What must be true of two rational expressions before they can be added?

A They must have common numerators.
B They must be of the same degree.
C They must have the same variables.
D The must have common denominators.

Final answer:

The best estimate of the total amount of cleaning products that the cleaning service orders is 1,194 Oz.

Explanation:

To find the best estimate of the total amount of cleaning products that the cleaning service orders, we need to calculate the total amount of cleaning products in the large bottles and small bottles separately and then add them together.

Each large bottle has 122 Oz, and the cleaning service orders 7 of them. So the total amount of cleaning products in the large bottles is 7 x 122 = 854 Oz.

Each small bottle has 68 Oz, and the cleaning service orders 5 of them. So the total amount of cleaning products in the small bottles is 5 x 68 = 340 Oz.

To get the best estimate of the total amount of cleaning products, we add the amounts in the large bottles and small bottles together: 854 + 340 = 1,194 Oz.

Answer:

22 strips.

Step-by-step explanation:

In order to solve this you just have to divide the total inches of paper that she actually has by the size of the strips that she´s going to make:

[tex]9 inches/2/5\\\frac{ 9inches}{\frac{2}{5} } \\\frac{45}{2}\\22\frac{1}{2}[/tex]

So as you can see she can make a total of 22 strips and a half, but the half won´t be useful so she can make 22 strips.

The calculated z-score is -2.5, and the corresponding probability is 0.9938, meaning there is a 99.38% chance of drawing a sample with a mean greater than 75.

To find the probability of obtaining a sample mean greater than m = 75 for a sample of n = 25 scores when the population mean is m = 80 and the standard deviation is s = 10, we will use the concept of sampling distributions and the Central Limit Theorem.

First, we need to calculate the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the sample mean.

The SEM is calculated using the formula [tex]SEM = s / \sqrt{n[/tex] where s is the population standard deviation and n is the sample size.

Here, SEM = [tex]10 / \sqrt{25[/tex]

= 10 / 5

= 2.

Next, we convert the sample mean to a z-score to find out how many standard errors the sample mean is from the population mean.

The z-score is calculated using the formula z = (M - m) / SEM, with M being the sample mean and m the population mean.

Therefore, z = (75 - 80) / 2 = -5 / 2 = -2.5.

Looking at the standard normal distribution table or using statistical software, we find that the probability associated with a z-score of -2.5 is approximately 0.9938. This means that the probability of obtaining a sample mean greater than 75 is 0.9938.

To find the average value of the function f(x, y) = 7xy over the triangular region defined by vertices (0, 0), (1, 0), and (1, 8), compute the area of the triangle and then calculate the double integral of the function over the region, divided by the area. The bounds for the double integral will be defined by the region.

To find the average value of f over the given triangular region, we first need to find the area of the region. The given region is a triangle with vertices (0, 0), (1, 0), and (1, 8). This triangle has a base of 1 (the difference in x coordinates) and a height of 8 (the difference in y coordinates), so its area is (1/2)*base*height=(1/2)*1*8=4.

Next, we integrate the function f(x, y) = 7xy over the triangular region, and divide by the area of the region, to find the average value. Setting up and computing the double integral will provide the total value of the function over the region. The bounds for the double integral will be defined by the region, so we will integrate x from 0 to 1 and y from 0 to 8. The average value is then given by the total value divided by the area, or (1/4)*double integral of f(x, y) dy dx.

Without performing the actual calculation, this is the best process to solve the problem as presented.

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Answer with explanation:

When we prove two triangles are congruent, either by following four congruent Axioms

1. S AS

2. SSS

3. A AS

4. A SA

Then C P CT C stands for Corresponding part of Congruent Triangles.

So, C P C TC is useful for proving , those corresponding parts of triangle that is side and Angles equal which are not used while proving Congruency of two triangles.

g^2 14g+40

replace g with 5

5^2 +14(5) +40 = 25 + 70 +40 = 135 square feet

Area =L x W

 using your choices multiply 15 x 9 = 135

 so answer is 15 feet by 9 feet

Margo will pay $36 in interest after borrowing $600 with a 4% annual interest rate for 18 months. We calculate this using the simple interest formula.

The question is asking us to figure out how much interest Margo will pay after borrowing $600 with a 4% annual interest rate, or simple interest rate, over the course of 18 months. A core concept here is understanding how simple interest is calculated.

The simple interest formula we'll be using is: Interest = Principal x Rate x Time.  The Principal is the amount of money initially borrowed, Rate is the annual interest rate (in decimal form), and Time is the length of time the money is borrowed for, expressed in years.

So in Margo's case, the Principal is $600, the Rate is 4% (or 0.04 in decimal form), and Time is 18/12 or 1.5 years, because 18 months is equal to 1.5 years.

When we apply these amounts to the formula we get: Interest = $600 x 0.04 x 1.5, which equals $36. So Margo will pay $36 in interest.

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The explicit rule for the remaining train sets after 'n' months is represented by the formula T(n) = 35 - 3n, where T(n) is the total number of train sets, and 'n' is the number of months.

The explicit rule for the number of train sets a store has after ‘n’ months, given that the store starts with 35 train sets and sells 3 each month, can be represented by a linear equation. The initial amount of train sets is the starting point, and the number of sets sold each month is the rate of change.

