A numbered die has sides labeled 1 to 8. What is the probability of landing on a number greater than 3?

The first step to solving this problem is determining the difference in speed between the first and second car - you can see that the second car (at 52mph) is twice as fast as the first (26mph) therefore it will take half the time to cover the same distance.

As Car 1 has a 2 hour head start, it will be 52 miles ahead after 2 hours.

In the next 2 hours, Car 1 will travel 52 miles - so 104 in total after 4 hours, and car 2 will travel 104 miles, meaning that it will have caught up after 4 hours.

A)

To calculate distance per minute, divide the miles per hour by 60 (as there's 60 minutes in an hour), so:

Car 1 = 26/60 = 0.43 miles per minute

Car 2 = 52/60 = 0.867 miles per minute

To check your calculation, Car 2 should be exactly twice as far

B) The street, as far as we know, is at least 104 miles

C) See calculation at the top - the first car is 52miles from the start line when the second car starts

D) 2 cars are competing in this race

8 0

3 years ago

The American Water Works Association reports that the per capita water use in a single-family home is 67 gallons per day. Legacy

inessss [21]

Answer:

We conclude that the null hypothesis is rejected which means residents of Legacy Ranch use less water on average.

Step-by-step explanation:

We are given that the American Water Works Association reports that the per capita water use in a single-family home is 67 gallons per day.

Twenty-three owners responded, and the sample mean water use per day was 63 gallons with a standard deviation of 8.1 gallons per day.

Let $\mu$ = average water usage by residents of Legacy Ranch.

So, Null Hypothesis, $H_0$ : $\mu \geq$ 67 gallons {means that the residents of Legacy Ranch uses more or equal to 67 gallons water on average}

Alternate Hypothesis, $H_A$ : $\mu$ < 67 gallons {means that the residents of Legacy Ranch use less water on average}

The test statistics that will be used here is One-sample t test statistics as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean water use per day = 63 gallons

s = sample standard deviation = 8.1 gallons

n = sample of responded = 23

So, test statistics = $\frac{63-67}{\frac{8.1}{\sqrt{23} } }$ ~ $t_2_2$

= -2.368

The value of the test statistics is -2.368.

Now at 0.025 significance level, the t table gives critical value of -2.074 at 22 degree of freedom for left-tailed test. Since our test statistics is less than the critical values of t as -2.368 < -2.074, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the residents of Legacy Ranch use less water on average.

8 0

3 years ago

Which ordered pair is in the solution set?

erik [133]

The answer would be letter C

8 0

3 years ago

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