According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 65 inches and a standard deviation of 2.4 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible.

The materials travel faster on Belt One, considering the constants of the proportional relationships.

A proportional relationship is a linear function with intercept zero in which the output variable symbolized by y is given by the multiplication of the input variable symbolized by x and the constant of proportionality symbolized by k, according to the equation presented as follows:

y = kx

For each belt in this problem, the constant gives the velocity that the materials travel.

For Belt One, the relation is:

y = 157.1x.

Hence the velocity is of 157.1 inches per minute.

For Belt Two, the velocity is obtained as follows:

k = 125.6/2 = 62.8 inches per minute.

157.1 > 62.8, hence it travels faster on Belt One.

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[tex]4(x)+4(-b)=x\\4x-4b=x\\4x-x=4b\\3x=4b\\\frac{3x}{3} =\frac{4b}{3} \\x=\frac{4b}{3}[/tex]

⇒They simply wanted you to simplify and make x the subject of the equation.

Answer: _______________________________

72

For each goody bag we need 3.4 cookies

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

We are given that there are 17 cookies that will be divided equally among 5 goody bags.

17 cookies = 5 goody bags.

For each goody bag.

Thus,

17/5 = 3.4 cookies.

Therefore, 3.4 cookies needed.

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The factors are mentioned in the table given below.

Number    Number of factors        prime or composite

12                    6                                      composite

20                   6                                      composite

21                    4                                       composite

31                    2                                      prime

43                   2                                        prime

Factors are those numbers which when divide the given number leaves zero as a remainder.

Factor of 12 = 1, 2 ,3, 4, 6 , 12

Factor of 20 = 1, 2 , 4,5,10 , 20

Factor of 21 = 1 ,3, 7, 21

Factor of 31 = 1, 31

Factor of 43 = 1, 43.

Prime number is a number which has only 2 factors that is number one(1) and the number itself.

Composite numbers which has more than 2 factors.

Therefore, the number of factors are mentioned in the table.

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There are 15 crates and 35 boxes in the van when it is completely full.

Given,

Total number of crates and boxes=50

For every 7 crates the van can hold, there is room of 3 boxes.

let,

Number of crates =x

Number of boxes =y

As given,

Equation for total number of crates and boxes can be written as

[tex]x+y=50....i[/tex]

Space for 7 crates is equal to space for 3 boxes in van, it's equation can be written as

[tex]7x=3y\\\\x=\frac{3y}{7}[/tex].

Substituting 'x' in eq.[tex]i[/tex]

[tex]\frac{3y}{7}+y=50\\\\ \frac{3y+7y}{7}=50 \\\\10y=7*50\\\\10y=350\\\\y=\frac{350}{10}\\ \\y=35[/tex]

Substituting 'y' in eq.[tex]i[/tex]

[tex]x+35=50\\\\x=50-35\\\\x=15[/tex]

Thus, there are 15 crates and 35 boxes in the van when it is completely full.

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The probability of winning the minimum award is [tex]\frac{^4C_3 . ^{53}C_1}{^{57}C_4} \times \frac{1}{47}[/tex].

The Player chooses 4 numbers from white balls numbered 1 to 59 and

1 number from gold ball numbered 1 to 47

He has to choose 3 correct numbers out of 4 numbers in the white ball

and 1 number from the gold balls.

He can do in [tex]^4C_3 . ^{53}C_1[/tex] and 1 way respectively.

So, the probability can be given by;

Probability = probability of choosing white ball * probability of choosing red ball

Probability = [tex]\frac{^4C_3 . ^{53}C_1}{^{57}C_4} \times \frac{1}{47}[/tex]

Thus, the probability of winning the minimum award when players pick four different numbers from 1 to 59 and one number from 1 to 47 and a player wins a minimum award of $225 by correctly matching three numbers drawn from the white balls (1 through 59) and matching the number on the gold ball (1 through 47) is [tex]\frac{^4C_3 . ^{53}C_1}{^{57}C_4} \times \frac{1}{47}[/tex].

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Answer:

81 degrees

This is an acute angle since it’s less then 90 degrees

Step-by-step explanation:

All three angles of a triangle always equal 180 degrees

180-(78+31)

180-109

81 degrees

Hopes this helps please mark brainliest

Answer: 15 cm

Step-by-step explanation:

just divide 60 by 4 and because a squar has 4 sides and that is it

The measure of <FEG= 61 and <HEG = 119.

The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal.

when two lines in a plane intersect, one of the angles that are directly across from one another.

