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Harlamova29_29 [7]
2 years ago
10

5a^2 -25b^2..Factorise fully​

Mathematics
2 answers:
Pani-rosa [81]2 years ago
8 0

\mathbb  \: \huge  \fbox {\blue{{ANSWER}}} \\  \\   \: \: \: \:\: \: \sf \:  \implies \: \:  \green {\fbox {5(a {}^{2}  - 5b {}^{2} )} }

→ Given equation : 5a² – 25b²

Apply formula for this : a²–b² = (a+b) (a-b)

5a² - 25b² = 5 • (a² - 5b²)

Factoring: a²- 5b²

Theory : A difference of two perfect squares, A² - B² can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 5 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

\: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \rightarrow \fbox{ \pink{5(a {}^{2}  - 5b {}^{2} )}}

djyliett [7]2 years ago
5 0

Answer:

= 5(a^2 - 5b^2)

Step-by-step explanation:

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Leakage from underground gasoline tanks at service stations can damage the environment. It is estimated that 25% of these tanks
Gnesinka [82]

Answer:

a) 3.75

b) 23.61% probability that fewer than 3 tanks will be found to be leaking

c) 0% the probability that at least 600 of these tanks are leaking

Step-by-step explanation:

For each tank there are only two possible outcomes. EIther they leak, or they do not. The probability of a tank leaking is independent of other tanks. So we use the binomial probability distribution to solve this question.

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 C_{n,x} 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.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

To solve question c), i am going to approximate the binomial distribution to the normal.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

It is estimated that 25% of these tanks leak.

This means that p = 0.25

15 tanks chosen at random

This means that n = 15

a.What is the expected number of leaking tanks in such samples of 15?

E(X) = np = 15*0.25 = 3.75

b.What is the probability that fewer than 3 tanks will be found to be leaking?

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

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

P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134

P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668

P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0134 + 0.0668 + 0.1559 = 0.2361

23.61% probability that fewer than 3 tanks will be found to be leaking

c.Now you do a larger study, examining a random sample of 2000 tanks nationally. What is the probability that at least 600 of these tanks are leaking?

Now we have n = 2000. So

\mu = E(X) = np = 2000*0.25 = 500

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{2000*0.25*0.75} = 19.36

This probability is 1 subtracted by the pvalue of Z when X = 600. So

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

Z = \frac{600 - 500}{19.36}

Z = 5.16

Z = 5.16 has a pvalue of 0.

0% the probability that at least 600 of these tanks are leaking

4 0
3 years ago
Number 4 I have no idea how to do.
natta225 [31]

Volume is a three-dimensional scalar quantity. The cost of the glass is $1312.24.

<h3>What is volume?</h3>

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the colony must be able to take a volume of 200,000 cubic meters, therefore, the diameter of the hemisphere will be,

The volume of Hemisphere = (2/3)πr³

200,000 = (2/3) × π × R³

R = 45.7

The area of the base of the hemisphere is,

Area of the base = πR² = π×(45.7)  = 6561.185 meters²

Given the cost of glass is $0.20 per square meter, therefore, the cost of the glass of the base will be,

Cost of glass = 6561.185 × 0.20 = $1312.24

Hence, the cost of the glass is $1312.24.

Learn more about Volume:

brainly.com/question/13338592

#SPJ1

3 0
2 years ago
Two 5-year girls, Alyse and Jocelyn, have been training to run a 1-mile race. Alyse's 1 mile time A is approximately Normally di
tatyana61 [14]

Answer:

1.7 × 10⁻⁴

Step-by-step explanation:

The question relates to a two sample z-test for the comparison between the means of the two samples  

The null hypothesis is H₀:  μ₁ ≤ μ₂

The alternative hypothesis is Hₐ: μ₁ > μ₂

z=\dfrac{(\bar{x}_1-\bar{x}_2)-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}

Where;

\bar {x}_1 = 13.5

\bar {x}_2 = 12

σ₁ = 2.5

σ₂ = 1.5

We set our α level at 0.05

Therefore, our critical z = ± 1.96

For n₁ = n₂ = 23, we have;

z=\dfrac{(13.5-12)-(0)}{\sqrt{\dfrac{2.5^{2} }{23}-\dfrac{1.5^{2}}{23}}} = 3.5969

We reject the null hypothesis at α = 0.05, as our z-value, 3.5969 is larger than the critical z, 1.96 or mathematically, since 3.5969 > 1.96

Therefore, there is enough statistical evidence to suggest that Alyse time is larger than Jocelyn in a 1 mile race on a randomly select day and the probability that Alyse has a larger time than Jocelyn is 0.99983

Therefore;

The probability that Alyse has a smaller time than Jocelyn is 1 - 0.99983 = 0.00017 = 1.7 × 10⁻⁴.

8 0
3 years ago
Complete the factorization of 3r? – 10x + 8.
Sveta_85 [38]
Would you do inverse operation ?
5 0
3 years ago
Please help
poizon [28]

Answer:

D

Step-by-step explanation:

4 people = 15 days

1 people = 15/4 = 3.75

so, 6 people = 3.75 × 6

= 22.5

7 0
2 years ago
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