Final answer:
For the expression R(x)=(500+ax)(50-bx), a represents the increase in yearbooks sold for each $5 decrease in price and b represents the corresponding decrease in price per yearbook. The correct values for a and b are 100 and 5 respectively, resulting in the revenue expression R(x) = (500 + 100x)(50 - 5x).
Explanation:
The student's question revolves around the concept of revenue generation based on the number of items sold and the selling price per item.
When examining revenue, we understand it as the product of price per unit times the number of units sold. In the given example, a school is selling yearbooks with a base scenario of 500 yearbooks at $50 each. We are given that for every $5 decrease in price, the school can sell an additional 100 yearbooks. This can be formulated as:
R(x) = (500 + ax)(50 - bx)
Here x represents the number of $5 decreases from the original price. With each decrease, the number of books sold increases by 100, and the price decreases by $5.
Therefore, variable a must represent the increase in quantity sold for each $5 price decrease (a = 100), and variable b must represent the decrease in price per yearbook for each price decrease (b = 5).
Therefore, the values of a and b are 100 and 5, respectively.
The expression for the revenue becomes:
R(x) = (500 + 100x)(50 - 5x)
A particular hybrid car travels approximately 204 mi on 4 gal of gas. Find the amount of gas required for a 714-mi trip.
The car needs 14 gallons of gas for the 714 mile trip.
To determine the amount of gas required for a 714-mile trip, we can set up a proportion based on the given information:
We know that the car travels 204 miles on 4 gallons of gas. We need to find the amount of gas needed for 714 miles. Let the gas required for 714 miles be X gallons
First, let us set up the proportion:
204 mi / 4 gal = 714 mi / X galNext, we solve for x (the amount of gas required for 714 miles):
204 mi × X gal = 714 mi × 4 gal204X = 2856X = 2856 / 204X = 14Therefore, the car requires 14 gallons of gas for a 714-mile trip.
Supposed a Visa card had a credit card number of 4162 0012 3456789a where a is the check number what is the check number? A) 0 B) 3 C) 9 D) 7
Answer:
Option B) 3
Step-by-step explanation:
we have the number
4162 0012 3456 789a
Find the value of a (check number)
step 1
Multiply every even-position digit (when counted from the right) in the number by two. If the result is a two digit number, then add these digits together to make a single digit
4162 0012 3456 789a
9(2)+7(2)+5(2)+3(2)+1(2)+0(2)+6(2)+4(2)
(18)+(14)+(10)+(6)+(2)+(0)+(12)+(8)
Remember that If the result is a two digit number, then add these digits together to make a single digit
so
(1+8)+(1+4)+(1+0)+(6)+(2)+(0)+(1+2)+(8)
(9)+(5)+(1)+(6)+(2)+(0)+(3)+(8)=34
step 2
add every odd-position digit
4162 00123456 789a
so
8+6+4+2+0+2+1=23
step 3
Adds the result in step 1 and the result in step 2
34+23=57
The check-digit is what number needs to be added to this total to make the next multiple of 10
In our case, we’d need to add 3 to make 60
therefore
The check number is 3
What are the correct coefficients (reading from left to right) when the chemical equation is balanced?__pbr3(l)+__h2o(l)→__h3po3(aq)+__hbr(aq)what are the correct coefficients (reading from left to right) when the chemical equation is balanced?________1, 3, 1, 31, 3, 3, 13, 5, 1, 81, 2, 1, 2?
The correct coefficients (reading from left to right) are chemical equation is balanced as 1PBr₃(l) + 3H₂O(l) → H₃PO₃(aq) + 3HBr(aq). which is the correct answer would be an option (A).
What is the rule of conservation of mass?Mass, according to the rule of conservation of mass, cannot be generated or destroyed. As a result, the mass of products must match the mass of reactants. Each element's atom count must be identical on the reactant and product sides. As a result, chemical equations are balanced.
According to the given question,
We have to substitute the coefficients (reading from left to right) are 1,3,1,3 in the given chemical equation
Thus, the correct coefficients (reading from left to right) are balanced chemical equation as :
⇒ 1PBr₃(l) + 3H₂O(l) → H₃PO₃(aq) + 3HBr(aq).
