what perfect square goes into the square root of 108

The median of the following set of numbers  (18, 26, 29, 18, 44) is 26. The correct option to this question is option A

To find median of the following sequence (18, 26, 29, 18, 44) we will arrange them in ascending order

                            18 , 18 , 26 , 29 , 44   . . . . . .  . . . .(1)

Since the number of terms is odd we will apply the formula

                     Median  = \(\frac{(n+1)}{2} th\) term . . . . . . .(2)

       Here n = number of terms

As per question the n = 5

Therefore putting in equation 2 we get

                      Median = \(\frac{(5+1)}{2} th\) term

                      Median = \(\frac{6}{2} th \\\)  term

                      Median = 3 term

Hence the third term from the sequence ( shown in 1 ) we get the median that is 26

Hence the median of the following set of numbers (18, 26, 29, 18, 44) is 26 .

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The median is:

26

Explanation:

First, we will arrange the numbers from least to greatest.

18, 26, 29, 18, 44

Rearrange

18, 18, 26, 29, 44.

Now, the median is the number in the middle, which is 26.

Answer:

the factored form of 9x²-4 is (3x-2)(3x+2)

W is a subspace of R4 since it satisfies closure under vector addition, closure under scalar multiplication, and contains the zero vector.

(a) W is a subspace of R4.

To prove that W is a subspace of R4, we need to show that it satisfies three conditions: closure under vector addition, closure under scalar multiplication, and contains the zero vector.

Closure under vector addition: Let's take two vectors (a₁, a₂, a₃, a₄) and (b₁, b₂, b₃, b₄) from W. We need to show that their sum is also in W.

(a₄ - a₃) + (b₄ - b₃) = (a₂ - a₁) + (b₂ - b₁)

(a₄ + b₄) - (a₃ + b₃) = (a₂ + b₂) - (a₁ + b₁)

This satisfies the condition and shows closure under vector addition.

Closure under scalar multiplication: Let's take a vector (a₁, a₂, a₃, a₄) from W and multiply it by a scalar c. We need to show that the result is also in W.

c(a₄ - a₃) = c(a₂ - a₁)

(c * a₄) - (c * a₃) = (c * a₂) - (c * a₁)

This satisfies the condition and shows closure under scalar multiplication.

Contains zero vector: The zero vector (0, 0, 0, 0) satisfies the equation a₄ - a₃ = a₂ - a₁, so it is in W.

Therefore, W satisfies all the conditions and is a subspace of R4.

(b) S is a spanning set of W.

The subset S = {(1, 0, 0, 1), (0, 1, 1, 0)} is given. To verify that S is a spanning set of W, we need to show that any vector (a₁, a₂, a₃, a₄) in W can be expressed as a linear combination of the vectors in S.

Let's consider an arbitrary vector (a₁, a₂, a₃, a₄) in W. We need to find scalars c₁ and c₂ such that c₁(1, 0, 0, 1) + c₂(0, 1, 1, 0) = (a₁, a₂, a₃, a₄).

Expanding the equation, we get:

(c₁, 0, 0, c₁) + (0, c₂, c₂, 0) = (a₁, a₂, a₃, a₄)

From this, we can see that c₁ = a₁ and c₂ = a₂, which means:

c₁(1, 0, 0, 1) + c₂(0, 1, 1, 0) = (a₁, a₂, a₃, a₄)

Therefore, any vector in W can be expressed as a linear combination of the vectors in S, proving that S is a spanning set of W.

(c) A basis for W is {(1, 0, 0, 1), (0, 1, 1, 0)}.

To find a basis for W, we need to ensure that the set is linearly independent and spans W. We have already shown in part (b) that S is a spanning set of W.

Now, let's check if S is linearly independent. We want to determine if there exist scalars c₁ and c₂ (not both zero) such that c₁(1, 0, 0, 1) + c₂(0, 1, 1, 0) = (0, 0, 0, 0).

Solving the equation, we get:

c₁ = 0

c₂ = 0

Since the only solution is when both scalars are zero, S is linearly independent.

Therefore, the set S = {(1, 0, 0, 1), (0, 1, 1, 0)} is a basis for W.

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(a) The distance traveled by motorcycle is 1548 ft.

(b) The distance traveled by motorcycle is 1512 ft.

(c) (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.

What is velocity?

The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.

Given table is:

t (s)        0       12      24     36     48      60

v (ft/s)   30      28     25     21      25      27

The distance traveled by motorcycle during this time period using the velocities at the beginning of the time intervals is:

12(30 + 28 + 25 + 21 + 25)

=12 × 129

= 1548 ft

The distance traveled by motorcycle during this time period using the velocities at the end of the time intervals is:

12(28 + 25 + 21 + 25 + 27)

=12 × 126

= 1512 ft

The distance traveled by motorcycle at the end of the time intervals is greater than the distance traveled by motorcycle at the beginning of the time intervals.

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Answer:

Step-by-step explanation:

I gather that you need to find the area of the sector and then subtract from it the area of the segment to get the area of the triangle (although there are other ways in which to find the area of the triangle).

The area of a sector is:

\(A=\frac{\theta}{360}\pi r^2\) where our angle is given as 34, pi is 3.1415, and the radius is 5:

\(A=\frac{34}{360}(3.1415)(25)\) and if you multiply and divide that all out you get that the area of the sector is:

A = 7.417

Now subtract from it the area of the segment, 2.209. to get the area of the triangle:

7.417 - 2.209 = 5.208

you should probably try reading the question first.

the arc measure and radius are given to you. now, it is up to you to use your brain and put two and two together. good luck.

The picture is represented by the absolute value function g(x) = |x - 5| - 4. (Correct choice: A)

Absolute values are functions defined by the following piecewise function:

The function in the picture is the consequence of the following rigid transformations:

Now we proceed to obtain the image of f(x):

Horizontal translation

f'(x) = |x - 5|

Vertical translation

g(x) = |x - 5| - 4

The picture is represented by the function g(x) = |x - 5| - 4.

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The absolute value of the elasticity coefficient for Toasty Hands' gloves is 394,265.23.

The elasticity coefficient is calculated as follows:

Elasticity coefficient = (Change in demand)/(Change in price) * (Original price)/(Original demand)

In this case, the change in demand is 540,000 - 440,000 = 100,000 pairs. The change in price is 239 - 279 = -40. The original price is $279, and the original demand is 440,000 pairs.

Plugging these values into the formula, we get:

Elasticity coefficient = (100,000)/(-40) * (279)/(440,000) = -394,265.23

The absolute value of the elasticity coefficient is 394,265.23. This means that the demand for Toasty Hands' gloves is elastic, meaning that a small change in price will lead to a large change in demand.

Here is a more detailed explanation of the calculation:

The change in demand is calculated by subtracting the original demand from the new demand. In this case, the new demand is 540,000 pairs, and the original demand is 440,000 pairs. So the change in demand is 540,000 - 440,000 = 100,000 pairs.

The change in price is calculated by subtracting the original price from the new price. In this case, the new price is $239, and the original price is $279. So the change in price is 239 - 279 = -40.

The original price is $279, and the original demand is 440,000 pairs.

Plugging these values into the formula, we get the elasticity coefficient of -394,265.23.

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Answer:

To find the slope-intercept form of the line that passes through the points (−2, 6) and (−1, 18), we can use the slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept.

First, we need to find the slope of the line. The slope of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Substituting the coordinates of the points given in the problem, we have:

m = (18 - 6) / (−1 - (−2)) = 12 / 3 = 4

Next, we need to find the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, which has an x-coordinate of 0. Substituting the slope and the coordinates of one of the points given in the problem, we can solve for b:

y = mx + b

6 = 4 * (−2) + b

6 = −8 + b

b = 6 + 8 = 14

Therefore, the slope-intercept form of the line that passes through the points (−2, 6) and (−1, 18) is y = 4x + 14.

Step-by-step explanation:

The image of the point (5, -3) after reflection about the line y=x is (-3, 5).

It is the image of the point which is located in the opposite direction of a given point.

Given

The point (5, -3)

The reflecting line is y = x.

Then the point of the image will be about the line y = x

For x = 5, the value of y will be

y = 5

For y = -3, the value of x will be

x = -3

Thus, the point of the image is (-3, 5).

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I know I am late but for the future people the answer is C!

- have a good day.

- got it right on edge. :)

The simplified expression is 26 - 4x.

To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.

6 - 4(x - 5)

First, distribute -4 to the terms inside the parentheses:

6 - 4x + 20

Now, combine like terms:

(6 + 20) - 4x

Simplifying further:

26 - 4x

Therefore, the simplified expression is 26 - 4x.

