SIMPLIFY: 4 (1-x + x²)-2 ( 5x) x +3+5x​

For this question, since we need to show that Eric and Nancy contributes the same amount to their monthly income, we just need to equate both expressions with each other, and then solve for the value of x.

In order to check if we got the right answer, we just need to substitute the value of x to both equations.

Therefore, we can conclude that Eric and Nancy has to sell 6 fish tanks each.

Example that demonstrates the contrapositive of the limit comparison test. Let's consider a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges.

Let's define the series an and bn as follows:
- an = 1/\(n^2\)
- bn = 1/n

Now, let's examine the limit:
lim(n→∞)(an/bn) = lim(n→∞)((1/\(n^2\)) / (1/n))

To simplify the limit expression, we multiply both numerator and denominator by \(n^2\):
lim(n→∞)(\(n^2\)(1/\(n^2\)) / \(n^2\)(1/n)) = lim(n→∞)(n/\(n^2\)) = lim(n→∞)(1/n)

As n approaches infinity, the limit becomes:
lim(n→∞)(1/n) = 0

Now, let's check the convergence of the series an and bn:
- an = Σ(1/\(n^2\)) is a convergent p-series with p = 2 > 1.
- bn = Σ(1/n) is a divergent p-series with p = 1.

Thus, we have provided an example of a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges. This demonstrates the contrapositive of the limit comparison test, as requested.

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There will be 38 elk in the herd one year from now, rounded to a whole number.

To solve the given problem, we must use the formula for exponential growth or decay.

We'll use the following formula:

N = N0ert

Where,N is the final population;

N0 is the initial population;

r is the intrinsic growth rate;

e is the base of the natural logarithm; and

t is the time (in years).

According to the problem, the carrying capacity for a population of elk is 52, and there are currently 33 elk in the population.

The intrinsic growth rate of elk is 0.2 per year. We need to find out how many elk will be in the herd one year from now, rounded to a whole number.

Using the formula above, we can write:

N = 33e0.2 × 1= 37.98 ≈ 38

Therefore, there will be 38 elk in the herd one year from now, rounded to a whole number. Answer: 38.

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Answer:

1114 ft

Step-by-step explanation:

tan 22°=450/d

==>d=450/tan 22°=1113.7890... ≈1114 (ft)

When we want to estimate a population parameter then we use hypothesis test.

What is hypothesis test?

In hypothesis testing, an analyst examines a statistical sample with the aim of demonstrating the plausibility of the null hypothesis.

By measuring and reviewing a representative sample of the population under study, statistical analysts test a hypothesis. All analysts use a random population sample to test the null hypothesis and the alternative hypothesis.

Main body:

As the researchers want to understand the difference between to states they need to do a hypothesis test.

Hence a hypothesis test is done.

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From the given data, lim x->∞ (cf(x))/g(x) = 0, which means that cf(x) is o(g(x)). Therefore, we have shown that if f(x) is o(g(x)) and c is a constant, then cf(x) is also o(g(x)).

A positive constant function is a function that always returns a fixed positive value, regardless of the input.

Given that f(x) is o(g(x)), we know that:

lim x->∞ f(x)/g(x) = 0

We want to show that cf(x) is also o(g(x)), which means we need to show that:

lim x->∞ (cf(x))/g(x) = 0

We can rewrite (cf(x))/g(x) as:

c (f(x)/g(x))

Since f(x)/g(x) approaches 0 as x approaches infinity, we know that for any positive constant ε, there exists a positive constant M such that:

|f(x)/g(x)| < ε/|c|

for all x > M

Multiplying both sides by |c|, we get:

|cf(x)/g(x)| < ε

for all x > M

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Lines have a larger m value, that is, m > 1 have steeper slope and lines having an m value between 0 and 1, usually in the form of a fraction have a flatter slope .

Slope is the rate of change in the dependent variable with respect to the independent variable.

For an equation of line of the type - y= mx +c , the slope is given by the m value.

Now, if the value of m > 1 like m=1,2,3, ... , the lines have a steeper slope and have a steep nature.

Similarly, if the value of m < 1 i.e. 0 < m < 1 like m=1/2,2/3, ... fractional values,  the lines have a flatter slope and do not have a steep nature.

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Answer:

2.08 or 2

Step-by-step explanation:

26 = 12.5x

y=mx+b

it will approximately take  2 hours, but to be exact, 2.08

Answer: x =-9/5

Step-by-step explanation:

EXPLANATION

Let's see the facts:

Ipad pen cost = -$105

Best friend ----> +$12

---------------

-$93

Babysitting Saves +$20/week

We are still needing $93 dollars to buy the pen, so, if she earns $20 peer week, then she should work:

$93 = 20 $/week * number of weeks

Calling x to the number of weeks and turning this into an inequality:

12 + 20x ≥ 105

Subtracting -12 to both sides:

20x ≥ 105-12

Simplifying:

20x ≥ 93

Dividing both sides by 20:

x ≥ 93/20

Simplifying:

x ≥ 4.65

Answer: Amelia should at least work 5 weeks in order to save the money to buy the Ipad pen.

