Answer:
The detailed work and solution can be found in the attachment
Step-by-step explanation:
To determine how many 3/64 gallon servings can be filled from a total of 2/3 gallon of punch, perform the division of 2/3 by 3/64. The outcome is not a whole number, but this method illustrates the solution. Vinny's total is 2/3 of a gallon of punch, with each guest receiving a measure of 3/64 gallon, which tells us how many can be accommodated by performing<span> (2/3) / (3/64).</span>
To find out the number of days, we should create equations based on the values provided. The total distance Kayla aims to travel combines both her running distance and her biking distance.
200 miles = (6 miles/day)x + (10 miles/day)y
where x signifies the days she spent running and y represents the days bike riding.
If the minimum biking days are set to be 15, indicated by y = 15, we have:
200 miles = (6 miles/day)x + (10 miles/day)(15 days)
Solving for x gives:
200 = 6x + 150
50 = 6x
x = 8.3333 days
Total days = 15 days biking + 8.3333 days running = 23.3333 days, approximately making it 24 days.
Each LED bulb, along with installation labor, is priced at
.. $6.95 +$3 = $9.95
For 100 bulbs over a span of 10 years, that equals (100*10) = 1000 bulb·years. At $9.95 per bulb, 5 bulb·years are obtained, and thus the projected total cost for 1000 bulb·years is
.. (1000 b·y)*($9.95/(5 b·y)) = $1990
In summary, for a decade, the installation and changes of 200 bulbs in 100 lamps amount to $1990. Therefore, the yearly cost is...
.. $1990/(10 yr) = $199/yr
Answer:
Option C is the right choice.
Step-by-step explanation:
The given coordinates define a rectangle, and our objective is to show that the diagonals JL and KM are congruent.
We know that rectangles possess four right angles.
To prove the congruence of the diagonals JL and KM, we will utilize the Pythagorean theorem.
In triangle KLM, KL has a length of b units while LM has a length of a units. By applying the Pythagorean theorem 
In triangle JML, JM is b units long, and LM remains a units long. We again can apply the Pythagorean theorem 
Thus, we find that 
and option C is the correct choice.
