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3 years ago

6

Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or

green. Half of the numbers 1 - 36 are colored red and half are black and the numbers 0 and 00 are green. Each number occurs only once on the wheel. What is the probability of landing on a red space?

1 answer:

EleoNora [17]3 years ago

5 0

Answer:

18/38 or 9/19

Step-by-step explanation:

18 squares are red

18 squares are black

2 squares have 0 or 00

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Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 181.5 square cen

3241004551 [841]

Answer:

The base and height of the solid is 5.5cm

<em></em>

Step-by-step explanation:

Given

$Surface\ Area = 181.5cm^2$

Required

Determine the dimensions that maximizes the volume

Let the base dimension be x and the height be h

The volume is calculated as:

$Volume =x^2 * h$

$Volume =x^2h$

181.5 =x^2h

The surface area (S) is calculated as this:

$S = 2(x^2 + xh + xh)$

$S = 2(x^2 + 2xh)$

$S = 2x^2 + 4xh$

Substitute 181.5 for S

$181.5 = 2x^2 + 4xh$

Make h the subject:

$4xh = 181.5 - 2x^2$

$h = \frac{181.5 - 2x^2}{4x}$

Substitute $h = \frac{181.5 - 2x^2}{4x}$ in $Volume =x^2h$

$V = x^2(\frac{181.5 - 2x^2}{4x})$

$V = x(\frac{181.5 - 2x^2}{4})$

$V = \frac{1}{4}(x)(181.5 - 2x^2)$

$V = \frac{181.5x}{4} - \frac{2x^3}{4}$

$V = \frac{181.5x}{4} - \frac{x^3}{2}$

To get the maximum, we differentiate V with respect to t and set the differentiation to 0

$dV = \frac{181.5}{4} - \frac{3x^2}{2}$

Set to 0

$0 = \frac{181.5}{4} - \frac{3x^2}{2}$

$\frac{3x^2}{2} = \frac{181.5}{4}$

Multiply through by 4

$4 * \frac{3x^2}{2} = \frac{181.5}{4} * 4$

$2*3x^2 = 181.5$

$6x^2 = 181.5$

$x^2 = \frac{181.5}{6}$

$x^2 = 30.25$

$x = \sqrt{30.25$

$x = 5.5$

Recall that:

$h = \frac{181.5 - 2x^2}{4x}$

$h = \frac{181.5 - 2 * 5.5^2}{4 * 5.5}$

$h = \frac{181.5 - 60.5}{22}$

$h = \frac{121}{22}$

$h = 5.5$

So, we have:

$h = 5.5$

$x = 5.5$

<em>Hence, the base and height of the solid is 5.5cm</em>

7 0

3 years ago

Adding integers different signs answers

Zina [86]

Answer:

Step-by-step explanation:

19) 340-76= 264 ft

20) -320+23 = -297 F

21) 50-85-12+93 = 46 points

22) 26-5-2+1-6 = 14$

23) -3 + 18 = 15 F

3 0

3 years ago

Can somebody please help this is due very soon

joja [24]

Your answer is

Slope = -1.000/2.000 = -0.500
x-intercept = 7/1 = 7.00000
y-intercept = 7/2 = 3.50000

Step-by-step explanation:

4 0

3 years ago

Which expression is equivalent to

g100num [7]

Answer:

16 x¹⁰ + 88 x⁵ + 121

step-by-step explanation:-

( 4 x⁵ + 11)²

use ( a + b)² = a² + 2ab + b² to expand the expression

( 4x ⁵)² +2 ( 4x⁵) ( 11 ) + ( 11 )²

calculate we get

16 x¹⁰ + 88 x⁵ + 121

6 0

3 years ago

Terrance is 3.5 years older than Stephanie. Stephanie is 22.5 years old.

LuckyWell [14K]

Answer:

Terrance is 25.5

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers