'a' can hit a target 4 times with 5 shots.'b' can hit 3 times with 5 shots and 'c' can hit 3 times with 5 shots as well. if two hits will damage the target (each person aims a target) then find probability that: i)target will be damaged. ii)two shots hit the target [ans with appropriate explanation will get the i got same ans for both question which is 57/125 and i am not sure about my ans]

i) 93/125

ii) 57/125

Step-by-step explanation:

If we assume each shooter gets one shot, that shot hits the target with probability equal to the average hit rate, and all shots are independent, then we seem to have ...

p(A) = probability A hits the target = 4/5

p(B) = probability B hits the target = 3/5

p(C) = probability C hits the target = 3/5

ii) Then the probability exactly two shots will hit the target is ...

... p(2) = p(A)·p(B)·p(C') +p(A)·p(B')·p(C) +p(A')·p(B)·p(C)

... = 4·3·2/125 +4·2·3/125 +1·3·3/125 = (24 +24 +9)/125

... p(2) = 57/125

i) The probabiilty the target will be damaged is the probability that 2 or 3 shots will hit the target. The probability that 3 shots will hit is ...

... p(3) = p(A)·p(B)·p(C) = 4·3·3/125 = 36/125

So ...

... p(damage) = p(2) +p(3) = (57+36)/125

... p(damage) = 93/125

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.