The explicit rule for the number of train sets the store has after 'n' months can be represented by the linear function:

\[ T(n) = 35 - 3n \]

Here, \( T(n) \) represents the number of train sets after 'n' months, 35 is the initial number of train sets, and 3n represents the number of train sets sold each month. The negative coefficient (-3) indicates the decrease in the number of train sets each month. By plugging in different values for 'n', you can determine the number of train sets the store will have at any given month.

This is reflected in the equation:

T(n) = 35 - 3n

where T(n) represents the total number of train sets after n months, and n is the number of months that have passed.

The value of [tex]z[/tex] which divides the standard normal distribution so that half the area is on one side and half is on the other is [tex]0.00[/tex].

A normal distribution with a mean of [tex]0[/tex] and a standard deviation of [tex]1[/tex] is known as a standard normal distribution.

The typical normal distribution is divided into two equal halves with 50% on each side when the [tex]z[/tex] value is [tex]0.00[/tex].

Hence, the  value of [tex]z[/tex] which divides the standard normal distribution so that half the area is on one side and half is on the other is [tex]0.00[/tex].

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Answer: 160 seats

Step-by-step explanation: Got it right on TTM

To find the measures of angles ∠A and ∠B, we can use the fact that they are supplementary angles and the given relationship between their measures. By solving a system of equations, we can determine that m∠A is 135 and m∠B is 45.

To find the measures of the angles ∠A and ∠B, we need to use the fact that they are supplementary angles and the relationship between their measures. Let's start by understanding what supplementary angles are.

Supplementary angles are two angles that add up to 180 degrees. In this case, ∠A and ∠B are supplementary, so we can write the equation:

m∠A + m∠B = 180

We are also given that the measure of ∠A is three times the measure of ∠B, so we can write another equation:

m∠A = 3m∠B

Now we can substitute m∠A in the first equation with 3m∠B:

3m∠B + m∠B = 180

Combining like terms, we get:

4m∠B = 180

Finally, we can solve for m∠B by dividing both sides of the equation by 4:

m∠B = 45

Since m∠A is three times m∠B, we can find m∠A by multiplying 45 by 3:

m∠A = 135

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You can use it when like confirming a policy. You can use it when like confirming a policy.

Answer:

c

Step-by-step explanation:

Option (C) √3 + 8.486 is an irrational number.

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. Those real numbers that are not rational numbers are known as irrational numbers.

For the given situation,

We need to check the options, that is irrational.

Option A: 7.51... x -4

⇒ 7.51 (-4)

We can express this as fraction. So it is not an irrational number.

Option B: root 16 + 3/4

⇒ √16 + 3/4

⇒ 4 + 3/4

We can express this as fraction. So it is not an irrational number.

Option C: root 3 + 8.486

⇒ √3 + 8.486

⇒ √3  is an irrational number, so the sum is also an irrational number.

Option D: 8 2/3 × 17.75

⇒ 8 2/3 × 17.75

We can express this as fraction. So it is not an irrational number.

Hence, we can conclude that option (C) √3 + 8.486 an irrational number.

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To calculate the probability that at least 150 individuals will cooperate and respond to the questions in a new sample of 400 telephone numbers with a historical response rate of 44%, we use the binomial distribution formula.

To calculate the probability that at least 150 individuals will cooperate and respond to the questions, we need to use the binomial distribution formula. The formula is:

P(X ≥ k) = 1 - P(X

Where n is the sample size, k is the desired number of successes, p is the historical response rate, q = 1 - p is the failure rate.

In this case, n = 400, k = 150, p = 0.44, q = 1 - 0.44 = 0.56. Plugging these values into the formula, we get:

P(X ≥ 150) = 1 - P(X<150)

We can use a software or calculator to evaluate this expression. The probability is approximately 0.9328 to 4 decimal places.

The correct answer is 43-a. In other words, the result of simplifying algebraic expressions 43 + a - 2a is 43 - a.

To simplify the expression 43 + a - 2a, you can combine like terms.

The expression consists of three terms: 43, a, and -2a.

Starting with the numbers, 43 is a constant term and does not contain any variables. Since there are no other terms with numbers, 43 remains unchanged.

Next, let's simplify the terms with variables. We have a and -2a. To combine these terms, we can group them together as a single term.

The term with a is positive a, and the term with -2a is negative 2a. When we combine them, we subtract 2a from a. This gives us a - 2a, or -a.

Therefore, the simplified expression is 43 - a.

Therefore, the correct answer is 43-a. In other words, the result of simplifying algebraic expressions 43 + a - 2a is 43 - a.

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The expression '2+8' simplifies to 10. Factoring using the Greatest Common Factor (GCF) is commonly used with expressions that contain variables.

The expression you're looking to factor, 2+8, does not really involve any complex mathematical concepts, and there's no variable to enable factoring in its usual way. However, we can simplify it by adding the numbers. So, 2+8 equals to 10. Factoring using the greatest common factor(GCF) is most often used when you're handling expressions that involve variables, for instance, 2x + 8x. In this case, the GCF would be 2x, and the expression would factor to 2x(1 + 4).

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