Answer: (x+4) (x-3) (x+3)
Solving Steps:
According to the statement,
(5/6)a - (1/3)a = 13
(5 - 2) a / 6 = 13
a = 26 gallons
<span>The roots of a quadratic equation ax²+bx+c=0 can be determined by calculating the discriminant Δ=b²-4ac.
If Δ>0, there are two distinct real solutions.
If Δ=0, there is one real solution.
If Δ<0, there are no real solutions and two complex solutions.
Δ>0, so there are two distinct real solutions. The answer is A.
</span>
14 + [(2*12) /3]
= 14 + [24 /3]
= 14 + 8
= 22
Answer:
The calculated χ² = <u> 0.842 </u> does not fall in the critical region χ² ≥ 5.99 so we accept the null hypothesis that all the proportions are equal and there is not enough evidence to doubt the supermarket's claim.
<u />
Step-by-step explanation:
1) We set up our null and alternative hypothesis as
H0: p1= 5/18, p2= 4/18, p3= 9/18
against the claim
Ha: p1≠ 5, p2≠ 4, p3≠ 9
2) the significance level alpha is set at 0.05
3) the test statistic under H0 is
χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency
which has an approximate chi square distribution with 2 d.f
4) Computations:
Observed Expected χ²= ∑ (O - E)²/ E
5 5.4 0.0296
4 5.4 0.3629
<u>9 7.2 0.45 </u>
<u>∑ 0.842 </u>
<u />
5) The critical region is χ² ≥ χ² (0.05)2 = 5.99
6) Conclusion:
The calculated χ² = <u> 0.842 </u> does not fall in the critical region χ² ≥ 5.99 so we accept the null hypothesis that all the proportions are equal and there is not enough evidence to doubt the supermarket's claim.
<u />