a. What is the cost expression for the newspaper?
The cost would be the sum of fixed cost and the variable cost. The fixed cost
is 70 while the variable cost is 0.40 x, where x stands for the number of
copies made. That is:
Cost = 70 + 0.40 x
where x = number of copies made
b. What is the revenue expression for the newspaper?
The revenue would simply be the product of selling price and number of copies sold or made, that is:
Revenue = 0.50 x
c. Put the cost and revenue expressions into an inequality that would represent
a successful newspaper.
To have a successful newspaper, the difference of revenue and cost must be
greater than 0, that is:
Revenue – Cost > 0
0.50 x – (70 + 0.40 x) > 0
d. How many copies should be sold to make a profit? Show all work! An answer
with no work will receive 0 points.
From the above equation, we solve for x.
0.50 x – (70 + 0.40 x) > 0
0.50 x – 70 – 0.40 x > 0
0.10 x > 70
x > 700
Number of copies made should be more than 700 copies
e. Now go back to your answer for d. On every line of your solution write what
property of math you would use to justify the transformation that
occurred.
0.50 x – (70 + 0.40 x) > 0 Distribution property
0.50 x – 70 – 0.40 x > 0 Addition property
0.10 x > 70 Addition property
x > 700 Division property
Final answer:
The cost expression for the newspaper is $70 + $0.40c. The revenue expression is $0.50c. A successful newspaper would have $0.50c > $70 + $0.40c. To make a profit, 700 copies should be sold.
Explanation:
a. The cost expression for the newspaper can be calculated by adding the fixed production cost per edition to the cost of printing and distributing each copy. So the cost expression is:
Cost = $70 + $0.40c
where 'c' represents the number of copies.
b. The revenue expression for the newspaper can be calculated by multiplying the selling price per copy by the number of copies sold. So the revenue expression is:
Revenue = $0.50c
c. To represent a successful newspaper, the revenue should be greater than the cost. So the inequality would be:
$0.50c > $70 + $0.40c
d. To calculate the number of copies needed to make a profit, we need to find the point where the revenue is equal to or greater than the cost. So we set the inequality from part c to equality and solve for 'c':
$0.50c = $70 + $0.40c
$0.10c = $70
c = $700
e. At every step in the solution, we used the property of equalizing the equation by adding or subtracting the same value on both sides, and also dividing by the same value on both sides.
Solve. (–16.1) • 9.4 • (–7.2) = x • (–7.2) • (–16.1) A. 9.4 B. 1 C. –7.2 D. –16.1
List 3 prime numbers between 30 and 60...
Answer:
The three prime numbers are, 31, 37, and 41.
How I got the answer:
1. 31 is a prime number: 31 x 1 = 31
1 x 31 = 31
2. 37 is a prime number: 37 x 1 = 37
1 x 37 = 37
3. 41 is a prime number: 41 x 1= 41
1 x 41 = 41
A train travels at a constant speed of 75 mi/h. The function f(x) = 75x gives the distance that the train travels in x hours. Graph this function and give its domain and range.
f(x) = 75x represents the distance covered by a train traveling at a constant speed of 75 mi/h. The graph is a line with a constant slope of 75, originating from (0,0). The domain and range of the function are both all non-negative real values ([0, +∞)).
Explanation:To graph the function f(x) = 75x, where x represents time in hours and f(x) represents distance in miles, we construct a simple 2D graph. In this case, the graph will be a straight line sloped upward, starting from the origin (0,0), since the time and distance both start from zero. The slope of the line corresponds to the speed of the train, 75 mi/h, indicating that the train covers 75 miles each hour.
The domain, or possible x-values, of this function are all non-negative real numbers since time cannot be negative. In mathematical terms, this is [0, +∞). The range, or possible f(x)-values, are also all non-negative real numbers as the distance covered also cannot be negative. So, the range is also [0, +∞).
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factor the following polynomial completely.
0.3x^2-3x+7.2
A bread making machine costs $99.The ingredients to make a one pound loaf of bread costs $0.45 .At store, you pay 2.19 for the same size loaf of bread.How many whole loaves of bread will you have to make in order for the cost of the machine and ingredients to be less than the cost of buying an equivalent Amount of bread at the store.
To determine the number of loaves of bread needed to make the cost of the machine and ingredients less than buying bread at the store, set up an inequality and solve for 'x'. With the given values, you would need to make at least 5 whole loaves of bread.
Explanation:To determine how many loaves of bread will need to be made for the cost of the machine and ingredients to be less than the cost of buying bread at the store, we need to compare the costs of making bread and buying bread.
