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The remainder when (4x^37 + 12x^15 - 2x^4 - 28) is divided by (x + 1) using the remainder theorem is -22.

To determine the remainder of the polynomial expression (4x^37 + 12x^15 - 2x^4 - 28) divided by (x + 1) using the remainder theorem, Kayla evaluates the numerator of the rational expression when x = -1.

When x = -1, the expression simplifies as follows:

(4(-1)^37 + 12(-1)^15 - 2(-1)^4 - 28)

Since any odd power of -1 is equal to -1 and any even power of -1 is equal to 1, we can simplify further:

(4(-1) + 12(1) - 2(1) - 28)

(-4 + 12 - 2 - 28)

(-4 - 2 - 28 + 12)

(-6 - 28 + 12)

(-34 + 12)

-22

Therefore, the remainder when (4x^37 + 12x^15 - 2x^4 - 28) is divided by (x + 1) is -22.

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Answer: 5 and 6

33 lies between 5^2 and 6^2.

Answer:

x=10

Step-by-step explanation:

2/3+5/6x=9

5/6x=8 1/3

5/6x=25/3

5x=50

x=10

Answer:

No, because the longest side is too short to be the hypotenuse of a right triangle.

Step-by-step explanation:

To see if the sides form a right triangle

6² + 8² = 9²

36 + 64 = 81

100 ≠ 81

The the 3rd side is too short

If my answer is incorrect, pls correct me!

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-Chetan K

C) 26,000 < (6,182 - 2,306)y

1) Gathering the data

Spent = $6,812 per yer

More efficient car = $26,000

Costs with fuel per year (average) = $2,306

2) So let's write an inequality, where y stands for the number of years that the total amount of fuel savings will exceed the purchase price of the new vehicle.

2306y+

26,0000< 2,306y-6812

Since 6812 y is the expense with fuel yearly, then and 2,306 depends on the number of years then the option is

C) 26,000 < (6,182 - 2,306)y

68

Answer:

12 feet

Step-by-step explanation:

30 divided by 5= 6

6 times 3= how far youve already swam(18 feet)

6 times 2= how far you have left(12 feet)

Answer:

b. 8a-35s

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

x + y + z  = 0   →-  -(x + y)  = z  →   z^3 =  - (x^3 + 3x^2y + 3xy^2 + y^3)

xyz  = 17

xy [ -(x + y) ]  = 17

xy (x + y)  = -17  →  x^2y + xy^2  = -17  →  3x^2y + 3xy^2  = -51

So......

x^3  + y^3  +  [ z^3 ]

x^3  + y^3  +  [ -  ( x^3 + 3x^2y + 3xy^2 + y^3) ]  =

-3x^2y - 3xy^2  =

-[ 3x^2y + 3xy^2]  =

- [-51]  =

51

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The magnitude or length of AB, represented as ||AB||, is calculated using the distance formula resulting in √101.

To sketch AB, plot the initial point A(8, -4) and the terminal point B(-2, -3) on a coordinate plane. Then, draw a line segment connecting these two points. The line segment AB represents the vector AB.

To write AB in component form, subtract the x-coordinates of B from the x-coordinate of A and the y-coordinates of B from the y-coordinate of A. This gives us the vector (-2 - 8, -3 - (-4)), which simplifies to (-10, 1). Therefore, AB can be represented as the vector (-10, 1).

To find the magnitude or length of AB, we can use the distance formula. The distance formula calculates the distance between two points in a coordinate plane. Applying the distance formula to AB, we have √((-2 - 8)² + (-3 - (-4))²). Simplifying the equation inside the square root, we get √(100 + 1), which further simplifies to √101. Thus, the magnitude or length of AB, denoted as ||AB||, is √101.

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Based on the ratings system and the summarize() and mean() functions, the code chunk to add is summarize(mean(Rating)) and the mean rating is 3.185933.

To find the mean rating, the complete code should be trimmed_flavors_df %>% summarize(mean(Rating)).

