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4 years ago

Any suggestions or answers

Mathematics

1 answer:

katrin [286]4 years ago

3 0

Answer:

(6, - 2)

Step-by-step explanation:

To determine which point is a solution to the system, substitute the coordinates of the point into the left side of the inequalities and compare the value to the right side

(6, 1)

6 - 1 = 5 < 7

6 + 2 = 8 > 5

(6,1) does not represent a solution

(8, - 1)

8 + 1 = 9 > 7

8 - 2 = 6 > 5

(8, - 1) does not represent a solution

(6, 2)

6 - 2 = 4 < 7

6 + 2 = 8 > 5

(6, 2) does not represent a solution

(6, - 2)

6 + 2 = 8 > 7

6 - 4 = 2 < 5

(6, 2) represents a solution to the system

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Suppose a random sample of n measurements is selected from a binomial population with probability of success p = .39. Given n =

Oksi-84 [34.3K]

Answer:

The answer is below

Step-by-step explanation:

a) Given that the number of sample (n) = 300, therefore since n > 30, the distribution of the sample means is going to be normally distributed.

b) The mean of the distribution of sample means (also known as the Expected value of M) is equal to the population mean μ.

$\mu_x=\mu=np=300*0.39=117$

c) The standard deviation of the distribution of sample means is called the Standard Error of M, it is given by:

$\sigma_x=\sqrt{np(1-p)} =\sqrt{300*0.39(1-0.39)} =8.44$

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3 years ago

The function f(t) = t2 + 6t − 20 represents a parabola.

NeX [460]

Answer:

Step-by-step explanation:

Part A:

To complete the square, we will do the first few steps all at once, since they are necessary but not complicated to follow all at once. Set the function equal to 0 first, then move the constant over to the other side:

$t^2+6t=20$

The most important rule for completing the square is that the leading coefficient (the number on the t-squared term) is a positive 1. Ours is, but if it wasn't it would need to be factored out.

Next, take half the linear term, square it, and add it to both sides. Our linear term is 6. Half of 6 is 3, and 3 squared is 9, so we add 9 to both sides:

$t^2+6t+9=20+9$

On the right is simple addition, but on the left side, during this process we created a perfect square binomial that will reflect the h coordinate of the vertex. We will state that binomial and do the addition on the right both at the same time:

$(t+3)^2=38$

If you FOIL out the (t + 3)(t + 3) you will get back the polynomial $t^2+6t+9$

Now we can move the constant back over and set the polynomial back to equal f(t):

$(t+3)^2-38=f(t)$

From this we determine the vertex to sit at (-3, -38)

Part B:

Because this is a positive parabola that opens upwards, the function will have a minimum value (if it was negative and opened upside down, it would have a minimum value). In other words, you know the vertex is a minimum because this is a positive parabola that opens upwards.

Part C:

The axis of symmetry is the line that cuts the parabola in half, creating 2 identical, mirror images. Because this parabola opens upwards, a vertical line is required to cut it into 2 identical halves. The vertical line has an equation " x = ". In the case of a positive parabola that opens upwards, the line of symmetry, what x = , will ALWAYS be the number that is inside the parenthesis with the x. Since the standard vertex form is

$f(t)=(t-h)^2+k$