Math Answers

Two gardens. A fence of length 100 ft is to be used to enclose two

gardens. One garden is to have a circular shape, and the other to be

square.

Determine how the fence should be cut so that the sum of the areas

inside both gardens is as large as possible.

Find the area under the standard normal distribution curve.

1. Between z = 0 and z = 1.66

2. Between z = 0 and z = -0.35

3. To the right of z = 1.10

4. To the left of z = -0.48

5. Between z = 1.23 and z = 1.90

6. Between z = - 1.56 and z = -1.83

7. To the left of z = - 2.15 and to the right of z = 1.62

8. To the left of z = 2.11

9. To the right of z = -0.15

10. To the right of z = 1.92 and to the left of z = 0.44

DETERMINE WHETHER THE FOLLOWING STATEMENTS HAVE A KNOWN OR UNKNOWN POPULATION VARIANCE. IDENTIFY ALSO THE FORMULA TO BE USED TO ESTIMATE THE STANDARD ERROR OF THE MEAN.

An SHS teacher claims that the average time it takes a group of students to complete the Statistics and Probability examination is 50.5 minutes with a variance of 17.64 minutes squared. She randomly selected 45 students and found them to have a mean of 52 minutes and a standard deviation of 3.5 minutes. She then used the z-distribution to find out if the group can complete the exam faster than the population.

Complete { (2, 0, 3)} to form an orthogonal

basis of R³

How many significant digits are there in the number 10,430?

Suppose a random variable is normally distributed. The probabilities for a85 and 142 are 10% and 65%, respectively. Find the mean and standard deviation to the nearest whole number.

Reducible to homogeneous differential equations or by simple substitution.

1. (2𝑥 − 3𝑦 − 4)𝑑𝑥 − (3𝑥 − 4𝑦 − 2)𝑑𝑦 = 0

2. (2𝑥 − 𝑦 − 3)𝑑𝑥 − (𝑥 + 4𝑦 + 3)𝑑𝑦 = 0

3. (𝑥 − 𝑦 − 6)𝑑𝑦 = (𝑥 − 𝑦 + 2)𝑑𝑥

4. (𝑥 − 2𝑦 + 4)𝑑𝑥 + (2𝑥 − 4𝑦 − 1)𝑑𝑦 = 0

5. (𝑥 + 4𝑦 + 3)𝑑𝑥 = (2𝑥 − 𝑦 − 3)𝑑𝑦

B. Exact differential equations (include checking for exactness).

1. (𝑤3 + 𝑤𝑧 2 − 𝑧)𝑑𝑤 + (𝑧 2 + 𝑤2 𝑧 − 𝑤)𝑑𝑧 = 0

2. (cos 2𝑦 − 3𝑥 2𝑦 2 )𝑑𝑥 + (cos 2𝑦 − 2𝑥 sin 2𝑦 − 2𝑥 3𝑦)𝑑𝑦 = 0

Let x be Bin(n,p). Find the mean square error of the p parameter estimator

Let f(x) = 5 + 12x -x^3. Using the differentiation techniques learnt, find

a. The intervals on which f is increasing

The data for a certain test is provided below

X 100 200 300 400 500 600 700

Y 30 50 60 80 100 110 130

Compute the value of the correlation.

Find the equation of the regression lime.