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2 years ago

In the data set below, what is the interquartile range?

Mathematics

1 answer:

satela [25.4K]2 years ago

3 0

Answer:

Step-by-step explanation:

To find the interquartile range (IQR), first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

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Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

<u>Step-by-step explanation:</u>

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

3 years ago

If the following system of equations was written as a matrix equation in the form AX = C,? and matrix A was expressed in the for

LenaWriter [7]

The given equations are
5x + 7y = 7
3x - 2y = 9

As a matrix equation,
A = [5 7
3 -2]

X = [x
y]

C = [7
9]
That is
a =5, c=7; and b=3, d=-2

a - b + c + d = 5 - 3 + 7 + (-2) = 7

Answer: 7

4 0

3 years ago

Read 2 more answers

MARQUE UN PUNTO Y TRACE VARIAS RECTAS QUE PASEN POR EL.¿QUE CONCLUYE?

VladimirAG [237]

The generic equation of a line is:
y-yo = m (x-xo)
Where,
(xo, yo): It's an ordered pair either.
m: is the slope of the line.
We observe that for a point (xo, yo) infinite lines with different slope m can pass.
Answer:
The conclusion is that for the ordered pair (xo, yo) can pass infinite lines that satisfy:
y-yo = m (x-xo)

8 0

3 years ago

12 less than 3 times a number, the result is 24. Find the number

slamgirl [31]

Answer:

We have 3n - 12 = 24 so 3n = 36 so n = 12

Hope this helps and brainliest please

4 0

3 years ago

Someone help me please my friends don’t even know this question thank you

8090 [49]

Step-by-step explanation:

from the question:R=x^2/y

where x=3.8*10^5

y=5.9*10^4

it then mean

R=(3.8*10^5)^2/5.9*10^4

=144400000000/59000

=2447457.63

7 0

2 years ago