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The standard deviation of the population function x is 2.

We have,

To find the standard deviation of the population function x, we need the mean M(x) and the mean of the squared values M(x²).

So,

Standard Deviation = √[M(x²) - (M(x))²]

Given that M(x) = 2 and M(x²) = 8, we can substitute these values into the formula:

Standard Deviation = √[8 - (2)²]

Standard Deviation = √[8 - 4]

Standard Deviation = √4

Standard Deviation = 2

Therefore,

The standard deviation of the population function x is 2.

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Answer:

$0.75

Step-by-step explanation:

Step 1:

5 ibs for $3.75    Given

Step 2:

$3.75 ÷ 5     Divide

Answer:

$0.75

Hope This Helps :)

The missing integer that makes the following addition statement true is -1.

The commutative law of addition is also known as the law of cumulative addition and it states that when two numbers are added together, then, the outcome is equal to the addition of their interchanged position because addition is considered as a binary operation.

Mathematically, the commutative law of addition can be represented using the following formula:

A + B = B + A.

An integer can be defined as a whole number that may either be positive, negative, or zero such as -1, 0, 1, 2, 3, etc.

Now, we would determine the missing number:

x + 3 = 2

x = 2 - 3

x = -1.

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Complete Question:

Find the missing integer that makes the following addition statement true.

+ 3 = 2

Answer:

See below.

Step-by-step explanation:

These work just like ordinary algebraic expresssions, except you have to remember always:  i^2 = -1    i squared is negative one!

(4 - 3i)(4 + 3i)   "FOIL" the expression to get 16 - 3i + 3i - 9i^2.  But i^2 = -1, so this is the same as 16 - 3i + 3i + 9.  Combine like terms.

Ans. 25

(4 - 3i)(i)  Distribute the i to the two terms of the binomial.

4i - 3i^2 = 4i - 3(-1)

Ans. 4i + 3

(6i)(4 + 3i) = (6i)(4) + (6i)(3i) = 24i + 18i^2 = 24i + 18(-1)

Ans. 24i -18

(6i)(i) = 6i^2 = 6(-1)

Ans. -6

(-5)(4 + 3i) = -20 - 15i   That's it; there's no i^2 to deal with.

Ans. -20 - 15i

(-5)(i)   = -5i  Again, that's all there is to it.

Ans. -5i

Answer:

\( - 12 > x - 7\)

\( - 5 > x\)

\(x < - 5\)

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The term that best describes the figure shown is (a) line LM

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

Points L and M

On the figure, we have two arrows that extend indefinetely

By definition of lines, lines extend indefinetely

This means that the term that best describes the figure shown is (a) line LM

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Answer: 4.80952380952

Step-by-step explanation: 4.80952380952 even it to 4.8

Answer:

4.80952380952

Step-by-step explanation:

4.80952380952

Answer:

21 squares

Step-by-step explanation:

1 = 1

2 = 3

3 = 6

The pattern follows squares use in the previous stage + new stage = squares use the new stage

Squares used in stage 2 = Squares used in stage 1 + stage 2

= 1 + 2

= 3 squares

Squares used in stage 3 = Squares used in stage 2 + stage 3

= 3 + 3

= 6 squares

Squares used in stage 4 = Squares used in stage 3 + stage 4

= 6 + 4

= 10 squares

Squares used in stage 5 = Squares used in stage 4 + stage 5

= 10 + 5

= 15 squares

Squares used in stage 6 = Squares used in stage 5 + stage 6

= 15 + 6

= 21 squares

4 = 10

5 = 15

6 = 21

Answer:

The 90% confidence interval for the average bonus that all employees working for financial companies in New York City received last year is between $43,819 and $50,181

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 62 - 1 = 61

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 61 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.9}{2} = 0.95\). So we have T = 1.67

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 1.67\frac{15000}{\sqrt{62}} = 3181\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 47000 - 3181 = $43,819

The upper end of the interval is the sample mean added to M. So it is 47000 + 3181 = $50,181

The 90% confidence interval for the average bonus that all employees working for financial companies in New York City received last year is between $43,819 and $50,181

Answer:

no solution

Step-by-step explanation:

plug in -3 and -2 for x and y

-2=-3-2

-2=-5

it's false

no solution

The solutions to the equation \($x^2 = 6 - x$\) are \($x = -3$\) and \(x = 2$.\)

What is square of a number?

