An "A" train leaves a subway station every 12 minutes. An "E" train leaves every 9 minutes. If both trains just left the station on parallel tracks, when will both leave the station together again?

A. 108 minutes
B. 36 minutes
C. 72 minutes
D. 24 minutes

The solution is 3/2

The product of the numbers is given by the equation A = ( 3/4 ) x 2 and the value of A = 3/2 or A = 1.5

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be p

The value of p = 3/2

Let the second number be q

The value of q = 2

Now , the equation will be

A = first number x second number

Substituting the values in the equation , we get

A = ( 3/4 ) x 2

On simplifying the equation , we get

A = ( 3 x 2 ) / 4

A = 3/2

A = 1.5

Therefore , the value of A is 3/2

Hence , the value of the equation is 3/2

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The factor pairs are (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), and (6, 10) of the number 60.

A number system is defined as a system of writing to express numbers.

To find the factor pairs of 60

we need to list all the possible pairs of two positive integers that can be multiplied to give 60.

1 x 60 = 60

2 x 30 = 60

3 x 20 = 60

4 x 15 = 60

5 x 12 = 60

6 x 10 = 60

Therefore, the factor pairs of 60 are (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), and (6, 10).

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To minimize the amount of material needed for the sides of the sandbox, the sandbox should be square-shaped, with each side measuring 4 feet, resulting in a perimeter of 16 feet, which is the smallest perimeter for a 16-square-foot area.

The student is tasked with designing a rectangular sandbox such that the bottom has an area of 16 square feet and the dimensions of the sandbox require the least material for the sides. To achieve the least amount of material for the sides, we aim for a shape that has the smallest possible perimeter while maintaining the given area. This is achieved with a square-shaped sandbox.

Since the area is 16 square feet, we calculate the side length of the square by finding the square root of 16, which is 4 feet. Therefore, each side of the sandbox should be 4 feet long. This shape will have a perimeter of 16 feet (4 sides * 4 feet), which is the smallest perimeter possible for a rectangular shape with an area of 16 square feet.

In conclusion, the dimensions of the sandbox that will require the least amount of material for the sides are 4 feet by 4 feet.

Answer:

1. The correct answer choice is C $132.

2. The correct answer choice is B -$13.05

Step-by-step explanation:

1. 12 x 4 = 48.

180 - 48 = 132

2. -65.25/5 = -13.05

Yes, I know this is already answer.

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Option (C) The expression that has a value less than 32 is 32  times 3 / 4, which equals 24. The other expressions result in values greater than 32.

The student has asked which expression has a value less than 32. To compare the given expressions, we should evaluate them:

32  times 4 / 3 is greater than 32 since 4/3 is greater than 1.

32  times 3 / 4 is 32 multiplied by a fraction less than 1, so this will be less than 32. Multiplying 32 by 3 gives us 96, and dividing 96 by 4 yields 24.

32  times 3 / 4 or 24 is mentioned twice, and it remains less than 32.

32  times 5 / 2 is greater than 32 because 5/2 is more than 2.

Therefore, both instances of 32  times 3 / 4 (or 24) represent the expression that has a value less than 32.

The sofa at (4, 3) and the bed at (7, 5) are within the 5-meter range of good WiFi coverage from the router at (2, 5), whereas the desk at (6, 1) is outside this range.

The WiFi router is located at point (2, 5), and the radius of good coverage is within 5 meters. Let's use the distance formula d = √{(x_2 - x_1)^2 + (y_2 - y_1)^2} to calculate the distance to each location:

The sofa at (4, 3): d =√{(4 - 2)^2 + (3 - 5)^2} = √{4 + 4} = √{8} ≈ 2.83 meters

The bed at (7, 5): d = √{(7 - 2)^2 + (5 - 5)^2} = √{25 + 0} = √{25} = 5 meters

The desk at (6, 1): d = √{(6 - 2)^2 + (1 - 5)^2} = √{16 + 16} = √{32} ≈5.66  meters

Locations A (The sofa) and B (The bed) are within the 5-meter range of good coverage. Location C (The desk) is outside the 5-meter range.

