MATHEMATICS COLLEGE

Suppose that a box contains 6 cameras and that 3 of them are defective. A sample of 2 cameras is selected at random (with replacement). Define the random variable X as the number of defective cameras in the sample. Note: For X to have a binomial probability distribution the sample must be with replacement, otherwise the trials are dependent. Write the probability distribution for X . k P( X = k ) 0 Correct .2 Incorrect 1 Correct .5 Correct 2 Correct .2 Incorrect What is the expected value of X ?

Answers

Answer 1

Answer:

p = 3/6 = 0.5

X ~ B(6, 0.5)

P(X=k) = 6Ck × 0.5^k × 0.5^(6-k)

E(X) = np = 6(0.5) = 3

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A fox leaves its den and travels 725 yards northeast, then 950 yards west. How far, in yards is the fox from its den

Answers

Using Pythagoras,the distanceof the fox from its den would be 533.26 yards

Hypotenus = 900 yards

Adjacent = 725 yards

Distance from den = opposite

Opposite = √hypotenus² - adjacent²

Distance = √(900)² - (725)²

Distance = √810000 - 525625

Distance = √284375

Distance = 533.26yards

Therefore, the fox is 533.26yards from his den.

Learn more : Opposite = √hypotenus² - adjacent²

Answer:

1,675

Step-by-step explanation:

add it

An advertising company designs a campaign to introduce a new product to a metropolitan area of population 3 Million people. Let P(t) denote the number of people (in millions) who become aware of the product by time t. Suppose that P increases at a rate proportional to the number of people still unaware of the product. The company determines that no one was aware of the product at the beginning of the campaign, and that 50% of the people were aware of the product after 50 days of advertising. The number of people who become aware of the product at time t is:

Answers

Answer:

$P(t)=3,000,000-3,000,000e^(0.0138t)$

Step-by-step explanation:

Since P(t) increases at a rate proportional to the number of people still unaware of the product, we have

$P'(t)=K(3,000,000-P(t))$

Since no one was aware of the product at the beginning of the campaign and 50% of the people were aware of the product after 50 days of advertising

P(0) = 0 and P(50) = 1,500,000

We have and ordinary differential equation of first order that we can write

$P'(t)+KP(t)= 3,000,000K$

The integrating factor is

$e^(Kt)$

Multiplying both sides of the equation by the integrating factor

$e^(Kt)P'(t)+e^(Kt)KP(t)= e^(Kt)3,000,000*K$

Hence

$(e^(Kt)P(t))'=3,000,000Ke^(Kt)$

Integrating both sides

$e^(Kt)P(t)=3,000,000K \int e^(Kt)dt +C$

$e^(Kt)P(t)=3,000,000K((e^(Kt))/(K))+C$

$P(t)=3,000,000+Ce^(-Kt)$

But P(0) = 0, so C = -3,000,000

and P(50) = 1,500,000

$e^(-50K)=(1)/(2)\Rightarrow K=-(log(0.5))/(50)=0.0138$

And the equation that models the number of people (in millions) who become aware of the product by time t is

$P(t)=3,000,000-3,000,000e^(0.0138t)$

Find the distance between the points.
(1, 6, 3), (-5, 3, 7)

Answers

Answer:

Step-by-step explanation:

From data gathered in the period 2008−2012, the yearly value of U.S. exports can be modeled by the function E(x) = −228x3 + 2,252.8x2 − 6,098.5x + 11,425.8 where x is the number of years after 2008 and E(x) is the value of exports in billions of dollars. The yearly value of U.S. imports can be modeled by the function I(x) = −400.4x3 + 3,954.4x2 − 11,128.8x + 17,749.6 where x is the number of years after 2008 and I(x) is the value of imports in billions of dollars. Estimate the total value the U.S. imported and exported in 2011. Round to the nearest whole number. About billion dollars were imported and exported by the U.S. in 2011.

Answers

Answer:you got this:)

Step-by-step explanation:

WILL MARK BRAINLIEST ONLY HAVE 30 MINUTES

Answers

Answer:

Step-by-step explanation:

the answer is 21

Answer:

its 21

Step-by-step explanation:

you add 9 +12= 21 inches

out of 24 students, 6 preferred to use pastels for their portraits while 4 preferred to use watercolours watercolours. what percentage of the class preferred pastels? % Jasmin bought a box of 40 assorted coloured pastels, 1/5 are blue, 3/10 are green, 20% are red and 5 are yellow. Of which colour are there most pastels? How many pastels are colours other than blue, green, red or yellow?

Answers

The percentage of the class-preferred pastels will be 25%. The color there has most pastels will be Green. And the number of pastels that are colors other than blue, green, red, or yellow will be 7.

What is the percentage?

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

Out of 24 students, 6 preferred to use pastels for their portraits while 4 preferred to use watercolors. Then the percentage of the class preferred pastels will be

P = 6 / 24 x 100

P = 0.25 x 100

P = 25%

Jasmin bought a box of 40 assorted colored pastels, 1/5 are blue, 3/10 are green, 20% are red and 5 are yellow. Then the number of pastels of each color will be

Blue = 1/5 = 8 / 40 = 8

Green = 3/10 = 12 / 40 = 12

Red = 0.2 = 1/5 = 8 / 40 = 8

Yellow = 5

The number of pastels are colors will be

⇒ 40 - 8 - 12 - 8 - 5

⇒ 40 - 33

⇒ 7

The color there has most pastels will be Green. And the number of pastels that are colors other than blue, green, red, or yellow will be 7.

More about the percentage link is given below.

brainly.com/question/8011401

#SPJ2

Answer:

4% used pastels.

Step-by-step explanation:,,

green is the most

5 isnt blue.green,yello or red

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