Answer:
a. d = 1500 - 300t. b. after 2 hours and after 4 hours
Step-by-step explanation:
a. Since Jamie hikes up the mountain at a rate of 300 ft/hr, and the mountain is 1500 ft high, his distance, d from the peak of the mountain at any given time,t is given by
d = 1500 - 300t.
b.If Jamie distance d = 900 ft, then the equation becomes,
900 = 1500 - 300t
900 - 1500 = -300t
-600 = -300t
t = -600/-300
t = 2 hours
The equation d = 1500 - 300t. also models his distance from the peak of the mountain if he hikes down at a constant rate of 300 ft/hr
At d = 900 ft, the equation becomes
900 = 1500 - 300t
900 - 1500 = -300t
-600 = -300t
t = -600/-300
t = 2 hours
So, on his hike down the mountain, it takes him another 2 hours to be 900 ft from the peak of the mountain.
So, he is at 900 ft on his hike down after his start of hiking up the mountain at time t = (2 + 2) hours = 4 hours. Since it takes 2 hours to climb to the peak of he mountain and another 2 hours to climb down 900 ft from the peak of the mountain.
Answer:
12 blue necklaces + 12 red necklaces = 24 necklaces. He will have 1 blue bead left over and 1 red bead left over.
Step-by-step explanation:
37/3 = 12.333 or 12 r1
25/2= 12.5 or 12 r1
1+1=2
Answer:
(x-7) (x^2-5)
Step-by-step explanation:
x^3-7x^2-5x+35
Factor out an x^2 from the first two terms and -5 from the last 2 terms
x^2 (x-7) -5(x-7)
Factor out (x-7)
(x-7) (x^2-5)
Answer:
a. 11.26 % b. 6.76 %. It appears so since 6.76 % ≠ 15 %
Step-by-step explanation:
a. This is a binomial probability.
Let q = probability of giving out wrong number = 15 % = 0.15
p = probability of not giving out wrong number = 1 - q = 1 - 0.15 = 0.75
For a binomial probability, P(x) = ⁿCₓqˣpⁿ⁻ˣ. With n = 10 and x = 1, the probability of getting a number wrong P(x = 1) = ¹⁰C₁q¹p¹⁰⁻¹
= 10(0.15)(0.75)⁹
= 1.5(0.0751)
= 0.1126
= 11.26 %
b. At most one wrong is P(x ≤ 1) = P(0) + P(1)
= ¹⁰C₀q⁰p¹⁰⁻⁰ + ¹⁰C₁q¹p¹⁰⁻¹
= 1 × 1 × (0.75)¹⁰ + 10(0.15)(0.75)⁹
= 0.0563 + 0.01126
= 0.06756
= 6.756 %
≅ 6.76 %
Since the probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.
