Find the average rate of change over the given interval:
F(x)=3 to the power of x, [1, 4]
3
26
78
81

Answer:

\((\frac{-3}{2}, 5)\)

Step-by-step explanation:

To find a midpoint you would use the midpoint formula.

The midpoint formula is \((x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)

By using the 2 points you have you can plug it into the formula.

So then you would get\((x_m, y_m) = (\frac{-6+3}{2}, \frac{3+7}{2})\) which is equal to \((\frac{-3}{2}, 5)\)

We have this expression:

We need to do the following steps to solve the equation for t:

Then, t is the same as:

Then, the answer is (A - p)/pr.

Answer: Yes, you will make it on time

Step-by-step explanation:

The distance from San Antonio to Dallas is 274 miles

We take 274 divided by 65 = 4.2 hours or 4 hours and 12 minutes to get there at the speed of 65 mph

We have 4 1/2 hours to get there

4 1/2 hours = 4 hours 30 minutes

So, you will make it on time!

Answer:First we need to simplify the left side of the equation:

12,5(3x-1)+132,4 = 12,5*3x - 12,5 + 132,4 = 37,5x + 120,9

Now we need to simplify the right side of the equation:

2,8-4x = 2,8 - 4x

Now we have to set the two sides equal:

37,5x + 120,9 = 2,8 - 4x

Now we have to move all the x terms to one side of the equation:

37,5x - 4x + 120,9 = 2,8

Next step is to combine like terms:

33,5x + 120,9 = 2,8

Subtracting 120.9 from both sides of the equation:

33,5x = -118.1

Dividing both sides by 33,5

x = -3,54

So the solution of the equation is x = -3,54

Step-by-step explanation:

The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.

According to the statement

we have given that the 3 integers are in an arithmetic progression and their product is prime.

And we have to find the sum of their squares.

So, let the three integers which is A, B, C.

And according to the arithmetic progression the

A = x and B = x-d, C = x-2d. here d is the common difference and x is a 1st term.

So, there product is prime

then

(x) (x-d) (x-2d) = c -(1)

And

their sum of square is

(x)^2 + (x-d)^2 + (x-2d)^2 - (2)

So, The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.

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Answer:

p=1,2,3,4,5

or

p=6,7 I thank so

a) X'Y' + X'Y + XY simplifies to X' + Y.

b) A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the functions:

a) Complement is W' + X' + YZ.

b) Complement is (A' + B + C)(A'B' + C' + A'B).

a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:

X'Y' + X'Y + XY

= Y'(X' + X) + XY(Distributive Law)

= Y' + XY(X + X' = 1)

= X' + Y(Commutative Law)

Therefore, X'Y' + X'Y + XY simplifies to X' + Y.

b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:

A'BC' + ABC' + BC'D

= BC'(A' + A) + BC'D   (Distributive Law)

= BC' + BC'D(A + A' = 1)

= BC'(BC' + BC'D = BC' + BC'(1) = BC')

Hence, A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the given functions:

a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.

b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).

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Evaluating all possible values of a variable in a model is called a sensitivity analysis.

A sensitivity analysis is a technique used to assess the impact of changes in the values of input variables on the output or outcome of a model or system. It involves systematically varying the values of the variables within a defined range and observing the corresponding changes in the model's output.

The purpose of a sensitivity analysis is to understand how sensitive the model is to changes in the input variables and to identify which variables have the most significant influence on the model's results.

During a sensitivity analysis, different scenarios are created by varying one or more input variables while keeping others constant. By examining the resulting changes in the model's output, analysts can gain insights into the relationships and dependencies between the variables and assess the robustness of the model's predictions or decisions.

Sensitivity analysis helps in understanding the potential risks, uncertainties, and limitations associated with the model, and can aid in decision-making and improving the model's performance by identifying critical variables that need to be carefully monitored or controlled.

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Answer:

im pretty sure its A bc he just got a 5.0 rating and a thanks also i just got a 100% so thx to you for letting me get a try and thx to you above with a 5.0 rating

Step-by-step explanation:

According to the 4:3 ratio, that would mean that there were 32 seniors on the team at the start of summer training.

The mix of juniors and seniors on the team is a great combination that allows the younger players to learn from those with more experience. With the seniors showing the juniors the ropes, the team will be able to reach its full potential this season.

Overall, the varsity football team is in a great position heading into the upcoming season. With a balanced roster of 48 juniors and 32 seniors, the team is sure to be a strong contender in their division. The juniors and seniors will be a great combination, and the team is sure to benefit from the leadership and guidance of the seniors.

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Option B is the correct answer, The set of correlations which correctly shows the highest to lowest degree of relation is -0.91, +0.83, +0.10, -0.03.

What is correlation?

In statistics, the correlation is a technique used to determine the relationship between the two variables. The correlation's range is from -1 to +1. There are three primary categories of correlation: no correlation, positive correlation, and negative correlation. When the correlation value is zero, there is no association; the correlation value that is closest to zero indicates the weakest degree of relationship.

We must select the set of correlations in the question that accurately displays the highest to the lowest degree of relation.

