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2 years ago

Question 17 of 25

Mathematics

1 answer:

Brilliant_brown [7]2 years ago

3 0

Answer:

Step-by-step explanation:

y = $\frac{5}{2}$ x + 2 → (1)

2y = 5x + 4 ( divide through by 2 )

y = $\frac{5}{2}$ x + 2 → (2)

the 2 equations are the same and will have infinitely many solutions

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A coin is to be tossed as many times as necessary to turn up one head. Thus the elements c of the sample space C are H, TH, TTH,

slavikrds [6]

Answer:

Step-by-step explanation:

As stated in the question, the probability to toss a coin and turn up heads in the first try is $\frac{1}{2}$ , in the second is $\frac{1}{4}$ , in the third is $\frac{1}{8}$ and so on. Then, P(C) is given by the next sum:

$P(C)=\sum^{\infty}_{n=1}(\frac{1}{2} )^{n}=1$

This is a geometric series with factor $\frac{1}{2}$ . Then is convergent to $\frac{1}{1-\frac{1}{2}}-1=1.$ . With this we have proved that P(C)=1.

Now, observe that

$P(H)=\frac{1}{2}, P(TH)=\frac{1}{4},P(TTH)=\frac{1}{8},P(TTTH)=\frac{1}{16},P(TTTTH)=\frac{1}{32},P(TTTTTH)=\frac{1}{64}.$

Then

$P(C1)=P(H)+P(TH)+P(TTH)+P(TTTH)+P(TTTTH)=\frac{1}{2} +\frac{1}{4} +\frac{1}{8} +\frac{1}{16} +\frac{1}{32} =\frac{31}{32}$

$P(C2)=P(TTTTH)+P(TTTTTH)=\frac{1}{32}+\frac{1}{64} =\frac{3}{64}$

$P(C1\cap C2)=P(TTTTH)=\frac{1}{32}$

and

$P(C1\cup C2)=P(H)+P(TH)+P(TTH)+P(TTTH)+P(TTTTH)+P(TTTTTH)=\frac{1}{2} +\frac{1}{4} +\frac{1}{8} +\frac{1}{16} +\frac{1}{32} +\frac{1}{64}=\frac{63}{64}$

5 0

2 years ago

A builder planned to build dog houses for his pets .each dog house will be on 1/3 of an acre of land .how much land will he need

ryzh [129]

You will need 1/2 of an acre

5 0

2 years ago

Jillian rolled a number cube 360 times. About how many times do you expect her to roll a 2

Gnoma [55]

Answer: If it is split by equal sections then the answer Would be 60

Give Brainliest plz

3 0

3 years ago

A coin bank has 250 coins dimes and quarters worth 39.25 how many of each type of coins are there?

Maurinko [17]

Set up a system of equations.

0.10d + 0.25q = 39.25
d + q = 250

Where 'd' represents the number of dimes, and 'q' represents the number of quarters.

d + q = 250

Subtract 'q' to both sides:

d = -q + 250

Plug in '-q + 250' for 'd' in the 1st equation:

0.10(-q + 250) + 0.25q = 39.25

Distribute 0.10:

-0.10q + 25 + 0.25q = 39.25

Combine like terms:

0.15q + 25 = 39.25

Subtract 25 to both sides:

0.15q = 14.25

Divide 0.15 to both sides:

q = 95

Now plug this into any of the two equations to find 'd':

d + q = 250

d + 95 = 250

Subtract 95 to both sides:

d = 155

So there are 95 quarters and 155 dimes.

8 0

3 years ago

Read 2 more answers

What Is -0.75-(-2/50)+0.4(-3/4)? Explain and answer the question please

lilavasa [31]

The answer is -1.01
I first changed the signs of the ones i could. So -0.75+(2/50)+0.4(-3/4)
Then i multiplied the 0.4*-3/4 which equals -0.3
So you are left with -0.75+(2/50)-0.3
2/50 is equal to 0.04 so now it is -0.75+0.04-0.3 and the rest is simple math. Which equals -1.01

3 0

3 years ago