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2 years ago

Find the value of a.

Mathematics

1 answer:

Vlad1618 [11]2 years ago

5 0

Answer:

b and c

Step-by-step explanation:

plato

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

dusya [7]

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 = Number of question that are correct

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

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

= 0.0078

6 0

3 years ago

Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

Allisa [31]

Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

Using first principle, this gives:

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

Hence, the smallest sum is 2

3 0

3 years ago

Find the rate of change of the area of a square with respect

Romashka [77]

Let the side length of the square be x, then A = x^2
but diagonal (z) = sqrt(2x^2)
z^2 = 2x^2
x^2 = 1/2 z^2

Thus, A = 1/2 z^2
dA/dz = 1/2 (2z) = z
The rate of change is z.

When z = 4, the rate is 4.

4 0

3 years ago

Evaluate: Sigma 50 over 1 (4n - 1) = [?]

iogann1982 [59]

Answer:

50 over 1 (4n - 1) = 5050

I hope I helped you^_^

7 0

2 years ago

HELP ASAP!!! Find the slope of this equation: 6x+6=−4y

Dmitriy789 [7]

Answer:

the slope is -3/2

Step-by-step explanation:

We need to get the equation in the form

y = mx +b where m is the slope and b is the y intercept

6x+6 = -4y

Divide by -4

-6x/-4 +6/-4 = -4y/-4

-3/2 x -3/2 = y

The slope is -3/2 and the y intercept is -3/2

3 0

2 years ago

Read 2 more answers