A cylindrical glass of soda has a mass of 700g. The glass itself has a mass of 80g. If the glass has a radius of 4cm and a heigh
1 answer:
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<span>1.
"The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x"
means that if the monthly income of John is $ 5,000 ,he can spend at most
f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22, 500 (dollars)
Or for example
if Johns monthly income is $8,000, then he can spend at most
</span>f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)<span>
2.
Now, assume that the maximum amount that John can spend is y.
Then, y=15,000+1.5x
we can express x, the monthly income, in terms of y by isolating x:
</span>y=15,000+1.5x
<span>
1.5x = y-15,000
</span>
<span>
thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:
</span>
since we generally use the letter x for the variable of a function, we write g again as:
<span>
for example :
</span>
<span>
tells us that if the maximum amount that John can spend is 50,000 $, then his monthly income is 23,333 $.
3.
If John's limit is $60,000, his monthly income is
</span>
<span>
dollars.
Answer: $ 30,000
Remark: g is called the inverse function of f, since it undoes what f does.
instead of g(x), we could use the notation </span>
<span>
</span>
"The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x"
means that if the monthly income of John is $ 5,000 ,he can spend at most
f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22, 500 (dollars)
Or for example
if Johns monthly income is $8,000, then he can spend at most
</span>f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)<span>
2.
Now, assume that the maximum amount that John can spend is y.
Then, y=15,000+1.5x
we can express x, the monthly income, in terms of y by isolating x:
</span>y=15,000+1.5x
<span>
1.5x = y-15,000
</span>
<span>
thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:
</span>
since we generally use the letter x for the variable of a function, we write g again as:
<span>
for example :
</span>
<span>
tells us that if the maximum amount that John can spend is 50,000 $, then his monthly income is 23,333 $.
3.
If John's limit is $60,000, his monthly income is
</span>
dollars.
Answer: $ 30,000
Remark: g is called the inverse function of f, since it undoes what f does.
instead of g(x), we could use the notation </span>
</span>
Answer:
Step-by-step explanation:
a) H0:
Ha:
(Two tailed test at 5% significance level)
b) n=30
Mean difference =
Std error of mean =
b) Test statistic t = mean diff/std error = -1.552
df = 30-1 =29
p value=0.0657
c) Since p > 0.05 our signi. level, we accept null hypothesis.
There is no significant difference between the means.
d) Using critical value we find that test statistic is > critical value left
So accept H0