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lesya [120]
2 years ago
13

A real estate agent has 8 master keys to open several new homes. Only 1 master key will open any given house. If 40% of these ho

mes are usually left unlocked, what is the probability that the real estate agent can get into a specific home if the agent selects 3 master keys at random before leaving the office?
Mathematics
1 answer:
riadik2000 [5.3K]2 years ago
5 0

Answer:

Step-by-step explanation:

Suppose F represents the value that a room is unlocked.

Then, we can assume that the probability of unlocked homes is:

P(unlocked homes) = P(U)

P(unlocked homes) = 40%

P(unlocked homes) = 0.40

Also, let us represent the value of the locked room with G.

P(locked homes) = P(G)

P(locked homes) = (1 - 0.40)

P(locked homes) = 0.60

Let the probability of selecting a correct key be P(S)

It implies that for the agent to use 3 keys, we have a combination of ^8C_3 possible ways for the set of keys.

Now; since only one will open the house, then:

P(select correct key) = P(S)

P(S) = \dfrac{ (^1_1) (^7_2)   }{   ^8_3 }

P(S) = \dfrac{21}{56}

P(S) = 0.375

Finally, for the real estate agent to have access to specific homes supposing the agent select three master keys at random prior to the time he left his office, Then:

P(F ∪ (G∩S) = P(F) + P(G∩S)

P(F ∪ (G∩S) = P(F) + P(G) × P(S)

P(F ∪ (G∩S) = 0.40 + (0.60×0.375)

P(F ∪ (G∩S) = 0.40 + 0.225

P(F ∪ (G∩S) =0.625

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Fiesta28 [93]
A² + b² = c²   a and b are the legs and c is the hypotenuse.

7² + 24² = c²

49 + 576 = c²

625 = c²

√625 = √c²

25 = c

hope that helps, God bless!

4 0
3 years ago
What is the length of the apothem of a regular hexagon with 10-cm sides?
vodka [1.7K]

Answer:

The length of apothem of given hexagon is 8.66 cm

Step-by-step explanation:

Apothem of a polygon is given by:

apothem = \frac{s}{2\ tan\ (\frac{180}{n})}

Here

s is length of side

tan is trigonometric function

and n denotes number of sides

Given that the polygon is a hexagon

s = 10cm\\n = 6

Putting the values in the formula

apothem = \frac{10}{2\ tan\ (\frac{180}{6})}\\= \frac{10}{2\ tan\ 30}\\=\frac{10}{2 * 0.5773}\\=\frac{10}{1.1546}\\=8.6610\\Rounding\ off\ to\ nearest\ hundredth\\= 8.66\ cm

Hence,

The length of apothem of given hexagon is 8.66 cm

6 0
3 years ago
The equations 8x +4y = 32 and 16x +12y = 72 represent the cost for lunch and dinner for a family eating out on vacation. If x is
Nookie1986 [14]

Answer:

There are 3 adults in the family.

Step-by-step explanation:

The equations 8x + 4y = 32 and 16x + 12y = 72 represent the cost of lunch and dinner for a family in which x is the number of adults and y is the number of children.

We have to find the number of adults or the value of x by solving these equations.

equations are 8x + 4y = 32 -------(1)

16x + 12y = 72 --------(2)

Now we will multiply equation 1 by 3 and subtract it by equation 2.

(16x + 12y) -3(8x + 4y) = 72 - 96

16x + 12y - 24x - 12y = -24

(16x - 24x) + (12y - 12y) = -24

-8x = - 24

8x = 24

x = 3

Therefore, there are 3 adults in the family.

8 0
3 years ago
Find the area of the shape shown below.
mina [271]

Answer:

28 square units

Step-by-step explanation:

8 0
3 years ago
plz help In Alexis’ English class, 21 students completed an essay by the due date. There are 30 students in Alexis’ English clas
yarga [219]

Answer:

70%

Step-by-step explanation:

I'm sorry but I don't really know how to explain it other than 70% of 30 is 21 so that means that 30% of the students turned their essay in on time.

(sorry for not being able to explain it but I hope it helped)

8 0
3 years ago
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