simplify. evaluate. ​

The normal distribution is also known as the Gaussian distribution. The percentage of all possible values of the variable that are less than 4 is 15.87%.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

A.) The percentage of all possible values of the variable that lie between 5 and 9.

P(5<X<9) = P(X<9) - P(5<X)

               = P(z<1.5) - P(-0.5<z)

               = 0.9332 - 0.3085

               = 0.6247

               = 62.47%

B.) The percentage of all possible values of the variable that exceed 1.

P(X>1) = 1 - P(X<-2.5)

          = 1-0.0062

          = 0.9938

          = 99.38%

C.) The percentage of all possible values of the variable that are less than 4.

P(X<4) = P(X <4)

           = P(z<-1)
           = 0.1587

           = 15.87%

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Answer:

Yellow: 4

blue: 2

red: 12

green: 2

Step-by-step explanation:

all the details see in the attachment.

Step-by-step explanation:

the correct answer will be 93

Answer:

The equation of a parallel line is y = x

Step-by-step explanation:

Parallel lines have the same slope

hence the new lines slope is = 1

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

          b represents the y-intercept

where the format of a point is (x, y)

Given:

we need to find b, y = 1x + b

we can plug in the point (2, 2)

2 = 1(2) + b

2 = 2 + b

0 = b

Hence, the equation of the line through point

(2, 2) and parallel to y = x+4 is y = x

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Answer:

Step-by-step explanation:

(h+k)(1)=h(1)+k(1)=2+(-1)=2-1=1

(k-h)(4)=k(4)-h(4)=0-(-1)=1

(k/h)(3)[tex]=\frac{k(3)}{h(3)} =\frac{-1}{0} =- \infty[/tex]

(h.k)(0)=h(0).k(0)=3(-2)=-6

(k.h)(0)=k(0).h(0)=-2(3)=-6

(h.k)(3)=h(3).k(3)=0(-1)=0

h(k(-2))=h(-3)=0

Answer: For this real-valued function;

[tex]fog = 2\sqrt{x-1} + 1\\ Domain = [1, )[/tex]

Step-by-step explanation:

If f and g are functions, then the composite function or composition, of g and f is defined by

[tex]( f o g ) (x) = f(g(x))[/tex]

Given the functions [tex]f(x)=2x+1[/tex] , [tex]g(x)=\sqrt{x-1}[/tex],

Now composition for this;

[tex]fog = f(g(x))f(g(x)) = f(\sqrt{x-1} )[/tex]

[tex]f(\sqrt{x-1})[/tex]means we are to interchange variable x in [tex]f(x)[/tex] with the function [tex]\sqrt{x-1}[/tex]

[tex]f(\sqrt{x-1}) = 2(\sqrt{x-1})+1f(\sqrt{x+1}) = 2(\sqrt{x-1})+1fog = 2(\sqrt{x-1})+1[/tex]

The function inside the square root, x-1, must be more significant than or equal to zero (x-10), for the function to exist on any real-valued function.

[tex]if, x-1 \geq 0\\x\geq 0+1\\x \geq 1[/tex]

As a result, the range of the variable x must only include values that are larger than or equal to 1.

Hence, Domain = [1, )

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Answer:

Step-by-step explanation:

→ Find the gradient

( -3 --4 ) ÷ ( 0 --3) = 1/3

→ Write into format

y = 1/3x + c

→ Substitute in a coordinate pair

-3 = 0 + c

→ Solve for c

c = -3

→ Write into format

y = 1/3x - 3

The equation of the red graph is g(x)=^x+2-3.

Since the upscaling in the y-axis is not the main focus of this equation (being g(x) and not g(y)), the change is not applied to the x-axis.

The y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. The slope is the change in y over the change in x.

Hence, we can rule out (-3)^2 and (x+3)^2 since they apply changes to the x-axis.

Finally, since this is an upscaling of the y-value on the y-axis, the answer is x^2 + 3 and not x^2 - 3.

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Answer:

sorry I don't know the answer

Answer:

3

Step-by-step explanation:

24 divided by 6 is 4, subtract Doug, there were 3 friends

Answer:

40 divided by 10

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer: 10°

Step-by-step explanation:

Since an exterior angle and its corresponding interior angle are supplementary, meaning they have a fixed sum, to minimize the exterior angle, we need to maximize the interior angle.

This means we need to consider the 170° interior angle, so the corresponding exterior angle is 10°.

