When dividing x' + 3x + 2x + 1 by x² + 2x +3 in Z:[x], the remainder is 3 O 2 0 4. Question * 1 is a root for f(x) Let S(x) = x' + x + 2x+ – 1 € 23[x]. Then x of multiplicity: 2 3 O 1 O 4

Answer: 1

Step-by-step explanation: Fractions are the same as division, so what this is really saying is 8 ➗ 8 which is 1.

Answer:

y=8

Step-by-step explanation:

Slope-intercept form

y=mx+b

Plug in values

y=0x+b

8=0(-4)+b

b=8

substitute

y=8

Answer:

4/7 = 0.57142857……

Step-by-step explanation:

integer NO cause it has a decimal

irrational NO cause it can be written as a fraction

Natural NO cause it has decimals

Rational YES because it’s a fraction

whole NO cause decimals

Real YES cause it’s a number

The estimated probability of a success in this scenario would be 0.6, or 60%.

To estimate the probability of success in this scenario, we need to determine the frequency of success (occurrence of numbers 1, 2, and 3) in the randomly generated list of integers from 0 to 4.

Let's assume we have a large sample of these randomly generated lists, and we record the number of successes in each list. The estimated probability of success can be calculated by dividing the total number of successes by the total number of trials (lists).

For example, if we have observed 5000 lists and found that the number of successes (1, 2, or 3) occurred in 3000 of those lists, the estimated probability of success would be:

Estimated probability of success = Number of successes / Total number of trials

Estimated probability of success = 3000 / 5000

Estimated probability of success = 0.6

Therefore, the estimated probability of a success in this scenario would be 0.6, or 60%.

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The intervals start from 0 and increase by 1 for each subsequent set. The interval notation [a, b) represents all the real numbers greater than or equal to a and less than b.

1. Let's evaluate each set operation:

a) A ∩ (B ∪ C):

B ∪ C = {2, 3, 4, 5}

A ∩ (B ∪ C) = {2, 3}  (the elements that are common to both A and (B ∪ C))

b) (A ∩ B) ∪ C:

A ∩ B = {2, 3}

(A ∩ B) ∪ C = {2, 3, 4, 5}  (the elements that are either in A ∩ B or in C)

c) (A ∩ B) ∪ (A ∩ C):

A ∩ C = {3}

(A ∩ B) ∪ (A ∩ C) = {2, 3}  (the elements that are either in A ∩ B or in A ∩ C)

Comparing the results:

A ∩ (B ∪ C) = {2, 3}

(A ∩ B) ∪ C = {2, 3, 4, 5}

(A ∩ B) ∪ (A ∩ C) = {2, 3}

From the above evaluations, we can see that (A ∩ B) ∪ C = (A ∩ B) ∪ (A ∩ C), so these two sets are equal.

2. Examples of partitions:

a) A partition of Z (integers) consisting of 2 sets:

{..., -2, 0, 2, 4, ...} and {..., -3, -1, 1, 3, ...}

b) A partition of R (real numbers) consisting of infinitely many sets:

{[0, 1)}, [1, 2), [2, 3), [3, 4), ...}

In this example, each set in the partition includes all the real numbers within a specific interval. The intervals start from 0 and increase by 1 for each subsequent set. The interval notation [a, b) represents all the real numbers greater than or equal to a and less than b.

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(a) To sketch a graph of the speed over a 3-second time span, we need to know the equation that describes the relationship between speed and time. Without this information, we cannot create an accurate graph.

(b) To find the volume of blood that passes along the artery in one second, we need to use the formula Q = A * v, where Q is the flow rate, A is the cross-sectional area of the artery, and v is the speed of blood flow. The cross-sectional area of the artery is given by A = pi * r^2, where r is the radius of the artery.

Thus, substituting the given values, we get:

A = pi * (5mm)^2 = 78.54 mm^2

v = 0.2 + 0.1 sin(2pit/0.8) (using the given information)

Q = A * v = 78.54 * (0.2 + 0.1 sin(2pit/0.8))

To find the volume of blood that passes along the artery in one second, we need to evaluate Q at t = 1 second, so we get:

Q = 78.54 * (0.2 + 0.1 sin(2pi1/0.8)) = 31.39 mm^3/s

Therefore, the volume of blood that passes along the artery in one second is approximately 31.39 cubic millimeters.

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Answer:

\(\boxed{\pink{\tt \leadsto Sum \ of \ first \ five \ terms \ is \ 50 . }}\)

Step-by-step explanation:

Given that , the sum of the first nine terms of an arithmetic series is 162 and the sum of the first 12 terms is 288.

\(\boxed{\red{\bf \bigg\lgroup For \ answer \ refer \ to \ attachment \bigg\rgroup }}\)

• The sum of n terms of an AP is

\(\boxed{\orange{\sf S_n = \dfrac{n}{2}[2a+(n-1)d] }}\)

• nth term of an AP is given by ,

\(\boxed{\blue{\sf T_n = a+(n-1)d }}\)

The value of side length w is 13.75 .

