What is the degree of the polynomial?

Answer:

addition add 3 to both sides to isolate the variable term

Based on the information, we can infer that Lin's graph has an error because each fragment must equal 35 pages and not 55.

To identify and explain Lin's error, we must take into account how many pages the book has. In this case there are 175 pages, if Andre says that he has read 1/5 of the book we must divide the total number of pages by 5 to find out how many pages Andre has read.

So if Andre has read 1/5, he has read 35 pages and Elena will have read 55 pages. Due to the above, the error in Lin's graph is that each of the segments that divide the total pages into 5 has the wrong value because each one should equal 35 and the fragment that Elena read must take a complete segment and part of another

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Question 1: Write the arithmetic sequence 20, 16, 12, 8, ... in the standard form: an =To find the general term of the sequence in the standard form, we need to find its common difference, d.

We do this by finding the difference between any two consecutive terms; 16 - 20 = -4, 12 - 16 = -4, and 8 - 12 = -4, so the common difference is -4.Thus, the general term of the arithmetic sequence in the standard form is given by: an = a1 + (n - 1)d where a1 is the first term and d is the common difference. Substituting the values of a1 and d, we have:an = 20 + (n - 1)(-4)an = 24 - 4nAnswer: an = 24 - 4nQuestion 2: Find the sum: 3 + 10 + 17 + ... + 94To find the sum of the arithmetic sequence, we can use the formula:

Sn = n/2(2a1 + (n - 1)d)where Sn is the sum of the first n terms of the sequence, a1 is the first term, and d is the common difference. We are given the first and last terms, so we need to find the common difference and the number of terms. n = ?a1 = 3an = 94d = an - a1d = 94 - 3d = 91n = (an - a1)/d + 1n = (94 - 3)/91 + 1n = 12So there are 12 terms in the sequence. We can now find the sum using the formula:

Sn = n/2(2a1 + (n - 1)d)Sn = 12/2(2(3) + (12 - 1)7)Sn = 6(6 + 77)Sn=

522Answer: The sum is 522.

Question 3: Find a formula for the general term an of the sequence assumi More information is needed to answer this question. Please provide the arithmetic sequence.

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The number of laps around the lake did Heather run last week when the Ken ran 10 laps around the lake is 20/3.

Fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,

\(\dfrac{a}{b}\)

Here (a) is the numerator and (b) is the denominator.

Last week, Ken ran 10 laps around the lake. Heather ran 2/3 as many laps around the lake as Ken did. Thus, the number of laps heather ran is,

\(x=\dfrac{2}{3}\times10\\x=\dfrac{20}{3}\)

Hence, the number of laps around the lake did Heather run last week when the Ken ran 10 laps around the lake is 20/3.

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We can infer from the data that f(8) = 202. This value is substituted into g(x), and the result is: g(f(8)) = g (202)

We may calculate the value of g(202) by using the formula g(202) = 7(202) - 5) g(202) = 1,409

g(f(8)) = g(202) = 1,409 as a result.

In mathematics, a function is a relationship between a set of inputs (known as the domain) and a set of outputs (known as the range), where each input has a unique output.

A function is usually denoted by a letter (often f, g, or h) and is defined by a set of rules that determine the output value for each input. For example, the function f(x) =\(x^2\) defines a function where the output is the square of the input value.

Functions are useful in mathematics for describing various relationships between quantities, such as the distance traveled by an object as a function of time or the area of a rectangle as a function of its dimensions. They are often used to model real-world situations, and can be used to make predictions and solve problems.

Mathematical functions can take many forms, such as linear functions, quadratic functions, exponential functions, trigonometric functions, and logarithmic functions, among others. They can also be combined to form more complex functions, such as composite functions and inverse functions.

Functions are an essential concept in mathematics and are used extensively in many areas of science, engineering, and economics.

We are given that f(8) = 202 and g(x) = 7x - 5. To find g(f(8)), we need to first find the value of f(8) and then substitute it into the function g(x).

From the given information, we know that f(8) = 202. Substituting this value into g(x), we get:

g(f(8)) = g(202)

Using the function g(x) = 7x - 5, we can evaluate g(202) as:

g(202) = 7(202) - 5

g(202) = 1,409

Therefore, g(f(8)) = g(202) = 1,409.

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Answer:

D.

Step-by-step explanation:

Use Pythagoras to solve for the longest side of the triangle

Add up the side lengths to find the perimeter

Multiply half the base by the height for the area

The exact numerical value of this expression depends on the precision of the decimal approximations of e.

To find the area A of the region bounded between the curve f(x) = 4 - e²x - 1 and the line g(x) = 2x + 1 over the interval [-2, 2], we need to calculate the definite integral of the absolute difference between the two functions over that interval.

