Answer: There is sufficient evidence to support the claim that the bags are under-filled.
Step-by-step explanation:
Since we have given that
Sample mean = 411
Standard deviation = 20
n = 9
So, the test statistic value is given by
At 0.025 level of significance,
critical value z = -2.306
since -2.306<-1.05
so, we will reject the null hypothesis.
Yes, there is sufficient evidence to support the claim that the bags are underfilled.
Answer:
other root: x = 9
p = 7
Step-by-step explanation:
first, find p:
(8)² - (3p - 4)8 + 11p -5 = 0
64 - (24p - 32) + 11p - 5 = 0 –––––> 64 - 24p + 32 + 11p - 5 = 0
91 - 13p = 0
-13p = -91
p = 7
<u>plug in p to find the polynomial:</u>
x² - (3(7) - 4)x + 11(7) - 5 = 0
x² - (21 - 4)x + 77 - 5 = 0
x² - 17x + 72
<u>find the roots:</u>
we know that 8 is one of the roots, so one factor is (x - 8)
the other number needs to be something that equals -17 when added with -8 and 72 when multiplied by -8
that number is -9
so the poly nomial factors to be: (x-8)(x-9)
so the roots are x = 8 and x = 9
∠ a: x
∠ b: x
∠ c: x + 21
∠ d: x - 53
∠ a + ∠ b + ∠ c + ∠ d = 360 <em>sum of the angles of a rectangle is 360° </em>
(x) + (x) + (x + 21) + (x - 53) = 360
4x - 32 = 360
4x = 392
x = 98
∠ c: x + 21 = (98) + 21 = 119
∠ d: x - 53 = (98) - 53 = 45
Answer: ∠ a = 98°, ∠ b = 89°, ∠ c = 119°, ∠ d = 45°