From the given price function, we have;
(a) [tex] \frac{dp}{dq} = - 13[/tex]
(b) The point elasticity of demand is 0.0256; inelastic demand
(c) $46.6
(d) Increase
How can the elasticity of demand be found?a. The given function is presented as follows;
[tex]p = 50 \times (151 - q) ^{0.02 \times \sqrt{q + 19} } [/tex]
Differentiating the above function with a graphing calculator and setting q = 150 gives;
[tex] \frac{dp}{dq} = - 13[/tex]
b. The point elasticity of demand is given by the formula;
[tex] e \: = \frac{dq}{dp} \times \frac{p}{q} [/tex]
When q = 150, we have;
P = 50
Which gives;
[tex]e \: = \frac{1}{13} \times \frac{50}{150} = 0.0256[/tex]
The point elasticity of demand, E = 0.0256
The demand is inelastic (less than 1) when the quantity demanded is 150 unitsc. If the quantity demanded decreases from 150 to 140 units, we have;
[tex]0.0256 \: = \frac{1}{13} \times \frac{p}{140} = [/tex]
Which gives;
p = 46.6
The price when the quantity demanded decreases to 140 is $46.6d. Given that increase in price, from 46.6 to 50, increases the quantity demanded from 140 to 150, therefore;
The manufacturer should increase the price, p to increase the revenue, R.R = p × q
Learn more about elasticity of demand here;
https://brainly.com/question/19141990
50 POINTS!
Exploiting for points will be reported.
Sophie deposited money into an account in which interest is compounded semiannually at a rate of 3.7%. She made no other deposits or withdrawals and the total amount in her account after 15 years was $12,158.10. How much did she deposit?
SHOW WORK FOR BRAINLIST
$7,015.11
total money accrued : $12,158.10years : 15 years rate of interest : 3.7%deposited : ADepth meanings:
P is deposited moneysemiannually : 2 times in a yearA is received or acquired moneyt is time in yearsr is rate in percentage[tex]\sf P = \dfrac{A} { (1 + \dfrac{r}{n})^{nt}}[/tex]
[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{3.7\%}{2})^{(2)(15)}}[/tex]
[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{0.037}{2})^{(2)(15)}}[/tex]
[tex]\rightarrow \sf P = 7015.113646[/tex]
find x correct to 2 decimal places
Answer:
Step-by-step explanation:
The value of x in the triangle is 205.24 calculated by using tan function.
By using tan function we find the value of x.
Let us divide x to two parts which includes two right triangles.
We know than tan function is a ratio of opposite side and adjacent side.
tan 55 = 106/adj
adj= 106/1.428
adj=74.22
Now let us find the adjacent side length of larger triangle similarly.
tan 39 = 106/ adj
0.809 = 106/adj
adj=106/0.809
adj=131.025
So the value of x is 74.22+131.025
=205.245
Hence, the value of x in the triangle is 205.24.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ3
How do I solve for X?
The value of x in the special right triangle is 39.60 ft.
Right angle triangleRight angle triangle has one of its angles as 90 degrees. The side and angles can be found using trigonometric ratios.
Therefore, let's find the base of the triangle with 30 degrees.
sin 30° = opposite / hypotenuse
1 / 2 = 7 / b
b = 14 ft
Let's use the value(14 ft) to find the height of the biggest triangle.
sin 30 = opposite / hypotenuse
sin 30 = 14 / h
0.5h = 14
h = 14 / 0.5
h = 28 ft
Therefore, let's find the value of x .
sin 45° = 28 / x
x = 28 / 0.70710678118
x = 39.5979797464
x = 39.60 ft
learn more on right triangle here: https://brainly.com/question/10412877
Determine the value of y, if x is -1
equation: y= | x |-4
Answer:
y = -3
Step-by-step explanation:
y = | x | - 4
y = | -1 | - 4
y = 1 - 4
y = -3
Comment any questions!
When asked to factor the trinomial 6x^2 - 18 + 12, a student gives the answer (x - 2)(x - 1). What is the one thing wrong with this answer?
A. 6 is also a factor of this trinomial
B. The minus signs should always be plus signs
C. There is nothing wrong with the answer
D. The factors are not simplified
Answer:
the answer is C which one is this
Problem 1: Verify whether these two functions are inverses: (x + 5) f(x) = (2x + 1) and g(x) = (5 - x) (2x - 1) What is g(x))? Use your keyboard and the keypad to enter your answer. Then click Done
g(f(x)) = x
What is inverse function?
An inverse function is defined as a function, which can reverse into another function.
[tex]f(x)= \frac{(x + 5)}{(2x + 1)}[/tex]
[tex]g(x)= \frac{(5 - x)}{(2x - 1)}[/tex]
[tex]g(f(x))=g( \frac{(x+5)}{(2x +1)})[/tex]
Substitute the value of f(x),
[tex]g(f(x))= \frac{(5 - \frac{(x + 5)}{(2x + 1)})}{(2 \frac{(x + 5)}{(2x + 1)} - 1)}[/tex]
[tex]g(f(x))= \frac{\frac{10x+5-x-5}{2x+1} }{ \frac{2x+10-2x-1}{2x+1}}[/tex]
[tex]g(f(x)) = \frac{9x}{9}[/tex]
g(f(x)) = x
Hence, g(f(x)) = x
Learn more about inverse function
https://brainly.com/question/2541698
#SPJ2
A minibus drives with a constant speed
of 32 km/h. How long will it take to travel
a distance of 80 kilometers?
✰ Given Information :-
⠀
A minibus drives with a constant speed of 32 km/hr⠀
✰ To Find :-
⠀
Time taken to travel a distance of 80 kilometers⠀
✰ Formula Used :-
⠀
[tex] \qquad \star \: \red{ \underline{ \boxed{ \sf Time = \dfrac {Distance} {Speed} }}} \: \star[/tex]
⠀
✰ Solution :-
⠀
Putting the values in the formula, we get,
⠀
[tex] \sf \longrightarrow Time = \dfrac{80 }{32} \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = \cancel{\frac{80}{32} } \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = \dfrac{10}{4} \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = 2.5 \: hrs \\ \\ [/tex]
Thus, the time taken to travel 80 km with that speed is 2.5 hours.
⠀
[tex] \underline{ \rule{227pt}{2pt}}[/tex]
⠀
what is the volume of a rectangular prism with height of 12 inches and a base with an area of 2 square inches.
Answer:
24 cubic inches
Step-by-step explanation:
Volume is side x side x side. You already have done side x side so it is just side x area.
9
Emily drives 186 miles in 3 hours.
(a) What is her average speed?
Answer:
Her average speed would be 62 mph.
Step-by-step explanation:
Step 1. Do 186 divided by 3
Step 2. The answer you would get is 62
Step 3. Label to get 62 miles per hour (mph)
I hope that this helps! :)
Step-by-step explanation:
Displacement = 186 miles
Time taken = 3hours
Average speed = ?
Now,
[tex]average \: speed = \frac{total \: distnce}{total \: time \: } \\ = \frac{186}{3} \\ [/tex]
= 62 miles per hour
11. Maria's age is 3 years more than twice George's age. Which expression represents George's age in terms of Maria's?
Answer:
C
Step-by-step explanation:
Okay, the catch of this question is that they do a very good job of explaining Maria's age in terms of George's age, but they leave George's age in terms of Maria's all up to you.
First start off by doing an expression of what they explicitly give you. Maria's age in terms of George's age.
Let's use variables g, representing George's age and m representing Maria's age
m = 2g + 3
Okay, this is all dandy and all, but they ask us for George's age in terms of Maria's, so we need to isolate for g.
subtract the 3 from both sides, like so:
m - 3 = 2g
then divide 2 from both sides: (remember we're dividing the whole thing)
(m-3)/2 = g
Now we have an expression for George's age in terms of Maria's.
g = (m-3)/2 or [tex]g = \frac{m-3}{2}[/tex]
The answer that gives us this, is C.
Choose the multiplication problem that correctly shows partial products.
