What is the domain of the function y= ^3-/ x-1

a) Mean for the first year of the contract: $63,500

The standard deviation for the first year of the contract: $2,000.

b) Mean for the second year of the contract: $65,405.

The standard deviation for the second year of the contract: $60.

We have,

To find the mean and standard deviation for the first year of the contract, we can use the given information and the properties of the normal distribution.

Given:

The mean salary for professors in the previous year = $62,000

Standard deviation in the previous year = $2,000

Raise in the first year = $1,500

Mean for the first year of the contract:

The mean salary for the first year can be obtained by adding the raise to the previous mean:

Mean = Previous Mean + Raise

Mean = $62,000 + $1,500

Mean = $63,500

The standard deviation for the first year of the contract:

Since each professor receives the same raise, the standard deviation remains the same:

Standard Deviation = $2,000

Therefore, for the first year of the contract, the mean salary is $63,500, and the standard deviation remains $2,000.

Now,

In the second year of the contract, each professor receives a 3% raise based on their salary during the first year of the contract.

To find the mean and standard deviation for the second year, we can use the given information and the properties of the normal distribution.

Mean for the second year of the contract:

To calculate the mean for the second year, we need to add a 3% raise to the mean salary of the first year:

Mean = Mean of the first year + (3% * Mean of the first year)

Mean = $63,500 + (0.03 * $63,500)

Mean = $63,500 + $1,905

Mean = $65,405

The standard deviation for the second year of the contract:

Since each professor receives a raise based on their salary from the first year, the standard deviation also increases. To calculate the standard deviation, we multiply the standard deviation from the first year by the percentage increase:

Standard Deviation = Standard Deviation of the first year * (Percentage Increase / 100)

Standard Deviation = $2,000 * (3 / 100)

Standard Deviation = $2,000 * 0.03

Standard Deviation = $60

Therefore, for the second year of the contract, the mean salary is $65,405, and the standard deviation is $60.

Thus,

a) Mean for the first year of the contract: $63,500

The standard deviation for the first year of the contract: $2,000.

b) Mean for the second year of the contract: $65,405.

The standard deviation for the second year of the contract: $60.

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Answer:

1.324

Step-by-step explanation:

Answer:

1.0324

Step-by-step explanation:

This is based on place value see below

1.1111

It goes ones, decimal, tenths, hundredths, thousandths, ten thousandths, and so on.

Answer: There are no choices so unfortunately I can't give you an answer

Step -by-step explanation:

Answer:

10% or 5%

Step-by-step explanation:

By translating (shifting) the graph of f(x) vertically downward by 2 units and right 5 units, the formula for g(x) is equal to g(x) = 2√(x - 5) - 2.

Generally, there are different types of transformation and these include the following:

A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

Since the graph of f(x) is translated (shifted) vertically downward by 2 units and right 5 units, the formula for g(x) would be given by:

Note: f(x) = 2√x

To translate (shift) vertically downward by 2 units, we would subtract 2:

g(x) = 2√x - 2

To shift right by 5 units, we would replace the value of x with (x - 5):

g(x) = 2√(x - 5) - 2

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The limit of the sum (6xi-3)/n as n approaches infinity is 9, which means that as the number of subintervals in the interval [0,3] becomes larger and larger, the sum of the values (6xi-3)/n approaches 9.

The limit is a concept in mathematics that helps us understand what happens as a function or a sequence approaches a certain value.

In this particular problem, we are looking at the limit of a sum of values as the number of subintervals in the interval [0,3] approaches infinity.

The interval [0,3] is divided into n equal subintervals and a number xi is chosen arbitrarily in the ith subinterval. We then look at the sum of the values (6xi-3)/n for all n subintervals.

Mathematically, we can write this sum as:

S = (6xi-3)/n for i = 1, 2, ..., n

And the limit of S as n approaches infinity can be written as:

lim n -> infinity S = lim n -> infinity (6xi-3)/n

Now, we use the concept of a Riemann Sum to evaluate the limit of this sum. A Riemann Sum is a way of approximating the area under a curve by breaking it down into rectangles and summing their areas.

In our case, we can think of the sum S as a Riemann Sum for the function f(x) = 6x-3 over the interval [0,3]. As n approaches infinity, the width of the subintervals approaches 0, and the sum S approaches the definite integral of f(x) over [0,3].

Using the fundamental theorem of calculus, we can find the definite integral of f(x) over [0,3] as:

∫f(x)dx = 6x^2/2 - 3x evaluated from 0 to 3

And this value is 9, so the limit of S as n approaches infinity is 9.

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Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer: 306

Step-by-step explanation:

Each child has 34 stickers and 9 bottles. To find the total number of stickers, we need to multiply the number of stickers per child by the number of children.

34 stickers x 9 children = 306 stickers

So there are 306 stickers in total.

Answer:

THE ANSWER IS 81/16 OR C

The answer to this problem is 1/6.

The share of the pizza each friend will have is 1 / 6.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that three friends equally share 1/2 of a pizza. The fraction of the pizza shared by each friend will be:-

Fraction of pizza = ( 1 / 2 ) x ( 1 / 3 )

Fraction of pizza = ( 1 / 6 )

Therefore, the share of the pizza each friend will have is 1 / 6.

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Answer:

Find the dimensions of a rectangle given that its perimeter is 116

 cm and its length is 1

 cm more than twice its width.

Set up your solution using the variables L

 for the length, W

 for the width, and P

 for the perimeter. 

Part a: Using the definition of perimeter, what is an equation for P

 in terms of L

 and W

.

Part b: You also have to write an equation for L in terms of W

 in terms of W

.

Solve the equations from parts a and b.

Part c: The length is   cm.

Part d: The width is   cm.

Answer:

P=2L+2W

116=2(1+2w)+2(w)

length= 39 cm

width= 19 cm

Step-by-step explanation:

Perimeter: 116 cm                                            116=2(1+2w)+2(w)

                                                                        116=2+4w+2w

l=1+2w                                                              114=6w

____________                                                w=19

|                        |

|                        | w

|___________|

The most appropriate reason for Christie making changes to her budget at the end of every month in terms of smart financial planning is B. She is reviewing her goals and aligning the budget to work toward them.Option B is correct.

Smart financial planning involves regularly evaluating and adjusting one's budget to ensure that it reflects their financial goals and current circumstances. By reviewing her goals, Christie can assess if her budget is still aligned with those goals and make any necessary changes to stay on track.

Life circumstances, such as changes in income, expenses, or financial priorities, may warrant adjustments to the budget. Christie recognizes that her needs may change over time, and by modifying her monthly budget, she can ensure that her financial resources are allocated appropriately to meet her evolving goals.

Regularly revisiting and modifying the budget allows Christie to adapt her financial plans, optimize her spending, and make informed decisions to achieve her financial objectives. Option B is correct.

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The equation representing the story 2 is equivalent to -

3(x + 6) = 24.

Given is are the mathematical word problems as stories.

According to the story 2 -

Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends, and then adds 6 more ounces for each.

Let the amount of juice poured for each friend at the start be {x}. Then, we can write it as {3x}. For six ounce more per friend, the expression will be (6 x 3). Total juice will be equal to -

3x + (6 x 3) = 24

3x + 3(6) = 24

3(x + 6) = 24

Therefore, the equation representing the story 2 is equivalent to -

3(x + 6) = 24.

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Answer:

19, 20, 21, and 22

Step-by-step explanation:

19+20+21+22 = 82

Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.

We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.

Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.

Therefore,  y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.

Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.

Simplifying, we have :3x = $90000 + 75 = $90075.

Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.

Therefore, Jane received $30025 and Lydia received $60000.

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The next three terms in the geometric sequence will be 24, 48 and 96.

We are given a geometric sequence:

3, 6, 12 …

We need to find the next 3 terms of the sequence.

We can see that:

a = initial term of the sequence

a = 3

r = common ratio between the consecutive terms.

r = 6 / 3 = 2

Now, nth term will be represented by:

aₙ = a rⁿ⁻¹

Substituting the values of a and r in the formula, we get that:

aₙ = 3 (2)ⁿ⁻¹

Now, the 4th term will be ( put n = 4)

a₄ = (3) (2)⁴⁻¹

a₄ = (3) (2)³

a₄ = (3) × (8)

a₄ = 24

The 5th term will be: (put n = 5)

a₅ = (3) (2)⁵⁻¹

a₅ = (3) (2)⁴

a₅ = (3) × (16)

a₅ = 48

6th term will be: (put n = 6)

a₆ = (3) (2)⁶⁻¹

a₆ = (3) (2)⁵

a₆ = (3) × (32)

a₆ = 96

Therefore, the next three terms in the geometric sequence will be 24, 48 and 96.

