Ask question

Ask question

All categories

olga nikolaevna [1]

2 years ago

6

A student uses a solution that contains 16 grams of water to conduct an evaporation experiment. At the end of one hour, the am

ount of water in the solution has decreased by 3.5%. At the end of two hours, the amount of water in the solution has decreased by another 4.25%. Which calculations can be used to determine the amount of water, in grams, remaining in the solution at the end of the second hour?

2 answers:

Dima020 [189]2 years ago

8 0

Good evening

Answer:

<h2>14.7838 grams</h2>

Step-by-step explanation:

<em><u>Rule : </u></em>_____________________________________________________

decrease something by p% then decrease by q% means multiply by

$(1-\frac{p}{100})(1-\frac{q}{100})$

__________________________________________________________

Note : <em>in our case the amount of water in the solution has decreased by 3.5% then by 4.25% consecutively</em>____________________________________

Let’s apply what we have learnt:

the amount of water remaining in the solution at the end of the second hour is

$16(1-\frac{3.5}{100})(1-\frac{4.25}{100})=14.7838$

Hope this helps.

yanalaym [24]2 years ago

5 0

Answer:

3.5% decrease means 96.5% remaining

0.965(16)

4.25% decrease means 95.75% remaining

0.9575(0.965(16))

= 14.7838 grams

You might be interested in

The equation of the tangent to the curve x^2 = 4y at the point on the curve where x=-2 is?

aleksandrvk [35]

$x^2 = 4y \Rightarrow y= \frac{x^2}{4}$
$\frac{dy}{dx} = \frac{2x}{4} = \frac{x}{2}$

(x = -2) $\frac{dy}{dx} = \frac{x}{2} = \frac{-2}{2} = -1$
(x = -2) $y= \frac{x^2}{4}= \frac{(-2)^2}{4} = 1$

$y-y_1=m(x-x_1)$
$y-1 = -1(x--2)
$
$y-1 = -1(x+2)$
$y-1 = -x-2$
$y=-x-1 = -(x+1)$

7 0

3 years ago

Read 2 more answers

In a game the player wins if he rolls a 6 on a number cube. If the number cube is rolled 18 times, then what is a reasonable pre

monitta

Answer:

15/18

Step-by-step explanation:

A single di has 6 sides, meaning the probability of rolling a 6 is 1/6. So if you roll a di 18 times you would probably get 6 three times. Meaning the number of unsuccesful rolls would be (18/18 - 3/18). Hope this helps.

8 0

2 years ago

Someone please help plz

yaroslaw [1]

Answer: 14

Step-by-step explanation:

12^2+8^2=208 square root is 14

4 0

3 years ago

Read 2 more answers

What is the 50th term of the sequence that begins with -6, 0, 6, 12...

vazorg [7]

Answer:

The 50th term is 288.

Step-by-step explanation:

A sequence that each term is related with the prior by a sum of a constant ratio is called a arithmetic progression, the sequence in this problem is one of those. In order to calculate the nth term of a setence like that we need to use the following formula:

an = a1 + (n-1)*r

Where an is the nth term, a1 is the first term, n is the position of the term in the sequence and r is the ratio between the numbers. In this case:

a50 = -6 + (50 - 1)*6

a50 = -6 + 49*6

a50 = -6 + 294

a50 = 288

The 50th term is 288.

5 0

3 years ago

The hourly median power (in decibels) of received radio signals transmitted between two cities

trasher [3.6K]

Using the lognormal and the binomial distributions, it is found that:

The 90th percentile of this distribution is of 136 dB.

There is a 0.9147 = 91.47% probability that received power for one of these radio signals is less than 150 decibels.

There is a 0.0065 = 0.65% probability that for 6 of these signals, the received power is less than 150 decibels.

In a <em>lognormal </em>distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{\ln{X} - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

The mean is of $\mu = 3.5$ .

The standard deviation is of $\sigma = \sqrt{1.22}$

Question 1:

The 90th percentile is X when Z has a p-value of 0.9, hence <u>X when Z = 1.28.</u>

$Z = \frac{\ln{X} - \mu}{\sigma}$

$1.28 = \frac{\ln{X} - 3.5}{\sqrt{1.22}}$

$\ln{X} - 3.5 = 1.28\sqrt{1.22}$

$\ln{X} = 1.28\sqrt{1.22} + 3.5$

$e^{\ln{X}} = e^{1.28\sqrt{1.22} + 3.5}$

$X = 136$

The 90th percentile of this distribution is of 136 dB.

Question 2:

The probability is the <u>p-value of Z when X = 150</u>, hence:

$Z = \frac{\ln{X} - \mu}{\sigma}$

$Z = \frac{\ln{150} - 3.5}{\sqrt{1.22}}$

$Z = 1.37$

$Z = 1.37$ has a p-value of 0.9147.

There is a 0.9147 = 91.47% probability that received power for one of these radio signals is less than 150 decibels.

Question 3:

10 signals, hence, the binomial distribution is used.

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

For this problem, we have that $p = 0.9147, n = 10$ , and we want to find P(X = 6), then:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 6) = C_{10,6}.(0.9147)^{6}.(0.0853)^{4} = 0.0065$

There is a 0.0065 = 0.65% probability that for 6 of these signals, the received power is less than 150 decibels.

You can learn more about the binomial distribution at brainly.com/question/24863377

5 0

2 years ago