2. Evaluate f(3) for f(x) = 2x - 9

The number of 2 letter codes that can be formed is 6 with no letter repeated using Permutation.

A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already sorted, or arranging its members into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

A permutation is a combination and an ordered arrangement of possible outcomes. For instance, there are 5 chairs, and 3 people should occupy them. There are five different methods to seat the first person, four ways to sit the person after them, and three ways to seat the third. As a result, we multiply the alternatives at our disposal to get the total number of configurations for seating 3 people in 5 seats. 5 4 3 are the methods we carry it out. It can be done in 60 different ways. You may write 5 4 3 as (5!) / (2!) (or) (5!) / (5 - 3), as you can see. .

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

The first 3 letters of alphabet are a, b and c

The number of 2 letter codes that can be formed is 3*2 = 6 with no letter repeated.

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By reading the question, note that we want to describe the fact that a polynomial functions is symmetric about the y-axis. By symmetric, it means that the y-axis acts like a "mirror". That is, the right side of the graph looks exactly the same as the one on the left. This means that if we take one value for x, then the value of f(x) should be the same as if we take -x and calculate f(-x).

So

if f(x)=f(-x), then the graph of the polynomial function is symmetric about the y-axis.

That is the second option is the correct one.

Answer:

70 +60muinte= 13

Step-by-step explanation:

so that the ans

In h hours you will go 70h far from the original position and domain of the function is the amount of hours you drive option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is:

Driving on the highway, you can safely drive 70 miles per hour. “How far can you drive in ‘h’ hours?” What is the domain of the function which defines this situation?

A.)The amount of gas you use.

B.) 70.

C.) The amount of hours you drive.

D.)The distance you drive

We have:

Driving on the highway, you can safely drive 70 miles per hour.

The speed of the vehicle = 70 miles per hour

As we know,

Distance = speed×time

1 hour → 70 miles

h hour → D miles

D(t) = 70h

The above expression represents the situation.

Thus, in h hours you will go 70h far from the original position and domain of the function is the amount of hours you drive option (C) is correct.

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Answer:

42 cents per pound

Step-by-step explanation:

to find the price for 1 pound, divide money with weight

price of 1 pound

\( = 5 \div 12 \\ 0.4166 \\ 0.42\)

42 cents approximately

Answer:

see explanation

Step-by-step explanation:

Calculate the slopes between pairs of the 3 points using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 9, 3) and (x₂, y₂ ) = (- 3, 9)

m = \(\frac{9-3}{-3-(-9)}\) = \(\frac{6}{-3+9}\) = \(\frac{6}{6}\) = 1

Repeat with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (- 3, 9)

m = \(\frac{9-1}{-3-5}\) = \(\frac{8}{-8}\) = - 1

If lines are perpendicular then the product of their slopes = - 1 , then

1 × - 1 = -1

Thus there is a right angle between the 2 lines

Then triangle is right- angled

Answer:

1st option

Step-by-step explanation:

Consider the coordinates of F and F'

F (- 3, 4 ) and F' (- 1, 3 )

To go from - 3 → - 1 in the x- directions , means adding 2

To go from 4 → 3 in the y- direction means subtracting 1

Then translation rule is

(x, y ) → (x + 2, y - 1 )

Answer:

10 small bows; 8 large bows

Step-by-step explanation:

Let x = number of small bows.

Let y = number of large bows.

x + y = 18;

3x + 5y = 70

      -3x - 3y = -54

  +   3x + 5y = 70

  -----------------------

               2y = 16

y = 8

x + y = 18

x + 8 = 18

x = 10

Answer: 10 small bows; 8 large bows

Answer:

\(V_{cone} =65.94\: cm^3\)

Step-by-step explanation:

a) ACME's total money flow over the interval from t=0 years to t=20 years is $14,000. b) this integral, we need to use techniques like integration by parts. c) The cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

(a) To find ACME's total money flow over the interval from t=0 years to t=20 years, we need to calculate the definite integral of the income flow function f(t) from t=0 to t=20:

Total money flow = ∫(500+40t) dt (from 0 to 20)

To evaluate this integral, we can apply the power rule of integration:

Total money flow = [500t + 20t^2/2] (from 0 to 20)

               = [500(20) + 20(20^2)/2] - [500(0) + 20(0^2)/2]

               = [10000 + 4000] - [0 + 0]

               = 14000

Therefore, ACME's total money flow over the interval from t=0 years to t=20 years is $14,000.

