X = amount of 50% solution
y = total amount after mixing
Note that the amount of alcohol in the 20% solution is 80 (0.2) = 16 oz.
We have 2 unknowns, so we need 2 equations:
first, we can write the equation for the total volume:
y = x + 80
next, apply the percentages to get an equation for the amount of alcohol:
0.4 y = 0.5 x + 16
Finally, solve the pair of equations (in this case, by substitution of the 1st into the second:
0.4 (x + 80) = 0.5x + 16
0.4 x + 32 = 0.5X + 16
rearrange and combine like terms:
0.1x = 16
x = 160
from the 1st equation:
y = 160 + 80 = 240
Answer:
Length of the garden = 69.28 meters.
Step-by-step explanation:
See the attached diagram.
Let CD is the pole with a height of 30 m and the elevation of the top of the pole from the endpoints of the length A and B are 60° and 30° respectively.
So, ∠ DAC = 60° and ∠ DBC = 30°
Now, Δ ACD is a right triangle and
⇒ meters.
Now, from Δ BCD which is a right triangle,
⇒ meters.
Hence, AB = AC + CB = 17.32 + 51.96 = 69.28 meters. (Answer)
Answer:
1500
Step-by-step explanation:
The area of the regtangular floor is 360m². The floor is going to be retired with tiles having area of 240cm² . We need to find the number of times . Therefore ,
And , the number of tiles required will be ,
<u>Hence </u><u>the</u><u> </u><u>required</u><u> answer</u><u> is</u><u> </u><u>1</u><u>5</u><u>0</u><u>0</u><u> </u><u>.</u>
Answer:
The test statistic is z = -2.82.
Step-by-step explanation:
A marketing research firm believes that more than half of adults drink mostly either regular or diet soda.
This means that the null hypothesis is:
The alternate hypothesis is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.
0.5 tested at the null hypothesis:
This means that:
Gallup took a nationally representative sample of 2027 adults and asked them about their soda consumption. The survey shows that 950 of those surveyed drink mostly either regular or diet soda.
This means that
Test statistic:
The test statistic is z = -2.82.