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3 years ago

Solve the equation by completing the square. 0 = x2 − 14x

Mathematics

1 answer:

Roman55 [17]3 years ago

8 0

Answer:

X = 0

Also If you are trying to correct it the correct way to write this is

0=2x - 14x

Step-by-step explanation:

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A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 7

SCORPION-xisa [38]

Answer:

The probability that exactly eight of them take more than 93.6 minutes is 5.6015 $\times 10^{-6}$ .

Step-by-step explanation:

We are given that it is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes.

A random sample of twelve service calls is taken.

So, firstly we will find the probability that service calls take more than 93.6 minutes.

Let X = times for service calls.

So, X ~ Normal( $\mu=75,\sigma^{2} =15^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean time = 75 minutes

$\sigma$ = standard deviation = 15 minutes

Now, the probability that service calls take more than 93.6 minutes is given by = P(X > 93.6 minutes)

P(X > 93.6 min) = P( $\frac{X-\mu}{\sigma}$ > $\frac{93.6-75}{15}$ ) = P(Z > 1.24) = 1 - P(Z $\leq$ 1.24)

= 1 - 0.8925 = 0.1075

The above probability is calculated by looking at the value of x = 1.24 in the z table which has an area of 0.8925.

Now, we will use the binomial distribution to find the probability that exactly eight of them take more than 93.6 minutes, that is;

$P(Y = y) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; y = 0,1,2,3,.........$

where, n = number of trials (samples) taken = 12 service calls

r = number of success = exactly 8

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

it takes more than 93.6 minutes, i.e. p = 0.1075.

Let Y = Number of service calls which takes more than 93.6 minutes

So, Y ~ Binom(n = 12, p = 0.1075)

Now, the probability that exactly eight of them take more than 93.6 minutes is given by = P(Y = 8)

P(Y = 8) = $\binom{12}{8}\times 0.1075^{8} \times (1-0.1075)^{12-8}$

= $495 \times 0.1075^{8} \times 0.8925^{4}$

= 5.6015 $\times 10^{-6}$ .

6 0

4 years ago

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th

grandymaker [24]

Answer:

Step-by-step explanation:

The rocket will hit the ground when y = 0. If you use the quadratic equation:

x = (-248±√(2482-4(-16)(116))/(2(-16))

4 0

3 years ago

Shayla is having a picnic and wants to buy enough hamburgers so that each guest can have one. If she is planning on having 52 gu

yKpoI14uk [10]

Answer:

6 ≤ x ≤ 7

Step-by-step explanation:

Dividing 52 by 8 gives you a decimal between 6 and 7. Since you can only but hamburgers in packages of 8, the inequality is 6 ≤ x ≤7 with x being the number of hamburger bags.

8 0

3 years ago

If an object is propelled upward from a height of 72 feet at an initial velocity of 90 feet per second, then its height h after

kifflom [539]

Answer:

6.34 seconds.

Step-by-step explanation:

The object will hit the ground when h = 0.

-16t^2 + 90t + 72 = 0

8t^2 - 45t - 36 = 0

We can then use the quadratic formula to solve.

[please ignore the A-hat; that is a bug]