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3 years ago

Express each ratio as a unit rate.round to the bearest tenth,if necessary. 2 note books for $0.60

Mathematics

2 answers:

Vladimir79 [104]3 years ago

8 0

Answer:

(B) $0.30 per notebook

Step-by-step explanation:

FrozenT [24]3 years ago

6 0

Option B

2 notebooks for $ 0.60 expressed as unit rate is $ 0.30 per notebook

<h3>Solution:</h3>

We have to express ratio as unit rate

Given that, 2 notebooks for $ 0.60

Number of notebooks = 2

Cost of 2 notebooks = $ 0.60

So we have to find cost of 1 notebook

$\begin{array}{l}{\text { cost of } 1 \text { notebook }=\frac{\text { cost of } 2 \text { notebook }}{2}} \\\\ {\text { cost of } 1 \text { notebook }=\frac{0.60}{2}=0.30}\end{array}$

So unit rate = cost of 1 notebook = $ 0.30

So 2 notebooks for $ 0.60 as unit rate is $ 0.30 per notebook

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Use variation of parameters to find a general solution to the differential equation given that the functions y1 and y2 are linea

Aleks [24]

Recall that variation of parameters is used to solve second-order ODEs of the form

y''(t) + p(t) y'(t) + q(t) y(t) = f(t)

so the first thing you need to do is divide both sides of your equation by t :

y'' + (2t - 1)/t y' - 2/t y = 7t

You're looking for a solution of the form

$y=y_1u_1+y_2u_2$

where

$u_1(t)=\displaystyle-\int\frac{y_2(t)f(t)}{W(y_1,y_2)}\,\mathrm dt$

$u_2(t)=\displaystyle\int\frac{y_1(t)f(t)}{W(y_1,y_2)}\,\mathrm dt$

and W denotes the Wronskian determinant.

Compute the Wronskian:

$W(y_1,y_2) = W\left(2t-1,e^{-2t}\right) = \begin{vmatrix}2t-1&e^{-2t}\\2&-2e^{-2t}\end{vmatrix} = -4te^{-2t}$

Then

$u_1=\displaystyle-\int\frac{7te^{-2t}}{-4te^{-2t}}\,\mathrm dt=\frac74\int\mathrm dt = \frac74t$

$u_2=\displaystyle\int\frac{7t(2t-1)}{-4te^{-2t}}\,\mathrm dt=-\frac74\int(2t-1)e^{2t}\,\mathrm dt=-\frac74(t-1)e^{2t}$

The general solution to the ODE is

$y = C_1(2t-1) + C_2e^{-2t} + \dfrac74t(2t-1) - \dfrac74(t-1)e^{2t}e^{-2t}$

which simplifies somewhat to

$\boxed{y = C_1(2t-1) + C_2e^{-2t} + \dfrac74(2t^2-2t+1)}$

4 0

3 years ago

A triangle is removed from the rectangle. Find the area of the remaining figure.

Mariulka [41]

Answer

C) 160 in^2

Step by step explanation

First, let's find the area of the rectangle.

Area of a rectangle = length x width

The area of the rectangle = 20 * 10

= 200 in^2

Now let's find the area of the triangle that is removed.

Area of a triangle = 1/2 base * height.

Here base = 10 and height = 8. Plug in these values into the formula, we get

Area of the triangle = 1/2 * 10*8

= 5* 8

The area of the triangle = 40 in^2

The area of the remaining figure = Area of the rectangle - area of the triangle

= 200 - 40

= 160 in^2

The answer is "160 in^2"

Thank you.

5 0

3 years ago

There is a sale on the 3D doodler it is now only $83 It was originally $95 what percent did the 3D doodler decrease

Furkat [3]

Just divide then subtract

95/83= 1.14= move decimal to right one time so it would be 11.4 then subtract 11.4 from 95= 95-11.4= about $83.55

7 0

3 years ago

Read 2 more answers

225% of what number is 81

Airida [17]

To find a percentage of a number we multiply the percentage times the number and get the result, here we have the percentage and the result and need to find out which number it corresponds to, lets write an equation to do so and keep in mind that the percentage itself can be written in a different way:
225% = 225 out of 100 = 225/100
So we have this equation, where we call x the number we are looking for:
(225%)(x) = 81
(225/100)(x) = 81
so we solve for x:
225x = 81*100 = 8100
x = 8100/225
x = 36
The original number is 36, hence 225% of 36 is 81

4 0

3 years ago

If two sides of a triangle are 5 and 7 inches longer than the third side and the perimeter measures 21, find the length of each

aleksandr82 [10.1K]

Hello

x
x +5
x + 7

x + x + 5 + x + 7 = 21
3 x = 21 - 12
3 x = 9
x = 3

3 , 5 et 7 pouces

7 0

3 years ago