Suppose n ≥ 0 is an integer and all the roots of x³ + αx + 4 − (2 × 2016ⁿ) = 0 are integers. Find all possible values of α.​

Answer:

Step-by-step explanation:

7k+8=71

7k=71-8

7k=63

k=63/7

k=9

-9=3-y

-9+3=y

-6=y

y=-6

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Salut! Comment allez-vous? Comment s'est passée ta journée?

The answer of the given question based on the image transformation is , (a) reflection over line BC⎯.

Reflection is a transformation in which a figure or an object is flipped across a line or a plane. The line or plane across which  figure is flipped is called line or plane of reflection. In two-dimensional geometry, a reflection can be thought of as a "flip" of the figure over the line of reflection. Any point on the figure that lies on the line of reflection will remain fixed, while all other points will be reflected across the line.

The pre-image ABC was transformed to create image A′B′C′ through a reflection over line BC⎯.

To visualize this transformation, imagine folding the original figure over line BC⎯, so that point A maps to point A′, point B maps to point B′, and point C maps to point C′. The resulting image is the reflection of the original figure over line BC⎯.

The other options listed (90° clockwise rotation around point C, translation up, and translation down) would create different images, but not the image A′B′C′ shown in the diagram.

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Answer: 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

You take items out of a square root if you have a pair of numbers or if you know the square root.  

[tex]\sqrt{48b^{7} }[/tex]=[tex]\sqrt{4*4*3*bbbbbbb}[/tex]

So I know the [tex]\sqrt{4}[/tex]=2 so i can take both out so outside the root will be 2*2 and inside the root will be 3

Now for the b's for every pair there are, you can take that out.  There are 3 pairs of b's so b³ is outside and one b is left inside.

Answer:

4b³[tex]\sqrt{3b}[/tex]

Answer:

Step-by-step explanation:

substitute:

2(5) + 3(3-5) + 3²     Do PEMDAS  order (parenthesis, exponent, mult/div, add/sub

2(5) + 3(-2) +3²

2(5) + 3(-2) + 9

10 + 3(-2) +9

10-6+9

4+9

13

The 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

A z-score calculates how many standard deviations an observation is from the mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative.

For the 3-year-old boy, the z-score is:

z = (43 - 38) / 2 = 2.5

The z-score for the 10-year-old girl is:

z = (57 - 54.5) / 2.5 = 1

The 3-year-old boy has a higher z-score than the 10-year-old girl, indicating that he is more unusually tall for his age and gender. This is due to his height, which is higher than the average for his age group 38 inches .

Therefore, the 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

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Answer: the answer is B

Step-by-step explanation:

The angle SWY is 59°.

What is points of tangency?

Points of tangency is a point When a line is tangent to a circle.

It intersects the circle at exactly one point.

This point is always perpendicular to the radius of the circle which passes through it which means that the tangent line and the radius form a right angle.

The measure of an arc is equal to the measure of the central angle which delete it. This means that if you know the measure of an arc.

We can find the measure of the central angle that subtends it.

If we assume that point Y is on the tangent line and is between point W and point S, then angle SWY is an inscribed angle that intercepts arc WS. In a circle, the measure of an inscribed angle that intercepts an arc is half the measure of the arc.

So, if the measure of arc WS is 118 degrees, then the measure of angle SWY is half of 118 degrees, which is 59 degrees.

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Answer:

B

Step-by-step explanation:

The unit of measurement that would typically be used to weigh an elephant is the ton. Elephants are very large animals, and they can weigh several tons, depending on their species and size. While other units of measurement like pounds, kilograms, or ounces could also be used to measure the weight of an elephant, the ton is the most appropriate unit for such a large animal.

Answer:

40

Step-by-step explanation:

In order to find your answer, you would need to multiply -5, by -8 which equals 40.

:)

-5(-8) = 40

Because both the 5 and 8 being multiplied are negative, the commutative multiplication property states that the product should be positive. Since 5*8=40, -5*-8=40

Answer:

Step-by-step explanation:

The formula for continuous compound interest is:

A = P(1 + r/100)^t

where A is the amount after t years, P is the principal, r is the annual interest rate as a decimal, and t is the time in years.

In this case, we have P = $380, r = 0.08 (8%), and t = 8 years. Plugging in these values, we get:

A = 380 x (1+8/100)^8

A= 380 x (1+0.08)^8

A=380 x (1.08)^8

A= 380 x 1.8509..

A= $703.35

Therefore, the amount in the account after eight years, rounded to the nearest cent, is  $703.35.

Answer :

Angle A = 19.6°

Step-by-step explanation :

According to the question It is given that,

Angle A = x

Angle B = 5x

Angle C = 4x - 16

We will apply angle sum property in the question.

