Which are the solutions of x2 = 19x + 1?

We recognize that two angles, ∠UVW and ∠XYZ, are complementary, which means their sum is 90°.

Their measures are given as:

∠UVW = x - 10

∠XYZ = 4x - 10

Adding these, we have:

(x - 10) + (4x - 10) = 90

Simplifying:

5x - 20 = 90

Adding 20 to both sides:

5x = 110

Dividing by 5:

x = 22

Substituting back:

∠UVW = 22 - 10 = 12°

∠XYZ = 4(22) - 10 = 78°

Therefore, the values are:

x = 22°

∠UVW = 12°

∠XYZ = 78°

Answer:

(A) 0.15625

(B) 0.1875

(C) Cannot be determined

Step-by-step explanation:

The time it takes for a student to finish a statistics quiz is uniformly distributed between 32 and 64 minutes.

Let's denote X as the duration needed for the student to complete the statistics quiz

Thus, X ~ U(32, 64)

The probability density function (PDF) for a uniform distribution is expressed as;

f(X) = ,  a < X < b      where a = 32 and b = 64

The cumulative distribution function (CDF) is given by P(X <= x) =

(A) The probability of a student taking longer than 59 minutes to complete the quiz = P(X > 59)

   P(X > 59) = 1 - P(X <= 59) = 1 - = 1 - = = 0.15625

(B) The probability that a student completes the quiz between 37 and 43 minutes = P(37 <= X <= 43)  = P(X <= 43) - P(X < 37)

    P(X <= 43) = = = 0.34375

    P(X < 37) = = = 0.15625

    P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875

(C) The probability that a student takes exactly 44.74 minutes to complete the quiz

     = P(X = 44.74)

This probability cannot be calculated as it is a continuous distribution, which doesn't provide probabilities for specific points.

Response:

The problem is summarized in the following explanation segment.

Detailed explanation:

The estimate of the slots or positions lost due to simultaneous transmission attempts can be calculated as follows:

Evaluating the likelihood of transmitting gives us "p".

When considering two or more attempts, we arrive at

Fraction of slots wasted,

=

Substituting the values yields

=

=

Thus, the answer appears to be correct.

Option b) 1960 is the total hours worked by the electrician.

Step-by-step explanation:

It is stated that a full-time electrician will put in 40 hours weekly.

Hence, we should determine the total hours he could work in a year, which consists of twelve months.

Thus, a year consists of 365 days.

To find the number of weeks in these twelve months:

Number of weeks = Total days in a year / 7 days of the week

⇒ 365 / 7

⇒ 52.14 (approximately 52 weeks)

It translates to 52 weeks within twelve months.

Out of these 52 weeks, three weeks are designated for vacation.

The total weeks the electrician will work = 52 weeks - 3 weeks

⇒ 49 weeks.

Thus, the electrician worked for 49 weeks.

To find his total worked hours = 49 weeks × 40 hours

⇒ 1960 hours.

So, the total hours the electrician worked amounts to 1960 hours, which corresponds to option b).