Answer:
Step-by-step explanation:
It can be solved analytically or graphically. Graphically is the fastest way if you know how to handle the two lines. Let's rearrange terms in either case:
<u>Graphic:</u> Red line is 
, solid blue line is 
, the thin extension is the parent line without the absolute value.
Solving the equation is equivalent to answer "when is the blue line higher than the red one?" Which obviously happens outside the two intercept points. Let's find the first coordinate of both - we don't really care what's the y coordinate of either point.
For the left point, the x coordinate is given by 
For the right point, we have
<u>Analytical:</u>
We split the problem in two parts: while the content absolute value is non negative, we have
Which admits as solutions all valeus of x greater than 1 (since both have to be satisfied at once, and values between 1/2 and 1 will not work for the second.
OR, with a negative quantity inside the absolute value, we get
which again is satisfied by all values of x less than -1.
Thus the solution is given by
A = 121, Vertical Angles Theorem
B = 59, Supplementary Angles Theorem
C = 59, Vertical Angles Theorem
D = 55, Alternate Interior Angles Theorem
E = 4, sum of all angles in a triangle is 180
F = 73, sum of all angles in a triangle is 180
G = 73, Alternate Interior Angles Theorem
H = 48, Alternate Interior Angles Theorem
I = 4, Alternate Interior Angles Theorem
Answer:
81 times the original size
Step-by-step explanation:
AA0ktA=3A0=?=?=25hours=A0ekt
Substitute the values in the formula.
3A0=A0ek⋅25
Solve for k. Divide each side by A0.
3A0A0=e25k
Take the natural log of each side.
ln3=lne25k
Use the power property.
ln3=25klne
Simplify.
ln3=25k
Divide each side by 25.
ln325=k
Approximate the answer.
k≈0.044
We use this rate of growth to predict the number of bacteria there will be in 100 hours.
AA0ktA=3A0=?=ln325=100hours=A0ekt
Substitute in the values.
A=A0eln325⋅100
Evaluate.
A=81A0
At this rate of growth, we can expect the population to be 81 times as large as the original population.
Answer:
The 95% confidence interval is 
Step-by-step explanation:
From the question we are told that
The sample mean difference is 
The standard error is SE = 0.03
Given that the confidence interval is 95% then the level of significance is mathematically evaluated as
Next we obtain the critical value of 
from the normal distribution table, the value is 
Generally the margin of error is mathematically represented as
substituting values
The 95% confidence interval is mathematically represented as
substituting values
Answer:
the percentage is 12%
Step-by-step explanation:
Given that
The 12 students picked up the vanilla cupcake
And, 88 students picked up the chocolate cupcake
We need to find out the percentage of the students picked up a vanilla cupcake
So, the percenatge is
= (12) ÷ (12 + 88) × 100
= 12 ÷ 100 × 100
= 12%
Hence, the percentage is 12%
