n = {2, 5, 0} holds true for 2n - 3 < 9
<em><u>Solution:</u></em>
Replacement set is the set of values that may be substituted for the variable.
Plug in each value from the replacement set and evaluate both sides of the inequality
If the inequality is true for a certain value, that value belongs in the solution set.
<em><u>Given equation is:</u></em>
2n - 3 < 9
<em><u>Substitute n = 2</u></em>
2(2) - 3 < 9
4 - 3 < 9
1 < 9
1 is less than 9 is true
Thus n = 2 is a solution to equation
<em><u>Substitute n = 5</u></em>
2(5) - 3 < 9
10 - 3 < 9
7 < 9
7 is less than 9 is true
Thus n = 5 is a solution to equation
<em><u>Substitute n = 0</u></em>
2(0) - 3 < 9
0 - 3 < 9
-3 < 9
-3 is less than 9 is true
Thus n = -3 is a solution to equation
Answer:
<u>Algebraically</u>
0.5x-7= √(-5x+29)
(0.5x-7)² = -5x+29
(0.5x)² - 2*0.5x*7 + 7² = -5x+29
0.25x² - 7x + 49 + 5x - 29 = 0
0.25x² - 2x + 20 = 0
Its discriminant is:
b² - 4*a*c
(-2)² - 4*0.25*20
-16 < 0
Therefore, the equation has no solutions.
<u>Graphically</u>
In the picture attached, the plots of the functions are shown. We can see that they don't intersect each other, and that is why there is no solution.
Answer:
272 cups
Step-by-step explanation:
so you need 34 cups for one batch if you need to make 8 batches then you would need to multiple them to find the answer.
34*8=272
Answer:
r = 6
Step-by-step explanation:
Given that p varies directly as r, then the equation relating them is
p = kr ← k is the constant of variation
To find k use the condition p = 4, r = 2
k = 
= 
= 2
p = 2r ← equation of variation
When p = 12
12 = 2r ( divide both sides by 2 )
hence r = 6
Answer - 1/6
EXPLANATION
For a six sides dice:
Possible numbers are: 1, 2, 3, 4, 5, and 6
Total of 6 possible numbers
Possible even number outcomes are: 2, 4, and 6
Total of 3 outcomes out of 6 possibilities
Probability that the roll is a even number, p(A) = 3/6
p(A) = 3/6 = 1/2
<span>Possible outcomes greater than 4 are: 5 and 6
Total of 2 outcomes out of 6 possibilities
</span>Probability that the roll is a number greater than 4, p(B) = 2/6
p(B) = 2/6 = 1/3
The probability that the first roll is a even number and the second roll is a number greater than 4 = p(A and B)
p(A and B) = p(A) x p(B)
p(A) = 1/2
p(B) = 1/3
p(A and B) = p(A) x p(B)
= 1/2 * 1/3
= 1/6
