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3 years ago

How can using properties help you to simplify expressions?

1 answer:

4 0

Well,properties can help you because you can shorten or make an equation more understandable, like using distributive property in the example 2(5x-3), you can rewrite it as 10x-6. See?

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Find an equation in rectangular coordinates for the cylindrical equation r = 2sintheta

frutty [35]

Answer:

$x^2+(y-1)^2=1$

Step-by-step explanation:

The given cylindrical equation is

$r=2\sin \theta$

Multiply both sides by r.

$r^2=2r\sin \theta$ .... (1)

The required formulas are

$x=r\cos \theta,y=r\sin \theta,r^2=x^2+y^2$

Substitute $r\sin \theta =y,r^2=x^2+y^2$ in equation (1).

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

$x^2+y^2-2y=0$

Add 1 on both sides.

$x^2+(y^2-2y+1)=1$

$(x-0)^2+(y-1)^2=1^2$ $[\because (a-b)^2=a^2-2ab+b^2]$

It is the equation of a circle centered at (0,1) with radius 1.

Therefore, the equation in rectangular coordinates is $x^2+(y-1)^2=1$ .

3 0

3 years ago

Mr. jovanovski is having wood flooring put in his rectangular living room. the area of the room is 234 square feet. the length o

OlgaM077 [116]

By definition the area of a rectangle is:
A = l * w
Where,
l: long
w: width
So we have to clear the width:
w = A / l
Substituting the values:
w = (234) / (18) = 13
w = 13 feets
answer
the width, in feet, of the room is 13

5 0

3 years ago

Read 2 more answers

A study of class attendance and grades among first-year students at a state university showed that, in general, students who mis

ratelena [41]

Answer:

the numerical value of the correlation between percent of classes attended and grade index is r = 0.4

Step-by-step explanation:

Given the data in the question;

we know that;

the coefficient of determination is r²

while the correlation coefficient is defined as r = √(r²)

The coefficient of determination tells us the percentage of the variation in y by the corresponding variation in x.

Now, given that class attendance explained 16% of the variation in grade index among the students.

coefficient of determination is r² = 16%

The correlation coefficient between percent of classes attended and grade index will be;

r = √(r²)

r = √( 16% )

r = √( 0.16 )

r = 0.4

Therefore, the numerical value of the correlation between percent of classes attended and grade index is r = 0.4

3 0

3 years ago

For each of the following functions, determine if they are injective. Also determine if theyare surjective. Also determine if th

timurjin [86]

Answer:

Check below

Step-by-step explanation:

1. Definition for intervals

$(a,b)=\left \{ x\in\Re : a$

2. Functions

1) $\Re \rightarrow \Re \\ f(x)=x$

Let's perform graph tests.

That's an one to one, injective function. Look how any horizontal line touches that only once. Also, It's a surjective and a bijective one.

2) $\Re\geq0\rightarrow\Re , f(x)=x+1\\$

Injective, surjective and bijective.

Injective: a horizontal line crosses the graph in one point.

3) $f:\Re\geq 0\rightarrow\Re, f(x) = cos(x)$

The cosine function is not injective, bijective nor surjective.

4) $f:\Re\rightarrow\Re \:f(x)=ex$

Since e, is euler number it's a constant. It's also injective, surjective and bijective.

5) Quite unclear format

$6) \:f:\Re\rightarrow(0,\infty), f(x) =ex$

Despite the Restriction for the CoDomain, the function remains injective, surjective and therefore bijective.

$7) f:\Re\geq 0 \rightarrow \Re\geq0, f(x) =x^{4}$

Not injective nor surjective therefore not bijective too.

$8).f:\{-1,2,-3\}}\rightarrow \{1,4,9\}, f(x) =x^{2}$

$f(-1)=1, f(2)=4, f(-3)=9$

Injective (one to one), Surjective, and Bijective.

$10) f:\Re\geq 0\rightarrow [-1,1], f(x)= cos(x)\\-1=cos(x) \therefore x=\pi,3\pi,5\pi,etc.$

Surjective.

$11.f:R\geq 0[-1,1], f(x) = 0\\$

Surjective

12.f: US Citizens→Z, f(x) = the SSN of x.

General function

13.f: US Zip Codes→US States, f(x) = The state that x belongs to.

Surjective

7 0

2 years ago

HELPPPPPPPPPPP

True [87]

Answer:

Part A

C. 7.25

Part B

B. Ryan Shafer has been more consistent because his mean absolute deviation is less than Norm Duke’s.

Step-by-step explanation:

<u>Given data:</u>

299, 281, 285, 269, 280, 269, 286, 287

<u>Find the mean of the data above:</u>

(299 + 281 + 285 + 269 + 280 + 269 + 286 + 287)/8 = 282

<u>Find absolute deviations, an absolute value of the difference of data and the mean:</u>

299 - 282 = 17 ⇒ 17
281 - 282 = -1 ⇒ 1
285 - 282 = 3 ⇒ 3
269 - 282 = -13 ⇒ 13
280 - 282 = 2 ⇒ 2
269 - 282 = -13 ⇒ 13
286 - 282 = 4 ⇒ 4
287 - 282 = 5 ⇒ 5

<u>Find mean absolute deviation:</u>

(17 + 1 + 3 + 13 + 2 + 13 + 4 + 5)/8 = 7.25

Correct choice is C

Less mean absolute deviation is the sign of more consistent data.

Since Ryan Shafer has smaller mean absolute deviation, he has been more consistent 7 < 7.25

Correct choice is B.

5 0

3 years ago