d = 3 , a₁₂ = 40 and S = 7775
In an arithmetic sequence the nth term and sum to n terms are
<h3>• a
= a₁ + (n-1)d</h3><h3>• S
=
[2a + (n-1)d]</h3><h3>
where d is the common difference</h3><h3>a₆ = a₁ + 5d = 22 ⇒ 7 + 5d = 22 ⇒ 5d = 15 ⇔ d = 3</h3><h3>a₁₂ = 7 + 11d = 7 +( 11× 3) = 7 + 33 = 40</h3><h3>S₁₀₀ =
[(2×7) +(99×3)</h3><h3> = 25(14 + 297) = 25(311)= 7775</h3>
Use inverse to solve this problem. Tan-1(5/27). =10.491 which rounded to the nearest degree equals 11.
Answer:
P(X > 8) = 0.323
Step-by-step explanation:
We are given that a softball pitcher has a 0.507 probability of throwing a strike for each pitch. Also, the softball pitcher throws 15 pitches.
The above situation can be represented through Binomial distribution;
where, n = number of trials (samples) taken = 15 pitches
r = number of success = more than 8
p = probability of success which in our question is probability of
throwing a strike for each pitch, i.e., 0.507
<em>LET X = Number of strikes</em>
So, it means X ~
So, Probability that more than 8 of them are strikes = P(X > 8)
P(X > 8) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)
= =
= 0.323
Therefore, probability that more than 8 of them are strikes is 0.323.
Answer:
$242.08
Step-by-step explanation:
Let's find the hourly rate first. We can find this by dividing the amount of money he earned by the amount of hours he worked.
299.04/42 = 7.12
He earns $7.12/hr.
Now to find the amount of money he'll earn, multiply the hourly rate by the amount of hours he's going to work.
7.12*34 = 242.08
He's going to earn $242.08 next week if he works 34 hours.