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1 year ago

Find the square. (4x – 6y3)2

Mathematics

1 answer:

Artyom0805 [142]1 year ago

6 0

Answer:

16x^2 -48xy^3 +36y^6

Step-by-step explanation:

Use FOIL or the distributive property or the form of the square of a binomial to expand the square.

(4x -6y^3)(4x -6y^3) = 4x(4x -6y^3) -6y^3(4x -6y^3)

= (4x)^2 -(4x)(6y^3) -(6y^3)(4x) +(6y^3)^2

= 16x^2 -48xy^3 +36y^6

_____

The form referred to above is ...

(a +b)^2 = a^2 +2ab +b^2

You might be interested in

What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 7.2 cm?

ololo11 [35]

central angle of a circle whose radius is 8 cm and intercepted arc length is 7.2 cm is 0.9 radians

Step-by-step explanation:

We need to find the central angle of a circle whose radius is 8 cm and intercepted arc length is 7.2 cm.

arc length l== 7.2 cm

radius =r= 8 cm

central angle=Ф = ?

The formula used is:

$l=r\theta$

Putting values:

$\theta=\frac{l}{r}\\ \theta=\frac{7.2}{8} \\\theta=0.9\,\,radians$

So, central angle of a circle whose radius is 8 cm and intercepted arc length is 7.2 cm is 0.9 radians

Keywords: central angle of circle

Learn more about central angle of circle at

#learnwithBrainly

4 0

1 year ago

The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds prod

True [87]

Answer:

a) 57.35%

b) 99.99%

c) 68.27%

Step-by-step explanation:

When we have a random variable X that is normally distributed with mean $\large\bf \mu$ and standard deviation $\large\bf \sigma$ , then

The probability that the random variable has a value less than a, P(X < a) = P(X ≤ a) is the area under the normal curve with mean $\large\bf \mu$ and standard deviation $\large\bf \sigma$ to the left of a.

The probability that the random variable has a value greater than b, P(X > b) = P(X ≥ b) is the area under the normal curve with mean $\large\bf \mu$ and standard deviation $\large\bf \sigma$ to the right of b.

The probability that the random variable has a value between a and b, P(a < X < b) = P(a ≤ X ≤ b) = P(a < X ≤ b)= P(a ≤ X < b) is the area under the normal curve with mean $\large\bf \mu$ and standard deviation $\large\bf \sigma$ between a and b.

In this case, the random variable is the collagen amount found in the extract of the plant. The mean is 63 g/ml and the standard deviation is 5.4 g/ml

(a) What is the probability that the amount of collagen is greater than 62 grams per mililiter?

As we have seen, we need to find the area under the normal curve with mean 63 and standard deviation 5.4 to the right of 62 (see picture).

You can find this value easily with a calculator or a spreadsheet. If you prefer the old-style, then you have to standardize the values and look up in a table.

If you have access to Excel or OpenOffice Calc, you can find this value by introducing the formula:

1- NORMDIST(62,63,5.4,1) in Excel

1 - NORMDIST(62;63;5.4;1) in OpenOffice Calc

and we will get a value of 0.5735 or 57.35%

(b) What is the probability that the amount of collagen is less than 90 grams per mililiter?

Now we want the area to the left of 90

NORMDIST(90,63,5.4,1) in Excel

NORMDIST(90;63;5.4;1) in OpenOffice Calc

You will get a value of 0.9999 or 99.99%

(c) What percentage of compounds formed from the extract of this plant fall within 1 standard deviations of the mean?

You can use either the rule that 68.27% of the data falls between $\large\bf \mu -\sigma$ and $\large\bf \mu +\sigma$ or compute area between 63 - 5.4 and 63 + 5.4, that is to say, the area between 57.6 and 68.4

In Excel

NORMDIST(68.4,63,5.4,1) - NORMDIST(57.6,63,5.4,1)

In OpenOffice Calc

NORMDIST(68.4;63;5.4;1) - NORMDIST(57.6;63;5.4;1)

In any case we get a value of 0.6827 or 68.27%

3 0

2 years ago

the distribution of scores on a recent test closely followed a normal distribution wotb a mean of 22 and a standard deviation of

soldi70 [24.7K]

Answer:

1) 22.66%

2) 20

Step-by-step explanation:

The scores of a test are normally distributed.

Mean of the test scores = u = 22

Standard Deviation = $\sigma$ = 4

Part 1) Proportion of students who scored atleast 25 points

Since, the test scores are normally distributed we can use z scores to find this proportion.

We need to find proportion of students with atleast 25 scores. In other words we can write, we have to find:

P(X ≥ 25)

We can convert this value to z score and use z table to find the required proportion.

The formula to calculate the z score is:

$z=\frac{x-u}{\sigma}$

Using the values, we get:

$z=\frac{25-22}{4}=0.75$

So,

P(X ≥ 25) is equivalent to P(z ≥ 0.75)

Using the z table we can find the probability of z score being greater than or equal to 0.75, which comes out to be 0.2266

Since,

P(X ≥ 25) = P(z ≥ 0.75), we can conclude:

The proportion of students with atleast 25 points on the test is 0.2266 or 22.66%

Part 2) 31st percentile of the test scores

31st percentile means 31%(0.31) of the students have scores less than this value.

This question can also be done using z score. We can find the z score representing the 31st percentile for a normal distribution and then convert that z score to equivalent test score.

Using the z table, the z score for 31st percentile comes out to be:

z = -0.496

Now, we have the z scores, we can use this in the formula to calculate the value of x, the equivalent points on the test scores.

Using the values, we get:

$-0.496=\frac{x-22}{4}\\\\ x=4(-0.496) + 22\\\\ x=20.02\\\\ x \approx 20$

Thus, a test score of 20 represent the 31st percentile of the distribution.

3 0

2 years ago

Randy collected 30 signatures from fifth grade students at his school. He noticed that 3/5 of the signatures were done in pencil

inna [77]

Answer:

18 signatures

Step-by-step explanation:

Take the total number of signatures and multiply by the fraction that were done in pencil to determine the number done in pencil

30 * 3/5

90/5

3 0

2 years ago

Read 2 more answers

The income distribution in a county is a normal distribution with a mean income of $10,000. The top 2.5% of the wage earners ear

earnstyle [38]

Answer:

84% of the wage earners earn less than $14,000 each.

Step-by-step explanation:

The Empirical Rule (68-95-99.7%)-

According to this around 95% of the data will fall within two standard deviations of the mean.

As the bell curve is symmetrical, so the remaining 5% will be divided into 2 equal parts. So 2.5% will be above 2 standard deviation and 2.5% will be below 2 standard deviation.

As it is given that, the top 2.5% of the wage earners earn $18,000 or more, so 18,000 is 2 standard deviation away from the mean 10,000.

i.e $2\sigma=18000-10000=8000$