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3 years ago

9

Ten children in a kindergarten class own a dog. Fourteen children in the class do not own a dog. Find the ratio of the number of

children who own a dog to the number of children in the class. Express the ratio as a simplified fraction.

1 answer:

Bond [772]3 years ago

3 0

5/7 which means for every 7 kids, one owns a dog

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statuscvo [17]

Answer:

Step-by-step explanation: so to convert degrees to radians, you multiply your number by pi/180. You then have 96pi/180 radians. Reduce the fraction to simplest form and u have 8pi/15

3 0

3 years ago

A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria

forsale [732]

Answer:

11 meters

Step-by-step explanation:

First, we can say that the square has a side length of x. The perimeter of the square is 4x, and that is how much wire goes into the square. To maximize the area, we should use all the wire possible, so the remaining wire goes into the triangle, or (11-4x).

The area of the square is x², and the area of an equilateral triangle with side length a is (√3/4)a². Next, 11-4x is equal to the perimeter of the triangle, and since it is equilateral, each side has (11-4x)/3 length. Plugging that in for a, we get the area of the equilateral triangle is

(√3/4)((11-4x)/3)²

= (√3/4)(11/3 - 4x/3)²

= (√3/4)(121/9 - 88x/9 + 16x²/9)

= (16√3/36)x² - (88√3/36)x + (121√3/36)

The total area is then

(16√3/36)x² - (88√3/36)x + (121√3/36) + x²

= (16√3/36 + 1)x² - (88√3/36)x + (121√3/36)

Because the coefficient for x² is positive, the parabola would open up and the derivative of the parabola would be the local minimum. Therefore, to find the maximum area, we need to go to the absolute minimum/maximum points of x (x=0 or x=2.75)

When x=0, each side of the triangle is 11/3 meters long and its area is

(√3/4)a² ≈ 5.82

When x=2.75, each side of the square is 2.75 meters long and its area is

2.75² = 7.5625

Therefore, a maximum is reached when x=2.75, or the wire used for the square is 2.75 * 4 = 11 meters

3 0

3 years ago

Penelope goes to work after school for 4.5 hours on Mondays, Tuesdays, and Fridays. She doesn’t have classes on Wednesdays or Th

iVinArrow [24]

Answer:

Her hourly rate is <u>$14</u>.

Step-by-step explanation:

Given:

Penelope goes to work after school for 4.5 hours on Mondays, Tuesdays, and Fridays.

She works 8 hours each on Wednesdays or Thursdays.

Now, to find her hourly rate.

So, total hours Penelope work on Mondays, Tuesdays, and Fridays:

$4.5+4.5+4.5=13.5\ hours.$

And, total hours she work on Wednesdays and Thursdays:

$8+8=16\ hours.$

Now,<em><u> the total hours each week she work:</u></em>

$13.5+16=29.5\ hours.$

<u><em>Total money she makes each week</em></u> = $413.

Now, to get the hourly rate we divide the total hours each week she work by total money she makes each week:

$413\div 29.5$

$=\$14.$

Therefore, her hourly rate is $14.

6 0

3 years ago

A rabbit hopped 11 meters in 6 minutes. At that rate, how far did the rabbit hop in 8 minutes?

ad-work [718]

It hopped 14 meters in 8 minutes.

6 0

3 years ago

Read 2 more answers

साधारण ब्याज<br>PXT XR<br>I<br>100

-Dominant- [34]

Answer:

Yes

Step-by-step explanation:

SI=PRT/100

SI=A-P

R=SI×100/P×T

T=SI×100/R×T

P=SI×100/R×T

8 0

3 years ago