2s^3+27+18s+3s^2

factor by grouping

To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

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Answer:

After step 5, you will add 32 branches to get to step 6

Step-by-step explanation:

let's solve this question using geometric sequence;

\( {a \times r}^{n - 1} \)

since step 1, we will add 2 branches to get to step 2. we call as well as say

\( {a \times r}^{1 - 1} = {a \times r}^{0} = a\)

T1 = a = 2

to get step 2 we will need to add 4 branches to get step 3

T2 = 4

\(t2 = {a \times r}^{2 - 1} = a \times r = 4\)

since a = 2. we will just substitute for the values

2 × r = 4

2r = 4

\( \frac{2r}{2} = \frac{4}{2} \)

r = 2

Therfore:-

a = 2

r = 2

now lets solve the question

in order to get to step 4 we need to go through step 3

\(t3 = {a \times r}^{3 - 1} = {a \times r}^{2} \)

By substituting

\( {2 \times 2}^{2} = 2 \times 4 = 8\)

so in order to get to step 4 we will add 8 branches

in order to get to step 5 we need to go through step 4

\(t4 = {a \times r}^{4 - 1} = {a \times r}^{3} \)

by substituting

\( {2 \times 2}^{3} = 2 \times 8 = 16\)

in order to get to step 5 we need to add 16 branches

To get to step 6 we need to go through step 5

\(t5 = {a \times r}^{5 - 1} = {a \times r}^{4} \)

by substituting

\( {2 \times 2}^{4} = 2 \times 16 = 32\)

in order to get to step 6 we need to add 32 branches

i hope this helps

The linear optimization problem is to maximize the objective function 250x + 150y, subject to the constraints x + y ≤ 60, 3x + y ≤ 90, and 2x + y > 30, where x and y are both greater than or equal to 20.

The feasible region can be determined by graphing the constraints and finding the overlapping region that satisfies all the conditions. In this case, the feasible region is the area where the lines x + y = 60, 3x + y = 90, and 2x + y = 30 intersect. This region can be visually represented on a graph.

To find the corner points of the feasible region, we need to find the points of intersection of the lines that form the constraints. By solving the systems of equations, we can find that the corner points are (20, 40), (20, 60), and (30, 30).

The optimal solution and the optimal objective function value can be determined by evaluating the objective function at each corner point and selecting the point that yields the maximum value. By substituting the coordinates of the corner points into the objective function, we find that the maximum value is achieved at (20, 60) with an objective function value of 10,500.

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The number line for the set of jump distances to make a new record.

Option B is the correct answer.

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

We have,

The school record in the long jump = 518 cm

Now,

To make a new record the set of jump distances should be greater than 518 cm.

To represent the set of jump distances on a number line we can not have a black dot on 513 on the number line.

The dot should be an open dot.

Thus,

Option B is the number line for the set of jump distances to make a new record.

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The parabola widens when an is between 0 and 1, narrows when an is greater than 1, and is mirrored across the x-axis when an is less than 0.

Give three particular examples of how a parabola can change depending on the type of "a" value. y= 2(x+1)? Stretch y= as E parabola descends. (x-2)Parabola reduces by 2+1, y = x2-1. E opens up with no alteration. 7.

Here, the curve turns 180 degrees when an is negative.

The parabola opens broader when |a| is less than 1.

The parabola expands more narrowly when |a| exceeds 1.

The parabola widens when an is between 0 and 1, narrows when an is greater than 1, and is mirrored across the x-axis when an is less than 0.

Therefore, the curve widens when an is between 0 and 1.

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Step-by-step explanation:

LCM for 7 by 24=168

LCM for 17 by 36=612

Answer:

Removing the outlier lowers the standard deviation by 1.09

Step-by-step explanation:

Find the standard deviation of the data WITHOUT the outlier first.

If you don't know how to do standard deviation, here are the steps:

1. Find the mean

2. Subtract the mean by the data set values

3. Square the differences

4. Add the squared numbers together and divide by the number of data set values

5. What you have now is the variance, and all you have to do now is square the variance and you have the standard deviation

Repeat this, but WITH the outlier this time.

Final step, just subtract the smaller number (answer you got from the data with the outlier) by the greater number (answer you got from the data without the outlier) and you have your answer: 1.09!

Answer: x+6

Step-by-step explanation:

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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Answer:

\(10, 20, 202, 404, 505\) and \(1010\) has more than \(3\) factors.

Step-by-step explanation:

Given: A number \(2020\)

To find: How many factors of \(2020\) have more than 3 factors?

Solution:

We have,

Factors of \(2020\) are \(1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010\)

Now, we have to find the number of factors that has more than \(3\) factors. So, let us consider each factor of \(2020\) one by one.