Given:

m< DEF= 119

Now, <DEF + <FEG= 180 (Linear Pair)

119+ <FEG = 180

<FEG = 180- 119

<FEG = 61

and, <DEF= <HEG = 119  (Vertical opposite angle)

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Answer:

Measures of center generally tell us about the middle , or center of a distribution. They are the mean , the Mexican , and the mode. Each plays a useful role in statistics. The mean or arithmetic average , is calculated by adding all the data values and dividing by the number of values.

The Z-score for a GPA of 2.98 is 1.60345

A Z-score is a numerical value or measurement that explains the relationship between a value of data and the mean of a group of values. It will be calculated in terms of standard deviations from the mean.

The formula to calculate the Z -score is given by

                     Z - score =  [tex]\frac{( \bar{x} -\mu) }{\sigma}[/tex]    

Where  [tex]\bar {x}[/tex]  = test value

μ = mean and σ = standard deviation

Here we have

GPAS at CCCOnline are normally distributed with a mean of 2.05 and a standard deviation of 0.58

⇒ mean μ = 2.05

⇒ Standard deviation σ = 0.58  

And we need to find the z-score for a GPA of 2.98

⇒  [tex]\bar {x}[/tex] = 2.98

From above observations

Z - score =  [tex]\frac{( 2.98 -2.05) }{0.58}[/tex]  

= [tex]\frac{( 0.93) }{0.58}[/tex]

= 1.60345  

Therefore,

The Z-score for a GPA of 2.98 is 1.60345

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Answer: 1/2

Step-by-step explanation:

I'm assuming this is rise over run. The rise is 1 and the run is 2.

Remember, [tex]\frac{rise}{run}[/tex]

Answer: -1.631

Step-by-step explanation:

[tex]\log_{3} \frac{a}{3}=\log_{3} a-\log_{3} 3=-0.631-1=-1.631[/tex]

Answer: C or D(they appear the same, the answer is 5 hours)

Step-by-step explanation:

after 5 hours, train a has gone 5*50 miles, or 250 miles

after 5 hours, train b has gone 5*30 miles, or 150 miles

250miles + 150miles = 400 miles

Step-by-step explanation:

y = mx+ b

m is the slope = 5

you can get x,y from point (x,y); x=2, y=1

substitute all information we have to find b

1 = 5(2) + b

1 = 10 + b

1 - 10 = b

-9 = b

the function for line:

y = 5x - 9

Answer:

27/256

Step-by-step explanation:

=(27)(1/4)(1)/(64)

=27/256

The unit rate of orange could be found by Sara and Daniel by ratio to be $1.50

If Sara's mother bought 8 large oranges for $12.00

Sara may have thought of it like if $12 is for 8 oranges the how much is for 1

12 : 8 then X : 1

12/8 then x/1

12/8 = x/1

x = $1.50

Daniel would have taken this method, if 8 oranges costs $12 then 1 orange would cost ?

8 oranges : $12 then 1 orange : ?

8 : 12 = 1 : ?

8/12 = 1/?

8 * ? = 1 * 12

? = 12/8

? = $1.5

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The equation for the line parallel to the given line and passing through the given point is y = -4x + 5.

Given:

3y = -12x + 4 and point (1,1)

3y = -12x+4

divide by 3 on both sides

3y/3 = -12x/3 + 4/3

y = -4x + 4/3.

m = -4.

y = mx + c

substitute m and (1,1)

1 = -4*1 + c

1 = -4 + c

c = 1 + 4

c =5

substitute c and m value in y = mx+c

y = mx + c

y = -4x + 5.

Therefore the equation for the line parallel to the given line and passing through the given point is y = -4x + 5.

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The graph of the function f(x) = x³ and g(x) = (x - 3)³ are related to each other that the function g(x) is shifted right to 3 points.

Function

Basically, function is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Given,

Here we need to find how the graph of g(x)=(x-3)³ related to the graph of f(x) = x³.

Here we have the two equations of the function that are,

f(x) = x³

g(x) = (x - 3)³

By looking at the given functions, we have identified that f(x) be the parent function:

And it can be written as,

=> f(x) = x³

And the first transformation is applied as,

f(x) → f(x) - 3

Now, the function f(x)  will shift right side by 3 units

Therefore, the function f(x) = x³ and g(x) = (x - 3)³ are related to each other that the function g(x) is shifted right to 3 points.

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If a nonagon has 9 sides. One angle of a regular nonagon measures (3w + 15)°. The value of w is: D. w = 42.

Given data:

Nonagon= 9 sides

Angle of a regular nonagon =(3w + 15)°

Value of w =?

