Find the domain and range of the function represented by the graph.

Answer: Lim (1 - 1/(n + 1)) ^ (n ^ 2) = 1^infinity = 1

Step-by-step explanation: The expression given is the limit of the sequence (1 - 1/(n + 1)) ^ (n ^ 2) as n approaches infinity.

We can start by looking at the exponent first. The n^2 will grow faster than any polynomial function, making the entire expression go to zero as n approaches infinity.

Now let's look at the base (1 - 1/(n + 1))

As n increases, the value of the base becomes closer and closer to 1, since 1/(n+1) becomes smaller and smaller.

Therefore, the limit of the expression is:

Lim (1 - 1/(n + 1)) ^ (n ^ 2) = 1^infinity = 1

As n goes to infinity, the expression goes to 1

Please note that this is true for the limit, for a specific value of n, the expression will not be 1.

Answer:

The limit of (1 - 1/(n + 1)) ^ (n ^ 2) as n approaches infinity is 0.

As n becomes larger, the term 1/(n + 1) becomes smaller and closer to zero, which means that (1 - 1/(n + 1)) becomes closer and closer to 1. Therefore, the expression (1 - 1/(n + 1)) ^ (n ^ 2) becomes closer and closer to 1^(n^2) = 1. And any number powered by infinity (n^2) will be approaching zero, so the limit of the expression is 0.

The solution for f(3) in the function is -7772

From the question, we have the following equation that can be used in our computation:

f(x) = 4 − (x + 3)⁵

Also from the question, we have

f(3)

This means that the value of x is 3, and we calculate f(x) when x = 3

Substitute the known values in the above equation, so, we have the following representation

f(3) = 4 − (3 + 3)⁵

Evaluate

f(3) = −7772

Hence, the solution is −7772

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Complete question

Given f ( x ) = 4 − ( x + 3 )^5, find f(3).

f(x) is continuous at z = 3. a-3 Check the option from the following that best represents this information O A. limit f(x) = 2 O B. lim f(x) = 2 OC.

What is a limit?

A limit is given by the value of function f(x) as x tends to a value.

For this problem, at x = 0, we have that to the left the function goes to positive infinity, while to the right it goes to negative infinity, hence:

1. lim f(x) = ∞

x->0-

2. lim f(x) = -∞

x->0+

At x = 2, the function goes to infinity to the left and to the right, hence:

3. lim f(x) = ∞

x->2

To the left of the graph, the function goes to negative infinity, while to the right it goes to 1, hence:

4. lim f(x) = 1

x-> ∞

5. lim f(x) = -∞

x-> -∞

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Total 18 different paths are there from a to b that go through the point circled in the following lattice

In the given question, we have to find how many different paths are there from a to b that go through the point circled in the following lattice.

The diagram of the lattice is given below:

Therefore, we must first go from A to the encircled point.

We must travel 2 horizontally and 2 vertically to do that.

Now, to get to this point, we have ways = [tex]C_{2}^{4}[/tex] ways

Total ways to go from A to the encircled point = [tex]\frac{4!}{2!(4-2)!}[/tex]

Total ways to go from A to the encircled point = 6 ways

Additionally, we must travel 2 horizontal and 1 vertical units to get from the encircling point to B.

As a result, total ways to go from the encircling point to B = [tex]C^{3}_{1}[/tex]

Total ways to go from the encircling point to B = [tex]\frac{3!}{1!(3-1)!}[/tex]

Total ways to go from the encircling point to B = 3 ways

So, different paths are there from a to b = 6×3

Different paths are there from a to b = 18 ways

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The ratio of rubies to diamonds is given as follows:

4.

The ratio between two amounts is obtained applying proportions, as the ratio between the amounts a and b is given by the division of a by b, as follows:

r = a/b.

The amounts in this problem are given as follows:

The number of rubies is four times the number of diamonds, hence:

x = 4y.

Then the ratio between the number of rubies and the number of diamonds is given as follows:

r = 4y/y

r = 4.

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Answer:

[tex]x = 2 \: and \\ y = 5[/tex]

Step-by-step explanation:

greetings!!!

look at the attachment above

Hope it helps!!!

In the expression n + 23 ,23 is a constant because it contains two part and other part is variable.