Let's denote the absolute difference between f(x) and g(x) as h(x):

h(x) = |f(x) - g(x)| = |(4 - e²x - 1) - (2x + 1)| = |3 - e²x - 2x|

To find the area A, we integrate h(x) over the interval [-2, 2]:

A = ∫[-2,2] |3 - e²x - 2x| dx

Since the integrand is not continuous on the interval, we need to break it down into two separate integrals based on the intervals where the function changes sign. In this case, it happens at x = -1.

Therefore, the area A is given by:

A = ∫[-2,-1] (e²x + 2x - 3) dx + ∫[-1,2] (-e²x - 2x + 3) dx

Evaluating the integrals, we get:

A = [e²x + x²2 - 3x] [-2,-1] + [-e²x - x²2 + 3x] [-1,2]

Substituting the limits of integration, we have:

A = [(e²-1 + 1 - 3) - (e²-2 + 4 - 6)] + [(-e²2 - 4 + 6) - (-e²-1 - 1 + 3)]

Simplifying, we get:

A = [-e²-2 + e²-1 - 1] + [-e²2 + e²-1 + 3]

Therefore, the exact area A of the region bounded between the given curve and line over the interval [-2, 2] is:

A = -e²-2 + e²-1 - 1 - e²2 + e²-1 + 3

Note: The exact numerical value of this expression depends on the precision of the decimal approximations of e.

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Answer:

Let x represent the number of 2 pointers made.

Let y represent the number of 3 pointers made.

We have to create a system of equations to solve this problem:

Isolate for  in Equation #1:

Substitute the new Equation #1 into Equation #2:

Solve for  :

Distribute the Parenthesis:

Combine like terms:

Add -46 to both sides:

Substitute this value into Equation #1:

Add -7 to both sides:

The Solution Is:

Jake made 16 two-pointers and 7 three-pointers!

I hope this helped!

Step-by-step explanation:

Answer:

Exact Form:

1

81

Decimal Form:

0.01234567

…

Step-by-step explanation:

Answer:

The first one

Step-by-step explanation:

Answer:

A the first option

Step-by-step explanation:

negative is the least 1 5/6 is greatest

Therefore, the simplified expression is:

(3 - √637) / (49/√237) = (3 - √637) * (√237/49)

To get rid of the irrationality in the denominator of the fraction and simplify the expression, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.

The given expression is:

(3 - √637) / (8/√49 - 1/√237)

Let's rationalize the denominator:

(3 - √637) / (8/√49 - 1/√237) * (√49/√49)

Simplifying the numerator:

(3 - √637)

Simplifying the denominator:

(8√49 - √49)/√237

(8*7 - 7)/√237

(56 - 7)/√237

49/√237

Therefore, the simplified expression is:

(3 - √637) / (49/√237) = (3 - √637) * (√237/49)

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The probability that Melinda will be able to make an integer between 10 and 20 (inclusive) is 1/6.

The probability that Melinda will be able to make an integer between 10 and 20 (inclusive) with the two numbers she rolls can be calculated by determining the number of favorable outcomes and dividing it by the total number of possible outcomes.

To find the number of favorable outcomes, we need to identify the combinations of two numbers that will result in a two-digit number between 10 and 20. We can list these combinations as follows:

11, 12, 13, 14, 15, 16

Notice that we only have six favorable outcomes.

Now, let's determine the total number of possible outcomes when rolling two six-sided dice. Each die has six possible outcomes (1, 2, 3, 4, 5, 6), so the total number of outcomes is 6 multiplied by 6, which equals 36.

To calculate the probability, we divide the number of favorable outcomes (6) by the total number of possible outcomes (36):

Probability = Favorable outcomes / Total outcomes
Probability = 6 / 36
Probability = 1 / 6

Therefore, the probability that Melinda will be able to make an integer between 10 and 20 (inclusive) is 1/6.

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The absolute maximum value of f on D is 2, which occurs at the point (1,0), and the absolute minimum value of f on D is -6, which occurs at the point (0,0).

To find the absolute max and min values of the function f(x,y) = 2x^3 y^4 - 6 on the set D, we need to first find the critical points and boundary points of the set D.

First, we find the critical points by setting the partial derivatives equal to zero:

fx = 6x^2 y^4 = 0

fy = 8x^3 y^3 = 0

From the first equation, we get x = 0 or y = 0. From the second equation, we get x = 0 or y = 0. Thus, the critical points are (0,0) and (0,1/2).

