The formula for the volume of a sphere can be derived as follows. We will approach this through calculus, utilizing the concept of a solid of revolution; this is a three-dimensional shape formed by rotating a two-dimensional curve around a straight line (the axis of revolution) that lies within the same plane. From calculus, we know that we will generate a shape by rotating the specified circumference. Next, we isolate y and utilize certain limits for this integral.
Answer:
The standard ticket price was $12.
Step-by-step explanation:
Let’s denote
the normal ticket price, which would total
if she had purchased tickets for that amount.
However, since Holly received a $4 discount on each ticket, her cost for one ticket became
and with 23 tickets, her total cost was

amounting to $184; thus, we conclude

we will solve this equation as follows:





Therefore, the regular price amounted to $12.
Begin by creating a system of equations: let 'a' represent the amount Mary earns per student, and 'b' denote her fixed amount. The equations are 90=15a+b (subtracting the lower from the upper equation) and 62=8a+b. From these, we have 90-62=28, leading to 15a-8a=7a, and b cancels itself out. This gives us 7a=28, resulting in a=4. Substituting 'a' into 62=8a+b reveals b=30. Since Lisa earns half of Mary's base, her fixed amount is 15, but she makes twice as much per student, bringing her rate to 8 per student. Thus, we can formulate: m=4c+30 for Mary's earnings, and l=8c+15 for Lisa's. Setting c=20 results in m=110 and l=175, showing that Lisa makes more when teaching a class of 20 students. I trust this information helps.
The likelihood stands at 6 out of 120, or 1/20, equivalent to a 5% probability. You can calculate this by defining the total number of outcomes. When organizing items within a set, the factorial function on your calculator, denoted by "!", is a straightforward way to arrive at a solution. This function indicates the product of all integers less than that number down to 1 multiplied together. Therefore, since there are 5 letters in the word poker, we utilize 5! which can be expanded to 1*2*3*4*5 = 120. Next, we must identify how many combinations begin with k and conclude with p. There are precisely 6 such configurations: koerp, korep, kreop, kroep, kerop, and keorp. Finally, we divide the number of favorable outcomes by the total possibilities.
Let x = time in weeks.
Let y = length of Rip van Winkle's beard, measured in mm
At the beginning, his beard was 888 mm long, thus
when x = 0, y = 888.
Each week, y increases by 222 mm.
Hence
y = 222x + 888
This represents a linear equation with
slope = 222,
y-intercept = 888
At x = 1, y = 222 + 888 = 1110 mm
To plot the straight line, select two points:
(0, 888) from the y-intercept
(1, 1110)
The straight line graph is illustrated below. The two points are depicted on the line.