Greatest Common Factor and Least Common Multiple

Juan and Joe start walking around a track at the
same time and at the same place. It takes Joe 8
minutes to walk around the track, and it takes Juan
10 minutes. After how many minutes will they reach
the starting point at the same time?

Answer:

A = {2, 4}

Step-by-step explanation:

This can be written as

A = {2, 4}

Answer:

I am thinking  180

Step-by-step explanation:

The reason why I say this is because 180 over 12 equals to 15

Boris can expect to break even ( neither gain or lose money) is the answer.

The probability of a number is calculated by dividing Favorable outcome by Total outcome.

The probability of a number between 1 to 10 = Favorable outcome/Total outcome

Favorable outcome =1 (any one number )

Total outcome = 10

Here p(x) is equal to 1 divided by 10

P(X)= 1/10= 0.1

The table gives us the Amount when we multiple X to P(X),

Expected value = (XiP(Xi))

When we substitute the value we get,

=(10.1)+(-50.1)+(30.1)+(-50.1)+(50.1)+(-50.1)+(70.1)+(-50.1)+(90.1)+(-50.1)

=0

So we will get zero after substituting the value.

Hence, option C Bories can Expect to break even (Neither gain or lose money) is the correct answer.

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Answer:

$35 for 12 slices

Monthly cost for x slices of pizza = 20 + 1.25x

Step-by-step explanation:

Monthly Membership cost = $20
Discounted cost per slice of pizza = $1.25
Discounted total cost for 12 slices = $1.25 x 12 = $15

Total cost = 20 + 15 = $35 this momth

For x slices of pizza, monthly cost = 20 + 1.25x

Answer: it is 4.76785714286

Step-by-step explanation:

Answer:

[tex]2x^2 -5x - 7 =0[/tex]

Step-by-step explanation:

We have the equation
[tex]x + 9 = 2(x-1)^2[/tex]

[tex](x-1)^2 = x^2-2x+1[/tex]   using the formula [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]

[tex]x + 9 = 2(x^2-2x\cdot \:1+1^2)[/tex] =  [tex]2x^2-4x+2[/tex]

Switch sides

[tex]2x^2-4x+2=x+9[/tex]

Subtract 9 from both sides
[tex]2x^2-4x+2 - 9=x+9-9[/tex]

[tex]2x^2 -4x -7 = x[/tex]

Subtract x on both sides
[tex]2x^2 - 4x -7 -x = 0[/tex]

[tex]2x^2 - 4x - x -7 = 0[/tex]

[tex]2x^2 -5x - 7 =0[/tex]

where

[tex]a = 2, b = -5, c = -7[/tex]

Answer: I hope this helps.

Step-by-step explanation:

Answer:

impossible

Step-by-step explanation:

what is in the absolute value have to be positive so it's impossible that |2x+5| is < or = at -7

The material that remains from the original price is 3 1/16 inches.

A fraction is a non-integer that consists of a numerator and a denominator. A mixed fraction is made up of a whole number and a proper fraction. A proper fraction is a fraction where the numerator is less than the denominator.

Material left = initial length - length of the first plate - length of the second plate - (2 x 1/16)

[tex]19\frac{3}{8} - 9\frac{1}{4} - 6\frac{15}{16} - \frac{2}{16}[/tex]

[tex]4\frac{6 - 4 - 15 - 2}{16}[/tex]

4[tex]\frac{-15}{16}[/tex]= 3 1/16 inches

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Answer:

The answer is 8,937.5

Step-by-step explanation:

71500÷8

8×8=64

71-64=7

7500÷8

8×9=72

75-72=3

300÷8

8×3=24

30-24=6

60÷8

8×7=56

60-56=4

4.0÷8

8×5=40

40-40=0

The graph of the equation is shown below

From the question, we are to graph the given equation

The given equation is

-3 = 5x - y

To graph the equation,

First we will determine the x-intercept and y-intercept

x-intercept

Put y = 0 in the equation

-3 = 5x - 0

-3 = 5x

x = -3/5

y-intercept

Put x = 0 in the equation

-3 = 5(0) - y

-3 = 0 - y

-3 = -y

y = 3

Using the x-intercepts and y-intercepts, we can plot the graph of the equation.

The graph of the equation is shown below

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The number of cars that would pass through the intersection in 8 hours is 19,656.

In order to determine the number of cars that would pass through the intersection in 8 hours, the cars that passed through in one hour would be multiplied by the number of hours.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. Multiplication is the process of adding one number to another over a number of times. The sign used to represent multiplication is x.

