I know question on central limit theorem has been asked numerous times
and I have searched around the website but still couldn't get what I wanted
to find out(probably most people who asked the question is stuck at
different parts of the theory).
Attached in my question is a lecture slide for the search for a
transformation of x that has a limiting distribution.I do not understand
why x and u is multiply by vn instead of n.Also,why when the statistic /n(x
-μ）is used，μbecomes zero?
Thank you in advance!

The volume of the rectangular solid is: 11,960 units³.

The formula to find the volume of a rectangular solid is: (length)(width)(height).

Given the dimensions as:

Volume = (20)(23)(26)

Volume of the rectangular solid = 11,960 units³.

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The partition point is (-7/2, 23/4)

The given parameters are:

(x1,y1) = (-6,-1)

(x2,y2) = (4,8)

a = 1 and b = 3

The partition point is calculated as:

(x, y) = ((bx1 + ax2)/(a + b) ,( by1+ay2)/a+b)

So, we have:

(x, y) = ((3 * -6 + 1 * 4)/(1 + 3) ,(3 * 8 + 1 * -1)/1+3)

Evaluate

(x, y) = (-14/4, 23/4)

Simplify

(x, y) = (-7/2, 23/4)

Hence, the partition point is (-7/2, 23/4)

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Answer:

when the question is rearranged so that y is by itself, any of the options that say - 2.5x will be parallel.

Step-by-step explanation:

5x + 2y = 1

to get y by itself, simple algebra rules must be applied.

1. subtract 5x from both sides.

5x - 5x + 2y = 1 - 5x

2y = 1 - 5x

divide both sides by 2

2y / 2 = 1 / 2 - 5x / 2

therefore the new equation is:

y = 0.5 - 2.5x

this is very close to standard form for a line which is y = mx + b

rearrange the right side of the equals sign:

y = -2.5x + 0.5

in a standard linear equation, the x value determines the gradient of the line. therefore, anything with the same gradient (in this case -2.5x) will be parallel to the given equation.

Hope this makes sense :)

The ethical issues about testing with animals is it resulting in suffering and they have the right to live without human interference.

This is defined as a procedure which is carried in order to support or refute a hypothesis.

The blood pressure returning to normal when the drugs were used on the animals is a good assumption as most parts of the animal and human body work similarly.

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The time it will take the roller coaster to reach the ground is 171.65 seconds

Given the roller coaster’s height given by the following parameters

h = –0.025t² + 4t + 50

On the ground level, the height will be zero. Substitute h = 0 and determine the value of t

–0.025t² + 4t + 50 = 0

0.025t² - 4t - 50 = 0

Factorize

On factorizing the time it will take the roller coaster to reach the ground is 171.65 seconds

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The domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11. Option C

The domain of a function refers to the entire area for which the function returns a value. The function in this case is; f(x) = x^2 - 3x - 28/x + 4. The domain of the function will be real numbers except -4.

Hence, we can say that domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11.

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Answer:

The answer is C.

Answer:

80°

Step-by-step explanation:

Congruent means the same size, so we know that the angle of the shapes made by the lines HK and GJ are the same, meaning that the angle of GOJ is simply 80°.

The solution of the system of equation of the matrix is as follows:

x = - 8

y = 3

3x + 10y = 6

x + 3y = 1

multiply equation(ii) by 3

3x + 10y = 6

3x + 9y = 3

Therefore,

y = 3

Hence,

x + 3y = 1

x + 3(3) = 1

x + 9 = 1

x = 1 - 9

x = -8

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The statement ' educators should ensure math instruction is only taught through structured activities rather than through everyday situations and routines is True. Option A

They include;

Thus, the statement ' educators should ensure math instruction is only taught through structured activities rather than through everyday situations and routines is True. Option A

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Answer:

Step-by-step explanation:

false

Answer:

The slope is -2

y =-2x - 1

Step-by-step explanation:

The slope is -2 or -2/1.

The slope is the change in y over the change in x.  The ordered pair is written in the form (x,y)  The first number is the x coordinate and the second number is the y coordinate.

(1, -3) (0, -1)  The -1 and the -3 are the y coordinates.  We subtract these.

-1 -(-3)  is the same as

- 1 + 3  which is 2.  

(1, -3) (0, 1,) the 1 and the 0 are the x coordinates.  We subtract these

0 - 1  is -1

The change in y is 2 and the change in x is -1, so our slope is -2/1 which is the same as -2.

