Answer:
The probability that at least one of the three smoke detectors functions properly = 0.996625
Step-by-step explanation:
Given that:
a certain brand of smoke detector functions properly 85 percent of the time
Let X represent the certain brand of smoke detector
X = 85%
X = 0.85
Let the probability that at least one of the three smoke detectors functions properly be P(Y)
P(Y) = 1- (1 - X)³
P(Y) =1 - (1 - 0.85)³
P(Y) = 1 - 0.003375
P(Y) = 0.996625
∴
The probability that at least one of the three smoke detectors functions properly = 0.996625
Answer:
The ratio of their corresponding side lengths is equal to
Step-by-step explanation:
step 1
<em>Find the scale factor</em>
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z-------> the scale factor
x----> the area of the smaller solid
y----> the area of the larger solid
so
In this problem we have
substitute
square root both sides
------> scale factor
Simplify
step 2
<em>Find the ratio of their corresponding side lengths</em>
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
In this problem we have that the scale factor is equal to
therefore
The ratio of their corresponding side lengths is equal to
Answer:
The mean monthly salary of these 100 graduates is $2388.5
Step-by-step explanation:
First, lets make all of the salaries a set, so:
S = {S1,S2,S3,S4,S5}
where
S1 = {1001-1400}
S2 = {1401-1800}
S3 = {1801-2200}
S4 = {2201-2600}
S5 = {2601-3000}
Each element S1,S2,..,S5 will have it's own mean, that will be the upper range + lower range divided by 2.
So
M(S1) = (1400+1001)/2 = 2401/2 = 1200.5
M(S2) = (1401+1800)/2 = 3201/2 = 1600.5
M(S3) = (1801+2200)/2 = 4001/2 = 2000.5
M(S4) = (2201+2600)/2 = 4801/2 = 2400.5
M(S5) = (2601+3000)/2 = 5601/2 = 2800.5
To find the approximate mean, now we calculate a weigthed mean between M(S1),M(S2),...,M(S5)
So the mean will be
M = (M(S1)+11*M(S2)+14*M(S3)+38*M(S4)+36*M(S5))/100
M = 238850/100
M = 2388.5
So the mean monthly salary of these 100 graduates is $2388.5