Since no possible correct method is posted, I will suggest a couple.
Method 1: guess and check
Works well for simple problems involving integers like this one.
Victor's age must be zero or greater than one, say one.
Guess v=1, find m=v+6=7, check m=5v-2=5-2=3 no good.
we need to make v bigger
Guess v=2, find m=v+6=2+6=8, check m=5v-2=5*2-2=8 ✔
So v=2, m=8.
Method 2:
Solve the system of two equations.
since the left-hand sides is m in both equations, and since m=m, we just have to equate the right-hand sides to solve for v.
5v-2=v+6
Solve for v
5v-v = 6+2
4v=8
v=2,
so again, v=2, m=v+6=2+6=8.
(a) By the fundamental theorem of calculus,
<em>v(t)</em> = <em>v(0)</em> + ∫₀ᵗ <em>a(u)</em> d<em>u</em>
The particle starts at rest, so <em>v(0)</em> = 0. Computing the integral gives
<em>v(t)</em> = [2/3 <em>u</em> ³ + 2<em>u</em> ²]₀ᵗ = 2/3 <em>t</em> ³ + 2<em>t</em> ²
(b) Use the FTC again, but this time you want the distance, which means you need to integrate the <u>speed</u> of the particle, i.e. the absolute value of <em>v(t)</em>. Fortunately, for <em>t</em> ≥ 0, we have <em>v(t)</em> ≥ 0 and |<em>v(t)</em> | = <em>v(t)</em>, so speed is governed by the same function. Taking the starting point to be the origin, after 8 seconds the particle travels a distance of
∫₀⁸ <em>v(u)</em> d<em>u</em> = ∫₀⁸ (2/3 <em>u</em> ³ + 2<em>u</em> ²) d<em>u</em> = [1/6 <em>u</em> ⁴ + 2/3 <em>u</em> ³]₀⁸ = 1024
Answer:
0.3085 = 30.85% probability that the next car will be traveling less than 59 miles per hour.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
Calculate the probability that the next car will be traveling less than 59 miles per hour.
This is the pvalue of Z when X = 59. So
has a pvalue of 0.3085
0.3085 = 30.85% probability that the next car will be traveling less than 59 miles per hour.
Answer:
I'm pretty sure it's a
Step-by-step explanation:
