A publishing company expects to sell 5000 copies of a new book from its web site, if the company charges $30 per book. The company expects that 500 more books would be sold for each price reduction of $2. What price would maximize the company's revenue?
Solution :
Let the revenue be = R
Therefore, R = price x quantity
R = (30 - 2x) ( 5000 + 500x)
= [tex]150000 + 5000x - 1000x^2[/tex]
For the maximum revenue,
[tex]$\frac{dR}{dx} = 0$[/tex]
[tex]$-2000x+5000=0$[/tex]
[tex]$x=2.5$[/tex]
[tex]$\frac{d^2R}{dx^2}=-2000<0$[/tex]
At [tex]x=2.5[/tex], the revenue is maximum.
So the price for the maximum company revenue = [tex]$30-2x$[/tex]
[tex]$=30-2(2.5)$[/tex]
= 30 - 5
= 25
Therefore, the price that will maximize the company's revenue is $25.
The Ramirez family and the Stewart family each used their sprinklers last summer. The water output rate for the Ramirez family's sprinkler was 40 L per hour.
The water output rate for the Stewart family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total
water output of 1575 L. How long was each sprinkler used?
Answer:
15.5
Step-by-step explanation:
Yes
write the equation in standard form. y=4/7x+3
Answer:
4x-7y = -21
Step-by-step explanation:
1. Move 4/7x to the other side
-4/7x+y=-3
2. Multiply both sides by -7
4x-7y=-21
3x-7y=28 is it in standard form
A walking trail is 1,580.76 feet long. A lake is located 70.62 feet away from the end of the trail. What is the total distance from the start of the trail to the lake? 1,510.14 feet 1,651.38 feet 2,286.96 feet 8,642.76 feet
Answer:[tex]1651.38\ ft[/tex]
Step-by-step explanation:
Given
A walking trail is [tex]1580.76\ ft[/tex] long and a lake is located [tex]70.62\ ft[/tex] away from end of the trail
The distance from the start of the trail to the lake is the sum of the length of the trail and lake
[tex]\Rightarrow 1580.76+70.62\\\Rightarrow 1651.38\ ft[/tex]
Answer:
B
Step-by-step explanation:
Use the diagram. Solve for p.
Answer:
A the first one.
Step-by-step explanation:
Wy = 28
WX = 12
XY = WY - WZ
XY = 28 - 12
XY = 16
4P = 16
P = 16/4
P = 4
In the parallelogram below,
z = [ ? ]°
124°
2z+16°
Helpp!
2z+16+124=180
2z=180-16-124
2z=40
z=40/2
Z=20°
I hope I helped you ^_^
5/9+8/9 can someone please help me with this math question? All I know is that you have to add the fractions, Express the sum as a proper fraction or a mixed number.
Answer:
13/9
Step-by-step explanation:
Given
5/9 + 8/9
Both fractions have the same denominator.
Therefore, pick one of the denominator and add the numerators
5/9 + 8/9
= (5+8) / 9
= 13/9
5/9 + 8/9 = 13/9
Which number best represents the slope of the graphed line?
A. -5
B. -1/5
C. 1/5
D. 5
Answer:
A. -5
Step-by-step explanation:
First of all this is a line that shows a negative slope.
Secondly, the formula for slope is rise/ run.
5 is your rise and 1 is your run, therefore: -5/1
And this can be reduced to : -5
Venita is factoring the expression 32 a b minus 8 b. She determines the GCF and writes the factored expression as 8 b (4 a minus 0). Which best describes Venita’s error?
Answer:
8b(4a-1)
Step-by-step explanation:
32ab-8b
8b(4a-1)
Answer:
Did ur question get answered ??
Step-by-step explanation:
This one is really confusing me
Answer:
D) 9
Step-by-step explanation:
8 + 9 + 10 + 7 =39
48 - 39 = 9
Answer:
Last option: 9
Step-by-step explanation:
48-8-9-5-10-7=9
10 boys cleared a piece of land for 21 days how many days will it take 7 boys to clear the same land if they work at the same rate
Answer:
it took 7 boys 21 days to clear a piece of land.
