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4 years ago

Please solve and explain to me the steps

Mathematics

1 answer:

Gnom [1K]4 years ago

6 0

√(75m^3b

Whenever you are looking to simplify a radical, you want to see what the prime factorization of the elements under the radical...

√(3*5*5*m*m*m*b) now you can move out the squared terms (we move out all of the terms that appear twice in this case(

5m√(3mb)

You might be interested in

A professor knows that her statistics students' final exam scores have a mean of 79 and a standard deviation of 11.3. In his cla

OverLord2011 [107]

For each student, there are only two possible outcomes. Either they score an A, or they do not. The probability of a student scoring an A is independent of any other student, which means that the binomial probability distribution is used to solve this question.

Additionally, to find the proportion of students who scored an A, the normal distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Proportion of students that scored an A:

Scores have a mean of 79 and a standard deviation of 11.3, which means that $\mu = 79, \sigma = 11.3$

Scores of 90 or higher are graded an A, which means that the proportion is 1 subtracted by the p-value of Z when X = 90, so:

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

$Z = \frac{90 - 79}{11.3}$

$Z = 0.97$

$Z = 0.97$ has a p-value of 0.8340.

1 - 0.8340 = 0.166

The proportion of students that scored an A is 0.166.

Probability that 6 students or more will score an "A" on the final exam:

Binomial distribution.

22 students, which means that $n = 22$

The proportion of students that scored an A is 0.166, which means that $p = 0.166$

The probability is:

$P(X \geq 6) = 1 - P(X < 6)$

In which

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

Then

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

$P(X = 0) = C_{22,0}.(0.166)^{0}.(0.834)^{22} = 0.0184$

$P(X = 1) = C_{22,1}.(0.166)^{1}.(0.834)^{21} = 0.0807$

$P(X = 2) = C_{22,2}.(0.166)^{2}.(0.834)^{20} = 0.1687$

$P(X = 3) = C_{22,3}.(0.166)^{3}.(0.834)^{19} = 0.2239$

$P(X = 4) = C_{22,4}.(0.166)^{4}.(0.834)^{18} = 0.2117$

$P(X = 5) = C_{22,5}.(0.166)^{5}.(0.834)^{17} = 0.1517$

Then

$P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0184 + 0.0807 + 0.1687 + 0.2239 + 0.2117 + 0.1517 = 0.8551$

$P(X \geq 6) = 1 - P(X < 6) = 1 - 0.8551 = 0.1449$

Thus

0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.

For a problem that used the normal distribution, you can check brainly.com/question/15181104, and for a problem that used the binomial distribution, you can check brainly.com/question/15557838

3 0

3 years ago

A student thinks that the regular pentagon in the diagram

Nadya [2.5K]

Answer:

Step-by-step explanation:

The student must have thought that every single arrowhead is a line of symmetry, so since there are 10 arrowheads, there must be 10 lines of symmetry. This is incorrect because if you look closely at the diagram, each line has 2 arrowheads, so the student is overcounting by a factor of 2. They should have just counted the number of lines, not arrowheads. Therefore, there must be 10/2 = 5 lines of symmetry, not 10. Hope this helps!

4 0

3 years ago

At a certain time of day, the angle of elevation of the sun is 30°. A tree has a shadow that is 25 feet long. Find the height of

Sergio039 [100]

The is 750 Because 30
X25
750
You're welcome

4 0

4 years ago

Olive sold $6,000 worth of tickets to the game and spent $25 per person on catering. If she made a profit of $4,000, how many pe

erma4kov [3.2K]

$6,000 - $4,000 = $2,000
$2,000/$25 = 80

Therefore, 80 people attended the game

8 0

3 years ago

Pls help me answer this question thx

nadya68 [22]

Answer:

$\large\boxed{\dfrac{1}{115}}$

Step-by-step explanation:

$\text{Use}\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}\\\\(a\cdot b)^n=a^n\cdot b^n\\\\a^{-1}=\dfrac{1}{a}\\--------------------------\\\\\dfrac{5^{2n-1}-4(25^{n-1})}{(5^n\cdot2)^2+3(5^{2n-1})}=\dfrac{5^{2n}\cdot5^{-1}-4\left[(5^2)^n\cdot25^{-1}\right]}{(5^n)^2\cdot2^2+3\left[(5^2)^n\cdot5^{-1}\right]}$

$=\dfrac{5^{2n}\cdot\frac{1}{5}-4\left(5^{2n}\cdot\frac{1}{25}\right)}{5^{2n}\cdot4+3\left(5^{2n}\cdot\frac{1}{5}\right)}=\dfrac{5^{2n}\left(\frac{1}{5}-\frac{4}{25}\right)}{5^{2n}\left(4+\frac{3}{5}\right)}=\dfrac{\frac{5}{25}-\frac{4}{25}}{4\frac{3}{5}}=\dfrac{1}{25}:\left(\dfrac{4\cdot5+3}{5}\right)\\\\=\dfrac{1}{25}\cdot\dfrac{5}{23}=\dfrac{1}{5}\cdot\dfrac{1}{23}=\dfrac{1}{115}$

8 0

3 years ago