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3 years ago

9

5. To prevent a flooded basement, a homeowner has installed two special pumps that work automatically and independently to pump

water if the water level gets too high. One pump is
rather old and does not work 28% of the time, and the second pump is newer and does not work 9% of the time. Find the probability that both pumps will fail to work at the same time.

1 answer:

NeX [460]3 years ago

7 0

Answer:

The probability that both pumps will fail to work at the same time is 0.025 or 2.5%.

Step-by-step explanation:

The probability that both pumps will fail to work at the same time is the multiplication of the probabilities that the pomps fail.

That is

the probability that the old pump fail = $\frac{28}{100}$

the probability that the newer pump fail = $\frac{9}{100}$

Then, the probability that both fail at the same time is:

$\frac{28}{100} * \frac{9}{100} = 0.025$

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In 2015 as part of the General Social Survey, 1289 randomly selected American adults responded to this question:

Radda [10]

Answer:

B (0.312, 0.364)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , 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:

1289 randomly selected American adults responded to this question. This means that $n = 1289$ .

Of the respondents, 436 replied that America is doing about the right amount. This means that $\pi = \frac{436}{1289} = 0.3382$ .

Determine a 95% confidence interval for the proportion of all the registered voters who will vote for the Republican Party. 

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3382 - 1.96\sqrt{\frac{0.3382*0.6618}{1289}} = 0.312$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3382 + 1.96\sqrt{\frac{0.3382*0.6618}{1289}} = 0.364$

The 95% confidence interval is:

B (0.312, 0.364)

5 0

3 years ago

What are the verter and x-intercepts of the graph of the function given below?<br> y=x2-2x-35

horsena [70]

For x intercepts, plug in 0 for y.

0 = (x^2) - 2x - 35

*factoring* = (x-7)(x+5)

x intercepts = 7,-5

As for the vertex, you can use the equation -b/2a for the x-coordinate of the vertex

so,

x = -b/2a = -(-2)/2 = 1

then just find the y value by plugging it back in to the equation.

y = ((1)^2) - 2(1) - 35

= -36

so, vertex is at (1,-36)

5 0

3 years ago

En un aeropuerto dos aviones A1 y A1 se acercan para aterrizar, si la ecuación de la trayectoria del primero es -x+2y-100=0, mie

liraira [26]

No hay solución en la que ambas trayectorias estén en la misma posición, puesto que no existe el riesgo de que sufran un choque entre ellos.

-------------------------

La trayectoria del primero es:

$-x + 2y - 100 = 0$

$x_1 = 2y - 100$

Para el segundo, tiene-se que:

$-x + 200 + 2y = 0$

$x_2 = 2y + 200$

Igualando los valores de x:

$x_1 = x_2$

$2y - 100 = 2y + 200$

$0y = 300$

No hay solución en la que ambas trayectorias estén en la misma posición, puesto que no existe el riesgo de que sufran un choque entre ellos.

Un problema similar es dado en brainly.com/question/24653364

3 0

3 years ago

What is the length, in centimeters, of the hypotenuse of a right triangle with legs measuring V2 cm and 3 cm?

WINSTONCH [101]

Answer:

$\sqrt{13}$

Step-by-step explanation:

A is the hyp. And b/c are the sides

A²=b²+c²=3²+2²=9+4=13

Now take the square root of 13 as the answer

5 0

3 years ago

6) the circular base of a hemisphere of radius 2 rests on the base of a square pyramid of height 6. the hemisphere is tangent to

Rasek [7]

The length of the square base is thus $2 x 3\sqrt{2}/2 = 3\sqrt{2}$ = A

<h3>What is hemisphere?</h3>

Consequently, a hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape. It is created by precisely cutting a spherical along its diameter, leaving behind two identical hemispheres.

EXPLANATION; Let ABCDE be the pyramid with ABCD as the square base. Let O and M be the center of square ABCD and the midpoint of side AB respectively. Lastly, let the hemisphere be tangent to the triangular face ABE at P.

Notice that triangle EOM has a right angle at O. Since the hemisphere is tangent to the triangular face ABE at P, angle EPO is also 90 degree. Hence, triangle EOM is similar to triangle EPO.

OM/2 = 6/EP

OM = 6/EP x 2

OM = $6\sqrt{6^2 - 2^2} x 2 = 3\sqrt{2}/2}$

The length of the square base is thus $2 x 3\sqrt{2}/2 = 3\sqrt{2}$ = A

To know more about Hemisphere, visit;

brainly.com/question/13625065?referrer=searchResults

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6 0

1 year ago