Solve the following subtraction problems. Remember to borrow as necessary.

two pairs of different sizes contain 34.5 liters of water altogether. when 0.68 liter of water is poured from the bigger pail in

zzz [12365]

There will still be 34.5 L of water in the two pails combined because no water is lost.
Thus the total remains 34.5 L after transferring water between them.
Let the final amount in the smaller pail be x.
Then the larger pail contains 9x.
So x + 9x = 34.5.
That simplifies to 10x = 34.5.
Dividing both sides by 10 gives x = 3.45.
Therefore the smaller pail held 3.45 L at the end.
Because 0.68 L was poured into it, its initial volume was 2.77 L (3.45 minus 0.68)
We can also deduce the larger pail initially contained 31.73 L
(either 35 minus 2.77, or 9 times 3.45 plus 0.68)

6 0

1 month ago

According to a survey by Bankrate, of adults in the United States save nothing for retirement (CNBC website). Suppose that adult

tester [12383]

Complete Question

The complete question appears in the first uploaded image

Answer:

a) Yes, selecting 15 corresponds to a binomial experiment

b)

c)

d) $P(r = 15) = 3.2768 *10^{-11}$

Step-by-step explanation:

Regarding question a:

For an experiment to qualify as binomial

the trials have to be independent

each trial must yield one of two possible outcomes

Given that the selection of 15 individuals is random, we ascertain that the trials are independent and the outcomes are “either the individual saves for retirement or does not save for retirement.”

Therefore, we conclude that the selection of 15 people at random is indeed a binomial experiment.

In question b:

The probability that all selected adults do not save for retirement is mathematically modeled as

$P(r = n) = ^nC_r * p^r * q^{n-r}$

Here C signifies combination

r = 15 implies all selected adults

n refers to the population size equating to 15

From the problem, p = 0.20

and q can be calculated as

=>

=> $q = 1 - p$

Thus

$P(r = 15) = ^{15}C_{15} * p^{15} * q^{15-15}$

$P(r = 15) = 3.2768 *10^{-11}$ Regarding question c:

The probability that exactly five of the selected adults do not save for retirement is mathematically modeled as

$P(r = 5) = ^{15} C_5 * (0.20)^5 * (0.80)^{15}$

$P(r = 5) = 0.1032$

In relation to question d:

The probability that at least one of the selected adults opts not to save for retirement can be mathematically expressed as

$P(r \ge 1 ) = 1 - P (r = 0 )$

$P(r \ge 1 ) = 1 - [ ^{15} C _ 0 * (0.20)^{0} * (0.80 )^{15}]$

$P(r \ge 1 ) = 1 - 0.0352$

$P(r \ge 1 ) = 0.9648$

4 0

2 months ago

If the volume of a cube is increased by a factor of 10, by what factor does the surface area per unit volume change

tester [12383]

Answer:

(1/10)∛100 ≈ 0.4642

Step-by-step explanation:

For a cubic shape with volume V, the edge length is defined as...

s = ∛V

and the surface area is given by...

A = 6s² = 6V^(2/3)

The area-to-volume ratio is therefore...

r1 = A/V = 6V^(2/3)/V = 6V^(-1/3)

When the volume V is increased by a factor of 10, the new area-to-volume ratio becomes...

r2 = 6(10V)^(-1/3)

Consequently, the change factor for the ratio is...

r2/r1 = (6(10V)^(-1/3))/(6V^(-1/3)) = 10^(-1/3) = (1/10)∛100

The change in surface area per unit volume results in a factor of (∛100)/10.

___

Example

For a cube with side length 2, the corresponding volume equals 2³ = 8, with a surface area of 6·2² = 24. The resulting area-to-volume ratio is 24/8 = 3.

The area-to-volume ratio changed by a factor of (0.3∛100)/3 = (∛100)/10, as previously noted.

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8 0

2 months ago