A) A
B) B
C) C
Answer:
B
Step-by-step explanation:
62x4=248
4x2=8
6x4=24 and carry the 0 and get 240
240+8=248 and you get B
Solve by completing the square:
x2 + 2x-8= 0
-8
a.
x = -4 or 2
b. X= 4 or 2
-
=
c.
x= -4 or - 2
d. X= 4 or - 2
x
hey guys can you please help me with these questions please explained them
B for question 12
B for question 13
Step-by-step explanation:
U = Union
n= intercestion
B'= not b
A"= not a
so AnB'
should be B
if 2.50 = 1
2.50x8=
20
1×8 =
8
should be $8
13. The diagram shows the support bracket for a restaurant sign. AB=60 cm, AC=109 cm and ZBAD=41°. A 41° 109 cm 60 cm NOT TO SCALE B С D THE BROTHERS CONCH DINNERS Calculate (a) the length of BC [3] [3] (b) the angle C (c) [3] the length of AD
Answer:
(a) BC = 91 cm
(b) ∠C = 33.4° (nearest tenth)
(c) AD = 79.5 cm (nearest tenth)
Step-by-step explanation:
(a) Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = AB = 60 cmb = BCc = AC = 109 cm⇒ 60² + BC² = 109²
⇒ 3600 + BC² = 11881
⇒ BC² = 11881 - 3600
⇒ BC² = 8281
⇒ BC = √(8281)
⇒ BC = 91 cm
(b) Sine rule to find an angle:
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles, and a, b and c are the sides opposite the angles)
Given:
∠B = 90°b = AC = 109 cmc = AB = 60 cm[tex]\implies \dfrac{\sin (90)}{109}=\dfrac{\sin C}{60}[/tex]
[tex]\implies \sin C=60 \cdot\dfrac{\sin (90)}{109}[/tex]
[tex]\implies \sin C=\dfrac{60}{109}[/tex]
[tex]\implies C=33.39848847...\textdegree[/tex]
[tex]\implies C=33.4\textdegree \ \sf(nearest \ tenth)[/tex]
(c) Sine rule to find a side length:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles, and a, b and c are the sides opposite the angles)
Sum of interior angles of a triangle = 180°
Given:
∠B = 90°b = AD∠D= 180° - 41° - 90° = 49°d = AB = 60 cm[tex]\implies \dfrac{AD}{\sin (90)}=\dfrac{60}{\sin (49)}[/tex]
[tex]\implies AD=\sin (90) \cdot \dfrac{60}{\sin (49)}[/tex]
[tex]\implies AD=79.5007796...[/tex]
[tex]\implies AD=79.5 \ \sf cm \ (nearest \ tenth)[/tex]
What happens to the coordinates of a shape when the shape reflects about the x-axis? What happens to the
coordinates when the shape reflects about the y-axls? Explain.
Hey there!
Here's what happens to the coordinates of a point when it's reflected around the x-axis:
(x, y) --> (x, -y) or (x, -y) --> (x, y)
So the point's x-coordinate hasn't changed.
Here's what happens to the coordinates of a point when it's reflected around the y-axis:
(x, y)--> (-x, y) or (-x, y) --> (x, y)
So the point's y-coordinate hasn't changed.
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power!
If tanθ= 2/5 find cosθ using identities. This is in quad. 1.
Answer: 5/2
Step-by-step explanation:
Put the expressions in order from least to greatest.
Answer:
[tex]\frac{11^{4} }{11^{11} } ,\frac{1}{11^{-4} }, 11^{5}*11^{2}, (11^{-3})^{-3}[/tex]
Step-by-step explanation:
For this, you need to know the rules of exponents:
If the coefficient is the same, you can do things to it (which I will get into)
In this case, all the coefficients are 11, so we don't have to worry about the coefficients being different.
For the first one, you can subtract the denominator exponent by the numerator exponent like so:
[tex]11^{4} * 11^{-11} = 11^{-7}\\[/tex]
(When you multiply, you add the exponents)
Also, the rule is: [tex]x^{-y} = \frac{1}{x^{y} }[/tex] or [tex]\frac{1}{x^{-y} } = x^{y}[/tex]
For the second one, you can use the rule mentioned before:
[tex]\frac{1}{11^{-4} } = 11^{4}[/tex]
For the third one, you want to multiply the exponents (in these kinds of cases, you can multiply the exponent by the exponent)
So:
[tex](11^{-3} )^{-3} = 11^{9}[/tex]
Finally, the fourth one, you can simply just add the exponents:
[tex]11^{5} * 11^{2} = 11^{7}[/tex]
Then, just order them from least to greatest by their exponents value :)
Solve: 101x-99y=103
-99x+101y=-97
Answer:
[tex]x=2; y=1[/tex]
Step-by-step explanation:
Let's remember that if we replace one equation in a system with a linear combination of the equations (ie adding or subtracting them together, after multiplying them with some nice numbers) we are left with an equivalent system. So let's add and subtract them together, and use the new equations to work with.
