$20 haircut ; 10% tip

An experiment consists of drawing a marble out of a bag, observing the color, and then placing it back in the bag. Suppose the e

Elan Coil [88]

The experimental data suggest that

$\mathbb P(\text{red})\approx\dfrac{38}{75}$
$\mathbb P(\text{blue})\approx\dfrac{23}{75}$
$\mathbb P(\text{green})\approx\dfrac{11}{75}$
$\mathbb P(\text{yellow})\approx\dfrac3{75}$

Because the marble is replaced after being drawn, and so the number of marbles of a given color remains the same, the event of drawing any given color is independent of what was drawn before. So

$\mathbb P(\text{2 consecutive yellows})\approx\dfrac3{75}\cdot\dfrac3{75}=\dfrac1{625}$

5 0

3 years ago

Read 2 more answers

The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial

GREYUIT [131]

Answer:

P(0) = 7,917

Step-by-step explanation:

The population of the community is given by the following formula:

$P(t) = P(0)(1+r)^{t}$

In which P(0) is the initial population and r is the growth rate.

The initial population P0 has doubled in 5 years.

This means that

$P(5) = 2P(0)$

Which lets us find r.

$P(t) = P(0)(1+r)^{t}$

$2P(0) = P(0)(1+r)^{5}$

$(1+r)^{5} = 2$

Applying the 5th root to both sides

$1+r = 1.1487$

$r = 0.1487$

So

$P(t) = P(0)(1.1487)^{t}$

Suppose it is known that the population is 12,000 after 3 years.

With this, we find P(0)

$P(t) = P(0)(1.1487)^{t}$

$12000 = P(0)(1.1487)^{3}$

$1.5157P(0) = 12000$

$P(0) = \frac{12000}{1.5157}$

$P(0) = 7917$

4 0

3 years ago

2. The height of one square pyramid is 24 m. A similar pyramid has a height of 8 m. The volume of the larger pyramid is 648 m3.

Dmitrij [34]

Larger PyramidHeight 24 Volume 648

Pyramid Volume = (Area of the Base * Height) ÷ 3648 = Base Area * 24 / 3Base Area = 648 * 3 / 24Base Area = 648 / 8Base Area = 81Base Length = 9
a) The Scale Factor between the Small & Large PyramidLength - 3LATERAL Area - 9Volume - 27

Slant Height^2 = 4.5^2 + 24^2Slant Height^2 = 596.25 Slant Height^2 = 24.4182308941 
b)
Large Pyramid Area = (½ * Perimeter of Base * Slant Height) + Base AreaLarge Pyramid Area = (.5 * 36 * 24.4182308941) + 81
Large Pyramid Area = 439.5281560938 + 81
Large Pyramid TOTAL Area = 520.5281560938 Large Pyramid LATERAL Area = 439.5281560938 

**********************************************************************************c)
Smaller PyramidHeight 8Surface Area = 124
This pyramid has dimensions that are one third of the larger pyramid.Therefore, it has a base length of 3.Base Area = 9.
Its base perimeter would be 12.
Small Pyramid Volume = (Area of the Base * Height) ÷ 3Small Pyramid Volume = ( 9 * 8 ) / 3Small Pyramid Volume = 72 / 3
c) Small Pyramid Volume =24 cubic meters

d) Ratio of larger pyramid volume to smaller pyramid volume648 / 24 = 27The reason? Volume is a 3 dimensional quantity. The Larger pyramid is 3 times larger in terms of the base measurement.9 meters vs 3 meters - a factor of 3When we compare volumes, we have to cube this factor.3^3 = 27

Source : http://www.1728.org/volpyrmd.htm

3 0

3 years ago

There are 10 red marbles and 20 green marbles in a bag. Colleen says the ratio of red marbles to green marbels is 19 to 20. Frit

nadezda [96]

Fritz is correct, in that the ratio is 1:2

Think of the ratio as a division

10:20 = 10/20

When you divide 10 with 20, you will get a decimal (or simplified fraction)

10/20 = 0.5

0.5 = 50 percent, or 1:2

Fritz is correct, in that 1:2 is the ratio

hope this helps

6 0

3 years ago

Read 2 more answers

The students to faculty ratio at a small college is 17:3. The total of total if student and faculty is 740. How many faculty mem

Rom4ik [11]

So, the ration is 17:3, you know that. Therefore, the change from # of students to the 17 is the same change as # teachers to 3. Knowing this, you also know that the total # of people ihas the same change as the total ratio. So 17+3 = 20. 740/20 = 37. So the change is 37. 3x37= 111 17x37=629
You can check to make sure this answer is correct by adding the two final numbers. 111+629 = 740. (Some find it easier to see lined up really pretty)
17 -- 3 total 20
x -- y total 740
Or, if you are visual, look at the picture I drew:

3 0

3 years ago