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2 years ago

The sum of -2m and 3m is equal to the difference of 1/2 and 1/3

Mathematics

2 answers:

Mice21 [21]2 years ago

6 0

Hello!

Let's write out this problem symbolically:

-2m + 3m = (1/2) - (1/3)

m = (3/6) - (2/6) = 1/6

The sum of -2m and 3m is equal to the difference of 1/2 and 1/3 is m = 1/6.

geniusboy [140]2 years ago

3 0

Equation: -2m+3m=1/2-1/3

For you need to combine the like terms on each side. -2m+3m=1m. 1-2-1/3=1/6

Equation now: m=1/6
So your answer is 1/6

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The probability is 10/12. If you need it as a decimal, it should be about 8.3%

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2 years ago

The graph of f(x) = StartRoot x EndRoot is reflected across the x-axis and then across the y-axis to create the graph of functio

Anna35 [415]

Answer:

The only value that is in the domains of both functions is 0

The range of g(x) is all values less than or equal to 0

Step-by-step explanation:

As the original function is

$f(x) = \sqrt{x}$

Since, domain is the set of all possible input values that define the function, and range is the set of all possible output values for all possible domain values for which the function is defined.

The domain of $f(x) = \sqrt{x}$ will be [0, ∞)

The range of $f(x) = \sqrt{x}$ will be [0, ∞)

Please check the attached figure a for visualizing the graph of $f(x) = \sqrt{x}$ .

Impact of double transformation:

When the function $f(x) = \sqrt{x}$ is reflected across x-axis, the function becomes $y = -\sqrt{x}$ after first transformation

After the second transformation across y-axis, the function $y = -\sqrt{x}$ becomes $g(x) = -\sqrt{-x}$

For

$g(x) = -\sqrt{-x}$

$-x$ must be equal to or greater than zero for $g(x) = -\sqrt{-x}$ to be defined i.e. -x ≥ 0.

So,

-x ≥ 0 can be written as x≤ 0

So,

The domain of $g(x) = -\sqrt{-x}$ will be (∞, 0]
The range of $g(x) = -\sqrt{-x}$ will be (∞, 0]

Please check the attached figure a for visualizing the graph of $g(x) = -\sqrt{-x}$ .

So, from the above discussion, we can say that

0 is the only that is in the domain of both function.
The range of g(x) is all values less than or equal to 0

So,

Only two statements are true about the functions f(x) and g(x) are true which are:

The only value that is in the domains of both functions is 0

The range of g(x) is all values less than or equal to 0

Keywords: graph, function

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8 0

1 year ago

Read 2 more answers

A researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of th

anyanavicka [17]

Answer:

a. The sample has more than 30 grade-point averages.

Step-by-step explanation:

Given that a researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample

We are asked to find the conditions under which that sample mean can be treated as a value from a population having a normal distribution

Recall central limit theorem here

The central limit theorem states that the mean of all sample means will follow a normal distribution irrespective of the original distribution to which the data belonged to provided that

i) the samples are drawn at random

ii) The sample size should be atleast 30

Hence here we find that the correct conditions is a.

Only option a is right

a. The sample has more than 30 grade-point averages.

7 0

2 years ago

A rectangular garden is 6 feet long and 4 feet wide. A second rectangular garden has dimensions that are double the dimensions o

sergey [27]

Answer:

100 percent increase

Step-by-step explanation:

1st garden

Length = 6 ft

Width = 4 ft

Perimeter = 2 (l+w)

= 2 (6+4) = 2(10) = 20

2nd garden

The length and width are 2 times the 1st garden

Length = 2 *6 = 12

Width = 2 *4 = 8

Perimeter = 2 (l+w)

= 2 (12+8) = 2(20) = 40

Percent change = (new - old )/old * 100 percent

The 1st garden is the old garden = 20 and the 2nd garden is the new garden = 40

Substituting in

Percent change = (40-20)/20 = 20/20 =100 *100 percent

= 100 percent increase

5 0

2 years ago

QUICK! 75 POINTS !!Select all that are part of the solution set of csc(x) > 1 and over 0 ≤ x ≤ 2π.

Vladimir79 [104]

Answer:

$\frac{\pi}{4}$

$\frac{5\pi}{6}$

Step-by-step explanation:

The answer uses the unit circle and that sine and cosecant are reciprocals.

The first choice doesn't even fit the criteria that $x$ is between $0$ and $2\pi$ (inclusive of both endpoints) because of the $x=\frac{-7\pi}{6}$ .

Let's check the second choice.

$\csc(\frac{\pi}{4})=\frac{2}{\sqrt{2}} \text{ since } \sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$ .

$\csc(\frac{\pi}{4})>1 \text{ since } \frac{2}{\sqrt{2}}>1$

$\csc(\frac{\pi}{2})=1 \text{ since } \sin(\frac{\pi}{2})=1$ which means $\csc(\frac{\pi}{2})=1$ which is not greater than 1.

So we can eliminate second choice.

Let's look at the third.

$\csc(\frac{5\pi}{6})=2 \text{ since } \sin(\frac{5\pi}{6})=\frac{1}{2}$ which means $\csc(\frac{5\pi}{6})>1$ .

$\csc(\pi)$ isn't defined because $\sin(\pi)=0$ .

So we are eliminating 3rd choice now.

Let's look at the fourth choice.

$\csc(\frac{7\pi}{6})=-2 \text{ since } \sin(\frac{7\pi}{6})=\frac{-1}{2}$ which means $\csc(\frac{7\pi}{6})$ and not greater than 1.

I was looking at the rows as if they were choices.

Let me break up my choices.

So we said $x=-\frac{7\pi}{6}$ doesn't work because it is not included in the inequality $0\le x \le 2\pi$ .

How about $x=0$ ? This leads to $\csc(0)$ which doesn't exist because $\sin(0)=0$ .

So neither of the first two choices on the first row.

Let's look at the second row again.

We said $\frac{\pi}{4}$ worked but not $\frac{\pi}{2}$

Let's look at the choices on the third row.

We said $\frac{5\pi}{6}$ worked but not $x=\pi$

Let's look at at the last choice.

We said it gave something less than 1 so this choice doesn't work.

6 0

2 years ago

Read 2 more answers