The concept that will be used here is algebraic equation, The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables. One example is x3 + 1.

We were given n + 23

n is the dependent variables which changes with the input.

23 is the constant that never changes.

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The solution of the inequality is 8 ≥  x  or x > 10. The graph of the solution is attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Solving for x:

11≥ 2x - 5 or 2x - 5 > 15

Collect like terms:

11 + 5 ≥ 2x  or 2x > 15 + 5

16 ≥ 2x  or 2x > 20

8 ≥  x  or x > 10

Note:  8 ≥  x can also be written as x ≤ 8

We can combine the two as follow:

Inequality notation: 8 ≥  x > 10

The graph of the solution is attached

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Answer:

Step-by-step explanation:

5 quart to gallon is 1.25

5 quart to cup is 20

5 Quart to oz is 160

5 Quart to tablespoon is 320

Answer: C

Answer: To solve for all values of x in the equation x^2 - 2x - 48 = 0 by completing the square, we can follow these steps:

Bring the x term to one side of the equation by adding 2x to both sides: x^2 - 2x = 48

Divide the coefficient of the x^2 term (which is 1) by 2 and square it to find the value to add to both sides of the equation to complete the square: (1/2)^2 = 1/4. Add 1/4 to both sides of the equation: x^2 - 2x + 1/4 = 48 + 1/4

Take the square root of both sides of the equation: (x - 1)^2 = 192 + 1

Solve for x by taking the square root of both sides of the equation: x - 1 = ± √193

Add 1 to both sides of the equation to find the values of x: x = 1 ± √193

So the solutions of the equation are x = 1 + √193 and x = 1 - √193

It is important to notice that these are the solutions in radical form, so they are not exact values of x.

Step-by-step explanation:

The probability that exactly seven claims will be received during a given two-week period=1/64.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject because it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

An insurance company determines that N, the number of claims received in a week, is a random variable with P[N = n] = 1/2n+1, where n > 0 .

Let N1 and N2 represent the number of claims during weeks one and two, respectively,

then since N1 and N2 are independent.

[tex]Pr[N_1+N_2=7]=\sum_{n=0}^7Pr[N1=n]Pr[N2=7-n]\\\\=\sum_{n=0}^7\frac{1}{2^{n+1}}\frac{1}{2^{8-n}}\\\\=\sum_{n=0}^7\frac{1}{2^{9}}\\\\=\frac{8}{2^9}=\frac{1}{64}[/tex]

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Answer:

f(-2)=14

Step-by-step explanation:

 f(x)=x^2 +2x - 10 and  f=(-2)

f(-2)=-2^2 +2(-2) - 10

4+0+10

14

f(-2)=14

:)

Answer: this is a function since there is only one value of y for every value of

Step-by-step explanation:

The amount to save according to the recommendation of 3/10 of income is $17400.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

Given that the amount made in a year is $58,000.

The recommended savings is 3/10 thus:

(58000) (3/10) = 17400

Hence, according to the recommendation the amount that needs to be saved in one year is, $17400.

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The conditions that are required to validate the use of t for the significance test would be:

D). l and ll only

A response variable, also known as a dependent variable, is a variable that is being studied or measured in an experiment or statistical analysis. It is the outcome or output of the study, and its value is influenced by one or more predictor variables, also known as independent variables.

The goal of a study is often to understand how the response variable is affected by the predictor variables.

For example, in a medical study, the response variable might be the level of a certain protein in the blood, and the predictor variable might be the dosage of a new drug being tested.

In a marketing study, the response variable might be the number of units sold of a product, and the predictor variables might be the price of the product and the advertising budget.

Therefore, The conditions that are required to validate the use of t for the significance test would be:

D). l and ll only

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The inequality graphed on the number line is the one on the fourth option, we will get:

x > -2

On the number line we can see that we have an open circle at x = -2 (that means that x = -2 is not a solution to the inequality) and then a line that extends to the right side of that value.

Then the inequality is just the set of all numbers larger than -2, then we will get:

x > -2

That is the graphed inequality, and thus, the correct option is the last one.

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Answer:

yes u would be on track.

Step-by-step explanation:

yes; 10 miles in 12 days is equivalent to 10 ÷ 2 = 5 miles in 12 ÷ 2 = 6 days.

