Answer:
(a)
![P=0.7N+2.2](https://tex.z-dn.net/?f=P%3D0.7N%2B2.2)
(b)
the price of 50 cloud markers is $37.2
Step-by-step explanation:
(a)
Let's assume
price is P
number of markers is N
We are given
The price of a box of 15 cloud markers is $12.70
so, ![N_1=15,P_1=12.70](https://tex.z-dn.net/?f=N_1%3D15%2CP_1%3D12.70)
The price of a box of 42 cloud markers is $31.60
so, ![N_2=42,P_2=31.60](https://tex.z-dn.net/?f=N_2%3D42%2CP_2%3D31.60)
Firstly, we will find slope
![m=\frac{P_2-P_1}{N_2-N_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7BP_2-P_1%7D%7BN_2-N_1%7D)
now, we can plug values
![m=\frac{31.60-12.70}{42-15}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B31.60-12.70%7D%7B42-15%7D)
![m=0.7](https://tex.z-dn.net/?f=m%3D0.7)
now, we can use point slope form of line
![P-P_1=m(N-N_1)](https://tex.z-dn.net/?f=P-P_1%3Dm%28N-N_1%29)
we can plug value
![P-12.70=0.7(N-15)](https://tex.z-dn.net/?f=P-12.70%3D0.7%28N-15%29)
now, we can solve for P
![P-12.70=0.7N-10.5](https://tex.z-dn.net/?f=P-12.70%3D0.7N-10.5)
add both sides by 12.70
![P-12.70+12.70=0.7N-10.5+12.70](https://tex.z-dn.net/?f=P-12.70%2B12.70%3D0.7N-10.5%2B12.70)
![P=0.7N+2.2](https://tex.z-dn.net/?f=P%3D0.7N%2B2.2)
(b)
now, we can plug N=50
![P=0.7\times 50+2.2](https://tex.z-dn.net/?f=P%3D0.7%5Ctimes%2050%2B2.2)
![P=37.2](https://tex.z-dn.net/?f=P%3D37.2)
So,
the price of 50 cloud markers is $37.2
Answer:
There would be 6 candles.
Step-by-step explanation:
So you said that there would be 2 candles per 20 cakes, so I simplified it to 1 candle per 10 cakes. So, if there were 60 cakes, there would be 6 candles.
I hope it helped!
~Flipohrama
Your answer will be 2.6 pounds of apples, 1.2 pounds of bananas.
We have the following expression
![4\cdot\text{cis(}\frac{\pi}{4})\cdot5\text{cis(}\frac{\pi}{6})](https://tex.z-dn.net/?f=4%5Ccdot%5Ctext%7Bcis%28%7D%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5Ccdot5%5Ctext%7Bcis%28%7D%5Cfrac%7B%5Cpi%7D%7B6%7D%29)
This is equivalent to
![4\cdot\text{cis(}\frac{\pi}{4})\cdot5\text{cis(}\frac{\pi}{6})=(4\times5)cis(\frac{\pi}{4}+\frac{\pi}{6})](https://tex.z-dn.net/?f=4%5Ccdot%5Ctext%7Bcis%28%7D%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5Ccdot5%5Ctext%7Bcis%28%7D%5Cfrac%7B%5Cpi%7D%7B6%7D%29%3D%284%5Ctimes5%29cis%28%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cfrac%7B%5Cpi%7D%7B6%7D%29)
Since
![\frac{\pi}{4}+\frac{\pi}{6}=\frac{6\pi+4\pi}{24}=\frac{10}{24}\pi=\frac{5}{12}\pi](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cfrac%7B%5Cpi%7D%7B6%7D%3D%5Cfrac%7B6%5Cpi%2B4%5Cpi%7D%7B24%7D%3D%5Cfrac%7B10%7D%7B24%7D%5Cpi%3D%5Cfrac%7B5%7D%7B12%7D%5Cpi)
we have that
![4\cdot\text{cis(}\frac{\pi}{4})\cdot5\text{cis(}\frac{\pi}{6})=20cis(\frac{5\pi}{12})](https://tex.z-dn.net/?f=4%5Ccdot%5Ctext%7Bcis%28%7D%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5Ccdot5%5Ctext%7Bcis%28%7D%5Cfrac%7B%5Cpi%7D%7B6%7D%29%3D20cis%28%5Cfrac%7B5%5Cpi%7D%7B12%7D%29)
Therefore, the answer is the second option from top to bottom.
Answer:
i.e. 393650 kg.
Step-by-step explanation:
Given that Radium-226 is a radioactive substance with an annual decay rate of 0.04 %
Let the year 1937 be 0 year
Initially population was = 400,000 kg
Since decay rate is 0.04% per year after t years population would be
![P(t) = 400,000 (1-0.0004)^t](https://tex.z-dn.net/?f=P%28t%29%20%3D%20400%2C000%20%281-0.0004%29%5Et)
=![400,000*0.9996^t](https://tex.z-dn.net/?f=400%2C000%2A0.9996%5Et)
In 2017, t = 40 years (i.e. years lapsed form 1937)
Hence population
= ![P(40) = 400,000 (0.9996)^{40} \\=393649.66](https://tex.z-dn.net/?f=P%2840%29%20%3D%20400%2C000%20%280.9996%29%5E%7B40%7D%20%5C%5C%3D393649.66)
i.e. 393650 kg.