To write the equation we need the slope and the y intercept.  We have the slope now.  We need to find the y-intercept.  We will use the slope and one of the points to find the y-intercept.  It does not matter which of the two points (1,-3) or (0,-1).  I will use (0,-1)

y = mx + b The b is the y-intercept which is what we are looking for

-1 = -2(0) + b

-1 = 0 + b

-1 = b

y = -2x -1

The standard deviation is 1.43 below the mean

The given parameters are:

Mean = 98.249

Standard deviation = 0.733

x = 97.2

To calculate the number of standard deviation below the mean, we use

[tex]x = \bar x - n\sigma[/tex]

So, we have:

[tex]97.2 = 98.249 - n * 0.7333[/tex]

Evaluate the like terms

[tex]-1.049 =- n * 0.7333[/tex]

Divide both sides by -0.733

n =1.43

Hence, the standard deviation is 1.43 below the mean

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Answer:

14

Step-by-step explanation:

let the number be x

2x is larger than half of x by 21: 2x = 0.5+21

Solve:

2x = 0.5+21

1.5x = 21

x = 14

The triangle is an isosceles triangle and the four triangles are similar

The coordinates are given as:

A (0, 0), B (5, 0), and C (2, 4).

Calculate the distance between the coordinates using:

[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(0 -5)^2 +(0-0)^2} =5[/tex]

[tex]AC = \sqrt{(0 -2)^2 +(0-4)^2} =4.5[/tex]

[tex]BC = \sqrt{(5 -2)^2 +(0-4)^2} =5[/tex]

The above shows that two sides are congruent.

Hence, the triangle is an isosceles triangle

This is calculated using:

(x, y) = 0.5 * (x1 + x2, y1 + y2)

So, we have:

AB = 0.5 * (0 + 5, 0 + 0) = (2.5, 0)

AC = 0.5 * (0 + 2, 0 + 4) = (1, 2)

BC = 0.5 * (5 + 2, 0 + 4) = (3.5, 2)

From the attached graph, we can see that the triangles are similar

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Answer:

the third answer (-3, -3, 3)

Step-by-step explanation:

the dotted lines indicate that these lines (or part of lines) are invisible due to being inside or behind the cube.

so, we know that A is the left-back-upper corner of the cube.

the x-axis goes front-back. front is positive.

the y-axis goes left-right. right is positive.

the z-axis goes up-down. up is positive.

since the origin (0, 0, 0) is the center of the cube, and the sides are all 6 units long, the corners can have only -3 or +3 coordinates (half of a side length on either side of the origin) in each direction.

as we said : left-back-upper corner.

left means negative y.

back means negative x.

upper means positive z.

so, the coordinates of A are

(-3, -3, 3)

Answer:

The function has 4 roots.

Step-by-step explanation:

Since the degree of the polynomial has is 4, there are a total of 4 roots (both real and complex).

Answer:

4 roots, two real and two complex.

Step-by-step explanation:

The degree of the polynomial indicates the number of solutions

Hope this helps

Answer:

a: Angle EBD

b: Can't really phrase this well, a semicircle that is to the left or right of diameter BD

c: Arc EDC

d: 80 degrees

e: 180

Step-by-step explanation:

An inscribed angle is an angle with all 3 points on the circumference of a circle.

A semicircle is half a circle

A major arc is an arc greater than 180 degrees

The inner angle is 80 degrees

Arc BCD is half a circle so its 360/2=180 degrees

Series are sum of a given sequence.. The sum of the given expression is -33

Series are sum of a given sequence. According to the given expression

∑∑k=1 (k^2-5k-3)

Taking the sum from k = 1 to k = 4

Sum = (1-5-3) + (4-10-3) +(9-15-3)+(15-20-3)

Sum = (-7) + (-9) + (-9) + (-8)

Sum = -33

Hence the sum of the given expression is -33

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From the calculation, the growth rate is 0.88.

To find the relative growth rate

P1 = Poe^rt

P2 = Poe^rt

Thus;

1920 = Poe^4r ------ (1)

1966080 =Poe^12r -------(2)

P2/P1 gives;

1966080/1920 = Poe^12r/Poe^4r

1024 = e^12r/e^4r

1024 =e^8r

1024 = (e^r)^8

2^10 = (e^r)^8

e^r = 2^1.25

e^r = 2.38

r = ln(2.38)

r = 0.88

The initial size of the culture is;

1920 = Poe^(0.88 * 4)

Po = 1920/e^(0.88 * 4)

Po = 57

The  expression for the exact number of bacteria after t hours is

P(t) = 57e^0.08t

The growth (in bacteria per hour) after 9.5 hours is

P(t) = 57e^(0.88 * 9.5)

P(t) = 243544

For the number to reach 72,000;

72,000 =  57e^0.88t

72,000/57 = e^0.88t

ln 126 = ln[e^0.88t]

4.8 = 0.88t

t = 4.8/0.88

t = 5.5 hours

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Answer:

10

Step-by-step explanation:

The unit rate of each of the brands are:

Brand A's unit rate = 37 cents per ounce.

