CPhill

A)    r  = 1.80 √ [m / v^2]

7  = 1.80 √ [80 / v^2]        divide both sides by 1.80

7 / 1.80  = √ [80 / v^2]        square both sides

[ 7 / 1.80]^2  = 80/v^2        rearrange as

v^2  =  80 / [ 7 / 1.80]^2      take the square root of both sides

v = √80 / [ 7 / 1.80]   = about 2.3 m/s

B)  9 = 1.80  √ [m /2^2]     divide both sides by 1.80   and simplify inside the root

5 = √ [m / 4]      square both sides

25  = m / 4       multiply both sides by 4

100 = m  = 100 kg

The csc can't = 12/13  because  the relationship  is :  r / y   .......  and r is always ≥  y

Your teacher is correct and I was incorrect.......let's try this again  !!!!

Call the total number born  = x

Then, ten more than 1/2   =  (1/2)x + 10  = the number of girls born   .....so we have

(1/2)x + 10 + 16   = x      simplify

(1/2)x + 26  = x      subtract (1/2)x  from both sides

26  = (1/2)x      multiply both sides by by 2

52  =   x   =  the total born

This makes more sense than my previous answer.........

1/2 (52)  = 26........and 10 more than that = 36.....so  36 girls were born and 16 boys were born.......

Sorry for the previous mistake   !!!!

Let's go from this step :

3x-5=x^2-4x+4        subtract 3x  from both sides and add 5 to both sides

0  = x^2 -7x + 9       this will not factor........using the quadratic formula, the two solutions are :

[ 7 + √13] / 2     = about   5.3028    or

[ 7 - √13] / 2     = about   1.6792

The second solution is extraneous, since it makes the right side of the original equation negative......and we can't ever get a negative answer from a positive root......this solution results from the squaring of both sides   [which often happens in these types of problems].....so.....

Only the first solution is "good"

Let the number of 3 point questions = x..........then......the number of 4 point questions = 29 - x   and we have

Number of 3 point questons  x  point value each  +  Number of 4 point questions x point value each = total points.......so.....

x(3)  + (29 - x)4  = 100    simplify

3x + 116 - 4x  = 100

-1x + 116 = 100    subtract  116 from each side

-1x  = -16          divide both sides by -1

x = 16  =  number of 3 point questions

And    (29 - x )  = (29 - 16)  = 13   = number of  4 point questions

Probability of A = probability of picking a male who likes chocolate ice cream  = 3/75

Probability of B = probability of picking a female who doesn't lke ice cream at all  = 1/75

P (A ∩ B )  =  3/75 * 1/75   = 3 / 5625   = about .053 %

Thanks for that answer, heureka.........could you explain how you derived your final formula?

I'm just someone who likes to help answer questions............

Probability that it will rain at least 6 days  = probability that it will rain 6 days + probability it will rain all 7 days

Probability it will rain 6 days  .....we want to choose 6 of any 7 days.......and, on each of those days, the probability of rain is 90%.....and on the remaining day, the probability is only 10%.......so......we have this binomial probability:

C(7,6) (.90)^6(.10)  = about  37.2%

Probability it will rain all 7 days =  (.9)^7   = about 47.8%

So.....summing the probabilities, we have   [ 37.2 + 47.8]%  =  about 85%

Thanks, GM, for the compliment....but....I'm definitely NOT the smartest person on this website, by a long shot !!!!