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4 years ago

Can someone help me solve for x+y=3 and x-y=1?

1 answer:

8 0

$\underline{+\left\{\begin{array}{ccc}x+y=3\\x-y=1\end{array}\right}\ \ \ \ |\text{add both sides of the equations}\\\\.\ \ \ \ 2x=4\ \ \ \ |:2\\.\ \ \ \ x=2\\\\\text{put the value of x to the first equation}\\\\2+y=3\ \ \ \ |-2\\\\y=1\\\\Answer:\ x=2,\ y=1\to(2,\ 1)$

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The following data represent the pH of rain for a random sample of 12 rain dates. A normal probability plot suggests the data co

pshichka [43]

Answer:

(1) The point estimate for the population mean is 4.925.

(2) Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

(3) Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

(4) As the level of confidence increases, the width of the interval increases.

Step-by-step explanation:

We are given that the following data represent the pH of rain for a random sample of 12 rain dates.

X = 5.20, 5.02, 4.87, 5.72, 4.57, 4.76, 4.99, 4.74, 4.56, 4.80, 5.19, 4.68.

(1) The point estimate for the population mean is given by;

Point estimate, $\bar X$ = $\frac{\sum X}{n}$

= $\frac{5.20+5.02+ 4.87+5.72+ 4.57+ 4.76+4.99+ 4.74+ 4.56+ 4.80+5.19+ 4.68}{12}$

= $\frac{59.1}{12}$ = 4.925

(2) Let $\mu$ = mean pH of rainwater

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean = 4.925

s = sample standard deviation = 0.33

n = sample of rain dates = 12

$\mu$ = population mean pH of rainwater

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.201 < $t_1_1$ < 2.201) = 0.95 {As the critical value of t at 11 degrees of

freedom are -2.201 & 2.201 with P = 2.5%}

P(-2.201 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.201) = 0.95

P( $-2.201 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.201 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.201 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.201 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.201 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.201 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $4.925-2.201 \times {\frac{0.33}{\sqrt{12} } }$ , $4.925+2.201 \times {\frac{0.33}{\sqrt{12} } }$ ]

= [4.715, 5.135]

Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

The interpretation of the above confidence interval is that we are 95% confident that the population mean pH of rainwater is between 4.715 & 5.135.

(3) Now, 99% confidence interval for the population mean, $\mu$ is ;

P(-3.106 < $t_1_1$ < 3.106) = 0.99 {As the critical value of t at 11 degrees of

freedom are -3.106 & 3.106 with P = 0.5%}

P(-3.106 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 3.106) = 0.99

P( $-3.106 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $3.106 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

P( $\bar X-3.106 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+3.106 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X-3.106 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+3.106 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $4.925-3.106 \times {\frac{0.33}{\sqrt{12} } }$ , $4.925+3.106 \times {\frac{0.33}{\sqrt{12} } }$ ]

= [4.629, 5.221]

Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

The interpretation of the above confidence interval is that we are 99% confident that the population mean pH of rainwater is between 4.629 & 5.221.

(4) As the level of confidence increases, the width of the interval increases as we can see above that the 99% confidence interval is wider as compared to the 95% confidence interval.

4 0

4 years ago

Don’t get it please helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp

UNO [17]

What do you don’t get

7 0

4 years ago

3 times the complement of an angle is 30 more than the supplement of the original angle. What is the measure of the angle?

taurus [48]

3 times the complement of an angle is 30 more than the supplement of the original angle.

so if the angle is x then its complement is 90-x & supplement is 180-x
so 3(90-x)=(180-x)+30
or 270-3x=210-x

or 3x-x=270-210
or 2x=60
or x=30 the original angle

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

3 0

4 years ago

Simplify 13 + 2 - 5 - 15 a -25 b -5 c 5

Neko [114]

Answer:

−5c5−15a−25b+10

Step-by-step explanation:

13+2−5−15a−25b−5c5

=13+2+−5+−15a+−25b+−5c5

Combine Like Terms:

=13+2+−5+−15a+−25b+−5c5

=(−5c5)+(−15a)+(−25b)+(13+2+−5)

=−5c5+−15a+−25b+10

Answer:

=−5c5−15a−25b+10

4 0

4 years ago

Read 2 more answers

Do parallel rays have to be coplanar?

Vikki [24]

No I belive they don’t have to be

5 0

4 years ago