Answer:
D
Step-by-step explanation:
6.8 = (6/5)^x
6.8 = 1.2^x
x ln 1.2 = ln 6.8
x = ln 6.8 / ln 1.2
= 10.513966
90° is the correct answer ✨
Answer:
Step-by-step explanation:
3/5 = 0.6
1 - 0.6 = 0.4 students left
Multiply the amount of students remaining by the fractional amount that take German
0.4 x 1/4 = 0.1
1 - 0.6 - 0.1 = 0.3
0.3 x 100 = 30%
Therefore 30% of students take French
Answer:
The probability that a fish caught by a fisherman is between 0.25 feet and 2 feet long is 0.4375.
Step-by-step explanation:
The probability density function or p.d.f. for the length <em>x,</em> in feet, of some type of fish caught by sport fishermen is :
![p(x) = \left \{{{(\frac{1}{4})\ ;\ 0\leq x\leq 4 } \atop{0\ ;\ otherwise} \right.](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%5Cleft%20%5C%7B%7B%7B%28%5Cfrac%7B1%7D%7B4%7D%29%5C%20%3B%5C%20%200%5Cleq%20x%5Cleq%204%20%7D%20%5Catop%7B0%5C%20%3B%5C%20otherwise%7D%20%5Cright.)
The probability that a fish caught by a fisherman is between 0.25 feet and 2 feet long is:
![P(0.25\leq X\leq 2)=\int\limits^{0.25}_{2} {(\frac{1}{4})} \, dx \\=|(\frac{1}{4})x|^{2}_{0.25}\\=(\frac{1}{4})(2-0.25)\\=0.4375](https://tex.z-dn.net/?f=P%280.25%5Cleq%20X%5Cleq%202%29%3D%5Cint%5Climits%5E%7B0.25%7D_%7B2%7D%20%7B%28%5Cfrac%7B1%7D%7B4%7D%29%7D%20%5C%2C%20dx%20%5C%5C%3D%7C%28%5Cfrac%7B1%7D%7B4%7D%29x%7C%5E%7B2%7D_%7B0.25%7D%5C%5C%3D%28%5Cfrac%7B1%7D%7B4%7D%29%282-0.25%29%5C%5C%3D0.4375)
Thus, the probability that a fish caught by a fisherman is between 0.25 feet and 2 feet long is 0.4375.
Triangles are congruent
so
4x + 1 = 13
4x = 12
x = 3
In case you need to find y
2x + y = 8x - 2y
2(3) + y = 8(3) - 2y
6 + y = 24 - 2y
3y = 18
y = 6