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2 years ago

Rationalize the denominator and simplify. 5/4-√3

1 answer:

4 0

I assume the denominator is (4-√3)
Multiple both top and bottom by (4+√3)
[5(4+√3)]/[(4-√3)(4+√3)]
=[20+5√3]/[4²-(√3)²]
=[20+5√3]/13

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Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.

ycow [4]

This involves quite a lot of arithmetic to do manually.

The first thing you do is to make the first number in row 2 = to 0.

This is done by R2 = -3/2 R1 + R2

so the matrix becomes

( 2 1 1) ( -3 )

( 0 -13/2 3/2) (1/2 )

(5 -1 2) (-2)

Next step is to make the 5 in row 5 = 0

then the -1 must become zero

You aim for the form

( 1 0 0) (x)

(0 1 0) (y)

(0 0 1) ( z)

x , y and z will be the required solutions.

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3 years ago

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Someone?! answer please

Sonbull [250]

The answer is "$94."

If all 6 friends spent $420 on kayaks, and $144 on food, then they spent $564 in total. Divide $564 by 6 people to see how much each person payed.

420+144=564
564÷6=94

8 0

2 years ago

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What is the value of Z?

sukhopar [10]

Answer:

Step-by-step explanation:

Both x and y are inscribed angles. The value of an inscribed angle is half the measure of its intercepted arc. This means that x has a value of 33°, and y has a value of 48°. That means that, according to the triangle angle sum theorem, the third angle has to equal 180 - 33 - 48 = 99°.

This angle is vertical with angle z, so angle z also equals 99°

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3 years ago

Suppose that a local TV station conducts a survey of a random sample of 120 registered voters in order to predict the winner of

forsale [732]

Answer:

a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.

So 120 - 62 = 58 favored the Republican candidate, so:

$n = 120, \pi = \frac{58}{120} = 0.4833$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a p-value of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001$

The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.

The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

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2 years ago

Here are 3 number 1 2 4 what it the 4 and 5 terms of the sentance

zzz [600]

‘1 2 4 8 16’
my thinking is the numbers are squared.

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2 years ago

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