Factor of \(1: 1\)

Factors of \(2: 1, 2\)

Factors of \(4: 1, 2, 4\)

Factors of \(5: 1, 5\)    

Factors of \(10: 1, 2, 5, 10\)

Factors of \(20: 1, 2,4, 5, 10, 20\)

Factors of \(101: 1,101\)

Factors of \(202: 1,2, 101, 202\)

Factors of \(404: 1, 2, 4, 101, 202, 404\)

Factors of \(505: 1, 5, 101, 505\)

Factors of \(1010: 1, 2, 5, 10, 101, 202, 505, 1010\)

Clearly, \(10, 20, 202, 404, 505\) and \(1010\) has more than \(3\) factors.

Hence, \(10, 20, 202, 404, 505\) and \(1010\) has more than \(3\) factors.

Answer:

you can ask questions that are on tests or live exams. I have reported this to brainly. Please don't do that again.

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Since you didn't attach an image of the graph I'll have to do this the hard way.

x + 2y = 2  (1)

2x + 4y = -8 (2)

x + 2y = -4 (Divide equation (2) by 2)

0 = 6 (Subtract the third equation from the first)

Since 0 is not equal to 6 the answer is No Solutions.

Answer:

no solutions

Step-by-step explanation:

x+2y=2

2x+4y=−8​

Multiply the first equation by -2

-2x -4y = -4

Add this to the second equation

-2x-4y = -4

2x +4y = -8

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

0x+0y = -12

0 = -12

This is never true so there are no solutions

Tan(3/4 - \(\pi\) ) = 1, which is the ratio of a right triangle with a 45° angle's opposite side to its adjacent side. This is different from value of \(tan(3\pi /4)\), which is -1, it corresponds to a different angle.

The tangent of the angle 3/4 (or 135 degrees) is equal to -1 because \(tan(3/4)\)has a value of -1. The ratio of the opposite side to the adjacent side can be calculated by drawing a right triangle with an angle of 135 degrees.

To obtain the value of\(tan(3\pi /4 - \pi )\), we first need to simplify the phrase \(3\pi /4 - \pi\), which gives us\(\pi /4\) (or 45 degrees). Therefore, we need to find the tangent of the angle 45 degrees.

The ratio of the opposite side to the adjacent side of a right triangle with a 45-degree angle has the value of \(tan(45)\), which is equal to 1.

So, \(tan(3\pi /4 – \pi ) = tan(\pi /4) = 1.\)

In summary, the value of\(tan(3\pi/4 - \pi)\)) is equal to 1, which is the ratio of the opposite side to the adjacent side of a right triangle with an angle of 45 degrees. This is distinct from the value of \(tan(3\pi /4)\), which is -1, as it corresponds to a different angle.

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\(f(x) =4 x {}^{3} - 4x {}^{2} - 16x + 16\)

\(divide \: by \: x - 2\)

\(4x {}^{2} \: into \: (x - 2) = 4x {}^{3} - 8x {}^{2} \)

\(g(x) = 4x {}^{2} - 16x + 16\)

\(4x \: into \: (x - 2) = 4x {}^{2} - 8x\)

\(z(x) = - 8x + 16\)

\( - 8 \: into \: (x - 2) = - 8x + 16 \\ no \: remainder\)

\(f(x) = (x - 2)(4x {}^{2} + 4x - 8)\)

\(f(x) = 0 \\ x - 2 = 0 \: \: \: \: \: \: \: \: \: 4x {}^{2} + 4x - 8 = 0 \\ \)

\(x = \frac{ - 4 + \sqrt{4 {}^{2} - 4(4)( - 8) } }{2(4)} = \frac{ - 4 + \sqrt{144} }{8} = \frac{ - 4 + 12}{8} = 1\)

\(x = 2\)

\(x = \frac{ - 4 - 12}{8} = \frac{ - 16}{8} = - 2\)

Answer: B

Step-by-step explanation:

Edge 2023

Answer:

1

Step-by-step explanation:

since the formula is

y=x+5 and x is the slope

1 is the slope

Answer:

the slope is 1 and the y intercept is 5

Answer:

she raked 11 bags of leaves

Step-by-step explanation:

24.75 divided by 2.25= 11

The volume of each ball is (32/3)π cubic inches, and the volume of water just enough to cover the four balls is also (32/3)π cubic inches.

First, let's calculate the volume of each ball. The diameter of each ball is given as 4 inches, so the radius (half the diameter) of each ball is 2 inches. The formula to calculate the volume of a sphere is V = (4/3)πr^3, where V represents volume and r represents the radius.

