Answer:
height = 10.23 m
Step-by-step explanation:
sin 25 = x/42
0.4226 = x/42
x = 17.75
tan 30 = height/17.75
0.5774 = height/17.75
height = 10.23 m
Answer:
24% chance
Step-by-step explanation:
First, find the total number of graduates in the table, that number is 2610, that will be your numerator.
You will look at the table for the total number of students, that is 10730, that will be the denominator.
Now divide the smaller number/numerator (2610) by the larger number/denominator (10730)
= 0.2432432...
Then, multiply by 100 to get the percentage: 24.32432...%
Now, round to the nearest percentage: 24%
(a) Suppose we let
![x=2+4=6](https://tex.z-dn.net/?f=x%3D2%2B4%3D6)
Modulo 7, we're left with
![x\equiv2+4\pmod7=6\mod7](https://tex.z-dn.net/?f=x%5Cequiv2%2B4%5Cpmod7%3D6%5Cmod7)
, but we want a remainder of 2, so multiply 4 by 7 to assure that that remainder vanishes. So now
![x=2+4\cdot7=30](https://tex.z-dn.net/?f=x%3D2%2B4%5Ccdot7%3D30)
and
![x\equiv2\pmod7](https://tex.z-dn.net/?f=x%5Cequiv2%5Cpmod7)
, but modulo 11, we have
![x=\equiv2+28\equiv2+4\equiv6\pmod{11}](https://tex.z-dn.net/?f=x%3D%5Cequiv2%2B28%5Cequiv2%2B4%5Cequiv6%5Cpmod%7B11%7D)
. But we want the remainder to be 4, so multiply the first term by 11 to guarantee this. So we write
![x=2\cdot11+4\cdot7=50](https://tex.z-dn.net/?f=x%3D2%5Ccdot11%2B4%5Ccdot7%3D50)
but now, we get a remainder of 1 modulo 7 and 6 modulo 11. To fix the first case, multiply the first term by 2. For the second case, first find the inverse of 6 modulo 11. We have
![2\cdot6=12](https://tex.z-dn.net/?f=2%5Ccdot6%3D12)
, and
![12\equiv1\pmod{11}](https://tex.z-dn.net/?f=12%5Cequiv1%5Cpmod%7B11%7D)
, so the inverse is 2. Multiply the second term by 2, so that the second term's remainder modulo 11 becomes 1. Then multiply by 4, so that now
![x=2\cdot11\cdot2+4\cdot7\cdot2\cdot4=268](https://tex.z-dn.net/?f=x%3D2%5Ccdot11%5Ccdot2%2B4%5Ccdot7%5Ccdot2%5Ccdot4%3D268)
We have
![x=268=3\cdot77+37\implies x\equiv37\pmod{77}](https://tex.z-dn.net/?f=x%3D268%3D3%5Ccdot77%2B37%5Cimplies%20x%5Cequiv37%5Cpmod%7B77%7D)
(b) This is done similarly. Modulo 3, we want a remainder of 2, so we can start with
![x=2+3+3=8](https://tex.z-dn.net/?f=x%3D2%2B3%2B3%3D8)
Then taken modulo 4, we need to multiply the first term by 2 and the third term by 4 to ensure the remainder becomes 3. The second term can be left alone.
![x=2\cdot2+3+3\cdot4=19](https://tex.z-dn.net/?f=x%3D2%5Ccdot2%2B3%2B3%5Ccdot4%3D19)
Now taken modulo 5, we can multiply the first two terms by 5 and the third term by the inverse of
![3\times2\equiv12\equiv2\pmod5](https://tex.z-dn.net/?f=3%5Ctimes2%5Cequiv12%5Cequiv2%5Cpmod5)
. We have
![3\cdot2\equiv6\equiv1\pmod5](https://tex.z-dn.net/?f=3%5Ccdot2%5Cequiv6%5Cequiv1%5Cpmod5)
, so we multiply by 3.
![x=2\cdot2\cdot5+3\cdot5+3\cdot4\cdot3=71](https://tex.z-dn.net/?f=x%3D2%5Ccdot2%5Ccdot5%2B3%5Ccdot5%2B3%5Ccdot4%5Ccdot3%3D71)
Now
![x=71=1\cdot(3\cdot4\cdot5)+11=1\cdot60+11](https://tex.z-dn.net/?f=x%3D71%3D1%5Ccdot%283%5Ccdot4%5Ccdot5%29%2B11%3D1%5Ccdot60%2B11)
which means the smallest positive solution for the system would be
![x=11](https://tex.z-dn.net/?f=x%3D11)
.
Answer:
![\frac{6}{8} = \frac{3}{4} (simplifed)](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%7D%7B8%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28simplifed%29)
Step-by-step explanation:
First add up all the dresses 6+2=8
thats your total of dresses.
Then place it into a fraction.
![\frac{ 6}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%206%7D%7B8%7D%20)
6 is the amount of red dresses you have.
Probability can be placed as a percentage, a decimal or a fraction.
Answer:
200 baseballs
Step-by-step explanation:
Mike put 400 baseballs into 10 trash bins. He put the same number of baseballs in each bin.
Hence, the number of baseballs he puts in each bin is:
400 / 10 = 40 baseballs
He took 5 trash bins of baseballs. This means that the number of baseballs he took is:
5 * 40 = 200 baseballs
He took 200 baseballs.