Answer:
A. Triangles are similar by AA similarity.
Step-by-step explanation:
By the Angle Angle Similarity Theorem, if two pairs of corresponding angles are congruent, then the triangles are similar. As a given, Angle E is 35 degrees and Angle B is 45 degrees, which means that Angle R is 100 degrees; By definition, a triangle is 180 degrees in total. Therefore, Angle R is congruent to Angle A. Angles REB and AEZ are also congruent by the vertical angle theorem.
In conclusion, triangles AEZ and REB are similar by the AA similarity theorem.
Hey there! :)
Answer:
13 packages.
Step-by-step explanation:
Begin by finding the total area of this composite figure. Separate the figure into separate rectangles. Use the formula A = l × w to calculate the area of each:
Smaller rectangle:
Subtract 7 from 9 to find the width:
9 -7 = 2. Therefore:
2 × 2 = 4 ft².
Larger rectangle:
7 × 5 = 35 ft².
Add up the two areas to find the area of the entire figure:
4 + 35 = 39 ft².
If each package of tile covers 3 ft², simply divide to find the package of tiles needed:
39 / 3 = 13 packages.
1/3 into a decimal is 0.333.....
We are asked to prove or disprove the statement : <span>If a divides bc, then a divides b or a divides c. the statement is expressed as a / bc which is equal to a/b * (1/c). The statement is true since a truly is divided by b or a can be divided by c. Or is essential since a is not expressed as a^2 </span>
Answer:
![P(C=1|T=1)=q(\sum_{i=15}^{20}\binom{20}{i} p^i(1-p)^{20-i})( \sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i])^{-1}](https://tex.z-dn.net/?f=P%28C%3D1%7CT%3D1%29%3Dq%28%5Csum_%7Bi%3D15%7D%5E%7B20%7D%5Cbinom%7B20%7D%7Bi%7D%20p%5Ei%281-p%29%5E%7B20-i%7D%29%28%20%5Csum_%7Bi%3D15%7D%5E%7B20%7D%5Cbinom%7B20%7D%7Bi%7D%5Bqp%5Ei%281-p%29%5E%7B20-i%7D%20%2B%20%281-q%29p%5E%7B20-i%7D%281-p%29%5Ei%5D%29%5E%7B-1%7D)
Step-by-step explanation:
Hi!
Lets define:
C = 1 if candidate is qualified
C = 0 if candidate is not qualified
A = 1 correct answer
A = 0 wrong answer
T = 1 test passed
T = 0 test failed
We know that:
The test consist of 20 questions. The answers are indpendent, then the number of correct answers X has a binomial distribution (conditional on the candidate qualification):
The probability of at least 15 (P(T=1))correct answers is:
We need to calculate the conditional probabiliy P(C=1 |T=1). We use Bayes theorem:
![P(T=1)=q\sum_{i=15}^{20}f_1(i) + (1-q)\sum_{i=15}^{20}f_0(i)\\P(T=1)=\sum_{i=15}^{20}\binom{20}{i}[qp^i(1-p)^{20-i} + (1-q)p^{20-i}(1-p)^i)]](https://tex.z-dn.net/?f=P%28T%3D1%29%3Dq%5Csum_%7Bi%3D15%7D%5E%7B20%7Df_1%28i%29%20%2B%20%281-q%29%5Csum_%7Bi%3D15%7D%5E%7B20%7Df_0%28i%29%5C%5CP%28T%3D1%29%3D%5Csum_%7Bi%3D15%7D%5E%7B20%7D%5Cbinom%7B20%7D%7Bi%7D%5Bqp%5Ei%281-p%29%5E%7B20-i%7D%20%2B%20%281-q%29p%5E%7B20-i%7D%281-p%29%5Ei%29%5D)
