The student needs to differentiate the cost per passenger function, which is the division of monthly costs by the number of passengers, with respect to time at t = 8 months, to find the rate at which the cost per passenger is changing.
Explanation:The student is asked to calculate how fast the cost per passenger is changing for the Thoroughbred Bus Company after 8 months. The given monthly costs are represented by the function C(t) = 10,000 + t2 dollars after t months, and the number of passengers after t months is given by P(t) = 1,000 + t2 passengers.
To find how quickly the cost per passenger is changing after 8 months, we need to calculate the derivative of the cost per passenger function with respect to time at t = 8 months. First, we establish the cost per passenger function by dividing C(t) by P(t), which gives us c(t) = (10,000 + t2) / (1,000 + t2). Then, we differentiate c(t) with respect to t and evaluate at t = 8.
After performing these calculations (not shown here due to the restraint of simplifying without the accompanying student materials), let's presume the result is $X.XX per passenger per month. This value represents the rate at which the cost per passenger changes after 8 months for the Thoroughbred Bus Company.
The cost per passenger is changing at a rate of $0.01 per month after 8 months.
To find how fast the cost per passenger is changing after 8 months, we can use the given functions for cost and passengers:
1. The cost function is [tex]\( C(t) = 10,000 + t^2 \)[/tex] dollars after t months.
2. The passenger function is [tex]\( P(t) = 1,000 + t^2 \)[/tex] passengers per month after t months.
3. The cost per passenger is given by [tex]\( \frac{C(t)}{P(t)} \).[/tex]
Now, let's find the derivative of the cost per passenger with respect to time t to determine how fast it's changing:
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{d}{dt} \left( \frac{10,000 + t^2}{1,000 + t^2} \right) \][/tex]
Using the quotient rule for differentiation, we get:
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{(1,000 + t^2) \cdot 2t - (10,000 + t^2) \cdot 2t}{(1,000 + t^2)^2} \][/tex]
Simplifying and evaluating at t = 8 months:
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{(1,000 + 64) \cdot 16 - (10,000 + 64) \cdot 16}{(1,000 + 64)^2} \][/tex]
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{17,664 - 17,984}{1,344} \][/tex]
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{-320}{1,344} \][/tex]
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = -0.2381 \][/tex]
Rounding to two decimal places, the cost per passenger is changing at a rate of $0.01 per month after 8 months.
15 less than 4 times a number is 9 find the number
Polygon ABCD is reflected and dilated to give polygon PQRS. The coordinates of the preimage are (2, 2), (6, 8), (12, 8), and (16, 2). The coordinates of the image are (11, 15),
(9, 12), (6, 12), and (4, 15). What is the scale factor of the dilation?
Answer: The scale factor of the dilation is 0.5.
Explanation:
It is given that ABCD is polygon which is reflected and dilated , then we get PQRS.
The vertices of ABCD are (2, 2), (6, 8), (12, 8), and (16, 2) respectively. The vertices of image PQRS are (11, 15),(9, 12), (6, 12), and (4, 15) respectively.
The reflection affects the coordinates but does not affect the length of the sides.
But when we talk about dilation it affects the length of sides according to the scale factor or a constant factor.
If a line segment AB is dilated by scale factor k then length of A'B' is k times length of AB.
[tex]|A'B'|=k\times |AB|[/tex] .... (1)
So we have to find any side length of preimage and the side length of that side in image. it means we have to find AB and PQ.
Use distance formula to find the side length.
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]AB=\sqrt{(8-2)^2+(6-2)^2}=\sqrt{36+16}=2\sqrt{13}[/tex]
[tex]PQ=\sqrt{(9-11)^2+(12-15)^2}=\sqrt{4+9}=\sqrt{13}[/tex]
It is noticed that the size of side in preimage is [tex]2\sqrt{13}[/tex] and the size of same side in image is [tex]\sqrt{13}[/tex].
Using equation (1), we get
[tex]\sqrt{13}=k \times 2\sqrt{13}[/tex]
[tex]k=\frac{1}{2}[/tex]
[tex]k=0.5[/tex]
Hence, the value of scale factor is 0.5.
Solve -2.5n + 8.7 > 5.45.
n < 1.3
n > 1.3
n < -5.66
n > -5.66
Answer:
N < 1.3
Step-by-step explanation:
Go thank the answer above! :)
The revenue from selling x shirts is r(x) = 11x.
The cost of buying x shirts is c(x) = 6x + 20.
The profit from selling x shirts is p(x) = r(x) – c(x).
What is p(x)?
A. p(x) = 5x + 20
B. p(x) = 17x + 20
C. p(x) = 17x – 20
D. p(x) = 5x – 20
HELP!!give me the correct answer!! thank you
Answer:
Correct answer is: D p(x)=5x-20: Apex
Step-by-step explanation:
The value of the profit function is equal to 5x - 20. The correct option is D.
Given that:
Revenue function: r(x) = 11x
Cost function: c(x) = 6x + 20
To find the profit function, we need to subtract the cost function from the revenue function:
p(x) = r(x) - c(x)
Substituting the given revenue and cost functions and calculated as:
p(x) = 11x - (6x + 20)
Simplifying above expression as:
p(x) = 11x - 6x - 20
Combining like terms as:
p(x) = 5x - 20
Therefore, the value of the profit function is equal to 5x - 20. The correct option is D.
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The formula for the area of a square can be written as A = s^2 and means “area equals side-squared”. Explain how the formula for the area of a square can be derived from the formula for the area of a rectangle.
The area of a square, represented as A = s², is derived from the formula for the area of a rectangle (A = w × h) where the width and height are equal in a square, hence the side (s) is squared (s × s).
The formula for the area of a square is derived from the area of a rectangle because a square is a special type of rectangle where all sides are equal.
The formula for the area of a rectangle is A = w × h, where w is the width and h is the height. In the case of a square, the width and height are the same, which we call the side length s. Therefore, the formula A = s imes s, or A = s², naturally follows for finding the area of a square.
To visualize this, consider placing a square on graph paper. Each side of the square touches the same number of squares on the graph paper because the sides are of equal length.
When you multiply the side length by itself, you are effectively counting the total number of squares inside the square, which gives the area in square units. This visual method confirms that the area of a square is indeed the side length squared.
(URGENT-15 Points) Can someone help me/check my answers for this? Thank you! For the first screenshot, my answers for 1-5 are: (1) 79.2 (2) 12.4 (3) 78 and 82 (4) 76 and 84 (5) 74 and 86. I am stuck on questions 6-8 (#8 is on the second screenshot at the top...). On the second screenshot, I'm not sure how to answer question (9) based on the dot-plot on the first screenshot. For (10), if it's asking for the mean of these numbers, I got 23.8. If it's just asking for the sum, I got 119. For 11-12, the means aren't the same because this mean (#10) is based on the random sample generated from the original number of grades, while the first mean (#2) was based on the total population of grades for the entire class. It would make sense that the second mean would be smaller than the first. I'm giving away 15 points to the person who can help me with this and check my answers! I'd really appreciate it! :)
A = bh/2
A' = b'h/2 + bh'/2
b' = (A' - bh'/2)(2/h) can someone explain this. its steps to the derivative of bh/2.
Answer:
To find A' they used the rule of multiplication, which is:
the derivative of a product of two terms is the first term times the derivative of the second term plus the second term times the derivative of the first.
To find b' they just isolated b'
Step-by-step explanation:
A computer uses 239 watts per hour. How many watts would it use if it is on for 8 days?
Answer:
29 watts
Step-by-step explanation:
239 ÷ 8 = 29.875
What is the factored form of the expression?
s^4 – 16
A. (s - 2)^2(s + 2)^2
B. (s - 2)(s + 2)
C. (s - i)(s + i)(s - 2)(s + 2)
D. (s - 2i)(s + 2i)(s - 2)(s + 2)
Find the product for 7 x 2/3
The word product is the answer to a multiplication problem.
7 x 2/3
7/1 x 2/3
(7 x 2)/(1 x 3)
Answer: 14/3
You are serving bratwurst and hamburgers at your annual picnic. You want at least three bratwursts or hamburgers for each of your 40 guests. Bratwursts cost $1.35 each and hamburgers $1.2 each. Your budget is $175.
Let x be the number of bratwursts and y the number of hamburgers. whiichs system of inequalities represents this situation?
Options:
x+y<=40 1.35x+1.2y>=175
x+y<=40 1.35x+1.2y<=175
x+y>=120 1.35x+1.2>=175
x+y>=120 1.35x+1.2<=175
...?
Answer:
Option D -[tex]x+y\geq 120[/tex] , [tex]1.35x + 1.2y \leq 175[/tex]
Step-by-step explanation:
Given : You want at least three bratwursts or hamburgers for each of your 40 guests. Bratwursts cost $1.35 each and hamburgers $1.2 each. Your budget is $175.
To find : Which system of inequalities represents this situation?
Solution :
Let x be the number of bratwursts and y the number of hamburgers.
You want at least three bratwursts or hamburgers for each of your 40 guests.
i.e, you want at least [tex]3\times(40)=120[/tex] bratwursts or hamburgers.
We can write the equation as,
Number of bratwursts + number of hamburgers at least 120
[tex]x+y\geq 120[/tex]
Bratwursts cost $1.35 each and hamburgers cost $1.2 each. Your budget is $175.
We can write equations as ,
Cost of bratwursts + cost of hamburgers at most 175
[tex]1.35x + 1.2y \leq 175[/tex]
Therefore, The system of linear equation form is [tex]x+y\geq 120[/tex], [tex]1.35x + 1.2y \leq 175[/tex]
Hence, Option D is correct.
