All categories

3 years ago

What are three different whole numbers whose sum and product are the same

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

6 0

Answer:

1,2, and 3

Step-by-step explanation:

If you add together 1, 2, and 3, you will get 6. However, if you multiply them together, you will also get 6. Hope this helps!

You might be interested in

1. The probability of telesales representative making a sale on a customer call is 0.15.

Mumz [18]

Answer:

$n = 33$

$n = 19$

Step-by-step explanation:

From the question we are told that

The probability of telesales representative making a sale on a customer call is $p = 0.15$

The mean is $\mu = 5$

Generally the distribution of sales call made by a telesales representative follows a binomial distribution

i.e

$X \~ \ \ \ B(n , p)$

and the probability distribution function for binomial distribution is

$P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}$

Here C stands for combination hence we are going to be making use of the combination function in our calculators

Generally the mean is mathematically represented as

$\mu = n* p$

=> $5= n * 0.15$

=> $n = 33$

Generally the least number of calls that need to be made by a representative for the probability of at least 1 sale to exceed 0.95 is mathematically represented as

$P( X \ge 1) = 1 - P( X < 1 ) > 0.95$

=> $P( X \ge 1) = 1 - P( X =0 ) > 0.95$

=> $P( X \ge 1) = 1 - [ ^{n}C_0 * (0.15 )^0 * (1- 0.15)^{n-0}] > 0.95$

=> $1 - [1 * 1* (0.85)^{n}] > 0.95$

=> $[(0.85)^{n}] > 0.05$

taking natural log of both sides

$n = \frac{ln(0.05)}{ln(0.85)}$

=> $n = 19$

3 0

2 years ago

A painter charges an initial fee of $50 and $30 for each hour of labor. Write a linear function to determine the total cost. How

il63 [147K]

The initial fee of $50 is essentially the y intercept because this is the value when x = 0 (x is the number of labor-hours). So b = 50.

The slope is m = 30 because each increase of 1 hour leads to the cost bumping up by 30 dollars. In other words, slope = rise/run = (change in cost)/(change in hours) = 30/1

So we plug m = 30 and b = 50 into the y = mx+b formula to get y = 30x+50

Replace y with f(x) to get f(x) = 30x+50

The linear function for the cost is f(x) = 30x+50

Note: Some books may use other letters (instead of x and f(x)), but the idea is still the same

Once you know the cost function, you replace x with 4.5 to find the amount it will cost to have a painter work for 4.5 hours.

f(x) = 30x+50
f(4.5) = 30*4.5+50
f(4.5) = 135+50
f(4.5) = 185

It will cost 185 dollars to have the painter work for 4.5 hours

7 0

3 years ago

How to prove this???

swat32

$\cos^3 2A + 3 \cos 2A \\
\Rightarrow \cos 2A (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (1 - \sin^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - \sin^2 2A) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - (2\sin A \cos A)(2\sin A \cos A)) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - 4\sin^2 A \cos^2 A) \\ 
\Rightarrow 4(\cos^2 A - \sin^2 A) (1 - \sin^2 A \cos^2 A) 
$

go to right side now

$4( \cos^6 A - \sin^6 A)\\
\Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A)$

use $x^3 - y^3 = (x-y)(x^2 + xy + y^2)$ and $x^3 + y^3 = x^2 - xy + y^2$

$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A) \\
\Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\
~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A)$

so $\sin^2 A + \cos^2 A = 1$

$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\ ~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 + \cos A \sin A )(1- \cos A \sin A ) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \cos^2 A \sin^2 A )\\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \sin^2 A \cos^2 A ) \\
 \Rightarrow Left hand side$

4 0

2 years ago

Help me with this problem please

Ymorist [56]

Answer:

-15

Step-by-step explanation:

3^2 - 3 x [(5^2 - 9) / 2 ]

9 - 3 x [(25 - 9) / 2]

9 - 3 x (16/2)

9 - 3 x 8

9 - 24

-15

5 0

3 years ago

Read 2 more answers

Fraction multiplying by fractions

Amanda [17]

$\bf \cfrac{2}{9}\times a=\cfrac{3}{15}\implies \cfrac{2a}{9}=\cfrac{1}{5}\implies 2a=\cfrac{9\cdot 1}{15}\implies 2a=\cfrac{3}{5}
\\\\\\
a=\cfrac{3}{2\cdot 5}
\implies 
a=\cfrac{3}{10}\\\\
-------------------------------\\\\
\cfrac{2}{5}\times b=\cfrac{7}{12}\implies \cfrac{2b}{5}=\cfrac{7}{12}\implies 2b=\cfrac{5\cdot 7}{12}\implies 2b=\cfrac{35}{12}
\\\\\\
b=\cfrac{35}{2\cdot 12}\implies b=\cfrac{35}{24}$

3 0

2 years ago