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2 years ago

It takes 20 minutes to fill a wading pool. The pool has developed a leak through which it will empty in 30 minutes.

1 answer:

4 0

In t minutes, t/20 of the pool is filled and t/30 of it is emptied.

t/20 - t/30 = 1
multiply both sides by LCM 60.

3t - 2t = 60
t = 60

The pool is filled in 60 minutes.

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Evelyn wants to estimate the percentage of people who own a tablet computer she surveys 150 indvidals and finds that 120 own a t

igomit [66]

Answer:

The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%

Step-by-step explanation:

Confidence interval for the proportion of people who own a tablet:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 150, \pi = \frac{120}{150} = 0.8$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.576$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 - 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.7159$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8 + 2.575\sqrt{\frac{0.8*0.2}{150}} = 0.8841$

Percentage:

Multiply the proportion by 100.

0.7159*100 = 71.59%

0.8841*100 = 88.41%

The 99% confidence interval for the percentage of people who own a tablet computer is between 71.59% and 88.41%

8 0

2 years ago

Help me please I beg

valentina_108 [34]

Answer:

$8,500

Step-by-step explanation:

Interest = 5000 x 5 x 0.14

= 1000 x 0.14 x 25

= 140 x 25

= 3500

5000 + 3500 = 8500

8 0

1 year ago

Johnson Chemicals is considering two options for its supplier portfolio. Option 1 uses two local suppliers. Each has a "unique-e

sashaice [31]

Answer:

a) P=0.0175

b) P=0.0189

Step-by-step explanation:

For both options we have to take into account that not only the chance of a "superevent" will disable both suppliers.

The other situation that will disable both is that both suppliers have their "unique-event" at the same time.

As they are, by definition, two independent events, we can calculate the probability of having both events at the same time as the product of both individual probabilities.

a) Then, the probability that both suppliers will be disrupted using option 1 is

$P_1=P_{se}+P_{ue}^2=0.015+(0.05)^2=0.015+0.0025=0.0175$

b) The probability that both suppliers will be disrupted using option 2:

$P_2=P_{se}+P_{ue}^2=0.002+(0.13)^2=0.002+0.0169=0.0189$

Pue = probability of a unique event

Pse = probability of a superevent

3 0

2 years ago

A 25 ft ladder leans against a building. The ladder’s base is 13.5 feet from the building. Find the angle of elevation, which th

Goryan [66]

Answer:

57.3°

Step-by-step explanation:

A 25 feet ladder leans against a building.

The ladder's base is 13.5 feet from the building.

The ladder, the wall of the building and the ground form a right-angled triangle of:

Hypotenuse = 25 feet

Base = 13.5 feet

We are to find the angle of elevation which the ladder makes with the ground (or rather the angle created by hypotenuse and base)

Let's say the angle = X°

According to a trigonometric equation;

cos X° = adjacent side ÷ hypotenuse = $\frac{13.5}{25}$ = 0.54

$cos ^{-1} X$ = 57.5=3° (Answer rounded up to nearest one decimal place).

∴ The angle of elevation = 57.3°

4 0

2 years ago

Help me plz!!!!!!!!!!!!!!!!!

prohojiy [21]

Answer:

Step-by-step explanation:

You're passing to the left first and getting back to your side on the right

5 0

2 years ago