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Fudgin [204]
1 year ago
12

4. A bank vault has 3 locks with a key for each lock. Key A is owned by the bank manager. Key B is owned by the senior bank tell

er. Key C is owned by the trainee bank teller. In order to open the vault door at least two people must insert their keys into the assigned locks at the same time. The trainee bank teller) can only open the vault when the bank manager is present in the opening. X= Bank Manager Y= Senior Bank teller Z= Trainee bank teller. (25 marks) LO 01 a) Construct a truth table for this system
Mathematics
1 answer:
Amanda [17]1 year ago
6 0

1 means that he is present, 0 means that he is not.

True means that they can open.

\begin{array}{cccccccccccc} \text{X} &&& \text{Y} &&& \text{Z} &&& \text{True} \\1 &&& 1 &&& 1&&& 1  \\ 1 &&& 1 &&& 0&&&1 \\  0 &&& 1 &&& 1&&&0 \\  1 &&& 0 &&& 1&&&1 \\  0&&& 1 &&& 0&&&0 \\   0 &&& 0 &&& 1&&&0 \\  1 &&& 0 &&& 0&&&0 \\  0 &&& 0 &&& 0&&&0 \\ \end{array}

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Let X denote the number of bars of service on your cell phone whenever you are at an intersection with the following probabiliti
lorasvet [3.4K]

Answer:

Step-by-step explanation:

Hello!

Given the variable

X: number of bars of service on your cell phone.

The posible values of this variable are {0, 1, 2, 3, 4, 5}

a. F(X) is the cummulative distribution function P(X≤x₀) you can calculate it by adding all the point probabilities for each value:

X: 0; 1; 2; 3; 4; 5

P(X): 0.15; 0.25; 0.25; 0.15; 0.1; 0.1

F(X): 0.15; 0.4; 0.65; 0.8; 0.9; 1

The maximum cumulative probability of any F(X) is 1, knowing this, you can calculate the probability of X=5 as: 1 - F(4)= 1 - 0.9= 0.1

b.

The mean of the sample is:

E(X)= ∑Xi*Pi= (0*0.15)+(1*0.25)+(2*0.25)+(3*0.15)+(4*0.1)+(5*0.1)

E(X)= 2.1

V(X)= E(X²)-(E(X))²

V(X)= ∑Xi²*Pi- (∑Xi*Pi)²= 6.7- (2.1)²= 2.29

∑Xi²*Pi= (0²*0.15)+(1²*0.25)+(2²*0.25)+(3²*0.15)+(4²*0.1)+(5²*0.1)= 6.7

c.

P(X<2)

You can read this expression as the probability of having less than 2 bars of service. This means you can have either one or zero service bars, you can rewrite it as:

P(X<2)= P(X≤1)= F(1)= 0.4

d.

P(X≤3.5)

This expression means "the probability of having at most (or less or equal to) 3.5 service bars", this variable doesn't have the value 3.5 in its definition range so you have to look for the accumulated probability until the lesser whole number. This expression includes the probabilities of X=0, X=1, X=2, and X=3, you can express it as the accumulated probability until 3, F(3):

P(X≤3.5)= P(X≤3)= F(3)= 0.80

I hope it helps!

5 0
1 year ago
Given: mTRV = 60° mTRS = (4x)° Prove: x = 30 What is the missing reason in step 3? substitution property of equality angle addit
mihalych1998 [28]

Answer: Angle addition postulate.

Explanation: If \angle TRV= 60^{\circ} and \angle TRS=4x^{\circ}

here, if we have to prove x=30

If there is a condition that TR is a line which meets with the line segment VS at point R then by the Angle addition postulate,  we can say that \angle TRV+\angle TRS=180^{\circ}⇒x=30^{\circ}

But,

In option (1) substitution property of equality

If there is condition that  \angle TRV=\angle TRS

then we can use  substitution property of equality,

And, in this case 4x^{\circ}=60^{\circ}⇒x=15^{\circ}

which is wrong. So, we can not use this property here.

In option (3) subtraction property of equality

There is no use of this property to find the value x.

In option (4) addition property of equality

There is no use of this property to find the value x.

8 0
1 year ago
Read 2 more answers
butter and flour are mixed in the ratio 2:3. paul has 640 grams of butter and 880 grams of flour. how much more flour does he ne
madam [21]

Answer:

80g

Step-by-step explanation:

Here's why:

SO you have 2:3 ratio which means the ratio for grams of butter/grams of flour has to be 2:3.

So we set up the following equation:

2/3 = 640/x (solve for x)

x= 960g

960g is what you should have to get to ratio, but the question is asking how much more you need from the initial given flour.

So you need  (suppose x is the grams of flour you need)

x+880g = 960g (solve for x)

x=80g

3 0
1 year ago
Associate the average of the numbers from 1 to n (where n is a positive integer value) with the variable avg.
Kaylis [27]
This is a simple programming question. To calculate the average of any two numbers, where one number is 1 and the other is n, simply add the two numbers and divide by 2. Therefore, the answer is:
<span>avg = (1 + n) / 2</span> 
5 0
1 year ago
You and a friend have a hula hoop competition. you win 3 out of every 7 trials. your friend wins 5 more trials than you. how man
Ivenika [448]

Answer:

Total number of trials is 35.

Step-by-step explanation:

Given : Me and my friend have a hula hoop competition. I win 3 out of every 7 trials. My friend wins 5 more trials than me.  

To find : How many trials are in the competition?

Solution :

Probability of my winning is 3 out of 7 trials =\frac{3}{7}

and probability of my friend's winning is  =1-\frac{3}{7}=\frac{4}{7}  

Let there be n numbers of trials.

Therefore, my score after n trials =\frac{3n}{7}

and my friend's score after n trials   =\frac{4n}{7}

Now, the number of trials my friend won more than me is

\frac{4n}{7}-\frac{3n}{7}=\frac{n}{7}

We know, that my friend won 5 more trials than me so comparing the actual and given we get,

\frac{n}{7}=5\\n=7\times5=35

Therefore, total number of trials is 35.

We can also verify our answer by placing value of n,

After 35 trials I will win \frac{3\times 35}{7}=15 trials

and my friend will win \frac{4\times 35}{7}=20  trials.

Hence, my friend won 5 more trials than me.

3 0
1 year ago
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