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STatiana [176]
3 years ago
6

What is the simplified form of x plus 1 over x squared plus x minus 6 divided by x squared plus 5x plus 4 over x plus 3 ?

Mathematics
2 answers:
kirill115 [55]3 years ago
6 0
X² +  x - 6 = x² + 3 x - 2 x - 6 = x ( x + 3 ) - 2 ( x + 3 ) = ( x + 3 ) ( x - 2 )
x² + 5 x + 4 = x² + x + 4 x + 4 = x ( x + 1 ) + 4  ( x + 1 ) = ( x + 1 ) ( x + 4 )
( x + 1 )  / ( x² + x - 6 )   :    ( x² + 5 x + 4 ) / ( x + 3 ) =
= ( x + 1 ) / ( x² + x + 6 )  ·  ( x + 3 ) / ( x² + 5 x + 4 ) =
= ( x + 1 )   / ( x + 3 ) ( x - 2 )  ·  ( x + 3 )  / ( x + 1 ) ( x + 4 ) =
= 1 / ( x - 2)( x + 4 ) 
Jobisdone [24]3 years ago
3 0

Answer:

1 / (x + 3) (x - 2)

Step-by-step explanation:

This is the correct answer i just took the test!

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There are 400 animals that live at a zoo. You find that 22 of 65 randomly chosen animals are
snow_tiger [21]

Answer:

About 135.

Step-by-step explanation:

As the sample is random the number of monkeys likely to be in the zoo

=  (22/65) * 400

= 135.38

8 0
3 years ago
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $23 monthly fee
Daniel [21]

Answer:

100

Step-by-step explanation:

.15x + 23 = .10x + 28

4 0
3 years ago
Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a math
NISA [10]

Answer:A=\frac{14}{9}\cdot \sqrt{2}\ unit^2

Step-by-step explanation:

Given

Two curves are given

y=10 x^2

and y=x^2+2

the two curves intersect at

10x^2=x^2+2

x=\pm \frac{\sqrt{2}}{3}

to get the we need to integrate the curves over x axis

A=\int_{-\frac{\sqrt{2}}{3}}^{\frac{\sqrt{2}}{3}}\left ( x^2+3-10x^2\right )dx

A=2\int_{0}^{\frac{\sqrt{2}}{3}}\left ( 3-9x^2\right )dx

A=2\left [ 3\left ( \frac{\sqrt{2}}{3}\right )-\frac{9}{3}\left ( \frac{\sqrt{2}}{3}\right )^3\right ]

A=2\sqrt{2}\left [ 1-\frac{2}{9}\right ]

A=\frac{14}{9}\cdot \sqrt{2}\ unit^2

3 0
3 years ago
The CEO of a large electric utility claims that more than 75 percent of his customers are very satisfied with the service they r
vichka [17]

Answer:

z=\frac{0.77-0.75}{\sqrt{\frac{0.75(1-0.75)}{100}}}=0.462  

Now we can find the p value using the alternative hypothesis with this probability:

p_v =P(z>0.462)=0.322  

Since the p value is large enough, we have evidence to conclude that the true proportion for this case is NOT significanctly higher than 0.75 since we FAIL to reject the null hypothesis at any significance level lower than 30%

Step-by-step explanation:

Information provided

n=100 represent the random sample selected

\hat p=0.77 estimated proportion of students that are satisfied

is the value that we want to test

z would represent the statistic

p_v represent the p value

System of hypothesis

We want to verify if more than 75 percent of his customers are very satisfied with the service they receive, then the system of hypothesis is.:  

Null hypothesis:p\leq 0.75  

Alternative hypothesis:p > 0.75  

The statistic is given by:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing the info given we got:

z=\frac{0.77-0.75}{\sqrt{\frac{0.75(1-0.75)}{100}}}=0.462  

Now we can find the p value using the alternative hypothesis with this probability:

p_v =P(z>0.462)=0.322  

Since the p value is large enough we have evidence to conclude that the true proportion for this case is NOT significanctly higher than 0.75 since we FAIL to reject the null hypothesis at any significance level lower than 30%

4 0
3 years ago
Find the probability of at least one
zmey [24]

Answer:

99.8% probability of at least one failure.

Step-by-step explanation:

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.

Probability of success is 30%.

This means that p = 0.3

Five trials:

This means that n = 5

Find the probability of at least one failure in five trials of a binomial experiment in which the probability of success is 30%.

Less than five sucesses, which is:

P(X < 5) = 1 - P(X = 5)

In which

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

P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{0} = 0.002

P(X < 5) = 1 - P(X = 5) = 1 - 0.002 = 0.998

0.998*100% = 99.8%

99.8% probability of at least one failure.

8 0
3 years ago
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