Answer:
Probability that the sample mean score is less than 522 = 0.0166 .
Step-by-step explanation:
We are given that in 2010 the mean mathematics SAT score was 555, and the standard deviation was 125 i.e.;
Mean, 
= 555 and Standard deviation, 
= 125
Also, Z = 
~ N(0,1) where, X bar = sample mean
n = sample size
Now, Probability(X bar < 522) = P( < 
) = P(Z < -2.1284)
= P(Z > 2.1284) = 0.0166
The above probability is calculated using z table.
Therefore, the probability that the sample mean score is less than 522 is 0.0166 .
Answer:
5(2a − 3) = (2a − 3) ⋅ 5
Step-by-step explanation:
Commutative Property of Multiplication is switching the order of the numbers around, and that answer demonstrates just that.
<span>for the first part, realize that the hour and minute hands are moving at different rates; in one hour, the minute hands moves all the way around the face of the clock, and thus moves a total of 360 degrees or 2 pi radians; the hour hand moves only 1/12 away around the clock, so covers only 30 degrees or Pi/6 radians.
Now, the LINEAR distance traveled by the tip of each hand is also determined by the length of the hand. In the case of the minute hand, it sweeps out a circle of radius 10 cm, so traces out a circle of radius 10 cm. Since the circumference of a circle is 2*pi*r, the minute hand (remember it made one complete cycle) covers a distance of 2*pi*10cm=20 Pi cm
The hour hand covers only 1/12 a circle, but that circle is only 6 cm in radius, so the distance traveled by the tip of the minute hand is:
1/12 *[2 *pi*r]=1/12*[12*pi]=pi
so the difference is 19pi
for the last part, you should draw a diagram of the two hands, the minute hand is 10 cm in length, the hour hand is 6 cm in length, and they are 30 degrees apart...from that drawing, see if you can figure out the remaining leg of the triangle you can form from them
good luck</span><span>
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