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1 year ago

19 A trapezoid has an area of 216 square

Mathematics

1 answer:

Vanyuwa [196]1 year ago

6 0

Answer:

A)18in.

Step-by-step explanation:

Given,

A trapezoid Area= 216 sq

The length of its longer base=2x

The length of its shorter base= x

Height of Trapezoid = 8in

Area of Trapezoid= 1/2h(a+b)

216=1/2 x 8(2x+x)

216=4(2x+x)

216/4=3x

54=3x

54/3=x

18=x

Length of shorter base=18

Length of longer base=2x18=36

Hence, the length of the shorter base is 18in

Option A) is correct

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3 years ago

In a particular faculty 60% of students are men and 40% are women. In a random sample of 50 students what is the probability tha

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Answer:

a) The expected value is given by:

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And we can find this probability with the following Excel code:

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And we got:

$P(X>25)= 1-P(X\leq 25)=0.0573$

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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".

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

$X \sim Binom(n=50, p=0.4)$

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:

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Part a

The expected value is given by:

$E(X) = np = 50*0.4 = 20$

and the variance is given by:

$Var(X) =np(1-p) = 50*0.4*(1-0.4) = 12$

Part b

For this case we want to find this probability:

$P(X>25)= 1-P(X\leq 25)$

And we can find this probability with the following Excel code:

=1-BINOM.DIST(25,50,0.4,TRUE)

And we got:

$P(X>25)= 1-P(X\leq 25)=0.0573$

Part c

1) Random sample (assumed)

2) np= 50*0.4= 20 >10

n(1-p) =50*0.6= 30>10

3) Independence (assumed)

Since the 3 conditions are satisfied we can use the normal approximation:

$X \sim N(\mu = 20 , \sigma= 3.464)$

Part d

We want this probability:

$P(X>25) = 1-P(Z< \frac{25-20}{3.464}) = 1-P(z$

Part e

For this case we use the continuity correction and we have this:

$P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)$

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Step-by-step explanation:

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Step-by-step explanation:

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