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2 years ago

6

Consider the following differential equation. (A computer algebra system is recommended.) (1 + t2)y' + 4ty = (1 + t2)−2 (a) Draw

a direction field for the given differential equation.

1 answer:

alina1380 [7]2 years ago

3 0

Answer:

Step-by-step explanation:

a. Draw a direction field for the given differential equation

b. Based on the inspection of the direction field, describe ow solutions behave for large t.

The solution appear oscillatory

All solutions seems to converge to the function y0(t)=4

All solutions seems to converge to the function y0(t)=0

All solutions seems to seems to eventually have negative slopes a and hence decrease without bound

All solutions seems to seems to eventually have positive slopes a and hence increase without bound

C

As t-infinity

All solutions seems to seems to eventually have positive slopes a and hence decrease without bound

All solutions seems to converge to the function y0(t)=0

All solutions seems to seems to eventually have negative slopes a and hence decrease without bound

All solutions seems to converge to the function y0(t)=4

The solution are oscillatory

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In choice situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in t

victus00 [196]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

The probability that he or she would choose the pair of socks in the center position is $p =\frac{1}{5}$

The correct answer choice is

X has a binomial distribution with parameters n=100 and p=1/5

b

The mean is $\mu = 20$

The standard deviation is $\sigma=4$

c

The probability, $P =0.0002$

d

The correct answer is

The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.

Using the R the probability $Pe = 0.0003$

The probabilities $P \approx Pe$

Step-by-step explanation:

Since the person selects his or her desired pair of socks at random , then the probability that the person would choose the pair of socks in the center position from all the five identical pair is mathematically evaluated as

$p =\frac{1}{5}$

$=0.2$

The mean of this distribution is mathematical represented as

$\mu = np$

substituting the value

$\mu = 100 * 0.2$

$\mu = 20$

The standard deviation is mathematically represented as

$\sigma = \sqrt{np (1-p)}$

substituting the value

$= \sqrt{100 * 0,2 (1-0.2)}$

$\sigma=4$

Applying normal approximation the probability that 34 or more subjects would choose the item in the center if each subject were selecting his or her preferred pair of socks at random would be mathematically represented as

$P=P(X \ge 34 )$

By standardizing the normal approximation we have that

$P(X \ge 34) \approx P(Z \ge z)$

Now z is mathematically evaluated as

$z = \frac{x-\mu}{\sigma }$

Substituting values

$z = \frac{34-20}{4}$

$=3.5$

So using the z table the $P(Z \ge 3.5)$ is 0.0002

The probability P and Pe that 34 or more subject would choose the center pair is very small So

The correct answer is

The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.

6 0

2 years ago

An adult meerkat weighed 0.776 kilograms . this is 7.47 hectograms more than the weight of a baby meerkat . how much dose a baby

Firlakuza [10]

Let x = weight of adult meerkat, y=weight of baby meerkat, Find y.
x=0.776 kg
y+7.47hectogram=x=0.776
Since 1 hectogram = 0.1 kg,
Therefore the weight of baby meerkat is, y= 0.029 kg

7 0

2 years ago

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A particular personal trainer works primarily with track and field athletes. She believes that her clients run faster after goin

masya89 [10]

Answer:

A matched-pairs hypothesis test for μD

Step-by-step explanation:

The trainer wants to compare each athlete's time before the program to the time after the program. Since we're comparing times for the same athlete, the data is paired, so we should use a matched-pairs test.

7 0

2 years ago

There are 252 pieces of candy in a 14-ounce jar. How many pieces of candy are there per ounce in the jar?

djyliett [7]

"Per" essentially means "divided by." To find pieces per ounce, divide pieces by ounces.

(252 pieces)/(14 ounces) = (252/14) pieces/ounce = 18 pieces/ounce

5 0

2 years ago

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A group of campers is going to occupy 3 campsites at a campground. There are 17 campsites from which to choose. In how many ways

Alexeev081 [22]

Answer:

Campsites be chosen in 680 ways.

Step-by-step explanation:

Given:

Number of campsites= 17

Number of campsites that are to be occupied=3

To Find:

Number of ways can the campsites be chosen=?

Solution:

Combination:

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

nCr = n(n - 1)(n - 2) ... (n - r + 1)/r! = n! / r!(n - r)!

No of ways in which campsites can be chosen= $\frac{17!}{3!(17-3)!}$ 17C3

=> $\frac{17!}{3!(14!)}$

=> $\frac{15\times16\times17}{3\times 2\times 1}$

=> $\frac{4080}{6}$

=>680

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2 years ago