On Saturday morning, Ahmed decided to take a bike ride from one end of the 15-mile bike trail to the other end of the bike trail
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The perimeter of triangle ABC is 24 units
Step-by-step explanation:
If a segment joining the mid points of two sides of a triangle, then
this segment is:
- Parallel to the third side
- Its length is half the length of the third side
In The triangle XYZ
∵ A is the mid point of XY
∵ B is the mid point of YZ
∴ AB = XZ
∵ XZ = 18 units
- Substitute the value of XZ in AB
∴ AB = × 18 = 9 units
∵ B is the mid point of YZ
∵ C is the mid point of XZ
∴ BC = XY
∵ AY = 7 units
∵ AY = XY
∴ XY = 2 × AY
∴ XY = 2 × 7
∴ XY = 14 units
∴ BC = × 14 = 7 units
∵ A is the mid point of XY
∵ C is the mid point of XZ
∴ AC = YZ
∵ BZ = 8 units
∵ BZ = YZ
∴ YZ = 2 × BZ
∴ YZ = 2 × 8
∴ YZ = 16 units
∴ AC = × 16 = 8 units
∵ The perimeter of a triangle = the sum of the lengths of its sides
∴ Perimeter Δ ABC = AB + BC + AC
∴ Perimeter Δ ABC = 9 + 7 + 8 = 24 units
The perimeter of triangle ABC is 24 units
Learn more:
You can learn more about triangles in brainly.com/question/5924921
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Answer:
63% of the values lies between 70 and 85.
Step-by-step explanation:
We are given that a normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97.
<em>Let X = Set of numbers</em>
The z-score probability distribution for is given by;
Z = ~ N(0,1)
where, = mean value = 75
= standard deviation = 7.97
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, percentage of values that lies between 70 and 85 is given by = P(70 < X < 85) = P(X < 85) - P(X 70)
P(X < 85) = P( <
) = P(Z < 1.25) = 0.89435 {using z table}
P(X 70) = P(
) = P(Z
-0.63) = 1 - P(Z < 0.63)
= 1 - 0.73565 = 0.26435
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.25 and x = 0.63 in the z table which has an area of 0.89435 and 0.73565 respectively.</em>
Therefore, P(70 < X < 85) = 0.89435 - 0.26435 = 0.63 or 63%
<em>Hence, 63% of the values lies between 70 and 85.</em>