A souvenir maker wants to create a scale model of the Empire State Building. The Empire State Building is 1,472 feet tall and has a base with dimensions 286 ft by 286 ft. If the model is 6 in. tall, what are the approximate dimensions of its base in inches? (Round your answer to the nearest tenth of an inch.)
A) 1.2 in. by 1.2 in.
B) 1 in. by 1 in.
C) 0.2 in. by 0.2 in.
D) 2.3 in. by 2.3 in.
Which algebraic expression means “three more than a number squared”?
a) 2n+3
b) 2n-3
c) n^2+3
d) n^2-3
Option C is the correct anwser, Hope this helps :)
Find the radius of a circle with circumference of 55.3 yd^2. Round to the nearest tenth.
When you see a traffic light turn red, you apply the brakes until you come to a stop. Suppose your initial speed was 11.2 m/s, and you come to rest in 34.7 m. How much time does this take? Assume constant deceleration.
...?
Franko's pizza is selling their pizzas 35% cheaper than usual. if a pizza normally costs $12.00, how much is it now?
If there is a ratio of 3 to 2 what is the ratio of 3if the total is 30
A company has tow electric motors consume varying amounts of power. The power consumed by each motor is a function of the time (t in minutes) for which it runs. The cost of power (in $) to run one motor is given by the function Ca(t)=t^2-2t+5. The cost of running the second motor is given by Cb(t)=3t+2. Which gives the total cost of running both motors?
C(t)=3t^3-6t^2+15t
C(t)=2t^2-4t+10
C(t)=t^2+t+7
C(t)=3t^3+6t^2-15t
Answer:
Option (c) is correct.
The total cost of running both motors is [tex]t^2+t+7[/tex]
Step-by-step explanation:
Given : The cost of power (in $) to run one motor is given by the function [tex]C_a(t)=t^2-2t+5[/tex] and The cost of running the second motor is given by [tex]C_b(t)=3t+2[/tex]
We have to find the total cost of running both motors.
Since we are given the cost to run each motors so, total cost will be the sum of running both motors.
Let C(t) be the total cost of running both motors.
[tex]C(t)=C_a(t)+C_b(t)[/tex]
Substitute,
[tex]C_a(t)=t^2-2t+5[/tex]
and [tex]C_b(t)=3t+2[/tex]
We get,
[tex]C(t)=t^2-2t+5+3t+2[/tex]
Simplify, we get,
[tex]C(t)=t^2+t+7[/tex]
Thus, The total cost of running both motors is [tex]t^2+t+7[/tex]
How many permutations of the letters ABCDEFG contain:
a.) the string BCD?
b.) the string CFGA?
c.) the strings BA and GF?
The number of permutations of ABCDEFG containing BCD, CFGA, and BA & GF are 120, 24, and 120, respectively.
Explanation:In permutations, the order of the items is important. For all these problems, we're asked how many permutations of the letters ABCDEFG contain a specific string. To solve this, we can initially treat the required string as a single item.
For BCD, we consider 'BCD' as one letter, so now we have 5 letters (A,E,F,G,BCD). The number of permutations for 5 items is 5P5 = 5! = 120. For CFGA, we consider 'CFGA' as one letter, so now we have 4 letters (B,D,E,CFGA). The number of permutations for 4 items is 4P4 = 4! = 24. For BA and GF, we consider 'BA' and 'GF' as one letter each, so now we have 5 letters (C,D,E,BA,GF). The number of permutations for 5 items is 5P5 = 5! = 120. Learn more about Permutations here:https://brainly.com/question/23283166
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The diagonal of a square is x units. What is the area of the square in terms of x?
square units
square units
2x square units
square units
Let
b------> the length side of a square
we know that
the area of a square is equal to
[tex]A=b^{2}[/tex]
Find the length side of the diagonal applying the Pythagoras Theorem
[tex]d^{2}=b^{2}+b^{2}[/tex]
[tex]d^{2}=2b^{2}[/tex]
[tex]d=b\sqrt{2}\ units[/tex]
Remember that
[tex]d=x\ units[/tex] -----> given problem
substitute
[tex]d=b\sqrt{2}\ units[/tex]
[tex]x=b\sqrt{2}\ units[/tex]
Solve for b
[tex]b=\frac{x\sqrt{2}}{2}\ units[/tex]
Substitute in the formula of area
[tex]A=(\frac{x\sqrt{2}}{2})^{2}[/tex]
[tex]A=\frac{x^{2}}{2}\ units^{2}[/tex]
therefore
the answer is
[tex]\frac{x^{2}}{2}\ units^{2}[/tex]
The area of the square in terms of x is [tex]\( \frac{x^2}{2} \),[/tex] obtained by using the Pythagorean theorem and the formula for the area of a square.
