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Sedaia [141]
3 years ago
9

The life of light bulbs is distributed normally. The variance of the lifetime is 900 and the mean lifetime of a bulb is 520 hour

s. Find the probability of a bulb lasting for at most 576 hours. Round your answer to four decimal places.
Mathematics
1 answer:
Alex73 [517]3 years ago
8 0

Answer:

0.969

Step-by-step explanation:

Given that:

Mean lifetime (m) = 520 hours

Variance = 900

Hence, standard deviation (s) = √900 = 30

Probability that bulb will last for at most 576 hours

X ≤ 576

Obtain the standardized score :

Using the relation :

Zscore = (x - m) / s

Zscore = (576 - 520) / 30

Zscore = 56 / 30

Zscore = 1.867

P(Z ≤ 1.867) : using the z probability calculator ;

P(Z ≤ 1.867) = 0.96905

Hence, P(Z ≤ 1.867) = 0.969

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Need help with inscribed angles If M
Cloud [144]

Given:

In the given circle O, BC is diameter, OA is radius, DC is a chord parallel to chord BA and m\angle BCD=30^\circ.

To find:

The m\angle AOB.

Solution:

If a transversal line intersect two parallel lines, then the alternate interior angles are congruent.

We have, DC is parallel to BA and BC is the transversal line.

\angle OBA\cong \angle BCD        [Alternate interior angles]

m\angle OBA=m\angle BCD

m\angle OBA=30^\circ

In triangle AOB, OA and OB are radii of the circle O. It means OA=OB and triangle AOB is an isosceles triangle.

The base angles of an isosceles triangle are congruent. So,

\angle OAB\cong \angle OBA      [Base angles of an isosceles triangle]

m\angle OAB=m\angle OBA

m\angle OAB=30^\circ

Using the angle sum property in triangle AOB, we get

m\angle OAB+m\angle OBA+m\angle AOB=180^\circ

30^\circ+30^\circ+m\angle AOB=180^\circ

60^\circ+m\angle AOB=180^\circ

m\angle AOB=180^\circ-60^\circ

m\angle AOB=120^\circ

Hence, the measure of angle AOB is 120 degrees.

4 0
3 years ago
How does the graph of the function h(x)=3x^2 different from the graph of the function f(x)=x?
Tasya [4]
The graph of h(x) = 3x^2 is a curved "bowl" like shape that opens upward. The curve is called a parabola. The two ends go on forever upward. It has symmetry along the y axis. 

In contrast, the graph f(x) = x is a straight line that goes through (0,0) and (1,1). This is known as a linear equation. 
5 0
3 years ago
ABCD- parallelogram, If the perimeter of Triangle CPQ is 15cm, Find the perimeter of triangle BAQ. Find the perimeter of triangl
melamori03 [73]

Answer:

The answer is below

Step-by-step explanation:

A parallelogram is a quadrilateral (has 4 sides and 4 angle) with two pair of parallel and opposite sides. Opposite sides of a parallelogram are parallel and equal.

Given parallelogram ABCD:

AB = CD = 18 cm; BC = AD = 8 cm

∠P = ∠P, ∠PDA = ∠PCQ (corresponding angles are equal).

Hence ΔPCQ and ΔPDA are similar by angle-angle similarity theorem. For similar triangles, the ratio of their corresponding sides equal. Therefore:

\frac{CD}{PC}= \frac{AD}{CQ}\\\\\frac{18}{6}=\frac{8}{x}  \\\\x=\frac{6*8}{18}=\frac{8}{3}\ cm

Perimeter of CPQ = CP + CQ + PQ

15 = 6 + 8/3 + PQ

PQ = 15 - (6 + 8/3)

PQ = 6.33

∠CQP = ∠AQB (vertical angles), ∠QCP = ∠QBA (alternate angles are equal).

Hence ΔCPQ and ΔABQ are similar by angle-angle similarity theorem

\frac{AQ}{QP}=\frac{AB}{CP}  \\\\\frac{AQ}{6.33} =\frac{18}{6} \\\\AQ=\frac{18}{6}*6.33\\\\AQ = 19

\frac{BQ}{CQ}=\frac{AB}{CP}  \\\\\frac{BQ}{8/3} =\frac{18}{6} \\\\BQ=\frac{18}{6}*\frac{8}{3} \\\\BQ =8

Perimeter of BAQ = AB + BQ + AQ = 18 + 8 + 19 = 45cm

PA = AQ + PQ = 19 + 6.33 = 25.33

PD = CD + DP = 18 + 6 = 24

Perimeter of PDA = PA + PD + AD = 24 + 25.33 + 8 = 57.33 cm

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tia_tia [17]
Airplane I DONT KNOW ANYTHING LOL
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3 years ago
It takes a while for new factory workers to master a complex assembly process. During the first month that the new
Citrus2011 [14]

Answer:

Will I think it will be A

Step-by-step explanation:

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