[tex]I+II: 2x+2y=6\\I-II:200x-200y=200[/tex]
Better, now let's simplify the expression and let's use the new system
[tex]x+y=3\\x-y=1[/tex]
Done. At this point you can use whatever method you like to solve the system to get to the final solution. Adding and subtracting works great, and you get [tex]x=2, y=1[/tex] which, if you check by replacing in the original, is indeed a valid solution.
Need help with math probelm if do 5 stars and brainly points
Set up:-
Find volume of closet storageFind volume of each cubeDivide and get no of cubesSolution:-
Here it's a cuboid
Length=L=6.5ftBreadth=B=4ftHeight=H=12.5ftVolume:-
[tex]\\ \rm\rightarrowtail V=LBH[/tex]
[tex]\\ \rm\rightarrowtail V=6.5(4)(12.5)[/tex]
[tex]\\ \rm\rightarrowtail V=325ft^3[/tex]
For cubes
sides=0.25ftVolume:-
[tex]\\ \rm\rightarrowtail V=side^3[/tex]
[tex]\\ \rm\rightarrowtail V=(0.25)^3[/tex]
[tex]\\ \rm\rightarrowtail V=0.015625ft^3[/tex]
Now
Total cubes:-
[tex]\\ \rm\rightarrowtail \dfrac{325}{0.015625}[/tex]
[tex]\\ \rm\rightarrowtail 20800cubes[/tex]
What is the value of X?
Sin 55° = cos X.
Enter your answer in the box.
Answer:
x = 35°
Step-by-step explanation:
sin x = cos (90° - x)
sin 55° = cos (90° - 55°)
sin 55° = cos 35°
x = 35°
How do I find the difference in the simplest form?
Answer:
2
Step-by-step explanation:
[tex] \frac{8x}{4x - 7} - \frac{14}{4x - 7} \\ \\ = \frac{8x - 14}{4x - 7} \\ \\ = \frac{2 \cancel{(4x - 7)}}{\cancel{(4x - 7)}} \\ \\ = 2[/tex]
A rectangular room measures 18 ft by 37 ft. How many
square feet of tile are needed to cover the floor?
Step-by-step explanation:
the area of a rectangle is length × width.
in our case
37 × 18 = 666 ft²
so, we need 666 ft² of tiles.
Answer:
666 square feet
Step-by-step explanation:
To find the number of square feet of tile, we need to find the area:
A = L × W
A = 18 × 37
A = 666 ft²
Find a degree 3 polynomial whose coefficient of x^3 equal to 1. The zeros of this polynomial are -5, -4i, and 4i. Simplify your answer so that it has only real numbers as coefficients.
I got an answer by solving (x^3+5x^2-16x-80) but it says thats incorrect.
Answer:
x^3+5x^2+16x+80
Step-by-step explanation:
You know that you can write your polynom this way : (x-r1)(x-r2)(x-r3) with r1,r2 and r3 the roots so you get :
(x+5)(x+4i)(x-4i)
Simplify (x+4i)(x-4i) with the formula (a-b)(a+b)=a²-b²
so you have (x^2+16)=(x+4i)(x-4i)
Your polynom looks like this :
(x^2+16)(x+5) just expand it
and you get x^3+5x^2+16x+80
When 3(2x^2+4x+7)−(x^2−8x+11) is simplified, what is the coefficient of the x term?
Answer:
Step-by-step explanation:
when 3(2x^2+4x+7)−(x^2−8x+11) is solved you get
5x^2 + 20x + 10.
the x term is
−
2
+
√
2
,
0
)
,
(
−
2
−
√
2
,
0
)
[tex]3(2x^2+4x+7)-(x^2-8x+11)\\\\=6x^2 +12x + 21 -x^2+8x -11\\\\=5x^2+20x +10\\\\\text{The coefficient of the x term is 20}[/tex]
Martin is an artist who molds plaster into unique shapes.
