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Lorico [155]
3 years ago
8

85.87 J or heat energy is added to a 34.8 g mass of substance the temperature rises from 21.76°C

Mathematics
1 answer:
Andru [333]3 years ago
7 0

Answer:

The required specific heat is 196.94 joule per kg per °C  

Step-by-step explanation:

Given as :

The heat generated = Q = 85.87 J

Mass of substance  (m)= 34.8 gram = 0.0348 kg

Change in temperature = T2 - T1 = 34.29°C - 21.76°C = 12.53°C

Let the specific heat = S

Now we know that

Heat = Mass × specific heat × change in temperature

Or, Q = msΔt

Or, 85.87 = (0.0348 kg ) × S × 12.53°C

Or , 85.87 = 0.4360 × S

Or, S = \frac{85.87}{0.4360}

∴ S = 196.94 joule per kg per °C

Hence the required specific heat is 196.94 joule per kg per °C   Answer

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Answer:

y≤3

Step-by-step explanation:

5y+4≤22−y

<em>Step 1: Simplify both sides of the inequality.</em>

5y+4≤−y+22

<em>Step 2: Add y to both sides.</em>

5y+4+y≤−y+22+y

6y+4≤22

<em>Step 3: Subtract 4 from both sides.</em>

6y+4−4≤22−4

6y≤18

<em>Step 4: Divide both sides by 6.</em>

6y/6≤18/6

y≤3

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2 years ago
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Four cards are dealt from a standard fifty-two-card poker deck. What is the probability that all four are aces given that at lea
elena-s [515]

Answer:

The probability is 0.0052

Step-by-step explanation:

Let's call A the event that the four cards are aces, B the event that at least three are aces. So, the probability P(A/B) that all four are aces given that at least three are aces is calculated as:

P(A/B) =  P(A∩B)/P(B)

The probability P(B) that at least three are aces is the sum of the following probabilities:

  • The four card are aces: This is one hand from the 270,725 differents sets of four cards, so the probability is 1/270,725
  • There are exactly 3 aces: we need to calculated how many hands have exactly 3 aces, so we are going to calculate de number of combinations or ways in which we can select k elements from a group of n elements. This can be calculated as:

nCk=\frac{n!}{k!(n-k)!}

So, the number of ways to select exactly 3 aces is:

4C3*48C1=\frac{4!}{3!(4-3)!}*\frac{48!}{1!(48-1)!}=192

Because we are going to select 3 aces from the 4 in the poker deck and we are going to select 1 card from the 48 that aren't aces. So the probability in this case is 192/270,725

Then, the probability P(B) that at least three are aces is:

P(B)=\frac{1}{270,725} +\frac{192}{270,725} =\frac{193}{270,725}

On the other hand the probability P(A∩B) that the four cards are aces and at least three are aces is equal to the probability that the four card are aces, so:

P(A∩B) = 1/270,725

Finally, the probability P(A/B) that all four are aces given that at least three are aces is:

P=\frac{1/270,725}{193/270,725} =\frac{1}{193}=0.0052

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