The attraction that reaches a greater height and what it represent in terms of the context  is:

Ferris wheel

(x – 100)2 + (y – 75)2 = 4,900

y max= 75+70

y max=145 ft

Sling shot

y = –3x² + 48x – 30

dy/dx=-6+48=0

x=48/6

x=8

Hence:

y max = –3(8)² + 48(8) – 30
y max = –3×64+48(8)-30

y max = –192+384-30

y max =162 ft

Therefore slingshot reaches a greater height at  162 ft and Ferris wheel reaches a greater height at 145 ft.

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Answer:

a=9

b=9

c=18

Step-by-step explanation:

c(a+b)+a+b=36

2a+2b=36

a+b=18

c=18

Answer:

The coefficient of variation (CV)= 9.83

Step-by-step explanation:

look at the attachment above ☝️

Russell has to sell 270 cable packages to make the total pay of both the companies as same.

Suppose that Russell sells x cable packages such that the total pay of both the companies is the same.

Then the revenue Russell would make at the first company is $17000+20x

And, the revenue Russell would make at the second company is

$14300+30x

Since, the above two values are equal

so, 17000+20x=14300+30x

⇒17000-14300=30x-20x

⇒10x=2700

⇒x=270

The above problems are called mathematical modelling.

Mathematical modelling is the process of locating such equations to explain actual occurrences.

These formulae are referred to as mathematical models together with the definitions given to the variables.

Therefore, Russell has to sell 270 cable packages to make the total pay of both the companies as same.

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Answer:

(4, -3)

Step-by-step explanation:

A vertex is just a point where 2 lines going in different directions meet. so the answer is (4, -3)

Answer:

is the question no questions question ❓

Answer:

20

Step-by-step explanation:

To calculate f(2), just replace x in the equation of f(x) with 2:

[tex]f(x) = 5(x + 2)\\\\f(2) = 5(2+2)\\\\f(2) = 5(4)\\\\f(2) = 20[/tex]

Answer: B and C

Step-by-step explanation: For A, vertical angles can be complimentary or supplementary. For D, vertical angles can sometimes be acute but not always.

Answer:

Im pretty sure its B,  1.75. Not exactly sure though

Step-by-step explanation:

Answer:

.0032 .032 .32 3299

Step-by-step explanation:

0.32% =.0032

3.2% = .032

.32

3299

Answer:

Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x9+13 f - 1 ( x ) = x 9 + 1 3 is the inverse of f(x)=9x−3 f ( x ) = 9 x - 3

Answer:

y = x + 3/9

Step-by-step explanation:

Solve for y +3 +3

x+3 = 9y = y=x+3/9

Answer: it could be

[tex](10^{4} ) ^{4}[/tex]

Step-by-step explanation:

Answer:

Line LM

Step-by-step explanation:

First, we need to know what the slope is of a line that would be perpendicular to a line with a slope of -5/6. To find this, we take the reciprocal and multiply it by -1. Therefore, the line we are looking for needs to have a slope of 6/5.

Based on the fact that the slope is positive, we can eliminate lines PQ and JK as they have a negative slope. This leaves us with lines LM and NO.

To find out whether or not it is between LM and NO, you could eyeball it by looking at the graph and simply counting which might be faster if you understand how to do that (rise/run), or you can use the pair of coordinates given to you on each line to calculate for slope.

Line LM - [tex]\frac{-3-3}{-5-0}=\frac{-6}{-5}=\frac{6}{5}[/tex]

Line NO - [tex]\frac{-5-0}{-6-0}=\frac{-5}{-6}=\frac{5}{6}[/tex]

Based on this, we know that line LM is perpendicular to a line that has a slope of -5/6.

If you need help on calculating slope from two points, I'd suggest watching this video: https://www.brightstorm.com/math/algebra/linear-equations-and-their-graphs/finding-the-slope-of-a-line-from-2-points-problem-1/#:~:text=Use%20the%20slope%20formula%20to,second%20points%20are%20x2%2C%20y2.

Answer:

10a^2b^3−8a^3b^3+12a^2b^5−8ab^4

Step-by-step explanation:

The dimensions of each pen that will maximize the total enclosed area would be as; Length 81 feet; Width 81 feet.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let the Dimension of each pen

Length = x

Width = y

Area = xy

Perimeter equation

2(x + y) = 324

 x + y = 162

Substituting the perimeter equation

Area = x(162 - x)

Area = -x^2 + 162x

If the zeros of the quadratic are 0 and 162, then the median will be at where the maximum area occurs.

162/ 2

= 81

Hence, The dimensions of each pen that will maximize the total enclosed area would be as; Length 81 feet; Width 81 feet.

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