The total revenue that is gained from the sales of the cakes is determined by multiplying the number of cakes by the price. If we let x be the number of $1 that should be deducted from the price and y be the total revenue,
y = (25 - x)(100 + 5x)
Simplifying,
y = 2500 + 25x - 5x²
We get the value of x that will give us the maximum revenue by differentiating the equation and equating the differential to zero.
dy/dx = 0 = 25 - 10x
The value of x is 2.5.
The price of the cake should be 25 - 2.5 = 22.5.
Thus, the price of the cake that will give the maximum potential revenue is $22.5.
Possibilities of outcomes:
5, 5, 5
5, 5, 4
P(sum at least 14) = P(5,5,4) + P(5,5,5)
= 1/4 x 1/4 x 3/20 + 1/4 x 1/4 x 1/4
1/40
Answer:
Diameter of pound = 10 yd
Step-by-step explanation:
Given area of circular pond = 78.5 square yd
To find the diameter of the pond.
Solution:
The pond being circular in shape, the area of pond can be given as:
⇒ 
where 
represents radius of the pond.
Thus, we have:
⇒ 
Using 
⇒ 
Solving for
Dividing both sides by 3.14
⇒ 
⇒ 
Taking square root both sides.
⇒ 
⇒ 
So, radius = 5 yd, as distances are always positive.
Diameter = 
Thus, diameter of pound = 10 yd
Answer:
The null hypothesis is that all the different teaching methods have the same average test scores.
H0: μ1 = μ2 = μ3 = μ4 = μ5
The alternative hypothesis is that at least one of the teaching methods have a different mean.
Ha: at least one mean is different. (μ1 ≠ μi)
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For the case above, let μ represent the average test scores for the teaching methods:
The null hypothesis is that all the different teaching methods have the same average test scores.
H0: μ1 = μ2 = μ3 = μ4 = μ5
The alternative hypothesis is that at least one of the teaching methods have a different mean.
Ha: at least one mean is different. (μ1 ≠ μi)
Answer:
Option (3). 0.25(22 - d) + d = 10.75
Step-by-step explanation:
Total number of coins Giuliana has = 22
Let the number dollar coins Giuliana has = d
Number of quarters with Giuliana = (22 - d)
Value of dollar coins and quarters = $10.75
So the equation will be,
Number of dollars coins × $1 + Number of quarters × $0.25 = $10.75
d + 0.25 × (22 - d) = 10.75
Therefore, to determine the number of dollars with Giuliana equation will be used,
d + 0.25(22 - d) = 10.75
Option (3) will be the answer.
