(q20) Is the function f(x) = (x - 9)(x + 9)x even, odd, or neither?

Answer:2

Step-by-step explanation:

Answer: 1

Step-by-step explanation: You can do this by writing it all out.

The frequency tells you how many of the number there are.

Eg. there are 9 0s because it says it on the table.

So you would write

0,0,0,0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,2,2,2,3,4,4,4

Cancel one number from both sides going into the middle until.

Median = 1

Answer:

16

Step-by-step explanation:

7 feet x 12 inches/foot = 84 inches

Then we divide the total length of the string (84 inches) by the length of each piece (5 inches) to get the total number of pieces:

84 inches / 5 inches per piece = 16.8 pieces

Since we cannot have a fractional number of pieces, we round down to the nearest whole number to get the final answer:

16 pieces

The ratio of red apples to all apples in the basket is 3:11, whereas all apples to green is 11:8

Total number of green apples = 8

Total number of red apples = 3

Calculating the total number of apples -

Total number of green apples + Total number of red apples

= 8 + 3

= 11

Calculating the ratio of red apples to all apples in the basket -

= Total number of red apples / Total number of apples

= 3/11

Thus, for every 11 apples in the basket, 3 of them are red.

Calculating the ratio of all apples in the basket to green apples -

Total number of apples / Total number of green apples

= 11/8.

Thus, for every 8 green apples in the basket, there are a total of 11 apples in the basket.

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The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

Any five-sided polygon or 5-gon is referred to as a pentagon. The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

We have,

Any five-sided polygon or 5-gon is referred to as a pentagon. A basic pentagon's interior angles add up to 540°. A pentagon might be straightforward or self-intersecting.

We know the formula for the area of a pentagon, therefore, the area of the pentagon PQRST can be written as,

A = 1/4 * √5(5+25)*a²

Given that the side of the side length of pentagon ABCDE is 6 times the side length of pentagon PQRST, therefore, the area of the pentagon ABCDE can be written as,

ABCDE = 1/4 * √5(5+25)* 6a²

ABCDE = 36 * A

Hence, The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

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complete question:

Pentagon ABCDE is similar to pentagon PQRST. If the side length of pentagon ABCDE is 6 times the side length of pentagon PQRST, which

statement is true?

A.

The area of pentagon ABCDE IS 6 times the area of pentagon PQRST.

B.

The area of pentagon ABCDE is 12 times the area of pentagon PQRST.

C.

The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

D.

The area of pentagon ABCDE IS 216 times the area of pentagon PQRST.​

By creating equation, we can solve for x to get the following values:

8. x = 9;      9. x = 9

In order to solve for x in each problem, note that the segments are equal to each other, therefore, we would create an equation that will enable us solve for x.

8. 2x + 12 = 5x - 15

Combine like terms

2x - 5x = -12 - 15

-3x = -27

Divide both sides by -3:

-3x/-3 = -27/-3

x = 9

9. 8x - 63 = 4x - 27

8x - 4x = 63 - 27

4x = 36

4x/4 = 36/4 [division property]

x = 9

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The expressions are equivalent and help us find the product of two numbers, which are 30 and 2. This principle can be applied to solve complex equations. Here option A is the correct answer.

The two expressions, [tex]\left(30-2\right)\left(30+2\right) & 30^{2}-2^{2}[/tex], are equivalent due to the distributive property of multiplication over addition. By simplifying both expressions, we can see that they both evaluate to the same value of 868.

To find the product of two numbers, we can use the fact that [tex]30^{2}-2^{2}[/tex] is equal to (30+2)(30-2). This can be derived from the identity [tex](a+b)(a-b) = a^{2}-b^{2}[/tex], where a and b are any real numbers.

Therefore, we can conclude that the two numbers whose product is being calculated are 30 and 2. We can check this by multiplying 30 and 2, which gives us 60, and verifying that (30+2)(30-2) = 32*28 = 896, which is equal to the product of 30 and 2 added to the square of 2, i.e., [tex]30 \times 2+2^{2} = 60+4 = 64[/tex].

In conclusion, the expressions [tex]\left(30-2\right)\left(30+2\right)[/tex] and [tex]30^{2}-2^{2}[/tex] are equivalent and help us find the product of two numbers, which are 30 and 2. This mathematical principle can be applied to many other problems in algebra and can be a useful tool for solving complex equations and problems.