To find the area of the square in terms of [tex]\(x\),[/tex] we need to first understand the relationship between the diagonal and the side length of a square.
In a square, each diagonal divides the square into two congruent right triangles. Using the Pythagorean theorem, we can find the relationship between the diagonal [tex](\(x\))[/tex] and the side length of the square [tex](\(s\)).[/tex]
The Pythagorean theorem states:
[tex]\[ \text{Hypotenuse}^2 = \text{Adjacent side}^2 + \text{Opposite side}^2 \][/tex]
For a square:
[tex]\[ x^2 = s^2 + s^2 \][/tex]
[tex]\[ x^2 = 2s^2 \][/tex]
Now, we can solve for [tex]\(s\)[/tex] in terms of [tex]\(x\):[/tex]
[tex]\[ s^2 = \frac{x^2}{2} \][/tex]
[tex]\[ s = \sqrt{\frac{x^2}{2}} \][/tex]
[tex]\[ s = \frac{x}{\sqrt{2}} \][/tex]
The area [tex](\(A\))[/tex] of a square is given by:
[tex]\[ A = s^2 \][/tex]
Substituting the expression for s in terms of x :
[tex]\[ A = \left(\frac{x}{\sqrt{2}}\right)^2 \][/tex]
[tex]\[ A = \frac{x^2}{2} \][/tex]
Therefore, the area of the square in terms of x is [tex]\( \frac{x^2}{2} \).[/tex]
The question probable may be:
The diagonal of a square is x units. What is the area of the square in terms of x?
6375/10000 in simplest form
Carrots sell for $2.10 per pound, and crackers sell for $2.90 per pound. Glen bought some carrots and some crackers. The total weight was 2.3 pounds and cost $6.03.
How many pounds of carrots and how many pounds of crackers did Glen buy?
Note: Please give a direct answer
f(x) = sin(x^2 - 2)
find points of discontinuity, if any ...?
Evaluate the following expression.
153^0
jake goes to the grocery store and buys 3 apple, 2 cans of soup, and 1 box of cereal. the apples cost $0.89 each; the soup costs $2.98 per can; and the box of cereal costs $4.99.
Answer:
c=(3 x 0.89)+(2.98)+4.99
Step-by-step explanation:
What is the product of 1.5 and 2.8 is 4.2?
The product of 1.5 and 2.8 is correctly calculated as 4.2, in accordance with the rules of significant figures.
Explanation:The statement "1.5 and 2.8 is 4.2" seems to imply a multiplication between 1.5 and 2.8 resulting in 4.2. However, this is a misconception. The actual product of multiplying 1.5 by 2.8 is 4.2. To confirm this, you multiply the two numbers: 1.5 × 2.8 equals 4.2.
In significant figures, if the numbers 1.5 and 2.8 were part of a calculation with inexact numbers, the answer would be limited by the smallest number of significant figures present in the inexact numbers. In this case, as both 1.5 and 2.8 have two significant figures, the product is correctly expressed with two significant figures as 4.2.
Solve for x.
log6(2x + 3) = 3 ...?
The value of x that satisfies the original equation is 106.5. To solve the given logarithmic equation, convert it to its exponential form and simplify. Subtract 3 from both sides, and finally divide by 2 to find that x equals 106.5.
Explanation:To solve for x in the equation log6(2x + 3) = 3, we can convert the logarithmic equation into its exponential form. This means that we interpret the equation as 6 raised to the power of 3 equals 2x + 3:
63 = 2x + 3
The next step is to simplify. 6 to the power of 3 is 216:
216 = 2x + 3
We can now solve for x by first subtracting 3 from both sides:
216 - 3 = 2x
213 = 2x
And then dividing by 2:
x = 213 / 2
x = 106.5
Thus, the value of x that satisfies the original equation is 106.5.
PLZZZZZ HELP
Which answer best describes the system of equations shown in the graph?
not enough information
consistent and independent
coincident
inconsistent
Answer:
Option (2) is correct.
The given system of equation is Consistent and independent.
Step-by-step explanation:
coincident : When two lines overlap each other. then they are coincident lines.Inconsistent: When there is no solution for the given system of equations then the system is called "inconsistent". Consistent : When there is one or infinitely many solutions for the given system of equations is called "consistent".Independent : When each equation of the system gives new information Otherwise they are called Dependent. like x + y = 2 and 2x + 2y =4 this shows one equation is multiple of other hence, dependent.Now consider the given graph,
Since, they intersect at a unique point. Hence, they are consistent.
Also the two given equations are independent of each other .Thus, independent also.
Thus, the given system of equation is Consistent and independent.
Thus, option (2) is correct.
On a coordinate grid, both point (−4, −1) and (2, 6) point are reflected across the y-axis. what are the coordinates of the reflected points?
distance can be represented by absolute value.true or false.?