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3 years ago

20 of the 80 coffee mugs at Carson's Pancake House are dirty. What percentage of the coffee mugs at the pancake house are dirty?

Mathematics

2 answers:

erastova [34]3 years ago

5 0

We have:

$\dfrac{20}{80} = \dfrac{\%} {100}$

Solving for %:

$\% = \dfrac{20\cdot 100}{80} = 25\%$

<h2>R/ 25% of coffee mugs are dirty.</h2>

Dennis_Churaev [7]3 years ago

3 0

Answer:

25%

Step-by-step explanation:

20/80 in can be reduced to 1/4 and 1/4 equals 25%.

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A drink coaster in the shape of a circle has

egoroff_w [7]

The diameter of the coaster is 5 cm.

Step-by-step explanation:

Given,

The area of the circle = 19.63 sq inch

To find the diameter, we need to find the radius

Formula

The area of a circle with radius(r) = π $r^{2}$ sq cm

According to the problem,

π $r^{2}$ = 19.63

or, $r^{2}$ = $\frac{7 X 19.63}{22}$

= 6.2459

or, r = $\sqrt{6.2459}$ = 2.499 (approx)

= 2.5 cm

Hence the diameter of the circle = 2 × 2.5 cm = 5 cm

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2 years ago

If AD = 5x - 7 and AB = 2x +11, what is the length of AD

Norma-Jean [14]

Answer:

The length of AD is 6.

Step-by-step explanation:

Solve.

$5x - 7 = 2x + 11 \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 2x \: \: \: \: \: \: = - 2x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{3x - 7 = 11} \\ \frac{ \: \: \: \: \: \: \: \: \: + 7 = + 7}{3x = 18} \\ \\ \frac{3x}{3} = \frac{18}{3} \\ \\ x = 6$

Now plug in:

$5x - 7 \\ 5(6) - 7 \\ 30 - 7 \\ 23$

^Therefore, your result^

8 0

3 years ago

A poster is to have an area of 240 in^2 with 1 inch margins at the bottom and sides and a 2 inch margin at the top. Find the exa

Vsevolod [243]

Answer:

4√10 inches wide by 6√10 inches tall

Step-by-step explanation:

"Poster area" problems have an interesting general solution. The "printed area" is maximized, or the "poster area" is minimized, when the ratio of poster dimensions is equal to the ratio of margin dimensions.

Here, the top/bottom margins total 3 inches, and the side/side margins total 2 inches. That is, the printed area will be maximized when the poster has a width : height aspect ratio of 2 : 3. If w represents the width, then the total area is ...

(w)(3/2w) = 240 . . . . square inches

w^2 = 160

w = √160 = 4√10 . . . . width in inches

Then the height is ...

height = (3/2)w = (3/2)(4√10) = 6√10 . . . . height, inches

_____

<em>Graphical solution</em>

A graphing calculator gives the same result for x=width. Poster width is about 12.649 inches (=4√10), and printed area is a maximum of about 170.1 square inches.

_____

<em>Calculus solution</em>

Let x represent the width of the poster. Then x-2 is the width of the printed area. The height of the poster will be 240/x, and the height of the printed area will be (240/x)-3. We want to maximize the printed area ...

a = (x -2)(240/x -3)

which means we want to find the value of x where the area derivative is zero.

a = 240 -480/x -3x +6

da/dx = 0 = 480/x^2 -3

Solving for x, we get ...

x^2 = 480/3 = 160

x = √160 = 4√10 . . . . . poster width, as above