A certain type of device has an advertised failure rate of 0.01 per hour. The failure rate is constant and the exponential distr
1 answer:
Response:
Detailed explanation:
It is given that a specific kind of device has a stated failure rate of 0.01 every hour.
Considering this constant failure rate, the duration needed for a single failure
is calculated as 1(100) = 100
Thus, in a span of 100 hours, one can anticipate 1 failure
a) Average time until failure
b) the chance that 300 hours will elapse before any failure is noted
equals: the first 5 hours without failure and the subsequent hour experiencing failure
=
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Answer:
(C) They have the same coefficient of variation
Step-by-step explanation:
The coefficient of variation (CV) is calculated using the formula:
Where represents standard deviation and
represents the mean.
Bob's average weight is 200 pounds with a standard deviation of 16 pounds
This indicates that .
Thus, his coefficient of variation is
Mary's average weight is 125 pounds, with a standard deviation of 10 pounds.
This implies
Therefore, her coefficient of variation is
Since both have the same coefficient of variation, the accurate response is.
(C) They have the same coefficient of variation
Important details about isosceles triangle ABC:
- The median CD, which is drawn to the base AB, also acts as an altitude to that base in the isosceles triangle (CD⊥AB). This indicates that triangles ACD and BCD are congruent right triangles, each with hypotenuses AC and BC.
- In isosceles triangle ABC, the sides AB and BC are equal, meaning AC=BC.
- The base angles at AB are equal, m∠A=m∠B=30°.
1. Consider the right triangle ACD. The angle adjacent to side AD is 30°, which dictates that the hypotenuse AC is double the length of the opposite side CD relating to angle A.
AC=2CD.
2. Now, for right triangle BCD, the angle next to side BD is also 30°, so hypotenuse BC is twice the opposite leg CD linked to angle B.
BC=2CD.
3. To calculate the perimeters of triangles ACD, BCD, and ABC:
4. If the total of the perimeters of triangles ACD and BCD is 20 cm greater than the perimeter of triangle ABC, then
5. Given that AC=BC=2CD, the lengths of legs AC and BC of the isosceles triangles are 20 cm.
Answer: 20 cm.
Answer:
C. The hypotenuse measures twice the distance of the shorter leg.
B. The longer leg is √3 times the length of the shorter leg.
Step-by-step explanation:
A 30-60-90 triangle is considered a right triangle. Triangles containing a right angle are classified as right triangles. Only one right angle can exist in such a triangle. The representation of this case is illustrated below. Let’s clarify why the proposed statements are valid:
The hypotenuse of a right triangle is always opposite to the right angle. If we designate as the shorter leg, the sine law affirms that the hypotenuse is:
This indicates that the hypotenuse is double the length of the shorter leg
The longer leg, which we can call , can be determined with the Pythagorean Theorem:
Thus, it is accurate that the longer leg is √3 times longer than the shorter leg.