Find the coordinates of the midpoints of a segment having the given endpoints.

The length of a rectangle is 6 cm less than twice its width. Find the dimensions of the rectangle if its areais 108cm

valentinak56 [21]

L=2w-6

area = L x W

108=(2w-6)w

108 = 2w^2-6w

2w^2-6w-108 = 0

2(w^2-3w-54)=0

2(w-9)(w+6) = 0

w=9

L= 2(9)-6 = 12

12*9 = 108

3 0

4 years ago

A marketing research consultant hired by Coca-Cola is interested in determining if the proportion of customers who prefer Coke t

wlad13 [49]

Answer:

A one-tailed hypothesis will be used to perform the test.

Step-by-step explanation:

The purpose of the marketing research consultant hired by Coca-Cola is to determine whether the the proportion of customers who prefer Coke to other brands is over 50%.

The marketing research consultant selected a random sample of n = 200 customers. The sample proportion of people who favored Coca-Cola over other brands was 55%.

The marketing research consultant can perform a single proportion hypothesis test to determine whether greater than 50% of customers prefer Coca-Cola to other brands.

Since we need to determine whether the population percentage is greater than a null value, the hypothesis is not two-tailed.

The hypothesis can be defined as:

H₀: The proportion of people who favor Coca-Cola over other brands was 55%, i.e. p = 0.50.

Hₐ: The proportion of people who favor Coca-Cola over other brands was more than 55%, i.e. p > 0.50.

Thus, a one-tailed hypothesis will be used to perform the test.

6 0

3 years ago

You are running a race. The probability that you win is 3/5. What is the probability that you lose at most 2 out of your 6 races

Veronika [31]

Answer:

The probability that you lose at most 2 out of your 6 races is 0.54432.

Step-by-step explanation:

We are given that you are running a race. The probability that you win is 3/5.

There are total of 6 races.

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 trials (samples) taken = 6 races

r = number of success = at most 2 lost

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

you lose a race = 1 - (3/5) = 2/5 or 0.4

Let X = Number of races lost

So, X ~ Binom(n = 6, p = 0.40)

Now, the probability that you lose at most 2 out of your 6 races is given by = P(X $\leq$ 2)

P(X $\leq$ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= $\binom{6}{0} \times 0.40^{0} \times (1-0.40)^{6-0} + \binom{6}{1} \times 0.40^{1} \times (1-0.40)^{6-1} + \binom{6}{2} \times 0.40^{2} \times (1-0.40)^{6-2}$