(b) To find the present value of ACME's money flow over the same interval, we need to discount the future cash flows by an appropriate discount rate. Let's assume the discount rate is r%.

Present value = ∫(500+40t)e^(-rt) dt (from 0 to 20)

To evaluate this integral, we need to use techniques like integration by parts or substitution, depending on the value of r. Please provide the value of r so that we can proceed with the calculation.

(c) The accumulated amount of ACME's money flow over the same interval represents the sum of all the money flows received at each point in time. It can be calculated as the definite integral of the income flow function from t=0 to t=20:

Accumulated amount = ∫(500+40t) dt (from 0 to 20)

Using the same integration technique as in part (a), we find:

Accumulated amount = [500t + 20t^2/2] (from 0 to 20)

                  = 14000

Therefore, the accumulated amount of ACME's money flow over the interval from t=0 years to t=20 years is $14,000.

(d) To find the present value of ACME's money flow assuming the money flows forever, we need to consider the concept of perpetuity. A perpetuity represents a constant cash flow received indefinitely into the future.

The present value of a perpetuity can be calculated using the formula:

Present value = Cash flow / Discount rate

In this case, the cash flow is the income flow function f(t) = 500 + 40t, and the discount rate is r%.

Present value = (500 + 40t) / r

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The question is:

ACME Exploding Faucets' income flows at the rate f(t) = 500 + 40t

(a) (2 pts) Find ACME's total money flow over the interval from t = 0 years to t = 20 (b) (2 pts) Find the present value of ACME's money flow over the same interval. (c) (1pt) Find the accumulated amount of ACME's money flow over the same interval. (d) (2 pts) Find the present value of ACME's money flow, assuming that the money flows forever. years.

For full (or any) credit, show your work and explain your reasoning, briefly

Answer:

The last 4th one is correct

Answer:

The answer would be 4/11

As the sample size grows, the distribution of the sampled means becomes normally distributed option (C) is correct.

With simple random sampling, each component of the population has an equal chance of being selected for the sample.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

Suppose a simple random sample of size n is obtained from a population whose distribution is skewed right.

As we know, the distribution of sample means will be normally distributed even if the individual samples do not, according to the Central Limit Theorem, if the mean values for increasing sample sizes are determined.

Thus, as the sample size grows, the distribution of the sampled means becomes normally distributed.

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Normal probability distribution is applied to a continuous random variable. The correct option is D.

The normal probability distribution, also known as the Gaussian distribution, is a probability distribution that is commonly used in statistics and probability theory. It is a continuous probability distribution that is often used to model the behavior of a wide range of variables, such as physical measurements like height, weight, and temperature.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). It is a bell-shaped curve that is symmetrical around the mean, with the highest point of the curve being located at the mean. The standard deviation determines the width of the curve, and 68% of the data falls within one standard deviation of the mean, while 95% falls within two standard deviations.

The normal distribution is widely used in statistical inference and hypothesis testing, as many test statistics are approximately normally distributed under certain conditions. It is also used in modeling various phenomena, including financial markets, population growth, and natural phenomena like earthquakes and weather patterns.

Overall, the normal probability distribution is a powerful tool for modeling and analyzing a wide range of continuous random variables in a variety of fields.

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Step-by-step explanation:

Can you take picture I don't understand the given

Step-by-step explanation:

Increasing linear functions are equations of the form y = mx + c, where m > 0.

Therefore y = -0.5x + 0.5 is not increasing.

We have the following line slopes:

The slopes in increasing order

are 0.5, 0.75, 4/3, 1.5 and 2.5 respectively.

Hence we have the answers for the boxes starting from the bottom-up:

Answer:

 D, F, E, C, A

The function has an average rate of change of -1.

