Match the change in the position of the minute hand with the angle made by the change

three tanks are capable of holding 108 litres, 168 litres and 180 litres of milk. determine the capacity of the greatest vessel

SpyIntel [72]

A vessel of 7,560 liters

Step-by-step explanation:

This means finding the Least Common Multiple for;

108 168 180

We begin by finding the multiples of each number;

Multiples of 108:

108, 216, 324, 432, 540, 648, 756, 864, 972, 1080, 1188, 1296, 1404, 1512, 1620, 1728, 1836, 1944, 2052, 2160, 2268, 2376, 2484, 2592, 2700, 2808, 2916, 3024, 3132, 3240, 3348, 3456, 3564, 3672, 3780, 3888, 3996, 4104, 4212, 4320, 4428, 4536, 4644, 4752, 4860, 4968, 5076, 5184, 5292, 5400, 5508, 5616, 5724, 5832, 5940, 6048, 6156, 6264, 6372, 6480, 6588, 6696, 6804, 6912, 7020, 7128, 7236, 7344, 7452, <u>7560</u>, 7668, 7776

Multiples of 168:

168, 336, 504, 672, 840, 1008, 1176, 1344, 1512, 1680, 1848, 2016, 2184, 2352, 2520, 2688, 2856, 3024, 3192, 3360, 3528, 3696, 3864, 4032, 4200, 4368, 4536, 4704, 4872, 5040, 5208, 5376, 5544, 5712, 5880, 6048, 6216, 6384, 6552, 6720, 6888, 7056, 7224, 7392, <u>7560</u>, 7728, 7896

Multiples of 180:

180, 360, 540, 720, 900, 1080, 1260, 1440, 1620, 1800, 1980, 2160, 2340, 2520, 2700, 2880, 3060, 3240, 3420, 3600, 3780, 3960, 4140, 4320, 4500, 4680, 4860, 5040, 5220, 5400, 5580, 5760, 5940, 6120, 6300, 6480, 6660, 6840, 7020, 7200, 7380, <u>7560</u>, 7740, 7920

The Least Common Multiple for the 3 number is;

= 7560

Therefore a vessel of 7,560 liters fills each one of them an exact number of times with no remainder.

Learn More:

For more on Least Common Multiple check out;

brainly.com/question/11978021

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5 0

3 years ago

Consider the line y=8x - 4.

Kamila [148]

Answer:

Parallel - 8

Perpendicular - -1/8

Step-by-step explanation:

If a line is parallel to another then they have the same slope

If a line is perpendicular to another line then the slope is just flipped and so is the sign

8 0

3 years ago

Writing in Math Describe a situation in which it would be better

NeTakaya

Answer:

the number 151

Step-by-step explanation:

this because if you round 151 to the nearest hundread it would give you 200 but if you round it to the nearest ten ot would give you 150 which is closer to the actual number than 200.

5 0

3 years ago

Mrs. Browning bought ice cream treats for 6 children. Each child picked either a sundae or a milkshake. The sundaes cost $2 each

Anna35 [415]

Answer:

3 milkshakes and 3 sundaes

Step-by-step explanation:

3 * 5 = $15 + 3 * 2 = $21

6 0

3 years ago

Read 2 more answers

The average student loan debt for college graduates is $25,150.

Aleks04 [339]

Using the normal distribution, it is found that:

a) $X \approx N(25150, 12050)$

b) There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.

c) Low: $23,519.65, High: $26,580.35.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

$\mu = 25150, \sigma = 12050$ .

Hence the distribution of X can be described as follows:

$X \approx N(25150, 12050)$

The probability that the college graduate has between $14,200 and $33,950 in student loan debt is the <u>p-value of Z when X = 33950 subtracted by the p-value of Z when X = 14200</u>, hence:

X = 33950:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{33950 - 25150}{12050}$

Z = 0.73

Z = 0.73 has a p-value of 0.7673.

X = 14200:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{14200 - 25150}{12050}$

Z = -0.91

Z = -0.91 has a p-value of 0.1814.

0.7673 - 0.1814 = 0.5859.

There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.

Considering the symmetry of the normal distribution, the middle 10% is between the 45th percentile(X when Z = -0.127) and the 55th percentile(X when Z = 0.127), hence:

$Z = \frac{X - \mu}{\sigma}$

$-0.127 = \frac{X - 25150}{12050}$

X - 25150 = -0.127(12050)

X = $23,519.65.

$Z = \frac{X - \mu}{\sigma}$

$0.127 = \frac{X - 25150}{12050}$

X - 25150 = 0.127(12050)

X = $26,580.35.

More can be learned about the normal distribution at brainly.com/question/4079902

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5 0

2 years ago