The standard deviation measures the spread of data points around the mean. It considers all data points, not just the farthest or nearest ones. A higher standard deviation indicates a greater spread.

The standard deviation is a statistical measure that tells us how much the data points in a set vary from the mean. It provides information about the spread or dispersion of the data. To calculate the standard deviation, we take the square root of the variance, which is the average of the squared differences between each data point and the mean.

By considering all data points, the standard deviation provides a comprehensive measure of how spread out the data is. Therefore, the statement "The difference between the mean and the data point farthest from the mean" is incorrect, as the standard deviation does not focus on just one data point.

The statement "The difference between the mean and the data point nearest to the mean" is also incorrect because the standard deviation takes into account the entire data set. The statement "The difference between the mean and the median" is incorrect as well, as the standard deviation is not specifically related to the median.

Hence, the correct answer is "None of the above."

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The value of a in the equation (3x869)+(19x528)+428(3)(1049)=a is 1359555

From the question, the equation to evaluate is given as

(3x869)+(19x528)+428(3)(1049)=a

Rewrite the above equation to make it legible

So, we have the following equation

(3 x 869) + (19 x 528) + 428(3)(1049) = a

Evaluate the products in the expression

So, we have the following equation

2607 + (19 x 528) + 428(3)(1049) = a

Evaluate the other products in the expression

So, we have

2607 + 10032 + 428(3)(1049) = a

Remove the brackets in the equation

So, we have the following equation

2607 + 10032 + 1346916 = a

Evaluate the sum

1359555 = a

Rewrite as

a = 1359555

Hence, the solution to the equation is 1359555

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Answer:

10/20-8/20=2/20

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

A lies between 665 and 670.

Let's answer the questions asked.

A rounded to the nearest ten

A rounded to the nearest hundred

Answer:

try 660

Step-by-step explanation:

because get to think it already says 670 and 680 so i believe the answer is 660

The volume of the triangular prism = base area x height

Since its base is a right triangle, then

From the figure leg1 = 6 ft and leg2 = 8 ft

Now multiply it by the height of the prism

Since its height = 12 ft, then

The answer is A

Answer:

1

Step-by-step explanation:

-9+10=1

Answer:

1

Step-by-step explanation:

Answer:  You should solve by equal method not substitution.  y=7     x=2

Step-by-step explanation: Equal value method is when two things equal each other and in this case both 3x+1 and 5x-3 equal y so they also equal each other.   3x+1=5x-3                  add 3 to each sides

                      3x+4=5x                     subtract 3x from each side

                      4=2x                           divide by 2

                        x=2                                                             solve for y=3x+1

                                                                                                           y=3(2)+1

                                                                                                          y=7

1) Therefore, if f(x) = x², then f(x + h) = x² + 2xh + h² and 2) Therefore, to make the statement true, we need to swap "a" and "b". We can say that "a is a function of b" to mean that "b determines the value of a".

1. If f(x) = x² then f(x + h) = (x + h)². The correct way to write this statement to make it true is:

If f(x) = x² then f(x + h) = x² + 2xh + h².

For a function written in the form f(a) = b, we would say that "b is a function of a.

"The correct way to write this statement to make it true is:

For a function written in the form f(a) = b, we would say that "a is a function of b."Explanation:1.

To correct the given statement, we can use the formula for the square of a binomial:

(a + b)² = a² + 2ab + b². If we let a = x and b = h, we can write:

f(x + h) = (x + h)²= x² + 2(x)(h) + h²= x² + 2xh + h²

Therefore, if f(x) = x², then f(x + h) = x² + 2xh + h².

2. The statement given is incorrect because the independent variable is usually represented by "x" in a function, and the dependent variable is represented by "y" or "f(x)".

Therefore, to make the statement true, we need to swap "a" and "b". We can say that "a is a function of b" to mean that "b determines the value of a".

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Step-by-step explanation:

To figure out this answer, you need to figure out how much 9% is in $64.00

  ?              9

-------   =   --------  

 64           100

Now to solve this you have to multiply diagonally and divide the neighbor

(let me explain)

basically in this case, you would multiply 64 and 9, then divide by 100

64 * 9 = 576

576 / 100 = $5.76

In short: your answer is 'A' $5.76

Hope this helps <3

Solving a simple linear equation we can see that the value of b is 7.

Here we have the point (5, b - 7) and we want to find the value of b such that the point lies on the x-axis.

