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3 years ago

Solve each system by elimination. 1) 10x + 7y=9 -4x - 7y=9

Mathematics

1 answer:

stellarik [79]3 years ago

8 0

Answer:

(3, -3)

Step-by-step explanation:

When asked to solve by elimination, you put them on top of one another, like you're going to add it.

10x + 7y = 9

-4x - 7y = 9

See that 7y? You can cancel those out because one is negative, and one is positive. So those are gone. You finish adding the rest of the numbers as usual and solve for x.

6x = 18

x = 3

Take x, and plug it into either equation to find y.

10(3) + 7y = 9

7y = -21

y = -3

(3, -3)

Hope this helped!

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Calcium-41 is being used in studies testing the effectiveness of drugs for preventing osteoporosis. The half-life of calcium-41

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Answer:

332,193 years

Step-by-step explanation:

From the question above, we are to calculate the time in an half life question, hence, the formula is given as

t = In(Nt/No) ÷ -(In2/t½)

Where

t = time is takes for an substance to decay or reduce

Nt = Amount of sample after time = 2g

No = Initial amount of sample = 20g

t½ = Half life = 100,000 years

Hence,

t = In(2/20) ÷ (In 2/ 100,000)

t = 332192.80948874 years

Approximately = 332,193 years

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3 years ago

Write a vector equation of the line that passes through P(4, 7) and is parallel to a = (3, 8).

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Answer:

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3 years ago

A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100.

yawa3891 [41]

Answer:

The probability is 0.003

Step-by-step explanation:

We know that the average $\mu$ is:

$\mu=500$

The standard deviation $\sigma$ is:

$\sigma=100$

The Z-score is:

$Z=\frac{x-\mu}{\sigma}$

We seek to find

$P(x800)$

For P(x>800) The Z-score is:

$Z=\frac{x-\mu}{\sigma}$

$Z=\frac{800-500}{100}$

$Z=3$

The score of Z = 3 means that 800 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

$P(x>800)=0.15\%$

For P(x<200) The Z-score is:

$Z=\frac{x-\mu}{\sigma}$

$Z=\frac{200-500}{100}$

$Z=-3$

The score of Z = -3 means that 200 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

$P(x$

Therefore

$P(x800)=P(x800)$

$P(x800)=0.0015 + 0.0015$

$P(x800)=0.003$

6 0

3 years ago