I will designate the hourly rate for weekdays as x and for weekends as y. The equations are arranged as follows:
13x + 14y = $250.90
15x + 8y = $204.70
This gives us a system of equations which can be solved by multiplying the first equation by 4 and the second by -7. This leads to:
52x + 56y = $1003.60
-105x - 56y = -$1432.90
By summing these two equations, we arrive at:
-53x = -$429.30 --> 53x = $429.30 --> (dividing both sides by 53) x = 8.10. This represents her hourly wage on weekdays.
Substituting our value for x allows us to determine y. I will utilize the first equation, but either could work.
$105.30 + 14y = $250.90. To isolate y, subtract $105.30 from both sides --> 14y = $145.60 divide by 14 --> y = $10.40
Thus, we find that her earnings are $8.10 per hour on weekdays and $10.40 per hour on weekends. The difference shows she earns $2.30 more on weekends than on weekdays.
Answer:
Step-by-step explanation:
Player A has a red marble and a blue marble, while Player B also has a red marble and a blue marble.
Therefore, the probability of selecting one marble is equal, at 0.5.
Due to the independence of A and B's choices, the joint event is calculated by multiplying the probabilities.
Let A represent the amount that player A wins.
If both players select one marble, the sample space can be considered as
(R,R) (R,B) (B,R) (B,B)
Probability 0.25 0.25 0.25 0.25
A's winnings 3 -2 -2 1
E(A) 0.75 -0.5 -0.5 0.25 = 0
Thus, the game is even, offering equal expected values for both A and B.
It does not influence the outcome whether you are A or B.
8 = 4N - 2.8. Add 2.8, leading to 10.8 = 4N. Divide 4, giving the population of Nevada as 2.7 million.
Given:
In triangle GHJ, the angles measure ∠G = 110°, ∠J = 40°, and ∠H = 30°.
To find:
The response to finish the provided statements.
Solution:
Based on the relationship between angles and sides in a triangle, the largest angle corresponds to the longest opposite side while the smallest angle corresponds to the shortest side.
We know that ∠G = 110°, ∠J = 40°, and ∠H = 30°.
Here, it is clear that ∠G is greater than both ∠J and ∠H, confirming that it is the largest angle.
Since angle G is the largest, side JH is the longest.
Clearly,
110° > 40° > 30°.
Thus, ∠G > ∠J > ∠H
Following the triangle's side and angle relationship leads to the conclusion:
JH > GH > GJ
The arrangement of side lengths from the longest to the shortest is JH, GH, and GJ.
Total weight = 50 lb
x = count of 3-lb weights
y = count of 10-lb weights
weight from 3-lb weights = 3x
weight from 10-lb weights = 10y
overall weight = 3x + 10y
equation
3x + 10y = 50
