Suppose that the demand and supply for artificial Christmas trees is given by the functions below where p is the price of a tree in dollars and q is the quantity of trees that are demanded/supplied in hundreds. Find the price that gives the market equilibrium price and the number of trees that will be sold/bought at this price.p=109.70−0.10q (demand function)p=0.01q2+5.91 (supply function)
Answers
The equilibrium price is the price at which the demand function is equal to the supply function.
Hence it is given by:
[tex]\begin{gathered} 109.70-0.10q=0.01q^2+5.91 \\ 0.01q^2+0.10q-103.79=0 \end{gathered}[/tex]Solve the quadratic equation to get:
q=97,-107.
Now the quantity cannot be negative hence the value of q=97. Hence 97 hundred trees is the demand.
The equilibrium price is given by:
[tex]p=109.70-0.10q=100\text{ dollars}[/tex]Hence Option A is correct and the boxes to be filled is given by the statement given below:
The equilibrium price of $100 gives a demand that is equal to a supply of 97 hundred trees.
Related Questions
Which of the following represents the synthetic division form of the long division problem below? x - 3x+4/ x-5
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The number on the left in the synthetic division form is the root of the divisor polynomial. The root of x-5 is 5
The numbers on the right are the coefficients of the dividend polynomial: 1 -3 4
The correct answer is option B
Write an equation in slope-intercept form for the line with slope-2 and y-intercept 3.
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Answer:
wait I will do it
Step-by-step explanation:
i will sent it after sometimes
Can you help me i need the answers
Answers
Given that
The figure is given on the coordinate plane. And we have to find the vertices of the figure after a 90-degree clockwise rotation.
Explanation -
So the figure will be rotated from its position clockwise as
Since the given points are J(-9, -8)
K(-2, -8)
L(-2, -3)
M(-9, -3)
After rotating the points will be
J(
K(-7, -3)
L(-2, -3)
M(-2, 4)
Find the value of angle B, rounding to the nearest tenth of a degree.
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Law of Cosines.
- For a triangle ABC with sides labeled a,b, and c:
[tex]a^2=b^2+c^2-2bc\cos A[/tex][tex]b^2=a^2+c^2-2ac\cos B[/tex][tex]c^2=a^2+b^2-2ab\cos C[/tex]
Since we are asked to look for angle B, we will use
[tex]b^2=a^2+c^2-2ac\cos B[/tex]Given:
a = 12 cm
b = 8 cm
c = 15 cm
Substituting the given values to our equation:
[tex]b^2=a^2+c^2-2ac\cos B[/tex][tex](8)^2=(12)^2+(15)^2-2(12)(15)\cos B[/tex][tex]64=144+225-(360)\cos B[/tex][tex]360\cos B=369-64[/tex][tex]360\cos B=305[/tex][tex]\frac{360\cos B}{360}=\frac{305}{360}[/tex][tex]B=\cos ^{-1}\frac{305}{360}[/tex][tex]B=32.089[/tex]Since we are asked to round the answer to its nearest tenth, the final answer would be 32.1 degrees.
Evaluate the function f(x) = 5 -√x at each specified value and simplify. 1. f(9)
Answers
Answer:
f(9)=2
Explanation:
The function f(x) is defined as follows:
[tex]f(x)=5-\sqrt[]{x}[/tex]To find the value of f(9), we substitute 9 for x in f(x) as follows:
[tex]\begin{gathered} f(9)=5-\sqrt[]{9} \\ =5-3 \\ =2 \end{gathered}[/tex]21= ______hL how many hL
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We want to convert litres L to Hectolitres hL.
[tex]1L=0.01L[/tex]one litre equals 0.01 hectolitre.
So, to convert 2L to hL, we have;
[tex]\begin{gathered} 1L=0.01L \\ 2L=0.02L \end{gathered}[/tex]A company installs a rectangular septic tank 10 ft long by 15 ft wide and 8 ft deep. Calculate the capacity of the tank in gallons. (Use 1ft^3 = 7.48 gal.)The capacity of the tank is:enter your response here gallons. (Round to the nearest gallon as needed.)
