Each quart of syrup could fill 2 jars. How many quarts of syrup would be needed to<br> 16 jars?

Nitrates are groundwater contaminants derived from fertilizer, septic tank seepage and other sewage. Nitrate poisoning is partic

o-na [289]

Answer:

a) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

b) $n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

Part a

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.02$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have prior information about the population proportion we can use ase estimator $\hat p =0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

Part b

For thi case the estimator for p is $\hat p =0.07$

$n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

4 0

2 years ago

Find the p-value in a test of the claim that the mean College Algebra final exam score of engineering majors equal to 88, give

Orlov [11]

Answer: 0.9332.

Step-by-step explanation:

Claim : College Algebra final exam score of engineering majors equal to 88.

Given that : The test statistic is z equals to 1.50.

To find the p-value (Probability value), we use standard normal distribution table, and search the p-value corresponds to the z-score.

In a Standard Normal Distribution Table below, the p-value corresponds z equals 1.5 is 0.9332.

Hence, the p-value is 0.9332.

8 0

2 years ago

RS=4y+4, ST=3y+4, and RT=43 <br> What is the value of y?

Shkiper50 [21]

The value of y is 5

<h3>How to determine the value </h3>

From the given line, it can be concluded that:

The segment RT is divided into RS and ST

But we have the following parameters

The length of the sides are:

RS=4y+4
ST=3y+4
RT=43

Since RT is RS added to ST:

We have;

RT = RS + ST

substitute the values

43 = 4y + 4 + 3y + 4

collect like terms

43 = 4y + 3y + 4 + 4

Add like terms

43 = 7y + 8

Make '7y' subject of formula

7y = 43 - 8

7y = 35

Make 'y' the subject of formula

y = 35/ 7

y = 5

Thus, the value of y is 5

Learn more about segments here:

brainly.com/question/2437195

#SPJ1

5 0

1 year ago

What are the solutions to the equation 2(x-3)^2=54 ?

erastova [34]

Answer:

x =(6-√108)/2=3-3√ 3 = -2.196

x =(6+√108)/2=3+3√ 3 = 8.196

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

2 • (x - 3)2 - 54 = 0

Step 2 :

2.1 Evaluate : (x-3)2 = x2-6x+9

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

2x2 - 12x - 36 = 2 • (x2 - 6x - 18)

Adding 9 has completed the left hand side into a perfect square :

x2-6x+9 =

(x-3) • (x-3) =

(x-3)2 (x-3)1 =

x-3

Now, applying the Square Root Principle to Eq. #4.3.1 we get:

x-3 = √ 27

Add 3 to both sides to obtain:

x = 3 + √ 27

Since a square root has two values, one positive and the other negative

x2 - 6x - 18 = 0

has two solutions:

x = 3 + √ 27

or

x = 3 - √ 27

Solve Quadratic Equation using the Quadratic Formula

4.4 Solving x2-6x-18 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = -6

C = -18

Accordingly, B2 - 4AC =

36 - (-72) =

108

Applying the quadratic formula :

6 ± √ 108

x = —————

2

Can √ 108 be simplified ?

Yes! The prime factorization of 108 is

2•2•3•3•3

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 108 = √ 2•2•3•3•3 =2•3•√ 3 =

± 6 • √ 3

√ 3 , rounded to 4 decimal digits, is 1.7321

So now we are looking at:

x = ( 6 ± 6 • 1.732 ) / 2

Two real solutions:

x =(6+√108)/2=3+3√ 3 = 8.196

or:

x =(6-√108)/2=3-3√ 3 = -2.196

7 0

2 years ago

How many different primes are in the prime factorization of 65529009

Tems11 [23]

Answer:

6 different primes.

3, 7, 13, 29, 31 , 89.

Step-by-step explanation:

Try dividing by primes starting with 3:

3 ) 65529009

3 ) 21843003

7) 7281001

13) 1040143

29) 80011

31 ( 2759

89. 89 is a prime number.

7 0

2 years ago

Each quart of syrup could fill 2 jars. How many quarts of syrup would be needed to 16 jars?