The interest rate required to accumulate simple interest of $ 10.20 from a principal of $ 425.00 over 2 years is 1.2% per year.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

J.D. opened a savings account with $425

After 2 years, the total interest he earned was $10.20

We need to find the annual interest rate.

The rate of interest can be done by using below equation

r = 10.2 / ( 425 × 2 ) = 0.012

r = 0.012

convert r to the percentage by multiplying with 100

R = 0.012 × 100 = 1.2%year

Hence, the interest rate required to accumulate simple interest of $ 10.20 from a principal of $ 425.00 over 2 years is 1.2% per year.

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To calculate the annual interest rate, use the simple interest formula I = PRT, where I is the total interest earned ($10.20), P is the initial deposit ($425), and T is the time period in years (2). Solving for R gives us the annual interest rate, which in this case is 1.2%.

The student is asking how to calculate the annual interest rate based on the total amount of interest earned over a specific period. In this question, J.D. earned a total interest of $10.20 over 2 years on an initial deposit of $425. To find the annual interest rate, we can use the formula for simple interest since compound interest is not mentioned.

To solve for the interest rate, we use the simple interest formula I = PRT, where I is the interest earned, P is the principal amount (initial deposit), R is the rate of interest per year, and T is the time in years. Based on the information provided:

Plugging these values into the formula and solving for R, we get:

10.20 = 425 × R × 2

To isolate R, divide both sides by 850 (which is 425 × 2):

R = 10.20 ÷ 850

R = 0.012

The annual interest rate as a percentage is R × 100:

R × 100 = 0.012 × 100

R = 1.2%

Therefore, the annual interest rate was 1.2%.

The first angle measures 39 degrees, the second angle measures 78 degrees, and the third angle measures 63 degrees.

The sum of the angle measures of any triangle is always 180 degrees. Let's denote the measure of the first angle as 'x'. According to the given information, the second angle measures twice the first angle, which means it is 2x. Lastly, the third angle measures 15 degrees less than the second angle, so it is 2x - 15.

To find the angle measures of the triangle, we need to set up an equation and solve for 'x'. The sum of all three angles is 180 degrees, so we have the equation: x + 2x + (2x - 15) = 180. Simplifying this equation gives us 5x - 15 = 180. Adding 15 to both sides and then dividing by 5, we get x = 39.

Therefore, the first angle measures 39 degrees, the second angle measures 2x = 2(39) = 78 degrees, and the third angle measures 2x - 15 = 2(39) - 15 = 63 degrees.

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The probability of drawing a blue crayon first and then a green crayon is 2/21.

To find the probability of drawing a blue crayon first and then a green crayon, we need to consider the total number of crayons and the number of blue and green crayons in the bag.

There are a total of 7 crayons in the bag (2 red + 4 blue + 1 green).

The probability of drawing a blue crayon first is 4/7 because there are 4 blue crayons out of the total 7 crayons.

After drawing a blue crayon, there are 6 crayons left in the bag (1 blue + 2 red + 1 green + 2 blue). The probability of drawing a green crayon second is 1/6 because there is only 1 green crayon left out of the 6 crayons.

Therefore, P(blue, then green) = (4/7) * (1/6) = 4/42 = 2/21.

The probability of selecting a blue crayon followed by a green crayon from the bag is 1/10.5.

The probability of selecting a blue crayon and then a green crayon from a bag containing 2 red crayons, 4 blue crayons, and 1 green crayon is calculated by multiplying the probability of each individual event. The probability of drawing a blue crayon first is 4 divided by the total number of crayons, which is 7 (4/7). After drawing a blue crayon, it is kept out of the bag, reducing the total number of crayons to 6. The probability of then drawing a green crayon is 1 divided by the remaining total, which is 6 (1/6). Multiplying these probabilities together gives us the compound probability: (4/7) × (1/6), which equals 4/42 or 1/10.5 after simplification.

Answer: 8/3g cm

Step-by-step explanation:

Perimeter of a square = distance round the square

Since 1 side = 2/3g cm

A square has 4 side and all sides are equal

so each of the 4 side of the square is 2/3 g cm

Therefore perimeter = 2/3g cm + 2/3g cm+ 2/3g cm + 2/3g cm

Perimeter = 8/3g cm