Angle sum property states that sum of all the angles of triangle is 180°

[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180

[tex]\: :\implies [/tex] x + 5x + 4x - 16 = 180

[tex]\: :\implies [/tex] 10x - 16 = 180

[tex]\: :\implies [/tex] 10x = 180 + 16

[tex]\: :\implies [/tex] 10x = 196

[tex]\: :\implies [/tex] x = 196/10

[tex]\: :\implies [/tex] x = 19.6

Hence,

Angle A = x

[tex]\: :\implies [/tex] 19.6 °

Angle B = 5x5 × 19.6

[tex]\: :\implies [/tex] 98

Angle c = 4x - 16

[tex]\: :\implies [/tex] 4 × 19.6 - 16

[tex]\: :\implies [/tex] 78.4 - 16

[tex]\: :\implies [/tex] 62. 4

We must also check our answer.

Sum of all angles = 180°

[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180

[tex]\: :\implies [/tex] 19.6 + 98 + 62.4 = 180

[tex]\: :\implies [/tex] 117.6 + 62.4 = 180

[tex]\: :\implies [/tex] 180 = 180

Hence, Verified.

Therefore, The Measure of Angle A is 19.6°

Answer:

angle A = 19.6°

Explanation:

angle ABC + angle ACB + angle BAC = 180°

5x + (4x - 16)° + x = 180°

Simplifying:

5x + x + (4x + -16) = 180

Reorder the terms:

5x + x + (-16 + 4x) = 180

Remove parenthesis around (-16 + 4x)

5x + x + -16 + 4x = 180

Reorder the terms:

-16 + 5x + x + 4x = 180

Combine like terms: 5x + x = 6x

-16 + 6x + 4x = 180

Combine like terms: 6x + 4x = 10x

-16 + 10x = 180

Solving

-16 + 10x = 180

Solving for variable 'x'.

Add '16' to each side of the equation

-16 + 16 + 10x = 180 + 16

Combine like terms: -16 + 16 = 0

0 + 10x = 180 + 16

10x = 180 + 16

Combine like terms: 180 + 16 = 196

10x = 196

Divide each side by '10'

x = 19.6

The measure of angle A is 19.6°

Wesley's class collected 253/18 pounds of clothing, which can also be written as 14 1/18 pounds (rounded to the nearest hundredth).

Whole numbers include natural numbers that begin from 1 onwards. Let us look at some examples of whole numbers. The set of whole numbers is denoted by the alphabet 'W'. W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,.…}

Jada's class collected 7 2/3 kilograms of clothes. Wesley's class collected 15/6 times as many clothes as Jada's class, which means they collected:

1 5/6 x (7 2/3) pounds of fabric

To multiply fractions, you can first convert the mixed numbers to improper fractions, then multiply the numerators and denominators separately and simplify if possible.

Convert mixed numbers to improper fractions:

7 2/3 = (37 + 2)/3 = 23/3

1 5/6 = (61 + 5)/6 = 11/6

Multiply Fractions:

(11/6) * (23/3) = (1123)/(63) = 253/18

Therefore, Wesley's class collected 253/18 pounds of clothing, which can also be written as 14 1/18 pounds (rounded to the nearest hundredth).

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Answer:

its 32 square units

Step-by-step explanation:

The Shape is a rectangle. Area of a rectangle is Length x Width

8 x 4 = 32

Answer:

32 Square units

Step-by-step explanation:

You can see that there are 8 spaces of width by using the graph. And 4 spaces of height. So, assuming each space is 1 Square unit. All you have to do is 8×4 which is 32.

Step-by-step explanation:

(x-3)(x-1 +2i)(x-1-2i)        The imaginary roots always come in pairs :   1+- 2i

The equation is  [tex]g(x) = -\frac{1}{16} (x - 1)^2 + 2[/tex]  Graphing this equation below, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).

To demonstrate the connection between the two variables, a line or curve is drawn between the plotted points.

To graph function g, we need to find its equation that satisfies the given properties. We know that the y-intercept of g is less than that of f, so we can choose it to be 1. Also, the parabola of g opens downwards and its vertex is between the two x-intercepts, which are at x = -2 and x = 4. We can use these points to find the equation of the parabola in the standard form: g(x) = a(x - h)² + k. Using the fact that g(0) = 1 and the x-intercepts, we can solve for a, h, and k. The resulting equation is:

[tex]g(x) = -\frac{1}{16} (x - 1)^2 + 2[/tex]

Graphing this equation, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).

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Answer:

[tex] \frac{10}{3} = 10 \div 3 = 3 \frac{1}{3} [/tex]

Answer: Mixed Number Form: 3[tex]\frac{1}{3}[/tex]

Decimal Form: 3.3 repeating

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The best method to ensure an unbiased sample is to randomly select parents from the entire population of parents with enrolled students at the school.

