Answer:
Answer 1; Angles forming a linear sum to 180°
Answer 2; Substitution
Answer 3; Definition of perpendicular lines
Step-by-step explanation:
The two column proof is presented as follows;
Statement 
Reason
1. ∠SWT ≅ ∠TWU Given
2. m∠SWT + m∠TWU = 180° Angles forming a linear sum to 180°
3. m∠SWT + m∠SWT = 180° Substitution
4. m∠SWT = 90° Algebra
5. 
⊥ 
Definition of perpendicular lines
Perpendicular lines are defined as lines that are at right angles (90°) to each other, therefore given that the angle formed by the lines and m∠SWT = 90°, therefore, the lines and are perpendicular to each other.
Answer:
1. 50%
2. 3%
3. 20%
4. 200%
Step-by-step explanation:
Here, we want to find the worth of each coin as a percentage of $1
We simply divide the worth by $1 and multiply by 100%
$1 is same as 100 cents
Thus;
1. 50 cent
= 50/100 * 100% = 50%
2. 3 cents
= 3/100 * 100% = 3%
3. 20 cents
= 20/100 * 100% = 20%
4. $2
= 2/1 * 100% = 200%
Because a beach volleyball is a sphere, so the volume formula is V= 4pi r^3/r
so the answer would be <span>24,429.024 </span>
Answer:
Hence, (75,40) is the maximum point and maximum profit is $192.5
Step-by-step explanation:
Let the breakfast be x
And let the lunch or afternoon be y
Inequalities will become
And objective function will be
Z=1.5x+2.0y
You can see the graph in the attachement
ABCD is the feasible region
Points of feasible region is (0,90) ,(0,0) ,(75,40) and(105,0)
We have to find Z by substituting the points of feasible region
At (0,90) we get
Z=1.5(0)+2(90)
Z=180
At (0,0)
Z=1.5(0)+2(0)
Z=0
At (75,40)
Z=1.5(75)+2(40)
Z=192.5
At (105,0)
Z=1.5(105)+2(0)
Z=157.5
The maximum number we are getting is 192.5 which is at (75,40)
Hence, (75,40) is the point of maximum
Answer:
$14.39
Step-by-step explanation:
The formula for continuous compounding of interest is:
A = Pe^(rt), were P is the initial dollar amount, A is the final amount, r is the interest rate as a decimal fraction, and t is the time in years.
Here we have $2109 = $500e^(10r) and need to solve for r.
To do this, take the natural log of both sides, obtaining:
ln 2109 = ln 500+ 10r.
Then 10r = ln 2109 - ln 500, and
ln 2109 - ln 500
r = --------------------------------------------
10
= .1439
The interest rate was 14.39%.
