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3 years ago

6x+4y=22 2x-y=1 solve by elimination

Mathematics

1 answer:

liq [111]3 years ago

3 0

6x + 4y = 22
+
2x - y = 1
____________
8x + 3y = 23

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3 years ago

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Find an equation of the circle whose diameter has endpoints (1,-4) and (-3,6).

MAVERICK [17]

Answer:

$(x+1)^2+(y-1)^2=58$

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To find the equation of this circle, we must know the center and the radius.

We can find the radius by dividing the value of the distance formula by 2 (since $r=\frac{d}{2}$ ):

$d=\sqrt{(-3-1)^2+(6-(-4))^2}=\sqrt{116}\\r=d/2=\frac{\sqrt{116}}{2}$

We can then find the center of the circle by averaging the coordinates:

$\frac{1+(-3)}{2}=-1$

$\frac{-4+6}{2}=1$

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4 years ago

A manufacturer claims that fewer than 6% of its fax machines are defective. to test this claim, he selects a random sample of 97

AfilCa [17]

Let P be the population proportion, p be the sample proportion, n be the sample size.

A manufacturer claims that fewer than 6% of its fax machines are defective. It means P=0.06

Sample size n=97 and sample proportion p=0.05

The hypothesis to be tested is

H0: P ≥ 0.06 V/s Ha: P < 0.06

Here the hypothesis for testing population proportion we use z test statistics. Z test statistics is give by

Z = $\frac{p -p_{0}}{\sqrt{p_{0}(1-p_{0})/n}}$

Where p =sample proportion = 0.05

p0 = hypothesized proportion value =0.06

Using given values into test statistics we get

Z = $\frac{0.05 -0.06}{\sqrt{0.06(1-0.06)/97}}$

Z = -0.41

The p-value for left tailed alternative hypothesis is given by

P-value = P(z < z cal)

where zcal = Z test statistics value

Here zcal = -0.41

P-value = P(Z < -0.41)

Using z score table to find probability below z=-0.41

P-value = 0.3409

P-value for testing the given claim is 0.3409

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4 years ago