To ensure an unbiased sample for the survey, the method used should not favor any particular group or exclude any group from the population.

Option A: Surveying all parents attending the next PTO meeting would not be an unbiased sample as not all parents attend PTO meetings.

Option B: Surveying every fifth person on a list of parent volunteers would also not be an unbiased sample as it may exclude parents who are not on the list.

Option C: Surveying all parents waiting in the pick-up line after school may not be an unbiased sample as it may exclude parents who do not pick up their children from school.

Option D: Surveying all parents of students whose birthdays are on even-numbered days may not be an unbiased sample as it excludes parents whose children's birthdays are on odd-numbered days.

Therefore, the best method to ensure an unbiased sample is to randomly select parents from the entire population of parents with enrolled students at the school.

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Answer:

Step-by-step explanation:

assuming that every square is 1 unit, the distance from the store to home should be 5 units, I hope this helped

Answer:

Let's call the speed of the bus on the winding road "s". Then we know that the bus traveled at a speed of "s + 20" on the level road. We also know that the time spent on the winding road was 4 hours, so the distance traveled on the winding road is:

distance = speed × time = s × 4

Similarly, the distance traveled on the level road is:

distance = speed × time = (s + 20) × 4

Since the entire trip was 400 miles, we can write:

4s + 4(s + 20) = 400

Simplifying this equation, we get:

8s + 80 = 400

8s = 320

s = 40

Therefore, the speed of the bus on the winding road was 40 mph, and the speed on the level road was 40 + 20 = 60 mph.

To check that this solution is correct, we can calculate the distance traveled on each road:

distance on winding road = 40 × 4 = 160 miles

distance on level road = 60 × 4 = 240 miles

The total distance traveled is indeed 160 + 240 = 400 miles, so our solution is correct.

Therefore, the average speed on the level road was 60 miles per hour.

Answer:

It could be 0, is the question multiple choice?

a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}[/tex]

The expression can be rewriten as a single radical as:

[tex]\sqrt[5]{4} *\sqrt{2} = \sqrt[10]{2^9}[/tex]

We want to rewrite the expression below as a single radical:

[tex]\sqrt[5]{4} *\sqrt{2}[/tex]

First remember that 4 = 2², then we can replace that to get:

[tex]\sqrt[5]{4} *\sqrt{2} = \sqrt[5]{2^2} *\sqrt{2}[/tex]

Converthing the roots to exponents we will get.

[tex]\sqrt[5]{2^2} *\sqrt{2} = 2^{2/5}*2^{1/2}[/tex]

Now the exponents are just added:

[tex]2^{2/5}*2^{1/2} = 2^{2/5 + 1/2} = 2^{4/10 + 5/10} = 2^{9/10} = \sqrt[10]{2^9}[/tex]

That is the correct option.

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Answer:

The matrix with row 1 showing 6 and 3 and 10, row 2 showing 8 and 9 and 9, row 3 showing 4 and 7 and 12 can be used to accurately represent the data.

The following matrix that can be used to accurately represent the data is the matrix:

[tex]\left[\begin{array}{ccc}6&3&10\\8&9&9\\4&7&12\end{array}\right][/tex]

A matrix is a collection of numbers, encompassed by brackets.

The numbers are known as matrix elements or entries. The components are organized in rows (horizontal) or columns (vertical), which determine the matrix's size (dimension or order).

As per the question, the entry in row i and column j represents the number of type j clubs offered by school i.

The matrix that can be used to accurately represent the data is the matrix:

[tex]\left[\begin{array}{ccc}6&3&10\\8&9&9\\4&7&12\end{array}\right][/tex]

This is because the rows represent the three different schools, and the columns represent the number of each of the types of clubs they offer.

The given data matches the entries in this matrix, so it can be used to accurately represent the data.

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According to probability, the answer to the question is that an average surgeon performs 8 operations, of which 5 are successful. 18.9%.

In a fixed number of independent trials, each of which can only have one of two outcomes—success or failure—the number of successes is expressed as a probability distribution known as a binomial probability. Additionally, it is presummated that each trial has an equivalent chance of success.

The binomial probability formula can be used to determine the likelihood that a surgeon will perform 5 successful operations out of 8 given that each operation has a 92% chance of being successful.

You may find the binomial probability formula by using:

[tex]P(X = k) = C(n, k)*p^k*(1 - p)^{(n - k)}[/tex]

Where:

P(X = k) is the likelihood that, out of n surgeries, exactly k will be successful.

The binomial coefficient, C(n, k), is defined as the number of ways to select k successful operations among n surgeries C(n, k) = n! / (k! * (n - k)!), where ! denotes factorial.

p is the likelihood that a single surgery will succeed (92% in this case, or 0.92).

