Determine whether f is even, odd, or neither.
65. f(x) х x2 + 1 х 67. f(x) X + 1 69. f(x) = 1 + 3x2 - x4 X

Answer:

Step-by-step explanation:

Define Variables:

Let p= the price of each peach

Let m=the price of each mango

One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangos cost 6m. The total cost 5p+6m equals $17.75:

5p+6m=17.75

Likewise, if 2 peaches and 3 mangos cost $8, then:

2p+3m=8

Write System of Equations:

5p+6m=17.75

2p+3m=8

System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.

Let p= the price of each peach

Let m=the price of each mango

One peach costs $p, so 5 peaches cost 5p. One mango costs $m, so 6 mangoes cost 6m. The total cost 5p+6m equals $17.75:

5p+6m=17.75

Likewise, if 2 peaches and 3 mangoes cost $8, then:

2p+3m=8

System of Equations:

5p+6m=17.75

2p+3m=8

Therefore System of equations that could be used to determine the price of each peach and the price of each mango is 5p + 6m = 17.75 and 2p + 3m = 8.

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Answer:

Its height would be 7 meters.

Overall, a bar graph would effectively convey the color information of fish found in Lake Powell by visually representing the different color categories and their corresponding frequencies or proportions.

The best option would depend on the specific data and purpose of the visualization. However, if the goal is to represent the color categories of fish in Lake Powell, a bar graph could be a suitable choice. Each bar would represent a color category, and the height of the bar could represent the frequency or proportion of fish in that color category.

By assigning each color category to a bar and varying the height of each bar based on the frequency or proportion of fish in that category, the bar graph provides a clear and visual representation of the distribution of fish colors in Lake Powell.

This allows viewers to easily compare the prevalence of different color categories, identify any dominant or rare colors, and gain insights into the overall color composition of the fish population in the lake.

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Answer:

a and d

Step-by-step explanation:

these simplify to .77 for A and .81 for B

True. Small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.

Small p-values indicate that the observed sample data provides strong evidence against the null hypothesis. The p-value is a measure of the strength of evidence against the null hypothesis in a hypothesis test. It represents the probability of observing the obtained sample data, or more extreme data, if the null hypothesis is true.

When the p-value is small (typically less than a predetermined significance level, such as 0.05), it suggests that the observed sample data is unlikely to have occurred by chance under the assumption of the null hypothesis. In other words, a small p-value indicates that the observed data is inconsistent with the null hypothesis.

Conversely, when the p-value is large (greater than the significance level), it suggests that the observed sample data is likely to occur by chance even if the null hypothesis is true. In such cases, there is not enough evidence to reject the null hypothesis. Therefore, small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.

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In fractional notation, the smallest number is 45/2

To find the smallest number for which ∑=11≥8, we need to use the formula for the sum of consecutive integers, which is:

sum = (n/2)(first + last)

where n is the number of terms, first is the first term, and last is the last term.

In this case, we want the sum to be 11 and we know that there are at least 8 terms. So we can set up the following inequality:

11 = (n/2)(first + last) ≥ 8

Simplifying this inequality, we get:

22/3 ≤ n(first + last) ≤ 44/5

Now, since we want to find the smallest number, we can start by assuming that there are 8 terms. Then, we need to find two numbers that add up to a sum of 11. The easiest way to do this is to start with the smallest possible numbers and work our way up. So we can try:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

This sum is too large, so we need to add a smaller number and subtract a larger number to get closer to 11. We can try:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 9 = 37

This sum is still too large, so we can try:

1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 = 38

This sum is still too large, so we can try:

1 + 2 + 3 + 4 + 5 + 7 + 8 + 9 = 39

This sum is still too large, so we can try:

1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 = 40

This sum is still too large, so we can try:

1 + 2 + 3 + 5 + 6 + 7 + 8 + 9 = 41

This sum is still too large, so we can try:

1 + 2 + 4 + 5 + 6 + 7 + 8 + 9 = 42

This sum is still too large, so we can try:

1 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 43

This sum is within the range we want, so the smallest number for which ∑=11≥8 is 43.

In symbolic notation, we can write this as:

n = 8, first = 1, last = 10

sum = (n/2)(first + last) = (8/2)(1 + 10) = 44

Therefore, the smallest number that works is n = 9, which gives us:

n = 9, first = 1, last = 9

sum = (n/2)(first + last) = (9/2)(1 + 9) = 45/2

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Let the width of the rectangle be 'w'

According to the question length of the rectangle (l) is three feet more than twice it's width;

\( \longrightarrow \) l = (2w + 3) ft

Perimeter of rectangle = 78 ft

Formula of perimeter of rectangle = 2(Length + Width)

So,

\( \rm \implies 2(Length + Width) = 78 \\ \\ \rm \implies 2(2w + 3 + w) = 78 \\ \\ \rm \implies 2(3w + 3) = 78 \\ \\ \rm \implies 2 \times 3(w + 1) = 78 \\ \\ \rm \implies 6(w + 1) = 78 \\ \\ \rm \implies w + 1 = \dfrac{78}{6} \\ \\ \rm \implies w + 1 = 13 \\ \\ \rm \implies w = 13 - 1 \\ \\ \rm \implies w = 12 \: ft\)

\( \therefore \) Width of the rectangle (w) = 12 ft

Answer:

for part A the answer is B and for part B I think the answer is B too.

