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Question 1

counting the sum of intergers form x to y

Answer 1

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-solving-equations/linear-equations-word-problems/v/sum-consecutive-integers

Question 2

2.5/3

Answer 2

is not a fraction, fraction must have an integers as a nominator and denominator

Question 3

To reproduce an old photograph, a photographer charges x dollars to make a negative, 3x53/5 dollars for each of the first 10 prints, and 5x/5 dollars for each print in excess of 10 prints. If $45 is the total charge to make a negative and 20 prints from an old photograph, what is the value of x [x=5]

Answer 3

x + 3x/5 (n - first 10) + 5x/5 (x - 10) = 45

https://greprepclub.com/forum/to-reproduce-an-old-photograph-a-photographer-3x-charges-x-8710.html

Question 4

long polynomial division

Answer 4

https://www.youtube.com/watch?v=RPXMBIFG_W4

Question 5

finding the two different values (quadratic equation-parabola) that will resut the same output

f(x)=x^2 - 8x +12

Answer 5

1. find the roots of the equation
   (x+-a)(x-+b)
2. finding vaules by symetry e.x x=6 and x=2 lower point = 4 (6+2=8, 8/2=4); next point 3 & 5
3. there are infinite number of pairs

Question 6

ratio
The ratio of men to women is 9 to 20. The total number of people of 58
Ratio does not give any information about actual number of things, people ect. e.x the ratio of apples to oranges is 3:5 = the actual number of fruit might be 8, 16, 24, 32, 40 - all depends on the multiplier

Answer 6

1. make the equation 9x/20y=9/20 M+W=58

2. find the multiplier (x) that will give you the right number

Question 7

2x^2=(2x)^2

Answer 7

2x^2=4x^2

0=2x^2
x=0

Question 8

(x-1)(x+1)=

Answer 8

(x^2-1)

Question 9

number of multiples of 7 from 1 to 1000

Answer 9

counting the last multiple of 7 1000/7=142.85
ignore the desmo
142*7=994

last - first/# +1
994-7/7+1 = 142

Question 10

angle bisector inside a triangle

Answer 10

https://www.youtube.com/watch?v=6WZRypy7ry0

Question 11

slope = -1/2

Answer 11

y=-1/2x + 1 the slope will be one down the y-axis and 2 right the x-axis
https://www.wolframalpha.com/input/?i=y%3D-1%2F2x+%2B+1

Question 12

the same line ex y=x+3 and y=x+3

Answer 12

1. inifnite number of solutions
2. the slope is the same (pararell lines)
3. the y-intersept is the same

Question 13

1

Answer 13

factor and divisior of every numer

is not a prime number

Question 14

1/3 + 1/3

Answer 14

=2/3

Question 15

7/11*2/9

Answer 15

=14/99

Question 16

k^2=m^2

Answer 16

I k I = I m I

Question 17

agebraic term

Answer 17

3x^2 - 1 term

3x^2 + 5 - 2 terms

the number (only) next to the letter is called coefficient, the number without the letter is called constant

Question 18

4x^2 - 36

Answer 18

= (2x-6)(2x+6)

Question 19

if n=33^43 + 43^33 what is the unit digit of n

Answer 19

1. pattern for 3 is 3, 9, 27, 81
   the pattern repeat itself every 4 numbers so look for multiples of 4
   the closest multiple of 4 is 40 (unit digit=1) therefore the unity digit of 33^43 is 7

the colosest multiple of 4 in 43^33 is 32 (unit digit=1) therefore unit digit is 3

the unit digit of n = 0

Question 20

final exam grade = 70% of final grade, John got 75%

midterm exam grade = 30% of final grade, John got 40%

Answer 20

total = 70 + 30 = 100

0.75 * ( 70 ) + 0.40 * ( 30 ) / 100 = 52.5 + 12 / 100 = 64. 5

Kim’s midtem exam is worth 20% of final grade and she got 35/50 = 0.70 * 20 = 14

Question 21

solution A, consisting of 40% bleach and 60% orange juice, is mixed Solution B consisting of 20% and 80% orange juice. The resulting mixture contains 24% bleach. Solution A accounts for what percentage of the mixture.?

Answer 21

bleach

20 (B) 24 40(A)
ratio is 16:4 = 4(B):1(A) B is more to 24 so the ratio is going to be bigger is B side

answer 1/5 = 20% (A accounts for 1, the total is 4+1=5)

Question 22

y > 2x + 1

Answer 22

https://www.wolframalpha.com/input/?i=y+%3E+2x+%2B+1

Question 23

y=x^2

Answer 23

parabola
https://www.wolframalpha.com/input/?i=y%3Dx%5E2

https: //www.wolframalpha.com/input/?i=y%3Dx%5E2+%2B1 (y=x^2 + 1)
https: //www.wolframalpha.com/input/?i=y%3Dx%5E2+-2 (y=x^2 - 2)
https: //www.wolframalpha.com/input/?i=y%3D%28x%2B1%29%5E2 (y=(x+1)^2)
https: //www.wolframalpha.com/input/?i=y%3D%28x-1%29%5E2+%2B+3 (y=(x-1)^2 + 3)

Question 24

y=-x+2, y=x^2

Answer 24

https://www.wolframalpha.com/input/?i=y%3D-x%2B2%2C+y%3Dx%5E2
-x+2=x^2
(x-1)(x+2)=0
x=1, x=-2 | points (1,1) and (-2,4)

Question 25

interior vs. exterior volume

Answer 25

the volume of a box is 2688 but the box is 1/4 thick all around. 12-1/4-1/4 = 11.5 interior volume = 11.5 * 13.5 * 15.5 = 2406.375

Question 26

1. numbers form 1 to 10, what’s the probability of getting first 1 and then 3 (order matter)
2. numbers form 1 to 10, what’s the probability of getting first 1 and then 3 (order does not matter)

Answer 26

1/10 * 1/9 = 1/90

1/90 * 2

Question 27

permutation

Answer 27

order does matter (10) = 10 * 9 * 8

order does not matter (10) = n! / (n-r)! * r!

Question 28

1. the value of overall change in graphs

2. the average of x changes in graphs

Answer 28

1. = range

2. = first - last / x

Question 29

standard deviation

adding/multiplying numbers by the same number

Answer 29

how far apart are the numbers (from the mean) e.x 1, 3 = the mean is 2 = the s.d is 1
if all numbers are the same, the s.d = 0

an equation with the biggest slope has the biggest s.d ( the bigger the slope - the bigger the s.d )
adding/subtracting = s.d stays the same
multiplying/dividing = s.d will be mutiplied by the number ( 0 is the exeption )

Question 30

normal distribution: properties

Answer 30

1. mean, median mode are nearly equal

2. 2/3 of the data are within 1 s.d of the mean