The cost of making a one pound loaf of bread using the machine and ingredients is $0.45. The cost of buying a one pound loaf of bread at the store is $2.19.
Let's assume the cost of making each whole loaf of bread is $0.45. We can set up an inequality to represent the situation:
0.45x < 2.19
Where 'x' is the number of loaves of bread that need to be made.
To solve for 'x', we divide both sides of the inequality by 0.45:
x > 2.19/0.45
Using a calculator, we find that x > 4.87. Rounded up, this means you would need to make at least 5 whole loaves of bread in order for the cost of the machine and ingredients to be less than buying bread at the store.
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The measure of angle A = ____ degrees.
He outdoor furniture center buys wooden benches for $50each. The furniture store owner adds a 200% markup to the cost of the bench. After hearing from customers that the selling cost of the bench is too high the owner changes the markup to 120% how much less per bench does the store owner make with the lower markup?
The amount that is reduced from the bench price is $40.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the outdoor furniture centre buys wooden benches for $ 50 each. The furniture store owner adds a 200% markup to the cost of the bench. After hearing from customers that the selling cost of the bench is too high the owner changes the markup to 120%.
The price at 200% markup is,
Price = 50 x 2 = $100
The price at 120% markup is,
Price = 50 x 1.2 = $60
The reduced price is,
Reduced = 100 - 60 = $40
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round 54.953 to the nearest whole number
16.9÷(-1.3)
[tex]16.9 \div ( - 1.3)[/tex]
Plz help really easy but don't guess asap plz
What values are needed to make each expression a perfect square trinomial?
x2 + 4x +_____________
x2 – 10x + ____________
Answer:
Part a) [tex]x^{2}+4x+4[/tex]
Part b) [tex]x^{2}-10x+25[/tex]
Step-by-step explanation:
we know that
A perfect square trinomial is equal to
[tex](x+a)^{2} =x^{2}+2ax+a^{2}[/tex]
Part a) we have
[tex]x^{2}+4x[/tex]
Compare with the formula of a perfect square trinomial
[tex]x^{2}+4x=x^{2}+2ax+a^{2}[/tex]
so
[tex]4x=2ax[/tex]
[tex]4=2a[/tex]
[tex]a=2[/tex]
therefore
[tex](x+a)^{2} =(x+2)^{2}=x^{2}+4x+4[/tex]
Part b) we have
[tex]x^{2}-10x[/tex]
Compare with the formula of a perfect square trinomial
[tex]x^{2}-10x=x^{2}+2ax+a^{2}[/tex]
so
[tex]-10x=2ax[/tex]
[tex]-10=2a[/tex]
[tex]a=-5[/tex]
therefore
[tex](x+a)^{2} =(x-5)^{2}=x^{2}-10x+25[/tex]
The values are needed to make each expression a perfect square trinomial x^2 + 4x + 4 and x^2 – 10x + 25.
What is a perfect square?A perfect square is a number system that can be expressed as the
square of a given number from the same system.
A. [tex]x^{2} +4x+4[/tex]
A perfect square trinomial is
[tex](x+a)^2 = x^2 + 2ax + a^2[/tex]
Compare with the formula of a perfect square trinomial
4x = 2ax
4 = 2a
a = 2
Therefore, [tex](x+a)^2 = (x+2)^2 = x^{2} +4x+4[/tex]
B. [tex]x^{2} -10x + 25[/tex]
A perfect square trinomial is
[tex](x+a)^2 = x^2 + 2ax + a^2[/tex]
Compare with the formula of a perfect square trinomial
-10x = 2ax
-10 = 2a
a = -5
Therefore, [tex](x+a)^2 = (x-5)^2 = x^{2} -10x+25[/tex].
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What is 15 divide by 5/9
What is the angular position in radians of the minute hand of a clock at 10:35?
evaluate (-B)2 for A=5,B=-4, and C=2
Final answer:
To evaluate [tex](-B)^2[/tex] for A=5, B=-4, and C=2, substitute the given values into the expression. The result is 16.
Explanation:
To evaluate [tex](-B)^2[/tex] for A=5, B=-4, and C=2, we substitute the given values into the expression. Since B=-4, we have [tex](-B)^2=(-(-4))^2=4^2=16.[/tex]
The significance of raising a number to a power lies in its ability to represent repeated multiplication in a concise and efficient manner. Powers allow us to express large numbers and complex mathematical relationships in a compact form. They are fundamental in various mathematical operations, such as arithmetic, algebra, calculus, and number theory. Additionally, powers play a crucial role in scientific notation, where they facilitate the representation of very large or very small numbers in a more manageable format. Overall, understanding powers is essential for comprehending a wide range of mathematical concepts and applications.
