$\text{Hello there!}\\ \\ \text{In this question, you need to simplify by adding like terms}\\ \\\text{Both terms are}\,\,b^4,\,\,\text{in which you can combine them}\\\\-23b^4+(-7b^4)\\\\\text{Add them}\\\\-30b^4\\\\\large\boxed{-30b^4}$

5 0

3 years ago

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In a survey of 300 college graduates, 53% reported that they entered a profession closely related to their college major. If 9 o

ExtremeBDS [4]

Answer:

0.1348 = 13.48% probability that 3 of them entered a profession closely related to their college major.

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they entered a profession closely related to their college major, or they did not. The probability of a graduate entering a profession closely related to their college major is independent of other graduates. This, coupled with the fact that they are chosen with replacement, means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

53% reported that they entered a profession closely related to their college major.

This means that $p = 0.53$

9 of those survey subjects are randomly selected

This means that $n = 9$

What is the probability that 3 of them entered a profession closely related to their college major?

This is P(X = 3).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{9,3}.(0.53)^{3}.(0.47)^{6} = 0.1348$

0.1348 = 13.48% probability that 3 of them entered a profession closely related to their college major.

6 0

3 years ago

where does the graph of the function y=tan(x) have asymptotes? at the values of x where cos(x)=0 at the values of x where sin(x)

Gnom [1K]

Answer: at the values where cos(x) = 0

Justification:

1) tan(x) = sin(x) / cos(x).

2) functions have vertical asymptotes at x = a if Limit of the function x approaches a is + or - infinity.

3) the limit of tan(x) approaches +/- infinity where cos(x) approaches 0.

Therefore, the grpah of y = tan(x) has asymptotes where cos(x) = 0.

You can see the asympotes at x = +/- π/2 on the attached graph. Remember that cos(x) approaches 0 when x approaches +/- (n+1) π/2, for any n ∈ N, so there are infinite asymptotes.

7 0

3 years ago

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