Answer:
Interest earned at 3.9 percent rate is $31.2
Interest earned at 2 percent rate is $5.8
Step-by-step explanation:
A = P(1 + rt)
Where 'A' is the amount, 'r' is the rate and 't' is the time in years
When;
P = $1200
r = 3.9%
t =
years
Then,
A = $1200(1 + 0.039(
))
A = $1200 + $31.2 = $1231.2
Interest = Amount - Principal
Interest earned at 3.9 percent rate is $1231.2 - $1200 = $31.2
When;
P = $580
r = 2%
t =
years
Then,
A = $580(1 + 0.02(
))
A = $580 + $5.8 = $585.8
Interest earned = Amount - Principal
Interest earned at 2 percent rate = $585.8 - $580 = $5.8
Answer:
multiply the first equation by -2, then add them
Step-by-step explanation:
7x+4y=-4 *-2 7x+4y=-4 *-2 = -14x-8y=8
5x+8y=28
-14x-8y=8 x=-4, y=6
-9x=36
x=-4
7(-4)+4y=-4
-28+4y=-4
4y=24
y=6
<h3>
Answer: Choice B ![\frac{\sqrt{15}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B4%7D)
</h3>
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Work Shown:
Angle theta is between 0 and pi/2, so this angle is in quadrant Q1.
Square both sides of the given equation
![\sin \theta = \frac{1}{4}\\\\\sin^2 \theta = \left(\frac{1}{4}\right)^2\\\\\sin^2 \theta = \frac{1}{16}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3D%20%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5C%5Csin%5E2%20%5Ctheta%20%3D%20%5Cleft%28%5Cfrac%7B1%7D%7B4%7D%5Cright%29%5E2%5C%5C%5C%5C%5Csin%5E2%20%5Ctheta%20%3D%20%5Cfrac%7B1%7D%7B16%7D)
Then use the pythagorean trig identity to get
![\sin^2 \theta + \cos^2 \theta = 1\\\\\cos^2 \theta = 1-\sin^2 \theta\\\\\cos \theta = \sqrt{1-\sin^2 \theta} \ \ \ \text{cosine is positive in Q1}\\\\\cos \theta = \sqrt{1-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16}{16}-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16-1}{16}}\\\\\cos \theta = \sqrt{\frac{15}{16}}\\\\\cos \theta = \frac{\sqrt{15}}{\sqrt{16}}\\\\\cos \theta = \frac{\sqrt{15}}{4}\\\\](https://tex.z-dn.net/?f=%5Csin%5E2%20%5Ctheta%20%2B%20%5Ccos%5E2%20%5Ctheta%20%3D%201%5C%5C%5C%5C%5Ccos%5E2%20%5Ctheta%20%3D%201-%5Csin%5E2%20%5Ctheta%5C%5C%5C%5C%5Ccos%20%5Ctheta%20%3D%20%5Csqrt%7B1-%5Csin%5E2%20%5Ctheta%7D%20%5C%20%5C%20%5C%20%5Ctext%7Bcosine%20is%20positive%20in%20Q1%7D%5C%5C%5C%5C%5Ccos%20%5Ctheta%20%3D%20%5Csqrt%7B1-%5Cfrac%7B1%7D%7B16%7D%7D%5C%5C%5C%5C%5Ccos%20%5Ctheta%20%3D%20%5Csqrt%7B%5Cfrac%7B16%7D%7B16%7D-%5Cfrac%7B1%7D%7B16%7D%7D%5C%5C%5C%5C%5Ccos%20%5Ctheta%20%3D%20%5Csqrt%7B%5Cfrac%7B16-1%7D%7B16%7D%7D%5C%5C%5C%5C%5Ccos%20%5Ctheta%20%3D%20%5Csqrt%7B%5Cfrac%7B15%7D%7B16%7D%7D%5C%5C%5C%5C%5Ccos%20%5Ctheta%20%3D%20%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B%5Csqrt%7B16%7D%7D%5C%5C%5C%5C%5Ccos%20%5Ctheta%20%3D%20%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B4%7D%5C%5C%5C%5C)
ATTACHED is the written out response.
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Answer:
5/9
Step-by-step explanation:
First, find the total number of mL in the drink:
20 + 10 + 15
= 45
There are 10 mL of apple juice, so the proportion will be 10/45
Simplify this by dividing the numerator and denominator by 5:
10/45
= 5/9
So, 5/9 is the proportion of the cocktail that is apple juice