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Nataly_w [17]
3 years ago
12

Forty percent of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random: Wh

at is the probability all three of the selected homes have a security system
Mathematics
1 answer:
suter [353]3 years ago
6 0

Answer: 0.064

Step-by-step explanation:

Binomial probability formula :-

P(X)=^nC_x \ p^x\ (1-p)^{n-x}, where P(x) is the probability of getting success in x trials, n is total number of trials and p is the probability of getting succes in each trial.

Given : The proportion of the homes constructed in the Quail Creek area include a security system :  p=0.40

Now, if three homes are selected at random, then the probability all three of the selected homes have a security system is given by :-

P(3)=^3C_3 \ (0.40)^3\ (1-0.40)^{3-3}\\\\=(0.40)^3=0.064

Hence, the probability all three of the selected homes have a security system = 0.064

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In which step did Rob make a mistake?
Karolina [17]
Answer:

Explanation:

Using the PEMDAS rule:
P = parentheses
E = exponent
M = multiplication
D = division
A = Addition
S = subtraction

Step 1: 6 + 4 x 3 - 10/5

Step 2: 6 + 12 - 2

Step 3: 18 - 2

Step 4: 16


6 0
3 years ago
In how many ways can 6 competitors finish a race assuming there are no ties?In how many ways can we sit n people on r < n cha
VLD [36.1K]

Answer:  a) 720, b) ^nC_r=\dfrac{n!}{(n-r)!r!} c) 336, d) 30240 e) 120.

Step-by-step explanation:

Since we have given that

a) Number of competitors  = 6

We need to find the number of ways that 6 competitors can finish a race and there are no ties.

So, Number of ways would be

6!=720

b) number of people = n

Number of chairs = r (r<n)

so, the number of ways we can sit n people on r<n chairs is given by

^nC_r=\dfrac{n!}{(n-r)!r!}

c) If there are three awards :

Gold, silver, bronze.

We need to find the number of ways that these medals can be awarded.

Number of ways is given by

^8P_3\\\\=336

d) Number of 5-digit zip codes are possible is given by

^{10}P_5=30240

e) Number of poeple = 10

Number of people required in committee = 3

Number of different 3 person committee that are selected from 10 people is given by

^{10}C_3=120

Hence, a) 720, b) ^nC_r=\dfrac{n!}{(n-r)!r!} c) 336, d) 30240 e) 120.

6 0
3 years ago
£750 is divided between Bridget, Caroline &amp; Sarah so that Bridget gets twice as much as Caroline, and Caroline gets three ti
Sladkaya [172]

Answer: £225

Step-by-step explanation:

Let Sarah's amount be represented by x.

Since Caroline gets three times as much as Sarah, Caroline will get: 3x

Bridget gets twice as much as Caroline, therefore Bridget will get: 2 × 3x = 6x

Sarah = x

Caroline = 3x

Bridget = 6x

Total = x + 3x + 6x = 10x

Caroline's faction is 3/10. We then multiply the fraction by £750. This will be:

= 3/10 × £750

= 0.3 × £750

= £225

Caroline will get £225

4 0
3 years ago
If 5&lt;2x+3&lt;11, what is the possible range of value of -4x-6
Lady bird [3.3K]

Answer:

-10 > (-4x - 6) > -22

Step-by-step explanation:

Given inequality is 5 < 2x + 3 < 11

Now we will multiply this inequality by (-2) resulting,

5(-2) > (2x + 3)(-2) > 11(-2)

-10 > (-4x - 6) > -22 (Sign of inequality gets reversed when the inequality is multiplied or divided by a negative number)

Therefore, the possible range of (-4x - 6) is between -22 and -10.

4 0
3 years ago
F(x) = 3x2 - 11<br> Find f(-5)
Over [174]
F(x)=3x2-11
f(5)=6-11
5f=-5
5f/5=-5/5
f=-1
6 0
3 years ago
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