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Vesnalui [34]
3 years ago
8

The data from 200 endothermic reactions involving sodium bicarbonate are summarized as follows: calculate the probability mass f

unction of final temperature
Mathematics
1 answer:
In-s [12.5K]3 years ago
8 0
Given the table below which contains data from 200 endothemic reactions involving <span>sodium bicarbonate:

\begin{tabular}&#10;{|c|c|}&#10;Final Temperature Conditions&Number of Reactions\\[1ex]&#10;266 K&48\\&#10;271 K&60\\&#10;274 K&92&#10;\end{tabular}

We find the probability distribution function as follows:

Let X denote the final temperature, then
</span>
<span>P(X = 266) =  \frac{48}{200} =0.24\\ \\ P(X = 271) =  \frac{60}{200} =0.3\\ \\ P(X = 274) =  \frac{92}{200} =0.46</span>
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Tamir bought 2 1/2 pounds of fish at $5.50 per pound, and two bananas at the price shown
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2 years ago
A quiz-show contestant is presented with two questions, question 1 and question 2, and she can choose which question to answer f
Mrrafil [7]

Answer:

The contestant should try and answer question 2 first to maximize the expected reward.

Step-by-step explanation:

Let the probability of getting question 1 right = P(A) = 0.60

Probability of not getting question 1 = P(A') = 1 - P(A) = 1 - 0.60 = 0.40

Let the probability of getting question 2 right be = P(B) = 0.80

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To obtain the better option using the expected value method.

E(X) = Σ xᵢpᵢ

where pᵢ = each probability.

xᵢ = cash reward for each probability.

There are two ways to go about this.

Approach 1

If the contestant attempts question 1 first.

The possible probabilities include

1) The contestant misses the question 1 and cannot answer question 2 = P(A') = 0.40; cash reward associated = $0

2) The contestant gets the question 1 and misses question 2 = P(A n B') = P(A) × P(B') = 0.6 × 0.2 = 0.12; cash reward associated with this probability = $200

3) The contestant gets the question 1 and gets the question 2 too = P(A n B) = P(A) × P(B) = 0.6 × 0.8 = 0.48; cash reward associated with this probability = $300

Expected reward for this approach

E(X) = (0.4×0) + (0.12×200) + (0.48×300) = $168

Approach 2

If the contestant attempts question 2 first.

The possible probabilities include

1) The contestant misses the question 2 and cannot answer question 1 = P(B') = 0.20; cash reward associated = $0

2) The contestant gets the question 2 and misses question 1 = P(A' n B) = P(A') × P(B) = 0.4 × 0.8 = 0.32; cash reward associated with this probability = $100

3) The contestant gets the question 2 and gets the question 1 too = P(A n B) = P(A) × P(B) = 0.6 × 0.8 = 0.48; cash reward associated with this probability = $300

Expected reward for this approach

E(X) = (0.2×0) + (0.32×100) + (0.48×300) = $176

Approach 2 is the better approach to follow as it has a higher expected reward.

The contestant should try and answer question 2 first to maximize the expected reward.

Hope this helps!!!

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3 years ago
Three forces of 300 N in the direction of N30E, 400N in the direction of N60E and
andreyandreev [35.5K]

Split up each force into horizontal and vertical components.

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The resultant force is the sum of these forces,

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∑ F ≈ (546.632 i + 988.814 j) N

so ∑ F has a magnitude of approximately 1129.85 N and points in the direction of approximately N61.0655°E.

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