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A kite , at a height of 60 ft. is moving
horizontally at a rate of 5ft/sec. away from
the boy who flies it. How fast is the string
being released when 100 ft. are out.
An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and prices (in hundreds of dollars) of these cars.
Age
8
3
6
9
2
5
6
3
Price
45
210
100
33
267
134
109
235
- What is the independent variable?
- What is the dependent variable?
- Develop the regression model
- Predict the price of a 7-year-old car of this model.
- Estimate the price of an 18-year-old car of this model. Comment on this finding
Under certain conditions, cane sugar is converted into dextrose at a rate, which is proportional to the amount unconverted at any time. If out of 60 grams of sugar at t = 0 6 grams are converted during the first 4 minutes, find the amount converted in 2 hours.
1. Solve the following Bernoulli's Differential Equations. Show your solutions.
a. dy/dx + (1/3) y = e^x y²
b. x (dy/dx) + y = xy³
c. dy/dx + (2/x) y = -x² cos x y²
d. x²y-x³ (dy/dx) = y² cos x
The following contingency table represents the voters’ opinion concerning a new tax
reform bill and their level of income.
Levels of Income
Opinion Low Medium High
For 213 203 182
Against 138 110 154
Apply chi-square (χ2
) test to examine whether the opinion of people on new tax bill is
independent from their income level. [Table value of chi- square (χ2
) at 5% level of
significance and for 2 degrees of freedom is 5.99]
3.2 4.7 3.8 4.3 3.5 5.0 4.3 5.2 5.1 4.2
1.Constuct a frequency destribution mode.
2.Determined the interval where k=10.
3.Compute for mean,median ,mode ,variance and standard deviation of grouped date
Suppose we roll two dice and let X be the maximum of the two numbers obtained and let Y be their minimum. Write down the distribution tables of X, Y and Z = (X, Y ).
(2xy+3y2)dx-(2xy+X2)dy=0
A condenser of capacity C=5*10^5 farad is charged through a resistance R=200ohms by steady voltage E=2000volts.Calculate the current at the instant of closing the switch
From a sack of fruit containing 3 bananas, 3 oranges, and 3 apples , a random sample of 4 pieces of fruit is selected. Suppose X is the number of bananas and Y is the number of apples in the sample.
(a) Find the joint probability distribution of X and Y.
(b) Find P[(X,Y)A], where A is the region that is given by (x,y)
Question content area bottom
Part 1
(a) Complete the joint probability distribution below.
(Type integers or simplified fractions.)
#340153 on Dec 2023