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Answer:

Step-by-step explanation:

18%

Answer:

18%

Step-by-step explanation:

We can work this out in a simple way by first converting the fraction 9/50 to a decimal. To do that, we simply divide the numerator by the denominator:9/50 = 0.18 Once we have the answer to that division, we can multiply the answer by 100 to make it a percentage:0.18 x 100 = 18%

Answer:

A. Average Rate of Change

Step-by-step explanation:

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad R(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -2 +x}{2}~~~ ,~~~ \cfrac{ -4 +y}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE Q} }{(-5~~,~~1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -2 +x }{2}=-5\implies -2+x=-10\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -4 +y }{2}=1\implies -4+y=2\implies \boxed{y=6}\)

Answer:

The answer is (-8,6)

Answer:

Step-by-step explanation:

The imaginary number 'i' is equal to the square root of -1. If you were to square the square root, they both cancel and you get -1.

\(21i^2=21(\sqrt{-1} )^2=21(-1)=-21\)

In this question, we want to find a fraction of a value, which is found multiplying the fraction by the value.

Information:

Voldemort has brushed his teeth 14641 times.

5/11 of the time, he has flossed immediately beforehand.

\(1 - \frac{5}{11} = \frac{6}{11}\) of the time, he has NOT flossed immediately beforehand.

How many times total has Voldemort NOT flossed right before brushing his teeth?

6/11 out of 14641, so:

6*14641/11 = 7986.

Thus, Voldemort has NOT flossed right before brushing his teeth 7986 times.

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Lord Voldemort did not floss his teeth 7986 times.

According to this question, we know the following two facts:

1) Lord Voldemort has brushed his teeth 14641 times.

2) He flossed his teeth beforehand only \(\frac{5}{11}\) of the time.

There, he did not floss his teeth \(\frac{6}{11}\) of the time and the total number of time that he did not floss is obtained by multiplicating the total number of times that he brushed his teeth and the rational number deducted at the beginning of the paragraph. That is to say:

\(x = \left(\frac{6}{11} \right)\cdot (14641)\)

\(x = 7986\)

Lord Voldemort did not floss his teeth 7986 times.

Answer:f=1 over 4x + 1 over 12 y

Step-by-step explanation:

Let's solve for f.

y=−3x+2f(6)

Step 1: Flip the equation.

12f−3x=y

Step 2: Add 3x to both sides.

12f−3x+3x=y+3x

12f=3x+y

Step 3: Divide both sides by 12.

12f

12

=

3x+y

12

f=

1

4

x+

1

12

y

Answer:

1/4 or .25

Step-by-step explanation:

8x =2

Divide by 8 on both sides

8x=2

__. ___

8.     8

x = 2/8=1/4 or .25

Answer: x equals 1/4 or 25% or 0.25

Sam's experimental probability of getting heads in 30 coin flips was 20 out of 30, while the theoretical probability of getting heads is 1/2 or 0.5.

Sam's experimental probability of getting heads in the 30 coin flips was 20 out of 30, which can be written as 20/30 or simplified to 2/3. This means that in the experiment, heads appeared in approximately two-thirds of the flips. On the other hand, the theoretical probability of getting heads in a fair coin flip is 1/2 or 0.5. This is because there are two equally likely outcomes (heads or tails) and only one of them is heads.

Comparing the experimental and theoretical probabilities, we can see that Sam's results deviate slightly from the expected outcome. The experimental probability of getting heads is higher than the theoretical probability. This could be due to chance or random variation, as 30 coin flips may not be enough to perfectly represent the true probability. With a larger number of trials, the experimental probability would tend to converge towards the theoretical probability. However, in this specific experiment, Sam's results suggest a slightly biased coin favoring heads.

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Answer:

9/8 simply = 1 and 1/8

Step-by-step explanation:

all you do is subtract turn (10,1) into 10-1 = 9 and turn (2,10) into 2-10 the answer is 9/8 but you have to simply it

-2/5x - 9 < 9/10

-2/5x-9+9<9/10+9

-2/5x<99/10

(5/-2)*(-2/5 x)<(5/-2)*(99/10)

x>-99/4

Answer:

3(x - 4)(x + 4)

Step-by-step explanation:

\(3 {x}^{2} - 48 \\ = 3( {x}^{2} - 16) \\ = 3( {x}^{2} - {4}^{2} ) \\ = 3(x - 4)(x + 4)\)

By running at least 100 simulations and calculating the variance of the project duration, you can estimate the variance of the project based on the uniformly distributed time intervals for each activity.

