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3 years ago

Choose the smallest number 3 1/8 or 10/3

Mathematics

1 answer:

Aliun [14]3 years ago

8 0

Answer:

10/3

Step-by-step explanation:

31/8= 3.8

10/3= 3.3

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the population of a town increases at a rate proportional to its population with an initial population of 1000. The corect initi

anyanavicka [17]

Answer:

This means that the correct initial value problem for the population p(t) as a function of time is is $P(0) = 1000$

Step-by-step explanation:

The population of a town increases at a rate proportional to its population:

This means that this situation is modeled by the following differential equation:

$\frac{dP}{dt} = kP$

In which k is the growth rate.

By separation of variables, the solution is given by:

$P(t) = P(0)e^{kt}$

In which P(0) is the initial population.

Initial population of 1000.

This means that the correct initial value problem for the population p(t) as a function of time is is $P(0) = 1000$

5 0

2 years ago

Eddie made a video. The video included a 5-minute introduction followed by short segments. • Each segment was 8 minutes long • E

GalinKa [24]

Answer:

B - 18

Step-by-step explanation:

149 total minutes minus 5 for the introductions leaves 144.

144/5=18

5 0

2 years ago

A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use in minutes of one part

Sergeu [11.5K]

Answer:

The standard deviation increased but there was no change in the interquantile range

Step-by-step explanation:

We are given the following data in the question:

320, 411, 348, 537, 420, 449, 462, 403, 454, 517, 515, 358, 438, 541, 387, 368, 502, 437, 431, 428.

n = 20

a) Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{8726}{20} = 436.3$

Sum of squares of differences =

13525.69 + 640.09 + 7796.89 + 10140.49 + 265.69 + 161.29 + 660.49 + 1108.89 + 313.29 + 6512.49 + 6193.69 + 6130.89 + 2.89 + 10962.09 + 2430.49 + 4664.89 + 4316.49 + 0.49 + 28.09 + 68.89 = 75924.2

$S.D = \sqrt{\frac{75924.2}{19}} = 63.21$

Sorted Data = 320, 348, 358, 368, 387, 403, 411, 420, 428, 431, 437, 438, 449, 454, 462, 502, 515, 517, 537, 541

$IQR = Q_3 - Q_1\\Q_3 = \text{upper median},\\Q_1 = \text{ lower median}$

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

$Median = \frac{431 + 437}{2} = 434$

$Q_1 = \frac{387 + 403}{2} = 395\\\\Q_3 = \frac{462 + 502}{2} = 482$

IQR = $482 - 395 = 87$

b) After changing the observation

0, 411, 348, 537, 420, 449, 462, 403, 454, 517, 515, 358, 438, 541, 387, 368, 502, 437, 431, 428

$Mean =\displaystyle\frac{8406}{20} = 420.3$

Sum of squares of differences =

176652.09 + 86.49 + 5227.29 + 13618.89 + 0.09 + 823.69 + 1738.89 + 299.29 + 1135.69 + 9350.89 + 8968.09 + 3881.29 + 313.29 + 14568.49 + 1108.89 + 2735.29 + 6674.89 + 278.89 + 114.49 + 59.29 = 247636.2

$S.D = \sqrt{\frac{247636.2}{19}} = 114.16$

Sorted Data = 0, 348, 358, 368, 387, 403, 411, 420, 428, 431, 437, 438, 449, 454, 462, 502, 515, 517, 537, 541

$Median = \frac{431 + 437}{2} = 434$

$Q_1 = \frac{387 + 403}{2} = 395\\\\Q_3 = \frac{462 + 502}{2} = 482$

IQR = $482 - 395 = 87$

Thus. the standard deviation increased but there was no change in the interquantile range.

5 0

3 years ago

How do I simplify (6^-2)(3^-3)(3 x 6)^4? Not the answer, just the simplified expression.

Mazyrski [523]

The simplification form of the provided expression is 108 after applying the integer exponent properties.

<h3>What is integer exponent?</h3>

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have an expression:

$=\left(6^{-2}\right)\left(3^{-3}\right)\left(3\:\cdot \:6\right)^4$