:o)

Easy if writing/typing put P L S and an .

If speaking maybe instead say please

In JMP, open the data in Fit Model and choose scatterplot, and a residual usually looks like the scatterplot but more extended vertically.

(a): Yes, because there is not much of a trend in the data.

(b): The materials cost is a very small percentage of the average cost. It could be true that items that use fewer materials take more labor hours to make ready for the customer.

(c): chose a correct residual plot

In JMP, in the top red triangle, click on save columns, and then click on Residuals. Then go to the data table in JMP and in Graph, press GRAPH BUILDER... put residuals on y and # of labor hours on x

As the number of labor hours​ increases, the residual values from the regression also tend to​ increase, suggesting that the labor input is a lurking variable.

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Jennifier was paid $1.49 for each shirt, $4.99 for each pair of slacks and $7.99 for each sports coat.

Two or more expressions with an Equal sign is called as Equation.

Let x = shirts, y = slacks, z = sports coats.

Set up your systems of equations equations.

3x+2y=$14.45..(1)

6x+2y+z=$26.91...(2)

4x+2z=$21.94...(3)

From equation 2

$14.45+3x+z=$26.91

3x+z=12.46...(4)

Multiply equation 4 with 2

6x+2z=24.92..(5)

6x+2z-4x-2z=24.92-21.94

2x=2.98

Divide both sides by 2

x=$1.49

Now plug in x value in equation 1.

3(1.49)+2y=$14.45

4.47+2y=14.45

2y=9.98

Divide both sides by 2

y=$4.99

4x+2z=$21.94

4(1.49)+2z=21.94

5.96+2z=21.94

2z=21.94-5.96

2z=15.98

Divide both sides by 2

z=$7.99

Hence, Jennifier was paid $1.49 for each shirt, $4.99 for each pair of slacks and $7.99 for each sports coat.

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The best estimate we can give for the number of orange balls in the tub is 7, and the number of white balls in the tub is 43.

To calculate this, we take the number of orange balls picked (7) and divide it by the total number of balls picked (25) to get the proportion of orange balls in the tub. Then we multiply that proportion by the total number of balls in the tub (50) to get our estimate for the number of orange balls in the tub.

7 / 25 = 0.28

0.28 x 50 = 14

Similarly, we take the number of white balls picked (18) and divide it by the total number of balls picked (25) to get the proportion of white balls in the tub. Then we multiply that proportion by the total number of balls in the tub (50) to get our estimate for the number of white balls in the tub.

18 / 25 = 0.72

0.72 x 50 = 36

This method of calculation makes sense because it uses the data we have (the number of orange and white balls picked) to estimate the overall makeup of the tub. By using the proportion of orange and white balls picked, we can make an educated guess about how many of each color ball are in the tub without seeing it.

However, it's important to note that this best estimate is not necessarily accurate. The real number of orange and white balls in the tub could be different. The method used here is a probability method, it's best estimate based on the sample data. The sample data is based on a random selection of 25 balls, and the number of orange or white balls that would be picked could vary depending on the random draw. The more samples we take, the more accurate our estimate would be.

The square root of 6^2 (√6²) is 6.

What is square root?

Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts.

Suppose x is the square root of y, then it is represented as x=√y, or we can express the same equation as x^2 = y. Here, ‘√’ is the radical symbol used to represent the root of numbers. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number.

For example, the square of 3 is 9, 32 = 9 and the square root of 9, √9 = 3. Since 9 is a perfect square, hence it is easy to find the square root. But for an imperfect square like 3, 7, 5, etc., we have to use different methods to find the square root.

Now ,

given expression √6²

=√36

square root value of √6² =6

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The square root of 6^2 (√6²) is 6.

What is square root?

Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts.

Suppose x is the square root of y, then it is represented as x=√y, or we can express the same equation as x^2 = y. Here, ‘√’ is the radical symbol used to represent the root of numbers. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number.

For example, the square of 3 is 9, 32 = 9 and the square root of 9, √9 = 3. Since 9 is a perfect square, hence it is easy to find the square root. But for an imperfect square like 3, 7, 5, etc., we have to use different methods to find the square root.

Now ,

given expression √6²

=√36

square root value of √6² =6

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Equation of parallel line = y = 3x + 2 and equation of perpendicular line 3y = -x + 16, passing through the point (1,5).

