Answer:
Solution given:
Increase percentage=
%
=4%
<u>the percentage </u><u>increase</u><u> </u><u>is</u><u> </u><u>4</u><u>%</u><u>.</u>
1 gallon = 16 cups. so 16x3.5=56. so 56 cups
Answer: z(e) = 2.07
Step-by-step explanation:
1.-The problem is about a test of proportions. As research company claims than no more 55 % of Americans regularly watch Fox News
The null hypothesis is H₀ P₀ ≤ 0.55 from 55%
And the alternative hypothesis is Hₐ Pₐ > .55
Is one tail test
2.-We have to specify significance level we assume our test will be for a significance level α = 5% or α = 0,05
3.-Calculation of z (c) = ?? and z (e) = '??
For z (c) we find in z table the value of z(c) = 1.64
For z (e) = ( P -P₀)/√p₀q₀/n z(e) = 0.05 / √(0.55*0,45)/425 z(e) = 0,05/ 0.02413 z(e) = 2.07
z(e) > z(c) threfore z(e) is in the rejection zone . We reject null hyothesis
Answer:
V=25088π vu
Step-by-step explanation:
Because the curves are a function of "y" it is decided to take the axis of rotation as y
, according to the graph 1 the cutoff points of f(y)₁ and f(y)₂ are ±2
f(y)₁ = 7y²-28; f(y)₂=28-7y²
y=0; x=28-0 ⇒ x=28
x=0; 0 = 7y²-28 ⇒ 7y²=28 ⇒ y²= 28/7 =4 ⇒ y=√4 =±2
Knowing that the volume of a solid of revolution V=πR²h, where R²=(r₁-r₂) and h=dy then:
dV=π(7y²-28-(28-7y²))²dy ⇒dV=π(7y²-28-28+7y²)²dy = 4π(7y²-28)²dy
dV=4π(49y⁴-392y²+784)dy integrating on both sides
∫dV=4π∫(49y⁴-392y²+784)dy ⇒ solving ∫(49y⁴-392y²+784)dy
49∫y⁴dy-392∫y²dy+784∫dy =
V=4π(
) evaluated -2≤y≤2, or 2(0≤y≤2), also
⇒ V=25088π vu