For each ball, the volume is:

V = (4/3)π(2³)

V = (4/3)π(8)

V = (32/3)π cubic inches

Since there are three balls at the bottom of the jar, the combined volume of these three balls would be:

3 * (32/3)π = 32π cubic inches

Now, let's consider the fourth ball. Since it is dropped on top of the three balls, it will displace some water, and the volume of the water needed to cover the four balls will be equal to the volume of the fourth ball.

To find the volume of the fourth ball, we use the same formula:

V = (4/3)πr³

Since the diameter of the fourth ball is also 4 inches, its radius is 2 inches. Substituting this value into the formula, we get:

V = (4/3)π(2³)

V = (4/3)π(8)

V = (32/3)π cubic inches

Therefore, the volume of water required to cover the four balls is also (32/3)π cubic inches.

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See attachment for reply.

Answer:

Wheel & axle

Step-by-step explanation:

Answer: it is called a

wheel and axle

Step-by-step explanation:

sheeeeeeeeeeeeeeeeeeeeeeeeeeeesh

Answer:

39

Step-by-step explanation:

The algebraic form of the complex number whose modulus = 3 and its amplitude = π is , a. - 3.

As the name suggests it is a combination of real numbers and imaginary numbers.

A complex number (a + ib) where a is the real part and b is the imaginary part.

'i' here is called iota and i = √-1, i² = - 1, i³ = - i and i⁴ = 1.

Given, A complex number whose modulus is 3 and arg is π, Now this is in polar form, z = r(cosФ + isinФ).

z = 3(cosπ + isinπ).

cosπ = - 1 and sinπ = 0.

Therefore,

z = 3(cosπ + isinπ).

z = 3(- 1 + i0).

z = - 3.

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Answer:

Step-by-step explanation:

f(x) = x^2+2x

g(x) = 3x-9

g(3) = 3*3-9 = 0

(f∘g)(3) = f(g(3)) = 0^2 + 2*0 = 0

:::::

f(-2) = (-2)^2+2(-2) = 0

(g∘f)(-2) = g(f(-2)) = g(0) = 3(0)-9 = -9

Answer:

An unclosed shape or one with lines not straight.

Step-by-step explanation:

Answer:

I have provided a picture of the typical polygons so if an option doesn't look like this, then it's probably not a polygon. Also, polygons are any 2-d shape made with straight lines, so a circle or a 3D shape is wrong

The correlation close to 0, because there is no reason to believe that height and number of siblings are related to each other.

For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to 0. Explain your choice. (a) Weight of a car and gas mileage: There is a negative correlation, because heavier cars tend to get lower gas mileage. (b) Size and selling price of a house: There is a positive correlation, because larger houses tend to be more expensive. (c) Height and weight: There is a positive correlation, because taller people tend to be heavier. (d) Height and number of siblings: There is a correlation close to 0, because there is no reason to believe that height and number of siblings are related to each other.

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1) The value of the country's exports in 2024 is estimated to be approximately 3.43 billion dollars.

2) the doubling time for the value of the country's exports is approximately 18.17 years.

Export is defined as moving products to another country for the purpose of trade or sale

a) To estimate the value of the country's exports in 2009, we need to evaluate V(0), which gives:

V(0) = 1.4 \(e^{(0.0381*0)\) = 1.4

Therefore, the value of the country's exports in 2009 was approximately 1.4 billion dollars.

To estimate the value of the country's exports in 2024, we need to evaluate V(15), which gives:

V(15) = 1.4 \(e^{(0.0381*15)\) = 3.43

Therefore, the value of the country's exports in 2024 is estimated to be approximately 3.43 billion dollars.

b) To find the doubling time for the value of the country's exports, we need to use the formula for exponential growth:

V(t) = V0 \(\rm \bold{e^{(rt)}}\)

where V0 is the initial value, r is the annual growth rate, and t is the time in years.

We want to find the time it takes for the value of exports to double, so we can set V(t) = 2V0 and solve for t:

2V0 = V0 \(\rm e^{(rt)\)

Dividing both sides by V0, we get:

2 = \(\rm e^{(rt)\)

Taking the natural logarithm of both sides, we get:

ln(2) = rt

Solving for t, we get:

t = ln(2)/r

Substituting the given values, we get:

t = ln(2)/0.0381

Simplifying, we get:

t ≈ 18.17 years

Therefore, the doubling time for the value of the country's exports is approximately 18.17 years.

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Answer:

15

Step-by-step explanation:

=> \((15^{1/5})^5\)

=> \((15^{5/5})\)

=> \(15^1\)

=> 15

Hey there!

Answer:

15.

Step-by-step explanation:

When there is an exponent outside of the parenthesis, the two powers must be multiplied together. Therefore:

\((15^{1/5 })^{5}\)

Multiply '1/5' and '5':

\(15^{1/5*5}\)

\(15^{1}\)

= 15.

Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.