Hence, the correct answer would be option (A).
To learn more about the balanced chemical equation click here :
https://brainly.com/question/13870196
#SPJ5
Let ABCD be a cyclic quadrilateral. Let P be the intersection of AD and BC, and let Q be the intersection of AB and CD. Prove that the angle bisectors of angle DPC and angle AQD are perpendicular.
How to round 4.288 to the nearest hundredth
The image below is a triangle drawn inside a circle with center O:
A triangle is shown inscribed inside a circle. The leg of the triangle labeled 4 inches passes through the center of the circle, O. The other two legs are labeled as 2 inches and 3 inches.
Which of the following expressions shows the area, in square inches, of the circle?
(π = 3.14)
3.14 ⋅ 2
3.14 ⋅ 3
3.14 ⋅ 22
2 ⋅ 3.14 ⋅ 22
Answer:
3.14 2^2
Step-by-step explanation:
The expressions shows the area, in square inches, of the circle will be 3.14 × 2² square units. Then the correct option is C.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The image below is a triangle drawn inside a circle with center O:
A triangle is shown inscribed inside a circle.
The leg of the triangle labeled 4 inches passes through the center of the circle, O.
The other two legs are labeled as 2 inches and 3 inches.
The expressions shows the area, in square inches, of the circle will be
Area of circle = (π/4) d²
The diameter of the circle is passing through center. Then the length of the diameter is 4.
Then the area of circle will be,
Area = (π/4) 4²
A = 3.14 × 4
A = 3.14 × 2² square units
The expressions shows the area, in square inches, of the circle will be 3.14 × 2² square units.
Then the correct option is C.
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ2
X is a normally distributed random variable with a mean of 5 and a standard deviation of 2. the probability that x is greater than 10.52 is
Final answer:
The probability that X is greater than 10.52 for a normal distribution with a mean of 5 and a standard deviation of 2 is found by calculating the z-score of 10.52. The z-score is 2.76, and the area to the right under the normal curve represents a very small probability, typically less than 0.003.
Explanation:
To find the probability that X is greater than 10.52, when X is a normally distributed random variable with a mean of 5 and a standard deviation of 2, we first need to calculate the z-score for 10.52. Using the formula:
Z = (X - mean) / standard deviation
Substitute the given values into the formula:
Z = (10.52 - 5) / 2 = 5.52 / 2 = 2.76
This z-score tells us how many standard deviations above the mean our value lies. In this case, X = 10.52 is 2.76 standard deviations above the mean.
The probability of X being greater than 10.52 corresponds to the area under the standard normal distribution curve to the right of the z-score 2.76. Using standard normal distribution tables or software, we can find this probability to be very small, typically less than 0.003.
Hey can you please help me posted picture of question
Given rectangle PQRS with PQ=QR, PQ=SP, and SQ=6√2. Find SR. a)√2. b) 6. c) 5√2 d) not enough information
Tim answered all the questions on his math test but got 101010 answers wrong. He received 444 points for every correct answer, and there was no penalty for wrong answers. His score was 767676 points.
Write an equation to determine the total number of questions (q)(q)left parenthesis, q, right parenthesis on Tim's math test.
Find the total number of questions on his math test.
questions
Answers:
Equation: [tex]q=\frac{76}{4} +10[/tex]
Questions: [tex]29[/tex]
Also, the verified Tutor above is in fact correct, but this answer is way more simple and easier to understand, thank you for your time :D
Explanation:
First, we need to find out the questions, even though the first question is, "What is the equation?". So, to the find the answer to how many questions there are in total we need to grab the total points "[tex]76[/tex]" and divide that by "[tex]4[/tex]" because that'll tell us how many questions that he answered correct. Especially since the "[tex]10[/tex]" questions he got wrong didn't affect his points.
So [tex]\frac{76}{4} =19[/tex]. Now we must add 10 to 19. [tex]10+19=29[/tex]. And so [tex]29[/tex] is the total amount of questions. Now we must write down how we found out. We found out by dividing [tex]76[/tex] and [tex]4[/tex], then we added [tex]10[/tex]!
