Consider the function f(x) = -2x^3 + 21x^2 - 36x + 10. For this function there are three important = open intervals: ([infinity], A), (A, B), and (B, [infinity]) where A and B are the critical numbers. Find A and B.

Answer:

There are many times in algebra when you need to simplify an expression. The properties of real numbers provide tools to help you take a complicated expression and simplify it.

The associative, commutative, and distributive properties of algebra are the properties most often used to simplify algebraic expressions. You will want to have a good understanding of these properties to make the problems in algebra easier to work.

Step-by-step explanation:

Commutative Property of Multiplication

For any real numbers a and b, a · b = b · aOrder does not matter as long as the two quantities are being multiplied together. This property works for real numbers and for variables that represent real numbers.

just as subtraction is not commutative, neither is division commutative. 4 ÷ 2 does not have the same quotient as 2 ÷ 4.Associative Property of Addition

For any real numbers a, b, and c, (a + b) + c = a + (b + c).

Associative Property of Multiplication

For any real numbers a, b, and c, (a • b) • c = a • (b • c).Multiplication has an associative property that works exactly the same as the one for addition. The associative property of multiplication states that numbers in a multiplication expression can be regrouped using parentheses. For example, the expression below can be rewritten in two different ways using the associative property.

The parentheses do not affect the product, the product is the same regardless of where the parentheses are.

The distributive property of multiplication is a very useful property that lets you rewrite expressions in which you are multiplying a number by a sum or difference. The property states that the product of a sum or difference, such as 6(5 – 2), is equal to the sum or difference of products, in this case, 6(5) – 6(2).

   6(5 – 2) = 6(3) = 18

 65) – 6(2) = 30 – 12 = 18

The distributive property of multiplication can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2.3(10 + 2) = ?

According to this property, you can add the numbers 10 and 2 first and then multiply by 3, as shown here: 3(10 + 2) = 3(12) = 36. Alternatively, you can first multiply each addend by the 3 (this is called distributing the 3), and then you can add the products. This process is shown here.

3 (10 + 2) = 3(12) = 36

3(10) + 3(2) = 30 + 6 = 36

The products are the same.

since multiplication is commutative, you can use the distributive property regardless of the order of the factors.

Yes, you can use the statement as a question to the knowledge base to inquire about the color of apples in the base.

Specifically, the question seeks to confirm whether all apples in the knowledge base are either red or green.
1. Review the knowledge base to identify all statements related to apples.
2. Examine each statement to determine if it contains information about the color of the apples.
3. Check if the color mentioned in each statement is either red or green.
4. If all the relevant statements in the knowledge base confirm that apples are either red or green, then the answer to your question is "yes." Otherwise, the answer is "no."
In this process, the terms "knowledge," "statement," and "red or green" are used to analyze the information stored in the knowledge base and draw a conclusion about the colors of apples.

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\(\huge\pink{Answer}\)

Any odd number can be represented with 2n+1 where n is a whole number. Also, since the next consecutive number will be even (2n+1+1), then the next consecutive odd number must be 2n+1+2, or 2n+3. Since consecutive odd numbers are separated by 2, then the previous odd number should be 2n-1. So:

Now in order to find three odd consecutive numbers that will sum to 36, you must be able to divide 11 evenly by 2, and have a whole number as a result. This is impossible, so there aren't any 3 odd numbers that will sum to 36.

Answer:

Step-by-step explanation:

The order of the expression for congruent shapes indicate the

corresponding vertices between the two shapes that are congruent.

The option which is true is D. T = Q.

Reasons:

The given statement is; ΔRST ≅ ΔNPQ

By Corresponding Parts of Congruent Triangle are Congruent, CPCTC, we

have; The sides on ΔRST are congruent to the corresponding sides of ΔNPQ

Therefore;

RS ≅ NP

RT ≅ NQ

ST ≅ PQ

By CPCTC, we have that the angles on ΔRST are congruent to the corresponding angles of ΔNPQ

Therefore;

∠R ≅ ∠N

∠S ≅ ∠P

∠T ≅ ∠Q

Which gives, by definition of congruency;

∠R = ∠N

∠S = ∠P

∠T = ∠Q

Therefore, the true statement is D. T = Q.

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Answer:

$24

Step-by-step explanation:

Let the full price of $30 be 100%.

If the discount allowed is 20%, then the percentage of the original price that a customer will pay is:

\(P=100\%-20\%\\P=80\%\)

80% of a marked price of $30 is:

\(80\%*\$30\\\$24\)

A customer will pay $24.

Use 1-Prop Z Int to create a 95% confidence interval.

Z test should be employed because there is only one set of samples collected and the sample size is huge.

An observed percentage is compared to a theoretical one using a one proportion z-test. The test statistic is determined as follows:

z = (p-p0) / √(p0(1-p0)/n)

where:

p = observed sample proportion

p0 = hypothesized population proportion

n = sample size

You can reject the null hypothesis if the p-value associated with the test statistic z is less than your selected level of significance (popular choices are 0.10, 0.05, and 0.01).

