Pls help Will give brainiest

GHIJ is a parallelogram. find value of x and y. You need to show your work to earn full credit.

Anastaziya [24]

Answer:x=5 and y=8

Step-by-step explanation:

6 0

2 years ago

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

Travka [436]

Answer:

a) Point estimate of the population mean = 4.883

b) B.There is 95% confidence that the population mean pH of rain water is between 4.646 and 5.120.

c) C.There is 99% confidence that the population mean pH of rain water is between 4.549 and 5.217.

d) As the level of confidence increases, the width of the interval increases.

This makes sense since the margin of error increases as well.

Step-by-step explanation:

We have a sample for the pH of rain.

The mean of the sample is:

$M=\dfrac{1}{12}\sum_{i=1}^{12}(5.3+5.72+4.38+4.8+5.02+...+4.56+4.68)\\\\\\ M=\dfrac{58.59}{12}=4.883$

The sample standard deviation is:

$s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{12}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{11}\cdot [(5.3-4.883)^2+(5.72-4.883)^2+...+(4.68-4.883)^2]}\\\\\\$

$s=\sqrt{\dfrac{1}{11}\cdot [(0.17)+...+(0.1)+(0.04)]}\\\\\\s=\sqrt{\dfrac{1.526625}{11}}=\sqrt{0.1387841}\\\\\\s=0.373$

a) The point estimation for the population mean is the sample mean and has a value of 4.883.

b) We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=4.883.

The sample size is N=12.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.373}{\sqrt{12}}=\dfrac{0.373}{3.464}=0.108$

The t-value for a 95% confidence interval is t=2.201.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=2.201 \cdot 0.108=0.237$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 4.883-0.237=4.646\\\\UL=M+t \cdot s_M = 4.883+0.237=5.12$

The 95% confidence interval for the mean is (4.646, 5.120).

B.There is 95% confidence that the population mean pH of rain water is between 4.646 and 5.120.

c) We have to calculate a 99% confidence interval for the mean.

The t-value for a 99% confidence interval is t=3.106.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=3.106 \cdot 0.108=0.334$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 4.883-0.334=4.549\\\\UL=M+t \cdot s_M = 4.883+0.334=5.217$

The 99% confidence interval for the mean is (4.549, 5.217).

C.There is 99% confidence that the population mean pH of rain water is between 4.549 and 5.217.

d) When the confidence level is increased, the width also increases as it has to include more possible values for the true mean of the population.

As the level of confidence increases, the width of the interval increases.

This makes sense since the margin of error increases as well.

5 0

2 years ago

Student asked her maths teacher if he would reveal his age. Seeing an opportunity to test his student’s mental skills, the teach

bixtya [17]

Answer:

65 years old.

Step-by-step explanation:

If her age is 10 t + u (where t is the tens digit and u is the units digit) then reversing the digits gives 10 u + t. and the sum is 11 t + 11 u, which is a multiple of 11. We know this has to be a square number. Ong Xing Cong from Singapore sent in the following solution.

11 t + 11 u = 11 x 11 = 121

t + u = 11

65 - 56 = 3 x 3

She is 65 years old.

The best solutions do not need trial and improvement methods and they show that the answer or answers found are the only possible answers. Knowing the digits add up to 11 ( t + u = 11), you can also use (10 t + u ) - (10 u + t ) = 9 t - 9 u = 9( t - u ) As this is also a square number you know ( t - u ) is either 1, 4, or 9. The solutions for 4 and 9 don't give whole number values for t in 0 t 9.

7 0

1 year ago

Solve the triangle. A=63 a=8.6 b=11.1

VARVARA [1.3K]

I can help it all =82.1

7 0

2 years ago

Please this is a test it needs to be done correctly and fast!!!!

Lady bird [3.3K]

Answer:

See below.

Step-by-step explanation:

The answer would be (-7,1).

-hope it helps

7 0

1 year ago