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3 years ago

Find the particular solution of the differential equation that satisfies the initial condition. f '(x) = −8x, f(1) = −3

Mathematics

1 answer:

Iteru [2.4K]3 years ago

4 0

Step-by-step explanation:

f(x) = integral (-8x) dx = -4x^2 + C

f(1) = -3 = -4 + C

C = 1

f(x) = -4x^2 + 1

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Mr. Gardener invested $500,000. His annual interest was $40,000. What was the annual interest rate?

Archy [21]

Mr. Gardener's annual interest rate is 8%.

40,000/500,000 = 0.08

8 0

3 years ago

Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if:a) a

lara31 [8.8K]

Answer:

A) 0.0009765625

B) 0.0060466176

C) 2.7756 x 10^(-17)

Step-by-step explanation:

A) This problem follows a binomial distribution. The number of successes among a fixed number of trials is; n = 10

If a 0 bit and 1 bit are equally likely, then the probability to select in 1 bit is; p = 1/2 = 0.5

Now the definition of binomial probability is given by;

P(K = x) = C(n, k)•p^(k)•(1 - p)^(n - k)

Now, we want the definition of this probability at k = 10.

Thus;

P(x = 10) = C(10,10)•0.5^(10)•(1 - 0.5)^(10 - 10)

P(x = 10) = 0.0009765625

B) here we are given that p = 0.6 while n remains 10 and k = 10

Thus;

P(x = 10) = C(10,10)•0.6^(10)•(1 - 0.6)^(10 - 10)

P(x=10) = 0.0060466176

C) we are given that;

P((x_i) = 1) = 1/(2^(i))

Where i = 1,2,3.....,n

Now, the probability for the different bits is independent, so we can use multiplication rule for independent events which gives;

P(x = 10) = P((x_1) = 1)•P((x_2) = 1)•P((x_3) = 1)••P((x_4) = 1)•P((x_5) = 1)•P((x_6) = 1)•P((x_7) = 1)•P((x_8) = 1)•P((x_9) = 1)•P((x_10) = 1)

This gives;

P(x = 10) = [1/(2^(1))]•[1/(2^(2))]•[1/(2^(3))]•[1/(2^(4))]....•[1/(2^(10))]

This gives;

P(x = 10) = [1/(2^(55))]

P(x = 10) = 2.7756 x 10^(-17)

3 0

3 years ago

How do I do trigonometry:ratios and finding missing sides?

Bingel [31]

Answer:

Use trig ratios to find unknown sides in right triangles.

Step-by-step explanation:

3 0

3 years ago

7. What is the slope of the line that passes through the pair of points (3, 8) and (9, 5) ? (1 point)

agasfer [191]

7. D
8. D
9. D
10.C

for 7 & 8 you use the equation
$\frac{y2 - y1}{x2 - x1}$
your points are (3,8) & (9,5)

so you plug the numbers in
y2= 5
y1=8

x2=9
x1=3
you subtract them get a fraction and that is your slope

9 & 10
use the equation
$y - y1 = m(x - x1)$
plug you numbers in for y1 and x2 m is your slope plug it in and that is your equation

5 0

3 years ago

Read 2 more answers

A factory is going to hire 33 new employees. There are 79 applicants. Which

dedylja [7]

Answer:

33:79

Step-by-step explanation:

We are told that a factory is going to hire 33 new employees.

and the total applicants is 79

In this problem, we want to represent the situation as a ratio of new hires to applicants

Since the question says new hires to applicants

Hence, the ratio will be

33 to 79

33/79, we can simplify this as

33:79

5 0

2 years ago