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garik1379 [7]
3 years ago
12

A rectangle has a perimeter of 68 inches it’s length is 2 inches less than 3 times the width what is the area of the rectangle

Mathematics
1 answer:
Kruka [31]3 years ago
4 0

Answer:

225 inches²

Step-by-step explanation:

Let the length be l and width be w

Condition 1

2l+2w=68 (Perimeter=68)--------(i)

Condition 2

l=3w-2 ---------(ii)

Putting equation (ii) in (i)

2(3w-2)+2w=68

6w-4+2w=68

8w-4=68

8w=68+4

8w=72

dividing both sides by 8

w=9 inches

now putting w=9 in (ii)

l=3(9)-2

l=27-2

l=25 inches

Now

Area of rectangle =  l × w

=9 × 25

=225 inches²

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In a certain college, 33% of the physics majors belong to ethnic minorities. Find the probability of the event from a random sam
mel-nik [20]

Answer:

The probability that no more than 6 students belong to a ethnic minority is 0.9815.

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to an ethnic minority?</em>

We can model this with a random variable, with sample size n=10 and probability of success p=0.33.

The probability that k answers are guessed right in the sample is:

P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{10}{k}\cdot0.33^k\cdot0.67^{10-k}

We have to calculate the probability that 6 or less students belong to a ethnic minority. This can be calculated as:

P(x\leq6)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)\\\\\\

P(x=0)=\dbinom{10}{0}\cdot0.33^{0}\cdot0.67^{10}=1\cdot1\cdot0.0182=0.0182\\\\\\P(x=1)=\dbinom{10}{1}\cdot0.33^{1}\cdot0.67^{9}=10\cdot0.33\cdot0.0272=0.0898\\\\\\P(x=2)=\dbinom{10}{2}\cdot0.33^{2}\cdot0.67^{8}=45\cdot0.1089\cdot0.0406=0.1990\\\\\\P(x=3)=\dbinom{10}{3}\cdot0.33^{3}\cdot0.67^{7}=120\cdot0.0359\cdot0.0606=0.2614\\\\\\

P(x=4)=\dbinom{10}{4}\cdot0.33^{4}\cdot0.67^{6}=210\cdot0.0119\cdot0.0905=0.2253\\\\\\P(x=5)=\dbinom{10}{5}\cdot0.33^{5}\cdot0.67^{5}=252\cdot0.0039\cdot0.135=0.1332\\\\\\P(x=6)=\dbinom{10}{6}\cdot0.33^{6}\cdot0.67^{4}=210\cdot0.0013\cdot0.2015=0.0547\\\\\\\\\\\\

P(x\leq6)=0.0182+0.0898+0.1990+0.2614+0.2253+0.1332+0.0547\\\\\\P(x\leq6)=0.9815

The probability that 6 or less students belong to a ethnic minority is 0.9815.

5 0
3 years ago
1. Evaluate the expression when x=2, y = 3, and z= -9:
kupik [55]

Answer:

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Step-by-step explanation:

substitute the given values into the expression

xy-<em>x</em>

<em>(</em>-2 times 3<em>)</em>-1

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6 0
3 years ago
What is the equation of the inverse function A(n)=3n-20
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Answer:

A^{-1}(n)=\frac{1}{3}n+\frac{20}{3}

Step-by-step explanation:

First, let's change those variables to x and y, just for the sake of convenience.  In order to find the inverse of a function algebraically, switch the x and y coordinates, then solve for the new y.  Letting y = A(n) and x = n (we will switch them back when we're done):

y = 3x - 20.  This is linear; a line with a slope of 3 and a y-intercept of -20.  When we switch the x and the y, we get:

x = 3y - 20.  Now we solve for the new y.  Begin by adding 20 to both sides:

x + 20 = 3y.  Now divide both sides by 3:

\frac{x+20}{3}=y, or to write it in slope-intercept form, like the function you started with:

y=\frac{1}{3}x+\frac{20}{3}

This is also a line, with a slope of 1/3 and a y-intercept of +20/3

Now, replacing:

A^{-1}(n)=\frac{1}{3}n+\frac{20}{3}

That is how to write the inverse using function notation.  The little -1 as an exponent tells us that this is the inverse of the function A(n).

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