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Complete question:

The expressions [tex]\left(30-2\right)\left(30 2\right)[/tex] and [tex]30^{2}-2^{2}[/tex] are equivalent and can help us find the product of two numbers. which two numbers are they?

A - 30, 2

B - 30, 4

C - 4, 39

D - 5, 32

Answer:

--------------

Find 25% of 240:

Add 25% to 240:

The base of the right triangle is 3/2 ft.

The area of a right triangle is given by the formula:

Area = (base × height) / 2

We are given that the area of the triangle is 9/16 sq. ft. and the height is 3/4 ft. So, substituting these values in the above formula, we get:

9/16 = (base × 3/4) / 2

Multiplying both sides by 2, we get:

9/8 = base × 3/4

Dividing both sides by 3/4, we get:

9/8 ÷ 3/4 = base

Simplifying, we get:

9/8 × 4/3 = base

3/2 = base

Therefore, the base of the right triangle is 3/2 ft.

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Check the picture below.

[tex]\tan(23^o )=\cfrac{\stackrel{opposite}{h}}{\underset{adjacent}{35}} \implies 35\tan(23^o)=h \implies 15\approx h\\[/tex]

Make sure your calculator is in Degree mode.

The value of the correlation coefficient based on the R-Square for tree #2 would be the square root of 0.99115489, which is approximately 0.9956. So the answer would be option a, 0.9956.

The correlation coefficient can be determined by taking the square root of the R-squared value.

Therefore, the value of the correlation coefficient based on R-Square for tree #2 would be the square root of 0.99115489, which is approximately 0.9956.

So the answer would be option a, 0.9956. It is important to note that the correlation coefficient measures the strength and direction of the linear relationship between two variables, in this case, leaf water potential and sap flow velocity.

A correlation coefficient of 0.9956 indicates a strong positive linear relationship between these variables.

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As the level of significance increases, the probability of making a type II error decreases.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

If the level of significance of a hypothesis test is raised from 0.05 to 0.1, the probability of a type II error will decrease.

Type II error occurs when we fail to reject a null hypothesis that is actually false. It is the probability of accepting a false null hypothesis. By increasing the level of significance, we are making it easier to reject the null hypothesis, which in turn decreases the probability of accepting a false null hypothesis.

Hence, as the level of significance increases, the probability of making a type II error decreases.

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Check the picture below.

so the way I see it, we have a bunch of semicircies going from 0 to 5, and we're looking at the bottom of the object, the provided picture above is not very useful btw.

so we're looking at the bottom of the object and the semicircles are going from 0 to 5, however from 0 to 1 they vary, from small to large, then they reach a diameter of 6 and go steady with that 6 all the way to 5.

so we can say that from 1 to 5, we can simply get the integral of a semicircle with a steady radius of 3, in which case that'd be the fixed value of 4.5π for the area.

now, we can also say that from 0 to 1 it varies, now, the radius varies, the radius is really the vertical value of the line or namely the y-value of that slanted line from 0 to 1, anyhow, not to bore you to death, but if we use the points (0 , 0) and (1 , 3) to get the equation of the line, we end up with y = 3x, and that's our radius, and we'll get the integral of those semicircles from 0 to 1 with a radius of 3x, with an area of 4.5πx²

[tex]\stackrel{ \textit{areas from 0 to 1} }{\cfrac{1}{2}\cdot \pi (3x)^2\implies 4.5\pi x^2}\hspace{9em}\stackrel{ \textit{areas from 1 to 5} }{\cfrac{1}{2}\cdot \pi (3)^2\implies 4.5\pi} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \int_0^{1}4.5\pi x^2dx~~ + ~~\int_{1}^{5}4.5\pi dx\implies 4.5\pi\int_0^{1} x^2dx~~ + ~~\int_{1}^{5}4.5\pi dx \\\\\\ 4.5\pi \left. \cfrac{x^3}{3} \right]_{0}^{1}~~ + ~~4.5\pi \left. x\cfrac{}{} \right]_{0}^{1}\implies 4.5\pi ~~ + ~~18\pi \implies \boxed{22.5\pi}[/tex]

c = 0.71, which means that the probability of obtaining a z-score greater than 0.71 in a standard normal distribution is 0.2445. We need to use a standard normal distribution table or calculator.

