MATHEMATICS MIDDLE SCHOOL

List the factors of 15 and 30. Indicate which factors are common to both numbers and the Greatest Common Factor (GCF). 15= ___________            30= ____________      Common= ____________      GCF= _______

Answers

Answer 1
Answer: Factors of 15 . . . 1, 3, 5, 15

Factors of 30 . . . 1, 2, 3, 5, 6, 10, 15, 30

Common factors (numbers on both lists) . . . 1, 3, 5, 15

Greatest common factor (biggest number on both lists) . . . 15

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John is thinking of a number. He gives the following 3 clues. ``My number has 125 as a factor. My number is a multiple of 30. My number is between 800 and 2000.'' What is John's number?Please answer correctly

Answers

Answer:

John's number is 1500

Step-by-step explanation:

* Lets explain how to solve the problem

- Factors of a number are the numbers you multiply to get the number

- Ex: Factors of 12 are 1 × 12 , 2 × 6 , 3 × 4

- The factors of a number smaller than or equal the number

- Multiple of a number is that number multiplied by an integer

- Ex: 2, 4, 6, 8, and 10 are multiples of 2

- The multiples of a number greater than or equal the number

* Lets solve the number

- John is thinking of a number

- He gives the following 3 clues

# The number has 125 as a factor

# The number is a multiple of 30

# The number is between 800 and 2000

∵ 125 is a factor of the number

- Assume that the number is 125 (its factors 1 , 5 , 25 , 125)

∵ The number is a multiple of 30

- Assume the number is 30 (the first multiple of 30)

- To solve the problem lets find the lowest common multiple of 125

  and 30 by using prime numbers only

∵ The prime factors of 125 = 5 × 5 × 5

∵ The prime factors of 30 = 2 × 3 × 5

- L.C.M of the two numbers is the product of their prime factors

 without reputation

∴ L.C.M = 5 × 5 × 5 × 2 × 3 = 750

∵ 750 has 125 as a factor

∵ 750 is a multiple of 30

- But 750 is not between 800 and 2000

∴ Find a multiple of 750 and between 800 and 2000

∵ 2 × 750 = 1500

* lets check the three clues

∵ 1500 has 125 as a factor

∵ 1500 is a multiple of 30

∵ 1500 is between 800 and 2000

∴ John's number is 1500

Help me with number 6 pls and tell me how

Answers

The answer would be D

Hope this helps!
D. because there is about 7 hours between 8:30 am and 3:15 pm, so to find the average time 351 needs to be divided by 6.75

Melillo Middle School prepared 30 cups of trail mix for a carnival. The ratio of nuts to dried fruit in the trail mix was 3 to 2. If the teachers ate 6 cups of nuts out of the mix, how many cups of dried fruit would need to be taken out in order to keep the original ratio?

Answers

4 cups of dried fruit would need to be taken out to keep the original ratio.

Given:
30 cups of trail mix.
ratio of nuts to dried fruit is 3 to 2.

3:2 = 6:x
3x  = 2*6
3x = 12
3x/3 = 12/3
x = 4  cups of dried fruits
ratio is 3:2
30 total
3+2=5
30=5 units
divide by 5
6=1 unit

at first there is
3(6):2(6)=18:12
18 nuts and 12 dried fruit
if teachers ate 6 nunts then hoa much fruit must be taken out to keep it same

18-6=12
12:x=3:2
treat as fraction
12/x=3/2
multiply both sides by x to clear x
12=3x/2
multiply both sides by 2 to cleaer fraction
24=3x
divide by 3
8=x

it needs to be 8
12-x=8
subtract 12 from both sides
-x=-4
multiply -1
x=4



4 cups must be taken out

In the first year of ownership, a new car can lose 20% of its value. If a car lost $4200 of value in the first year, how much did the car originally cost?

Answers

$5250
$5250-20%=$4200

Answer:

5250

Step-by-step explanation:

What is 14 49ths in simplest form

Answers

The answer would be 2/7. This is because you find a Greatest Common Factor, also known as a GCF. In this problem the Greatest Common Factor would be seven because it is the largest number that goes into both 14 and 49. Once you find the GCF (7) you would divide both numbers by that (7) to get them into simplest form. In this problem you would take your GCF (7) and divide both numbers (14 and 47) by your GCF (7) and you would get an answer of 2/7. (2 7ths)
The simplest firm is 2/7

The scatter plot below represents the change in global sea level from 1993-2017, according to the National Aeronautics and Space Administration (NASA) The equation of the regression line is written below, where Y represents the predicted change in sea level and t represents the years since 1993.
y = 0 + 3.2t

Part a:
Identify the y-intercept of the regression line and explain what it represents in the context of the data.

Answers

Answer:

The y-intercept is zero and it means that in the year 1993 there was no change in the seawater level.

Step-by-step explanation:

See the scatter plot graph attached.

It represents the change in global sea level from 1993-2017, according to the National Aeronautics and Space Administration (NASA).

The equation of the regression line is written below, where Y represents the predicted change in sea level in mm and t represents the years since 1993.

y = 0 + 3.2t .............. (1)

Therefore, the equation is in the slope-intercept form and the y-intercept is zero for this graph.

That means in the year 1993 there was no change in the seawater level. (Answer)
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