Question and Answers Forum

A man has a wife with six children and his total income is Gh$8500.He was allowed the following free tax personal:......$1200 wife:...........$300 each child:.....$250 for a maximum of 4 dependant relative:$400 insurance:........$250 Taxed: the first $2000 at 10% the next $2000 at 15% the next $2000 at 20% the next $2000 at 25% calculate a)his tax free income b)his income tax c)his monthly income d)his net monthly income

$A m a n h a s a w i f e w i t h s i x$ $c h i l d r e n a n d h i s t o t a l i n c o m e i s$ $G h $ 8500 . H e w a s a l l o w e d t h e$ $f o l l o w i n g f r e e t a x$ $p e r s o n a l : . . . . . . $ 1200$ $w i f e : . . . . . . . . . . . $ 300$ $e a c h c h i l d : . . . . . $ 250 f o r a m a x i m u m o f 4$ $d e p e n d a n t r e l a t i v e : $ 400$ $i n s u r a n c e : . . . . . . . . $ 250$ $T a x e d :$ $t h e f i r s t $ 2000 a t 10 %$ $t h e n e x t $ 2000 a t 15 %$ $t h e n e x t $ 2000 a t 20 %$ $t h e n e x t $ 2000 a t 25 %$ $c a l c u l a t e$ $a) h i s t a x f r e e i n c o m e$ $b) h i s i n c o m e t a x$ $c) h i s m o n t h l y i n c o m e$ $d) h i s n e t m o n t h l y i n c o m e$

Question Number 120202 Answers: 0 Comments: 0

Show for the equation a^n = b^2 −1 where n>1 and a>2 are any natural numbers , there are no positive integer solutions for a and b ?

$S h o w f o r t h e e q u a t i o n a^{n} = b^{2} - 1$ $w h e r e n > 1 a n d a > 2 a r e a n y n a t u r a l$ $n u m b e r s, t h e r e a r e n o p o s i t i v e i n t e g e r$ $s o l u t i o n s f o r a a n d b ?$

Question Number 120049 Answers: 2 Comments: 0

f(x+2)+f(x−2)=f(x) f(1)=1 ,f(2)=2,f(3)=3,f(4)=4 then f(100)=?

$f (x + 2) + f (x - 2) = f (x)$ $f (1) = 1, f (2) = 2, f (3) = 3, f (4) = 4$ $t h e n f (100) = ?$

Question Number 119956 Answers: 2 Comments: 0

Given a = 1+3+3^2 +3^3 +3^4 +...+3^(100) Find the remainder of dividing the number by 5 . (a) 2 (b) 0 (c)4 (d)1 (e) 3

$G i v e n a = 1 + 3 + 3^{2} + 3^{3} + 3^{4} + . . . + 3^{100}$ $F i n d t h e r e m a i n d e r o f d i v i d i n g t h e n u m b e r$ $b y 5 .$ $(a) 2 (b) 0 (c) 4 (d) 1 (e) 3$

Question Number 119790 Answers: 2 Comments: 0

Let x,y,z be nonnegative real numbers, which satisfy x+y+z=1 Find minimum value of Q=(√(2−x)) + (√(2−y)) + (√(2−z)) .

$L e t x, y, z b e n o n n e g a t i v e r e a l$ $n u m b e r s, w h i c h s a t i s f y x + y + z = 1$ $F i n d m i n i m u m v a l u e o f$ $Q = \sqrt{2 - x} + \sqrt{2 - y} + \sqrt{2 - z} .$

Question Number 119657 Answers: 1 Comments: 2

Suppose that the greatest common divisor of the positive integers a,b and c is 1 and ((ab)/(a−b)) = c . Prove that a−b is a perfect square

$S u p p o s e t h a t t h e g r e a t e s t c o m m o n d i v i s o r o f$ $t h e p o s i t i v e i n t e g e r s a, b a n d c i s 1 a n d$ $\frac{a b}{a - b} = c . P r o v e t h a t a - b i s a$ $p e r f e c t s q u a r e$

Question Number 119600 Answers: 2 Comments: 0

Find gcd of x^4 +x^3 −4x^2 +x+5 and x^3 +x^2 −9x−9

$F i n d g c d o f x^{4} + x^{3} - 4 x^{2} + x + 5$ $a n d x^{3} + x^{2} - 9 x - 9$

