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Degger [83]
4 years ago
6

B) Sally has a GPA of 3.35. What percentage of the students have a GPA above her GPA? Show all work. (Note: GPA is normally dist

ributed).
All GPA's: 2.59
3.49
3.78
3.91
3.47
3.36
3.14
2.80
2.93
3.49
3.32
3.72
3.08
3.90
3.33
1.78
3.22
3.36
3.47
2.89
3.34
2.96
3.10
3.38
3.09
3.59
3.93
3.02
3.45
3.49
3.54
3.49
3.82
1.86
Mathematics
1 answer:
Cerrena [4.2K]4 years ago
3 0
13 gpas are higher than 3.35. There are a total of 34 gpas. 13 divided by 34 is 0.382 (rounded to 3 dp). 0.382 x 100 = 38.2 therefore 38.2% of students have a higher gpa than Sally.
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Match the expressions with their equivalent simplified expressions.
Tasya [4]

Answer:

\sqrt[4]{\frac{16x^6y^4}{81x^2y^8}}\rightarrow\frac{2x}{3y}\\\sqrt[4]{\frac{81x^2y^{10}}{81x^6y^6}} \rightarrow\frac{3y}{2x}\\\sqrt[3]{\frac{64x^8y^7}{125x^2y^{10}}}\rightarrow\frac{4x^2}{5y}\\\sqrt[5]{\frac{243x^{17}y^{16}}{32x^7y^{21}}}\rightarrow\frac{3x^2}{2y}\\\sqrt[5]{\frac{32x^{12}y^{15}}{243x^7y^{10}}} \rightarrow\frac{2xy}{3}\\\sqrt[4]{\frac{16x^{10}y^{9}}{256x^2y^{17}}}\rightarrow\frac{x}{2y}


Step-by-step explanation:

\sqrt[4]{\frac{16x^6y^4}{81x^2y^8}} =\sqrt[4]{\frac{(2^4)(x^{6-2})(y^{4-8})}{(3^4)}} =\sqrt[4]{\frac{2^4x^4y^{-4}}{3^4}} =\frac{2xy^{-1}}{3}=\frac{2x}{3y}

\sqrt[4]{\frac{81x^2y^{10}}{81x^6y^6}} =\sqrt[4]{\frac{(3^4)(x^{2-6})(y^{10-6})}{(2^4)}} =\sqrt[4]{\frac{3^4x^{-4}y^{4}}{2^4}} =\frac{3x^{-1}y^1}{3}=\frac{3y}{2x}

\sqrt[3]{\frac{64x^8y^7}{125x^2y^{10}}} =\sqrt[3]{\frac{(4^3)(x^{8-2})(y^{7-10})}{(5^3)}} =\sqrt[3]{\frac{4^3x^6y^{-3}}{5^3}} =\frac{4x^2y^{-1}}{5}=\frac{4x^2}{5y}

\sqrt[5]{\frac{243x^{17}y^{16}}{32x^7y^{21}}} =\sqrt[5]{\frac{(3^5)(x^{17-7})(y^{16-21})}{(2^5)}} =\sqrt[5]{\frac{3^5x^{10}y^{-5}}{2^5}} =\frac{3x^2y^{-1}}{2}=\frac{3x^2}{2y}

\sqrt[5]{\frac{32x^{12}y^{15}}{243x^7y^{10}}} =\sqrt[5]{\frac{(2^5)(x^{12-7})(y^{15-10})}{(3^5)}} =\sqrt[5]{\frac{2^5x^{5}y^{5}}{3^5}} =\frac{2x^1y^{1}}{3}=\frac{2xy}{3}

\sqrt[4]{\frac{16x^{10}y^{9}}{256x^2y^{17}}} =\sqrt[4]{\frac{(2^4)(x^{10-2})(y^{9-17})}{(4^4)}} =\sqrt[4]{\frac{2^4x^{8}y^{-8}}{4^4}} =\frac{2x^{1}y^{-1}}{4}=\frac{x}{2y}

Thus,

\sqrt[4]{\frac{16x^6y^4}{81x^2y^8}}\rightarrow\frac{2x}{3y}\\\sqrt[4]{\frac{81x^2y^{10}}{81x^6y^6}} \rightarrow\frac{3y}{2x}\\\sqrt[3]{\frac{64x^8y^7}{125x^2y^{10}}}\rightarrow\frac{4x^2}{5y}\\\sqrt[5]{\frac{243x^{17}y^{16}}{32x^7y^{21}}}\rightarrow\frac{3x^2}{2y}\\\sqrt[5]{\frac{32x^{12}y^{15}}{243x^7y^{10}}} \rightarrow\frac{2xy}{3}\\\sqrt[4]{\frac{16x^{10}y^{9}}{256x^2y^{17}}}\rightarrow\frac{x}{2y}

3 0
3 years ago
Chloe and Libby want to tie Ryan to a bunch of approximately spherical helium balloons of diameter 0.3m. The volume of each ball
dem82 [27]

Answer:  Aproximately 2,525 balloons

Step-by-step explanation:

 1. Find the volume of a balloon with the formula given in the problem, where r is the radius (r=\frac{0.3m}{2}=0.15m), then:

V=4(0.15m)^{3}=0.0135m^{3}

2. Convert the volume from m³ to lliters by multiplying it by 1,000:

V=0.0135m^{3}*1000=13.5L

3. You know that that 1 liter of helium can lift 1 gram and that Ryan weighs 5 stone and 5 pounds. So you must make the following conversions:

1 g=0.0022 lb

From 5 stones to pounds

(5stone)(\frac{14pounds}{1stone})=70pounds=70lbs

4. Then Ryan's weigh is:

5lb+70lb=75lb

5. Then, if 1 liter of helium can lift 0.0022 lb, to lift 75 lb (which is the weight of Ryan) they need:

\frac{75lb*1L}{0.0022lb}=34,090.90L

6. Then, to calculate the aproximated number of balloons they need to make him float (which can call n), you must  divide the liters of helium needed to lift the weight of Ryan by the volume of a balloon, then the result is:

n=\frac{34,090.90L}{13.5L}

n=2,525.25≈2,525 balloons.

5 0
4 years ago
A wheel with a circumference of 3 inches is rotating at 5 rotations per minute. I is the distance the wheel travels in one minut
Andreas93 [3]
So circumference is the distance around the wheel
that is the part that is actually touching the ground
so therefor the wheele travels 3 inches per rotations
5 rotations per minute
we have to find the distance
3 times (number of roations) times 1 minute=3 times 5 times 1=15
answer is 15 in per miute
I=15
7 0
3 years ago
If someone could please help me then that would be great.
postnew [5]

Answer: Infinite Solutions

Step-by-step explanation: Make the top x and y values times -2 to cancel all the variables and numbers out to get 0 = 0 so it would be Infinite Solutions.

And if you multiply by 2 you get the exact same equation.

If I am wrong let me know!

Hope this helps!  

6 0
3 years ago
Wilma is twice as old as Jamal, and Jamal is 3 years older than Tim. The sum of all their ages is 17. Let j be Jamal's age. Writ
m_a_m_a [10]
Jamal's age is 5 because Tim is 3 years younger which is 2 and add those two together and you get 7 and Wilma is twice his age so 10 and add the others
7 0
3 years ago
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