How much plaster can Martin fit into the mold shown?
Step-by-step explanation:
the volume of this object is the sum of the volume of the 2 blocks.
the large block is a cube of 4×4×4 = 64 ft³
the small block is 1×1×2 = 2 ft³
so, in total, he can fit 64+2 = 66 ft³ of plaster into the mold.
Find the domain of
[tex]y = \frac{1}{(1 - \sin(x) } [/tex]
Let's see
Denominator must not be equal to zero or the function becomes undefined[tex]\\ \rm\rightarrowtail 1-sinx\neq 0[/tex]
[tex]\\ \rm\rightarrowtail sinx\neq 1[/tex]
[tex]\\ \rm\rightarrowtail x\neq \dfrac{n\pi}{2}[/tex]
So
[tex]\\ \rm\rightarrowtail Domain\in R-\left\{\dfrac{n\pi}{2}\right\}[/tex]
In the diagram, the length of Line segment Y Z is twice the length of Line segment A Z.
Triangle X Y Z is shown. Angle X Y Z is a right angle. An altitude is drawn from point Y to point A on size Z X to form a right angle.
Line segment Y A is an altitude of ΔXYZ. What is the length of Line segment Y A?
5 StartRoot 3 EndRoot units
10 StartRoot 3 EndRoot units
15 units
20 units
Answer:
5 startrood 3 endroot units .
The length of YA from the figure is 10√3 units
Pythagoras theoremAccording to the pythagoras theorem;
YZ² = AZ² + YA²
Given that YZ = 2AZ, hence;
20² = 10² + YA²
YA² = 400 - 100
YA² = 300
YA = √300
YA = 10√3 units
Hence the length of YA from the figure is 10√3 units
learn more on Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ9
Peter is buying a circular rug for his bedroom. The rug has an area of 40 square feet. What is the approximate diameter of the rug? Show your work or explain your answer.
The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.
What is area?Area is the amount of space occupied by a two dimensional shape or object.
The area of a circle is given by:
Area = π * diameter²/4
The rug has an area of 40 square feet. Hence:
40 = π * diameter²/4
Diameter = 7.14 feet
The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.
Find out more on area at: https://brainly.com/question/25292087
Find MQ in parallelogram LMNQ .
Answer:
MQ = 16.4
By the Parallelogram Diagonals Theorem , MP = PQ
So MQ = 2 · MP
Step-by-step explanation:
Parallelogram Diagonals Theorem
The diagonals of a parallelogram bisect each other, i.e. they divide each other into two equal parts.
P is the point of intersection of the diagonals.
Therefore, MP = PQ and LP = PN
If MP = 8.2, then PQ = 8.2
⇒ MQ = 8.2 + 8.2 = 16.4
19, 19, 27, 93, 121, 203, 291, 372, 389, 405, 453, 493, 549, 565, 775
Find the (median, mode, range, and mean) of the data set, and pls show how to find each of them.
Answer:
mean: 318.266
median: 372
mode: 19
range: 756
Step-by-step explanation:
to find the mean or the average, add all the numbers up and divide them by how many there are. example: 5 + 5 + 5 = 15 ÷ 3 = 4
to find the mode, all you have to do is find the number that is most common, there can be multiple modes
for the range, you subtract the smallest number from the largest
finally, to get the median, you put all the numbers in order from smallest to biggest and make your way to the number in the middle, if there are two numbers in the middle, add them up and divide them by two
Answer:
Mean: 298.87
Mode: 19
Median: 372
Range: 756
Step-by-step explanation:
Mean is the sum of terms over the total number of terms.
(19+19+27+93+121+203+372+389+405+453+493+549+565+775)/15 = 298.87
Mode is the most repeated term or value in the set.
(19,19,27,93,121,203,372,389,405,453,493,549,565,775) the only value repeated is 19
Median is the middle of the data set.
With 15 values the middle is 372
Range is the extent of all values between smallest and largest values
Largest values is 775, and the smallest is 19. 775-19 = 756