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2 years ago

A chemist has three different acid solutions. The first acid solution contains 25%

1 answer:

8 0

Solution:
Let the volume (in litres) of acids used be:
x1=amount of 25% acid
x2=amount of 40% acid
x3=3*x2=amount of 60% acid

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Men consume on average 15 grams of protein a day. Assume a normal distribution with a standard deviation of 3 grams. A sample of

tatyana61 [14]

Using the normal distribution, there is a 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For this problem, the parameters are given as follows:

$\mu = 15, \sigma = 3, n = 40, s = \frac{3}{\sqrt{40}} = 0.4743$

The probability is the <u>p-value of Z when X = 16 subtracted by the p-value of Z when X = 15</u>, hence:

X = 16:

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{16 - 15}{0.4743}$

Z = 2.11

Z = 2.11 has a p-value of 0.9826.

X = 15:

$Z = \frac{X - \mu}{s}$

$Z = \frac{15 - 15}{0.4743}$

Z = 0

Z = 0 has a p-value of 0.5.

0.9826 - 0.5 = 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

More can be learned about the normal distribution at brainly.com/question/15181104

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4 0

1 year ago

What is the volume of a small cone if:

Amiraneli [1.4K]

Answer:

Volume of smaller cone =301.44

Step-by-step explanation:

First let angle of cone be $\alpha$ .

then $sin(\alpha )$ = 3/5 (For bigger triangle)

Same cone angle is for smaller one because they are similar.

$cos(\alpha )$ = 4/5

Now for smaller cone radius be R

3/5 =R/Slant height

Slant height =5/3R

Lateral surface area = $\frac{1}{2}R^{2}\beta$ [R = slant height]

Given lateral surface area =60 $\pi$ = $\frac{1}{2}(\frac{5R}{3} )^{2} \beta$ ...................................1

$2\pi R=\frac{5R}{3}\beta$ ................................................2

$\beta=\frac{6\pi }{5}$

Put angle beta in equation 1 and find the value of R

R =6 cm

Height = $\frac{4R}{3}$

Thus volume = $\frac{1}{3}\pi6^{2}*8$

=301.44

4 0

2 years ago

If m 6=51, then m 7=

Sophie [7]

Answer:

m 7=129

Step-by-step explanation:

if 6 and 7 are right next to each other. it makes 180 degrees so you would take 180-51 to get your answer

6 0

2 years ago

Suppose that the number of bacteria in a certain population increases according to an exponential growth model. A sample of 2600

melisa1 [442]

Answer: There is 3.994% continuous growth rate per hour.

Step-by-step explanation:

Since we have given that

Initial bacteria = 2600

After two and a half hours,

Number of bacteria = 2873

We need to find the continuous growth rate per hour.

As we know the equation for continuous growth rate per hour.

$y=y_0e^{rt}\\\\2873=2600e^{2.5r}\\\\\dfrac{2873}{2600}=e^{2.5r}\\\\1.105=e^{2.5r}\\\\\text{Taking log on both the sides}\\\\\ln 1.105=2.5r\\\\0.0998=2.5r\\\\r=\dfac{0.0998}{2.5}\\\\r=0.0399\times 100\\\\r=3.994\%$

Hence, there is 3.994% continuous growth rate per hour.

3 0

3 years ago

5у - 4х = -7 <br>2y + 4x = - 14

Nuetrik [128]

1. Y= 5/4x -1.4
2.Y=-2/4x -7
Formula is Y=MX+B
To solve these equations you have to make the Y separate so add or subtract the x value depending on the charge remember what you do to one side you do to the other after you divide everything by the number in the Y value and for the x you put the y value on-top and make it a fraction

3 0

2 years ago