Given right angled triangle,

Perpendicular = w

Hypotenuse = 17

Angle of triangle = 54°

So,

According to the trigonometric ratios,

tanФ = p/b

cosФ = b/h

sinФ = p/h

By using sinФ,

sinФ = p/h

sin 54° =  w/ 17

0.809 = w/17

w = 13.75 .

Thus after correction w will be 13.75

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Check the picture below.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{40}\\ o=\stackrel{opposite}{60} \end{cases} \\\\\\ AC=\sqrt{ 40^2 + 60^2}\implies AC=\sqrt{ 1600 + 3600 } \implies \boxed{AC=\sqrt{ 5200 }} \\\\[-0.35em] ~\dotfill\)

\(\tan(25^o )=\cfrac{\stackrel{opposite}{FC}}{\underset{adjacent}{60}} \implies \boxed{60\tan(25^o)=FC} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} \textit{ the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{A F}\\ a=\stackrel{adjacent}{\sqrt{5200}}\\ o=\stackrel{opposite}{60\tan(25^o)} \end{cases} \\\\\\ (A F)^2= (\sqrt{5200})^2 + (60\tan(25^o))^2\implies A F^2\approx 5200+27.98^2 \\\\\\ A F\approx\sqrt{5200+27.98^2}\implies \boxed{A F\approx 77.349~cm}\)

Answer:

The answer is 25

Step-by-step explanation:

I used a calculator. if this is for a quiz for other people do

A. 25

B. 34

C. -5

D. -65

The schedule for the number of hours worked by employees at Waterloo Park is represented by the functions b(x), t(x), r(x), and s(x) for Bill, Ted, Rufus, and Socrates, respectively, on a given day x.

In the schedule, the function b(x) represents the number of hours worked by Bill on a given day x. Similarly, the function t(x) represents the number of hours worked by Ted, the function r(x) represents the number of hours worked by Rufus, and the function s(x) represents the number of hours worked by Socrates on the same given day x.

By using these functions, you can determine the specific number of hours each employee worked on any given day. For example, if you have a value for x, you can substitute it into the functions to find the corresponding number of hours worked by each employee.

It's important to note that the functions b(x), t(x), r(x), and s(x) are specific to Waterloo Park and the employees mentioned. The given schedule provides a way to track the hours worked by each employee on different days. By utilizing these functions, you can analyze and calculate the hours worked by each employee effectively.

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The random variable X is the ounces of water in the bottle.

What is a random variable?

The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a sample space of potential outcomes to a measured space, frequently the real numbers.

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable is a numerical representation of the result of an experiment in statistics. Discrete random variables are those that can only take on a finite number or an infinite series of values.

Hence, According to the provided information, it is known that a bottle of water contains 12.05 fluid ounces; hence it is clear that the random variable X will be the ounces of water.

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complete question:

A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X in words.

Answer:

Option B is correct.

Step-by-step explanation:

{ -1 , 0 , 1 , 7 }

Hope this helps!

The range of the given function is {-1,0, 1,7}.

The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.

Given the function represented by ordered pairs, {(-2, 1), (0, 0), (3, -1), (-1, 7), (5, 7)},

We need to find the range,

So, we know that the all the y-values are called the range of a function,

here y-values are = 1, 0, -1, 7, 7

So, the range = {1, 0, -1, 7}

Hence the range of the given function is {-1,0, 1,7}.

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The probability that the sample average falls outside the 3-sigma control limits of the X-bar chart is 0.27%.

The 3-sigma control limits are calculated using the standard deviation of the process. If the process is in control, then 99.73% of the sample averages will fall within the 3-sigma control limits. The remaining 0.27% of the sample averages will fall outside the control limits.

In this case, the sample size is 4, which is smaller than the sample size of 9 that was used to construct the control chart. This means that the control limits for the sample of size 4 will be narrower than the control limits for the sample of size 9.

As a result, the probability that the sample average falls outside the control limits will be higher for the sample of size 4.

Specifically, the probability that the sample average falls outside the 3-sigma control limits for a sample of size 4 is 0.27%. This means that there is a 0.27% chance that the new employee will observe a sample average that falls outside the control limits, even if the process is in control.

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The value of y in the given proportion is 1/13.

In mathematics, a proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities, typically written as a fraction. For example, if we have two quantities, a and b, then the ratio of a to b is written as a/b.

A proportion is written in the form a/b = c/d, where a, b, c, and d are numbers. This means that the ratio of a to b is equal to the ratio of c to d. We can also write this as a:b = c:d.

To solve the proportion:

                   (4y+5):3=(y+7):4

We can cross-multiply and simplify:

                  4(4y+5) = 3(y+7)

                  16y + 20 = 3y + 21

Subtracting 3y from both sides:

                  3y + 20 = 21

Subtracting 20 from both sides:

                  13y = 1

Dividing both sides by 13:

                  y = 1/13

Therefore, the value of y that satisfies the proportion is y = 1/13.