Answers
To find the capacity in gallons we firs need to find the volume.
The volume is given by:
[tex]V=lwh[/tex]Plugging the values given we have:
[tex]V=(10)(15)(8)=1200ft^3[/tex]Now that we know that we need to convert it, to do this we multiply by the factor given:
[tex]1200(7.48)=8976[/tex]Therefore the capacity of the tank is 8976 gal
42.1069 rounded to the nearest thousandth is
Answers
ANSWER
42.107
EXPLANATION
To round a number to the nearest thousandth we have to look at the next number. If that number is 5 or greater than 5, then we have to add 1 to the thousandths. If it's less than 5, then we leave it like it is and eliminate the other decimals.
In this case, the next number to the thousandth is 9, which is greater than 5. Therefore, we have to turn the 6 into a 7: 42.107
Identify an equation in point-slope form for the line parallel to y = 1/2x - 7 thatpasses through (-3,-2).
Answers
ANSWER:
D.
[tex]y+2=\frac{1}{2}(x+3)[/tex]EXPLANATION:
Given:
[tex]y=\frac{1}{2}x-7[/tex]Recall that the slope-intercept form of the equation of a line is generally given as;
[tex]y=mx+b[/tex]where;
m = slope of the line
b = y-intercept of the line
Comparing both equations above, we can see that the slope(m) of the line is 1/2 and the y-intercept(b) is -7
Recall that parallel lines have the same slope. So the line that is parallel to the given line will have the same slope(m) of 1/2
Given the point (-3, -2), we can go ahead and write the equation of the parallel line in point-slope form as seen below;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=\frac{1}{2}[(x-(-3)] \\ y+2=\frac{1}{2}(x+3) \end{gathered}[/tex]Hi i need help finding the answer? If you could helpMe out?
Answers
Given:
Given a figure.
The side of the square is 8.
The radius of the semicirles is 4.
Required:
To find the perimeter of the given figure.
Explanation:
Here the circumference is
[tex]\begin{gathered} =2\pi r \\ \\ =2\times3.14\times4 \\ \\ =25.12 \end{gathered}[/tex]Now the perimeter is
[tex]\begin{gathered} =25.12\times2 \\ =50.24 \end{gathered}[/tex]Final Answer:
The perimeter of the given figure is 50.24 inches.
Solve the inequality - 12 > -16. Then graph the solution.
Answers
Solve the inequality c - 12 > -16.
[tex]\begin{gathered} c-12>-16 \\ c-12+12>-16+12 \\ c>-4 \end{gathered}[/tex]Plot the solution on the number line.
Complete the congruence statement.
Answers
Answer:
MCL
Step-by-step explanation:
Answer:
MCL
Step-by-step explanation:
the triangles are flipped in 2 directions so just write the angle like it’s opposite to each other
Hopes this helps please mark brainliest
Needing help with this practice problem please. Also, I need to show all work
Answers
ANSWER
L = 24 inches
W = 14 inches
EXPLANATION
Given tat
The length of the rectangular painting is 10 inches more than the width
Let the width of the rectangular painting be x
Recall, that the frame is 2 inches thick. This implies that there re 2 inches to the left ogf the length and 2 inches to the right of the length. So, there are more 4 inches to the length of the picture
Hence, the new length is
L = (x + 10) + 4
L = x + 10 + 4
L = x + 14
Also, for the width of the painting, we have
w = x + 4
Recall, that the area of a rectangle is given below as
Area = L x W
[tex]\begin{gathered} \text{ Area of a rectangle = L x W} \\ \text{ L = x + 14, and W = x + 4, and A = 336 in}^2 \\ \text{ 336 = \lparen x }+\text{ 14\rparen \lparen x }+\text{ 4\rparen} \\ \text{ Open the parentheses} \\ \text{ 336 = x}^2\text{ + 4x + 14x + 56} \\ \text{ 336 = x}^2\text{ + 18x + 56} \\ \text{ x}^2\text{ + 18x + 56 = 336} \\ \text{ x}^2\text{ + 18x + 56 - 336 =0} \\ \text{ x}^2\text{ + 18x - 280 = 0} \end{gathered}[/tex]Find the value of x by using factorizatin method
[tex]\begin{gathered} \text{ x}^2\text{ }+\text{ 28x - 10x - 280 = 0} \\ \text{ x\lparen x + 28\rparen - 10\lparen x + 28\rparen = 0} \\ \text{ \lparen x - 10\rparen \lparen x + 28 \rparen = 0} \\ \text{ \lparen x - 10\rparen = 0 or \lparen x + 28\rparen = 0} \\ \text{ x = 0 + 10 or x = 0 - 28} \\ \text{ x = 10 or x = -28} \end{gathered}[/tex]Find the length and the width of the rectngular painting
L = x + 14
L = 10 + 14
L = 24 inches
width
W = x + 4
W = 10 + 4
W = 14 inches
What is the value of the expression below when x = 5 and y 5? 6x — бу
Answers
We want to find the value of the given expression;
[tex]6x-6y[/tex]When x=5 and y=5;
Substituting these values in, we have;
[tex]\begin{gathered} 6(5)-6(5) \\ =30-30 \\ =0 \end{gathered}[/tex]Therefore, the answer to this question is zero.
What is the value of h? 48 sqrt 3168 sqrt 2
Answers
From definition:
[tex]\sin (angle)=\frac{\text{opposite side}}{\text{ hypotenuse}}[/tex]From the picture:
[tex]\begin{gathered} \sin (45)=\frac{8}{h} \\ \frac{1}{\sqrt[]{2}}=\frac{8}{h} \\ h=8\cdot\sqrt[]{2} \end{gathered}[/tex]Which statement justifies why ∠ABF measures 130°?Given: angles ABD and DBC are complementary
Answers
SOLUTION:
We are to find the statement that justifies why
Given that
50 degrees +
In conclusion, the justified statement is "a linear pair is two adjacent, supplementary angles.
Answer:
B
Step-by-step explanation:
another person person said it was n had 5stars
The percent markup on the cost price of a dress is the same as the cost price in dollars. If the dress is sold for $24, what was the cost price of the dress ?
Answers
Markup is the difference between a product's selling price and cost as a percentage of the cost.
If we call the cost of the dress as x, the markup is given by the following expression
[tex]markup=\frac{24-x}{x}\times100[/tex]The percent markup on the cost price of a dress is the same as the cost price in dollars, therefore, we can rewrite the previous expression as:
[tex]x=\frac{(24-x)\cdot100}{x}[/tex]Solving for x, we have:
[tex]\begin{gathered} x=\frac{(24-x)\cdot100}{x} \\ x^2=2400-100x \\ x^2+100x-2400=0 \\ \implies x=-120\:or\:x=20 \end{gathered}[/tex]Since we can't have a negative cost price, the markup is 20% and the cost price of the dress is $20.
If f(x) = x, the inverse off, f-1 could be represented by
Answers
Solution
For this case we have the following function given:
y=f(x)= x
And we want to find the inverse so we can do the following steps:
1) replace y with x
x= y
2) solve for y
y = x
Then the folution would be:
A) f-1 (x) =x
The size, x, in an automobile tire can affect its performance. Both over-sized and under-sized tires can lead to poor performance and poor mileage. The tire size that yields the best performance for the car Michael wants is given by 0.2(x - 25.5) + 0.3 = - 0.2(x - 16).Find the tire size that will yield the best performance for Michael’s car.
Answers
The tire size that will yield the best performance for Michael’s car is 20.
The equation given is,
0.2(x - 25.5) + 0.3 = - 0.2(x - 16)
From this, we have to solve for x, which will give the size of the tire.
Simplify the equation as follows to find x,
0.2(x - 25.5) + 0.2(x - 16) = - 0.3
0.2x - (0.2 × 25.5) + 0.2x - (0.2 × 16) = - 0.3
0.2x - 5.1 + 0.2x - 3.2 = - 0.3
0.4x - 8.3 = - 0.3
0.4x = - 0.3 + 8.3
0.4x = 8
x = 8/0.4 = 20.
Increasing the wheel diameter also increases the final deceleration which has two consequences. Acceleration potential is reduced but a higher final speed is achieved. In other words, the bigger the car's tires the slower it accelerates but the higher its top speed.
We recommend choosing smaller wheels for more power and as many times as possible for maximum traction. On average, a 15 x 3.75 or larger front wheel gives the best results. For the rear, a 15 x 10 wheelset is ideal.
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Create a real-world problem involving a cube - Use a perfect cube as its volume - Show using cube roots to find one edge
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PART A
A box of sugar has equal lengths of 6 inches. Calculate the volume of sugar that can fill the box.
The volume of the box can be calculated using the cubic volume formula given to be:
[tex]V=l^3[/tex]Therefore, the volume of the box of sugar is calculated to be:
[tex]\begin{gathered} V=6^3 \\ V=216\text{ cubic inches} \end{gathered}[/tex]PART B
An ice cube is said to contain a volume of 8 cubic inches of water. What will be the length of one side of the cube?
The length of the cube can be calculated using the formula:
[tex]l=\sqrt[3]{V}[/tex]Hence, we can solve to be:
[tex]\begin{gathered} l=\sqrt[3]{8} \\ l=2\text{ inches} \end{gathered}[/tex]The type and number of fish caught in the Charleston Harbor in March was recorded for a month. The results are recorded in the table below. Whatis the probability that the next fish caught is a drum or a flounder? Enter a fraction or round your answer to 4 decimal places, if necessary.Flounder262Number of Fish Caught in MarchBlack DrumBluefish336Red Drum382181Sea Trout190
Answers
1) The first thing we need to do in this question, is to find the sample space, i.e. the total number of outcomes, in this case, fishes.
[tex]262+382+181+336+190=1351[/tex]2) Since no one could pick simultaneously two types of fish, then we can tell that these events are mutually exclusive. So, we can write the following:
[tex]\begin{gathered} P(flounder)=\frac{262}{1351} \\ \\ P(black\:drum)=\frac{181}{1351} \\ \\ P(red\:drum)=\frac{382}{1351} \\ \\ P(drum\:or\:flounder)=\frac{262}{1351}+\frac{181}{1351}+\frac{382}{1351}=\frac{825}{1351}\approx0.6107 \end{gathered}[/tex]Note that by "drum" we are including black and red drum.
That is the answer.
2) Chang saves up enough money to surprise his momand buy her a new blouse for her birthday. The blousecosts about $70 and he uses a coupon for 20% off. Howmuch does he save by using the coupon?
Answers
2) Chang saves up enough money to surprise his mom and buy her a new blouse for her birthday. The blouse costs about $70 and he uses a coupon for 20% off. How much does he save by using the coupon?
_________________________________
coupon for 20% off
20% = 0.2
The total of 100% of the price minus the discount =
100% - 20% = 80% or 1- 0.2 = 0.8
So then,
$70* 0.8 = $ 56 he pays
70 - 56 = 14 he saves
__________________________
Answer
He saves 14 by using the coupon
____________________
70*0.2= 14
Determine if (−2,4) is a solution to the following system of inequalities.-3x > -7y -37x > -5y -4
Answers
Remember that ordered pairs are written in the form (x,y).
Then, to check if (-2,4) is a solution to the system of inequalities, both of the given inequalities should be verified when replacing x=-2 and y=4.
Replace x=-2 and y=4 into the inequalities and check if both of them are satisfied or not.
-3x > -7y - 3
[tex]\begin{gathered} \Rightarrow-3(-2)>-7(4)-3 \\ \Rightarrow6>-28-3 \\ \Rightarrow6>-31 \end{gathered}[/tex]Sice 6 is greater than -31, then this inequality is satisfied by (-2,4).
7x > -5y-4
[tex]\begin{gathered} \Rightarrow7(-2)>-5(4)-4 \\ \Rightarrow-14>-20-4 \\ \Rightarrow-14>-24 \end{gathered}[/tex]Since -14 is greater than -24, then this inequality is satisfied by (-2,4).
Since both inequalities are satisfied by (-2,4) then (-2,4) is a solution to the given system of inequalities.
Jeremiah wants to send some of his shirts to a dry cleaner. He usually takes his shirts
to Spot-Less Dry Cleaners, where he pays $4.50 per shirt. He sees a sign at No Mess
or Stress Dry Cleaners that says it's $21.00 to have 4 shirts cleaned. Which is the
better deal?
Answers
Answer: Spot-less dry cleaners
Step-by-step explanation:
21/4=$5.25
$4.50<$5.25
which function is equivalent to y = 3(x + 4)² + 5?A) y = 3x² + 21B) y = 3x² + 24x + 63C) y = 3x² + 24x + 53D) y = 3x² + 8x + 21
Answers
Given: The function
[tex]y=3(x+4)^2+5[/tex]To Determine: The equivalent function of the given function
Solution:
Step 1: Expand the parenthesis
[tex]\begin{gathered} y=3(x+4)^2+5 \\ (x+4)^2=(x+4)(x+4) \\ (x+4)^2=x(x+4)+4(x+4) \\ (x+4)^2=x^2+4x+4x+16 \\ (x+4)^2=x^2+8x+16 \end{gathered}[/tex]Step 2: Substitute the expanded into the function
[tex]\begin{gathered} y=3(x+4)^2+5 \\ y=3(x^2+8x+16)+5 \\ y=3x^2+24x+48+5 \\ y=3x^2+24x+53 \end{gathered}[/tex]Hence, the equivalent function to the given is y = 3x²+24x+53, OPTION C
The tables of ordered pairs represent some points on the graphs of Lines F and G.
Line F
x y
2 7
4 10.5
7 15.75
11 22.75
Line G
x y
-3 4
-2 0
1 -12
4 -24
Which system of equations represents Lines F and G?
1. y=1.75x+3.5
y=-4x-8
2. same as 1 but -8 is -2
3. 1.75 and 3.5 are switched
4. 2 and 3 combined
Answers
In linear equation, Equation for line F is y = 1.75x + 3.5 and equation for line G is y = -4x-8.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).y = 1.75x + 3.5 (For line F)
let's take the point (2,7) and put in the equation,
y = 1.75*2 + 3.5
= 3.5 +0.35
= 7
which is true.
Hence, (2,7) satisfies the equation.
y = -4x-8 (For line G)
lets take the point (-3,4) and put in the equation,
y = (-4)*(3) - 8
= 12 - 8
= 4
which is true.
Hence, (-3,4) satisfies the equation.
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give the function f(x)=-2x-5 determine the value of f(-3)
Answers
We have the next function
[tex]f(x)=-2x-5[/tex]And we must calculate f (-3).
To calculate it we must replace x = -3 in the function.
[tex]f(-3)=-2(-3)-5[/tex]Finally, we must simplify the answer
[tex]f(-3)=6-5=1[/tex]So, the answer is
[tex]f(-3)=1[/tex]acellus
Find the point-slope equation for
the line that passes through the
points (9, -9) and (-2, 13). Use the first point in your equation.
Answers
Answer:
y = -2x + 9
Step-by-step explanation:
→ Find the change in x
13 --9 = 22
→ Find the change in y
-2 - 9 = -11
→ Divide to find gradient
22 ÷ -11 = -2
→ Write in standard form
y = -2x + c
→ Substitute in ( 9 , -9 )
-9 = -18 + c
→ Find c
c = 9
→ Write in specified form
y = -2x + 9
is (18,302) a solution to the equation y=300?
Answers
No
Explanations:Note that:
the solutions to an equation are the values, if substituted into the equation, that will make the equation true.
The given equation is:
y = 300
(18, 302) means that x = 18, y = 302
Since the equation given is y = 300 and not y = 302, the point (18, 302) is not a solution to the equation.
Christina jarred 21 liters of jam after 3 days. How much jam did she jar if she spent 7 days making jam?
Answers
Answer:
49 liters
Explanation:
We know that Christina jarred 21 liters of jam in 3 days, so using this ratio, we can calculate the how much jam she jarred after 7 days as follows
[tex]7\text{ days}\times\frac{21\text{ liters}}{\text{ 3 days}}=49\text{ liters}[/tex]Therefore, the answer is 49 liters.