Answer: 15%
Step-by-step explanation:
% change = change/ actual value x 100
Change = 11 .50 - 10 = 1.5
Therefore % change = 1.5/10 x 100
= 15%
Answer:
Note: The full question is attached as picture below
a) Hо : p = 0.71
Ha : p ≠ 0.71
<em>p </em>= x / n
<em>p </em>= 91/110
<em>p </em>= 0.83.
1 - Pо = 1 - 0.71 = 0.29.
b) Test statistic = z
= <em>p </em>- Pо / [√Pо * (1 - Pо ) / n]
= 0.83 - 0.71 / [√(0.71 * 0.29) / 110]
= 0.12 / 0.043265
= 2.77360453
Test statistic = 2.77
c) P-value
P(z > 2.77) = 2 * [1 - P(z < 2.77)] = 2 * 0.0028
P-value = 0.0056
∝ = 0.01
P-value < ∝
Reject the null hypothesis. There is sufficient evidence to support the researchers claim at the 1% significance level.
The answer would be y=x-4
Answer:
Price = $4.50
Maximum revenue = $2,430
Step-by-step explanation:
The concession stand sells 600 bags of peanut at $4.00 (600, $4.00).
If there is a $1 increase in price, the number of bags old will decrease by 120, which mens that 480 bags of peanuts will be sold at $5.00 (480, $5.00).
Tracing a linear relationship between price and quantity sold with the two given points:
![m = \frac{5-4}{480-600}\\ m=-\frac{1}{120}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B5-4%7D%7B480-600%7D%5C%5C%20m%3D-%5Cfrac%7B1%7D%7B120%7D)
![P - P_0=m*(Q-Q_0)\\P-4.00=-\frac{1}{120} (Q-600)\\P= -\frac{1}{120}Q +9](https://tex.z-dn.net/?f=P%20-%20P_0%3Dm%2A%28Q-Q_0%29%5C%5CP-4.00%3D-%5Cfrac%7B1%7D%7B120%7D%20%28Q-600%29%5C%5CP%3D%20-%5Cfrac%7B1%7D%7B120%7DQ%20%2B9)
The revenue function is given by the price multiplied by the quantity sold:
![R=Q*P= (-\frac{1}{120}Q +9)*Q\\R=-\frac{1}{120}Q^2 +9Q](https://tex.z-dn.net/?f=R%3DQ%2AP%3D%20%28-%5Cfrac%7B1%7D%7B120%7DQ%20%2B9%29%2AQ%5C%5CR%3D-%5Cfrac%7B1%7D%7B120%7DQ%5E2%20%2B9Q)
The value of 'Q' for which the derivate of the revenue function is zero, is the output level for which revenue is maximum:
![R'=0=-\frac{2}{120}Q+9\\Q_{max} = 540\\P_{max} = -\frac{540}{120} +9\\P_{max} =\$4.50](https://tex.z-dn.net/?f=R%27%3D0%3D-%5Cfrac%7B2%7D%7B120%7DQ%2B9%5C%5CQ_%7Bmax%7D%20%3D%20540%5C%5CP_%7Bmax%7D%20%3D%20-%5Cfrac%7B540%7D%7B120%7D%20%2B9%5C%5CP_%7Bmax%7D%20%3D%5C%244.50)
The total revenue of 540 units at $4.50 per unit is:
![R = \$4.50*540\\R=\$2,430](https://tex.z-dn.net/?f=R%20%3D%20%5C%244.50%2A540%5C%5CR%3D%5C%242%2C430)
Answer:
2.3
Step-by-step explanation:
.5 - .3 = .2
.8 - .5 = .3
1.2 - .8 = .4
1.7 - 1.2 = .5
We should add .6 next
1.7+.6 = 2.3