For a certain breed of dog, suppose the offspring of a black dog is black with probability 0.6 and brown with probability 0.4. Also for this breed, suppose the offspring of a brown dog is black with probability 0.2 and brown with probability 0.8. If Rex is a brown dog of this breed, what is the probability that his grand-pup will be black?

Answers

Answer 1
Answer:

Answer:

0.28

Step-by-step explanation:

For a certain breed of dog,

OFFSPRING OF A BLACK DOG:

Is black = 0.6          Is brown = 0.4

OFFSPRING OF A BROWN DOG:

Is black = 0.2          Is brown = 0.8

If REX is a brown dog of this breed, what is the probability that his grand puppy will be black?

The probability that his grand pup will be black = Probability that his black pups produce black pups + the probability that his brown pups produce black pups.

The probability that his black pups produce black pups:

0.2 × 0.6 = 0.12

The probability that his brown pups produce black pups:

0.8 × 0.2 = 0.16

The probability that his grand pup will be black = 0.12 + 0.16 = 0.28

Answer 2
Answer:

Final answer:

The probability that the grand-pup of a brown dog (like Rex) will be black is calculated by multiplying the probability that a brown dog will produce a black offspring (0.2) by the probability that a black dog will produce a black offspring (0.6). This results in a probability of 0.12, or 12%.

Explanation:

In this problem, you're looking at the probability of a twice-removed descendent (a grand-pup) being a certain color, given the starting color of the ancestor (Rex). Since the color of the offspring is dependent on the color of the parent, this is a conditional probability problem.

The probability that the offspring of a brown dog will be black is 0.2. If that dog is black, the probability of its own offspring being black is 0.6. So, you multiply those probabilities together to find the probability that a brown dog will have a black grandpup, which is 0.2 * 0.6 = 0.12, or 12%. Therefore, the probability that Rex's grandpup will be black is 12%.

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The volume V of a growing spherical cell is V = 4 3 πr3, where the radius is measured in micrometers (1 µm = 10−6m). Find the average rate of change of V with respect to r when r changes from 6 to each of the following. (Round your answers to one decimal place.) (i) 6 to 9 µm
(ii) 5 to 6 µm
(iii) 5 to 5.1 µm

Answers

Final answer:

The average rate of volume change of a growing spherical cell for different changes in radius can be calculated using the formula for the volume of a sphere and the formula for average rate of change (ΔV/Δr).

Explanation:

To find the average rate of change of the volume V with respect to the radius r, you will need to subtract the initial volume from the final volume and then divide by the change in radius. This is represented by the formula ΔV/Δr, where Δ represents change in.

  1. For r changing from 6 to 9 µm, ΔV = V(9) - V(6) = 4/3π(9^3) - 4/3π(6^3). Therefore, ΔV/Δr = (4/3π(9^3) - 4/3π(6^3)) / (9 - 6).
  2. For r changing from 5 to 6 µm, ΔV = V(6) - V(5) = 4/3π(6^3) - 4/3π(5^3). Therefore, ΔV/Δr = (4/3π(6^3) - 4/3π(5^3)) / (6 - 5).
  3. For r changing from 5 to 5.1 µm, ΔV = V(5.1) - V(5) = 4/3π(5.1^3) - 4/3π(5^3). Therefore, ΔV/Δr = (4/3π(5.1^3) - 4/3π(5^3)) / (5.1 - 5).

These calculations will give you the average rate of volume change for each of the radius changes indicated.

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HELP PLEZ TRIGONOMETRY!

Answers

(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) = sin \alpha - cos \alpha

Solution:

Given that we have to simplify:

(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) ---- eqn 1

We know that,

sin^2 x = 1 - cos^2 x

Substitute the above identity in eqn 1

(2\left(1-\cos ^(2) \alpha\right)-1)/(\sin \alpha+\cos \alpha)

Simplify the above expression

(2-2 \cos ^(2) \alpha-1)/(\sin \alpha+\cos \alpha)

(1-2 \cos ^(2) \alpha)/(\sin \alpha+\cos \alpha) ------- eqn 2

By the trignometric identity,

(sin x + cos x)(sin x - cos x) = 1-2cos^2 x

Substitute the above identity in eqn 2

((\sin \alpha+\cos \alpha)(\sin \alpha-\cos \alpha))/(\sin \alpha+\cos \alpha)

Cancel the common factors in numerator and denominator

((\sin \alpha+\cos \alpha)(\sin \alpha-\cos \alpha))/(\sin \alpha+\cos \alpha)=\sin \alpha-\cos \alpha

Thus the simplified expression is:

(2 \sin ^(2) \alpha-1)/(\sin \alpha+\cos \alpha) = sin \alpha - cos \alpha

Which is the graph of y = 3/4x -3?

Answers

Answer:

A

Step-by-step explanation:

rise over run....up 3 and over 4

crosses y axis as -3

Can someone please help me with this?!!

Answers

Answer:

x=19

Step-by-step explanation:

x+8=2x-11

-11+11=0

8+11=19

x-x=0

2x-x=x

x=19

HELP!!!!! I do not understand how to do this! Could someone please explain to me how I would solve this problem? A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $10 million after 4 years, as shown in the graph:

There is a graph of a line with Years on the x axis and Profits in millions on the y axis that passes through 0, negative 20 and 4, 10.

Answers

Yeah man nearly there

jack spends 15 of his pocket money on sweets and 35% on magazines. he saves the rest.Work out how much he spends each week

Answers

Jack spends 15% on sweets each week and 35% on magazines. His total spendings(15%+35%=50%)equals 50%.Savings is 100% - 50%= 50%.So, if jack gets $100 each week, he spends $15 on sweets, $35 on magazines, and $50 goes towards savings. Hope this helps!

Final answer:

Jack spends $50 each week.

Explanation:

To calculate how much Jack spends each week, we need to find the amount he spends on sweets and magazines and subtract it from his pocket money. First, we calculate the amount Jack spends on magazines. Let's assume his pocket money is $100:

  1. Amount spent on sweets = 15% of $100 = $15
  2. Amount spent on magazines = 35% of $100 = $35

To find the amount Jack saves, we subtract the amount spent on sweets and magazines from his pocket money:

Total spent on sweets and magazines = $15 + $35 = $50

Amount saved each week = Pocket money - Total spent on sweets and magazines = $100 - $50 = $50

Therefore, Jack saves $50 each week.

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