Option B is the best choice since we must take the absolute value into account in order to determine the relationship's degrees. Here, the absolute values drop from 0.91 to 0.03.

Option A is incorrect since the absolute values decline from 0.91 to 0.03 and then climb to 0.10 in this situation.

Because the absolute values are not listed in decreasing order, Option C is incorrect.

Because the absolute values in this situation are not ordered in decreasing order, Option D is also a incorrect choice.

Therefore, option B, is the correct option.

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Answer:

6040

Step-by-step explanation:

140x31=4340

Add 1700

=6040

Answer:

1. -9 because -9x6= -54, -10 because 5 x -10= -50, and x=1 because -2 x 1= -2

Step-by-step explanation:

Answer:

1. = −9

2. = −10

3. = 1

Step-by-step explanation:

Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

Answer:

924

Step-by-step explanation:

Find the volume of the triangular pyramid to the nearest whole number. In this case its 924

The mean of samples 10, 10, 10, 10, 10, and 16 will be 11.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

In a sample of n = 6, five individuals all have scores of x = 10 and the sixth person has a score of x = 16.

Then the data set will be given below.

10, 10, 10, 10, 10, 16

Then the mean of the data set will be

Mean = (10 + 10 + 10 + 10 + 10 + 16) / 6

Mean = 66/6

Mean = 11

Thus, the mean of the sample will be 11.

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Answer:

11.49

Step-by-step explanation:

If A=8

And C=14 then

Answer:

4/1 = 4

8/1 = 8

Any number divided by 1 is always that number itself.

Answer: Choice C.  p = 250(0.79)^t

Work Shown:

p = a*b^t

p = a*(1+r)^t

p = 250*(1+(-0.21))^t

p = 250(0.79)^t

Note that r = -0.21 is negative to indicate we have exponential decay.

Answer: A quadrilateral with four interior acute angles

Step-by-step explanation:

If you add four angles for quadrilateral = 360 & acute angle is less than 90 degrees so it isn't possible.

Answer:

B. Right angles

Step-by-step explanation:

When perpendicular lines intersect, they create 90° angles (aka right angles)

The probability mass function of x is p(x) = 4/52 * (48/51)^(x-1) * (1/51)^(52-x) for x = 1, 2, ..., 52.

x indicates the number of cards removed

that means

x = 1, 2, ..., 52

The probability of picking an ace is

P(ace) = 4/52

that means:

P(Ace') = 48/51 ----- Cards are selected without replacement

If x Ace is chosen, remaining cards are 52 - x

Using the above as a guide, it looks like this:

For x = 1, 2, ..., 52, PMF = 4/52 * (48/51)^(x-1) * (1/51)^(52-x). 

Probability is the magnitude of the chance (likelihood) of something events will occur. Based on the definition of probability, there are the important things are the magnitude of the opportunity and the event will occur.

The probability that an event will occur is between 0 and with 1. If an event has a chance of happening 0, then this event is definitely not going to happen. If an event has chance will occur 1, then the event will definitely occur. With thus it can be concluded that the smaller the probability of an event (the closer the probability is to 0), the smaller the chance of the event

it will happen.

Conversely, the greater the probability of an event (the closer the probability is to 1), the greater the chance of the event it will happen.

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Answer:

B because it has more even than odd numbers

Step-by-step explanation:

Hope this helps :)

Answer:

gosh darn thats alot of point but its B

Step-by-step explanation:

4323÷2 = 2161.5  X

944÷2 = 472  √

291÷2 = 145.5  X

31÷2 = 15.5   X

Answer:

The answer is 1,200 meters

Step-by-step explanation:

So what I did was find the rate so we want to know how much Sheila can do in just 1 minute first so you would have to do 6,000/ 15 which gives you 400 so he does 400 meters in just 1 minute. So then you would have to multiply 400 by 3 which gives you 1,200, making that your answer.

hope that helped!

Answer: 800 meters

Step-by-step explanation:

We first find the speed of Sheila by the speed equation, which is:

v =d/t

d is the total distance traveled

t is the total time taken

And so, we get:

v = 6000m/ 15min

= 400m/min

Now, we find the distance traveled in 2 minutes by solving for distance in the speed equation, which becomes:

d=v⋅t

Inputting our values, we get:

400m/min ⋅ 2min=800

well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

0.2x + 2.7x - 8.1 = 6.9 + 1.1x

Combine like terms on left side:

0.2x + 2.7x = 2.9x

Now you have:

2.9x -8.1 = 6.9 + 1.1x

Subtract 1.1x from both sides:

1.8x - 8.1 = 6.9

Add 8.1 to both sides:

1.8x = 15

Divide both sides by 1.8:

X = 8.3333 ( round as needed) or as a fraction = 8 and 1/3

Answer:

8.3recurring

Explanation:

0.2x+2.7x =2.9x

rewrite the questions

2.9x-8.1=6.9+1.1x

like terms together. Therefore:

2.9x-1.1x = 1.8x

8.1 will go to the other side of the equal sign. Therefore:

8.1+6.9 = 15

Therefore: 1.8x = 15

x =15/1.8 which is equal to 8.3recurring