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Tanzania [10]
3 years ago
8

Gabe Amodeo, a nuclear physicist, needs 60 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution. Ho

w many liters of each does he need
to make the needed 60 liters of 60% acid solution?
Mathematics
1 answer:
timofeeve [1]3 years ago
3 0

Answer:

20 liters of the 40% solution

60-20=40 liters of the 70% solution

Step-by-step explanation:

40%x+70%(60-x)=60%(60)

0.4x+0.7(60-x)=0.6(60)

0.4x+42-0.7x=36

-0.3x+42=36

-0.3x=-42+36

-0.3x=-6

0.3x=6

3x=60

x=60/3

x=20 liters of the 40% solution

60-20=40 liters of the 70% solution

check: 0.4*20=8

0.7*40=28

8+28=36 and 0.6*60=36 also

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Jade wants to buy a $200,000 term life insurance policy. She is 34 years old. Using the premium table, what is her annual premiu
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Premium rates are usually for  premium per fixed face value. Jade's annual premium for a 10 year policy is given by Option b: $1,202

<h3>How to calculate the total annual premium for $x ?</h3>

If its given that the annual premium is $p per $y face value, then we can calculate the annual premium for $1 face value and then use it to calculate annual premium for $x.

Using proportions, we get:

\rm \$y \: face \: value : \$p \: annual \: premiun\\\\\rm \$1 \: face \: value : \$\dfrac{p}{y} \: annual \: premiun\\\\\rm \$x\:face\: value : \$\dfrac{p \times x}{y} \: annual \: premiun\\

For given case, from the tables, we see that for age 34, and 10 year life insurance for female gender , there is annual premium of 6.01 per $1000 face value.
Thus, we have p = 6.01, y = 1000

Since Jade wants to buy Life insurance for $200,000, thus, x = $200,000

Putting it in the above derived formula, we get:

\rm \$x\:face\: value : \$\dfrac{p \times x}{y} \: annual \: premium\\\\\rm \$200000\:face\: value : \$\dfrac{6.01 \times 200000}{1000} \: annual \: premium\\ = \$1202 \: annual \: premiun

Thus, Jade's annual premium for a 10 year policy is given by Option b: $1,202

Learn more about calculating annual premium cost here:

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A store has apples on sale for 28.00 for 8 pounds. If an apple is approximately 5 ounces, how many apples can you buy for $112.0
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

The rate of change is the same as the slope (I don't know if you have learned that term yet), but basically its the change in y's over the change in x's. to find this out, all you have to do is count from the point on the graph that is the farthest right (in this case, (6,1)), up to the y coordinate of the point farthest to the left (-2, 7) which is 6, and then count the number of spaces between the x coordinates, which is 8. put the rise (up and down count) over the run (horizontal count) in a fraction form, which gives you 6/8, and then notice how the line is pointing towards the bottom RIGHT hand corner making the line negative, so you need to make the rate of change negative, giving you the final answer of -6/8.  

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