In circle O, AC and BD are diameters.

Response:

Option B is correct

Step-by-step breakdown:

(One-tailed test at a significance level of 5%)

n = 16 and x̄ = 1.97

s = 0.1

Standard error of the mean =

Difference in means =

t statistic = Difference in means/se = -1.2

degrees of freedom = 16 - 1 = 15

p-value = 0.124375

(B) do not reject the null hypothesis since the test statistic (-1.2) is > the critical value (-1.7531).

Angles that are opposite to each other when two lines cross are equal, therefore angle 1 is equal to angle 4. This also implies that angle 1 = angle 5. When a line crosses two parallel lines, the angles corresponding to each other are equal. So, if r and s are parallel, the angles that are formed when line l intersects line r are equal to those when l intersects line s. Thus, we have angle 1 = angle 5, angle 2 = angle 6, and so on. Hence, since angle 1 is equal to angle 5, we deduce that lines r and s are parallel.

1) 4.55

2) Short hit

Step-by-step explanation:

1)

The score and corresponding probabilities are shown in the following table:

Score 3 4 5 6 7

Probability 0.15 0.40 0.25 0.15 0.05

Let us define

X = Miguel's score on the Water Hole

The expected value of the variable X can be represented as:

where

represents the different possible outcomes of X

denotes the associated probabilities

Accordingly, the expected value of Miguel's score is calculated as follows:

2)

Here, we will again consider:

X = Miguel's score on the Water Hole

In this case:

- For a successful long hit, the expected value of X is

- Conversely, if the long hit isn't successful, the expected value of X becomes

We also know that the likelihood of succeeding with a long hit is

Consequently, the chance of failure in a long hit is

Thus, the expected value of X when opting for the long hit strategy is:

In the first part of this question, we calculated the expected value using the short hit strategy, yielding:

Given that the expected value for X is smaller (which is better) when utilizing the short hit option, we can conclude that this approach is superior.

Answer:

y = 12x + 16

Step-by-step explanation:

First, simplify both sides of the equation and then isolate the variable.

In Step 1, add 11 to each side.

−1 /2 y+11+−11=6x+3+−11

−1 /2 y=6x−8

In Step 2, divide each side by (-1)/2.

This leads to

y = 12x + 16

For Offer 1:
33−33×0.4
=19.8
Now, applying an additional discount of 25%:
19.8−19.8×0.25
=14.85. Offer 2 provides a better deal:
34−34×0.55
=15.3, followed by a 5% discount:
15.3−15.3×0.05
=14.535. In total, the difference in price between the two offers is:
14.85−14.535
=0.315.