Answer: 24%
Step-by-step explanation:
Since we are informed that the Girl Scout Troop started with 25 girls and at the end of the year party there were 31 girls. The percentage change will be:
= (31 - 25) / 25 × 100
= 6/25 × 100
= 24%
The error that Gabby made was that she used 31 as the base. This is expressed below:
= 31 - 25) / 31 × 100
= 6/31 × 100
= 19.4%
Her friends drink 5/24 gallons of lemonade. (I hope I'm right)
Answer:
Step-by-step explanation:
Let's solve for 
in the first equation and then solve for 
in the second equation.
I will then use the following identity to get right of the parameter, 
:
(Pythagorean Identity).
Let's begin with .
Subtract 2 on both sides:
Divide both sides by -3:
Now time for the second equation, .
Subtract 1 on both sides:
Divide both sides by 4:
Now let's plug it into our Pythagorean Identity:
First way
arcsin(1/4) means that 1/4 sin of the angle.
sin(α)=1/4
sin²α+cos²α=1
(1/4)²+cos²α=1
cos²α=1-1/16 =15/16
cosα=+/-(√15)/4
<span>Second way
</span>
sin(α)=1/4 =opposite leg/hipotenuse
cos(α)=adjacent leg/hypothenuse
adjacent leg =√(hypotenuse²- Opposite²)=√(16-1)=√15
cosα=+/-√15/4
For one value of sinα, possible 2 values of cosα.
