Which of the following is an odd function? f(x) = x3 + 5x2 + x f(x) = x2 + x f(x) = –x

Mathematics

2 answers:

makkiz [27]2 years ago

8 0

The answer is D.

Edgen-uity

kodGreya [7K]2 years ago

5 0

A function f(x) is said to be odd provided that f(-x) = -f(x) .

1) f(x) = x³ + 5x² + x 

-f(x) = -(x³ + 5x² + x) = x³ - 5x² - x 

f(-x) = (-x)³ - 5(-x)² - (-x) = -x³ - 5x² + x 

f(-x) ≠ -f(x) , so this is not an odd function. 

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2) F(x) = √x is only defined for x ≥ 0 , so it makes no sense to consider F(-x). 
This function is neither odd nor even. 

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3) f(x) = x² + x 

-f(x) = -x² - x 

f(-x) = (-x)² + (-x) = x² - x 

f(-x) ≠ -f(x) , so this is not an odd function. 

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4) f(x) = - x 

-f(x) = x 

f(-x) = - (-x) = x 

-f(x) = f(-x) , so this is an odd function.

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200 students attend a school which offers French and History. 10% of those who take History also take French and 4 times as many

SIZIF [17.4K]

Answer: P(hist& french)=16/200=0.08

Step-by-step explanation:

To find the required probability we have to know what is the number of students that take both History and French ( Intersection of 2 circles in Venn diagram)

1. Lets find the number of students that take History or French or both.

We know that 8% from 200 take neither History or French. So number or students who take History or French or both is 200-200*0.08=184

2. Let number of students that takes French (or both Fr+Hist)=x (left circle)

So number of students that takes History (or both Fr+Hist)=4x (right circle)

So number of students that take both French+History= 10% from 4x or

0.1*4x=0.4x (circles' intersection)

3. Now we have the equation as follows:

x+4*x-0.4*x = 184

4.6*x=184

x=40 students takes French (or both French+ History)

4*x= 40*4=160 students takes History (or both French+ History)

10% from 160 =0.1*160=16 students takes both History and French

P(hist& french)=16/200=0.08

7 0

2 years ago

Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 20.0% but with equal end-of-month pay

Mariulka [41]

Answer:

100% of the 2nd monthly payment go toward the repayment of principal.

Step-by-step explanation:

The loan taken is the Principal which is mentioned as $72,500 with interest at a nominal rate of 20%. Firstly, it is important to understand that nominal rate means non-compounding rate. Simply put will be a "one-time charged" rate on the loan. Since this is given as 20% of the Principal. It is calculated thus: $\frac{20}{100}$ × $\frac{72,500}{1}$ = $14,500. So the interest on the loan is $14,500. Added to the Principal the total amount to be paid back by the company becomes: $72,500 + $14,500 = $87,000. To pay back this amount at equal end-of-month installments in 1 year (12 months), we divide the total amount by 12. i.e $\frac{87000}{12}$ = $7250. This means, the monthly payment will be $7,250. Since the monthly payment pays only 10% of the initial principal $72,500. By the second month only 20% of the Principal would have been paid. So all of the monthly payment will go towards repaying the principal