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2 years ago

3. Tom, Sam and Matt are counting drum beats.

Mathematics

1 answer:

just olya [345]2 years ago

6 0

Answer:

When 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.

Step-by-step explanation:

The Least Common Multiple ( LCM )

The LCM of two integers a,b is the smallest positive integer that is evenly divisible by both a and b.

For example:

LCM(20,8)=40

LCM(35,18)=630

Since Tom, Sam, and Matt are counting drum beats at their own frequency, we must find the least common multiple of all their beats frequency.

Find the LCM of 4,10,12. Follow this procedure:

List prime factorization of all the numbers:

4 = 2*2

10 = 2*5

12 = 2*2*3

Multiply all the factors the greatest times they occur:

LCM=2*2*3*5=60

Thus, when 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.

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Te probability is 0.5 that an artist makes a craf item with satisfactory quality. Assume the production of each craf item by thi

mina [271]

Answer:

The probability that at most 3 attempts are required to produce a craft item with satisfactory quality is 0.9375

Step-by-step explanation:

Let E be a random variable denoting the event that an artist makes a craft item with satisfactory level.

Then the random variable E follows a Geometric distribution.

A Geometric distribution is defined as the number of failures (k) before the first success.

The probability function of Geometric distribution is:

$P(X=k)=(1-p)^{k}p$ , p = Probability of success and k = 0, 1, 2, 3...

The probability of success is, p = 0.5 and the number of failures is, k = 3.

Compute the probability of at most 3 attempts before the first success is:

$P(X\leq 3) =P(X=3)+P(X = 2)+P(X=1) +P(X = 0)\\=[(1-0.5)^{0}*0.5]+[(1-0.5)^{1}*0.5]+[(1-0.5)^{2}*0.5]+[(1-0.5)^{3}*0.5]\\=0.9375$

Therefore, the probability that at most 3 attempts are required to produce a craft item with satisfactory quality is 0.9375.

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2 years ago

Mark and his friends order two pizzas of the same size the first pizza is cut into 6 slices of equal size the second pizza is cu

Anettt [7]

Answer:

The first pizza is 6 slices, so each slice is 1/6 of a pizza. The second pizza is 4 slices, so each slice is 1/4 of a pizza. If you were to take one slice of each, you would get 1/6 +1/4 slice, which would be 5/12 of a pizza, as opposed to if you took 2 slices of the first pizza, which would only be 4/12 of a pizza.

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2 years ago

Use two points to enter an equation for the function. Give your answer in the form a(b)^n. In the event that a = 1, give your an

levacccp [35]

Answer:

$m(n) = 24 (0.75)^n$

Step-by-step explanation:

1) The two points are:

a) On the first swing she swings forward by 18 degrees: (1, 18)

b) On the second swing she only comes 13.5 degrees forward: (2,13.5)

2) The general equation using the form given is:

$m(n)=A(B)^n$

3) Substitute the two points:

$18=A(B)\\ \\ 13.5=A(B)^2$

4) Divide the second equation by the first one:

⇒ 13.5 / 18 = B

⇒ B = 0.75

5) Substitue B = 0.75 into the first equation:

18 = A (0.75) ⇒ A = 18 / 0.75 = 24

Hence, the equation is:

$m(n) = 24 (0.75)^n$

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2 years ago

You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4000 per mont

Molodets [167]

Answer:

$311.74

Step-by-step explanation:

A financial calculator computes the payment amount to be $311.74.

___

Your graphing calculator may have the capability to do this. Certainly, such calculators are available in spreadsheet programs and on the web.

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The appropriate formula is the one for the sum of terms of a geometric series.

Sn = a1·((1+r)^n -1)/(r) . . . . . where r is the monthly interest rate (0.005) and n is the number of payments (480). Filling in the given numbers, you have ...

$620827.46 = a1·(1.005^480 -1)/.005 = 1991.4907·a1

Then ...

$620827.46/1991.4907 = a1 ≈ $311.74

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2 years ago

WILL GIVE BRAINILEST! Examine the paragraph proof. Which theorem does it offer proof for? lines WZ and XY intersect at point V P

aliya0001 [1]

Answer:

Vertical Angles Theorem

Step-by-step explanation:

Vertical angles have two sets of congruent angles; the angle acrooss the other are congruent to each other.

Also, I took the test and got it right. Hope this helps!!

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2 years ago

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