Total number of cars that passed through in 8 hours = cars that passed through in one hour x number of hours

2457 X 8

2457

x     8

19,656

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We get the fixed cost as $ 150, cost of 25 items as $ 750, range as [0, 1500] and the domain as [0,150].

We are given the cost function:

C(x) = 10x + 500.

Fixed cost is when x = 0

C(0) = Fixed cost = 10 ( 0 ) + 500

Fixed cost = $ 500

Cost of making 25 products is x = 25

C(25) = 10 (25) + 500

C(25) = 250 + 500 = $ 750

Maximum cost allowed = $ 1500

Function becomes:

10x + 500 ≤ 1500

x + 50 ≤ 150

x ≤ 150 - 50

x ≤ 100

Range = [0, 1500]

Domain = [0, 150]

Therefore, we get the fixed cost as $ 150, cost of 25 items as $ 750, range as [0, 1500] and the domain as [0,150].

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Option 2 is the answer.

No. on tickets sold = 6000

Proceedings of the tickets sold = $78,000

Cost of tickets for children = $8

Cost of tickets for adults = $16

Cost of tickets for seniors = $12

2 times more adults were present than the children.

Let the number of children be 'c.'
Let the number of adults be 'a.'
Let the number of seniors be 's.'

Since 2 times more adults were present than the children, we get the equation,

a = 2c

No. of tickets sold will be equal to the total no, of people.

∴ c + a + s = 6000

The proceedings will be equal to the sum of the amounts and number of people who bought tickets with that amount,

∴ 8c + 16a + 12s = $78,000

Thus, we have the three equations,

c + a + s = 6000
8c + 16a + 12s = $78,000
a = 2c

This series of equations are given in option 2 Thus, option 2 is the answer.

Answer) Option 2.

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If there are about 7,000,000,000 people in the world and  In Australia, there is a population of about 2.306 x [tex]10x^{7}[/tex] people, then the difference between the world's  and Australia's populations is 697.694×[tex]10^{7}[/tex]

Given,

The total population of world = 7,000,000,000 peoples

Convert to suitable standard form

7,000,000,000 peoples = 700×    [tex]10^{7}[/tex] peoples

The population of Australia = 2.306×[tex]10^{7}[/tex]

The difference = The population of world - The population of Australia

=700×    [tex]10^{7}[/tex]-2.306×[tex]10^{7}[/tex]

=(700-2.306)×[tex]10^{7}[/tex]

=697.694×[tex]10^{7}[/tex]

Hence, If there are about 7,000,000,000 people in the world and  In Australia, there is a population of about 2.306 x [tex]10x^{7}[/tex] people, then the difference between the world's  and Australia's populations is 697.694×[tex]10^{7}[/tex]

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Using proportions, the coordinates of point C are given as follows:

C(0, -0.67).

A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.

Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.

For this problem, the points are given as follows:

A(-4,-6), B(5,6), C(x,y).

The ratio of AC to CB is of 4:5, hence the following equation is constructed:

C - A = 4/9(B - A).

As the ratio of 4:5 means that the distance is 4/(4 + 5) = 4/9.

The x-coordinate of C is found applying the above equation as follows:

x + 4 = 4/9(5 + 4)

x + 4 = 4

x = 0.

The y-coordinate of C is also found applying the equation, as follows:

y + 6 = 4/9(6 + 6)

y + 6 = 5.33.

y = -0.67.

Hence the coordinates of point C are given as follows:

C(0, -0.67).

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Answer:

a = 37 y = 100

Step-by-step explanation:

Think of the inverse operation of addition which is subtraction. Then you can guess and check and see what fits where. The letters are just placeholders so I took the given number and added it to the answer to get the answers for the blanks.

Cheers!

Now, because the conditional and converse are true, then we have a biconditional relation between P and Q.

From that, we conclude that the truth values for the two above statements is true for both

A conditional statement is of the form:

If P, then Q.

The inverse statement is:

if Q, then P.

We assume that these two are true.

An example of this is:

P = a number is even.

Q = a number is a multiple of 2.

Then the two above statements are:

Now the inverse statement is:

if not P, then not Q.

The contrapositive is:

If not Q, then not P.

Now, because the conditional and converse are true, then we have a byconditional relation between P and Q.

From that, we conclude that the truth values for the two above statements is true for both, but let's check with our propositions:

Inverse: If a number is not even, then it is not a multiple of 2. (this is true)

Contrapositive: If a number is not multiple of 2, then it is not even (also true).