Answer:

5 hours

Step-by-step explanation:

100t + 80t = 900

First, you can add 100t to 80t because they are both like terms.

100t + 80t = 900

180t = 900

Now you multiply,

when t = 2,

180*2 = 360

when t = 4,

180*4 = 720

When t = 5,

180*5 = 900

So, it will take them 5 hours to make 900 papers

Answer:

  x = 7

Step-by-step explanation:

The integer values of x that satisfy |x| < 9 are ...

  {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7. 8}

Of these values, the only one listed as an answer choice is ...

  x = 7

__

Additional comment

The expression |x| means "the absolute value of x". It is the value of x with the sign made positive. That is |-10| = 10, a number greater than 9. Of course, |13| = 13, also a number greater than 9.

During the sale, the stereo system was sold for 30% less than its original price of $710, so the discount amount was:

0.30 x $710 = $213

Therefore, the sale price of the stereo system was:

$710 - $213 = $497

After the sale, the discounted price of $497 was marked up by 30%. The markup amount is:

0.30 x $497 = $149.10

So the final price of the stereo system after the markup is:

$497 + $149.10 = $646.10

Therefore, the price of the stereo system after the markup is $646.10.

Answer:

from the question the answer is 5mn=7

There are a total of 25⁸ ways to select an unordered group of eight numbers between 1 and 25 inclusive with repetition. This is because for each of the eight numbers, there are 25 options to choose from, and the choices are independent of each other.

To find the fraction of these ways in which the sum of the numbers is even, we need to use the principle of inclusion and exclusion. First, we count the total number of ways in which the sum of the numbers is odd. This is equal to the number of ways in which an odd number of the eight numbers are odd, and the rest are even. There are 12 odd numbers and 13 even numbers between 1 and 25 inclusive.

Using the binomial coefficient, the number of ways in which the sum of the numbers is odd is:

C(8,1) * 12¹* 13⁷ + C(8,3) * 12³ * 13⁵ + C(8,5) * 12⁵ * 13³ + C(8,7) * 12⁷ * 13¹ = 9,676,454,400

Therefore, the number of ways in which the sum of the numbers is even is:

25^8 - 9,676,454,400 = 6,400,821,094,400

And the fraction of these ways is:

6,400,821,094,400 / 25⁸ = 0.5351

So, approximately 53.51% of the ways to select an unordered group of eight numbers between 1 and 25 inclusive with repetition have an even sum.

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Answer:

= 5

Step-by-step explanation:

1) Subtract the numbers

  10 - 5 = 5

2) Apply the absolute rule

  IaI = a, a \(\geq\)0

3) Final Answer

   = 5

Answer:

42 3/4 ft²

Step-by-step explanation:

I don't know how to put this in words-

The value of "a" is approximately 1.83 given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive.

We are given that the absolute value of the difference between the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive. We need to find the value of "a".

Let the two roots of the equation be r1 and r2, where r1 is not equal to r2. Then, we have:

|r1 - r2| = √(61) / 3

The sum of the roots of the quadratic equation is given by r1 + r2 = -5 / a, and the product of the roots is given by r1 × r2 = -3 / a.

We can express the difference between the roots in terms of the sum and product of the roots as follows:

r1 - r2 = √((r1 + r2)² - 4r1r2)

Substituting the expressions we obtained earlier, we have:

r1 - r2 = √(((-5 / a)²) + (4 × (3 / a)))

Simplifying, we get:

r1 - r2 = √((25 / a²) + (12 / a))

Taking the absolute value of both sides, we get:

|r1 - r2| = √((25 / a²) + (12 / a))

Comparing this with the given expression |r1 - r2| = √(61) / 3, we get:

√((25 / a²) + (12 / a)) = √(61) / 3

Squaring both sides and simplifying, we get:

25 / a² + 12 / a - 61 / 9 = 0

Multiplying both sides by 9a², we get:

225 + 108a - 61a² = 0

Solving this quadratic equation for "a", we get:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61)

Since "a" must be positive, we take the positive root:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61) ≈ 1.83

Therefore, the value of "a" is approximately 1.83.

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The question is -

Given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive, what is the value of "a"?

Answer:

737.48 ft^2

Step-by-step explanation:

20.6*35.8

The required probability for the parts which are examined for defects are ;

1. Probability of both the parts are good is equal to 0.375.

2. Probability represents exactly one part has major defect is 0.2333.

Total number of parts to be examined for defects = 16

Number of good parts = 10

Number of parts with minor defects = 4

Number of parts with major defects = 2

Number of parts to be chosen at random without replacement = 2

Total number of outcomes = ¹⁶C₂

                                             = (16!) / ( 16 - 2 )!2!

