15)The demand equation for a certain product is given by the formulap = 32-10.0001x+1where x is the number of units sold in a month and p is the price perunit. If the price is set at $14.75 for the month, how many units will be sold?
Answers
The demand equation is given to be:
[tex]p=32-\sqrt{0.0001x+1}[/tex]where p is the price and x is the number of units sold.
If the price per unit is $14.75, the number of units will be calculated as follows:
[tex]\begin{gathered} p=14.75 \\ \therefore \\ 14.75=32-\sqrt{0.0001x+1} \end{gathered}[/tex]Subtracting 32 from both sides, we have:
[tex]\begin{gathered} -\sqrt{0.0001x+1}=14.75-32 \\ -\sqrt{0.0001x+1}=-17.25 \end{gathered}[/tex]Multiply both sides by -1:
[tex]\sqrt{0.0001x+1}=17.25[/tex]Square both sides:
[tex]\begin{gathered} 0.0001x+1=17.25^2 \\ 0.0001x+1=297.5625 \end{gathered}[/tex]Subtract 1 from both sides:
[tex]\begin{gathered} 0.0001x=297.5625-1 \\ 0.0001x=296.5626 \end{gathered}[/tex]Divide both sides by 0.0001:
[tex]\begin{gathered} x=\frac{296.5625}{0.0001} \\ x=2965625 \end{gathered}[/tex]The number of units sold will be 2,965,625 units.
Related Questions
Justin deposited $4000 into an account with 5.5% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have inthe account after 10 years?Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
First, divide the annual interest rate by 2 to find the semiannual interest rate:
[tex]\frac{5.5}{2}=2.75[/tex]Next, identify the number of periods when the 2.75% increase will be appliad. In a period of 10 years, there are 20 semiannual periods.
Each period, the initial investment gets multiplied by a factor of:
[tex]1+\frac{2.75}{100}=1+0.0275=1.0275[/tex]Over 20 semiannual periods, the initial investment will get multiplied by a factor of:
[tex]1.0275^{20}[/tex]Therefore, after 10 years, the amount of money in the account is:
[tex]\begin{gathered} 4000\times(1.0275)^{20}=4000\times1.7204\ldots \\ =6881.7137\ldots \end{gathered}[/tex]To the nearest cent, the amount of money in the account will be:
[tex]6881.71[/tex]What is the value of x? 50 points
Answers
Answer:
x=25
vertical angles are congruent so
4x-25=75
+25
4x=100
÷4
x=25
Answer:
x = 25°
Step-by-step explanation:
We know that,
→ opposite angles are equal.
Forming the equation,
→ (4x - 25)° = 75°
Now the value of x will be,
→ (4x - 25)° = 75°
→ 4x = 75° + 25°
→ x = 100°/4
→ [ x = 25° ]
Hence, the value of x is 25°.
Kevin needs to have a toilet Kevin needs to have a toilet repaired in his house. The cost of the new plumbing fixtures is $160 and the labor is $50/hr.(a) Write a model that represents the cost of the repair C (in $) in terms of the number of hours of labor x.
Answers
Given that:
Cost of the new plumbing fixtures = $160
Labor charge per hour = $50
Let x denotes the number of hours of labor. Then,
[tex]\begin{gathered} \text{Cost of repair = Cost of the new plumbing fixtures+Labor charge per } \\ \text{hour}\cdot Number\text{ of hours of labor} \\ C=160+50x \end{gathered}[/tex]It represents the required relation.
help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Annie wants to arrange several plates of fruit so that each plate
has the same number of apples and the same number of apricots.
What is the greatest number of plates Annie can arrange if she
plans to use 8 apples and 20 apricots? How many apples and
how many apricots will be on each plate?
Answers
The greatest number of plates Annie can arrange if she plans to use 8 apples and 20 apricots is 4 plates.
The number of apples Annie can arrange on each plate is 2The number of apricots Annie can arrange on each plates is 5What is the greatest number of plates Annie can arrange?Number of apples = 8Number of apricots = 20To find the greatest number of plates Annie can arrange, find the greatest common factor of and 20;
8 = 1, 2, 4, and 8
20 = 1, 2, 4, 5, 10, and 20
The greatest common factor of 8 and 20 is 4
Number of apples on each plate = 8/4
= 2
Number of apricots on each plate = 20/4
= 5
In conclusion, the greatest number of plates is 4 consisting of 2 apples and 5 apricots each.
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Answer:
Step-by-step explanation:
i am also confused with this one so...
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Order from least to greatest. -0.36, 0.65 , - 8/15, 1/5
Answers
Step-by-step explanation:
Order from least to greatest. -0.36, 0.65 , - 8/15, 1/5
-0.36 = -0.36
0.65 = 0.65
- 8/15 = - 0.533333
1/5 = 0.2
least to greatest:
- 8/15 , -0.36 , 1/5 , 0.65
Mr. Jones bought 2 and 1/7 lb. of salmon. He cooked 1/5 of it for lunch. How much salmon did he have left over?
