Math Is Fun Forum

Dharshi

Member

Registered: 2006-10-31

Posts: 56

Need help

The graph of a third-degree polynomial function has x-intercepts  -1,2  and 3 and a y intercept of -12, if the graph passes through (1,k), then the value of k is...

can anyone solve this problem?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Need help

You're given 3 roots of the function, and so you know that it must be of the form:

f(x) = a(x+1)(x-2)(x-3)

It needs to have those three factors, and since it's a cubic function the unknown part must then be a constant.

You can find a by using f(0) = -12, and after that you know the whole function so finding f(1) is easy.

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Why did the vector cross the road?
It wanted to be normal.

crazyxbeautiful005

Member

Registered: 2009-06-16

Posts: 1

Re: Need help

A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 15.

A. The professor has informed us that 16.6% of her students received grades of A. What is the minimum score needed to receive a grade of A? (Show the formulas, graph, and every step of the way in details).

B. If 12.1% of her students failed the course and received F's, what was the maximum score among those who received F? (Show the formulas, graph, and every step of the way in details).

C. Overall 5 students failed the test, how many students were enrolled in her course? (Show the formulas, graph, and every step of the way in details).

D. If 13% of the students received grades of B, what is the minimum score of those who received a B? (Show the formulas, graph, and every step of the way in details).

MIN:

E. If 50% of the students received grades of C, what is the minimum score of those who received a C? (Show the formulas, graph, and every step of the way in details).

MIN:

F. What is the minimum score of those who received a D? (Show the formulas, graph, and every step of the way in details).

MIN:

G. What percentage of students scored between 88 to 100 points?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help

Hi crazyxbeautiful005;

A:

Since 1 standard deviation is .3413 Or 34.13% and 16.6% is almost the remainder, you need a 94 or more to get a A.

B:

.5  - .121 = .3790

.3790 is equivalent to 1.17 standard deviations. (consult your tables)

x = 60.45

The .3790 or 37.9% stretches to the left from the mean 78 to 60.45.
The kids who got an F were below this (remember they represent the .121 or 12.1%).
So the highest score possible was 60 among those who failed.

C:

This is a little ambiguous.
If you mean that just the 12.1% who failed the test also failed the course then set up the proportion:

x = 41.322

The nearest integer is 41.

There are 41 students in her class.

G:

2/3 standard deviations away from the mean corresponds to 24.75 % of the Standard Normal Curve (you should have tables to verify this). Since the the right side (greater than the mean) is equal to ,5  the percentage of the students who scored 88 or more is 1/2 - .2475 = .2525 or 25.25%.

Last edited by bobbym (2009-06-16 06:21:09)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.