From the given information, we know that the area to the right of z (which is c in this case) is 0.2445. Looking up this value in a standard normal distribution table, we find that the z-score that corresponds to this area is approximately 0.71. Therefore, c = 0.71. We can also use a calculator to find the value of c. Using the inverse normal function (also known as the z-score function) on a calculator or spreadsheet, we can input the area to the right of c (0.2445) and get the corresponding z-score, which is 0.71.

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Answer:

The rectangular form of the complex number is -3√2 - 3√2i.

To see why, recall that cos(225°) = -sin(45°) = -√2/2 and sin(225°) = -cos(45°) = -√2/2.

So we have:

6(cos 225 + i sin 225)

= 6(-√2/2 - i√2/2)

= -3√2 - 3√2i

A contest is a type of promotional marketing strategy that requires participants to submit their entries based on specific criteria or requirements. The correct answer to your question is "contest."

A long answer to your question is that when a group of individuals selects a particular consumer-submitted entry, it is called a contest.

The entries are then judged by a panel or group of individuals who select the best or most appropriate entry.

The winner of the contest may receive a prize or premium, such as cash, gift cards, or products.

Unlike a sweepstake, which randomly selects a winner, a contest is based on merit or creativity and involves a selection process.

Therefore, the correct answer to your question is "contest."

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a. George has more money to start out with. He has $350, while Julie has $250. Therefore, George has $100 more than Julie to start out with.

b. To compare the rates of change for George and Julie, we need to look at the difference in the balance between consecutive months for each account. The differences are as follows:

George's Account: 50, 50, 50

Julie's Account: -100, -100, -100

From the differences, we can see that George is depositing more money each month, as his balance increases by $50 each month compared to Julie's decrease of $100 each month.

The statement is not necessarily true. Continuity at a point does not guarantee differentiability at that point.

A function can be continuous but not differentiable at a certain point if it has a sharp corner or a vertical tangent at that point. However, if a function is differentiable at a point, it must also be continuous at that point.

This is because differentiability implies continuity, but continuity does not imply differentiability. Therefore, it is possible for a function to be continuous at x=3 and not differentiable at x=3.

Additional information, such as the existence and continuity of the derivative, is needed to determine if a function is differentiable at a given point.

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A random variable is a numerical outcome that is generated by a probability experiment. It is a function that assigns a unique numerical value to each outcome of the experiment.

Random variables can be either discrete or continuous. Discrete random variables take on a countable number of distinct values, while continuous random variables can take on any value within a specified range. In statistical analysis, random variables are used to model the behavior of a system or population of interest. They are often used to describe the distribution of a population or the probability of different outcomes occurring in a given scenario. Random variables are an essential tool in probability theory, statistics, and other areas of mathematics and science.

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To transform the given initial value problem into an equivalent problem with the initial point at the origin, we need to use the substitution u=y/y0, where y 0 is the initial value of y, and make appropriate adjustments to the equation.

To transform the initial value problem dy/dt = t^2 + y^2, y(1) = 2 into an equivalent problem with the initial point at the origin, we first need to define a new variable u=y/y0, where y0=2 is the initial value of y at t=1.

Taking the derivative of u with respect to t, we get:

du/dt = (1/y0) * dy/dt = (1/2) * (t^2 + y^2)

Next, we substitute y=y0u into the original equation and simplify:

dy/dt = t^2 + y^2

d(y0u)/dt = t^2 + (y0u)^2

y0 * du/dt = t^2 + y0^2 u^2

Substituting the expression for du/dt derived earlier, we get:

y0 * (1/2) * (t^2 + y^2) = t^2 + y0^2 u^2

Simplifying and rearranging, we obtain the equivalent initial value problem:

du/dt = (2/t^2) * (1-u^2)

u(1) = y(1)/y0 = 2/2 = 1

Therefore, the equivalent problem with the initial point at the origin is du/dt = (2/t^2) * (1-u^2), u(1) = 1.

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To prove the validity of a Boolean algebra identity, apply Boolean algebra theorems and axioms to manipulate the expression, simplify it, and compare the result to the original identity.

A method for proving the validity of a Boolean algebra identity is as follows.

