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Mathematics

1 answer:

vlabodo [156]3 years ago

6 0

Step-by-step explanation:

the y-intercept is 1 because it's on the y(axis). the line from 1 goes down 1 over three so the slope is 1/3.

your equation would be y=1/3x+1

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The time t (in minutes) for a small plane to climb to an altitude of h feet is given by t = 50 log10 (18000/(18000-h)) where 180

Arlecino [84]

Domain = x<18000(You cant og a negative number)
Am I actually supposed to graph it? enter the equation on desmos.com
It takes longer to make the same altitudinal gain
t=50log(18000/(18000-4000))=50log(18000/14000)=5.457

5 0

3 years ago

An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These

Vladimir79 [104]

Answer:

Between 1000 and 5000 snowboards will make the function AP(x) >0.

Step-by-step explanation:

Since x can only take possitive values, we have that AP(x) = P(x)/x > 0 if and only if P(x) > 0.

In order to find when P(x) > 0, we find the values from where it is 0 and then we use the Bolzano Theorem.

P(x) = R(x) - C(x) = -x²+10x - (4x+5) = -x²+6x - 5. the roots of P can be found using the quadratic formula:

$r_1,r_2 = \frac{-6 ^+_- \sqrt{6^2-4*(-1)*(-5)} }{2*(-1)} = \frac{-6^+_-\sqrt{16}}{-2} = \{1, 5\}$

Therefore, P(1) = P(5) = 0. Lets find intermediate values to apply Bolzano Theorem:

P(0) = -5 < 0 ( P is negative in (-∞ , 1) )
P(2) = -4+6*2-5 = 3 > 0 (P is positive in (1,5) )
P(6) = -36+36-5 = -5 < 0 (P is negative in (5, +∞) )

The production levels that make AP(x) >0 are between 1000 and 5000 snowboards (because we take x by thousands)

5 0

3 years ago

Suppose in the University of Manitoba, 40% of the students live in apartments. If 600 students are randomly selected, then the a

just olya [345]

Answer:

$P(200\leq X\leq 400)=P(\frac{200-240}{12}\leq \frac{X-\mu}{\sigma}\leq \frac{400-240}{12})=P(-3.33\leq Z \leq 13.33)$

$=P(Z$

So then the correct answer would be:

B) .9996

Step-by-step explanation:

The exact way to solve this problem is using the binomial distribution, assuming that our random variable of interest is "number of students living in apartments" represented by X and $X \sim Bin(n=600, p =0.4)$

And we want this probability:

$P(200 \leq X \leq 400) [tex]In order to find this probability we can use the foloowing excel code:"=BINOM.DIST(400,600,0.4,TRUE)-BINOM.DIST(199,600,0.4,TRUE)"And we got:[tex] P(200 \leq X \leq 400) =0.999675[tex]But for this case the problem says that we need to approximate, so then we can use the normal approximation to the normal distribution. We need to check the conditions in order to use the normal approximation.
[tex]np=600*0.4=240\geq 10$