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2 years ago

26. A positive whole number is called stable if at least one of its digits has the same value

Mathematics

1 answer:

Kisachek [45]2 years ago

5 0

Answer:

Step-by-step explanation:

Given the value 78247 a s a stable number because at least one of its digits has the same value as its position in the number. The 4th number in the value is 4, this makes the number a stable number.

The following are the 3-digits stable numbers that appears in 78247

The first number is 824. This digits are stable numbers because 2 as a number is situated in the same place as the number (2nd position).

Hence, there are only 1 stable 3-digit numbers in the value 78247 since only a value exists as 2 in the value and there is no 1 and 3 in the value.

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Jennifer can run 12 miles in 2 hours, and she can bike 33 miles in 3 hours. What is Jennifer’s biking speed?

anastassius [24]

Answer:

11 miles per hour

Step-by-step explanation:

The biking speed is found by taking the miles and dividing by the hours

33 miles/ 3 hours

11 miles per hour

3 0

2 years ago

Harriet has a square piece of paper. She folds it in half again to form a second rectangle (the high is not a square). The perim

dlinn [17]

Answer:

The area of the original piece of paper is 60cm

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1 year ago

Read 2 more answers

There are two misshapen coins in a box; their probabilities for landing on heads when they are flipped are, respectively, .4 and

Leokris [45]

Answer:

E(X) = 6.0706

Step-by-step explanation:

1) Define notation

X = random variable who represents the number of heads in the 10 first tosses

Y = random variable who represents the number of heads in range within toss number 4 to toss number 10

And we can define the following events

a= The first coin has been selected

b= The second coin has been selected

c= represent that we have 2 Heads within the first two tosses

2) Formulas to apply

We need to find E(X|c) = ?

If we use the total law of probability we can find E(Y)

E(Y) = E(Y|a) P(a|c) + E(Y|b)P(b|c) ....(1)

Finding P(a|c) and using the Bayes rule we have:

P(a|c) = P(c|a) P(a) / P(c) ...(2)

Replacing P(c) using the total law of probability:

P(a|c) = [P(c|a) P(a)] /[P(c|a) P(a) + P(c|b) P(b)] ... (3)

We can find the probabilities required

P(a) = P(b) = 0.5

P(c|a) = (3C2) (0.4^2) (0.6) = 0.288

P(c|b) = (3C2)(0.7^2) (0.3) = 0.441

Replacing the values into P(a|c) we got

P(a|c) = (0.288 x 0.5) /(0.288x 0.5 + 0.441x0.5) = 0.144/ 0.3645 = 0.39506

Since P(a|c) + P(b|c) = 1. With this we can find P(b|c) = 1 - P(a|c) = 1-0.39506 = 0.60494

After this we can find the expected values

E(Y|a) = 7x 0.4 = 2.8

E(Y|b) = 7x 0.7 = 4.9

Finally replacing the values into equation (1) we got

E(Y|c) = 2.8x 0.39506 + 4.9x0.60494 = 4.0706

And finally :

E(X|c) = 2+ E(Y|c) = 2+ 4.0706 = 6.0706

6 0

1 year ago

Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in ye

sdas [7]

Answer:

$10 + (\frac{2}{3}) a = 50$ is the CORRECT equation.

Step-by-step explanation:

The given question is INCOMPLETE.

Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.” Javier writes the equation { 10 + 2/3} where a is the tree’s age in years. His equation is not correct. What error did he make?

Now here:

a: The tree’s age in years.

Also, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.”

⇒ 10 + two-thirds of that tree’s age = 50

$\implies 10 + (\frac{2}{3}) a = 50$

But in the equation written by Javier, the the third fraction is NOT MULTIPLIED by the age of the tree a in Years.

So, the written equation by Javier is Incorrect.

Now, solving the written correct equation for the value of a, we get:

$\implies 10 + (\frac{2}{3}) a = 50\\\implies (\frac{2}{3}) a = 40\\\implies a = 40 \times (\frac{3}{2}) = 60\\\implies a = 60$

Hence the correct age of the tree = 60 years

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2 years ago

After triangle ace is dilated by a factor of 5, it has an area of 100 square inches. What was its area before dilation?

NISA [10]

Answer:

20in^2

Step-by-step explanation:

Since you multiply the original area of the triangle by the scale factor to get the new area, you can find the original area (before dilation) by dividing the dilated triangle's area by the scale factor. Since 100 is the area of the dilated triangle, and 5 is your scale factor, you do 100/5 to get the area of the triangle before it was dilated.

5 0

1 year ago