Find the ordered pair that is a member of both x = -5y + 37 and x = -6y + 43

Answers

Answer 1

Answer:

(7,6)

Step-by-step explanation:

An ordered pair is a member of both equations if it satisfies both equations. In other words, we need to find values of x and y that make both equations true.

We can start by setting the two equations equal to each other, since they both represent the same variable, x. This gives us the equation -5y + 37 = -6y + 43. We can then solve this equation by subtracting -6y from both sides, which yields -5y + 37 - (-6y) = -6y + 43 - (-6y), or -5y - (-6y) + 37 = 43. This simplifies to -y + 37 = 43, or y = 43 - 37 = <<43-37=6>>6.

Now that we have found the value of y that satisfies both equations, we can plug this value into either equation to find the corresponding value of x. For example, we can plug y = 6 into the equation x = -5y + 37 to find that x = -5 * 6 + 37 = -30 + 37 = <<-30+37=7>>7. Therefore, the ordered pair that is a member of both equations is (7, 6).

Related Questions

Claim: all natural numbers are either even or odd. Proof: By induction. Base case:0 is even, since 0 = 2.0. Now suppose that n - 1 is either even or odd, and we must show that n is either even or odd. Case 1: If n - 1 is even, then n - 1 = 2k for some k, so n = 2k + 1, showing n must be odd. Case 2: If n - 1 is odd, thenn - 1 = 2k +1 for some k, so n = 2k + 2 = 2(k+1), showing n must be even. Is this proof correct?
• Yes • No

Answers

No. The proof is wrong.

Here we are asked to prove all Natural numbers are either even or odd.

Natural numbers start from 1 to infinity.

Hence to prove by mathematical induction, we need to take the base case to be n = 1.

here, 1 = 2X0 + 1, therefore 1 is odd

Then we need to assume that for any integer m < n, m is either even or odd.

Now n > 1

Therefore,

n -1 > 0

Hence n - 1 will be a natural number.

Hence by our earlier assumption where any number smaller than is either even or odd

n - 1 has to be either even or odd.

case 1

here n - 1 is odd

if n - 1 is odd then

n-1 + 1 is a sum of two odd numbers, hence n is even

Case 2- If n - 1 is even

then, n-1 + 1 is a sum of an even and n odd number hence n is odd

Therefore n will either be even or odd.

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Frosty the Snowman thought he could last in a greenhouse for 2 hours before melting. Unfortunately, it only took him 1 12
hours to melt.

Percent error is a way to describe error, expressed as a percentage of the actual amount. What is the percentage error in this situation?

Answers

The percentage error in this situation will be 33%.

How to calculate the percentage?

It's important to note that Percent error is a way to describe error, expressed as a percentage of the actual amount.

Since Frosty the Snowman thought he could last in a greenhouse for 2 hours before melting but it only took him 1 1/2 hours to melt. The percentage error in this situation will be:

= (2 - 1 1/2) / 1 1/2 × 100

= 1/2 ÷ 1 1/2 × 100

= 1/3 × 100

= 33.33%

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The least expensive
buttons cost
$0.28 each. Yellow bought all of
the buttons she could for $1.40 and
wore them proudly.

Answers

The number of buttons that she can wear proudly will be 5.

What are the ratio and proportion?

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another.

As per the given,

Cost of one button = $0.28

The cost of buttons that she can wear = $1.40

A number of buttons = $1.40/$0.28 = 5

Hence "She will be able to wear five buttons with pride.".

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An evergreen nursery usually sells certain shrub after 6 years of growth and shaping: The growth rate during those 6 years is approximated by dh/dt = 1.2t + 2, where t is the time in years and h is the height in centimeters. The seedlings are 15 centimeters tall when planted (t = 0). (a) Find the height after years h(t) (b) How tall are the shrubs when they are sold? cm

Answers

(a) After t years, the height is 18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

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Krystal is considering job offers from two companies. Company A offered her a starting salary of $45,000 with a $2100 raise at the end of each year. Company B offered her a starting salary of $45,000 with a 4.2% raise at the end of each year. Let f(t) represent Carissa's salary at Company At years after accepting a position at Company A, and let g(t) represent Carissa's salary at Company B t years after accepting a position at Company B. a. Find a function formula for f. b. Find a function formula for g. c. If Carissa was expecting to work for 5 years before going back to school, which company do you think she should work for? Use your functions to justify your answer. I d. If Carissa was expecting to work for 10 years before going back to school, which company do you think she should work for? Use your functions to justify your answer.

