Answer:
Given: Quadrilateral P QR S is a rectangle.
To prove :PR= Q S
Construction : Join PR and Q S.
Proof: In Rectangle PQRS, and
→ taking two triangles PSR and Δ QRS
1. PS = Q R
2. ∠ PS R = ∠ Q RS [Each being 90°]
3. S R is common.
→ ΔP SR ≅ Δ Q RS → [Side-Angle-Side Congruency]
∴ PR =Q S [ corresponding part of congruent triangles ]
Hence proved.
Answer:
0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 3 cm and a standard deviation of 0.04 cm.
This means that
What is the probability that a bolt has a length greater than 2.96 cm?
This is 1 subtracted by the p-value of Z when X = 2.96. So
has a p-value of 0.1587.
1 - 0.1587 = 0.8413
0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.