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The labor hours required for the eighth satellite are calculated to be 51,200 based on a learning curve value of 0.5120 and an expected improvement curve of 80%.

The learning curve concept suggests that as the cumulative production doubles, the labor hours required to produce each unit decrease by a certain percentage. In this case, the learning curve value for the eighth unit is given as 0.5120, which means that the labor hours needed for the eighth satellite is 51.20% of the labor hours required for the first unit.

To calculate the actual number of labor hours, we multiply the learning curve value by the total labor hours required for the first unit. Given that the total labor hours for the first unit is 100,000, we can calculate the labor hours for the eighth satellite as follows: 0.5120 * 100,000 = 51,200.

Therefore, based on the given learning curve value and the expected improvement curve of 80%, the number of labor hours for the eighth satellite is determined to be 51,200.

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PreAlg students spend significantly less time doing homework compared to ElemAlg and InterAlg students, while there is no significant difference in homework time between ElemAlg and InterAlg students.

What is significantly ?

Significantly" is the keyword that indicates a notable or meaningful difference or result in the context of statistical analysis. It is often used to describe findings that have a high level of confidence and statistical significance, indicating that the observed difference or relationship is unlikely to have occurred by chance.

Based on the given data and statistical analysis, the conclusion is as follows:

PreAlg compared to ElemAlg:

The sample mean for PreAlg (1.32) is significantly different from the sample mean for ElemAlg (3.18) with a t-value of 5.08 and a p-value of 0.000. Therefore, we can conclude that PreAlg students spend significantly less time doing homework compared to ElemAlg students.

PreAlg compared to InterAlg:

The sample mean for PreAlg (1.32) is significantly different from the sample mean for InterAlg (4.42) with a t-value of 3.64 and a p-value of 0.003. Hence, we can conclude that PreAlg students spend significantly less time doing homework compared to InterAlg students.

ElemAlg compared to InterAlg:

The sample mean for ElemAlg (3.18) is not significantly different from the sample mean for InterAlg (4.42) with a t-value of 1.49 and a p-value of 0.163. Therefore, we fail to reject the null hypothesis, and we cannot conclude a significant difference in homework time between ElemAlg and InterAlg students.

In summary, the PreAlg students have significantly lower homework time compared to both ElemAlg and InterAlg students. However, there is no significant difference in homework time between ElemAlg and InterAlg students.

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the probability that the sample mean will be smaller than m = 22 is 0.02275.

For the given question,

A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.

Here sample size, n = 4

mean, μ = 30

standard deviation, σ = 8

The probability that the sample mean will be smaller than m = 22 is

z = \(\frac{m-\mu}{\frac{\sigma}{\sqrt{n} } }\)

⇒ z =\(\frac{22-30}{\frac{8}{\sqrt{4} } }\)

⇒ z = \(\frac{22-30}{\frac{8}{2} }\)

⇒ z = \(-\frac{8}{4}\)

⇒ z = -2

Refer the Z table for p value,

Thus for P(z < -2) is 0.02275.

Hence we can conclude that the probability that the sample mean will be smaller than m = 22 is 0.02275.

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angle has a measure equal to the sum of the the question is ∠DQS.


According to the problem, we need to find an angle whose measure is equal to the sum of the measures of ∠SQR and ∠QRS. We can use the angle addition postulate which states that the measure of an angle formed by two adjacent angles is equal to the sum of their measures.

Let's consider angle ∠DQS. This angle is formed by adjacent angles ∠SQR and ∠QRS. Therefore, according to the angle addition postulate, the measure of angle ∠DQS is equal to the sum of the measures of ∠SQR and ∠QRS.



Thus, we can conclude that the angle ∠DQS has a measure equal to the sum of the measures of ∠SQR and ∠QRS.

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Answer:

Ans in attachment

hope it helps :)

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Answer:

The answer is "Expression: x+(x+2)".

Step-by-step explanation:

Given:

The sum of two consecutive even numbers

Proving:

Let,

The First number is = x

The second consecutive number is = x+2

Calculating value by adding value:

Expression:

\(\Rightarrow x+(x+2)\\\\\)

when x= 1, 2, 3 .... it gives:

\(\Rightarrow 1+(1+2)= 1+3=4\\\\\Rightarrow 2+(2+2)= 2+4=6\\\\\Rightarrow 3+(3+2)= 3+5=8\\\)

That's why the sum of consecutive numbers is even.

Answer:

4

because it is the greatest power in the polynomial

Answer:

8 years

Step-by-step explanation:

Currently

Abebe → 12 years old

Aster → 2 years

With every passing year, each of them will be 1 year older hence the difference between their ages will remain constant.

Difference in ages

= 12 -2

= 10

Let the age of Aster be x years old when Abebe is twice her age.

Abebe → 2x years old

Aster → x years old

Difference in age

= 2x -x

= x

x= 10

Aster is 10 years old when Abebe is twice her age.

Number of years passed

= 10 -2

= 8

Thus, Abebe will be twice as old as her sister in 8 years.