The square of a number is the result of multiplying the number by itself. In mathematical notation, the square of a number "\(x\)" is written as "\(x^2\)".

Let's call the number we are looking for "x".

According to the problem statement, we have:

\($$x^2 = 6 - x$$\)

We can rearrange this equation to get:

\($$x^2 + x - 6 = 0$$\)

Now, we can factor the left-hand side of this equation:

\($$(x + 3)(x - 2) = 0$$\)

So, either \($x + 3 = 0$\) or \(x - 2 = 0$.\) Solving for x in each case gives us:

\($$x = -3 \text{ or } x = 2$$\)

Therefore, the solutions to the equation \($x^2 = 6 - x$\) are \($x = -3$\) and \(x = 2$.\)

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Answer:

The answer is 40 because you have a ratio of 4:1 (16:4). If you multiply by ten, it becomes 40:10.

Step-by-step explanation:

Answer:

30 red and 20 yellow as 9 bead and 6 bead is the ratio of 3:2 50 in the ratio of 3:2 is 30=red and 20=yellow

Step-by-step explanation:

Answer:

\(h(t)=-25\cos(\pi t)+29\)

Step-by-step explanation:

First thing to understand is that we will be producing a sine or cosine function to solve this one. I'll use a cosine function for the sake of the problem, since it's most easily represented by a cosine wave flipped over. If you're interested in seeing a visualization of how a circle's height converts to one of these waves, you may find the Better Explained article Intuitive Understanding of Sine Waves helpful.

Now let's get started on the problem. Cosine functions generally take the form

\(y=a\cos(b(x-c))+d\)

Where:

\(|a|\) is the amplitude

\(\frac{2\pi}{b}\) is the period, or the time it takes to go one full rotation around the circle (ferris wheel)

\(c\) is the horizontal displacement

\(d\) is the vertical shift

Step one, find the period of the function. To do this, we know that it takes six minutes to do three revolutions on the ferris wheel, so it takes 2 minutes to do one full revolution. Now, let's find \(b\) to put into our function:

\(\frac{2\pi}{b}=2\)

\(2\pi=2b\)

\(\pi=b\)

I skipped some of the basic algebra to shorten the solution, but we have found our b. Next, we'll get the amplitude of the wave by using the maximum and minimum height of the wheel. Remember, it's 4 meters at its lowest point, meaning its highest point is 54 meters in the air rather than 50. Using the formula for amplitude:

\(\frac{\max-\min}{2}\)

\(\frac{54-4}{2}\)

\(\frac{50}{2}=25=a\)

Our vertical transformation is given by \(\min+a\) or \(\max-a\), which is the height of the center of the ferris wheel, \(4+25=29=d\)

Because cosine starts at the minimum, \(c=0\).

The last thing to point out is that a cosine wave starts at its maximum. For that reason, we need to flip the entire function by making the amplitude negative in our final equation. Therefore our equation ends up being:

\(h(t)=-25\cos(\pi t)+29\)

The equation of the relationship is f(200) = 0.75 * 200

From the question, we have the following parameters that can be used in our computation:

Total number of drinks = 200

Cost of each drink = 0.75

Using the above as a guide, we have the following:

f(x) = Cost of each drink * Total number of drinks

Where

f(x) = Total cost

Substitute the known values in the above equation, so, we have the following representation

f(200) = 0.75 * 200

Hence, the equation is f(200) = 0.75 * 200

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Answer: 0.7071

Step-by-step explanation:

The first thing to do is to calculate the R² which is the coefficient of determination. This will be:

= 1 - SSE/SS Total

= 1 - 600/1200

= 1 - 0.5

= 0.5

Then, the correlation coefficient will be:

= ✓0.5

= 0.7071

Answer:

Step-by-step explanation:

1- digit numbers:

2- digit numbers:

3- digit numbers:

This is more than we have, but we know the number of pages is 3-digit.

