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2 years ago

What best describes the improper fraction, in the simplest form, for 1.78787878...?

Mathematics

1 answer:

Evgesh-ka [11]2 years ago

7 0

Answer:

For 1.78787878..., it is called repeating decimal, that is periodic and the infinitely repeated non-zero portion (here it is 787878...)

Hope this helps!

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Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section 3.7). If the cup is 6 inche

aliya0001 [1]

Answer:

The water level rising when the water is 4 inches deep is $\frac{3}{8\times \pi} inch/s$ .

Step-by-step explanation:

Rate of water pouring out in the cone = R= $\frac{3}{2} inch^3/s$

Height of the cup = h = 6 inches

Radius of the cup = r = 3 inches

$\frac{r}{h}=\frac{3 inch}{6 inch}=\frac{1}{2}$

r = h/2

Volume of the cone = $V=\frac{1}{3}\pi r^2h$

$V=\frac{1}{3}\pi r^2h$

$\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi r^2h)}{dt}$

$\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi (\frac{h}{2})^2h)}{dt}$

$\frac{dV}{dt}=\frac{1}{3\times 4}\pi \times \frac{d(h^3)}{dt}$

$\frac{dV}{dt}=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}$

$\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}$

h = 4 inches

$\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3\times (4inches )^2\times \frac{dh}{dt}$

$\frac{3}{2} inch^3/s=\pi\times 4\times \frac{dh}{dt} inches^2$

$\frac{dh}{dt}=\frac{3}{8\times \pi} inch/s$

The water level rising when the water is 4 inches deep is $\frac{3}{8\times \pi} inch/s$ .

6 0

2 years ago

Put the following numbers in order from least to greatest: -3.15, 3.3, -3 1/5, -3.3

Bas_tet [7]

-3.15, -3.3,-3 1/5,3.3,

6 0

2 years ago

n 2018, homes in East Baton Rouge (EBR) Parish sold for an average of $239,000. You take a random sample of homes in Ascension p

Olenka [21]

Answer:

Conclusion

There is no sufficient evidence to conclude that the mean of the home prices from Ascension parish is higher than the EBR mean

Step-by-step explanation:

From the question we are told that

The population mean for EBR is $\mu_ 1 = \$239,000$

The sample mean for Ascension parish is $\= x_2 = \$246,000$

The p-value is $p-value = 0.045$

The level of significance is $\alpha = 0.01$

The null hypothesis is $H_o : \mu_2 = \mu_1$

The alternative hypothesis is $H_a : \mu_2 > \mu_1$

Here $\mu_2$ is the population mean for Ascension parish

From the data given values we see that

$p-value > \alpha$

So we fail to reject the null hypothesis

So we conclude that there is no sufficient evidence to conclude that the mean of the home prices from Ascension parish is higher than the EBR mean

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2 years ago

11. The equation T = 0.63s + 78 can be used to determine T, the temperature in degrees, inside an oven s seconds after the oven

riadik2000 [5.3K]

I think the second one is b

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2 years ago

Exercise 5.6.6: Selecting a committee of senators. About A country has two political parties, the Demonstrators and the Repudiat

krok68 [10]

Answer:

There are 4,148,350,734,528 ways

Step-by-step explanation:

We have

44 senators which are Demonstrators.
56 senators which are Repudiators.

(a) How many ways are there to select a committee of 10 senate members with the same number of Demonstrators and Repudiators?

We want to choose 5 Demonstrators and 5 Repudiators. The number of ways to do this is ${44} \choose {5}$ and $56 \choose 5$ respectively. Therefore, the number of ways to select the committee is given by:

${{44}\choose {5}} \times {{56}\choose{5}}=\frac{44!}{39!5!}\times\frac{56!}{51!5!}=\frac{44!56!}{51!39!5!5!}=\frac{44\times43\times42\times41\times40\times56\times55\times54\times53\times52}{5!5!}=\\\\=\frac{44\times43\times42\times41\times8\times56\times11\times54\times53\times52}{4!4!}= \frac{11\times43\times42\times41\times2\times56\times11\times54\times53\times52}{3!3!}=\\\\\frac{11\times43\times14\times41\times2\times56\times11\times18\times53\times52}{2!2!}=$

$11\times43\times14\times41\times28\times11\times18\times53\times52=4,148,350,734,528$

(b) Suppose that each party must select a speaker and a vice speaker. How many ways are there for the two speakers and two vice speakers to be selected?

<u>If the speaker and vice speaker are chosen between all senators:</u> In this case, the answer will be

$44\times43\times56\times55=5,827,360.$

This is because there are (in the case of Demonstrators) 44 possibilities to choose an speaker and after choosing one, there would be 43 possibilities to choose a vice speaker. The same situation happens in the case of Repudiators.

<u>If the speaker and vice speaker are chosen between the committee:</u> In this case, the answer will be

$5\times4\times5\times4=400$ .

3 0

2 years ago