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3 years ago

A triangle has a base of 7m and an area of 17.5 squared. What is the height?

1 answer:

4 0

Area of triangle = 1/2 x base x height17.5 = 1/2 x 7 x height17.5 = 3.5 x

height = 17.5 /3.5 = 5 meters

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Three cards are chosen at random from a standard 52-card deck. What is the probability that they are not all the same color?

rewona [7]

Three cards are selected from a standard deck of 52 cards. Disregarding the order in which they are drawn, the possible outcomes are (52/3). Out of these, how many include all cards of the same color (say red)? There are (13/3) ways in which you can get all 13 red cards.

8 0

3 years ago

The computer center at Dong-A University has been experiencing computer down time. Let us assume that the trials of an associate

Schach [20]

Answer:

(a)0.16

(b)0.588

Step-by-step explanation:

The matrix below shows the transition probabilities of the state of the system.

$\left(\begin{array}{c|cc}&$Running&$Down\\---&---&---\\$Running&0.90&0.10\\$Down&0.30&0.70\end{array}\right)$

(a)To determine the probability of the system being down or running after any k hours, we determine the kth state matrix $P^k$ .

(a)

$P^1=\left(\begin{array}{c|cc}&$Running&$Down\\---&---&---\\$Running&0.90&0.10\\$Down&0.30&0.70\end{array}\right)$

$P^2=\begin{pmatrix}0.84&0.16\\ 0.48&0.52\end{pmatrix}$

If the system is initially running, the probability of the system being down in the next hour of operation is the $(a_{12})th$ entry of the P^2$ matrix.$

The probability of the system being down in the next hour of operation = 0.16

(b)After two(periods) hours, the transition matrix is:

$P^3=\begin{pmatrix}0.804&0.196\\ 0.588&0.412\end{pmatrix}$

Therefore, the probability that a system initially in the down-state is running

is 0.588.

(c)The steady-state probability of a Markov Chain is a matrix S such that SP=S.

Since we have two states, $S=[s_1$ s_2]$

$[s_1$ s_2]\left(\begin{array}{ccc}0.90&0.10\\0.30&0.70\end{array}\right)=[s_1$ s_2]$

Using a calculator to raise matrix P to large numbers, we find that the value of $P^k$ approaches [0.75 0.25]:

Furthermore,

$[0.75$ 0.25]\left(\begin{array}{ccc}0.90&0.10\\0.30&0.70\end{array}\right)=[0.75$ 0.25]$

The steady-state probabilities of the system being in the running state and in the down-state is therefore:

$[s_1$ s_2]=[0.75$ 0.25]$

4 0

4 years ago

Which sentence about the diagram is true?

LUCKY_DIMON [66]

Answer is choice C: If a line is drawn through point A and point X, then it will bisect line segment BC.

This line is the third missing median of the triangle. A median goes from one vertex to the midpoint of the opposite side. The midpoint cuts the segment in half. For example, median CD cuts segment AB in half (AD = DB). All three medians of a triangle meet at the same point: the centroid

7 0

3 years ago

Using the figure of the bullseye above, what is the probability that a shooter will hit the 3rd ring? Express your answer as a p

melisa1 [442]

The probability of hitting the third ring is the same as finding what percentage is the area of the third ring out of the total area of the board.

The area of the third ring = The total area of the board - The area of the second circle.

Refer to the diagram below
The diameter for the whole circle = 32 in
The radius = 16 in
The area of the whole circle = π(16)² = 256π

The diameter for the second circle = 22 in
The radius = 11 in
The area of the second circle = π(11)² = 121π

The area of the third ring = 256π - 121π = 135π

Area of the third ring as a percentage of the total area = $\frac{135 \pi }{256 \pi } *100$ = 52.7%

7 0

3 years ago

Read 2 more answers

What is the length of AC?

Ket [755]

The answer is C. 136.

I hope this helps.

3 0

4 years ago

Read 2 more answers