Let it be x, then we have:

The dimensions of the rectangle after dilation by a sclae factor of 3 is,

Length = 15 inches

Breadth = 27 inches.

A dilation is a transformation that produces an image of a different size but with a similar overall shape to the original.

A dilation that enlarges an image is called an enlargement, and a dilation that shrinks an image is called a reduction.

The scale factor, which is employed to enlarge a mathematical entity, will determine the size of the image (compared to the original object). When the absolute value of the scaling factor is greater than 1, an expansion occurs.

The given rectangle dimension is :

width= 5 inches and

length= 9 inches.

When the sides of a rectangle are multiplied by a scale factor of 3, the rectangle is said to be dilated by that factor.

So, the width of rectangle is after dilation is 5×3 = 15  inches

So, the length of rectangle is after dilation is 9×3 = 27 inches

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Therefore , the solution of the given problem of fraction comes out to be Roman can thus perform 8 poster.

Any number of equal amounts or fractions can be used to represent a whole. In standard English, the quantity of a certain size is stated as a fraction. 8, 3/4. Wholes also include ratio. Numbers are represented in mathematics by the fraction to numerator ratio. These are all straightforward integer fractions. There is a fraction in the denominator of a difficult fraction. because the calculations, numerators, and numerators of actual fractions vary.

Here,

Given :

Roman divided a poster board sheet into ten equally sized pieces.

The entire sheet should be x.

then, one part of sheet=  1/1 0 of the sheet

Currently, only 8/10 of the poster is left after his brother used portion of it.

Roman can therefore use each remaining piece of the poster to create a sign if he so chooses.

The number of indications he is capable of making is then

=> 8/10/1/10

= > 8/10 * 10 = 8.

Roman can thus perform 8 signs.

Therefore , the solution of the given problem of fraction comes out to be

Roman can thus perform 8 poster.

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The measure of the angle ABD is (3x + 29)  

Bisecting angles is the process of dividing an angle into two congruent angles. In geometry, an angle bisector is a line or ray that divides an angle into two equal parts.

When an angle is bisected, each of the two angles formed is called a half-angle or bisector angle, and the point where the angle is bisected is called the vertex of the angle.

Here we have

BD bisects ABC and ∠ABC = 6x+58  

When a straight bisect an angle then the measure of the resultant 2 angles will be equal in measure

Here BD bisected ABC

The resultant angles will be ∠ABD and ∠DBC

Hence,

=> ∠ABC = ∠ABD + ∠DBC

=> ∠ABC = ∠ABD + ∠ABD   [ Since two angles are equal

=> ∠ABC = 2∠ABD  

From the given data,

=> 6x + 58 = 2∠ABD  

=> 2 ∠ABD = 2(3x + 29)

=> ∠ABD = (3x + 29)  

Therefore,

The measure of the angle ABD is (3x + 29)  

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Answer: 20

Step-by-step explanation:

Answer:

The answer is "28"

Step-by-step explanation:

\((LTPD) = 52\%\\\\(AQL) = 20\%\\\\\to \frac{LTPD}{AQL} = \frac{52\%}{20\%}= 2.6\\\\\)

The value of \(\frac{LTPD}{AQL} = 2.6\) that value of \(\frac{LTPD}{AQL} = 2.618\)

Acceptance number, \(c = 9\)

Value of \(n\times AQL = 5.426\)

Sample size \(n = n\times \frac{AQL}{AQL} =\frac{5.426}{20\%} = 27.13=28\)  

The value of JK is 30

A quadrilateral in geometry is a four-sided polygon with four edges and four corners.

Given;

JKLM and PQRS are shown, where JKLM is similar to PQRS. Some measurements of the sides of JKLM and PQRS are given.

MJ = 21, JK = 4y-2, KL = 6x +3, LM = 36, PQ = 10, QR = 11, and RS = 12.

So,

JK is similar to PQ.

JK / PQ = LM / RS

4y-2 /10 = 36 / 12

4y -2 = 30

4y = 32

y = 8

So, the value of JK is 4(8) - 2

JK = 30.

Therefore, 30 is the value of JK.

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Answer:

True mathematical statement.

"If x = 0, then for any real number y, we have: y*x = 0."

This is true, and we can prove it with the axioms of the real set.

A false mathematical statement can be:

"if n and x are integer numbers, then n/x is also an integer number."

And a counterexample of this is if we took n = 1 and x = 2, both are integer numbers, so the first part is true, but:

n/x = 1/2 = 0.5 is not an integer number, then the statement is false,

Answer:

True mathematical statement.

"If x = 0, then for any real number y, we have: y*x = 0."

This is true, and we can prove it with the axioms of the real set.

A false mathematical statement can be:

"if n and x are integer numbers, then n/x is also an integer number."

And a counterexample of this is if we took n = 1 and x = 2, both are integer numbers, so the first part is true, but:

n/x = 1/2 = 0.5 is not an integer number, then the statement is false,

Step-by-step explanation:

Answer:

b x h

Step-by-step explanation:

If y = aˣ, then y = exp(ln(aˣ)) = exp(x ln(a)). (Here I use exp(x) = eˣ.)

Then using the chain rule, the derivative of y is

dy/dx = exp(x ln(a)) • ln(a)

and undoing the rewriting, we end up with

dy/dx = ln(a) aˣ

Answer:

48=2/3

48×3÷2= Marcus older brother height

72 inches

By using basic arithematic operations we concluded that the temperature at 6 pm was - 9.8°F.

Arithmetic operation is the study of numbers and the operations on numbers that are used in all other branches of mathematics. It primarily consists of basic operations like addition, subtraction, multiplication, and division.

The temperature at 09:00 am = -6.9°F.

The tempertaure increased by 5.4°F till noon

So, the final tempertaure at noon = - 6.9°F + 5.4°F

                                                        = - 1.5°F

Then, again the temperature increased by 7.2°F from noon till 3 pm.

So, the final tempertaure at 3 pm = - 1.5°F + 7.2°F

                                                        =  5.7°F

Then, again the temperature by dropped 15.5°F from 3 pm to 6 pm.

So, the final tempertaure at 6 pm = 5.7°F - 15.5°F

                                                        = - 9.8°F

Therefore the temperature at 6 pm was - 9.8°F.

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The interval containing the middle 95% of the data based on the simulation results is approximately (0.35, 0.65), and the observed proportion of 0.55 falls within this interval, indicating that it is within the margin of error of the simulation results.

To create an interval containing the middle 95% of the data based on the simulation results, we can calculate the lower and upper bounds of the interval.

Let's analyze the simulation results and find the appropriate values.

Out of 200 simulations, we observe that the proportion of students who preferred Candidate A ranges from a minimum of 0.35 (35%) to a maximum of 0.65 (65%).

Since the simulations assume a 50-50 split, we can consider these values as the lower and upper bounds for the middle 95% of the data.

To find the range of the middle 95% of the data, we calculate the difference between the upper and lower bounds.

Upper bound: 0.65

Lower bound: 0.35

Range: 0.65 - 0.35 = 0.30  

To find the interval containing the middle 95% of the data, we divide the range by 2 and add/subtract it from the midpoint.

The midpoint is the average of the upper and lower bounds.

Midpoint: (0.65 + 0.35) / 2 = 0.50

Range / 2: 0.30 / 2 = 0.15

Lower bound of the interval: 0.50 - 0.15 = 0.35

Upper bound of the interval: 0.50 + 0.15 = 0.65

Therefore, the interval containing the middle 95% of the data based on the simulation results is approximately (0.35, 0.65).

Now let's compare the observed proportion from the poll to this interval. The poll indicates that out of a random sample of 80 students, 44 students said they would vote for Candidate A.

To calculate the observed proportion, we divide the number of students who preferred Candidate A (44) by the sample size (80).

Observed proportion: 44/80 = 0.55

The observed proportion of 0.55 is within the margin of error of the simulation results.

It falls within the interval (0.35, 0.65), indicating that the observed proportion is consistent with the simulation and aligns with the assumption of a 50-50 split in the population.

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Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)