The y coordinate is 7 more than the x coordinate

A randomly selected sample of 100 students had an average grade point average (GPA) of 3.2 with a standard deviation of 0.2.

alexdok [17]

Answer:

A. 0.020

Step-by-step explanation:

we calculate the standard error of the sample mean with the formula,

$E=\frac{s}{\sqrt{n} }$ ,

with E= standard error of the sample mean

s= standard deviation

n= sample

So,

s= 0.2

n= 100

$E=\frac{0.2}{\sqrt{100} } =\frac{0.2}{10}=0.02$

5 0

4 years ago

If function g has the factors (x − 7) and (x + 6), what are the zeros of function g?

Delicious77 [7]

Answer:

The zeros are x=7 and x= -6

Step-by-step explanation:

In order to find the zeros of a function with factors, we have to equate the factors to zero.

So x-7 = 0

and

x+6 = 0

Then we solve for x in each equation,

x= 7 and x= -6

These values are the zeros

6 0

3 years ago

the sum of two numbers is 21 if 8 less than the sum of the two numbers is 5 more than triple the smaller number find the two num

iragen [17]

x + y = 21

x + y - 8 = 3*y + 5

Subtract y from both sides.

x - 8 = 3y - y + 5

x - 8 = 2y + 5 Substitute x = 21 - y into the equation

21 - y - 8= 2y + 5

13 = 3y + 5 Subtract 5 from both sides

13 - 5 = 3y

8 = 3y Divide by 3

y = 8/3

x + y = 21

x + 8/3 = 21

x = 21 - 8/3

x = 18 1/3 or 18.333333

Check

The smaller number is 8/3

x + y - 8 = 3*(8/3) + 5 Remember that x + y = 21

21 - 8 = 8 + 5

13 = 13 and they check. Which one is the smaller number does not become a factor until you check your answer.

6 0

3 years ago

The maximum value of 1/4cos 2x is:

lukranit [14]

24 is the answer for your question

3 0

3 years ago

Polly's Polls asked 1850 second-year college students if they still had their original major. According to the colleges, 65% of

suter [353]

Answer:

The probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424

Step-by-step explanation:

The variable that assigns the value 1 if a person had its original major and 0 otherwise is a Bernoulli variable with paramenter 0.65. Since she asked the question to 1850 people, then the number of students that will have their original major is a Binomial random variable with parameters n = 1850, p = 0.65.

Since the sample is large enough, we can use the Central Limit Theorem to approximate that random variable to a Normal random variable, which we will denote X.

The parameters of X are determined with the mean and standard deviation of the Binomal that we are approximating. The mean is np = 1850*0.65 = 1202.5, and the standard deviation is √np(1-p) = √(1202.5*0.35) = 20.5152.

We want to know the probability that X is between 0.64*1850 = 1184 and 0.66*1850 = 1221 (that is, the percentage is between 64 and 66). In order to calculate this, we standarize X so that we can work with a standard normal random variable W ≈ N(0,1). The standarization is obtained by substracting the mean from X and dividing the result by the standard deviation, in other words

$W = \frac{X-\lambda}{\sigma} = \frac{X-1202.5}{20.5152}$

The values of the cummulative function of the standard normal variable W, which we will denote $\phi$ are tabulated and they can be found in the attached file.

Now, we are ready to compute the probability that X is between 1184 and 1221. Remember that, since the standard random variable is symmetric through 0, then \phi(-z) = 1-\phi(z) for each positive value z.

$P(1184 < X < 1221) = P(\frac{1184-1202.5}{20.5152} < \frac{X-1202.5}{20.5152} < \frac{1221-1202.5}{20.5152})\\ = P(-0.9018 < W < 0.9018) = \phi(0.9018) - \phi(-0.9018) = \phi(0.9018)-(1-\phi(0.9018))\\ = 2\phi(0.9018)-1 = 2*0.8212-1 = 0.6424$

Therefore, the probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424.

Download pdf

4 0

4 years ago