Answer:
<h2>
62 persons</h2>
Step-by-step explanation:
Step one:
given data
total budget=$2500
we are told that the hall charges $60 for cleanup, the amount is a fix charge
and per person is $39
let the number of persons be x
The model for the situation is described by y=mx+c
Step two:
2500=39x+60
solve for x
2500-60=39x
2440=39x
divide both sides by 39 we have
x=2440/39
x=62.56
The greatest number of people that they may invite and still stay within their budget. is 62
Answer:
Option C. The class average will go down
Step-by-step explanation:
we know that
If Billy's paper score is equal to the class average, then the class average stay the same
If Billy's paper score is less to the class average, then the class average will go down
If Billy's paper score is greater to the class average, then the class average will go up
In this problem we have
Billy's paper score is 80%
Class average is 93%
so
80% < 93% ----> Billy's paper score is less to the class average
therefore
The class average will go down
Answer:
270,650 is the answer
Step-by-step explanation:
first off, make sure you have a Unit Circle, if you don't do get one, you'll need it, you can find many online.
let's double up 67.5°, that way we can use the half-angle identity for the cosine of it, so hmmm twice 67.5 is simply 135°, keeping in mind that 135° is really 90° + 45°, and that whilst 135° is on the 2nd Quadrant and its cosine is negative 67.5° is on the 1st Quadrant where cosine is positive, so
![cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos(135^o)\implies cos(90^o+45^o)\implies cos(90^o)cos(45^o)~~ - ~~sin(90^o)sin(45^o) \\\\\\ \left( 0 \right)\left( \cfrac{\sqrt{2}}{2} \right)~~ - ~~\left( 1\right)\left( \cfrac{\sqrt{2}}{2} \right)\implies -\cfrac{\sqrt{2}}{2} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=cos%28%5Calpha%20%2B%20%5Cbeta%29%3D%20cos%28%5Calpha%29cos%28%5Cbeta%29-%20sin%28%5Calpha%29sin%28%5Cbeta%29%20%5C%5C%5C%5C%5C%5C%20cos%5Cleft%28%5Ccfrac%7B%5Ctheta%7D%7B2%7D%5Cright%29%3D%5Cpm%20%5Csqrt%7B%5Ccfrac%7B1%2Bcos%28%5Ctheta%29%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20cos%28135%5Eo%29%5Cimplies%20cos%2890%5Eo%2B45%5Eo%29%5Cimplies%20cos%2890%5Eo%29cos%2845%5Eo%29~~%20-%20~~sin%2890%5Eo%29sin%2845%5Eo%29%20%5C%5C%5C%5C%5C%5C%20%5Cleft%28%200%20%5Cright%29%5Cleft%28%20%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5Cright%29~~%20-%20~~%5Cleft%28%201%5Cright%29%5Cleft%28%20%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5Cright%29%5Cimplies%20-%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
