Answer:
We accept the null hypothesis and reject the alternate hypothesis. There is no evidence to conclude that the population mean is greater than 29. The population mean is less than or equal to 29.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 29
Sample mean, 
= 30
Sample size, n = 47
Alpha, α = 0.05
Population standard deviation, σ = 5
First, we design the null and the alternate hypothesis
a) This is a one-tailed test because the alternate hypothesis is in greater than direction.
We use One-tailed z test to perform this hypothesis.
b) 
, we reject the null hypothesis and accept the alternate hypothesis and if 
, we accept the null hypothesis and reject the alternate hypothesis.
c) Formula:
Putting all the values, we have
d) Now, 
Since,
We accept the null hypothesis and reject the alternate hypothesis. There is no evidence to conclude that the population mean is greater than 29. The population mean is less than or equal to 29.
e) P-value is 0.0853
On the basis of p value we again accept the null hypothesis.
Answer:
Explanation below.
Step-by-step explanation:
1. a. 
b. 
c. x=144
2. a. 
b. x= 14
3.
4.
1. The growth rate equation has a general form of:
y = A (r)^t
The function is growth when r≥1, and it is a decay when
r<1. Therefore:
y=200(0.5)^2t -->
Decay
y=1/2(2.5)^t/6 -->
Growth
y=(0.65)^t/4 -->
Decay
2. We rewrite the given equation (1/3)^d−5 = 81
Take the log of both sides:
(d – 5) log(1/3) = log 81
d – 5 = log 81 / log(1/3)
d – 5 = - 4
Multiply both sides by negative 1:
- d + 5 = 4
So the answer is D
To graph a situation that would involve a linear graph, first determine your x and y axes.
The x-axis will be the independent variable, one that does not change based on other variables. An example is time.
The y-axis, the dependent variable, depends on the independent variable.
The model equation for a linear line is y = mx + b.
"m" is the slope, and the "b" is the y-intercept (where the graph crosses the x-axis at x=0).
For example, a situtation could be that Joe starts with $10 in his account and adds $5 every day to his account.
The x-axis is time in days.
The y-axis is amount of money in his account.
The slope, or rate of change is 5.
The y-intercept, the amount of money he has at x=0 (0 days) is $10.
The equation would be y = 5x + 10
To draw this, plot the y-intercept at (0, 10), and the next point would be 5 units up and one unit to the right because the slope is 5, or 5/1 (remember slope is rise over run: "rise" up 5 and "over" to the right 1).
The correct answer is A. 1.5 cups
Explanation:
The total of polishing wooden furniture is equivalent to the total of olive oil plus the total of lemon juice. Additionally, in this case, the result should be given in cups. First, let's consider the values given.
50% of a cup of lemon juice + 25% of a quart with olive oil
The first quantity 50% of a cup of lemon indicates half cup of lemon was added, which is equivalent to 0.5 cups as 1 cup = 100% of a cup and 50% is the half.
Now, the second quantity is provided in quarts, which is not the same as a cup. Indeed 1 quart is equivalent to 4 cups, which represents 100%. This means 100% = 4 cups. Now, to calculate the 25% follow this procedure.
1. Write the values
4 = 100 (total percentage)
x = 25 (percentage to be calculated
2. Solve this by using cross multiplication
x100 = 4 × 25
x100 = 100
x = 100 ÷ 100
x = 1 (cups in 25%)
This means 1 cup of olive oil was added and this plus 0.5 cup of lemon juice is equivalent to 1.5 cups of solution.
