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AfilCa [17]
3 years ago
7

If Karri takes a 7 question true false test and guess on every question, what is the

Mathematics
1 answer:
dusya [7]3 years ago
6 0

Answer:

The  probability that she gets all 7 questions correct is 0.0078.

Step-by-step explanation:

We are given that Karri takes a 7 question true-false test and guess on every question.

The above situation can be represented through binomial distribution;

P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,........        

where, n = number of samples (trials) taken = 7 question

            r = number of success = all 7 questions correct

            p = probability of success which in our question is probability that

                   question is correct, i.e. p = 50%

Let X = <u><em>Number of question that are correct</em></u>

So, X ~ Binom(n = 7, p = 0.50)

Now, the  probability that she gets all 7 questions correct is given by = P(X = 7)

         P(X = 7)  =  \binom{7}{7} \times 0.50^{7} \times (1-0.50)^{7-7}

                        =  1 \times 0.50^{7} \times 0.50^{0}

                        =  <u>0.0078</u>

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a_sh-v [17]

Answer:

k = 30, y(t) = C_1e^{5t}+C_2e^{6t}

Step-by-step explanation:

Since y=e^{5t} is a solution, then it must satisfy the differential equation. So, we calculate the derivatives and replace the value in the equation. We have that

\frac{d^2y}{dt^2} = 25 e^{5t},\frac{dy}{dt} = 5e^{5t}

Then, replacing the derivatives in the equation we have:

25e^{5t}-11(5)e^{5t}+ke^{5t}=0 e^{5t}(25-55+k) =0

Since e^{5t} is a positive function, we have that

25-55+k = 0 \rightarrow k = 30.

Now, consider a general solution y(t) = Ae^{rt}, A \in \mathbb{R}, then, by calculating the derivatives and replacing them in the equation, we get

Ae^{rt}(r^2-11r+30)=0

We already know that r=5 is a solution of the equation, then we can divide the polynomial by the factor (r-5) to the get the other solution. If we do so, we get that (r-6)=0. So the other solution is r=6.

Therefore, the general solution is

y(t) = C_1e^{5t}+C_2e^{6t}

8 0
3 years ago
Can someone please find the volume of this shape and show work for how you did it??
castortr0y [4]

Answer:

221.4m^{3}

Step-by-step explanation:

To work out the volume of this shape you will first need to work out the area of the triangle. To work out the area of the triangle you would multiply the base of 12 by the height of 4.1, which gives you 49.2. You would then need to divide 49.2 by 2, which gives you 24.6. This is because the formula for the area of a triangle is the same as that of a square, however a triangle is half of a square with the same length and width. To work out the volume you would multiply the area of the triangle, which is 24.6 by the height of 9, which gives you 221.4m^{3}

1) Multiply 12 by 4.1.

12*4.1=49.2

2) Divide 49.2 by 2.

49.2/2=24.6

3) Multiply 24.6 by 9.

24.6*9=221.4m^{3}

6 0
3 years ago
If x2 = 30. what is the value of x? ​
kirza4 [7]

Answer:

5.4772255750516 that's if it is x squared

4 0
3 years ago
A 1.5m wire carries a 7 A current when a potential difference of 54 V is applied. What is the resistance of the wire?
borishaifa [10]

Answer:

R = 7.71 ohms

Step-by-step explanation:

By ohm's law: R= V/I

where,  R = resistance of wire, V = potential difference, I = electric current

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Plug in the above values in the ohm's law, we get

R = 54 V/7 A

R = 7.71 ohms

Hope this will helpful.

Thank you.

6 0
3 years ago
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agasfer [191]

The answers are 4,8, and 12.

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