Suppose the reaction temperature x (in °c) in a certain chemical process has a uniform distribution with a = −9 and b = 9. (a) compute p(x < 0). (no response) 0.5 (b) compute p(−4.5 < x < 4.5). (no response) 0.5 (c) compute p(−7 ≤ x ≤ 8). (round your answer to two decimal places.) (no response) 0.83 (d) for k satisfying −9 < k < k + 4 < 9, compute p(k < x < k + 4). (round your answer to two decimal places.) (no response) 0.22

A. P(x<0)=0,5

B. P(-4,5<x<4,5)=0,5

C. P(-7<x<8)=0,83

D. P(k<x<k+4)=0,22

Step-by-step explanation:

A. I hope that you need the reason why those answer are correct.

In a uniform distribution of probability, the probability of P(a<x<b) can be found as follows:

P(a<x<b)= (b-a)/B-A

where A,B are the limits of the function given A=-9, B=9. Because -9<x<9, then P(x<0)=P(-9>x>0) and now we use the formula:

P(-9<x<0)= 0-(-9)/( 9-(-9) )

P(-9<x<0)= 9/18 =0,5

B. We proceed using the formula as before:

P(-4,5<x<4,5)= (4,5-(-4,5)) / 18

P(-4,5<x<4,5)= 9/18 =0,5

C. And again, we use the formula:

P(-7<x<8)= (8-(-7)) / 18

P(-7<x<8)= 15/18 =0,8333... =0,83

D. This question could seem different because of the interval given there, let´s analyse it:

The inequality -9<k<k+4<9 it´s just a form to say that there is a probability for P(x<k) and P(x<k+4) because both k and k+4 belongs to the interval where the function is defined uniform. Now the question asks us, what is P(k<x<k+4), for all k that fills -9<k<k+4<9?

Because they fill -9<k<k+4<9, both of them belongs to [-9,9], then we can use the formula:

P(k<x<k+4)= k+4-(k) / 18

P(k<x<k+4)= 4/18 =0,2222... =0,22

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°