1. State the given Boolean algebra identity:

Write down the specific identity you want to prove. For example, let's consider the identity A + AB = A.

2. Apply Boolean algebra theorems and axioms:

Utilize the various theorems and axioms of Boolean algebra, such as the Identity law, Commutative law, Associative law, Distributive law, Complement law, and De Morgan's law, to manipulate the given expression.

3. Simplify the expression:

In our example, A + AB, we can apply the Distributive law to factor out the common term A: A(1 + B).

4. Use known identities to simplify further:

Now, apply the Identity law (A + 1 = 1) to the expression within the parenthesis: 1 + B = 1. So, the simplified expression becomes A(1), which, according to the Identity law, is just A.

5. Compare the simplified expression to the original identity:

If the simplified expression matches one side of the original identity, then the Boolean algebra identity is valid. In our example, the simplified expression A is equal to the left side of the original identity, proving its validity.

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The probability of the states of nature, after use of Bayes' theorem to adjust the prior probabilities based on given indicator information, is called b. posterior probability

Bayes' theorem is a formula used to calculate the conditional probability of an event or hypothesis based on prior knowledge or information. It allows us to update our prior beliefs or probabilities based on new evidence or information.

The probability of the states of nature, after using Bayes' theorem to adjust the prior probabilities based on given indicator information, is called the posterior probability. It represents the revised probability of each state of nature, given the observed indicator or evidence.

To calculate the posterior probability, we multiply the prior probability by the likelihood of the evidence given the state of nature, and then divide by the marginal probability of the evidence. The resulting probability represents the updated probability of the state of nature, given the observed evidence or indicator.

Therefore,

The probability of the states of nature, after use of Bayes' theorem to adjust the prior probabilities based on given indicator information, is called b. posterior probability

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Axiomatic semantics, a branch of formal semantics, is based on mathematical logic. It provides a formal framework for defining the behavior and meaning of programming languages or formal systems.

Mathematical logic serves as the foundation for axiomatic semantics, offering tools and methods to define and reason about formal systems. It encompasses propositional and predicate logic, set theory, and proof theory. In axiomatic semantics, mathematical logic is used to define syntax, semantics, and proof systems, allowing for precise specifications of program behavior and correctness.

While other branches of mathematics such as set theory and calculus may be utilized in defining underlying structures and functions, the core principles and techniques of axiomatic semantics are rooted in mathematical logic. This logical framework enables rigorous reasoning about program properties and supports the verification and analysis of programs and systems.

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The final amount is higher than the principal amount because of the effect of Compounding interest. The interest is calculated monthly and added to the principal, resulting in a higher amount at the end of the term.

We are given:

Principal amount (P) = $5000

Rate of interest (r) = 9% per annum

Compounding frequency (n) = 12 (monthly)

Time period (t) = 3 years

Using the formula for compound interest:

A = P(1 + r/n)^(nt)

Substituting the given values, we get:

A = $5000(1 + 0.09/12)^(12*3)

A = $5000(1.0075)^36

A = $6817.60

Therefore, Peter owes $6817.60 at the end of 3 years.

the final amount is higher than the principal amount because of the effect of compounding interest. The interest is calculated monthly and added to the principal, resulting in a higher amount at the end of the term.

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The experimental probability that Sue will hit the bullseye on her next toss is 2/7.

We have,

The proportion of outcomes where a specific event occurs in all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

Here, we have

Given: Sue is playing darts. So far, she has hit the bullseye 4 times and missed the bullseye 10 times.

We have to find the experimental probability that Sue will hit the bullseye on her next toss.

experimental probability = 4/(4+10) = 4/14 = 2/7

The next toss = P = 2/7

Hence,  the experimental probability that Sue will hit the bullseye on her next toss is 2/7.

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complete question:

Sue is playing darts. So far, she has hit the bullseye 4 times and missed the bullseye 10 times. What is the experimental probability that Sue will hit the bullseye on her next toss?

The percent of the days in April that it rains is 66.67%.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 2/3.

A percent is the value of a number out of 100. In order to convert a value to percent, multiply by 100.

Percent of the days that it rains = ( number of days it rains / total number of days) x 100

(2/3) x 100 = 66.67%

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The margin of error for the 95% confidence interval is given as follows:

M = $321.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 86 - 1 = 85 df, is t = 1.9883.

