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3 years ago

obtain the equation of two points passing of lines 4x-3y-1=0 and 2x-3y+3=0 and equally inclined to the axes

Mathematics

1 answer:

klasskru [66]3 years ago

8 0

Answer:By 8(4)P.5, the slope of the line equally inclined to axes is tan(±45

)=±1. Hence by P+λQ=0,

5λ+3

2λ+4

=±1

⇒λ=

,−1. Putting for λ, the two lines are

x−y=0,x+y−2=0.

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When using "mean" does it mean average of something if not please explain, I'm a bit confused.

lesya [120]

Mean the the total of all values, divided by the number of values

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3 years ago

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The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,00

ss7ja [257]

Answer:

The test statistics is $z = -1$

Step-by-step explanation:

From the question we are told that

The sample size is n = 100

The null hypothesis is $H_o : \mu = \$30000$

The alternative hypothesis is $H_a : \mu < \$ 30000$

The sample mean is $\= x = \$29,750$

The standard deviation is $\sigma = \$2,500$

The level of significance is $\alpha =0.05$

Generally the test statistics is mathematically represented as

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

=> $z = \frac{29750 - 30000 }{ \frac{ 2500}{ \sqrt{100} } }$

=> $z = -1$

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3 years ago

Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee a

rusak2 [61]

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that $\sigma = 2$

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when $M = 0.5$ . So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.5 = 1.96\frac{2}{\sqrt{n}}$

$0.5\sqrt{n} = 2*1.96$

Dividing both sides by 0.5

$\sqrt{n} = 4*1.96$

$(\sqrt{n})^2 = (4*1.96)^2$

$n = 61.5$

Rounding up

We would have to take a sample of 62 to achieve this result.

8 0

3 years ago

What is the area of this polygon?

ra1l [238]

Step 1) Draw a line from point F to point S. A rectangle forms (rectangle FSCW)

Step 2) Find the area of this rectangle. The area is 18 square units because it is 2 units high and 9 units across (9*2 = 18). You can count out the spaces or you can note how we go from x = -4 to x = 5 so subtracting the values gives -4-5 = -9 which has an absolute value of 9.

Step 3) Find the area of triangle FSN. The base is 9 units and the height is 6 units (count out the spaces or subtract y values). So the area is A = b*h/2 = 9*6/2 = 54/2 = 27

Step 4) Add up the area of the rectangle to the area of the triangle: 18+27 = 45

Final Answer: 45 square units

note: another way to find the answer is to find the area of rectangle WABC where point A is at (-4,4) and point B is at (5,4). Then subtract off the triangular areas of AFN and BNS

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EXTRA POINTS :) what is the value of x??

vlada-n [284]

Answer:

x = 17

Step-by-step explanation:

corresponding interior angles are supplementary, meaning they have to add up to 180 degrees so

6x + 8 + 4x + 2 = 180° then combine like terms ( 6x and 4x, 8 and 2 )

10x + 10 = 180 subtract 10 from both sides

-10 -10

10x = 170 divide each side by 10

/10 /10

x = 17

8 0

3 years ago

obtain the equation of two points passing of lines 4x-3y-1=0 and 2x-3y+3=0 and equally inclined to the axes​

obtain the equation of two points passing of lines 4x-3y-1=0 and 2x-3y+3=0 and equally inclined to the axes