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Your question was incomplete. Please refer the content below:

The first three terms of a geometric sequence are 3, 6, 12. What are the next three terms?

Answer:

the answer is 3/2

Step-by-step explanation:

the formula of the slope is

Answer:

-4/3

Step-by-step explanation:

Take any two points which lie on Line B :

Applying slope formula :

Solution:

Consider the following equation:

Solving for 5p, this is equivalent to:

this is equivalent to:

solving for p, we get:

so that, we can conclude that the correct answer is:

Answer:

5.1

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

32 is the greatest factor for 32 and 64

Answer:

Factors of 64 are 1, 2, 4, 8, 16, 32, 64. There are 7 integers that are factors of 64. The greatest factor of 64 is 64. 4.

What are the Factors of 32? Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.

Greatest common factor (GCF) of 32 and 64 is 32. We will now calculate the prime factors of 32 and 64, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32 and 64.

Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20..

To estimate the value of the vehicle after 4 years, we can use the given equation A = 39500(0.86)^t, where A represents the value of the vehicle and t represents the number of years.

Substituting t = 4 into the equation:

A = 39500(0.86)^4

A ≈ 39500(0.5996)

A ≈ 23726.20

Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20.

This estimation is based on the assumption that the vehicle's value decreases by 14% each year. The equation A = 39500(0.86)^t models the exponential decay of the vehicle's value over time. By raising the decay factor of 0.86 to the power of 4, we account for the 4-year period. The final result suggests that the value of the vehicle would be around $23,726.20 after 4 years of ownership.

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Answer:

$31.04

Step-by-step explanation:

Use the next relationships to convert rectangular coordinates to polar coordinates:

For the given rectangular coordinates:

Answer:

X, process, y

-2, 3(-2), -6

-1, 3(-1), -3

0, 3(0), 0

1, 3(1), 3

2, 3(2), 6

X = -2, -1, 0, 1, 2,

Y = -6, -3, 0, -3, -6

Step-by-step explanation:

Coordinates for the graph: (-2,-6), (-1,-3), (0,0), (1,3), (2,6)

Graph is the image I added onto this.

Solving for Y below:

3(-2)= -6

3(-1)= -3

3(0)= 0

3(1)= 3

3(2)= 6

Hope this helps.

Answer:

X= 24º

Explanation:

A straight line is 180º so, 180º - 151º = 29º - 5º = 24º

The mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

To find the mean number of movies the students saw, you need to calculate the average of the given data. Here are the reported numbers of movies seen by the 6 students: 14, 11, 15, 19, 12, 10.

To calculate the mean, you sum up all the reported numbers and divide by the total number of students. In this case, the total number of students is 6.

So, let's calculate the mean:

(14 + 11 + 15 + 19 + 12 + 10) / 6 = 81 / 6 = 13.5

Therefore, the mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

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Answer:

C

Step-by-step explanation:

By analyzing the graph and the y-intercept, we can conclude that the graphed function is:

f(x) = e^x

In the graph, we can see an exponential growth, such that it intercepts the y-axis at x = 1.

Remember that exponential growth is slow at the beginning and faster as x grows, while a logarithmic increase is fast at the beginning and then becomes slower. That is why we know this is an exponential growth.

Now, notice that when x = 0 we can see that the function intercepts the y-axis at y = 1, then we can conclude that this is just the exponential function, because:

f(0) = e^0 = 1

So we can conclude that the function is e^x.

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Answer:

11x+6

Step-by-step explanation:

Using FOIL

(x+1)-(-2x-5)-original

F-first=(x+2x)=3x

O-outside=(x+5)=5x

I-inside=(1+2x)=3x

L-last=(1+5)=6

11x+6

Answer:

Rational

Step-by-step explanation:

\( \sqrt{100} = 10 \\ \\ 10 \: is \: a \: rational \: number \\ so \: \sqrt{100} \: is \: rational\)