This code would allow you to see the mean rating of your data by combining the summarize() and mean() functions such that you can display summary statistics.

Because of the "mean()" function, the statistic that will be displayed is the mean rating which in this case would be 3.185933.

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Therefore, the annual annuity payment can be approximately $6,069,727.

To calculate the size of the annual annuity payment, we can use the present value formula for an ordinary annuity. The formula is given by:

PMT = PV / [(1 - (1 + r)⁻ⁿ) / r]

Where:

PMT = Annual annuity payment

PV = Present value of the annuity

r = Annual interest rate

n = Number of periods

Given:

PV = $230 million

r = 8% = 0.08

n = 40 years

Using the formula, we can calculate the annual annuity payment:

PMT = 230,000,000 / [(1 - (1 + 0.08)⁻⁴⁰) / 0.08]

PMT ≈ $6,069,727

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Answer:

\(d = -\frac{5}{6}\)

Step-by-step explanation:

7d – 4d – 3d – 5 = 6d

(7d - 4d = 3d)

3d - 3d -5 = 6d

(3d - 3d = 0)

0 - 5 = 6d

-5 = 6d

-5/6 = 6d/6

d = \(\frac{-5}{6}\)

Hope this helps ^-^

Answer:

5/9

Step-by-step explanation:

4+5=9 and there are 5 boys

The minimum number of candidates required to ensure that 2 candidates will have the same score is 31. Answer: \boxed{31}.

We are given that 20 problems in a mathematics competition. The scores of each problem are allocated in the following ways: 3 marks will be given for a correct answer, 1 mark will be deducted from a wrong answer, and 0 marks will be given for a blank answer.

We have to find the minimum number of candidates required to ensure that 2 candidates will have the same scores in the competition.Let's use the Pigeonhole Principle to solve the problem. In this case, the pigeons are the possible scores and the holes are the candidates.

The range of possible scores is 0 to 60 (inclusive). A score of 60 is possible if all 20 problems are solved correctly, and a score of 0 is possible if none of the problems are solved correctly.

Therefore, there are 61 possible scores: 0, 1, 2, 3, ..., 59, 60.To ensure that 2 candidates have the same score, we need at least 2 candidates to have each score.

The minimum number of candidates required is therefore the smallest integer n that satisfies:2n > 61n > 30.5The smallest integer greater than 30.5 is 31.

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The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

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Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

The time taken to finish the race is 3.49 hours

Speed is defined as. The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.

Given,

The total distance = 500 miles

The speed = 143.187 mph

We know, Speed = Distance / Time

Time = Distance / Speed

Substitute the values

Time = \(\frac{500}{143.187}=3.49\) hours

Hence, the time taken to finish the race is 3.49 hours

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Answer:

21°

angles don't change in dilutions but lengths do

plssmark brainliesttt

Answer:

B.)

Step-by-step explanation:

B.) Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations.

When you multiply the top by 3 you'd get 6x+24y=-9 and when you multiply the bottom equation by -2 you'd get -6x-12y=8

6x and -6x would cancel each other out eliminating the x variable.

Answer:

A:4.5

Step-by-step explanation:

all you need to do is count the spaces

Frederick Taylor's theory is known as "scientific management," which aimed to improve workplace productivity by emphasizing efficiency and standardization.

Here are some pros and cons of his theory:

Pros:

1. Increased productivity and efficiency: Taylor's approach helped companies streamline their processes and make better use of their resources. This led to increased productivity and efficiency, which can lead to greater profits and growth.

2. Improved worker skills: By breaking down work into smaller tasks and optimizing them, Taylor's method allowed workers to learn new skills and become more specialized in their work. This can lead to a sense of mastery and increased job satisfaction.

3. Clear division of labor: Taylor's method led to a clear division of labor, which allowed companies to better organize their workers and maximize their output. This also helped to reduce conflict and confusion in the workplace.

Cons:

1. Dehumanization of workers: Taylor's approach viewed workers as mere cogs in a machine rather than as human beings. This led to a lack of respect and dignity for workers, which can lead to low morale and high turnover rates.