To estimate the variance of the project duration using simulation in Excel, you can follow these steps:

1. Create a new Excel worksheet and label columns for activities A, B, and C.

2. In the cells under each activity, use the "RANDBETWEEN" function to generate random numbers within the given intervals. For example, for activity A, the formula would be "=RANDBETWEEN(1,5)".

3. In a separate cell, calculate the total duration of the project by summing the durations of activities A, B, and C. For example, if the durations are in cells A1, B1, and C1, the formula would be "=A1 + B1 + C1".

4. Repeat steps 2 and 3 at least 100 times to generate multiple random durations for the project.

5. Calculate the average duration of the project using the "AVERAGE" function. For example, if the durations are in cells D1:D100, the formula would be "=AVERAGE(D1:D100)".

6. Calculate the variance of the project duration using the "VAR.P" function. For example, if the durations are in cells D1:D100, the formula would be "=VAR.P(D1:D100)".

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Answer:

Step-by-step explanation:

x + 7 ≤ -9 subtract 7 from both sides

x≤-16  this is your answer

If you're plotting it will be (-∞,-16]

Answer:

Step-by-step explanation:

For this equation, all it is asking is to replace the unknown value with a number that completes the equation. However, the number must make the equation valid. Here is a few examples that could be a valid solution to this problem:

1. -55 + 7 < -9

(you don't need to solve this equation to tell that it's less than negative nine.)

2. 22 + (-98) + 7 < -9

(this is more complicated, but you can still tell that the sum is less than negative nine.)

So, basicly all that you have to do is replace the missing value with a number that gives the eqquation a sum less than negative nine. Hope this helped!!! :)

Answer:

It should be 14.14

Step-by-step explanation:

The volume of a cone equation is V=πr2h

3=π·1.52·6

3≈14.13717

You find the r(radius) by dividing the diameter in half

Answer: Answer is 6.11

Step-by-step explanation:

Lets solve this equation (2x-1)+4x+(12x+5)=114

step 1: we first add x variables

          ie. 2x + 4x + 12x = 18x

step 2: we add numbers

          ie. -1 + 5 = 4

step 3: now we arrange LHS part

         ie.  18x + 4 = 114

step 4: now move this 4 to right hand side and simplify them

         ie. 18x = 114 - 4 = 110

step 5: now we divide 110 by 18 to get the value of x

         ie. x = 110/18 = 6.11

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1. Using the given equation, the farms in Iowa in 2000 are 84,671.2046. 2. Using the same equation, the number is Iowa will be about 90,000 in 16 years.

a) We know that N(t) = 110,000(0.987\()^{t}\) .

Now the number of years from 1980 to 2000 = 2000 - 1980

= 20 years

N(20) = 110,000 × (0.987\()^{20}\)

N(20) = 110,000 × 0.7697382238421814

N(20) = 84,671.2046

So, the number of farms in Iowa in 2000 is 84,671.2046.

b) Now, we have to calculate in which year the number of farms will be 90,000. From the above answer it can be seen that it is definitely before 2000 because the farms are decreasing with increasing year. We will apply the same equation to find the year.

N (t) = 110,000 × (0.987\()^{t}\)

90,000 = 110,000 × (0.987\()^{t}\)

90,000 / 110,000 = (0.987\()^{t}\)

9 / 11 = (0.987\()^{t}\)

(0.818) = (0.987\()^{t}\)

It can be written as:

(0.987\()^{16}\) = (0.987\()^{t}\)

So, the value of t is 16.

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The standard form representation of the equation of a circle as given obviously in the task content is; (x + 12)² + (y + 3)² = 4².

It follows from the task content that the standard form representation of the equation of the circle as given in the task content is to be determined.

The given equation is;

137+6y=-y²-x²-24x

By rearrangement, we have;

x² + 24x + y² + 6y + 137 = 0.

Therefore by the use of completing the square method; we have;

(x + 12)² - 144 + (y + 3)² - 9 + 137 = 0.

Hence, the correct standard form representation of the equation is;

(x + 12)² + (y + 3)² = 16

(x + 12)² + (y + 3)² = 4²

Ultimately, the standard form representation of the equation of a circle as given obviously in the task content is; (x + 12)² + (y + 3)² = 4².

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Answer:

C

Step-by-step explanation:

Because equation C is telling us that the amount of caffeine is less than 400.

Hope this will help

Answer:

c

Step-by-step explanation:

cause dector recommended less than 400 or equal to 400...so answer is c