(a) To find an equation of the line that passes through the point (1,5) and is parallel to the line y = 3x - 5, we need to use the slope of the given line. The slope of a line is represented by m and it is equal to the coefficient of x. In this case, the slope of the line y = 3x - 5 is 3.

Therefore, the slope of the line that is parallel to y = 3x - 5 is also 3.

We can use the point-slope form of a line, which is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope.

Substituting the given point (1, 5) and the slope of 3, we get:

y - 5 = 3(x - 1)

Simplifying the equation, we get:

y = 3x + 2

So, the equation of the line that passes through the point (1, 5) and is parallel to the line y = 3x - 5 is y = 3x + 2

(b) To find the slope of a line that is perpendicular to the line y = 3x - 5, we need to take the negative reciprocal of the slope. The negative reciprocal of 3 is -1/3. So, the slope of a line that is perpendicular to y = 3x - 5 is -1/3

We can use the point-slope form of a line, which is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope.

Substituting the given point (1, 5) and the slope of -1/3, we get:

y - 5 = -1/3(x - 1)

Simplifying the equation, we get:

3(y - 5) = -x + 1

3y = -x + 16

So, the equation of the line that passes through the point (1, 5) and is perpendicular to the line y = 3x - 5 is 3y = -x + 16

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To determine the key terms refer to in the following conducted study in a local community will be as follows:

a. voted, didn't vote, voted will be variable.

b. a group of voters in the community who voted, randomly selected will be sample.

c. the number of eligible voters who actually plan to vote will be population.

d. the number of eligible voters in the study who actually plan to vote statistic.

e. the attendance of a single voter will be data

f. all eligible voters in the comunity will be parameter.

Any quantity calculated from sample values and taken into consideration for statistical purposes is referred to as a statistic (singular) or sample statistic. A population parameter estimate, a sample description, or a hypothesis evaluation are examples of statistical purposes. Statistics are expressed as the average (or mean) of sample values.

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the universal set be U = {1, 2, 3,..., 10}, and let A = {1, 4, 7, 10}, B = {1, 2, 3, 4, 5}, and C= {2, 4, 6, 8}. the elements of (A-C) - (An B) ={7,10}

Set is a collection of well-defined objects and it has distinct elements. The set formulas include the union, intersection, complement, and difference of sets. Venn diagrams are popularly used to visualize set formulas to arrive at their proof.

The universal set be U = {1, 2, 3,..., 10}, and let A = {1, 4, 7, 10}, B = {1, 2, 3, 4, 5}, and C= {2, 4, 6, 8}.

So, to calculate (A-C)-(A∩B)

FIRST A-C= {1, 4, 7, 10} -  {2, 4, 6, 8}.

A - C = { 1,7,10}

A∩B={1,4,}

(A-C)-(A∩B)= { 1,7,10} -{1,4,} = { 7, 10}

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We can only say that X+y=21 is a true statement for any values of X and y that satisfy this equation.

In mathematics, elimination is the process of solving a system of equations by eliminating variables. Elimination involves two steps: first, a variable is chosen to be eliminated and then the coefficients of the variable are used to modify the remaining equations so that they contain only the other variables.

To solve for the unknown variables, we can use the following methods:

Graphing: We can graph the equation on a coordinate plane by plotting the line of the equation. The point of intersection of the line with the x and y-axis represents the solution of the system of equations.

Substitution: We can solve for one variable in terms of the other by isolating one variable and substituting it into the other equation.

Elimination: We can eliminate one variable by adding or subtracting the equations to eliminate one of the variables.

In this case, we don't have any other equation to solve the system, so we can not find a unique solution, we can only say that X+y=21 is a true statement for any values of X and y that satisfy this equation.

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Answer:

C 16 km

Step-by-step explanation:

Pythagoras

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

in our case that is

27² = 21.5² + x²

729 = 462.25 + x²

x² = 266.75

x = sqrt(266.75) = 16.33248297... km ≈ 16 km

Answer:

Choice A

Step-by-step explanation:

1/5 = 9/15

2/3 = 10/15

so 3/5 < 2/3

QN is the answer to the equation that results from combining the slopes and y-intercepts of the equations MP and QR.

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