Remember that a point lies on the x-axis only if the y-value is zero, so we need to solve the linear equation:

b - 7 = 0

Adding 7 in both sides we get:

b - 7+ 7 = 0 + 7

b = 7

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Given a linked chain of integers reference by the variable head which contains data 20, 30, 10, 5 in that order. consider the impact of the execution of the following lines of code 65

Suppose we have the following lines of code:

integer sum = 0;

Node current = head;

while (current != null) {

sum += current.data;

current = current.next;

}

print(sum);

Line 1 initializes a variable called "sum" to 0. Line 2 initializes a pointer called "current" to the head of the linked list.

Line 3 starts a while loop that will execute as long as the "current" pointer is not null.

Line 4 adds the value of the "data" field of the current node to the "sum" variable.

Line 5 updates the "current" pointer to point to the next node in the sequence.

Line 6 closes the while loop.

Line 7 prints the final value of the "sum" variable.

When the above lines of code are executed, the program will iterate through each node in the linked list, starting from the head. At each node, it will add the value of the "data" field to the "sum" variable. After iterating through all the nodes, the final value of the "sum" variable will be printed.

In this case, the sum of the integers in the linked list is 20 + 30 + 10 + 5 = 65. Therefore, the output of this program will be "65".

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Use substitution or Elimination method. The number of two-point shots made by the team is 31. The number of three-point shots made by the team is 6.

The number of two-point shots and three-point shots made by the Meridian girl's basketball team, we can solve the system of equations:

Equation 1: 2x + 3y = 80

Equation 2: x + y = 37

We can use substitution or elimination method to solve this system. Let's use the substitution method.

From Equation 2, we can express x in terms of y:

x = 37 - y

Now substitute this value of x in Equation 1:

2(37 - y) + 3y = 80

74 - 2y + 3y = 80

74 + y = 80

y = 80 - 74

y = 6

So, the number of three-point shots made by the team is 6.

Now substitute the value of y in Equation 2 to find x:

x + 6 = 37

x = 37 - 6

x = 31

Therefore, the number of two-point shots made by the team is 31.

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Answer:

527.6 cubic inches

Step-by-step explanation:

The volume of a cylinder is represented by the formula \(V = \pi r^{2} h\), where r represents the radius of the base and h represents the height.

In this question, the diameter is given as 9 inches. Since the radius is half the diameter, the radius will be 4.5 inches.

Substituting in the values and solving, we get:

\(V =9 \pi (4.5)^{2}\\V = 9\pi(20.25)\\V = 182.25\pi\\V = 572.6\)

The Volume will be 527.6 cubic inches

Answer:

Option 3 and 4

Step-by-step explanation:

The amount she drank plus 10 equals 24 ounces, and rearranged, proves that 24 minus 10 ounces equals the amount of water she drank.

Answer:

C and D are the correct answers because you have to do the same work for the answer and those are the only equations that will help you find x

hope this helps

Answer:

When you multiply radical expressions you multiply the numbers under the radical symbols.3–√×7–√=21−−√

When you add radical expression you CANNOT add the numbers under the radical symbols.

3–√+7–√≠10−−√

Step-by-step explanation:

Answer:

The volume of a sphere is given by the formula:

V = (4/3)πr³

where r is the radius.

Substituting the given value of r=81cm, we get:

V = (4/3)π(81)³

V = (4/3)π(531441)

V = 904779.5π

Therefore, the volume of the sphere is approximately 2,847,892.22 cubic centimeters (rounded to two decimal places).

Volume of the sphere is 708588π cm³ when the radius of a sphere is 81 cm and formula is \(\frac{4}{3} \pi r^3\).

Given that,

The radius of a sphere is 81 cm.

We have to find what is the volume of the sphere.

We know that,

The amount of area occupied within a sphere is referred to as its volume. Every point on the surface of the sphere is equally spaced from its center, creating a three-dimensional round solid object.

The formula for the volume of the sphere is \(\frac{4}{3} \pi r^3\).

So,

r is the radius of the sphere is 81 cm.

We get,

Volume of the sphere = \(\frac{4}{3} \pi (81)^3\)

Volume of the sphere = 4×π×27×81×81

Volume of the sphere = 708588π cm³

Therefore, Volume of the sphere is 708588π cm³.

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The total amount of money that Marco has that week would be = $ d + 14.55.

An allowance income is defined as the amount of money an individual earns that can be used to solve their personal needs.

Marco received double payment, an allowance from the mother and from newspaper route.

The total amount of money received from his mother for allowance for that same week = $ d

The amount of money he earned from his newspaper = $14.55

Therefore the total amount of money Marco has that week =$ d + 14.55

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Complete question:

Marco's mom gave him d dollars for his allowance one week. He also earned \$14.55$14.55dollar sign, 14, point, 55 for his newspaper route that week.

How much money does Marco have?

Write your answer as an expression.