The number of successful operations that interests us is k.

The total number of operations is n, which in this case is 8.

By entering the values, we can determine the probability using the formula below:

P(X = 5) = C(8, 5) * 0.92⁵ * (1 - 0.92)⁽⁸⁻⁵⁾

C(8, 5) = 8! / (5! * (8 - 5)!) = 56

0.92⁵ = 0.659

(1 - 0.92)³ = 0.512

P(X = 5) = 56 * 0.512 * 0.659 = 18.89 or 18.9%

Given a 92% success rate for each surgery, the likelihood that a surgeon will perform 5 successful operations out of 8 is roughly 18.9%.

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The domain of function A and function B are compared by the statement of Option A: The domain of Function A is the set of real numbers greater than 0. The domain of Function B is the set of real numbers greater than or equal to 1.

What is a function?

A function is a fundamental concept in mathematics that relates a set of inputs (also known as the domain) to a corresponding set of outputs (sometimes referred to as the codomain). For each input, there exists exactly one output, and the output can be linked to its corresponding input in a unique manner.

The domain of a function refers to the set of all possible input values for which the function can produce an output.

In Function A, the domain consists of all real numbers greater than 0, since it is a logarithmic function that can take any positive number as an input.

In contrast, the domain of Function B includes all real numbers greater than or equal to 1, since it is a square root function that begins at (1,0) and continues to infinity.

This means that any number greater than or equal to 1 can be used as an input to produce a corresponding output.

It is essential to define the domain of a function accurately to ensure that the function is well-defined and to avoid potential errors or ambiguities in mathematical computations.

Therefore, the correct statement is A.

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Therefore, there are approximately 889 faculty members at the college.

Ratio is a mathematical concept that expresses the relationship between two or more quantities or values. It is a way to compare the size of two numbers, by dividing one number by the other. The result of this division is a numerical expression of the relative size of the two numbers.

Ratios are often expressed as a fraction or a colon (:) between the two numbers. For example, if there are 4 red balls and 6 blue balls in a bag, the ratio of red balls to blue balls can be expressed as 4/6 or 4:6. This means that for every 4 red balls in the bag, there are 6 blue balls.

Ratios are commonly used in various fields, such as finance, statistics, and science, to compare different values and make meaningful interpretations.

To solve this problem, we need to use the ratio between faculty members and students, which is given as 1:18. This means that for every one faculty member, there are 18 students.

If there are 16000 students in the college, we can find the number of faculty members by dividing the number of students by the ratio of students to faculty members:

Number of faculty members = 16000 / 18

This gives us 888.888, but since we are asked to round to the nearest whole number, we should round up to 889. Therefore, there are approximately 889 faculty members at the college.

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The average rate of change of a beach ball thrown according to the function[tex]f(x) = 12x - 4.8x^2[/tex] over the interval 0 < x < 2 is -9.6 feet per second.

To find the average rate of change, we need to find the height of the ball at x = 0 and x = 2, and then find the change in height over the time interval.

At x = 0, the height of the ball is:

[tex]f(0) = 12(0) - 4.8(0)^2 = 0[/tex]

At x = 2, the height of the ball is:

[tex]f(2) = 12(2) - 4.8(2)^2 = -19.2[/tex]

The change in height over the time interval 0 < x < 2 is:

-19.2 - 0 = -19.2

Therefore, -19.2/2 = -9.6 feet per second is the average rate of change over the range 0 x 2.

The average change throughout the range of 0 x 2 is therefore -9.6 feet per second.

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The direction of the vector is 27 degrees

The vector is the hypotenuse and the angle showing magnitude and direction.

To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem.

hypotenuse^2 = opposite^2 + adjacent^2

hypotenuse^2 = 88.4^2 + 174^2

hypotenuse ≈ 195.17 m

Therefore, the magnitude of the vector (hypotenuse of the right triangle) is approximately 194.8 m.

The direction

We can use the trigonometric function of tangent to find the angle between the opposite and adjacent sides of a right triangle.

tan(θ) = opposite/adjacent

We are given

so we can use these values to find the angle θ:

tan(θ) = 88.4/174

θ = arc tan (88.4/174)

θ ≈ 26.93 degrees

Therefore, the angle between the opposite and adjacent sides of the right triangle is approximately 27 degrees.

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The science class had a higher average of 85 compared to te math's average of 81

Maths class

The function si given as

f(x) = 0.5x + 80

After completing test 2, we have

f(2) = 0.5 * 2 + 80

f(2) = 81

Science class

The function si given as

The table

The equation of the table is

g(x) = 2x + 81

After completing test 2, we have

g(2) = 2(2) + 81

g(2) = 85

This means that the science class had a higher average

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