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4 years ago

How do you determine what your grade average is based on the following grades?:

Mathematics

1 answer:

fiasKO [112]4 years ago

5 0

Answer:

Test's average-95

Homework's average-96.67

Step-by-step explanation:

Average is mathematically defined as the sum of the values divided by the total number of values and is expressed as:

$\bar X=\frac{1}{n}\sum{x_i}, n=number \ of \ values.$

The Tests' average is calculated as:

$\bar X_t=\frac{1}{n}\sum{x_i}\\\\=\frac{1}{3}(98+92+95)\\\\=\frac{1}{3}\times 285\\\\=95$

Hence, the Tests' average is 95

#The Homework's average is calculated as:

$\bar X_h=\frac{1}{n}\sum{x_i}\\\\=\frac{1}{3}(93+97+100)\\\\=\frac{1}{3}\times 290\\\\=96.67$

Hence, the Homework's average is 96.67

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3 years ago

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3 years ago

A store has a coupon for $10 off and a discount of 20%. Write a function for the coupon. Use x for the original price and C for

Ludmilka [50]

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x for the original price.
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So from the statement 2, you can realize there are two types of discounts:

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3 years ago

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

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3 years ago

A skydiver is 760 meters above the ground when he opens his parachute. After opening the parachute, he descends at a constant sp

defon

Answer:

Part A: A linear function because there is a constant rate change.

Part B: y = 760 - 17x

Hope this helps!

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4 years ago