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3 years ago

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In a school band, the ratio of student late who play the tuba to the students who play the trumpets is 1:6. The ratio of student

s who play the to the students who play the flute is 3:4. If there are 3 student who play the tuba. How many student play the flute?

1 answer:

AlexFokin [52]3 years ago

7 0

A lot, 1:6 + 3:4 +3 = .116789465 hope this helps....

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A boat traveled 225 miles each way downstream and back. The trip downstream took 9 hours. The trip back took 15 hours. What is t

Karolina [17]

Answer:

Boat = 20 mph

Current = 5 mph

Step-by-step explanation:

If b is the speed of the boat, and c is the speed of the current, then:

b + c = 225 / 9 = 25

b − c = 225 / 15 = 15

Solve the system of equations with elimination.

2b = 40

b = 20

Plug back into either equation to find the speed of the current.

c = 5

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3 years ago

A food-packaging apparatus underfills 10% of the containers. Find the probability that for any particular 10 containers the numb

Maksim231197 [3]

Answer:

a) $P(X = 1) = 0.38742$

b) $P(X = 3) = 0.05740$

c) $P(X = 9) = 0.00000$

d) $P(X \geq 5) = 0.00163$

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it is undefilled, or it is not. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem

There are 10 containers, so $n = 10$ .

A food-packaging apparatus underfills 10% of the containers, so $p = 0.1$ .

a) This is P(X = 1)

$P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742$

b) This is P(X = 3)

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

c) This is P(X = 9)

$P(X = 9) = C_{10,9}.(0.1)^{9}.(0.9)^{1} = 0.00000$

d) This is $P(X \geq 5)$ .

Either the number is lesser than five, or it is five or larger. The sum of the probabilities of each event is decimal 1. So:

$P(X < 5) + P(X \geq 5) = 1$

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.1)^{0}.(0.9)^{10} = 0.34868$

$P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742$

$P(X = 2) = C_{10,2}.(0.1)^{2}.(0.9)^{8} = 0.1937$

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

$P(X = 4) = C_{10,4}.(0.1)^{1}.(0.9)^{9} = 0.38742$

So

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.34868 + 0.38742 + 0.19371 + 0.05740 + 0.01116 = 0.99837$

Finally

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.99837 = 0.00163$

3 0

3 years ago

pogonyaev

Answer:

You need to have both the opposite and adjacent side of the right angled triangle. Tan = Opp/Adj

Step-by-step explanation:

Tangents are pretty much everywhere. A good example is maybe a slide at the playground. You’d need the tangent to figure out the angle of the slide and how it is.

The radius from the center of a circle to the point of tangency point shows that it would be perpendicular to the tangent line considering that anything with a radius is circular and the tangent line is… a line, making it impossible to be parallel.

3 0

2 years ago

Find the missing number in each sequence.<br><br> 40, ___ , 37 1/3 , 36

seraphim [82]

The common difference is 1 1/3
40-1 1/3= 38 2/3
38 2/3-1 1/3=37 1/3
37 1/3-1 1/3=36
Therefore the missing number is 38 2/3

8 0

2 years ago

Read 2 more answers

Use the Pythagorean theorem and the following diagram to help you find the area and perimeter of the following triangle. Please

Mekhanik [1.2K]

Answer:

Perimeter = 30

Area = 30

Step-by-step explanation:

$(x+8)^2 -x^2 = 12^2$

$x^2 +16x +64 - x^2 = 144$

$16x+64=144$

$16x = 80$

$x = 5$

Double check:

$\sqrt{12^2 + 5^2} = (5+8)\\\sqrt{12^2 + 5^2} = 13\\13 = 13$

Perimeter:

$12+5+13=30$

Area( $\frac{1}{2}bh$ ):

$\frac{1}{2}$ × 12 × 5 = 30

5 0

2 years ago

Read 2 more answers