it taken 12 days for 10 men assemble a machine how long could it take for 15 men to assemble the machine?

A student said that since -9 is less than 4, then |-9| is less than |4|. Is the student correct? Explain why or why not.

IRISSAK [1]

No, that is not true. The absolute value is the distance a number is from zero. The distance of -9 to 0 is 9. 9 is not less than 4.

4 0

3 years ago

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Workers have been down the street installing two blinking red lights in front of the fire station. The two lights are always tur

daser333 [38]

Answer:

After 88 seconds, they will blink together.

Step-by-step explanation:

Time after which the first light blinks = 8 seconds

Time after which the second light blinks = 22 seconds

Initially, both the lights blink together.

To find:

The time at which they will blink together again.

Solution:

Let us have a look at the time after which each light will blink.

First light will blink after:

8 s, 16 s, 24 s, 32 s, 40 s, 48 s, 56 s, 64 s, 72 s, 80 s, 88 s, 96 s, 104 s, ......

Second light will blink after:

22 s, 44 s, 66 s, 88 s, 110 s, .....

It can be seen that common time is 88 second, at which the both will blink together.

So, the answer is 88 s.

This answer can also be computed by taking the LCM (Least Common Multiple) of both the numbers i.e. 8 and 22.

Using the factorization method:

$8=\underline{2}\times 2\times 2$

$22=\underline{2}\times 11$

Common is 2.

Therefore the LCM will be:

$2\times 2\times2\times 11 = \bold{88}$

So, the answer is 88 s.

5 0

3 years ago

For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains

AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

$f(x) = (1-p)^{x}p$

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

$\mu = \frac{1-p}{p}$

The standard deviation of the geometric distribution is given by the following formula:

$\sigma = \sqrt{\frac{1-p}{p^{2}}$

In this problem, we have that:

$p = 0.383$

So

$\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61$

$\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05$

(a) What is the probability that a drought lasts exactly 3 intervals?

This is $f(3)$

$f(x) = (1-p)^{x}p$

$f(3) = (1-0.383)^{3}*(0.383)$

$f(3) = 0.09$

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is $P = f(0) + f(1) + f(2) + f(3)$

$f(x) = (1-p)^{x}p$

$f(0) = (1-0.383)^{0}*(0.383) = 0.383$

$f(1) = (1-0.383)^{1}*(0.383) = 0.236$

$f(2) = (1-0.383)^{2}*(0.383) = 0.146$

Previously in this exercise, we found that $f(3) = 0.09$

So

$P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855$

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is $P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4)$ .

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

$P(X \leq 3) + P(X \geq 4) = 1$

$0.855 + P(X \geq 4) = 1$

$P(X \geq 4) = 0.145$

There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

8 0

3 years ago

Round to the nearest tenth wa hit is the perimeter of the triangle

klio [65]

Answer:

D. 11.8 cm

Step-by-step explanation:

This triangle is a 30°-60°-90° triangle. There is a shortcut to find the lengths of the sides of a 30°-60°-90° triangle. The longest side is the hypotenuse. The longest side is double the shortest side or, the shortest side is half the longest side. Here the longest side is 5, so the short leg (shortest side) is 2.5

The other shortcut is that the longer leg is the

short leg×sqroot3

Here, the short leg is 2.5, so the long leg is 2.5×sqroot3

Perimeter is all the sides added together.

5 + 2.5+ 2.5×sqrt3

Do the times first.

5 + 2.5 + 4.3

= 11.8

6 0

2 years ago

Find the area of each shaded sector. Round to the hundredths place.

kati45 [8]

Answer:

200

Step-by-step explanation:vbc i know

3 0

3 years ago

it taken 12 days for 10 men assemble a machine how long could it take for 15 men to assemble the machine?​

it taken 12 days for 10 men assemble a machine how long could it take for 15 men to assemble the machine?