Answers

The function formula for f and g are f(t) = $45000+$2100t and g(t) = $45000(1+0.042) to the power of t when Krystal is weighing two job offers from various organizations.

Given that,

Krystal is weighing two job offers from various organizations. She received a $45,000 beginning salary from Company A, with annual raises of $2100. Company B gave her a $45,000 beginning salary with an annual rise of 4.2%. Let f(t) stand for Carissa's pay at the company. Let g(t) stand in for Carissa's pay at Company B at Years after Accepting a Position at Company B, and at Years after Accepting a Position at Company A.

We have to find the function formula for f and g.

We know that,

Company A has

f(t) = $45000+$2100t

And

Company B has

g(t) = $45000(1+0.042) to the power of t.

Therefore, The function formula for f and g are f(t) = $45000+$2100t and g(t) = $45000(1+0.042) to the power of t when Krystal is weighing two job offers from various organizations.

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Hey WRLD... 999

Match each polynomial with its factorization. Type the number of the corresponding polynomial on the line of it’s factorization on the right.

1.
x2 – 2x – 48
_____ (x + 2)(9 – x)

2.
-3x2 + 14x - 8
____ (2 – 3x)(x – 4)

3.
X2 – 10x – 25
_____ (x + 6) (x – 8)

4.
-x2+7x+18
____ 3(x – 7) (x + 7)

5.
X4 – 16
_____ (x – 5)2

6.
3x2 – 147
_____ ( x – 2)( x + 2)( x2 + 4)

Answers

Each equation is expressed and mentioned in its factorized form are given above.

What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given are the polynomials along with their factorized forms.

The polynomials along with their correct factorized forms are as follows -

x² - 2x - 48 → (x + 6) (x – 8)-3x² + 14x - 8 → (2 – 3x)(x – 4)x² – 10x + 25 → (x - 5)²- x² + 7x + 18 → (x + 2)(9 – x)x⁴ - 16 → (x – 2)(x + 2)(x² + 4)3x² – 147 → 3(x – 7) (x + 7)

Therefore, each equation is expressed and mentioned in its factorized form are given above.

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Read the following prompt and type your response in the space provided.
Kim's teacher has marked this problem as one to recheck, but Kim cannot determine what she has done incorrectly. Identify Kim's error and write a correct solution.

Six less than 2 times a number is 50. What is the number?

2x – 6 = 50 (line 1)

2x – 6 – 6 = 50 – 6 (line 2)

2x = 44 (line 3)

2x ÷ 2 = 44 ÷ 2 (line 4)

x = 22 (line 5)

Answers

Kim’s error was in line 2 when she subtracted 6 instead of adding it. To cancel out -6, you would have to ADD 6, not subtract. So doing what Kim did would actually just make the problem 2x - 12 = 44, not have gotten rid of the -6.
If Kim had added 6 instead, she would’ve gotten
2x - 6 + 6 = 50 + 6 in line 2
2x = 56 in line 3
2x / 2 = 56 / 2 in line 4
x = 28 in line 5

sylvia went on a trip. The number of shirts she packed was 2 fewer than twice the number of pants she packed. The total number of pairs of pants and shirts was 16

Answers

Answer:

She packed 6 pairs of pants and 10 shirts.

Step-by-step explanation:

Say the number of pants is x. Then, the number of pants is 2x-2. Now you have the equation:

x+ (2x-2)=16

Solving this equation gives x=6.

Therefore, she packed 6 pairs of pants and 10 shirts.

The function g(x) is graphed below. According to the graph, what is the
value of g(4)?

