Answer:
160
Step-by-step explanation:
Using Exterior angle theorem
30+130=160
Answer:
Initial amount = 12
Rate of growth = 5%
value of the function when t t = 5 is 15.3
Step-by-step explanation:
The standard exponential growth equation is expressed as;
y = A(1+r)^t
A is the initial amount
r is the rate of growth
t is the time
Given the expression y = 12(1.05)^t
On comparing with the general formula;
A = 12
Hence the initial amount is 12
Also;
1 + r = 1.05
r = 1.05 -1
r = 0.05
r = 0.05 * 100
r = 5%
The rate of growth is 5%
To evaluate the function when t = 5, we will substitute t = 5 into the given function as shown;
Recall that y = A(1+r)^t
y = 12(1.05)^5
y = 12(1.2763)
y = 15.3 (to the nearest tenth)
Answer:
<em><u>Note: I'm not sure all of this is correct</u></em> O_o
Part A
- Male IQR = Q₃ - Q₁ ≈ 15 - 5 ≈ 10
- Female IQR = Q₃ - Q₁ ≈ 9 - 2 ≈ 7
Part B
- Male Median = Q₂ ≈ 9 to 10
- Female Median = Q₂ ≈ 6 to 7
Difference ≈ 10 - 7 or 10 - 6 ≈ 3 to 4
Part C
<em>Male data distribution</em>
- <u>Shape</u>: The distribution is skewed right.
- <u>Outliers</u>: There doesn't appear to be any clear outliers on the box-plot.
- <u>Center</u>: Because the data is skewed, use median because it's a resistant measure of center. The median appears to be around 9 to 10.
- <u>Spread</u>: Because the data is skewed, use IQR because it's a resistant measure of spread. The IQR is calculated by subtracting the third quartile from the first quartile and appears to be around 10.
<em>Female data distribution</em>
- <u>Shape</u>: The distribution is slightly skewed right, but appears to have more normality than the male distribution
- <u>Outliers</u>: There appears to be one significant outliers at around 30 to 35 that is greatly larger than the rest of the data and is represented as a dot outside the box plot.
- <u>Center</u>: Because the data is skewed, use median because it's a resistant measure of center. The median appears to be around 6 to 7.
- <u>Spread</u>: Because the data is skewed, use IQR because it's a resistant measure of spread. The IQR is calculated by subtracting the third quartile from the first quartile and appears to be around 7.
Median would be a better measure of center for each because both data distributions aren't as symmetric/normal and have a skewed shape. Therefore, the median should be used because of its resistance, as it's not as impacted by extreme values as the mean.
Part D
There doesn't appear to be an outlier in the male dataset, but there appears to be a significantly large outlier in the female dataset, which might mean that there is a significantly large number of females(around 30 to 40) attending the latest superhero movie during a specific day of the study month. This might be due to a discount to the movie ticket that day for females, which attracts large number of females to watch the movie.
Step-by-step explanation:
<u>Substitute x = -3, y = -3 into the </u><u>g</u><u>i</u><u>v</u><u>e</u><u>n</u><u> </u><u>equation:</u>
<u>Simplify and Solve:</u>
The point (-3, -3) doesn't satisfy the given equation.
The expression can be written in simplified form as:
x+2 occurs in both numerator and denominator. This means there is a hole at x=-2, this can also be seen from the graph.
So, the vertical asymtptote will occur at the point where:
x+5=0
⇒
x = -5
So, option A gives the correct equation of the vertical asymptote of the function