Mathematics, 07.04.2020 17:22 zoriahmendoza

The speed of cars passing through the intersection of Blossom Hill Road and the Almaden Expressway varies from 14 to 35 mph and is uniformly distributed. None of the cars travel over 35 mph through the intersection. What is the probability that the speed of a car is between 17 and 23 mph?

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Answer from: emmaguentherp3hjd3

28.57% probability that the speed of a car is between 17 and 23 mph

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d is given by the following formula:

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

14 to 35 mph and is uniformly distributed.

This means that a = 14, b = 35

What is the probability that the speed of a car is between 17 and 23 mph?

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

$P(17 \leq X \leq 23) = \frac{23 - 17}{35 - 14} = 0.2857$

28.57% probability that the speed of a car is between 17 and 23 mph

Answer from: Quest

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) = +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

Answer from: Quest

a) 40 more; b) old factory: 10%, new factory: 16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.

using the function, substituting 0 in for w,

$p(w)=230(1.1)^w\\\\p(0)=230(1.1)^0\\\\p(0)=230(1)=230$

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate. the equation for the old factory is $p(w)=230(1.1)^w$ ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1. this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

$\text{percent of change}=\frac{\text{amount of change}}{\text{original amount}}$

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337. this is the first week that the new factory surpasses the old.

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