Answers

Answer:

Step-by-step explanation:

g(4) tells us that we need to look for the y coordinate when g(x) reaches 4 on the x axis.

6 is the answer

HII EVERYONE can you help me and this problem TYSM

Answers

10) There is no solution to given the simultaneous equations

11) There is no solution to given the simultaneous equations

15) There is no solution to given the simultaneous equations

How to solve the system of simultaneous equations?

10) We are given the simultaneous equations as;

y = -6x - 8

y = -6x + 8

Plug -6x + 8 for y in eq 1 to get;

-6x + 8 = -6x - 8

Since the coefficient of the variable on both sides are equal, then there is no solution to the simultaneous equation.

11) We are given the simultaneous equations as;

3x - y = 6

-3x + y = -6

Add eq 1 to eq 2 to get;

0 = 0

Thus, there is no solution to the simultaneous linear equations.

12) We are given the simultaneous equations as;

9x - 15y = 24 ------(1)

6x - 10y = -16 ------(2)

Multiply eq 2 by 1.5 and eq 1 by 1 to get;

9x - 15y = 24 ------(3)

9x - 15y = -24 -----(4)

When we subtract eq 3 from eq 4, we get;

0 = -48

Thus, no solution exists.

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Diana
averages 6 mph walking
to school. Averaging 35 mph on
the way back home by car, she
takes 3/4 hour less time.
How far is the school
from her home?

Answers

The school is 5.43 miles from Diana's house. This is evaluated by using the speed-distance-time relationship.

What is the relation between the speed-distance-time?

The ratio of distance to time gives speed to an object.

I.e., S = D/T or D = ST ot T = D/S

Calculation:

It is given that,

Diana walks to her school at a speed of 6 mph.

So, the time taken for her to walk is t1 = d/6 hours

Diana returns home by car at a speed of 35 mph.

So, the time taken for her to return by car is t2 = d/35 hours

But it is given that, she takes 3/4 hours less time for returning by car.

Thus, we can write t2 = t1 - 3/4

⇒ d/35 = d/6 - 3/4

⇒ 3/4 = d/6 - d/35 = d(1/6 - 1/35)

⇒ 3/4 = d(29/210)

⇒ d = (3 × 210)/(4 × 29) = 5.431 miles

On rounding the obtained value to the nearest hundredths is 5.43 miles.

Thus, the distance between Diana's home and her school is 5.43 miles.

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The given point is reflected across the line indicated. Find the coordinates of the image.
R across y = -2
If the given point R is reflected across the line y = -2, the image is
(Type an ordered pair.)

Answers

When a point is reflected across a line, the resulting image is always the same distance from the line as the original point, but on the opposite side. Since the original point R is above the line y = -2, the image will be below the line.

To find the coordinates of the image, we can use the fact that the y-coordinate of the image will be 2 units below the y-coordinate of the original point R. If the original point R has coordinates (x,y), then the image will have coordinates (x, y-2).

Therefore, the coordinates of the image of point R reflected across the line y = -2 are (x, y-2).

Arianys invested $61,000 in an account paying an interest rate of 7% compounded
continuously. Yusuf invested $61,000 in an account paying an interest rate of 7%
compounded monthly. After 14 years, how much more money would Yusuf have in
his account than Arianys, to the nearest dollar?

Answers

Given the above information the amount Yusuf would have more in his account than Arianys is $9,929,539.57

How to calculate compound interest?

You should be aware that compound interest is sum of money that accrues on the capital over a stated period of time.

The given parameters are:

Arianys investment = $61,000, interest rate 7% compounded continuously

Yusufs investment = $61,000, rate 7% compounded monthly

number of years each 14 years

Arianys investment

Compound interest = [tex]P(1+r)^{t}[/tex] - 1

Applying the figures we have

CI= 61000(1+0.07)¹⁴ - 1

=61000(1.07)¹⁴ -1

CI=$96,290.58

For Yusuf investment

CI=[tex]P(1+\frac{r}{n})^{nt} - 1[/tex]

Applying the figures we have

Ci=61000(1+0.0121)²⁹⁶⁸ -1

Compound Interest = 61000(1.0058)¹⁶⁸ - 1

Simplifying this we have

61000(164.36)

CI=$10,025,830.12

Therefore the amount in Yusufs account more than Arianys account is $(10,025,830.12-96,290.58)

Amount = $9,929,539.57

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In a class of 25 students, there were 13 math majors, 10 were computer science majors, and 6 were dual majors in both.

