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3 years ago

A cafeteria can seat 5x102 students. Each table has 2x101 seats. How many tables are in the cafeteria?

Mathematics

1 answer:

frozen [14]3 years ago

8 0

Answer: 25 tables.

Step-by-step explanation:

5 • 10*2= 500 (10*2= 100, then 100 times 5)

2 • 10*1= 20 (10*1= 10, then times 2)

Therefore a cafeteria can seat 500 students. Each table had 20 seats.

Divide 500/20 and get 25.

Hope this helps

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Read 2 more answers

X and y are normal random variables with e(x) = 2, v(x) = 5, e(y) = 6, v(y) = 8 and cov(x,y)=2. determine the following: e(3x 2y

andriy [413]

The result for the given normal random variables are as follows;

a. E(3X + 2Y) = 18

b. V(3X + 2Y) = 77

c. P(3X + 2Y < 18) = 0.5

d. P(3X + 2Y < 28) = 0.8729

<h3>What is normal random variables?</h3>

Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Now, according to the question;

The given normal random variables are;

E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.

Part a.

Consider E(3X + 2Y)

$\begin{aligned}E(3 X+2 Y) &=3 E(X)+2 E(Y) \\&=(3) (2)+(2)(6 )\\&=18\end{aligned}$

Part b.

Consider V(3X + 2Y)

$\begin{aligned}V(3 X+2 Y) &=3^{2} V(X)+2^{2} V(Y) \\&=(9)(5)+(4)(8) \\&=77\end{aligned}$

Part c.

Consider P(3X + 2Y < 18)

A normal random variable is also linear combination of two independent normal random variables.

$3 X+2 Y \sim N(18,77)$

Thus,

$P(3 X+2 Y < 18)=0.5$

Part d.

Consider P(3X + 2Y < 28)

$Z=\frac{(3 X+2 Y-18)}{\sqrt{77}}$

$\begin{aligned} P(3X + 2Y < 28)&=P\left(\frac{3 X+2 Y-18}{\sqrt{77}} < \frac{28-18}{\sqrt{77}}\right) \\&=P(Z < 1.14) \\&=0.8729\end{aligned}$

Therefore, the values for the given normal random variables are found.

To know more about the normal random variables, here

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The correct question is-

X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following:

a. E(3X + 2Y)

b. V(3X + 2Y)

c. P(3X + 2Y < 18)

d. P(3X + 2Y < 28)

8 0

1 year ago

The function f(x) = (x − 4)(x − 2) is shown. What is the range of the function?

leonid [27]

The range of the quadratic function is [-1, ∞) after plotting the function on the coordinate plane.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The function is:

f(x) = (x - 4)(x - 2)

The above function is a quadratic function.

The above function can be written as:

f(x) = x² - 6x + 8

From the graph,

The minimum value of graph at x = 3 is y = -1

The range of the function is [-1, ∞)

Thus, the range of the quadratic function is [-1, ∞) after plotting the function on the coordinate plane.

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1 year ago

Is f(x)=13.7e^0.04t an example of exponential growth or decay

Katena32 [7]

<span>exponential growth becasue its multiplyin? decay is sbtracting or division. i think.</span>

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3 years ago

A cafeteria can seat 5x10*2 students. Each table has 2x10*1 seats. How many tables are in the cafeteria?

A cafeteria can seat 5x102 students. Each table has 2x101 seats. How many tables are in the cafeteria?