Conclusion:
As simple as that, we found out how many questions there were in total and how we found out! Thank you for sticking with me♥!
A pet store has 26 rabbits and hamsters. The number of rabbits is 2 more than double the number of hamsters. How many hamsters does the pet store have?
Let the number of rabbits in the pet store is x
And the number of hamsters in the pet store is y.
Now, we have been given that pet store has 26 rabbits and hamsters. Thus, we have the linear equation
[tex]x+y=26...........(1)[/tex]
Now, number of rabbits is 2 more than double the number of hamsters. Hence, we have
[tex]x=2+2y[/tex]
Substituting this value of x in equation 1, we get
[tex]2+2y+y=26\\ 3y=24\\ y=8[/tex]
Thus, there are 8 hamsters in the pet store.
Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x e2t2 − 4t dt 4
Using the Fundamental Theorem of Calculus Part 1, the derivative of the function g(x) = ∫ (x e2t2 - 4t) dt from x=4 is ex2 - 4x where 'x' is the variable 't' from the integral.
Explanation:The subject of this question is the use of part 1 of the Fundamental Theorem of Calculus to find the derivative of a complex function. This theorem states that if f is a function that is continuous over the interval [a, b] and F is an antiderivative of f on the interval [a, b], then the definite integral of f from a to b is equal to F(b) - F(a).
In your specific question, you are asked to find the derivative of the function g(x) = ∫ (x e2t2 - 4t) dt from x=4.
The derivative of a definite integral, from a constant to a variable, of a function is simply the original function evaluated at the upper limit.
Therefore, the derivative of the given function g(x) is simply ex2 - 4x, treating 'x' as the variable 't' from the integral.
Learn more about Derivative Calculations here:https://brainly.com/question/32605732
#SPJ3
simplify the expression 11x-(2x^2+8x).
A television is 36 inches by 18 inches. What is the area?
Which of the following is the graph of y=|x-1|-4y=∣x−1∣−4y, equals, vertical bar, x, minus, 1, vertical bar, minus, 4?
Answer:
The graph of given function is shown below.
Step-by-step explanation:
The given function is
[tex]y=|x-1|-4[/tex] .... (1)
The vertex form of a absolute function is
[tex]y=a|x-h|+k[/tex] .... (2)
where, a is a constant and (h,k) is vertex.
On comparing (1) and (2), we get
[tex]a=1,h=1,k=-4[/tex]
The vertex of the function is (1,-4). The table of values is
x y
3 -2
2 -3
1 -4
0 -3
-1 -2
Plot these points on a coordinate plane. Draw a V-shaped curve by connecting these points with vertex at (1,-4).
x·\sqrt[4]{x}
Rewrite simplest radical form
Answer:
b
Step-by-step explanation:
asdf
(08.06 MC) Carly and Janiya put some money into their money boxes every week. The amounts of money (y), in dollars, in their money boxes after certain amounts of time (x), in weeks, are shown by the equations below: Carly y = 60x + 40 Janiya y = 50x + 80 After how many weeks will Carly and Janiya have the same amount of money in their money boxes and what will that amount be? (1 point) 5 weeks, $280 5 weeks, $340 4 weeks, $280 4 weeks, $340
Answer:
$ 280 4 weeks
Step-by-step explanation:
In a school auditorium there are 33 seats in each row of seats. How many rows are needed for 528 students to each have a seat?
To find the number of rows needed for 528 students to each have a seat in a school auditorium with 33 seats in each row, divide the total number of students by the number of seats in each row. The answer is 16 rows.
Explanation:To find the number of rows needed for 528 students to each have a seat in a school auditorium with 33 seats in each row, we need to divide the total number of students by the number of seats in each row.
So, the number of rows needed would be:
Rows needed = Total number of students ÷ Number of seats in each row
Substituting the given values:
Rows needed = 528 ÷ 33 = 16
Therefore, 16 rows are needed for 528 students to each have a seat in the auditorium.