How many were in math only?

How many were not majoring in computer science?

How many were not math or computer science?

Answers

Answer:

How many were in math only?7

How many were not majoring in computer science?9

How many were not math or computer science?2

Step-by-step explanation:

Total students 25

-math major 13

-Science major 10

_______________

2 not majoring in math or CS majors

math major 13 -6 dual majors = 7 major in math only

math major 7+ not math or CS 2 = 9 not majoring in CS

Write the
slope-intercept form of the equation of
the line that passes through the point (1, 2) and
has the slope of 6.

Answers

2=6x1+b this is slope intercept form

An article reported the following frequencies with which ethnic characters appeared in recorded commercials that aired on Philadelphia television stations. Ethnicity: African, American, Asian, Caucasian, Hispanic Frequency: 69, 11, 330, 8, In a recent census, the proportions for these four ethnic groups are 0.177.0.020, 0.734, and 0.069, respectively. Does the data suggest that the proportions in commercials are different from the census proportions? Carry out a test of appropriate hypotheses using a significance level of 0.01. (Let P, PPs, and be the population proportions of the four ethnic groups (African American, Asian, Caucasian, and Hispanic respectively) appearing in commercials on Philadelphia television stations.) State the appropriate hypotheses. o H0: P1 = 0.165, P2 = 0.026, P3 = 0.789, P4 = 0.019 Ha: at least one P1 ≠ P10o H0: P1 = 0.069, P2 = 0.011, P3 = 0.330, P4 = 0. 008Ha: at least one P1 ≠ P10o H0: P1 = 0. 177, P2 = 0.020, P3 = 0.734, P4 = 0.069Ha: at least one P1 ≠ P10o H0: P1 = P2 = P3 = P4 = 0.250Ha at least one p1 ≠ 0.25 Calculate the test statistic (Round your answer to two decimal places.)x^2 = ______

Answers

When comparing the proportions of ethnic groups represented in television commercials on Philadelphia stations to census data, we can use a chi-squared test to see if there is a difference.

Suitable hypotheses for this test include the following: H0: P1 = 0.165, P2 = 0.026, P3 = 0.789, and P4 = 0.019 Ha: at least one P1 to P10, where P1, P2, P3, and P4 represent the proportions of the four main ethnic groups—African, Asian, Caucasian, and Hispanic—in the population.

The test statistic cannot be calculated until we get the predicted frequencies for each group under the null hypothesis. Given that N is the total number of observations and E I is the expected frequency for group I, E I = N * P I provides the expected frequency for each group.

the population percentage for group I is P i.

These equations allow us to determine the anticipated frequencies in the following ways:

E 1 = 69 * 0.165 = 11.485

E 2 = 11 * 0.026 = 0.286

E 3 = 330 * 0.789 = 261.67

E 4 = 8 * 0.019 = 0.152

After that, the chi-squared test statistic is calculated as follows: x2 = ∑_(i=1)4 [(O i - E i)2 / E i], where O i is the observed frequency for group I and E i is the anticipated frequency for group i.

The numbers for the observed and anticipated frequencies are substituted to produce the following equation: x2 = (69 - 11.485)2 / 11.485 + (11 - 0.286)2 / 0.286 + (330 - 261.67)2 / 261.67 + (8 - 0.152)2 / 0.152

= 57.015^2

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An organization needs to reach out to a specific target audience, and has decided that it wants to use social media advertising to do so. It wants to buy specific keywords to accurately target the audience who would want to see these ads. The aim is to get a high effective exposure rate and engagement rate without invading consumer privacy. Which of the following advertising revenue models would best suit the organizations' needs? a. Bidding for ad words b. Pay-per-click c. I-Traffic Index d. Pop-under ads e. Bidding for ad space

Answers

The advertising revenue model that would best suit the organization needs is Bidding for ad words.

Given that,

A company has made the decision to employ social media advertising to connect with a certain target population in order to accomplish this. To precisely target the demographic that would be interested in seeing these ads, it wants to purchase a set of keywords. The objective is to increase consumer involvement and exposure rates without violating their privacy.

The Organization investing to buy specific keywords for advertising, when someone searches for some words in a social media search engine, the search engine queries it's users looking for the keyword matches in it's ad group thus displaying the most relevant ad aiming for more exposure.

Therefore, bidding for ad words is the advertising income strategy that would best meet the organization's needs.

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What number is 0.1 less than 15.2?

Answers

Answer:

15.1

Step-by-step explanation:

Researchers in the Hopkins Forest (see Problem 7-16 from) also count the number of maple trees (genus
acer) in plots throughout the forest. The following is a histogram of the number of live maples in 1002 plots
sampled over the past 20 years. The average number of maples per plot was 19.86 trees with a standard
deviation of 23.65 trees.
a). If we took the mean of a sample of eight plots, what would be the standard error of the
mean?
b). Using the central limit theorem, what is the probability that the mean of the eight would be
within 1 standard error of the mean?
c). Why might you think that the probability that you calculated in (b) might not be very
accurate?

Answers

a) The standard error of the mean is equal to the standard deviation divided by the square root of the sample size. In this case, the standard error of the mean would be equal to 23.65/sqrt(8) = 6.61.

b) Using the central limit theorem, we can say that the probability that the mean of the eight plots would be within 1 standard error of the mean is approximately equal to 68%. This is because, under the central limit theorem, the distribution of the sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, in this case, we would expect that 68% of the sample means would be within 1 standard deviation of the population mean.

c) The probability that we calculated in (b) might not be very accurate because the central limit theorem assumes that the underlying population is normally distributed. However, it is not clear from the histogram whether the number of live maples per plot is normally distributed. If the distribution of the number of live maples per plot is not normal, then the central limit theorem would not be applicable and the probability we calculated might not be accurate.

nikki williams wishes to evaluate the risk and return behaviors associated with various combinations of assets x and y

Answers

Nikki can use modern portfolio theory to assess the risk and return behaviors associated with different combinations of assets X and Y.

Modern portfolio theory involves calculating the expected return and risk of a portfolio of assets by analyzing the correlations between the assets. It also looks at the diversification benefits of combining different assets and the impact of adding riskier assets to a portfolio. By quantifying the risk and return behaviors of different portfolios, Nikki can make informed decisions about which portfolios are most suitable for her.Modern portfolio theory is used to assess the risk and return behaviors of different combinations of assets X and Y. It considers correlations between the assets, the diversification benefits of combining them, and the impact of adding riskier assets. By quantifying the risk and return behaviors, Nikki can make informed decisions about which portfolios are most suitable for her.

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Brainly please don't delete my question it's not even breaking your guideline I even checked I just need my questions answered!

Answers

Answer:

Hey

you are correct

18x – 40

Step-by-step explanation:

2( x + 4 (2x – 5) )

= 2( x + 8x – 20)

= 2x + 16x – 40

= 18x – 40

Dont forget to rate the answer as brainliest

Have a good day

Answer: 18x-40

Step-by-step explanation: First, you have to isolate the 2, so now it would look like this:

=(2)(x+4(2x−5))

Now, You have to isolate the x, along with the 2 again, so it would look like this:

=(2)(x)+(2)(4(2x−5))

Now, you would combine the like terms of 2x & x, and all the numbers that don't have a variable, so it would look like this:

2x+16x−40

Now, finally, we can combine 2x + 16x, because they are like terms, so that is how we get 18x - 40

I hoped this helped friend!