how many square metres of floor are there in a room of 6 metres
ig something like that
Answer:
36² metres
Step-by-step explanation:
I'm assuming you mean 6 metre wide/long floor. Area is L*W so 6*6
Giải pt: 1 + 2sinxcosx = sinx + 2cosx
Answer:
even i dont know can help
In the PQRS triangle PQ=QR, QR side extended to S Show that PQ+RS=QS. -S Q R
pls explain too
Answer:
Step-by-step explanation:
from the picture:
QP = QR
and
QR = RS
so
PQ + RS = QS
Which of the following represents the set of possible rational routes for the polynomial shown below
2x^3+5x^2-8x-10=0
Answer:
The given polynomial is,
2x³+5x²-8x-10=0
all possible roots of a polynomial,
ax³+b²+c x +d=0 ← all possible factors of ration (d/a)
Therefore, eq (1), all possible factors are the factors of ratio (-10/2)
which are, B) { ± 1, 1/2, ± 2, ± 5/2, ±5, ± 10}
OAmalOHopeO
The graph is
function because it is symmetrical about the
Answer:
Functions can be symmetrical about the y-axis, which means that if we reflect their graph about the y-axis we will get the same graph. ... These are two types of symmetry we call even and odd functions.
Step-by-step explanation:
What is the length of leg s of the triangle below?
90°
45
6
172
45
O
A. 72
B. 5
C. 3
O O O O a
D. 6
E. 3.2
F. 36
Answer:
6
Step-by-step explanation:
It's a 45-45-90 triangle, it has two similar sides, since it has two similar angles, which are both 45°
so, side = s = 6
Answered by GAUTHMATH
The length of the leg s of the triangle below is 6.
Option D is the correct answer.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Applying the Pythagorean theorem in the triangle.
√72² = s² + 6²
72 = s² + 36
s² = 72 - 36
s² = 36
s = √36
s = 6
We can also say that,
Opposite angles of equal sides are equal
So,
s = 6.
Thus,
The length of the leg s of the triangle below is 6.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ7
Someone please help me find y if you don’t mind Thankyouu so much
Answer:
Step-by-step explanation:
Decreasing rate = 12% = 0.12
y = 2400 * (1- 0.12)^x = 2400*(0.88)^x
x = 8 years
[tex]y = 2400 *(0.88)^{8}\\\\= 2400*0.36\\\\= 863[/tex]
Will Mark Brainlest Helppp please
Answer:
6
Step-by-step explanation:
how often is that question posted here ?
this means that we need to find the value of x, so that the functional (result) value is 7.
7 = (3x - 4)/2
14 = 3x - 4
18 = 3x
x = 6
What does x equal in the following equation 3x + 5 = 17 A x = 2 B x = 4 C x = 5
Answer:
see below
Step-by-step explanation:
3x + 5 = 17
Subtract 5 from each side
3x+5-5 = 17-5
3x = 12
Divide each side by 3
3x/3 =12/3
x =4
Answer:
B (x=4)
Step-by-step explanation:
plug it in...
3(4)+5=17
Nêu mệnh đề phủ định của mệnh đề sau và xét tính đúng sai của mệnh đề phủ định: ∀x∈R:x^{2} ≠ 1
Answer:
true
Step-by-step explanation:
[tex]existential \: element \: of \: real \: number \: \binom{o}{o} x {}^{2} = 1[/tex]
Analyzing the
Predict which statements are true about the intervals of
the continuous function. Check all that apply.
х
f(x)
01
-3
-15
-2
0
f(x) > 0 over the interval (- 3).
f(x) < 0 over the interval [0, 2].
f(x) < 0 over the interval (-1, 1).
f(x) > 0 over the interval (-2, 0).
f(x) > 0 over the interval [2, o).
-1
3
0
0
1
-3
2
0
3
15
Answer:
1 NO
2 YES
3 NO
4 YES
5 ÝE
Step-by-step explanation:
The true statements about the continuous function are:
f(x) ≤ 0 over the interval [0, 2].
f(x) > 0 over the interval (–2, 0).
f(x) ≥ 0 over the interval [2, )
What are the correct intervals of the continuous function?Functions in Math's are used to show relationships between variables.
Next, let us test the given options;
(A) f(x) > 0 over the interval (-∞, 3).
Using the table of f(x), the values in (-∞, 3) are values less than 3; i.e. -3 to 2.
If f(2) = 0, then f(x) > 0 is not true
(B) f(x) ≤ 0 over the interval [0, 2].
The values in [0, 2] are values from 0 to 2; i.e. 0, 1 and 2.
If f(0) = 0, f(1) = -3 and f(2) = 0
Then, f(x) ≤ 0
(c) f(x) < 0 over the interval (−1, 1).
Using the table of f(x), the values in (-1, 1) are values between -1 and 1; i.e. 0
If f(0) = 0, then f(x) < 0 is not true
(d) f(x) > 0 over the interval (–2, 0).
