Answer:
true
Step-by-step explanation:
take away 1/3 from 5 and you get four and a third
Answer:
36 cups of water
Step-by-step explanation:
Make a proportion, where x is the number of cups of water needed:
= ![\frac{24}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B24%7D%7Bx%7D)
Cross multiply and solve for x:
2x = 72
x = 36
So, 36 cups of water will be needed
To find the difference of given expression:
![5\frac{2}{3} -3\frac{1}{5}](https://tex.z-dn.net/?f=%205%5Cfrac%7B2%7D%7B3%7D%20-3%5Cfrac%7B1%7D%7B5%7D%20%20)
First step is to subtract the whole number5 and 3.
So, 5 - 3 = 2.
Now we can find the difference of fractions.
To subtract the fractions , we need to find the common denominator.
Common denominator of 3 and 5 is 15.
So, we need to make both the denominator equal to 15.
![\frac{2}{3} =\frac{2*5}{3*5} =\frac{10}{15}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20%3D%5Cfrac%7B2%2A5%7D%7B3%2A5%7D%20%3D%5Cfrac%7B10%7D%7B15%7D%20%20)
Similarly, ![\frac{1}{5} =\frac{1*3}{3*5} = \frac{3}{15}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%7D%20%3D%5Cfrac%7B1%2A3%7D%7B3%2A5%7D%20%3D%20%5Cfrac%7B3%7D%7B15%7D%20%20)
Therefore, ![\frac{2}{3} -\frac{1}{5} =\frac{10}{15} -\frac{3}{15}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20-%5Cfrac%7B1%7D%7B5%7D%20%3D%5Cfrac%7B10%7D%7B15%7D%20-%5Cfrac%7B3%7D%7B15%7D%20%20)
=![\frac{10-3}{15}](https://tex.z-dn.net/?f=%20%5Cfrac%7B10-3%7D%7B15%7D%20%20)
= ![\frac{7}{15}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B15%7D%20%20)
So, the difference of given expression is
.
So, the correct choice is C.
Solution :
a). The probability that the student will
the 1st question after the 4th attempt.
P (correct in the 4th attempt)
= ![$(1-0.75)^3 \times 0.75$](https://tex.z-dn.net/?f=%24%281-0.75%29%5E3%20%5Ctimes%200.75%24)
= 0.01171875
b). The probability that the student will
3 questions after 10 total attempts.
P( X = 3) for X = B in (n = 10, p = 0.75)
= ![$C(10,30) \times 0.75^3 \times 0.25^7$](https://tex.z-dn.net/?f=%24C%2810%2C30%29%20%5Ctimes%200.75%5E3%20%5Ctimes%200.25%5E7%24)
= 0.0031
c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :
There are = 6 success, p = 0.75.
Therefore, this is a case of a negative binomial distribution.
![$E(X)=\frac{k}{p}$](https://tex.z-dn.net/?f=%24E%28X%29%3D%5Cfrac%7Bk%7D%7Bp%7D%24)
![$=\frac{6}{0.75}$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B6%7D%7B0.75%7D%24)
= 8
So, ![$\sigma = \frac{\sqrt{k(1-p)}}{p}$](https://tex.z-dn.net/?f=%24%5Csigma%20%3D%20%5Cfrac%7B%5Csqrt%7Bk%281-p%29%7D%7D%7Bp%7D%24)
![$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$](https://tex.z-dn.net/?f=%24%5Csigma%20%3D%20%5Cfrac%7B%5Csqrt%7B6%281-0.75%29%7D%7D%7B0.75%7D%24)
= 1.6330
we know that
<u>Unit Rate</u> is the ratio of two measurements in which the second term is ![1](https://tex.z-dn.net/?f=1)
we have
![2\frac{1}{2}\ liters=\frac{2*2+1}{2}=\frac{5}{2}\ liters](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B2%7D%5C%20liters%3D%5Cfrac%7B2%2A2%2B1%7D%7B2%7D%3D%5Cfrac%7B5%7D%7B2%7D%5C%20liters)
so
Corey bought
of paint for ![\$60](https://tex.z-dn.net/?f=%5C%2460)
by proportion
<u>Find the cost of one liter of paint</u>
![\frac{60}{(5/2)}\frac{\$}{liters}=\frac{x}{1}\frac{\$}{liters} \\ \\x*\frac{5}{2}=60\\ \\ x=2*60/5\\ \\x=\$24](https://tex.z-dn.net/?f=%5Cfrac%7B60%7D%7B%285%2F2%29%7D%5Cfrac%7B%5C%24%7D%7Bliters%7D%3D%5Cfrac%7Bx%7D%7B1%7D%5Cfrac%7B%5C%24%7D%7Bliters%7D%20%5C%5C%20%5C%5Cx%2A%5Cfrac%7B5%7D%7B2%7D%3D60%5C%5C%20%5C%5C%20x%3D2%2A60%2F5%5C%5C%20%5C%5Cx%3D%5C%2424)
therefore
<u>the answer is</u>
the cost per liter of the paint is equal to ![24\frac{\$}{liter}](https://tex.z-dn.net/?f=24%5Cfrac%7B%5C%24%7D%7Bliter%7D)