Given that mean=3750 hours and standard deviation is 300:
Then:
<span>a. The probability that a lamp will last for more than 4,000 hours?
P(x>4000)=1-P(x<4000)
but
P(x<4000)=P(z<Z)
where:
z=(x-</span>μ)/σ
z=(4000-3750)/300
z=0.833333
thus
P(x<4000)=P(z<0.8333)=0.7967
thus
P(x>4000)=1-0.7967=0.2033
<span>b.What is the probability that a lamp will last less than 3,000 hours?
P(x<3000)=P(z<Z)
Z=(3000-3750)/300
z=-2.5
thus
P(x<3000)=P(z<-2.5)=0.0062
c. </span><span>.What lifetime should the manufacturer advertise for these lamps in order that only 4% of the lamps will burn out before the advertised lifetime?
the life time will be found as follows:
let the value be x
the value of z corresponding to 0.04 is z=-2.65
thus
using the formula for z-score:
-2.65=(x-3750)/300
solving for x we get:
-750=x-3750
x=-750+3750
x=3000</span>
Answer:
B
Step-by-step explanation:
All functions have y with a power of 1.
option B. is the only one where y has a power of 1.
The complete question gives the following options:
A) The 7-inch side and the 10-inch side must make a 52° angle.
B) The 7-inch side and the 10-inch side must make the 38° angle.
C) It does not matter whether or not the 7-inch side and the 10-inch side make a 52° angle.
<span> D) It does not matter whether or not the 7-inch side and the 10-inch side make the 38° angle.
According to the SAS rule for triangle congruency, two triangles are congruent if they have congruent two sides and the angle included.
Therefore, the only way to build a triangle congruent to ABC is to say that the given angle is the one included between the two sides.
Therefore, the correct answer is: </span><span>B) The 7-inch side and the 10-inch side must make the 38° angle. </span>
Answer:
9%
Step-by-step explanation:
Let the required number be 100.
Now, according to the question, the number is first increased by 30 %
⇒ 100 + 30 % of 100
⇒ 100 + [(30*100)/100]
⇒ 100 + 30
⇒ 130
Then, it is decreased by 30 %
⇒ 130 - (30 % of 130)
⇒ 130 - [(30*130)/100]
⇒ 130 - 39
⇒ 91
Net Decrease = 100 - 91
= 9
Percent Decrease = (Change in number*100)/100
⇒ (9*100)/100
= 9 %