Hence let find the value of w

Value of w = 3w + 15°

Value of w = 3(9) + 15°

Value of w = 27 + 15

Value of w = 42

Therefore the correct option is D.

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Answer: the answer is D. W=42

Step-by-step explanation:

The earnings per hour be after working for 15 years is $11.4.

From the given table (2, 6.85), (4, 7.55), (6, 8.25).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)

1) Now, put (x1, y1)=(2, 6.85) and (x2, y2)=(4, 7.55) in slope formula, we get

m=(7.55-6.85)/(4-2)

= 0.7/2

= 0.35

Substitute m=0.35 and (x, y)=(2, 6.85) in y=mx+c, we get

6.85=0.35(2)+c

⇒ 6.85=0.7+c

⇒ c=6.85-0.7

⇒ c=6.15

Now, equation is y=0.35x+6.15

2). Put x=15 in the obtained equation, we get

y=0.35×15+6.15

⇒y=$11.4

3). Put y=9.65 in the obtained equation, we get

9.65=0.35x+6.15

⇒0.35x=9.65-6.15

⇒0.35x=3.5

⇒x=3.5/0.35

⇒x=10 years

Therefore, the earnings per hour be after working for 15 years is $11.4.

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Answer:

Step-by-step explanation:

we cant see the problem or there answers

Step-by-step explanation:

among other details this is the main thing about the standard form :

a polynomial in standard form is the sum of one or more terms; each term must be a monomial in standard form. also, the degrees of the terms should be decreasing as much as possible from left to right.

a monomial is the product of one or more factors: a constant coefficient and one factor for each variable in the expression. via exponent (e.g. 0) we control which variable is actually "showing", as any x⁰ = 1 and can therefore be omitted when writing as factor.

in other words :

e.g.

4x³ + 2x² + 5x + 1

2x + 3y + 7xy

are examples of the standard form.

in our case we have only x a variable. but we need to do all the squaring and multiplications and summing up to get the standard form.

that means

2(x - 1)² - 2 = ...

remember the priorities :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

2(x - 1)² - 2 = 2(x² - 2x + 1) - 2 =

= 2x² - 4x + 2 - 2 = 2x² - 4x

The volume of the cuboid is 153000 [tex]cm^{3}[/tex];

What is the volume of the cuboid?

In general, the volume of a cuboid is equal to the area that it takes up in space. It is dependent upon the cuboid's three dimensions, or its length, breadth, and height. Due to the fact that all of a cuboid's faces are rectangular, the term "Solid Rectangle" is also referred to as a cuboid. All of the angles and the opposite faces of a cuboid in a rectangular cuboid are at right angles. A cuboid's volume is determined by the product of its length, breadth, and height. Cubic units are used to measure cuboids' volume.

The product of a cuboid's base area and height determines its volume. We can therefore write;

Cuboid volume equals base area times height [in cubic units].

The cuboid's base is shaped like a rectangle. As a result, a cuboid's base area is determined by multiplying its length by its breadth. Hence,

A cuboid's volume is equal to its length, width, and height in cubic units, or

A cuboid's volume is equal to l b h [in cubic units].

l = length, b = width, and h = height.

In the given question, we have;

Length = 30 cm;

Breadth = 60 cm;

Height = 85 cm;

And,

we know that:

The volume of the cuboid = lbh

The volume of the cuboid  = 30×60×85 [tex]cm^{3}[/tex]

The volume of the cuboid  = 1800 ×85 [tex]cm^{3}[/tex];

The volume of the cuboid  = 153000 [tex]cm^{3}[/tex];

Hence,

The volume of the cuboid  = 153000 [tex]cm^{3}[/tex];

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Answer:

Step-by-step explanation:

The are 6 possibilities for each dice, so the number of outcomes is:

Outcomes with the sum of 10:

Probability of getting 10 is 3 out of 36:

The value of the function f(x) at x = -2 is ,  f(-2) = 1 , the correct option is (c) .

Function is defined as an expression that defines a relationship between one variable and another variable .

In the question ,

it is given that ,

the value of the function f(x) at different values of x is given ,

we have to find the value of the f(-2) , that is the value of the function f(x) at x = -2 .

from the table , we see that when x [tex]=[/tex] -2 , the value of f(x) is [tex]=[/tex] 1 ,

that means f(-2) [tex]=[/tex] 1 .

Therefore , The value of the function f(x) at x = -2 is ,  f(-2) = 1 , the correct option is (c) .

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Area of circle =  1764 pi in² in terms of pi .

area of circle = pi  r²

                      = 42 * 42 pi²

                      = 1764 pi in²

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