-Shining Dream

Test of Independence 6. Are the factors that contribute to a person's wellbeing, (ie: Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status. See the chart. Marital married Widowed/divorced totals 42 132 49 Factors contribution to a 50 33 110 person's wellbeing. 21 25 58 100 300 a. a. b. b. C. C. d. d. e. e. status single Friendship 41 and social life Job or 27 primary activity Health and physical condition totals 80 120 State the null and alternative hypothesis State the observed values State the expected values Give the p-value Give a conclusion for the hypothesis test. 12

Answers

The conclusion of the hypothesis test is 0.342112

What is meant by hypothesis?

In statistics, hypothesis means an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

Here we have given that the factors that contribute to a person's wellbeing, That is Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status.

And we need to find the null and alternative hypothesis and the conclusion of the hypothesis test.

As per the given table of data we have to calculated the p value in order to find the null and alternative hypothesis,

For that we gathered the value of the following,

Number of samples = 9

Then the mean value of data = 83.63

And the standard deviation of the data = 80.475

Then the p - value is calculated as,

p-value ≈ 0.342112

This decision is made at significance level α = 0.05.

Therefore, the result is not statistically significant: there is not enough evidence to reject the null hypothesis.

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A local university offers a review course for those who are planning to take the GRE exam. Thirty
percent of the people who took the exam had attended the university's GRE review course. The results
of the test showed that 60% of those who attended the review passed the exam, while among those who
did not attend the course, only 20% passed the exam. An individual has passed the exam. Knowing this,
what is the probability that he attended the review course?

Answers

The probability that an individual attended the course given he passed

is 37.5%.

What is conditional probability?

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

We know the probability of A given B is P(A/B) = P(A∩B)/P(B).

Let, The number of students be 100.

Given, Thirty percent of the people who took the exam had attended the university's GRE review course which is 30 and hence 70 people did not attend the review course.

60% of those who attended the review passed the exam,

= (60/100)×30.

= 18 people.

20% who passed the exam did not attend the review course.

= (20/100)×70.

= 14.

So, The no. of people who passed is (18 + 14)/100 = 32/100 = 0.32.

The probability that a student passed and taken the course is (18/30)×(14/70) = 0.12.

Therefore, Given that he passed, the likelihood that someone took the course is = (0.12/0.32) = 0.375 Or 37.5%.

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when max and evie were counting their items of candy after trik or treating. the total humber of items was at least 90 and at most 115. If Evie had 42 items of candy, which of the following inequalities represents all possible number of items, m, that Max could have had?

Answers

Answer:

48 ≤ m ≤ 73

Step-by-step explanation:

Evie has 42, Max has x.

Total candy = x + 42

90 ≤ x+42 ≤ 115

48 ≤ m ≤ 73

Max can have 48 or more, but no more than 73

elementary surveying two ridges b and c forms a valley having a at the bottom part in between the ridges. elevation difference between b nad c is 111..356 m. observing at point a, the angle of elevation is

Answers

the difference of elevation between a and b.Let AB = x, tan 36 = x/111.356 ,x = 111.356 tan 36= 64.39 m and Difference in elevation = 64.39m

We are given that two ridges B and C form a valley with a point A at the bottom part with an elevation difference of 111.356m between the ridges and and angle of elevation of 36 degrees at point A. To find the difference of elevation between A and B, we use the formula of tangent which is tan θ = Opposite/Adjacent. We substitute the values and solve for x, which is the elevation difference between A and B. So the difference in elevation between A and B is 64.39m.

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A random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations in parts a through d. Calculate a 95% confidence interval for ju for each of these situations. a. n=70, X = 27 b. n = 150, x= 115 c. n= 80. x = 18 d. n = 80, x=5.33

Answers

The 95% confidence interval for this situation is (0.95, 9.71).

What is the Standard deviation?

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

The formula for Confidence Interval for Population Mean When Population Standard deviation is known

[tex]\bar{x} \pm Z_{a/2} * \frac{\sigma}{\sqrt{n} }[/tex]

α for 95% confidence level = (100-95)/100 =0.05

[tex]Z_{\alpha/2}[/tex] = 0.05/2=0.025

[tex]Z_{\alpha/2}[/tex] = Z0.025 = 1.96

σ = 20

95% Confidence Interval for Population Mean When Population Standard deviation is known