Using the table of f(x), the values in (-2, 0) are values between -2 and 0; i.e. -1
If f(-1) = 3, then f(x) > 0 is true
(e) f(x) ≥ 0 over the interval [2, ∞)
Using the table of f(x), the values in [2, ) are values from 2; i.e. 2 and 3
If f(2) = 0 and f(3) = 15, then f(x) ≥ 0 is true
Finally, the true statements are:
f(x) ≤ 0 over the interval [0, 2].
f(x) > 0 over the interval (–2, 0).
f(x) ≥ 0 over the interval [2, ∞]
Read more about intervals of continuous functions at; https://brainly.com/question/11803482
<3 and <6 can be classified as:
a. alternate exterior angles
b. same side interior angles
c. corresponding angles
d. alternate interior angles
Answer: d. alternate interior angles
Note how the two angles are inside, or interior, of the lines L1 and L2. For me, I tend to think of such lines like train tracks. So that takes care of the "interior" portion.
As for the "alternate" portion, we can see that the angles are on either side of the transversal line T.
So that's why angles 3 and 6 are alternate interior angles.
If L1 and L2 are parallel, then angle 3 = angle 6.
Determine if \sqrt{36} 36 is rational or irrational and give a reason for your answer.
Answer:
Step-by-step explanation:
It's rational. The square root of 36 is either 6 or -6. Both are rational because both are integers.
| 3 x - 2 | = 4x + 4
Answer: -2/7
|3x - 2| - 4x = 4
1) (3х - 2) - 4х = 4, if 3x - 2 >= 0
2) -(3x - 2) - 4x = 4, if 3x - 2 < 0
1)
3х - 4х = 4 + 2
-x = 6
x = -6
3х - 2 >= 0
3х >= 2
x >= 2/3 - wrong
2)
-3х + 2 - 4х = 4
-7х = 2
x = -2/7
3x-2<0
3x<2
3(-2/7)<2-right
Classify the polynomial and determine its degree.
The polynomial –2x2 – x + 2 is a
with a degree of
.
Answer:
Trinomial, 2
Step-by-step explanation:
Answer:
Trinomial, 2
Step-by-step explanation:
Y and x have a proportional relationship, and y=4 when x=12
Answer:
multiply 4 by 12 okay bro
Answer:
y = [tex]\frac{1}{3}[/tex] x
Step-by-step explanation:
Given that y and x are proportional then the equation relating them is
y = kx ← k is the constant of proportion
To find k use the condition y = 4 when x = 12 , then
4 = 12k ( divide both sides by 12 )
k = [tex]\frac{4}{12}[/tex] = [tex]\frac{1}{3}[/tex]
y = [tex]\frac{1}{3}[/tex] x ← equation of proportion
Find the equation of the line that is perpendicular to y=1/6x+3
and contains the point (-3,23).
y = [?]x + [?]
Answer:
y = -6x + 6
Step-by-step explanation:
The general equation of a line is
y = mx + b
where m is the slope and b is the y-intercept
The slope in the first equation is 1/6
Mathematically, when two lines are perpendicular, the product of their slopes is -1
1/6 * m2 = -1
m2 = -6
So we have the equation as;
y-y1 = m(x-x1)
y-23 = -6(x + 3)
y = -6x -18 +23
y = -6x + 6
[tex]2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48}[/tex]
[tex]\\ \sf\longmapsto 2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48} \\\\ \sf\longmapsto 2 \sqrt{25 \times 3} - \sqrt{36 \times 3} + 5 \sqrt{16 \times 3} \\ \\ \sf\longmapsto 2 \times 5 \sqrt{3} - 6 \sqrt{3} + 5 \times 4 \sqrt{3} \\ \\ \sf\longmapsto 10 \sqrt{3} - 6 \sqrt{3} + 20 \sqrt{3} \\ \\ \sf\longmapsto (10 - 6 + 20) \sqrt{3} \\ \\ \sf\longmapsto 24 \sqrt{3} [/tex]
Answer:
24aprtment3
Step-by-step explanation:
John and Pablo caught fish that have the lengths, in centimeters, listed below. 45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44 Which box-and-whisker plot correctly represents the data?
The options for the box and whisker plots aren't given ; however using technology, a box and whisker plot could be generated from the data.
Answer:
Step-by-step explanation:
Given :
45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44
Using technology, the box and whisker plot generated for the data is attached below.
The 5 - number summary is also given below :
Minimum: 39
Median: 45
First quartile: 42
Third quartile: 47
Interquartile Range: 5
Maximum: 49
Outliers: none
Answer:
Step-by-step explanation:
