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3 years ago

9x2 - 6xy Factorise Fully

1 answer:

4 0

Remember distributive property, but reverse it
ab-ac=a(b-c)
a is a common factor

find common factors
factor each
9x^2=3*3*x*x
6xy=2*3*x*y
common factor is 3*x or 3x

9x^2-6xy=3x(3x)-3x(2y)=3x(3x-2y)

factored form is 3x(3x-2y)

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A nature park has two ticket plans. With one plan, you pay a $24 yearly membership fee plus $8

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

6 0

3 years ago

Grading managers. Some companies "grade on a bell curve" to compare the performance of their managers and professional workers.

Monica [59]

Answer:

$\mu = 250, \sigma = 175.781$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the grades of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,\sigma)$

For this case we have two conditions given:

$P(X$

$P(X>475) = 0.1$ or equivalently $P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

So we can find a value from the normal standard distribution that accumulates 0.1 and 0.9 of the area in the left, for this case the two values are:

$z= -1.28, z=-1.28$

We can verify that P(Z<-1.28) =0.1[/tex] and P(Z<1.28) =0.9[/tex]

And then using the z score we have the following formulas:

$-1.28 = \frac{25 -\mu}{\sigma}$ (1)

$1.28 = \frac{475 -\mu}{\sigma}$ (2)

If we add equations (1) and (2) we got:

$\frac{25 -\mu}{\sigma} + \frac{475 -\mu}{\sigma} =0$

We can multiply both sides of the equation by $\sigma$ and we got:

$25+ 475 -2 \mu = 0$

$\mu = \frac{500}{2}= 250$

And then we can find the standard deviation for example from equation (1) and we got:

$\sigma = \frac{25-250}{-1.28}=175.781$

So then the answer would be:

$\mu = 250, \sigma = 175.781$

3 0

3 years ago

Find the measure of angle s? a. 90° b. 45° c. 30° d. 15°

babymother [125]

It looks like the 45

What I did was add the 60+30=90 then subtract from 180 and divided my 2 and got 45 hopes this helps!

8 0

2 years ago

Two angles are complementary. The value of one angle is twice as that of the other one. Find the individual angle

aleksandrvk [35]

Answer:

60°

Step-by-step explanation:

Complementary angles both add up to 90°. Therefore if one angle is twice the other, then if we divide 90 by 3 then we get 30. Two parts of 30 is 60 plus the other 30 and we get 90. The individual angle is 60°and the other is 30°

3 0

3 years ago

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 52% of all such batches contain no defect

koban [17]

Answer:

P ( B0 / D0 ) = 0.59877

P ( B1 / D0 ) = 0.25793

P ( B2 / D0 ) = 0.14329

Step-by-step explanation:

Given:

- 0 be the event that the batch has 0 defectives = (0 ) = 0.52

- 1 be the event that the batch has 1 defectives = (1 ) = 0.28

- 2 be the event that the batch has 2 defectives = (2 ) = 0.2

- Two components are selected

Find:

What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions?

(a) Neither tested component is defective.

Solution:

Let 0 be the event that neither selected component is defective.

- The event 0 can happen in three different ways:

(i) Our batch of 10 is perfect, and we get no defectives in our sample of two;

P(i) = P(B0) = 0.52

(ii) Our batch of 10 has 1 defective, but our sample of two misses them;

P ( no defect / B1 ) = P ( no defect ) / P ( B 1 )

= 9C2 / 10C2 = 0.8

P ( ii ) = 0.28*0.8 = 0.224

(iii) Our batch has 2 defective, but our sample misses them.

P ( no defect / B2 ) = P ( no defect ) / P ( B 2 )

= 8C2 / 10C2 = 56/90

P ( iii ) = 0.2*56/90 = 0.124444

- Then,

P(Do) = P(i) + P(ii) + P(iii)

P(Do) = 0.52 + 0.224 + 0.124444 = 977/1125

We use the general conditional probability formula:

P ( B0 / D0 ) = P ( B0 & D0 ) / P( D0 )

P ( B0 / D0 ) = 0.52*1125 / 977 = 0.59877

P ( B1 / D0 ) = P ( B1 & D0 ) / P( D0 )

P ( B1 / D0 ) = 0.224*1125 / 977 = 0.25793

P ( B2 / D0 ) = P ( B2 & D0 ) / P( D0 )

P ( B2 / D0 ) = 0.12444*1125 / 977 = 0.14329

5 0

3 years ago