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3 years ago

If y varies directly with x and y = 2 when x = 10, then what is the value of y when x = 40? A. 8 B. 45 C. 200 D. 320

Mathematics

2 answers:

aivan3 [116]3 years ago

4 0

Answer:

Step-by-step explanation:

Leto [7]3 years ago

3 0

Answer:

Step-by-step explanation:

given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the given condition y = 2 when x = 10

k = $\frac{y}{x}$ = $\frac{2}{10}$ = $\frac{1}{5}$

y = $\frac{1}{5}$ x ← equation of variation

when x = 40, then

y = $\frac{1}{5}$ × 40 = 8 → A

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crimeas [40]

Answer:

a) $X \sim Binom(n=16, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

The expected value is given by this formula:

$E(X) = np=16*0.2=3.2$

b) $P(X=0)=(16C0)(0.2)^{0} (1-0.2)^{16-0}=0.02815$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Part a

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=16, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

The expected value is given by this formula:

$E(X) = np=16*0.2=3.2$

Part b

For this case we want this probability:

$P(X=0)$