Learn more about Finding the number of rows needed for students to have seats here:https://brainly.com/question/15049173
#SPJ3
which set of number could represent the length of the sides of a right triangle? A 9 11 14 B 15 18 21 C 7 24 25 D 8 9 10
Q9 Q4.) Write the augmented matrix for the system of equations to the right.
if I have 300 apples and eat 123 how many do I have left?
Turtle and vicent combine their coins to find they have all dimes and quarters .They have 8 more quarters them dimes and the coins are worth a total of 5.15 .How many dimes and quarters do they have?
PLEASE HURRY!! I WILL GIVE BRAINLIEST
Trapezoid K' is the image of trapezoid K after a series of transformations.
Bella and Marco described the sequence of transformations in different ways.Which sequence or sequences are correct and why?
Answer:
Option A
Step-by-step explanation:
From the graph attached, we will write the transformation as followed.
a. Trapezoid k is dilated by a scale factor of [tex]\frac{3}{2}[/tex]
[ Since scale factor = [tex]\frac{\text{Largest side of k'}}{\text{Largest side of k}}[/tex]
= [tex]\frac{12units}{8units}[/tex]
= [tex]\frac{3}{2}[/tex] ]
2. scaled trapezoid then rotated by 180°.
3. Then rotated trapezoid is shifted 1 unit down.
By these transformations Bella's sequence was correct.
Therefore, Option A is the answer.
A bank account earns interest at a rate of 3.5% per year ( in other words it increases in value by that percent) and starts with a balance of $350. Which of the following equations would give the account’s worth, W, as a function of the number of years, y, it has been gaining interest?
The account's worth, W, as a function of the number of years, y it has been gaining interest is given by the equation W = $350 + ($350 imes 0.035 imes y).
Explanation:The equation that gives the account's worth, W, as a function of the number of years, y, it has been gaining interest is:
W = $350 + ($350 imes 0.035 imes y)
Here's an example:
If the account has been gaining interest for 2 years, then W = $350 + ($350 imes 0.035 imes 2) = $364.70.
Learn more about Simple interest here:https://brainly.com/question/40405117
#SPJ12
Two quantities are related as shown in the table below:
x. y
2. 3
4. 4
6. 5
8. 6
Which equation best represents the relationship?
Where does the graph of y=sin x from x=0 to x=2pie start.
A- at its minimum
B- at an x intercept
C- at its maximum
D- between an x intercept and its maximum
It starts at 0, heads up to 1 by π/2 radians (90°) and then heads down to -1.
What is the probability that a randomly thrown dart that lands within the rectangle lands within a shaded region? All of the circles are congruent, and the diameter of each circle is 100 cm. A. 39/200 B. 49/250 C. 98/125 D. 157/200
Q7 Q26.) Find the quotient of the complex numbers and leave your answer in polar form.
Explain why a square is always a rectangle but a rectangle is not always a square.
Find the missing numerators in each of the following problems. a. 10⁄15 = ⁄60 b. ⁄108 = 4⁄9 c. 7⁄11 = ⁄121 d. ⁄144 = 2⁄6
Final answer:
The missing numerators are found by creating equivalent fractions. By multiplying both the numerator and the denominator by the same factor that converts the original denominator to the new denominator, we find the missing numbers: 40, 48, 77, and 48 for each problem respectively.
Explanation:
To find the missing numerators, we need to use the concept of equivalent fractions. Equivalent fractions have different numerators and denominators but represent the same value.
a. 10⁄15 = ⁄60
We find the factor that converts 15 to 60, which is 4 (since 15 * 4 = 60), and multiply the numerator by the same factor (10 * 4 = 40). So, the missing numerator is 40.
b. ⁄108 = 4⁄9
To convert 9 into 108, multiply by 12 (since 9 * 12 = 108), and do the same with the numerator (4 * 12 = 48). Hence, the missing numerator is 48.
c. 7⁄11 = ⁄121
11 times 11 equals 121, so we multiply the numerator 7 by 11 as well (7 * 11 = 77), giving us 77 as the missing numerator.
d. ⁄144 = 2⁄6
To get from 6 to 144, multiply by 24 (since 6 * 24 = 144), so multiply the numerator 2 by 24 to get 48 as the missing numerator.