Option A:
The probability that Everett and Finley end up with an even number and a blue disk is
.
Solution:
Given data:
Everett is rolling a block with numbers = {1, 2, 3, 4, 5, 6}
Finley is drawing one disk from basket with colors = {blue, red, yellow}
Total number of numbers = 6
Total number of colors = 3
![$\text { Probability }=\frac{\text {Number of possible outcomes}}{\text {Total number of outcomes}}](https://tex.z-dn.net/?f=%24%5Ctext%20%7B%20Probability%20%7D%3D%5Cfrac%7B%5Ctext%20%7BNumber%20of%20possible%20outcomes%7D%7D%7B%5Ctext%20%7BTotal%20number%20of%20outcomes%7D%7D)
![$P\text{(Even number)} =\frac{3}{6}$](https://tex.z-dn.net/?f=%24P%5Ctext%7B%28Even%20number%29%7D%20%3D%5Cfrac%7B3%7D%7B6%7D%24)
![$P\text{(Blue disk)} =\frac{1}{3}$](https://tex.z-dn.net/?f=%24P%5Ctext%7B%28Blue%20disk%29%7D%20%3D%5Cfrac%7B1%7D%7B3%7D%24)
![$P\text{(Even number and Blue disk)} =\frac{3}{6}\times\frac{1}{3}$](https://tex.z-dn.net/?f=%24P%5Ctext%7B%28Even%20number%20and%20Blue%20disk%29%7D%20%3D%5Cfrac%7B3%7D%7B6%7D%5Ctimes%5Cfrac%7B1%7D%7B3%7D%24)
![$=\frac{3}{18}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B3%7D%7B18%7D)
Divide numerator and denominator by the common factor 3.
![$=\frac{3\div3}{18\div3}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B3%5Cdiv3%7D%7B18%5Cdiv3%7D)
![$=\frac{1}{6}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B6%7D)
Option A is the correct answer.
Hence the probability that Everett and Finley end up with an even number and a blue disk is
.
Answer:
![\large{YES}\ \dfrac{BC}{YZ}=\dfrac{AC}{XY}=\dfrac{AB}{XZ}=\dfrac{2}{1}\\\\\text{and}\ \angle B\cong\angle Z,\ \angle C\cong\angle Y,\ \angle A\cong\angle X](https://tex.z-dn.net/?f=%5Clarge%7BYES%7D%5C%20%5Cdfrac%7BBC%7D%7BYZ%7D%3D%5Cdfrac%7BAC%7D%7BXY%7D%3D%5Cdfrac%7BAB%7D%7BXZ%7D%3D%5Cdfrac%7B2%7D%7B1%7D%5C%5C%5C%5C%5Ctext%7Band%7D%5C%20%5Cangle%20B%5Ccong%5Cangle%20Z%2C%5C%20%5Cangle%20C%5Ccong%5Cangle%20Y%2C%5C%20%5Cangle%20A%5Ccong%5Cangle%20X)
Step-by-step explanation:
![BC\to ZY\\AB\to XZ\\AC\to XY\\\angle A\to\angle X\\\angle B\to\angle Z\\\angle C\to\angle Y](https://tex.z-dn.net/?f=BC%5Cto%20ZY%5C%5CAB%5Cto%20XZ%5C%5CAC%5Cto%20XY%5C%5C%5Cangle%20A%5Cto%5Cangle%20X%5C%5C%5Cangle%20B%5Cto%5Cangle%20Z%5C%5C%5Cangle%20C%5Cto%5Cangle%20Y)
![\text{We have:}\\\\\triangle ABC:\ AB=20,\ BC=12,\ AC=18\\\triangle XZY:\ XZ=10,\ YZ=6,\ XY=9\\\\\text{check the ratio:}\\\\\dfrac{AB}{XZ}=\dfrac{20}{10}=2\\\\\dfrac{BC}{YZ}=\dfrac{12}{6}=2\\\\\dfrac{AC}{XY}=\dfrac{18}{9}=2\\\\\text{CORRECT :)}\\\\\angle B\cong\angle Z,\ \angle C\cong\angle Y\\\\\text{We know that: The sum of the acute angles in a right triangle is}\ 90^o.\\\\m\angle B+m\angle A=90^o\ \text{and}\ m\angle Z+m\angle X=90^o](https://tex.z-dn.net/?f=%5Ctext%7BWe%20have%3A%7D%5C%5C%5C%5C%5Ctriangle%20ABC%3A%5C%20AB%3D20%2C%5C%20BC%3D12%2C%5C%20AC%3D18%5C%5C%5Ctriangle%20XZY%3A%5C%20XZ%3D10%2C%5C%20YZ%3D6%2C%5C%20XY%3D9%5C%5C%5C%5C%5Ctext%7Bcheck%20the%20ratio%3A%7D%5C%5C%5C%5C%5Cdfrac%7BAB%7D%7BXZ%7D%3D%5Cdfrac%7B20%7D%7B10%7D%3D2%5C%5C%5C%5C%5Cdfrac%7BBC%7D%7BYZ%7D%3D%5Cdfrac%7B12%7D%7B6%7D%3D2%5C%5C%5C%5C%5Cdfrac%7BAC%7D%7BXY%7D%3D%5Cdfrac%7B18%7D%7B9%7D%3D2%5C%5C%5C%5C%5Ctext%7BCORRECT%20%3A%29%7D%5C%5C%5C%5C%5Cangle%20B%5Ccong%5Cangle%20Z%2C%5C%20%5Cangle%20C%5Ccong%5Cangle%20Y%5C%5C%5C%5C%5Ctext%7BWe%20know%20that%3A%20The%20sum%20of%20the%20acute%20angles%20in%20a%20right%20triangle%20is%7D%5C%2090%5Eo.%5C%5C%5C%5Cm%5Cangle%20B%2Bm%5Cangle%20A%3D90%5Eo%5C%20%5Ctext%7Band%7D%5C%20m%5Cangle%20Z%2Bm%5Cangle%20X%3D90%5Eo)
![\text{We know}\ m\angle B=m\angle Z\to \ m\angle A=m\angle X.\\\text{therefore}\ \angle A\cong\angle X](https://tex.z-dn.net/?f=%5Ctext%7BWe%20know%7D%5C%20m%5Cangle%20B%3Dm%5Cangle%20Z%5Cto%20%5C%20m%5Cangle%20A%3Dm%5Cangle%20X.%5C%5C%5Ctext%7Btherefore%7D%5C%20%5Cangle%20A%5Ccong%5Cangle%20X)
Answer: Option A, the square root of 40, is an irrational number.
Step-by-step explanation:
We are given 4 options:
- the sqrt of 40
- the sqrt of 49
- the sqrt of 100
- the sqrt of 9
All but one are perfect squares. Let's find out which one is not a perfect square.
The sqrt of 49 is 7. 7 times 7 is equal to 49.
The sqrt of 100 is 10. 10 times itself is equal to 100.
The sqrt of 9 is 3. 3 times 3 is equal to 9.
What about the square root of 40?
We know it's not a perfect square, and it's somewhere between 6 and 7. So, the hint from the question tells us that imperfect squares are irrational. Then this must be the answer!