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3 years ago

How do you compare and contrast decimals, fractions, and percents

1 answer:

6 0

You would have to make them all one form that is the same, for example if you wanted to find out if 80%, 0.75, 1/2 are the same you would have to change them into the same form. If you wanted to make them all decimals it would be 0.08, 0.75, 0.5, if you wanted to make them all percents it would be 80%, 75%, 50%, you wanted them all of be a fraction it would be 4/5, 3/4, and 1/2. I hope explained this well and this helped :)
-Madi

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which of the functions have a range of real numbers greater than or equal to 1 or less than or equal to-1

lilavasa [31]

The question is incomplete. Here is the complete question:

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. $y=\sec x$

B. $y= \tan x$

C. $y= \cot x$

D. $y= \csc x$

Answer:

A. $y=\sec x$

D. $y=\csc x$

Step-by-step explanation:

Given:

The range is greater than or equal to 1 or less than or equal to -1.

The given choices are:

Choice A: $y=\sec x$

We know that, the $\sec x=\frac{1}{\cos x}$

The range of $\cos x$ is from -1 to 1 given as [-1, 1]. So,

$|\cos x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\cos x|}\geq 1\\|\sec x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the secant function as:

$\sec x\leq -1\ or\ \sec x\geq 1\\$

Therefore, the range of $y=\sec x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

Choice B: $y= \tan x$

We know that, the range of tangent function is all real numbers. So, choice B is incorrect.

Choice C: $y= \cot x$

We know that, the range of cotangent function is all real numbers. So, choice C is incorrect.

Choice D: $y=\csc x$

We know that, the $\csc x=\frac{1}{\sin x}$

The range of $\sin x$ is from -1 to 1 given as [-1, 1]. So,

$|\sin x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\sin x|}\geq 1\\|\csc x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the cosecant function as:

$\csc x\leq -1\ or\ \csc x\geq 1\\$

Therefore, the range of $y=\csc x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

6 0

3 years ago

Sergio ate 3.5 cookies. Each cookie contained 5.7 grams of sugar. How many grams of sugar did Sergio eat?

FrozenT [24]

I’ll get it correct here :)

He ate 19.95 grams of sugar.

3.5 x 5.7 = 19.95

5 0

3 years ago

the 11th term in a geometric sequence is 48 and the common ratio is 4. the 12th term is 192 and the 10th term is what?

Soloha48 [4]

Given:

The 11th term in a geometric sequence is 48.

The 12th term in the sequence is 192.

The common ratio is 4.

We need to determine the 10th term of the sequence.

General term:

The general term of the geometric sequence is given by

$a_n=a(r)^{n-1}$

where a is the first term and r is the common ratio.

The 11th term is given is

$a_{11}=a(4)^{11-1}$

$48=a(4)^{10}$ ------- (1)

The 12th term is given by

$192=a(4)^{11}$ ------- (2)

Value of a:

The value of a can be determined by solving any one of the two equations.

Hence, let us solve the equation (1) to determine the value of a.

Thus, we have;

$48=a(1048576)$

Dividing both sides by 1048576, we get;

$\frac{3}{65536}=a$

Thus, the value of a is $\frac{3}{65536}$

Value of the 10th term:

The 10th term of the sequence can be determined by substituting the values a and the common ratio r in the general term $a_n=a(r)^{n-1}$ , we get;

$a_{10}=\frac{3}{65536}(4)^{10-1}$

$a_{10}=\frac{3}{65536}(4)^{9}$

$a_{10}=\frac{3}{65536}(262144)$

$a_{10}=\frac{786432}{65536}$

$a_{10}=12$

Thus, the 10th term of the sequence is 12.

8 0

2 years ago

On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The numb

liberstina [14]

This is a very long question br0(3b)Y=

5 0

1 year ago

Y= 1/2x + 2 Select points on the graph

Cloud [144]

Step-by-step explanation:

—x intercept, y = 0

y = 1/2 x + 2

0 = 1/2 x + 2

-2 = 1/2 x

-2.2 = x

-4 = x

X intercept = (-4 , 0)

—y intercept, x = 0

y = 1/2 x + 2

y = 1/2 . 0 + 2

y = 0 + 2

y = 2

Y intercept = (0 , 2)

Graph in the picture :)

8 0

2 years ago