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Yes, it is a rational number                            

Answer:

20.22 miles

Step-by-step explanation:

If 10 laps is 6.74 then 30 laps is 3*6.74 which is 20.22

Answer: an=40(n-1)+70

Step-by-step explanation:

70, 110, 150, ….

Notice the terms get bigger by 40 as the sequence progresses. Hence, we can model this sequence with a linear equation. y=40(x-1)+70 where y=term value, x=term number and 70 is the first term.

y=40(x-1)+70

an=40(n-1)+70    ==> an=term value/nth term. n=term number

The radius of the hole is 0.07 feet.

A cylinder is a three-dimensional object that is made up of a prism and a circular base.

Volume of a cylinder = πr²h

Radius = √volume / (π x h)

Where:

The volume of the hole and the height of the hole are in different dimensions. Thus, the height of the hole has to be converted to feet.

1 mile = 5280 feet

5280 x 2.9 = 15,312 feet

3500 / (22/7 x 15,312) = 0.07 feet

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The ordered pairs that represents a function y in terms of x are  {(-2, -3),(1, 3),(1, 6) (9, 8}, (12, 11)) and {(-3, -5), (3, 2), (6, 5), (7, 9), (10, 16)}

A set of ordered equation represents a linear function if the domain of the coordinates are not repeated.

For instance, the ordered pairs that is a function are the coordinates that do not have any repeated y-coordinates.

From the given linear functions, the ordered pairs that represents a function y in terms of x are  {(-2, -3),(1, 3),(1, 6) (9, 8}, (12, 11)) and {(-3, -5), (3, 2), (6, 5), (7, 9), (10, 16)}

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The values of f(0) that can be read from (a similar question in part (a) and (c)) the table, functions, and graph in the question are;

(a) f(0) = 1

(b) f(0) = 12

(c) f(0) = -2

Part of the question appears missing. From a similar question online, we have;

(a) A table of values;

x: -1, 0, 1, 2, 3

y: 7, 1, 6, -3, -4

Taking the function, f(x) = y, we have;

From the above values in the table, when x = 0, y = f(0) = 1

Therefore;

(b) y = 12 - 2•x²

Taking the function, f(x) = y, we have;

At x = 0, y = f(0) = 12 - 2 × 0² = 12

Therefore;

(c) A graph of a parabola passing through the points (-1, 3), (2, -6), (5, 3)

Let f(x) = a•x² + b•x + c, represent the function, we have;

f(-1) = 3 = a•(-1)² + b•(-1) + c = a - b + c

f(2) = -6 = a•(2)² + b•(2) + c = 4•a + 2•b + c

f(5) = 3 = a•(5)² + b•(5) + c = 25•a + 5•b + c

Solving the system of linear equations, (1), (2), (3) using a graphing calculator gives;

a = 1, b = -4, c = -2

Which gives;

f(x) = x² - 4•x - 2

Therefore;

f(0) = 0² + 4×0 - 2 = -2

Which gives;

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we get the the multiplication equations are 2 + 2 + 2 + 2 + 2 = 2 × 5, 5 + 5 + 5 + 5 + 5 = 5 × 5 and 4 groups of 3 = 3 × 4.

We are given some expressions and we need to find the multiplication equation for each one.

a) 2 + 2 + 2 + 2 + 2 will be

Since, 2 is repeating 5 times, we get that:

multiplication equation will be:

2 + 2 + 2 + 2 + 2 = 2 × 5

b) 5 + 5 + 5 + 5 + 5 will be

Since, 5 is repeating 5 times, we get that:

multiplication equation will be:

5 + 5 + 5 + 5 + 5 = 5 × 5

c ) 4 groups of 3  will be

Since, 3 is repeating 4 times, we get that:

multiplication equation will be:

4 groups of 3 = 3 × 4

Therefore, we get the the multiplication equations are 2 + 2 + 2 + 2 + 2 = 2 × 5, 5 + 5 + 5 + 5 + 5 = 5 × 5 and 4 groups of 3 = 3 × 4.

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Answer:

13

Step-by-step explanation:

When x=20

=x-7

=20-7

=13

Answer: 5/4

Step-by-step explanation: You go up five from point (-6,0) and across for to point (-2,4)

Answer:

7120.94 cubic feet

Step-by-step explanation:

volume of a cone =

pi times radius squared times (height ÷ 3)

pi times 20 squared times (17 ÷ 3)