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Answer: 1 + 1 = 2

2-1 = 1

Step-by-step explanation:

basic math stuff

Answer:

Experimental

Step-by-step explanation:

They are imposing a variable on the computers in an effort to have a explanatory variable to justify how they behave and not just watching how they behave naturally.

The given study of battery life of laptop is experimental study.

Experimental study is defined as when study is for something brought by performing practical test is said to be experiential study, while in observational study it does not require a practical test.

here,
in the given study researcher, put 30 new laptops of the same brand.
And Analysis all the laptop by using each laptop and that study directed the researchers to how long each machine's battery lasted. This practical study of battery of life tends that this study is experimental.

Thus, the given study of battery life of laptop is experimental study.

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Answer:

Step-by-step explanation:

The root which is 2 is the fractional portion of your exponent

\(\sqrt{x^{7} y^{12} }\)

=\((x^{7} y^{12} )^{\frac{1}{2} }\)              >You can distribute 1/2 to each term by multiplying

\(=x^{\frac{7}{2} } y^{6\)

Answer:

it's(-68) if you mean negative positive wise

Answer:

thanks for the points

Step-by-step explanation:

Answer:

The given polynomial is,

2x³+5x²-8x-10=0

all possible roots of a polynomial,

ax³+b²+c x +d=0 ← all possible factors of ration (d/a)

Therefore, eq (1), all possible factors are the factors of ratio (-10/2)

which are, B) { ± 1, 1/2, ± 2, ± 5/2, ±5, ± 10}

OAmalOHopeO

The perimeter of the pentagon ABCDE is given by:

From the figure, we can calculate the length of each side:

Finally, the perimeter is:

Answer: Out of the options on the online quiz the answer is 22 units

Step-by-step explanation: I got it right on the test

Answer:

14.625

Step-by-step explanation:

327.50- 230.00 = 91.5

91.5 x 0.15 = 14.625

Answer:

x = 12.489996 ft

Step-by-step explanation:

In order to solve one side length of a right triangle given two of other side lengths, you can use the pythagorean theory.

The theory states that the sum of the two adjacent side squares equals the square of the hypotenuse.

Basically:

\(x^2 + y^2 = h^2\)

Since the problem gives you the hypotenuse and one adjacent side length you rearrange the formula as so:

\(x^2 = h^2 - y^2\)

\(x=\sqrt{h^2 - y^2}\)

Then plug in the values:

\(x = \sqrt{16^2 - 10^2} = \sqrt{256-100}=\sqrt{156} = 2\sqrt{39}=12.489996\)

In order to have length twice width the answer should be 28 feet.

Let x be the width of the garden.

The length of the garden is 2x.

The perimeter of a rectangle is equal to 2(length + width)

So 42 = 2(2x + x)

42 = 2(3x)

x = 14

The width of the garden is 14 feet and the length is 2x = 2(14) = 28 feet.

The answer is 28 feet (Option a).

Mensuration is the branch of mathematics that deals with the measurement of geometric shapes and figures, such as length, area, and volume. It typically includes the study of geometric shapes, such as circles, triangles, and polygons, and their properties, such as perimeter, area, and volume. Mensuration is used in many fields, including engineering, physics, and computer graphics.

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Answer:

1 / 5^4  (or 1 / 625)

Step-by-step explanation:

The easiest way to understand and solve this is by expanding everything:

5^3 = 5*5*5

5^7 = 5*5*5*5*5*5*5

Now put those over each other like this:

        5*5*5

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

5*5*5*5*5*5*5

Then I essentially draw "1"s or lines over each pair of 5s (from the numerator to the denominator) until all of the 5s on the numerator or denominator are used up.

Note: This is completely legal as you are simply dividing pairs of 5/5 to get many 1s, and if you multiply everything by 1, it will eliminate the 1s.

So once you "cross all of them out" you are left with a 1 at the top and 5*5*5*5 at the bottom.

So you can simplify that down to

1 / 5^4  (or 1 / 625, however it's usually not necessary to calculate larger exponents)

a. The median number of calls = 55

b. The first and third quartiles, Q1 = 48 and Q3 = 66

c. The first decile and the ninth decile, D1 = 45 and D9 = 71.

d. The 33rd percentile = 52.5

To answer the questions, let's first organize the data in ascending order:

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

(a) The median is the middle value of a dataset when arranged in ascending order.

Since we have 40 observations, the median is the value at the 20th position.

In this case, the median is the 55th visit.

(b) The quartiles divide the data into four equal parts.

To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.

The first quartile is the value at the 10th position, which is 48.

To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.

The third quartile is the value at the 30th position, which is 66.

Therefore, Q1 = 48 and Q3 = 66.

(c) The deciles divide the data into ten equal parts.

To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.

The first decile is the value at the 4th position, which is 45.

To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.

The ninth decile is the value at the 36th position, which is 71.

Therefore, D1 = 45 and D9 = 71.

(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.

Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:

Lower value: 52

Upper value: 53

Position: 13

Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5

33rd percentile = Lower value + (Percentage * (Upper value - Lower value))

                = 52 + (0.5 * (53 - 52))

                = 52.5

Therefore, the 33rd percentile is 52.5.

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