Answer:
ABC - AAS
DEF - not enough information
GHI - not enough information
JKL - SAS
Step-by-step explanation:
SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
AAS postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.
HL postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
ASA postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
SSS postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
1. In triangles MNO and ABC, there are two congruent sides and non-included angle - AAS
2. In triangles MNO and DEF, there are two congruent sides - there is not enough information
3. In triangles MNO and GHI, there are three congruent angles - there is not enough information
4. In triangles MNO and JKL, there are two congruent sides and included angle - SAS
A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.
Yes, the large-sample confidence interval will be valid.
<h3>What is meant by normal distribution?</h3>
A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.
The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean.
The confidence interval will be valid regardless of the shape of the population distribution as long as the sample is large enough to satisfy the central limit theorem.
<h3>
What does a large sample confidence interval for a population mean?</h3>
A sample is considered large when n ≥ 30.
By 'valid', it means that the confidence interval procedure has a 95% chance of producing an interval that contains the population parameter.
To learn more about normal distribution, refer to:
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Answer:
8.49 inches
Step-by-step explanation:
x^2 + 7^2 = 11^2
x^2 + 49 = 121
X^2 = 121 - 49
x^2 = 72 (then take square root on both sides)
x = 8.49 inches
Answer with Step-by-step explanation:
We are given that
u+ v and u-v are orthogonal
We have to prove that u and v must have the same length.
When two vector a and b are orthogonal then
By using the property
We know that
Magnitude is always positive
When power of base on both sides are equal then base will be equal
Therefore,
Hence, the length of vectors u and v must have the same length.
