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2 years ago

What is ordered pairs are solutions to the system x+2y>_10 3x-4y>12

Mathematics

1 answer:

katovenus [111]2 years ago

8 0

Answer:

(10,2)

Step-by-step explanation:

It's simpler to evaluate the given points in the inequality system.

Starting with (16,9)

x+2y>= 10 results in 16+2*9 =34 >= 10 (this inequality is reached)

3x-4y>12 results in a contradiction, 3*16-4*9=12 > 12 (the inequality sign is not respected)

Continuing with (10,2)

x+2y>= 10 results in 10+2*2 =14 > 10 (this inequality is reached)

3x-4y>12 results in, 3*10-4*9=22 > 12 (the inequality sign is reached)

The point (10,2) is a solution for the system

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Find the hypotenuse (2) of the right triangle.

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Answer:

D) 13m

Step-by-step explanation:

To find the hypotenuse, use the formula for a² + b²= c², where a and b are the values of the triangle's two legs and c is the value of the hypotenuse.

In this case, a² = 7m and b² = 11m. Remember that there is no definite value for a or b, so they can be switched around.

So now our formula will look like this: 7² + 11² = c².

When squaring the two values, you will get a more simplified manner of the equation: 49 + 121 = c².

When we add them altogether, we get 170 = c²

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In order to do that, we must find the square root of √170, which is 13.0384048104, or just 13 when rounded to the nearest tenth.

So now we know that c², the hypotenuse, is approximately equal to 13.

Just to be sure, plug in all the value into the formula and try again.

7² + 11² = 13².
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3 years ago

An experiment was conducted to record the jumping distances of paper frogs made from construction paper. Based on the sample, th

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Answer:

$9.9676 - 2.326*0.5904 =8.594$

$9.9676 + 2.326*0.5904 =11.341$

Step-by-step explanation:

Notation

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

For this case the 9% confidence interval is given by:

$8.8104 \leq \mu \leq 11.1248$

We can calculate the mean with the following:

$\bar X = \frac{8.8104 +11.1248}{2}= 9.9676$

And we can find the margin of error with:

$ME= \frac{11.1248- 8.8104}{2}= 1.1572$

The margin of error for this case is given by:

$ME = t_{\alpha/2}\frac{s}{\sqrt{n}} = t_{\alpha/2} SE$

And we can solve for the standard error:

$SE = \frac{ME}{t_{\alpha/2}}$

The critical value for 95% confidence using the normal standard distribution is approximately 1.96 and replacing we got:

$SE = \frac{1.1572}{1.96}= 0.5904$

Now for the 98% confidence interval the significance is $\alpha=1-0.98= 0.02$ and $\alpha/2 = 0.01$ the critical value would be 2.326 and then the confidence interval would be: