Answer:
a) 11.7% of students study for more than 10 hours per week.
b) 35.6% of student spends between 7 and 9 hours studying.
c) 1.6% of students spend fewer than 3 hours studying.
d) 5% of all A students spend studying 4.0455 or less hours during a week.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 7.5 hours
Standard Deviation, σ = 2.1 hours
We are given that the distribution of amount of time is a bell shaped distribution that is a normal distribution.
Formula:
a) P(students study for more than 10 hours per week)
P(x > 10)
Calculation the value from standard normal z table, we have,
b) P(student spends between 7 and 9 hours studying.)
c) P(students spend fewer than 3 hours studying)
Calculating the value from the standard normal table we have,
d) P(X < x) = 0.05
We have to find the value of x such that the probability is 0.035
Calculation the value from standard normal z table, we have,
5% of all A students spend studying 4.0455 or less hours during a week.
Answer:
Let's solve your system by elimination.
3x+4y=29;6x+5y=43
Multiply the first equation by -2,and multiply the second equation by 1.
−2(3x+4y=29)
1(6x+5y=43)
Becomes:
−6x−8y=−58
6x+5y=43
Add these equations to eliminate x:
−3y=−15
Then solve−3y=−15for y:
−3y=−15
−3y
−3
=
−15
−3
(Divide both sides by -3)
y=5
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
3x+4y=29
Substitute5foryin3x+4y=29:
3x+(4)(5)=29
3x+20=29(Simplify both sides of the equation)
3x+20+−20=29+−20(Add -20 to both sides)
3x=9
3x
3
=
9
3
(Divide both sides by 3)
x=3
Answer:
x=3 and y=5
Step-by-step explanation:
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Answer:
Once you know the volume of the displaced water, you can immediately determine its weight by multiplying by the density of water at the relevant temperature. That's because the definition of density (d) is mass (m) divided by volume (v), so m = dv.
Step-by-step explanation:
Let f(x) = p(x)/q(x), where p and q are polynomials and reduced to lowest terms. (If p and q have a common factor, then they contribute removable discontinuities ('holes').)
Write this in cases:
(i) If deg p(x) ≤ deg q(x), then f(x) is a proper rational function, and lim(x→ ±∞) f(x) = constant.
If deg p(x) < deg q(x), then these limits equal 0, thus yielding the horizontal asymptote y = 0.
If deg p(x) = deg q(x), then these limits equal a/b, where a and b are the leading coefficients of p(x) and q(x), respectively. Hence, we have the horizontal asymptote y = a/b.
Note that there are no obliques asymptotes in this case. ------------- (ii) If deg p(x) > deg q(x), then f(x) is an improper rational function.
By long division, we can write f(x) = g(x) + r(x)/q(x), where g(x) and r(x) are polynomials and deg r(x) < deg q(x).
As in (i), note that lim(x→ ±∞) [f(x) - g(x)] = lim(x→ ±∞) r(x)/q(x) = 0. Hence, y = g(x) is an asymptote. (In particular, if deg g(x) = 1, then this is an oblique asymptote.)
This time, note that there are no horizontal asymptotes. ------------------ In summary, the degrees of p(x) and q(x) control which kind of asymptote we have.
I hope this helps!