Next, we find the boundary points of D. The boundary consists of the four lines x = -1, x = 1, y = -1, and y = 1. We evaluate f(x,y) along each of these lines:

Along x = -1: f(-1,y) = -2y^4 - 6

Along x = 1: f(1,y) = 2y^4 - 6

Along y = -1: f(x,-1) = -2x^3 - 6

Along y = 1: f(x,1) = 2x^3 - 6

Now, we need to evaluate f at the critical points and boundary points to determine the absolute max and min values of f on D:

f(0,0) = -6

f(0,1/2) = -3/4

f(-1,y) = -2y^4 - 6

f(1,y) = 2y^4 - 6

f(x,-1) = -2x^3 - 6

f(x,1) = 2x^3 - 6

The absolute maximum value of f on D is 2, which occurs at the point (1,0), and the absolute minimum value of f on D is -6, which occurs at the point (0,0).

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To compare her expense with those of her coworkers, Alena can calculate the average cost and determine where her expense falls in relation to the average. By comparing her cost to the average, she can assess whether her $2.75 expense for a 9-oz cup of coffee is typical or not.

To compare her expense with her coworkers, Alena can calculate the average cost of a 9-oz cup of coffee among her coworkers. She can add up the costs of the six coworkers and divide the sum by 6 (the number of coworkers) to find the average cost per cup.

Calculating the average:

(2.85 + 2.15 + 1.95 + 3.00 + 2.05 + 2.40) / 6 = 14.40 / 6 ≈ 2.40

The average cost per cup is approximately $2.40.

By comparing her expense of $2.75 to the average cost of $2.40, Alena can see that her expense is slightly higher than the average. This indicates that her cost for a 9-oz cup of coffee is slightly above what her coworkers typically pay.

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Answer:

There are many choices, but one answer is 2 3.1/5 and 2 3.2/5.

Step-by-step explanation:

These are equivalent to 2 6.2/10 and 2 6.4/10 which is between both.

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There are n different values that the remainder r can take on when \(n^2\) is divided by n 4.

We can use the Remainder Theorem to solve this problem. The Remainder Theorem states that when a polynomial f(x) is divided by (x-a), the remainder is f(a).

Using this theorem, we can see that \(n^2\) divided by n 4 leaves a remainder of \(n^2 - kn 4\), where k is some integer. We want to find how many different values r can take on, which is the same as finding how many different values \($n^2 - kn 4$\) can take on.

Let's rewrite \(n^2 - kn 4 as n(n - k 4)\). This expression tells us that n and n - k 4 have the same remainder when divided by n 4. Therefore, n - k 4 can only take on n different values, namely \(0, n, 2n, \ldots, (n-1)n.\)

For each of these n values, we can find a corresponding value of k that satisfies\($n^2 - kn 4 \equiv r \pmod{n 4}$\), namely \(k = (n^2 - r)/(n 4).\) Therefore, there are exactly n different values that r can take on.

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The correct interpretation of the 95% confidence level is that if we were to repeat this sampling process multiple times and construct confidence intervals in the same way, about 95% of the intervals would contain the true mean number of suitable apples produced per tree.

In other words, we are 95% confident that the true mean number of suitable apples produced per tree is between 375 and 520 based on this particular sample of 40 trees. However, we cannot say with certainty that the true mean falls within this interval, nor can we say that it falls outside of this interval with 95% confidence.

It's important to note that the confidence level refers to the long-run behavior of the method of constructing confidence intervals, rather than the probability that the true mean falls within the specific interval calculated from this one sample.

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Answer:

58

Step-by-step explanation:

The probability of buying coffee is 77%, the probability of buying a bagel is 36%, and the probability of buying both coffee and a bagel is 22%. Therefore, if one customer is selected at random, there is a 77% chance they will buy coffee, a 36% chance they will buy a bagel, and a 22% chance they will buy both coffee and a bagel.

The probability of buying coffee is 77%. This can be calculated as 77/100, which is equivalent to 0.77.

The probability of buying a bagel is 36%. This can be calculated as 36/100, which is equivalent to 0.36.

The probability of buying both coffee and a bagel is 22%. This can be calculated as 22/100, which is equivalent to 0.22.

At a Dunkin' Donuts drive-thru, the probability of buying coffee is 77%, the probability of buying a bagel is 36%, and the probability of buying both coffee and a bagel is 22%. This means that if one customer is selected at random, there is a 77% chance they will buy coffee, a 36% chance they will buy a bagel, and a 22% chance they will buy both coffee and a bagel. To calculate these probabilities, we divide the respective percentages (77%, 36%, and 22%) by 100. The result of this calculation is 0.77 for the probability of buying coffee, 0.36 for the probability of buying a bagel, and 0.22 for the probability of buying both coffee and a bagel. This means that if one customer is selected at random, there is a 77% chance they will buy coffee, a 36% chance they will buy a bagel, and a 22% chance they will buy both coffee and a bagel.

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Answer:

1) Alternate interior angles are congruent, hence x=115

2) Linear pairs add up to 180°, hence x=67

3) Alternate interior angles are congruent, hence x=89

4) Same side interior angles are supplementary, hence x=139

5) Linear pairs are supplementary, hence x=109

6) Alternate interior angles are congruent, hence x=88

7) Alternate interior angles are congruent, hence x=62

8) Same side interior angles are supplementary, hence x=74

Hope this helps!

ANSWER

EXPLANATION

We want to write the equation for the function g(x).

From the graph, we see that g(x) was moved 5 units upward from the parent function, f(x). In other words, f(x) was translated vertically upward to result in g(x).

When an exponential function is translated vertically, it changes as follows:

when b > 0, it is an upward translation

when b < 0, it is a downward translation

Therefore, the equation for the function g(x) can be written as:

Given:-

To find the value of x.

Since the corresponding opposite angles are equal and also the sum of angles inside a triangle is 180 degrees. we get,

So the required value of x is 5.

The number of square miles in a state and locating cities on a coordinate grid involves using formulas and calculations based on the Latitude and longitude coordinates of each city

As an AI language model, I  have the ability to post images or sketches. However, I can provide guidance on how to find the number of square miles in a state and locate cities on a coordinate grid.

Let's take the state of California as an example. To find the number of square miles in California, we can use the formula for the area of a polygon:

Area = 0.5 x perimeter x apothem

For a state like California, which has a complex shape, we can use the following steps to find the area:

1. Find the latitude and longitude of each corner of the state.

2. Plot these points on a coordinate grid.

3. Use the Pythagorean theorem to find the distance between each pair of cities.

4. Use the formula for the area of a polygon to find the area of California.

To locate cities on a coordinate grid, we can use the latitude and longitude coordinates of each city. The latitude measures the distance north or south of the equator, while the longitude measures the distance east or west of the prime meridian. We can use these coordinates to plot each city on a coordinate grid, with the x-axis representing longitude and the y-axis representing latitude.

Once we have located the cities on the coordinate grid and found the distances between them, we can use the formula for the area of a polygon to find the area of the state. This will give us the number of square miles in the state.finding the number of square miles in a state and locating cities on a coordinate grid involves using formulas and calculations based on the latitude and longitude coordinates of each city. By following these steps, we can accurately determine the size and location of each state and its cities.

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a) Contribution (objective value) = $132.14

b) The firm earns $132.14 at the optimal solution.

c) An additional hour of time available for the third machine is worth $0.14 to the firm.

d) An additional 5 hours of time available for the second machine will increase the objective value by $3.69.

The best result obtained from using computer software to solve the LP problem is: X1 = 11.43, X2 = 12.86, X3 = 5.71

b) The number of unused hours at the ideal solution is:

Machine 1 still has 8.57 hours of time left.

There are no hours left on Machine 2 at the moment.

There are still 94.29 hours left on Machine 3.

c) The shadow price of the third limitation is worth an extra hour of time available for the third machine. With the exception of increasing the right-hand side of the third constraint by one unit, we can solve the LP problem using the same constraints to determine the shadow price. Using LP to solve this issue, we discover that the shadow price for the third constraint is

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

\(mean = \frac{sum \: of \: all \: observations}{number \: of \: observations} \\ = > mean = \frac{( - 6) + ( - 10) + ( - 4) + 8 + 9 + ( - 2) + 5 + 6}{8} \\ = > mean = \frac{6}{8} \\ = > mean = 0.75\)

This is the answer.

Answer:

Step-by-step explanation:

f(x) = 3x² + 1

g(x) = 1 - x

To find (f - g)(2) first find (f - g)(x)

To find (f - g)(x) subtract g(x) from f(x)

That's

(f - g)(x) = 3x² + 1 - ( 1 - x)

(f - g)(x) = 3x² + 1 - 1 + x

(f - g)(x) = 3x² + x

To find ( f - g)(2) substitute 2 into (f - g(x)

That's

( f - g)(2) = 3(2)² + 2

( f - g)(2) = 3(4) + 2

( f - g)(2) = 12 + 2

We have the final answer as

Hope this helps you

The probability of randomly selecting a woman from a city depends on the proportion of women in the city's population.

The probability of selecting a woman from the city can be determined by the proportion of women in the population.

Let's assume there are 1000 people in the city, with 500 being women and 500 being men. In this case, the probability of randomly selecting a woman would be 500/1000, or 0.5 (or 50%).

However, if there are more or fewer women in the city, the probability will change accordingly.

For example, if there are 600 women and 400 men, the probability would be 600/1000, or 0.6 (or 60%).

Therefore, the probability of randomly selecting a woman from the city depends on the ratio of women to the total population.

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