2. Lack of creativity and innovation: Taylor's method emphasized standardization and efficiency over creativity and innovation.

3. Potential for abuse: Taylor's approach can be abused by employers who are more concerned with profit than with worker welfare.

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a) a6 + a7 + a8 = s8 - s6

b) The series ∑k=0^∞ ak diverges.

c) The limit of ak cannot be determined without additional information.

d) The series ∑k=6^∞ ak diverges.

e) The series ∑k=0^∞ sk diverges.

To solve the given problems, we'll analyze the properties of the sequence and the series based on the given information.

a) To find a6 + a7 + a8, we can use the formula for the partial sum Sn. Since s6 = ∑k=0^6 ak, s7 = ∑k=0^7 ak, and s8 = ∑k=0^8 ak, we can subtract the appropriate terms to find the desired sum:

a6 + a7 + a8 = (s7 - s6) + (s8 - s7) = s8 - s6

b) To determine whether the series ∑k=0^∞ ak converges or diverges, we need to examine the behavior of the sequence. From the given information, we know that sn = 7(43)n. As n approaches infinity, 43n grows exponentially. Therefore, the series diverges because the terms do not approach zero.

c) To find limk→∞ ak, we can observe that the terms of the sequence are not specified. Without additional information about the sequence {an}, we cannot determine the limit of ak.

d) The series ∑k=6^∞ ak can be analyzed using the same reasoning as in part b. Since the terms of the sequence {an} are not specified and the series ∑k=0^∞ ak diverges, the terms beyond k = 6 would contribute to the divergence. Therefore, the series ∑k=6^∞ ak also diverges.

e) To determine whether the series ∑k=0^∞ sk converges or diverges, we need to examine the behavior of the partial sums. From the given information, we know that sk = 7(43)k. As k approaches infinity, 43k grows exponentially. Therefore, the series also diverges because the partial sums do not approach a finite value.

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The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.

The probability of renting exactly three apartments in a week is given by the Poisson probability function:

\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)

Substituting the values, we get:

\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)

P(X = 3) = (0.09963 * 12.167) / 6

P(X = 3) = 0.2018

Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

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Answer:

The ratios 2.56/32 and 0.48/6 are equivalent; y = 0.08x.

Step-by-step explanation:

$2.56 for 32 oz is a unit price of $2.56/(32 oz) = $0.08/oz

$0.48 for 6 oz is a unit price of $0.48/(6 oz) = $0.08/oz

The unit prices are equal, so the cost of both sizes are proportional.

If x is the weight in oz, multiply the weight by 0.08 to get the cost, y, in dollars.

y = 0.08x

The ratios 2.56/32 and 0.48/6 are equivalent; y = 0.08x.

The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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Answer:

140 degrees

Step-by-step explanation:

isosceles triangle   so two angles are equal    20 and 20

ALL of the angles sum to 180 degrees

20+ 20 + vertex = 180

vertex = 140°

step by step explanation :

to converting yard to inches you have to multiply whatever number u are given in yard by 36 to get your figure in inches

o multiply whatever number u are given in yard by 36 to get your figure in inches so we multiply 6 *36 to give us 216

o multiply whatever number u are given in yard by 36 to get your figure in inches so we multiply 6 *36 to give us 216answer:

216

Answer: 23 meter

Step-by-step explanation:

meters "above"

elevation means the distance above sea level

There are 402.28 in2 of pasta in the container.

The mathematical branch is known as algebra deals with symbols and the rules governing their manipulation. These characters, which are now expressed as Latin and Greek letters, stand for variables, or quantities without set values, in elementary mathematics.

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.

The radius of cylinder (r) = 3.2 inches

Height of cylinder (h) = 14 inches

Height of pasta = 14 – 1.4 = 12.5 inches

Pasta in container = 22/7*(3.2)2*12.5

=402.8 in2

Hence, the container carries 402.8 in2 of pasta in it.

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