What is the rate of change for the set of ordered pairs?

A recipe calls for 3 1/2 cups of sugar. If you want to make only 1/3 of the recipe, how much sugar should you use?

Sav [38]

Answer: 1 1/6 cups of sugar

Step-by-step explanation:

First let’s convert 3 1/2 into an improper fraction: 7/2

Then we multiply 7/2 by 1/3: 7/2*1/3=7/6

Then finally we convert 7/6 into a mixed number, so your answer will be 1 1/6

3 0

3 years ago

Two assembly lines I and II have the same rate of defectives in their production of voltage regulators. Six regulators are sampl

Kamila [148]

Answer:

0.4546

Step-by-step explanation:

nCr = n!/(n-r)!r!

Number of ways of selecting the four defective voltage regulators from 12 = 12C4 = 12!/(12-4)!4! = 12!/8!4! = (12 *11*10*9)/(4*3*2*1)

12C4 = 495 ways

Number of ways of selecting 2 defectives from line 1 = 6C2 * 6C2

6C2 = 6!/(6-2)!2! = 6!/4!2! = (6*5)/(2*1) = 15

6C2 * 6C2 = 15*15 = 225 ways

Probability = Number of possible outcomes/ Number of total outcomes

Probability that exactly 2 of the defective regulators came from line 1 = 225/40.95 = 0.4546

4 0

3 years ago

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side

lorasvet [3.4K]

Answer:

Step-by-step explanation:

1.

cot x sec⁴ x = cot x+2 tan x +tan³x

L.H.S = cot x sec⁴x

=cot x (sec²x)²

=cot x (1+tan²x)² [ ∵ sec²x=1+tan²x]

= cot x(1+ 2 tan²x +tan⁴x)

=cot x+ 2 cot x tan²x+cot x tan⁴x

=cot x +2 tan x + tan³x [ ∵cot x tan x $=\frac{ \textrm{tan x }}{\textrm{tan x}}$ =1]

=R.H.S

2.

(sin x)(tan x cos x - cot x cos x)=1-2 cos²x

L.H.S =(sin x)(tan x cos x - cot x cos x)

= sin x tan x cos x - sin x cot x cos x

$=\textrm{sin x cos x }\times\frac{\textrm{sin x}}{\textrm{cos x} } - \textrm{sinx}\times\frac{\textrm{cos x}}{\textrm{sin x}}\times \textrm{cos x}$

= sin²x -cos²x

=1-cos²x-cos²x

=1-2 cos²x

=R.H.S

3.

1+ sec²x sin²x =sec²x

L.H.S =1+ sec²x sin²x

= $1+\frac{{sin^2x}}{cos^2x}$ [ $\textrm{sec x}=\frac{1}{\textrm{cos x}}$ ]

=1+tan²x $[\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}]$

=sec²x

=R.H.S

4.

$\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}} = \textrm{2 csc x}$

L.H.S= $\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}}$

$=\frac{\textrm{sinx(1+cos x)+{\textrm{sinx(1-cos x)}}}}{\textrm{(1-cos x)\textrm{(1+cos x})}}$

$=\frac{\textrm{sinx+sin xcos x+{\textrm{sinx-sin xcos x}}}}{{(1-cos ^2x)}}$

$=\frac{\textrm{2sin x}}{sin^2 x}$

= 2 csc x

= R.H.S

5.

-tan²x + sec²x=1

L.H.S=-tan²x + sec²x

= sec²x-tan²x

= $\frac{1}{cos^2x} -\frac{sin^2x}{cos^2x}$

$=\frac{1- sin^2x}{cos^2x}$

$=\frac{cos^2x}{cos^2x}$

=1

8 0

3 years ago

a particle moves along the x-axis so that anytime t comma measured in seconds it's position is given by...

Natali5045456 [20]

Given the position function s(t), you can get the acceleration function by differentiating s twice:

velocity = s'(t) = -5 sin(t ) + 3 cos(3t )

acceleration = s''(t) = -5 cos(t ) - 9 sin(3t )

Then when t = π, the particle's acceleration is

s''(π) = -5 cos(π) - 9 sin(3π)

… = -5 • (-1) - 9 • 0 = 5

7 0

2 years ago

V divided by 5 is equal to 60.

Schach [20]

Answer:

$\boxed{v=300}$

Step-by-step explanation:

Hey there!

To find v we’ll set up the following,

v ÷ 5 = 60

To get v by itself we’ll do

5*60 = 300

v = 300

Hope this helps :)

4 0

3 years ago