A coral reef grows 0.13 m every week how much does it grow in 12 weeks
Final answer:
To find out how much a coral reef grows in 12 weeks, with a weekly growth of 0.13 m, multiply the growth rate by the number of weeks, resulting in a total growth of 1.56 m.
Explanation:
If a coral reef grows 0.13 m every week, to find out how much it grows in 12 weeks, we simply need to multiply the weekly growth rate by the number of weeks:
Weekly growth rate = 0.13 m
Number of weeks = 12
Therefore, the total growth over 12 weeks is:
0.13 m/week × 12 weeks = 1.56 meters.
In 12 weeks, the coral reef grows by a total of 1.56 meters.
What is the percent of decrease from 58.3 to 40.7?
Round your answer to the nearest tenth of a percent and include a percent sign (%).
SO YOU HAVE TO IDENTIFY THE PARTS OF THE LISTED EXPRESSION
5t + 3y - 9
Terms:________________
Variable(s)_______________
Coefficent(s)____________________
Variable Term(s)__________________________
Constant Term(s)_________________________-
What number is 1/10 as greater as 7962
Aaron puts $1,000 in an account that pays 10% interest compounded quarterly. He leaves it in the account for six months. Estimate how much interest he earns.
A. $50
B. $100
C. $150
D. $200
Answer: . $50
Step-by-step explanation:
The formula to find the compound amount (compounded quarterly) is given by :-
[tex]A=P(1+\dfrac{r}{4})^{4t}[/tex], where P Is principal amount, r is the rate of interest in decimal and t is the time in years.
Given : Aaron puts $1,000 in an account that pays 10% interest compounded quarterly.
Then, P=1000, r=10%=0.1 ; t=[tex]\dfrac{6}{12}=0.5[/tex] year
Now, [tex]A=1000(1+\dfrac{0.1}{4})^{4(0.5)}[/tex]
[tex]A=1000(1.025)^{2}=1050.625[/tex]
Then , Compound interest=[tex]A-P=1050.625-1000=50.625\approx\$50[/tex]
Hence, he earns the estimated interest of $50.
plz help...Find f(-5)
f(x) = -4x + 3
A)
-17
B)
-7
C)
12
D)
23
These numbers are not square numbers. Which two consecutive square numbers is each number in between
a. 7
B.30
c.50
d.90
Ava read 110 books in 11 months. How many books per month did she read
Shaylyn measured her house as 5 meters tall. Which of these is an equivalent measurement?a. 0.3 milesb. 7.3 yardsc. 16.4 feetd. 27.2 inches
Solve the following proportion for x 6/7 = 48/x
NEED TO KNOW!!!!!
San rotated parallelogram ABCD 90 clockwise around the origin. If angle A is 130 and angle B is 50, what is the degree measurement of angle A
A: 80 degrees
B: 130 degrees
C: 50 degrees
D: 180 degrees
Jack travels 2.45 miles to school. Wanda travels 2.31 miles to school. Compare the distances using words
Add.
(5y - 1) + (-2y + 4)
A) 3y - 5
B) 3y + 3
C) 7y + 3
D) 7y - 3
this brain plus is BS u cant do anything all the stuff i need is blocked
Chalene wants to cut her hair but is a little nervous. She decides to cut it off slowly so she can get used to it as it gets shorter. Right now, her is is 11.5 inches past her shoulders. She decides to cut an inch and a half off her hair every week. Write an expression to describe the length of her hair in relationship to her shoulders.
Final answer:
The length of Chalene's hair in relation to her shoulders can be described using the expression:
Length of hair = 11.5 - 1.5n,
where 'n' represents the number of weeks. Each week, Chalene cuts 1.5 inches off her hair.
Explanation:
To describe the length of Chalene's hair in relation to her shoulders, we can use the expression:
Length of hair = 11.5 - 1.5n
where 'n' represents the number of weeks.
Each week, Chalene cuts 1.5 inches off her hair, so we subtract 1.5 from the previous length to get the new length.
For example, after 1 week, the length of her hair will be 11.5 - 1.5(1) = 10 inches past her shoulders.
PLEASE HELP!!!!!!!!!!!!!!!!
What value correctly fills in the blank so that the expressions are equivalent?
18 + 45 = ___ ´ (2 + 5)
2
3
7
9