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stepladder [879]

3 years ago

7

There is a mid ocean ridge between South America and Africa causing the two continents to drift away from each other. South Amer

ica and Africa have moved 250 cm away from each other in the last 100 years. What is their average speed?

1 answer:

Oksanka [162]3 years ago

5 0

Answer:

2.5 cm/year

Step-by-step explanation:

Just divide the total distance, 250 cm, by the years, 100, 250/100 = 2.5, the rate of the contintents drifting away is 2.5 cm per year, 2.5 cm/year

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Which decimal is between 6.4 and 6.6? A.) 6.04 , B.) 6.44 , C.) 6.60 , or D.) 6.06

m_a_m_a [10]

B 6.44 because 6.4 is equal to 6.40 and in between 6.40 and 6.60 there is 6.44.

4 0

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

5(g+8)-7=103<br>what's the answer?

castortr0y [4]

Do you need the steps? g=14

3 0

3 years ago

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Svetllana [295]

Composing functions means that the input of the outer functions is the output of the inner function.

In fact, you can rewrite the circle notation as

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So, we can substitute g(x) with its expression:

$(f\circ g)(x)=f(g(x))=f(4x+2)$

And since f(x)=x+5, we simply have to add 5 to its input:

$f(4x+2)=(4x+2)+5=4x+7$

Similarly, we have, substituting f with its expression,

$(g\circ f)(x)=g(f(x))=g(x+5)$

And since g(x)=4x+2, we have to multiply the input by 4 and add 2:

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7 0

3 years ago

The rent was increase by 7,5 what will be the new rent price

Shkiper50 [21]

Answer:

Is this the full question?

Step-by-step explanation:

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3 years ago