All categories

3 years ago

Which of the following is true?

Mathematics

1 answer:

mart [117]3 years ago

5 0

Answer:

Step-by-step explanation:

Consider all options:

A. $\sqrt{2}$ is irrational number because it cannot be represented as a fraction with integer numerator and natural denominator. This option is false.

B. Number 0 is integer number, therefore, its rational number. This option is false.

C. Repeating decimal $1.\overline{3}$ can be represented as $1 \dfrac{1}{3}$ that is $\dfrac{4}{3}$ and, therefore, this number is rational number. This number is not integer number, because this is a fraction when simplified to lowest terms. So, this option is true.

D. Number $-\sqrt{16}=-4$ and is integer, therefore, is rational number. So, this option is false.

You might be interested in

What number is ten thousand less than 842719

almond37 [142]

842,719-10,00= 832,719

4 0

3 years ago

Hattie accepted a job as a makeup artist after being offered a $550 signing

Radda [10]

The equation would be y=32x+550. 32 an hour is represented by 32x since she earned 32 an hour. 550 is the extra amount she is getting paid.

I hope this helps.

7 0

3 years ago

Ms. Jefferson is laying out a photo page. Each photo is cut to 2 3⁄4 inches wide. How many photos can she fit in a row that is 1

lisov135 [29]

Answer:

She can fit 8 photos in a row if there are no spaces between the photos.

Step-by-step explanation:

5 0

3 years ago

Match each time with a time in the box.

BigorU [14]

If you would like to match each time with a time above, you can do this using the following steps:

a 3h 18m 7s = 11887s
3h = 3 * 60m = 180m; 180m + 18m = 198m; 198m = 198 * 60s = 11880s; 11880s + 7s = 11887s

b 8300min = approximately 5 days 18 hours
8300min = 8300 * 60s = 498000s
8300 min / 60 min = 138h 20min; 138h / 24h = 5 days 18 hours 20min

c 1461 days
1461 days = 1461 * 24 hours = 35064 hours

d 44640min. = 31 days
44640min / 60min = 744 hours; 744 hours / 24 hours = 31 days

e 10:21:2.5
10:21:2.5 = 10 hours, 21 minutes, 2 seconds, 50 milliseconds

7 0

3 years ago

An article presents a new method for timing traffic signals in heavily traveled intersections. The effectiveness of the new meth

Anna35 [415]

Answer:

With 89.9% we can say that the mean improvement is between 583.1 and 728.1 vehicles per hour.

Step-by-step explanation:

We are given that the effectiveness of the new method was evaluated in a simulation study. In 50 simulations, the mean improvement in traffic flow in a particular intersection was 655.6 vehicles per hour, with a standard deviation of 311.7 vehicles per hour.

A traffic engineer states that the mean improvement is between 583.1 and 728.1 vehicles per hour.

Let $\bar X$ = sample mean improvement

The z-score probability distribution for sample mean is given by;

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

where, $\mu$ = mean improvement = 655.6 vehicles per hour

$\sigma$ = standard deviation = 311.7 vehicles per hour

n = sample of simulations = 50

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the mean improvement is between 583.1 and 728.1 vehicles per hour is given by = P(583.1 < $\bar X$ < 728.1) = P( $\bar X$ < 728.1) - P( $\bar X$ $\leq$ 583.1)

P( $\bar X$ < 728.1) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{728.1-655.6}{\frac{311.7}{\sqrt{50} } }$ ) = P(Z < 1.64) = 0.9495

P( $\bar X$ $\leq$ 583.1) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{583.1-655.6}{\frac{311.7}{\sqrt{50} } }$ ) = P(Z $\leq$ -1.64) = 1 - P(Z < 1.64)

= 1 - 0.9495 = 0.0505

So, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.64 in the z table which has an area of 0.9495.

Therefore, P(583.1 < $\bar X$ < 728.1) = 0.9495 - 0.0505 = 0.899 or 89.9%

Hence, with 89.9% we can say that the mean improvement is between 583.1 and 728.1 vehicles per hour.

6 0

3 years ago