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3 years ago

7

On the coordinate plane shown, each grid unit represents 10 feet. Polygon QRST has vertices Q(20, 30), R(−10, 30), S(−10, −20),

and T(20, −20), and represents the floor plan of a room. Find the perimeter and area of the room.

1 answer:

beks73 [17]3 years ago

4 0

The coordinate plane is missing, so i have attached it.

Answer:

Perimeter of room = 140 ft

Area of room = 1200 sq.ft

Step-by-step explanation:

From the cordinate plane attached, we can see the polygon QRST which represents the floor plan of the roo.

Thus;

The length of the sides of the room are;

ST = RQ = 30

QT = RS = 40

Perimeter of a rectangle is the sum of all sides of the rectangle.

Thus, perimeter of the room = (30 × 2) + (40 × 2) = 140 ft

Now, area of a rectangle is the product of two perpendicular sides.

Thus area of room = 40 x 30 = 1200 sq.ft

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In Illinois, 9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been arre

Veseljchak [2.6K]

Answer:

a) 21.58% probability that exactly 3 people are repeat offenders

b) 97.91% probability that at least one person is a repeat offender

c) 3.69

d) 1.83

Step-by-step explanation:

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 combinations 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.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders

This means that $p = 0.09$

41 people arrested for DUI in Illinois are selected at random.

This means that $n = 41$

a. What is the probability that exactly 3 people are repeat offenders?

This is P(X = 3).

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

$P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158$

21.58% probability that exactly 3 people are repeat offenders

b. What is the probability that at least one person is a repeat offender?

Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ .

Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791$

97.91% probability that at least one person is a repeat offender

c. What is the mean number of repeat offenders?

$E(X) = np = 41*0.09 = 3.69$

d. What is the standard deviation of the number of repeat offenders?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83$

4 0

3 years ago

Do i need to flip the reciprocal please explain your answer<br> 2y/2 < 10/2

saul85 [17]

Answer:

$\displaystyle \large \boxed{y < 5}$

Step-by-step explanation:

We are given the Inequality:

$\displaystyle \large{ \frac{2y}{2} < \frac{10}{2} }$

First, we can simplify the expression. On the left side of Inequality, we can cancel 2; on the right side, we can cancel 2 out as well.

Simply, division!

$\displaystyle \large{ \frac{ \cancel{2}y}{ \cancel{2}} < \frac{ \cancel{10}}{ \cancel{2} }}$

2 divides 2 is 1; 2 divides 10 is 5.

$\displaystyle \large{ \frac{1y}{1} < \frac{ 5}{ 1}}$

Generally, it is not recommended to write 1 beside the variable nor write 1 as a denominator.

Simplify the expression:-

$\displaystyle \large{ y < 5}$

Therefore, the value of y is less than 5.

Let me know if you have any questions after reading the explanation!

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2 years ago