The parameters are given as follows:

[tex]\overline{x} = 3600, s = 1500, n = 86[/tex]

Hence the margin of error is obtained as follows:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

[tex]M = 1.9833 \times \frac{1500}{\sqrt{86}}[/tex]

M = $321.

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The minimum order of the Taylor polynomial centred at O for cos x required to approximate cos (-0.85) with an absolute error no greater than 10-4 is 5.

The Taylor series for cos x centred at O is given by:

cos x = 1 - x^2/2! + x^4/4! - x^6/6! + ...

The nth-order Taylor polynomial for cos x centred at O is given by the first n terms of the Taylor series. We want to find the minimum n such that the absolute error between cos (-0.85) and the nth-order Taylor polynomial is no greater than 10-4.

The error term for the nth-order Taylor polynomial is given by:

Rn(x) = cos (c) * xn+1 / (n+1)!

where c is some value between 0 and x.

To find the minimum n, we need to find the value of n such that the error term is no greater than 10-4 for x = -0.85.

Substituting x = -0.85 into the error term and using the fact that |cos (c)| <= 1, we have:

|Rn(-0.85)| <= |(-0.85)^(n+1) / (n+1)!|

We want to find the minimum n such that the right-hand side is no greater than 10-4.

We can use a computer or calculator to find that n = 5 is the smallest integer that satisfies this condition. Therefore, the minimum order of the Taylor polynomial centred at O for cos x required to approximate cos (-0.85) with an absolute error no greater than 10-4 is 5.

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The correct function for the graph of dotted line is,

⇒ y = -  (x - 2)² + 3

We have to given that;

The function f (x) = x² is shown in image.

Here, The dotted graph is translation of f (x) = x² by 3 units up, 2 units right and jus opposite to f (x) = x²

Hence, The correct function for the graph of dotted line is,

⇒ y = -  (x - 2)² + 3

Thus, After translation, The correct function for the graph of dotted line is,

⇒ y = -  (x - 2)² + 3

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The probability of exactly 1 seed not growing is 31.36%. we can use the binomial probability formula, which is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k). P(X=k) is the probability of getting k successes in n trials n is the number of trials

k is the number of successes p is the probability of success in each trial.

To calculate the probability of exactly 1 failure, we can use the binomial probability formula, which is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

P(X=k) is the probability of getting k successes in n trials

n is the number of trials

k is the number of successes

p is the probability of success in each trial

(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items

In this case, n=6, k=1, p=0.65, and (n choose k) = 6. Plugging these values into the formula, we get:

P(X=1) = (6 choose 1) * 0.65^1 * (1-0.65)^(6-1) = 6 * 0.65 * 0.35^5 = 0.3136

Therefore, the probability of exactly 1 seed not growing is 31.36%.

In this case, the probability of getting exactly 1 failure in 6 trials, where the probability of success is 0.65. We use the binomial coefficient to count the number of ways to choose 1 item (the failure) from a set of 6 items (the seeds). We then multiply this by the probability of getting 1 failure and 5 successes, which is given by the formula p^k * (1-p)^(n-k), where p is the probability of success and k and n-k represent the number of successes and failures, respectively. Finally, we calculate the probability of exactly 1 failure by multiplying the binomial coefficient and the probability of getting 1 failure and 5 successes.

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Answer:

median

Step-by-step explanation:

49+45=94

94÷2=47

Answer:

The Median is : 36

The Mode is : Undefined

Step-by-step explanation:

    To find the median of a set of numbers, we need to arrange the numbers in order from least to greatest (or greatest to least) and then identify the middle number. If there is an even number of values, we take the average of the two middle numbers.

First, let's arrange the given numbers in ascending order:

13, 16, 31, 41, 45, 49

    We have six numbers in this set, and since there is an even number of values, we need to take the average of the two middle numbers, which are 31 and 41.

Therefore, the median of the given set of numbers is:

(31 + 41)/2 = 72/2 = 36

----------------------------------------------------------------------------------------------------------

    To find the mode of a set of numbers, we look for the number that appears most frequently. In the given set of numbers:

41, 13, 49, 45, 31, 16

    None of the numbers appear more than once, so there is no mode in this set of numbers.

    Therefore, the mode of this set of numbers is undefined or there is no mode.