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zmey [24]
3 years ago
15

Establish for which constants c the following function is a density.

Mathematics
1 answer:
Valentin [98]3 years ago
7 0
By "density" I assume you mean "probability density function". For this to be the case for f(x), we require

\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=1

Since

f(x)=\begin{cases}cx^{1/2}&\text{for }0

you have

\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=\int_0^2cx^{1/2}\,\mathrm dx=\dfrac{2c}3x^{3/2}\bigg|_{x=0}^{x=2}=\dfrac{2^{5/2}c}3=1

which means

c=\dfrac3{2^{5/2}}=\dfrac3{4\sqrt2}
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How many thousands are in 327,412?
Alexxandr [17]

Answer:

327

Step-by-step explanation:

In the thousands cateragory of the number lies the numbers 327 giving you your answer

8 0
3 years ago
Simon says "five time my age 4 years ago is the same as three time my age in 2 years" how old is simon
omeli [17]

Simon is 13 years old

Let x be Simon's age

Thus 4 years ago his age was (x - 4) and 2 years from now his age is (x + 2)

Hence 5(x - 4) = 3(x + 2)

distributing both sides gives

5x-20 = 3x + 6

subtract 3x from both sides of the equation

5x - 3x - 20 = 6

2x - 20 = 6

add 20 to both sides

2x = 6 + 20 = 26

divide both sides by 2

x = \frac{26}{2} = 13

Simon is 13 years old


7 0
3 years ago
Jayden sells snow cones for $3.75 each. He started the day with a total of 300 snow cones to sell. If he made a total of $843.75
Leni [432]

Number of cone left is 75 cone

<u>Given that;</u>

Cost of each cone = $3.75 each

Starting number of cone = 300

Total amount earn = $843.75

<u>Find:</u>

Number of cone left

<u>Computation:</u>

Number of cone sale = Total amount earn / Cost of each cone

Number of cone sale = 843.75 / 3.75

Number of cone sale = 225 cone

Number of cone left = Starting number of cone - Number of cone sale

Number of cone left = 300 - 225

Number of cone left = 75 cone

Learn more:

brainly.com/question/4115571?referrer=searchResults

7 0
3 years ago
A cube has a volume of 125 cubic inches. What is the length of each edge?
Phantasy [73]

Answer:

1.95

Step-by-step explanation:

8 0
3 years ago
You are opening a savings account with $500 that you have saved. The bank offers 3.2% interest, compounded yearly. How much mone
Nuetrik [128]

Answer:

You will have $623.3441462 in your account after 7 years

Step-by-step explanation:

The formula of the compounded interest is A = P (1+\frac{r}{n})^{nt} , where

  • A is the new value
  • P is the initial value
  • r is the rate in decimal
  • n is the number of periods
  • t is the time in years

∵ You are opening a savings account with $500  

∴ P = 500

∵ The bank offers 3.2% interest, compounded yearly

∴ r = 3.2% ⇒ divide it by 100 to change it to decimal

∴ r = 3.2 ÷ 100 = 0.032

∵ The interest is compounded yearly

∴ n = 1

∵ The time is 7 years

∴ t = 7

→ Substitute these values in the rule above to find A

∵ A = 500 (1+\frac{0.032}{1})^{1(7)}

∴ A = 500 (1.032)^{7}

∴ A = 623.3441462

∴ You will have $623.3441462 in your account after 7 years

8 0
3 years ago
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