40 = x% of 32
32x = 40
x = 40/32
x = 1.25
multiply by 100 to convert to percentage...
x = 125%
40 is 125% of 32
48
1st seat 6 possible for each 6 only 1 possible(spouse) for seat 2
3rd seat 4 possible for each 4 only 1 possible(spouse) for seat 4
5th seat 2 possible for each 2 only 1 possible(spouse) for seat 6
6 x 4 x 2 = 48
OR 3 couples possible arrangements 3 x 2 x1 = 6
each couple 2 possible 2 x 2 x 2 = 8
therefore 6 x 8 = 48
Answer:
Step-by-step explanation:
We are asked to represent
as the product of the GCF and another sum.
First of all, we will find the greatest common factor of 18 and 24.
Factors of 18: 1, 2, 3, 6, 9, 18.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
We can see that greatest common factor of 18 and 24 is 6. Let us write our given expression as product.
Factor our 6:
Therefore, our required expression would be
.
Answer:
see explanation
Step-by-step explanation:
(a)
x² + 2x + 1 = 2x² - 2 ( subtract x² + 2x + 1 from both sides
0 = x² - 2x - 3 ← in standard form
0 = (x - 3)(x + 1) ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x - 3 = 0 ⇒ x = 3
-----------------------------------
(b)
-
=
( multiply through by 15 to clear the fractions )
5(x + 2) - 2 = 3(x - 2) ← distribute parenthesis on both sides
5x + 10 - 2 = 3x - 6
5x + 8 = 3x - 6 ( subtract 3x from both sides )
2x + 8 = - 6 ( subtract 8 from both sides )
2x = - 14 ( divide both sides by 2 )
x = - 7
--------------------------------------------
(c) Assuming lg means log then using the rules of logarithms
log
⇔ nlogx
log x = log y ⇒ x = y
Given
log(2x + 3) = 2logx
log(2x + 3) = log x² , so
x² = 2x + 3 ( subtract 2x + 3 from both sides )
x² - 2x - 3 = 0
(x - 3)(x + 1) = 0
x = 3 , x = - 1
x > 0 then x = 3
Answer: 2.14 %
Step-by-step explanation:
Given : pH measurements of a chemical solutions have
Mean : 
Standard deviation : 
Let X be the pH reading of a randomly selected customer chemical solution.
We assume pH measurements of this solution have a nearly symmetric/bell-curve distribution (i.e. normal distribution).
The z-score for the normal distribution is given by :-

For x = 6.74

For x = 6.76

The p-value =

In percent, 
Hence, the percent of pH measurements reading below 6.74 OR above 6.76 = 2.14%