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Pie
3 years ago
9

The complementary angle of 85 degrees

Mathematics
1 answer:
guapka [62]3 years ago
4 0

Answer:

5 degrees

Step-by-step explanation:

Complementary angles sum up to 90 degrees.

If one angle is 85 degrees, then its complement is (90 - 85), or 5, degrees.

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$50 per day x 6 days = 300

20% = 0.2, times t = 0.2t

The equation would be: f(t) = 300 + 0.2t

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Show that if X is a geometric random variable with parameter p, then
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Answer:

\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}=-\frac{p ln p}{1-p}

Step-by-step explanation:

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

P(X=x)=(1-p)^{x-1} p

Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:

X\sim Geo (1-p)

In order to find the expected value E(1/X) we need to find this sum:

E(X)=\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}

Lets consider the following series:

\sum_{k=1}^{\infty} b^{k-1}

And let's assume that this series is a power series with b a number between (0,1). If we apply integration of this series we have this:

\int_{0}^b \sum_{k=1}^{\infty} r^{k-1}=\sum_{k=1}^{\infty} \int_{0}^b r^{k-1} dt=\sum_{k=1}^{\infty} \frac{b^k}{k}   (a)

On the last step we assume that 0\leq r\leq b and \sum_{k=1}^{\infty} r^{k-1}=\frac{1}{1-r}, then the integral on the left part of equation (a) would be 1. And we have:

\int_{0}^b \frac{1}{1-r}dr=-ln(1-b)

And for the next step we have:

\sum_{k=1}^{\infty} \frac{b^{k-1}}{k}=\frac{1}{b}\sum_{k=1}^{\infty}\frac{b^k}{k}=-\frac{ln(1-b)}{b}

And with this we have the requiered proof.

And since b=1-p we have that:

\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}=-\frac{p ln p}{1-p}

4 0
3 years ago
Eric randomly surveyed 150 adults from a certain city and asked which team in a contest they were rooting​ for, either North Hig
Romashka-Z-Leto [24]

Answer:

B

Step-by-step explanation:

  • A 95% confidence level interval will have 0.52 (lower interval) & 0.68 (upper interval) which means that that if 90 individuals root for North HS then p value is 0.6 which will fall in the 95% confidence interval range.
  • For the option B the p value will also be same as in case A hence B is true as an alternative hypothesis.
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         Confidence Interval = p ± z \sqrt{p(1-p)/n}

         

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3 years ago
Find the equation of a line with a slope 3 that includes the point (0,5)
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Answer:

B

Step-by-step explanation:

We want to find the equation of a line with a slope of 3 that includes the point (0, 5).

We can use the slope-intercept form, given by:

y=mx+b

Where m is the slope and b is the y-intercept.

Notice that the given point (0, 5) is already the y-intercept. So, b = 5.

By substitution, we acquire:

y=3x+5

Hence, our answer is B.

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3 years ago
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