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2 years ago

Find the area of the region (in square units) exact number

Mathematics

1 answer:

Margaret [11]2 years ago

3 0

The area of the region = area of the two rectangles = 64 units².

<h3>How to Find the Area of Rectangles?</h3>

A rectangle has a length and a width, and its area can be calculated using the formula below:

area of rectangle = (length)(width).

The region shown is composed of two rectangles. To find the area of the region, calculate the area of each of the rectangles in the image given.

Area of rectangle 1 = (length)(width)

Length = 12 units

Width = 4 units

Area of rectangle 1 = (12)(4)

Area of rectangle 1 = 48 units²

Area of rectangle 2 = (length)(width)

Length = 4 units

Width = 4 units

Area of rectangle 2 = (4)(4)

Area of rectangle 2 = 16 units²

The area of the region = area of the two rectangles = 48 + 16 = 64 units²

Learn more about the area of rectangle on:

brainly.com/question/25292087

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3 years ago

Expand 3(x+ 2.3) <br> Expand 1/3(9x-12)

Snezhnost [94]

Answer:

3x+6.9 and 3x-4

Step-by-step explanation:

since 3 x x is 3x and the sign in the bracket is addition you place it there then place 3 x 2.3

being 6.9.

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3 years ago

A bus travels on an east-west highway connecting two cities A and B that are 100 miles apart. There are 2 services stations alon

melamori03 [73]

Answer:

51/4

Step-by-step explanation:

To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.

X~ Uniform(0,100)

Then the probability mass function is given as follows.

$f(x) = P(X=x) = 1/100 \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0 \,\,\,\, \text{otherwise}$

Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located 70 meters away from city A then the mid point between 20 and 70 is (70+20)/2 = 45 then we can represent D as follows

$D(x) =\left\{ \begin{array}{ll} x & \mbox{if } 0\leq x \leq 20 \\ x-20 & \mbox{if } 20\leq x < 45\\ 70-x & \mbox{if } 45 \leq x \leq 70\\ x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.$

Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable $Y = D(X)$ , $Y$ is a random variable as well, remember that there is a theorem that says that

$E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx$

Where $f(x)$ is the probability mass function of X. Using the information of our problem

$E[Y] = \int\limits_{-\infty}^{\infty} D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx \bigg]\\= \frac{51}{4} = 12.75$