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3 years ago

Evaluate -6-(-5) x (-9)

Mathematics

2 answers:

Rom4ik [11]3 years ago

3 0

9.
That’s the answer

morpeh [17]3 years ago

3 0

Answer:

-6+5×(-9)

-1×-9

Step-by-step explanation:

hope this helps you!!!

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If the area of triangle is 1200 sq m and its length is 60 m , find the breadth .

Kruka [31]

Answer:

20 m

Step-by-step explanation:

The area of a triangle is 120 sq m

The length is 60 m

We are required to find the breadth

Therefore to find the breadth of the traingle the formular below will be applied

Area= length × breadth

120= 60 × breadth

Breadth= 120/60

= 20 m

Hence the breadth of the traingle is 20 m

3 0

3 years ago

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 6 minutes. Assu

denis-greek [22]

Answer:

43.46% probability that the person will need to wait at least 9 minutes total

Step-by-step explanation:

To solve this question, we need to understand conditional probability and the exponential distribution.

Conditional probability:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

Expontial distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

In this question:

Event A: Waited at least 4 minutes.

Event B: Waiting at least 9 minutes.

The length of time for one individual to be served at a cafeteria is an exponential random variable with mean of 6 minutes.

This means that $m = 6, \mu = \frac{1}{6}$

Probability of waiting at least 4 minutes.

$P(A) = P(X \geq 4) = P(X > 4)$

$P(A) = P(X > 4) = e^{-\frac{4}{6}} = 0.5134$

Intersection:

The intersection between a waiting time of at least 4 minutes and a waiting time of at list 9 minutes is a waiting time of 9 minutes. So

$P(A \cap B) = P(X > 9) = e^{-\frac{9}{6}} = 0.2231$

What is the probability that the person will need to wait at least 9 minutes total

$P(B|A) = \frac{0.2231}{0.5134} = 0.4346$

43.46% probability that the person will need to wait at least 9 minutes total

8 0

4 years ago

A cylinder with radius r and height 2r+4 contains a cube with edge length r + 2, as shown.

marishachu [46]

Volume is the amount of space in an object. The fraction occupied by the cube is: $\frac{r\sqrt2}{\pi(r + 2)}$

First, we calculate the volume of the cube.

$Volume = Length^3$

From the figure, we have:

$Length = r\sqrt 2$

So:

$V_1 = (r\sqrt2)^3$

$V_1 = (2\sqrt2)r^3$

Next, the volume of the cylinder

$Volume=\pi r^2h$

So, we have:

$V_2 = \pi r^2 (2r + 4)$

The fraction (n) occupied by the cube is:

$n = \frac{V_1}{V_2}$

So, we have:

$n = \frac{(2\sqrt2)r^3}{\pi r^2(2r + 4)}$

Factor out 2 in the denominator

$n = \frac{(2\sqrt2)r^3}{2\pi r^2(r + 2)}$

Cancel out common terms

$n = \frac{r\sqrt2}{\pi(r + 2)}$

<em>Hence, the fraction occupied by the cube is: </em> $\frac{r\sqrt2}{\pi(r + 2)}$ <em />