Answer:

I would take $1.980 / .20 = 99 I'm not 100% sure

Step-by-step explanation:

An isoline that connects all points of highest mean temperature on a world map is called the highest mean temperature isoline.

An isoline is a line on a map that connects points of equal value for a particular variable. In this case, the isoline connects all points of the highest mean temperature, indicating regions with the highest average temperatures.

Therefore, it is referred to as the "highest mean temperature isoline." The other options mentioned are not specifically related to the concept described.

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ann made a rectangle with the

right perimeter & area

ann doesn't try any other

rectangles to see if their areas are

different.

splitting the land , ann confuses perimeter and area

mapmathshellorg

Answer:

~ 340

Step-by-step explanation:

A = pi * r^2

The big circle is r1 = 12cm so the small r2=6cm

A= A1 - A2 = (pi * r1^2)-( pi*r2^2) = 339,29 ~ 340 square cm

If the radius of the small circle is 12cm then: r1 = 24cm and r2 = 12cm and calculate it the same way

Yes, Set K is a function.

To determine if Set K is a function, we need to check if for every x-value in Set K, there is a unique corresponding y-value.

Set K is defined as {(x, y) | x - y = 5}.

This means that any pair (x, y) in Set K must satisfy the equation x - y = 5.

To test if it is a function, we can consider two scenarios:

If we fix a value for x, is there a unique value for y that satisfies the equation x - y = 5?

If we fix a value for x, say x = 7, we can substitute it into the equation and solve for y:

7 - y = 5

-y = 5 - 7

-y = -2

y = 2

In this case, there is a unique value of y (y = 2) that satisfies the equation x - y = 5 when x = 7.

If we fix a value for y, is there a unique value for x that satisfies the equation x - y = 5?

If we fix a value for y, say y = 3, we can substitute it into the equation and solve for x:

x - 3 = 5

x = 5 + 3

x = 8

In this case, there is a unique value of x (x = 8) that satisfies the equation x - y = 5 when y = 3.

Since for every x-value in Set K, there is a unique corresponding y-value, and vice versa, we can conclude that Set K is indeed a function.

Therefore, Set K is a function.

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Answer:

4

Step-by-step explanation:

The n th term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given

\(a_{n}\) = 11 +(n - 1)4 , then

d = 4

The recursive formula allows a term in the sequence to be found by adding d to the previous term, thus

\(a_{n}\) = \(a_{n-1}\) + 4

Answer:

The answer is 4

Step-by-step explanation:

The median and quartiles fall in the middle age classes.

The median is the middle value in a set of data, meaning that half of the data falls below the median and half falls above it. The quartiles divide the data into four equal parts, with the first quartile (Q1) being the 25th percentile, the second quartile (Q2) being the median or 50th percentile, and the third quartile (Q3) being the 75th percentile.

In terms of age classes, the median and quartiles would fall in the middle age classes. For example, if the age classes were 0-10, 11-20, 21-30, 31-40, 41-50, 51-60, 61-70, 71-80, and 81-90, the median and quartiles would fall in the 21-30, 31-40, and 41-50 age classes.

It is important to note that the specific age classes that the median and quartiles fall in will depend on the distribution of the data. However, they will always fall in the middle age classes, as they represent the middle values of the data set.

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Answer:

1/4 is the answer or one-fourth

Step-by-step explanation:

Answer:

0.25 or 1/4 is the answer.

Step-by-step explanation:

Answer:

0, -3

Step-by-step explanation:

So remember, when they say reflect over the x intercept, they do not mean to reflect the x value, they mean to reflect over the hirzontal line of the graph.(x axis)

This is the same with reflection over the y intrecept. This doesnt mean y is flipped, this means that whatever point or line you have is reflected over the vertical line on the graph(y axis)

So our orginal value is (0, 3). We need to reflect over the x axis, which means that y will now be -3, since that is the opposite of what we can see when we flip the x axis.

The 0 x, of course, stays the same since its 0.

So your answer is (0, -3)

Hope this helps! :)

Answer:

Step-by-step explanation:

Givens

We know that the area of a rectangle is

\(A= w \times l\)

Where \(w\) is width and \(l\) is length.

We know by given that \(l= 7 \ in\) and \(A= 25 \ in^{2}\), replacing these values and solving for \(w\), we have

\(25=7w\) (this is the equation used to solve the problem).

\(w=\frac{25}{7} \approx 3.6 \ in\)

Answer:

The equation is Area = length × width.

The width is approximately 3.57 inches.

Step-by-step explanation:

Door sign length, l = 7 inches

Area, A = 25 square inches

Width (w) is unknow.

Since the area is the product of the length and the width,

A = l×w

25 = 7×w

Dividing both sides by 7

w = 25/7

≈ 3.57 inches

Answer:

27°

Step-by-step explanation:

The two lines are parallel, causing them to be equal

If my answer is incorrect, pls correct me!

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-Chetan K

so let's check how much is each interior angle in the pentagon first.

\(\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108\)

Check the picture below.

Answer:

48

Step-by-step explanation:

Answer:

48   because i divided it