The interest on an investment varies directly as the rate of interest. if the interest is $41 when the interest rate is 4%, find the interest when the rate is 7%.

$ 71.75

Step-by-step explanation:

Suppose r represents the interest rate and I represents the amount of interest,

∵ the interest on an investment varies directly as the rate of interest,

i.e. I ∝ r

⇒ I = kr

Where,

k = constant of variation,

If I = 41, r = 4% = 0.04,

Thus, the equation that shows the relation between I and r is,

I = 1025 r

If r = 7% = 0.07,

Thus, the interest would be,

I = 1025 × 0.07 = $ 71.75

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560