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3 years ago

1/2x+1/3y=5 and 1/4x+y=10 solve this system by substitution

Mathematics

1 answer:

qaws [65]3 years ago

5 0

Answer:

(x, y) = (4, 9)

Step-by-step explanation:

You can use the second equation to write an expression for y.

y = 10 - 1/4x . . . . subtract 1/4x from the given 2nd equation

Now, substitute that for y in the first equation:

1/2x + 1/3(10 -1/4x) = 5

1/2x + 10/3 -1/12x = 5 . . . . eliminate parentheses

You can work this a couple of ways from here. One is to multiply by 12 to eliminate fractions. Another is to work with the numbers as they are. We'll do that, because we don't get enough practice doing arithmetic with fractions.

5/12x = 5/3 . . . . . subtract 10/3

x = (5/3)/(5/12) = 12/3 = 4

From above, we can use our expression for y:

y = 10 - 1/4·4 = 9

The solution is (x, y) = (4, 9).

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The Highway Safety Department wants to study the driving habits of individuals. A sample of 40 cars traveling on a particular st

Ipatiy [6.2K]

Answer:

We need a sample size of at least 101

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.99}{2} = 0.005$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.005 = 0.995$ , so $z = 2.575$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

What sample size is needed to estimate the true average speed to within 2 mph at 99% confidence?

We need a sample of at least n.

n is found when M = 2. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$2 = 2.575*\frac{7.8}{\sqrt{n}}$

$2\sqrt{n} = 2.575*7.8$

$\sqrt{n} = \frac{2.575*7.8}{2}$

$(\sqrt{n})^{2} = (\frac{2.575*7.8}{2})^{2}$

$n = 100.85$

Rounding up

We need a sample size of at least 101

8 0

2 years ago

Read 2 more answers

How do change 13 1/4 into decimal form

Bess [88]

That would be 13.25, 13+1/4
= 13+(1 divided by 4 which is 0.25)
= 13+0.25
Which is 13.25 so your answer is 13.25, good luck hope that helps :D

7 0

2 years ago

5. The area of the trapezoid is 75 square inches. Find the height of the trapezoid. And it’s two bases are 10 and 15.

GaryK [48]

6

6
h/2(sum of bases) =75=area
h=3*2

Mark brainliest please

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2 years ago

There are stars to circle there are 4 stars and 2 circles how much is the ratio

kakasveta [241]

Answer:

2:1

Step-by-step explanation:

The original ratio is 4:2. Divide both sides by 2. Then you get 2:1.

3 0

3 years ago

Read 2 more answers

The human body has a normal temperature of 98.6°F. Doctors will get worried if a sick patient has a temperature that varies from

makvit [3.9K]

Answer:

$|T- 98.6| \geq 3$

And in order to solve this we have two possibilities:

Solution 1

$T -98.6 \leq -3$

And solving for T we got:

$T \leq 98.6- 3$

$T\leq 95.6$

Solution 2

And the other options would be:

$T -98.6 \geq 3$

$T \geq 101.6$

Step-by-step explanation:

For this case we can define the variable os interest T as the real temperature and we know that if we are 3 F more than the value of 98.6 we will be unhealthy so we can set up the following equation:

$|T- 98.6| \geq 3$

And in order to solve this we have two possibilities:

Solution 1

$T -98.6 \leq -3$

And solving for T we got:

$T \leq 98.6- 3$

$T\leq 95.6$

Solution 2

And the other options would be:

$T -98.6 \geq 3$

$T \geq 101.6$

6 0

3 years ago