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2 years ago

2. Find the median of the data set: 15, 6, 7, 10, 8, 9, 8, 14, 13.please help asap

Mathematics

1 answer:

dangina [55]2 years ago

4 0

To find the median the first thing we need to do is organize the numbers from smallest to largest:

6 7 8 8 9 10 13 14 15

Then if the amount of numbers is odd, the median is the number which is in the middle. In this case the middle number is 9.

6 7 8 8 9 10 13 14 15

Hope this helps mate! Best of luck to you. :)

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i f N(-7,-1) is a point on the terminal side of ∅ in standard form, find the exact values of the trigonometric functions of ∅.

Natali [406]

Answer:

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = -5\sqrt 2$

Step-by-step explanation:

Given

$N = (-7,-1)$ --- terminal side of $\varnothing$

Required

Determine the values of trigonometric functions of $\varnothing$ .

For $\varnothing$ , the trigonometry ratios are:

$sin\ \varnothing = \frac{y}{r}$ $cos\ \varnothing = \frac{x}{r}$ $tan\ \varnothing = \frac{y}{x}$

$cot\ \varnothing = \frac{x}{y}$ $sec\ \varnothing = \frac{r}{x}$ $csc\ \varnothing = \frac{r}{y}$

Where:

$r^2 = x^2 + y^2$

$r = \sqrt{x^2 + y^2$

In $N = (-7,-1)$

$x = -7$ and $y = -1$

So:

$r = \sqrt{(-7)^2 + (-1)^2$

$r = \sqrt{50$

$r = \sqrt{25 * 2$

$r = \sqrt{25} * \sqrt 2$

$r = 5 * \sqrt 2$

$r = 5 \sqrt 2$

<u>Solving the trigonometry functions</u>

$sin\ \varnothing = \frac{y}{r}$

$sin\ \varnothing = \frac{-1}{5\sqrt 2}$

Rationalize:

$sin\ \varnothing = \frac{-1}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$sin\ \varnothing = \frac{-\sqrt 2}{5*2}$

$sin\ \varnothing = \frac{-\sqrt 2}{10}$

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{x}{r}$

$cos\ \varnothing = \frac{-7}{5\sqrt 2}$

Rationalize

$cos\ \varnothing = \frac{-7}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$cos\ \varnothing = \frac{-7*\sqrt 2}{5*2}$

$cos\ \varnothing = \frac{-7\sqrt 2}{10}$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{y}{x}$

$tan\ \varnothing = \frac{-1}{-7}$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = \frac{x}{y}$

$cot\ \varnothing = \frac{-7}{-1}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{r}{x}$

$sec\ \varnothing = \frac{5\sqrt 2}{-7}$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = \frac{r}{y}$

$csc\ \varnothing = \frac{5\sqrt 2}{-1}$

$csc\ \varnothing = -5\sqrt 2$

3 0

2 years ago

Help with answer please!

lana [24]

Answer:

Step-by-step explanation:

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2 years ago

What multiplies to -12 but added together equals -10

Airida [17]

Let the two numbers be x and y, then,
xy = -12 . . . (1)
x + y = -10 . . . (2)
From (2), x = -10 - y . . . (3)
Putting (3) into (1), gives
(-10 - y)y = -12
-10y - y^2 = -12
y^2 + 10y - 12 = 0
$y= \frac{-10\pm \sqrt{10^2-(4\times(-12))} }{2} = \frac{-10\pm \sqrt{148} }{2} = \frac{-10\pm 2\sqrt{37} }{2} = -5\pm\sqrt{37}$

Therefore, the two numbers are $-5+\sqrt{37}$ and $-5-\sqrt{37}$

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3 years ago

Fill in the missing reason for the last step.

jek_recluse [69]

Answer:

Division

Step-by-step explanation:

You divided both sides of the inequality by -3. Multiplying/dividing by negative numbers change the sign of the inequality, so you have ">" turned into "<".

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3 years ago

What is the surface area of a cube of ice that is 64,000 cubic inches as the volume?

Lostsunrise [7]

I’m so sorry but I don’t have a clue! But you’ll get it eventually

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2. Find the median of the data set: 15, 6, 7, 10, 8, 9, 8, 14, 13.please help asap​

2. Find the median of the data set: 15, 6, 7, 10, 8, 9, 8, 14, 13.please help asap