Step 1
Write the demand function equation
[tex]Q=-9p^2+4p\text{ + 1970}[/tex]Step 2:
To find the price and quantity which maximize the revenue
You will find the derivative of Q with respect to price
[tex]\begin{gathered} \frac{dQ}{dp}\text{ = -18p + 4} \\ -18p\text{ + 4 = 0} \\ 18p\text{ = 4} \\ p\text{ = }\frac{4}{18}\text{ = }\frac{2}{9} \end{gathered}[/tex]Step 3:
Find the quantity demand by substituting p = 2/9
[tex]\begin{gathered} Q\text{ = -9 }\times\text{ (}\frac{2}{9})^2\text{ + 4 }\times\text{ }\frac{2}{9}\text{ + 1970} \\ =\text{ -0.44 + 0.888 + 1970} \\ =\text{ 1970.444} \\ =\text{ 1970} \end{gathered}[/tex]Final answer
The price which maximizes the total revenue is p = 2/9
The quantity is Q = 1970
Identify p, q, and r if necessary. Then translate each argument to symbals and use a truth table to decide if the argument is valid or invalid.
Let p denote the statement "It snows", and q denote tthe statement "I can go snowboarding"
The we need to draw a table for
(p => q)v(-p => q)
p q -p -q p=>q -p => -q (p => q)v(-p => q)
T T F F T T T
T F F T F T T
F T T F T F T
F F T T T T T
The argument is valid, since the last column has truth all through.
evaluate each expression if x=6 x/2 +9
Answer
x = -27
Explanation
x = 6 (x/2 + 9)
x = 3x + 54
x - 3x = 54
-2x = 54
Divide both sides by -2
(-2x/-2) = (54/-2)
x = -27
Hope this Helps!!!
Stacy loaned Robert $21,370 at an interest rate of 10 % for 171 days. How much will Robert pay Stacy at the end of 171 days? Roundyour answer to the nearest cent. Note: Assume 365 days in a year and 30 days in a month.
The simple interest formula is :
[tex]A=P(1+rt)[/tex]where A is the future amount
P is the principal amount
r is the rate of interest
and
t is the time in years
From the problem, we have :
P = $21,370
r = 10% or 0.10
t = 171 days or 171/365 year
Using the formula above :
[tex]\begin{gathered} A=21370(1+0.10\times\frac{171}{365}) \\ A=22371.17 \end{gathered}[/tex]The answer is $22,371.17
4. Multiply the two polynomials using the destructive property.5. Are the two products the same when you multiply them horizontally?4. A)
Given:
[tex](4x^2-4x)(x^2-4)[/tex]To multiply the two polynomials using the distributive property, we first follow the rule shown below:
For: (a+b)(c+d)=a(c+d)+b(c+d)=ac+ad+bc+bd
We let:
[tex]\begin{gathered} a=4x^2 \\ b=-4x \\ c=x^2 \\ d=-4 \end{gathered}[/tex]Now, we plug in what we know:
[tex]\begin{gathered} (4x^{2}-4x)(x^{2}-4) \\ =(4x^2)(x^2)+(4x^2)(-4)+(-4x)(x^2)+(-4x)(-4) \\ Simplify\text{ and rearrange} \\ =4x^4-16x^2-4x^3+16x \\ =4x^4-4x^3-16x^2+16x \end{gathered}[/tex]Therefore, the answer is:
[tex]=4x^4-4x^3-16x^2+16x[/tex]2 radical 6 minus -2 radical 24 adding and subtracting radicals
Substraction:
1. Find prime factors of 24
[tex]\sqrt[]{24}=\sqrt[]{2^2\cdot6}[/tex]2. As 2 squared has a exact square root extract it from the radical:
[tex]\sqrt[]{24}=2\sqrt[]{6}[/tex]Then, you have the next expression:
[tex]\begin{gathered} 2\sqrt[]{6}-2\sqrt[]{24}=2\sqrt[]{6}-2(2\sqrt[]{6}) \\ \\ =2\sqrt[]{6}-4\sqrt[]{6} \end{gathered}[/tex]Substract similar terms (taking square root of 6 as a common factor):
[tex]\begin{gathered} =(2-4)\cdot\sqrt[]{6} \\ \\ =-2\sqrt[]{6} \end{gathered}[/tex]Brightness up inequality which can be used to determine o, The number of outfit Joseph can’t purchase well staying within his budget.
let o be the number of outfits, then
o*53.96 shoud be less than or equal to 620 - all what he bought, so:
Total money: $620
Spent money: $620 - $440.12 - $19.26 - 25.72 = $134.9
The inequality will be:
53.96o ≤ 134.9
o ≤ 2.5
What is the difference between area and perimeter of a two-dimension figure? What is the difference in the area formulas for a parallelogram and triangle
The perimeter is a measure of the distance around the shape. This means that to find the perimeter we usually are going to add the lenghts of the sides of the figure (the circle is an exception to that rule since this is a curve figure).
The are is a measure of the space inside the figure. This means that to find the area we usually are going to multiply the lenghts of the sides of the figure to get the area.
Now the area of a triangle is given as:
[tex]A=\frac{1}{2}bh[/tex]whereas the area of a paralelogram is given by:
[tex]A=bh[/tex]From this we notice that the area of the triangle is half the area of a parallelogram.
in rectangle QRST , QS = 3x+7 and RT = 5X-3.find the lengths of the diagonals of QRSTeach diagonal has a length of ....... units.
Consider the rectangle drawn below,
Consider the properties of rectangle that the opposite sides are equal, and both the diagonals are also equal in length.
[tex]QS=RT\Rightarrow3x+7=5x-3\Rightarrow5x-3x=7+3\Rightarrow2x=10\Rightarrow x=5[/tex]Thus, the value of 'x' is 5.
Substitute the value to obtain the diagonal QS as,
[tex]QS=3(5)+7=15+7=22[/tex]Similarly solve for the diagonal RT as,
[tex]RT=5(5)-3=25-3=22[/tex]Already we knew that the diagonal will be equal with the length 22 units.
I am trying to exercise but can’t do number 6
Subtract 2π to the given angle as it is equivalent to one revolution.
[tex]\begin{gathered} \frac{35\pi}{9}-2\pi \\ \frac{35\pi}{9}-\frac{18\pi}{9} \\ =\frac{17\pi}{9} \\ \\ \text{Subtracting further by }2\pi\text{ will result with coterminal angles outside the interval }(0,2\pi) \\ \\ \text{therefore, the coterminal angle of }\frac{35\pi}{9}\text{ in the interval }(0,2\pi)\text{ is } \\ \frac{17\pi}{9} \end{gathered}[/tex]I don’t know which one it’s going to be maybe A?
SOLUTION
We want to find which region has a population less than 60 animals in the diagram below
Population desity is calculated as
[tex]\text{Population density = }\frac{\text{ number of animals }}{\text{area of region }}[/tex]So let's get the areas of triangles A, B, C, and D we have
[tex]\begin{gathered} \text{area of triangle =}\frac{1}{2}\times base\times\text{height} \\ A=\frac{1}{2}\times40\times35=700m^2 \\ B=\frac{1}{2}\times50\times38=950m^2 \\ C=\frac{1}{2}\times49\times42=1,029m^2 \\ D=\frac{1}{2}\times32\times51=816m^2 \end{gathered}[/tex]Population density for each becomes
[tex]\begin{gathered} \text{Population density = }\frac{\text{ number of animals }}{\text{area of region }} \\ \text{For A = }\frac{\text{ 42500 }}{\text{700 }}=60.714\cong61\text{ animals } \\ \text{For B = }\frac{60800}{950}=64\text{ animals } \\ \text{For C = }\frac{57300}{1029}=55.685\cong56\text{ animals } \\ \text{For D = }\frac{49200}{816}=60.29\cong60\text{ animals } \end{gathered}[/tex]Region C has a population density of 56 animals per square mile, which is less than 60.
Hence the answer is region C, option C
step by step on how to solve 3/4 - 1/2 × 7/8
EXPLANATION
Given the following operation:
3/4 - 1/2*7/8
First, let's solve 1/2*7/8:
Multiply fractions: a/b* c/d = (a*c)/(b*d)
[tex]=\frac{1\cdot7}{2\cdot8}[/tex]Multiply the numbers: 1*7 = 7
[tex]=\frac{7}{2\cdot8}[/tex]Multiply the numbers 2*8=16
[tex]=\frac{3}{4}-\frac{7}{16}[/tex]Now, we need the Least Common Multiplier of 4, 16:
The LCM of a, b is the samllest positive number that is divisible by both a and b:
Prime factorization of 4:
4 divides by 2 ---> 4= 2*2
2 is a primer number, therefore no further factorization is possible.
Prime factorization of 16:
Multiply each factor the greatest number of times it occurs in either 4 or 16
= 2*2*2*2
Multiply the numbers: 2*2*2*2 = 16
Adjust fractions based on LCM
For 3/4: multiply the denominator and numerator by 4
[tex]\frac{3}{4}=\frac{3\cdot4}{3\cdot4}=\frac{12}{16}[/tex][tex]=\frac{12}{16}-\frac{7}{16}[/tex]Since the denominators are equal, combine the fractions:
[tex]=\frac{12-7}{16}[/tex]Subtract the numbers: 12-7 = 5
[tex]=\frac{5}{16}[/tex]queremos hacer una tetra brik de base cuadrada de 8cm de lado y con capacidad de 2l¿cuanto cartón necesitaremos ?
transformamos las unidades de litros a centimetros cubicos, esto es:
1 L = 1000 cm3
2L = 2000 cm3
hallamos el area de la base
[tex]A=L^2=8^2=64cm^2[/tex][tex]\begin{gathered} V=A\times h \\ 2000=64\times h \\ \frac{2000}{64}=\frac{64h}{64} \\ h=31.25 \end{gathered}[/tex]hallamos el area lateral
[tex]Alateral=P\times h=(4\times8)\times31.25=32\times31.25=1000cm^2[/tex]luego el area total
[tex]\text{Atotal}=2Abase+Alateral=2(64)+1000=128+1000=1128\operatorname{cm}[/tex]respuesta: se necesitan 1128 cm2 de carton
Suppose you pick a card out of a standard deck of 52 cards. What is the probability that you will choose a spade? Express your answer as a fraction.
hello
to solve this problem, we should understand that a standard deck of cards have 52 cards which consists of 13 spade.
the probability of choosing a spade is
[tex]\frac{13}{52}=\frac{1}{4}[/tex]the answer to this question is 1/4
Which describes the effect of the transformations on the graph of f(x) = x? when changed to f(x) = - = (x - 2) = 3?A)B)reflected over x-axis, stretched vertically, shifted left 2 units, and shifteddown 3 unitsreflected over x-axis, compressed vertically, shifted right 2 units, and shiftedup 3 unitsreflected over y-axis, stretched vertically, shifted left 2 units, and shifteddown 3 unitsreflected over y-axis, compressed vertically, shifted right 2 units, and shiftedup 3 units09D)
Let me start by telling you that there is a typo in the actual question (given the answers they provide for selection)
I am going to tell you the transformations that have been applied to change the function:
[tex]f(x)=x^2[/tex]into the function:
[tex]f(x)=\frac{1}{8}(x-2)^2+3[/tex]Then, these transformations consist on:
a reflection around the x axis (due to the negative sign in front),
a horizontal shift in TWO units to the right (given by the subtraction of 2 inside the parenthesis,
then a vertical compression in 1/8 (due to the factor 1/8 outside the parenthesis
and then a vertical shift of 3 units UP due to the +3 added at the end
Then, please select answer B in the list provided
Hi, can you help me to solve this exercise please!
Step 1:
Write the equation
[tex]\sin (\theta\text{) = }\frac{5}{13}[/tex]Step 2:
Write the trigonometric inverse identity
[tex]\csc (\theta)\text{ = }\frac{1}{\sin \theta}[/tex]Step 3:
Substitute in the equation
[tex]\begin{gathered} \csc (\theta)\text{ = }\frac{1}{\frac{5}{13}} \\ \csc (\theta)\text{ = }\frac{13}{5} \end{gathered}[/tex]Final answer
[tex]csc(\theta)\text{ = }\frac{13}{5}[/tex]Solve the following system of equations for all three variables.-8x – 3y + 5z = -2X-2y – 5z = -94x + 7y + 5z = 4
In order to solve this system of equations, first let's add the second equation to the first and third ones:
[tex]\begin{gathered} \begin{cases}-8x-3y+5z+(x-2y-5z)=-2+(-9) \\ 4x+7y+5z+(x-2y-5z)=4+(-9)\end{cases} \\ \begin{cases}-7x-5y=-11 \\ 5x+5y=-5\end{cases} \end{gathered}[/tex]Now, adding the two resulting equations, we have:
[tex]\begin{gathered} -7x-5y+(5x+5y)=-11+(-5) \\ -2x=-16 \\ x=8 \\ \\ 5x+5y=-5 \\ 40+5y=-5 \\ 5y=-45 \\ y=-9 \\ \\ x-2y-5z=-9 \\ 8+18-5z=-9 \\ -5z=-35 \\ z=7 \end{gathered}[/tex]So the solution for this system is x = 8, y = -9 and z = 7.
Find the area of the circle with the diameter 8yd use the 3.14 for pie don’t round
Given:
a.) A circle with a diameter of 8 yards.
For us to get the area of the circle, we will be using the following formula:
[tex]\text{ Area = }\frac{\pi D^2}{4}[/tex]Where,
D = the diameter of the circle = 8 yards
We get,
[tex]\text{ Area = }\frac{\pi D^2}{4}[/tex][tex]\text{ = }\frac{(3.14)(8)^2}{4}[/tex][tex]\text{ = }\frac{(3.14)(64)}{4}[/tex][tex]\text{ = (3.14)(16)}[/tex][tex]\text{ Area = }50.24yd^2[/tex]Answer: 50.24 square yards
Amount of $28,000 is borrowed for nine years at 3.25 interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?Round your answer to the nearest dollar$=
Given:
Principal amount = $28,000
Time period = 9 years
Interest rate = 3.25
Required:
Find the total amount at the end of the period.
Explanation:
The amount formula when the interest is compounded annually is given by the formula:
[tex]A=P(1+r)^{nt}[/tex]Where P =principal amount
r = rate of interest
T = time period
n = Number of time
Substitute the given values in the amount formula.
[tex]\begin{gathered} A=28,000(1+0.0325)^9 \\ A=28,000(1.33355) \\ A=37,339.51 \\ A=37,340 \end{gathered}[/tex]Final Answer:
Thus the amount after 9 years is $37,340.
ten years ago a man's age was 6 times the age of his son 12 years later the age of the Son will be 27 years what is the present age of his father
From this problem let's begin with some notation: Let the man age denoted by M. With the info provided we can do this:
Son age = 27-12= 15
Finally with the condition given we can createthe following equation:
[tex]M-10=6(15-10)[/tex]And solving for M we got:
[tex]M=6\cdot(5)+10=40[/tex]So then basically the answer for the men age is 40 years
Hey can someone please help me with this problem? I would appreciate the help tysm!
Answer:
18m2
Step-by-step explanation:
1) To win the small county lottery, one must correctly select 3 numbers from 30 numbers. The order in which the selection is made does not matter. How many different selections are possible?
This problem involves combination with taken n Items taken r at a time
The formula for this combination is :
[tex]nC_r=\frac{n!}{(n-r)!r!}[/tex]Where n is the total number of items
and r is the objects taken at a time
The factorial, n! denotes n x (n-1) x (n-2) x (n-3) x ... x (1)
For example :
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 24
Now from the given problem :
we have n = 30 numbers
r = selection of 3
Then the formula will be :
[tex]30C_3=\frac{30!}{(30-3)!\times3!}[/tex]Simplifying :
27 up to 1 will be cancelled from numerator and the denominator..
Evaluating the expression will be :
24360/6 = 4060
The answer is 4060
At Tim Hortons, mike bought three coffees and 1 doughnut for $19. Bob bought one coffee and one doughnut for $9. Using the price of one coffee=c and the price of one doughnut=d . Answer the following questions 14,15,16 and 17
So first of all we need to write an algebraic equation for Mike. We know that he bought 3 coffees and 1 doughnut. Then the total price of these things is:
[tex]3c+1d=3c+d[/tex]And we know that he had to pay $19 so this expression is equal to 19:
[tex]3c+d=19[/tex]Then the answer to question 14 is the second option.
Bob bought one coffee and one doughnut so the total cost of his purchase is:
[tex]c+d[/tex]We know that this cost is equal to $9 so we get:
[tex]c+d=9[/tex]And the answer to question 15 is the third option.
In question2 16 and 17 we need to find c and d. For this purpose we need to use the algebraic equations for Mike and Bob:
[tex]\begin{gathered} 3c+d=19 \\ c+d=9 \end{gathered}[/tex]Let's take the second equation and substract c from both sides:
[tex]\begin{gathered} c+d-c=9-c \\ d=9-c \end{gathered}[/tex]Now we substitute this expression in place of d in the first equation:
[tex]\begin{gathered} 3c+d=3c+(9-c)=19 \\ 3c+9-c=19 \\ 2c+9=19 \end{gathered}[/tex]Now we substract 9 from both sides:
[tex]\begin{gathered} 2c+9-9=19-9 \\ 2c=10 \end{gathered}[/tex]And we divide both sides by 2:
[tex]\begin{gathered} \frac{2c}{2}=\frac{10}{2} \\ c=5 \end{gathered}[/tex]Then the price of one coffee is $5 so the answer to question 16 is the third option.
Now we are going to take the equation for Bob and take c=5:
[tex]c+d=5+d=9[/tex]If we substract 5 from both sides we get:
[tex]\begin{gathered} 5+d-5=9-5 \\ d=4 \end{gathered}[/tex]Then the price of one doughnut is $4 and the answer to question 17 is the second option.
Which equation shows that the Pythagorean identity is true for 0=3pi/2
Answer:
Given that,
To find the equation which shows Pythagoras identity is true for theta=3 pi/2
The equation is of the form,
[tex]\sin ^2(\frac{3\pi}{2})+\cos ^2(\frac{3\pi}{2})=1[/tex]we have that,
[tex]\frac{3\pi}{2}=\pi+\frac{\pi}{2}[/tex]Using this we get,
[tex]\begin{gathered} \sin \frac{3\pi}{2}=\sin (\pi+\frac{\pi}{2}) \\ =-\sin (\frac{\pi}{2}) \\ \sin \frac{3\pi}{2}=-1----\mleft(1\mright) \end{gathered}[/tex][tex]\cos \frac{3\pi}{2}=\cos (\pi+\frac{\pi}{2})=0-----(2)[/tex]Substitute the values in the given equation we get,
[tex](-1)^2+0^2=1[/tex]Answer is: Option B:
[tex](-1)^2+0^2=1[/tex]You need 3 sticks of butter for every 24 cookies you bake. How many cookies can I make with 5 sticks?
ANSWER
[tex]40\text{ cookies}[/tex]EXPLANATION
We want to find the number of cookies that can be made with 5 sticks.
To solve this, we have to apply proportions. Let the number of cookies that can be made be x.
We have that:
[tex]\begin{gathered} 3s=24c \\ 5s=x \end{gathered}[/tex]Now, cross-multiply:
[tex]\begin{gathered} 3\cdot x=24\cdot5 \\ \Rightarrow x=\frac{24\cdot5}{3} \\ x=40\text{ cookies} \end{gathered}[/tex]That is the number of cookies that can be made.
1.1.22Question HelpAngie and Kenny play online video games. Angie buys 1 software package and 3 months of game play, Kenny buys 2 software packages and 2 months of gameplay. Each software package costs $25. If their total cost is $125, what is the cost of one month of game play?
We have a system of linear equations:
Let S be the price of software package and M be the price of the month of game play.
Angie buys 1 software package and 3 months of gameplay, while Kenny buys 2 software packages and 2 months of game play. The total cost for them is $125.
We can write this as:
[tex]\begin{gathered} (1S+3M)+(2S+2M)=125 \\ 3S+5M=125 \end{gathered}[/tex]We also know that each software package cost $25. This can be written as:
[tex]S=25[/tex]We can replace this last equation in the first one, and calculate M:
[tex]\begin{gathered} 3S+5M=125 \\ 3(25)+5M=125 \\ 75+5M=125 \\ 5M=125-75 \\ 5M=50 \\ M=\frac{50}{5} \\ M=10 \end{gathered}[/tex]The cost of one month of game play is $10.
Based only on the information given in the diagram, which congruencetheorems or postulates could be given as reasons why ACDE=A OPQ?Check all that apply.СA. ASAB. HAC. SASD. LLE. HLF. AAS
The postulates of congruence for right triangles are
• Hypotenuse-Leg Theorem.
,• Leg-Leg Theorem.
,• Leg-Acute Angle Theorem.
,• Hypotenuse-Acute Angle Theorem.
In this case, we know that sides CE and OQ are congruent. (hypotenuses are congruent)
Angle C is congruent to angle O.
Angle E is congruent to angle Q.
To demonstrate the congruence between triangles we can use Hypotenuse-Acute Angle Theorem since they are congruent between triangles.
We can also use Hypotenuse-Leg Theorem because we have corresponding legs and hypotenuses congruent.
The hypotenuse-acute angle theorem states that two right triangles are congruent if they have congruent hypotenuse and one corresponding pair of acute angles congruent.
The hypotenuse-leg theorem states that two right triangles are congruent if they have congruent hypotenuse and one corresponding pair of congruent legs.
Therefore, the right choices are B and E.Which of the following describes the transformation of the graph y = x 2 in graphing y = -x 2 - 5?reflect over the x-axis and shift down 5reflect over the y-axis and shift down 5reflect over the x-axis and shift left 5
The parent function of the graph is,
[tex]y=x^2[/tex]The transformed image of the graph is,
[tex]y_1=-x^2-5[/tex]Let us sketch out the graph of both the parent function and the transformed function.
From the image above, the parent function, y=x² was first reflected over the y-axis. Therefore, the transformation resulted into y= -x² .
After that, it was now shifted down by 5 units, which now resulted into
[tex]y=-x^2-5[/tex]Hence, the correct answer is B(Second option), which is the parent function was reflected over the y-axis and shifted downward by 5 units.
2xsquare +17x-30Need to factor completelyAnswer is. (2x-3)(x+10)But, how to get to that answer????
Answer:
(2x-3)(x+10)
Explanation:
Given the expression 2x^2+17x-30, we are to factorize completely
2x^2+17x-30
= (2x^2+20x)-(3x-30)
Factor out the common terms
= 2x(x+10)-3(x+10)
= (2x-3)(x+10)
This gives the required factor
Hello, I need help with this precalculus homework question, please?HW Q8
Solution
Given the logarithmic statement below
[tex]\ln7=x[/tex]To change the statement to an exponential statement, we apply an exponent to both sides
[tex]e^{\ln7}=e^x[/tex]Simplifying the expression above gives
[tex]\begin{gathered} 7=e^x \\ e^x=7 \end{gathered}[/tex]Hence, the exponential statement is
[tex]e^x=7[/tex]what is 5-2 squared plus 8/4=
Question:
what is 5-2 squared plus 8/4:
Solution:
Notice that:
[tex](5-2)^2+\frac{8}{4}\text{ = }3^2\text{ + 2 = 9 +2}=11[/tex]then, we can conclude that the correct answer is:
[tex]11[/tex]
Answer:
Step-by-step explanation:
1. 5-2=3
2. 8/4=2
3. (3x3)+2
4. 9+2
5. 11