                                             = 120

1. Probability of both the parts to be good

Number of favourable outcomes = ¹⁰C₂

                                                        = 10! / (8!)(2!)

                                                        = 45

Required Probability = 45 / 120

                                   = 0.375

2. Probability of exactly one major defect

Number of favourable outcomes= ²C₁ × ¹⁴C₁

                                                      = 2 × 14

                                                      = 28

Required Probability = 28/ 120

                                   = 0.2333

Therefore, the probability of both are good is 0.375 and probability of exactly one major defect is 0.2333.

The above question is incomplete, the complete question is:

'16 parts are examined for defects. It is found that 10 are good, 4 have minor defects, and 2 have major defects. Two parts are chosen at random from the 16 without replacement; that is; the first part chosen is not returned to the mix before the second part is chosen:

1. What is the probability that both parts are good?

2. What is the probability that exactly one part has major defect?'

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Answer:

the answer is C

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

The area of 1 face is s^2

The area of 6 faces is 6s^2

6s^2 = 433.5                 Divide by 6

s^2 = 433.5 / 6

s^2 = 72.25                   Take the square root of both sides

sqrt(s^2) = sqrt(72.25)

s = 8.5

Normally you would find the volume of parallelepiped by using L * W * H

Since L W and H are all equal in a cube, the volume = s^3

S^3 = 8.5^3 = 614.125

Answer:

314

Step-by-step explanation:

This is because the area is r^2*3.14

Answer:

200 and 546

Step-by-step explanation:

dejar a = Primer periodo (first term)

dejar d = Diferencia común (common difference)

dejar 100th término = T100

dejar 273 término = T 273

utilizando

Tn = a + (n - 1)d

T100 = 2 + (100 - 1) 2

= 2 + 99 ×2

= 2 + 198

= 200

T273 = 2 + (273 - 1) 2

= 2 + 272 × 2

= 2 + 544

= 546

To interpret scores on it, he is presently administering the test to a representative sample of all golfers. Dr. zimmer is clearly in the process of validating their test.

Validation refers to the process of evaluating the accuracy and reliability of a test or measurement instrument. When Dr. Zimmer is administering the test to a representative sample of golfers, he is collecting data that will allow him to determine the validity of the test and its ability to accurately measure golfers' knowledge of the sport's history.

This process is important for ensuring that the test results are meaningful and can be used to make accurate inferences about the population being studied.

By comparing the scores on the test to other measures of golfers' knowledge, such as interviews or other tests, Dr. Zimmer can determine the test's ability to accurately measure the construct it is intended to measure. Therefore, Dr. Zimmer is in the process of validating his test by collecting data and evaluating its accuracy and reliability.

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We're adding n and m onto k to get P. Undo these operations to isolate k. So we subtract m from both sides

P = k+n+m

P-m = k+n+m-m

P-m = k+n

and we subtract n from both sides

P-m = k+n

P-m-n = k+n-n

P-m-n = k

Answer:

Please check explanations

Step-by-step explanation:

When we dilate a particular figure, we are simply increasing the dimensions of its sides

By dilating the pre-image by a factor of 3, we are simply increasing the dimensions of it by a multiple of 3

so say for example, the base of the pre-image has a measure of 4 ft, the base of the image which is the pre-image dilated by a scale factor of 3 will be 4 ft * 3 = 12 ft

What this mean is that we have succeeded in tripling the dimension of the pre-image to give the dimension of the image

The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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No, it is not reasonable to assume that the wage rate of the ethnic group is equivalent to that of a random sample of workers from those employed in the service industry.

What is standard deviations?
Standard deviation is a measure of how spread out a set of data is. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. Standard deviation is a measure of how much the individual observations in a data set vary from the mean. A low standard deviation indicates that most of the values are very close to the mean, while a high standard deviation indicates that the values are more spread out.

The average wage of the ethnic group is only $6.90 per hour, which is significantly lower than the average wage of $7.00 per hour for the entire industry. Even though the standard deviation of the industry is $.50, this does not account for the difference in wages between the ethnic group and the rest of the industry. Therefore, it is not reasonable to assume that the wage rate of the ethnic group is equivalent to that of a random sample of workers from those employed in the service industry.

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Answer:

335 jours (335 days)

Step-by-step explanation:

1675 / 5 = 335

Answer:

x=3
y=4

Step-by-step explanation:

y=3x-9
5x+4y=32

You substitute what y is into the equation:
5x + 4(3x - 9) = 32
5x + 12x - 36 = 32
17x - 36 = 32
17x = 68
x = 4
Now you substitute x into y:
y = 3x - 9
12 - 9 = 3
y = 3