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o-na [289]
3 years ago
15

A high school class consists of 7 ​seniors, 10 ​juniors, 12 ​sophomores, and 11 freshmen. Exactly 4 of the juniors are female​,

and exactly 2 of the sophomores are male. If two students are randomly selected from this​ class, what is the probability that the pair consists of a male junior and a female ​sophomore?
Mathematics
1 answer:
jekas [21]3 years ago
6 0

Answer:

1/13

Step-by-step explanation:

There exactly 7 seniors 10 Juniors, 12 sophomores and 11 freshman

in which 4 of the juniors are Female , and exactly 2 of the sophomores are male. Therefore,

10-4= 6 juniors are male

12-2 = 10 female sophomores

Total = 7+10+12+11= 40 students

P(male junior then female soph.)= \frac{6}{40}\times\frac{10}{39}= \frac{1}{26}

P(female soph then male junior)= \frac{10}{40}\times\frac{6}{39}= \frac{1}{26}

Therefore the final answer will be = 1/26 +1/26= 1/13

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In 1995, Hazel was 25 years older than her son Gary. In 2022, Hazel's age will be 150% of Gary's age. How old were they in 1995?
Kitty [74]
So find the difference between 1995 and 2022 to make it easier
2022-1995=27

so the rephrased question is
when hazel was x years old, she was 25 years older than son gary who was y old at that time (equation is x is 25 more than y or x=25+y)
in 27 years, (this means x+27 and y+27) hazel's age will be 150% of gary's age (x+27= 150% of y+27)
percent means parts out of 100  so 150%=150/100=15/10=1.5
'of' in math means multiply so
the equations are
x=25+y
x+27=1.5(y+27)
subsitute 25+y for x in second euation
25+y+27=1.5(y+27)
add like terms
y+52=1.5(y+27)
I personally dislike decimals to multiply both sides by 2 to make 2 0.5's or 1 (you are technically supposed to distribute or divide both sides by 1.5) so
2y+104=3(y+27)
distribute
2y+104=3y+81
subtract 2y from both sides
104=y+81
subtract 81 from both sides
23=y
subsitute
x=25+y
x=25+23
x=48


Hazel was 48 and Gary was 23 in the year of 1995
5 0
3 years ago
What ratio forms a proportion with 2/3?<br> A. 2/4 B. 3/4 C. 4/6 D. 3/2
LekaFEV [45]

Answer:

c

Step-by-step explanation:

because you can simplify 4/6 by 2.

2 goes into 4 twice and then 2 goes into 6 3 times

2/3

3 0
2 years ago
A line goes through the point (6,-2) and has a slope of -3. What is the value of a if the point (a,7) lies on the line?​
Vikki [24]

Answer:

<h2>a = 3</h2>

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

m =  \frac{ y_2 - y _ 1}{x_ 2 - x_ 1}  \\

From the question the slope is - 3

To find the value of a we have

- 3 =  \frac{7 -  - 2}{a - 6}  \\  - 3 =  \frac{7 + 2}{a - 6}  \\  - 3(a - 6) = 9 \\  - 3a + 18 = 9 \\  - 3a = 9 - 18 \\  - 3a =  - 9

Divide both sides by - 3

\frac{ - 3a}{ - 3}  =  \frac{ - 9}{ - 3}  \\

We have the final answer as

<h3>a = 3</h3>

Hope this helps you

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