     Time (hours)

2                                          y

3                                         1.5

The ordered pairs from the table are

(x, y) = (2, y) and (3, 15)

The table shows the proportional relationship

This means that the equation can be represented as

y = Y/X * x

Where

(x, y) = (2, y)

(X, Y) = (3, 1.5)

So, we have

y = 1.5/3 * 2

Evaluate the quotient

y = 0.5 * 2

This gives

y = 1 hour

Convert to minutes

y = 60 minutes

Hence, the time is 60 minutes

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The area of the right triangle is 24 square meters.

To find the area of a right triangle, we can use the formula:

Area = (1/2)×base × height

The adjacent side of the right triangle is given as 6 m, and the hypotenuse is given as 10 m.

We can use the Pythagorean theorem to find the length of the opposite side (height) of the right triangle:

opposite side = √(hypotenuse² - adjacent side²)

= √(10² - 6²)

= √(100 - 36)

= √64

= 8 m

Now, we can calculate the area using the formula:

Area = (1/2) × base × height

= (1/2) × 6 × 8

= 3 × 8

= 24 m²

Therefore, the area of the right triangle is 24 square meters.

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Answer:

$4.53

Divide 18.12 by 4

If we have a two sample confidence interval, then our point estimate is given by \((\bar X_1-\bar X_2)\).

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific degree of confidence, this is the range of values you anticipate your estimate to fall inside if you repeat the test. In statistics, confidence is another word for probability.

a) Select true for the part(s) of this formula that do not depend on the sample (n).

The confidence interval = True

The formula for confidence interval is

\(CI = \bar x \pm critical \space value * \frac{S.D}{\sqrt{n} }\)

The Point Estimate = True

The critical value is based on significance level and degree of freedom (df)

df = n-1

The standard error = True

\(SE = \frac{\sigma}{\sqrt{n} }\)

b) We call (Critical Value) x (Standard Error) the Margin of Error

c) If we have a two sample confidence interval, then our point estimate is

\(CI = (\bar x_1-\bar x_2) \pm t_c\sqrt{s^2(\frac{1}{n1} +\frac{1}{n2} )}\)

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Complete question:

a. Select true for the part(s) of this formula that depend on the sample. (In other words, which parts can change with each new sample?) True or False? The confidence interval True or False? v The point estimate True or False? ~ The critical value True or False? V The standard error b. We call (Critical Value)X(Standard Error) the ? Confidence Level Margin of Error Degrees of Freedom Plus/Minus Amount c. If we have a two sample confidence interval, then our point estimate is OH1 – 112 Old Од X – X₂ Xd OX

Answer:

2

Step-by-step explanation:

Answer:

5 cm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

let h be the hypotenuse , then

h² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )

h = \(\sqrt{25}\) = 5

The value of the given fraction 3/8 - 8/11 after the evaluation is -31/88.

So, evaluation of 3/8 - 8/11:

Now,

Therefore, the value of fraction 3/8 - 8/11 after the solution is -31/88.

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Based on the information provided, it appears that a study will be conducted to compare the mean weights of two populations of raccoons.

To do so, random samples will be selected from each population, and the mean weight of each sample will be calculated. By comparing the mean sample weights of the two populations, researchers can determine whether there is a significant difference in the mean weights between the two groups.

It is important to note that the use of random samples helps to ensure that the results are representative of the entire population and reduces the risk of bias in the study.

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The value of variable t =8.34.

We have  solve the equation  \(\frac{t}{3} = 2.78\)

A statement that the values of two mathematical expressions are equal.

We will use the steps below to solve this equation

First, multiply by 3 on both-side of the equation.

\(\frac{t}{3} \times 3= 2.78 \times 3\)

\(t=8.34\)

\(t = 8.34\)

We can further substitute 8.34 for t to check the correctness of the solution that is,

\(\frac{8.34}{3}= 2.78\)

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ANSWER

EXPLANATION

Given;

Recall;

Therefore, the time taken is 3.2hours.

Answer:

f(2) = 14

Step-by-step explanation:

Step 1: Define

f(x) = 2x³ - 2

f(2) = x = 2

Step 2: Substitute and evaluate

f(2) = 2(2)³ - 2

f(2) = 2(8) - 2

f(2) = 16 - 2

f(2) = 14