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3 years ago

Please help, this is due soon!

Mathematics

1 answer:

Oliga [24]3 years ago

6 0

Before outlier : 7.25
After outlier : 4

7.25 - 4 = 3.25

So the mean decreases by 3.25 when the outlier is removed.

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5/6 divided by 1/12 equals?

laila [671]

Answer:

0.06944444444

Step-by-step explanation:

4 0

3 years ago

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Determine whether the statements are True or False. Justify your answer with an explanation.

frez [133]

Problem 1

<h3>Answer: False</h3>

---------------------------------

Explanation:

The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.

So,

f(x) = x+1

f( g(x) ) = g(x) + 1 .... replace every x with g(x)

f( g(x) ) = 6x+1 ... plug in g(x) = 6x

(f o g)(x) = 6x+1

Now let's flip things around

g(x) = 6x

g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)

g( f(x) ) = 6(x+1) .... plug in f(x) = x+1

g( f(x) ) = 6x+6

(g o f)(x) = 6x+6

This shows that (f o g)(x) = (g o f)(x) is a false equation for the given f(x) and g(x) functions.

===============================================

Problem 2

<h3>Answer: True</h3>

---------------------------------

Explanation:

Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.

For example, let

f(x) = 1/(x+2)

g(x) = -2

The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.

So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).

7 0

3 years ago

What is the sign of the product (–5)(–3)(–8)(–6)? Positive, because the products (–5)(–3) and (–8)(–6) are negative, and the pro

chubhunter [2.5K]

Answer:

The product (–5)(–3)(–8)(–6) should be Positive.

Step-by-step explanation:

The product of 2 negative numbers equal a positive product.

N * N = P

-5*-3=15

-8*-6=48

The product of 2 positive numbers is positive.

P * P = P

15 * 48 = 720

Your answer should be: Positive because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive.

6 0

3 years ago

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If a ray bisects an angle, each newly formed angle measures 90 degrees.

prohojiy [21]

Answer:

A) Sometimes

A ) Sometimes is the correct answer because b) always and c) never is not possible

it cannot be always measured 90 degrees

3 0

3 years ago

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50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle

aalyn [17]

Answer:

$EF=4\sqrt{3}$

Step-by-step explanation:

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

ΔDEF is one-fourth the area of rectangle ABCD.

We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

$A_{\text{rect}}=8(6)=48\text{ cm}^2$

The area of the triangle is 1/4 of this. Therefore:

$\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2$

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

$\displaystyle 12=\frac{1}{2}(DE)(DF)$

Since DE = DF:

$24=DF^2$

Thus:

$DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE$

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

$(DE)^2+(DF)^2=(EF)^2$

Therefore:

$(2\sqrt6)^2+(2\sqrt6)^2=EF^2$

Square:

$24+24=EF^2$

Add:

$EF^2=48$

And finally, we can take the square root of both sides:

$EF=\sqrt{48}=\sqrt{16\cdot 3}=4\sqrt{3}$

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3 years ago

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