Brand B's unit rate = 31 cents per ounce.

The unit rate of each brand is simply how much a brand of tomatoes will cost per ounce.

To find the unit rate of each brand, do the following:

Brand A's unit rate = 2.99/8 = $0.37 per ounce = 37 cents per ounce.

Brand B's unit rate = 4.99/16 = $0.31 per ounce = 31 cents per ounce.

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Answer:

a)  0.0721

Step-by-step explanation:

Let the random variable X be the score on the ACT exam.

Given:

Therefore, the random variable X is normally distributed:

[tex]X \sim\textsf{N}(21,5^2)[/tex]

Z-score for a sample mean

[tex]\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \overline{X} \sim \left(\mu,\dfrac{\sigma^2}{n}\right) \implies Z=\dfrac{\overline{X}-\mu}{\sigma / \sqrt{n}} \sim \textsf{N}(0,1)[/tex]

[tex]\textsf{then the test statistic is}: \quad z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}[/tex]

Given:

Therefore, the test statistic is:

[tex]\implies z=\dfrac{19.8-21}{5/ \sqrt{37}}=-\dfrac{6\sqrt{37}}{25}=-1.459863007=-1.46\:\: \sf (3\:s.f.)[/tex]

Using the Z-tables to find the probability:

[tex]\implies \text{P}(Z \leq -1.46)=0.0721[/tex]

Answer: A

Step-by-step explanation:

[tex]-\frac{4}{x}+1=0\\\\1=\frac{4}{x}\\\\x=4[/tex]

Answer: 1 1/4 cups

Step-by-step explanation:

1 serving is half a cup so 2 servings would be 1 cup

and half of a serving would be 1/4 of a cup

for a drawing you could do something like this

Answer:

[tex]t=\frac{-5+\sqrt{505}}{8}[/tex]

Step-by-step explanation:

The ball strikes the ground when h = 0.

[tex]-16t^2 - 20t + 120 = 0 \\ \\ 4t^2 + 5t - 30=0 \\ \\ t=\frac{-5 \pm \sqrt{5^{2}-4(4)(-30)}}{4(2)} \\ \\ t=\frac{-5 \pm \sqrt{505}}{8}[/tex]

However, as time most be positive, we only consider the positive case.

So,

[tex]t=\frac{-5+\sqrt{505}}{8}[/tex]

The blank space to form a linear pair with m∠BPD is m∠APD.

Linear pair of angles are formed when two lines intersect each other at a single point.

Linear pair angles are adjacent to each other.

Therefore, the sum of a linear pair angles is equals to 180 degrees.

This means linear pair angles are supplementary.

Hence,

m∠APD + m∠BPD = 180°

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Step-by-step explanation:

4x2+8x−3=0

For this equation: a=4, b=8, c=-3

4x2+8x+−3=0

Step 1: Use quadratic formula with a=4, b=8, c=-3.

x=

−b±√b2−4ac

2a

x= −(8)±√(8)2−4(4)(−3)

2(4)

x= −8±√112

8  x=−1+

1 2 √7 or x=−1+

−1 2 √7

Answer:  x=−1+

1 2√7 or x=−1+

−1 2 √7

The rules that define the piecewise function graphed are as follows:

y = x + 2, y = 5.

A piecewise function is a function that has different definitions, depending on the input.

In this problem, for x between 0 and 3, a linear function is given, with slope given as follows:

m = (5 - 2)/(3 - 0) = 1.

The y-intercept is of 2, as y = 2 when x = 0, hence the definition is:

[tex]y = x + 2, 0 \leq x \leq 3[/tex]

For x greater than 3, the function is constant at y = 5, hence the definition is:

y = 5, x > 3.

Hence, the rules that are used to define the piecewise function graphed are as follows:

y = x + 2, y = 5.

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Answer:

1.138789 is equivalent to 8 to the second power to the -4 power.

Hope this helps :)

Answer:

A

Step-by-step explanation:

9|x-8|<36

|x-8|<4

-4<x-8<4

add 8

-4+8<x-8+8<4+8

4<x<12