Answer:a) 9cm
B) 729cm^3
C) 486cm^2
Step-by-step explanation:
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1 answer:
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Answer:
(a) The probability that a randomly selected athlete uses a stairclimber for less than 19 minutes is 0.2388.
(b) The probability that a randomly selected athlete uses a stairclimber for between 24 and 33 minutes is 0.3997.
(c) The probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is 0.0113.
Step-by-step explanation:
We are given that the amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 24 minutes and a standard deviation of 7 minutes.
Let X = <u><em>amounts of time per workout an athlete uses a stairclimber</em></u>
So, X ~ Normal()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = mean time = 24 minutes
= standard deviation = 7 minutes
(a) The probability that a randomly selected athlete uses a stairclimber for less than 19 minutes is given by P(X < 19 minutes)
P(X < 19 min) = P( <
) = P(Z < -0.71) = 1 - P(Z
0.71)
= 1 - 0.7612 = <u>0.2388</u>
The above probability is calculated by looking at the value of x = 0.71 in the z table which has an area of 0.7612.
(b) The probability that a randomly selected athlete uses a stairclimber for between 24 and 33 minutes is given by = P(24 min < X < 33 min)
P(24 min < X < 33 min) = P(X < 33 min) - P(X 24 min)
P(X < 33 min) = P( <
) = P(Z < 1.28) = 0.8997
P(X 24 min) = P(
) = P(Z
0) = 0.50
The above probability is calculated by looking at the value of x = 1.28 and x = 0 in the z table which has an area of 0.8997 and 0.50 respectively.
Therefore, P(24 min < X < 33 min) = 0.8997 - 0.50 = <u>0.3997</u>
(c) The probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is given by P(X > 40 minutes)
P(X > 40 min) = P( >
) = P(Z > 2.28) = 1 - P(Z
2.28)
= 1 - 0.9887 = <u>0.0113</u>
The above probability is calculated by looking at the value of x = 2.28 in the z table which has an area of 0.9887.
The event of probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is unusual because this probability is less than 5% and any even whose probability is less than 5% is said to be unusual.
IfIf AD BD, the following relationships that can be proved and why is: D. ΔACD ΔBCD, because of SAS.
<h3>Relationship that can be proved if AD=BD</h3>The relationship that can be proved is ΔACD ΔBCD, because of SAS.
The reason is that m<CDA=M<CDB=90°
CD=CD
AD=BD
Hence, ΔACD=ΔBCD because of SAS. SAS congruence can tend to be proved when the length of the two side correspond and when the angle between the two side is equal.
Therefore the correct option is D.
Learn more about Relationship that can be proved if AD=BD here:brainly.com/question/16906407
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