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Usimov [2.4K]
2 years ago
12

Fred the ant is on the real number line, and Fred is trying to get to the point $0.$

Mathematics
1 answer:
Pavlova-9 [17]2 years ago
6 0

Complete question is;

Fred the ant is on the real number line, and Fred is trying to get to the point 0

If Fred is at 1 then on the next step, Fred moves to either 0 or 2 with equal probability. If Fred is at 2 then on the next step, Fred always moves to 1

Let e1 be expected number of steps Fred takes to get to 0 given that Fred starts at the point 1. Similarly, let e2 be expected number of steps Fred takes to get to 0 given that Fred starts at the point 2

Determine the ordered pair (e1, e2)

Answer:

(e_1,e_2) = (2,3)

Step-by-step explanation:

We can track the probabilities using the scenario that Ant gets to 0 after 1 steps, 2 steps, 3 steps, 4 steps, 5 steps and so on.

This gives us e_1 = 1(1/2^(1)) + 2(1/2²) + 3(1/2³) + 4(1/2⁴) + ...

By arithmetico-geometric series, which is given by;

S_(∞) = [a/(1 - r)] + dr/(1 - r)²

From the online calculator, i got;

e_1 = 2

Similarly, e_2 = 2(1/2^(1)) + 3(1/2²) + 4(1/2³) + 5(1/2⁴) + ...

By arithmetico-geometric series, e_2 = 3,

Thus, (e_1,e_2) = (2,3).

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In Kayllie'srecipe for lemonade, the ratio of lemons to water is 7 to 4. People are complaining that the lemonade is too weak. W
katrin [286]

Answer:

B.) 10 to 5 and D.) 8 to 4.

Step-by-step explanation:

Since we are trying to make the lemon taste stronger, there would need to be more lemons than water. The ratio would need to have a larger difference than 7:4. The difference is 3.

Choice A has a difference of 2. Two is less than 3 so this would taste more watery than lemony. Choice C has a difference of 3. Because we want a <em>stronger</em> lemon taste, this won't work. It would taste the same.

Choice B has a difference of 5. This is greater than 3 so the lemon taste will be stronger. Choice D has a difference of 4, this is also greater than 3 and will also make the taste of lemon stronger.

Hope this helps,

♥<em>A.W.E.</em><u><em>S.W.A.N.</em></u>♥

5 0
3 years ago
Janet can plant nine feet of carrots in 15 minutes while her daughter Amy can plant 17 feet of carrots in half an hour.
Lena [83]

Answer:

Step-by-step explanation:

In order to find who is more efficient at planting carrots, we want to put both ratios in terms of the same amount of time.

For simplicity, lets see how many carrots each can make in 1 hour.

Janet:\\9ft \: in \: 15 \:minutes

\frac{9ft}{15min} = \frac{xft}{60min}\\x = \frac{60*9}{15} = 36

Janet can plant 36 feet of carrots in one hour

Amy:\\\frac{17ft}{30min} = \frac{xft}{60min}\\x = \frac{17*60}{30} = 34

Amy can plant 34 feet of carrots in one hour

So, Janet can plant carrots more quickly

6 0
2 years ago
Saturn's average distance from then sun is about 900 million miles.what is that distance in scientific notation?
IRINA_888 [86]
900,000,000. move the decimal until you have a number between 1-10 so move it 8 times and you'll have 9×10^8
3 0
3 years ago
you are riding a train. your carry-on bag can weigh no more than 50 pounds. Your bag weighs 38 pounds. How much more can you add
Strike441 [17]

Let the additional weight that can be added be = x

Current weight of the bag = 38 pounds

Total weight can be = 50 pounds

The equation becomes:

38+x\leq50

x\leq50-38=12

Hence, a weight of 12 pounds cab be added to the current wight.

8 0
3 years ago
What are the coordinates of the endpoints of the segment
Vsevolod [243]

Answer:

A) T'(-3, 6) and V'(0, 3)

Step-by-step explanation:

In the picture attached, triangle TVW is shown.

Transforming points T and V according to the rule (x,y) -> (3/4x, 3/4y), we get:

T(-4, 8) -> (-4*3/4, 8*3/4) -> (-3, 6) which corresponds to T'

V(0, 4) -> (0*3/4, 4*3/4) -> (0, 3) which corresponds to V'

6 0
2 years ago
Read 2 more answers
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