To find the average rate of change of a function, we can use the formula:

Average Rate of Change = (Change in y) / (Change in x)

Using the data provided in the table, we can calculate the average rate of change between each pair of consecutive points. Let's calculate it for each pair:

Between (-2, 7) and (-1, 6):

Change in y = 6 - 7 = -1

Change in x = -1 - (-2) = 1

Average Rate of Change = (-1) / (1) = -1

Between (-1, 6) and (0, 5):

Change in y = 5 - 6 = -1

Change in x = 0 - (-1) = 1

Average Rate of Change = (-1) / (1) = -1

Between (0, 5) and (1, 4):

Change in y = 4 - 5 = -1

Change in x = 1 - 0 = 1

Average Rate of Change = (-1) / (1) = -1

From the calculations, we can see that the function has a constant average rate of change of -1 between any two consecutive points in the table.

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Answer:

x=12, but if x2 is an exponent, x=1+ the square root of 17.

Step-by-step explanation:

Answer:

0.466

Step-by-step explanation:

Set up the equation 1.694 - 1.228 to find how much longer the blue ribbon is than the red ribbon. The answer is 0.466

Answer:

x=13/3

Step-by-step explanation:

Answer:
24. \(\frac{145}{100}\)=\(\frac{B}{11}\) and the answer is 16 people

25. 80 people

26. Type AB

Step-by-step explanation:

24. Putting 145 donors over 100% is equal to B over 11% because you are trying to find how many donors have type B blood out of 145. 100% is all the people who donated blood and 11% is how many people had type B blood.

\(\frac{145}{100}\)=\(\frac{B}{11}\)

You can solve this as well by cross-multiplying.

Then, you get:

319=20x and divide by 20 on each side. (I simplified 145/100 to 29/20)

x=15.95 then you round to 16.

25. Add up the percentage of people who do not have type O blood.
40%+11%+4%=55%. Multiply 145x55%=79.75 (round up) about 80 people.

26. You can use common sense here. The smallest percentage definitely has less than 10 donors. But to prove it just multiply 145x4%=5.8 (rounds to 6). 10>6 so Type AB

Answer:

two tens and five ones

Step-by-step explanation:

rename the place values then put them together

Answer:

Five fives

Step-by-step explanation:

5 times 5 is 25.

Hope this helped!

Answer:

5 × 3.25 (3 1/4)=16.25 (16 1/4)

Step-by-step explanation:

If each batch requires 3 1/4 cups, and she bakes it repeatedly 5 times, then you multiply 3 1/4 by 5 to get 16 1/4.

The answer is 16 1/4 cups of flour she will use.

Answer:

To find out how much flour Kristen used in total, we can start by multiplying the amount of flour per batch by the number of batches.

First, we need to convert the mixed number 3 1/4 to an improper fraction, which is 13/4.

So, the amount of flour per batch is 13/4 cups.

To find out how much flour Kristen used in total for 5 batches of cookies, we can multiply the amount of flour per batch by the number of batches:

13/4 cups per batch x 5 batches = 65/4 cups

We can simplify this fraction by dividing both the numerator and denominator by 5, which gives us:

65/4 ÷ 5/1 = 13/4 ÷ 1/1 = 13/4 cups

Therefore, Kristen used 13 and 1/4 cups of flour in total for 5 batches of cookies.

Answer:

a:

volume- 162

width- 5

height- 4

length- 5

b:

volume- 150.52

height- 5

length- 1

width- 2.5

Answer:

a:

volume- 162

width- 5

height- 4

length- 5:

Triangle KVM is similar to triangle BVG because angle M = angle G = 90° and angle V is common to both triangles.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

For two triangles to be similar, the corresponding angles must be congruent i.e equal.. Also the ratio of the corresponding sides of similar triangles are equal.

angle M and G are both 90° , this means they are equal.

angle KVM = BVG

therefore angle K = angle B

Since all the corresponding angles are equal, we can say triangle KVM is similar to triangle BVG

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Answer:

$104.14

Step-by-step explanation:

5.2% of $98.99

= $5.15

Price of the shoes + tax

= $98.99 + $5.15

= $104.14