Question Number 119094 Answers: 1 Comments: 0

Why the Fermat formula about prime numbers is for n = 5 and n = 6 fail? f(n) = 2^2^n + 1

$W h y t h e F e r m a t f o r m u l a a b o u t p r i m e n u m b e r s i s f o r n = 5 a n d n = 6 f a i l ?$ $f (n) = 2^{2^{n}} + 1$

Question Number 118880 Answers: 3 Comments: 0

8(1+(1/2))(1+(1/2^2 ))(1+(1/2^4 ))(1+(1/2^8 ))...(1+(1/2^(32) ))+ (1/2^(60) )=?

$8 (1 + \frac{1}{2}) (1 + \frac{1}{2^{2}}) (1 + \frac{1}{2^{4}}) (1 + \frac{1}{2^{8}}) . . . (1 + \frac{1}{2^{32}}) + \frac{1}{2^{60}} = ?$

Question Number 118357 Answers: 2 Comments: 0

Find the sum of the prime factors of 20^5 +21.

$Find the sum of the prime factors of$ $20^{5} + 21 .$

Question Number 118362 Answers: 1 Comments: 0

Prove that 𝛑 is an irrational number

$Prove that π is an irrational number$

Question Number 117848 Answers: 0 Comments: 0

Determine all functions f:R→R such that the equality f([x] y)= f(x) [f(y) ] holds for all x,y ∈R . Here by [x] we denote the greatest integer not exceeding x.

$D e t e r m i n e a l l f u n c t i o n s f : R \to R$ $s u c h t h a t t h e e q u a l i t y f ([x] y) = f (x) [f (y)]$ $h o l d s f o r a l l x, y \in R . H e r e b y [x] w e$ $d e n o t e t h e g r e a t e s t i n t e g e r n o t e x c e e d i n g x .$

Question Number 117369 Answers: 1 Comments: 0

Find the units digit of 2013^1 +2013^2 +2013^3 +...+2013^(2013)

$Find the units digit of 2013^{1} + 2013^{2} + 2013^{3} + . . . + 2013^{2013}$

Question Number 117045 Answers: 4 Comments: 0

If x is a complex number satisfying x^2 +x+1 = 0 , what is the value of x^(53) +x^(52) +x^(51) +x^(50) +x^(49) ?

$If x is a complex number satisfying$ $x^{2} + x + 1 = 0, what is the value of$ $x^{53} + x^{52} + x^{51} + x^{50} + x^{49} ?$

Question Number 116700 Answers: 1 Comments: 0

How many positive integral solutions does 3x+5y=300 have?

$How many positive integral$ $solutions does 3 x + 5 y = 300 have ?$

Question Number 116725 Answers: 4 Comments: 3

what the value of log _(10) (−1) in complex number

$what the value of \log_{10} (- 1) in$ $complex number$

Question Number 116356 Answers: 0 Comments: 0

Let S ={1,2,3,4,...,48,49} .What is the maximum value of n such that it is possible to select n numbers from S and arrange them in a circle in such a way that the product of any two adjacent numbers in the circle is less than 100?

$Let S = {1, 2, 3, 4, . . ., 48, 49} . What is$ $the maximum value of n such that$ $it is possible to select n numbers$ $from S and arrange them in a circle$ $in such a way that the product of$ $any two adjacent numbers in the$ $circle is less than 100 ?$

Question Number 115742 Answers: 1 Comments: 0

what the cooefficient of x^(10) from (1+x)×(1+2x^2 )×(1+3x^3 )×...×(1+2020x^(2020) )

$w h a t t h e c o o e f f i c i e n t o f x^{10} f r o m$ $(1 + x) \times (1 + 2 x^{2}) \times (1 + 3 x^{3}) \times . . . \times (1 + 2020 x^{2020})$

Question Number 115033 Answers: 2 Comments: 0

If a and b positive real number where a^(505) + b^(505) = 1, then minimum value a^(2020) + b^(2020) is __

$I f a a n d b p o s i t i v e r e a l n u m b e r w h e r e$ $a^{505} + b^{505} = 1, t h e n m i n i m u m v a l u e$ $a^{2020} + b^{2020} i s__$

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