The greater of two numbers is 1 more than twice smaller. three times greater exceeds 5 times the smaller by 10. find the three numbers.

x = 2y + 1

3x = 5y + 10

Because we have a value for x we can plug this value in to find the value of y.

3(2y + 1) = 5y + 10

Distributive property.

6y + 3 = 5y + 10

Subtract 5y from both sides.

y + 3 = 10

Subtract 3 from both sides.

y = 7

We can plug this value back into the original equation to find the value of x.

x = 2(7) + 1

x = 15

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet

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