Answers
Answer:
[tex]1\frac{5}{7}\text{ lb}[/tex]
Step-by-step explanation:
First, convert [tex]2\frac{1}{7}\text{ lb}[/tex] to an improper fraction (to make the math easier):
[tex]2\frac{1}{7}=\frac{15}{7}\text{ lb}[/tex]
Next, since the question asks about how much salmon is left over, find that fraction. After cooking one-fifth of the salmon, four-fifths remain:
[tex]\frac{5}{5}-\frac{1}{5}=\frac{4}{5}[/tex]
Then, multiply the two:
[tex]\frac{15}{7}\times\frac{4}{5}=\frac{60}{35}\text{ lb}[/tex]
Finally, convert back to a mixed fraction:
[tex]\frac{60}{35}\text{ lb}=1\frac{25}{35}\text{ lb}=1\frac{5}{7}\text{ lb}[/tex]
Re-write 2/5 1/15 as a unit rate
Answers
Answer:
6:1
Step-by-step explanation:
I helped a student with this answer
Which of the following graphs is described by the function given below?
y=x²-4x-12
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answers
B. graph B
Represents the quadratic equation y=x²-4x-12 with D > 0 . So the equation represents 2 zeros which comes to be 6 and -2.
What is Quadratic equation ??
A second-degree polynomial equation, which must contain at least one squared component, is what is known as a quadratic. Quadratic equations is another name for them. The quadratic equation's general form is as follows:
ax + by +c = 0
How to draw Graph of Quadratic equation ?
To draw the graph of quadratic equation:
First find the minima of the graph Then, calculate the zeros.Finally plot it and draw the graph.Given quadratic equation,
x²-4x-12 = y
Put y = 0
So we get zeros as 6 and -2
Hence the graph will cut the X axis at 6 and -2
We get the desired graph as graph B.
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Graph the line by locating ant tow order of pairs
Answers
start by writing the equation in standard form
[tex]-x+2y=0[/tex][tex]\begin{gathered} 2y=x \\ y=\frac{x}{2} \end{gathered}[/tex]then give values to x
for x=2
[tex]\begin{gathered} y=\frac{2}{2} \\ y=1 \\ A\colon(2,1) \end{gathered}[/tex]for x=4
[tex]\begin{gathered} y=\frac{4}{2} \\ y=2 \\ B\colon(4,2) \end{gathered}[/tex]Which of the following quantities are directly proportional?
the amount of homework received by an RSM teacher and the time that the teacher
spent grading it PLS HELP I WILL GIVE BRAINLEIST
Answers
The amount of homework received by an RSM teacher and the time that the teacher spent grading it is the case of directly proportional.
What are direct and indirect variations ?
One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.
When one parameter declines while the other rises or vice versa, this is known as inverse variation. This means that the magnitude or absolute value of one item decreases as the other quantity rises, resulting in a constant value for their product. This item is also referred to as the proportionality constant.
Direct proportion occurs when one value increases and the other also increases
As the amount of homework received by an RSM teacher increases, the time that the teacher spent grading it also increases.
So, this is a case of directly proportional.
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Please i need your help! What is the slope of each line segment of QRS
Answers
Answer:ez 90 degrees
Step-by-step explanation:
What value of x is in the solution set of the inequality 4x – 12 ≤ 16 + 8x?
–10
–9
–8
–7
Answers
Answer:
-7
Step-by-step explanation:
[tex]4x-12 \leq 16+8x \\ \\ -12 \leq 16+4x \\ \\ -28 \leq 4x \\ \\ 4x \geq -28 \\ \\ x \geq -7[/tex]
PLEASE I NEED HELP RIGHT AWAY
What is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1) ?
Responses
y+4=11/6(x+1)
=
y+1=6/11(x+4)
y−1=6/11(x−4)
y+1=6/7(x+4)
Answers
y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two points are (7, 5) and (−4, −1)
m=-1-5/-4-7
=-6/-11
=6/11
The point slope intercept form is y- y₁=m(x-x₁) through (-4,-1)
y-(-1)=6/11(x-(-4))
y+1=6/11(x+4)
Hence, y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).
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Kala and josh walk around a track.kala walks each lap in 6 minutes. josh walks each lap in 10 minutes. the two of them begin at the starting line at the same time. they walk until they meet again at the starting line. how many laps does kala complete?
Answers
Kala has done 5 laps in 30 minutes
10, 20, 30
Josh has done 3 laps in 30 minutes
Kala needs to do 5 laps to meet Josh at the line because 30 is the common number in the two people
A person is riding a 14 kg bike at velocity of 18m/s. The mass of the person is 60kg. What is the momentum of the person and the bike?
Answers
The momentum of the person is zero and the momentum of the bike is 1332.
A person is riding a 14 kg bike at velocity of 18m/s
The momentum of bike = mass x velocity
p = (14 + 60) 18
= 1332
The velocity of the person with respect to the bike is 0
p = mv
p = 60 x 0
p = 0
Therefore, the momentum of the person is zero and the momentum of the bike is 1332.
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If you invest $1500 in at an interest rate of 7% for 5 years and the interest is compounded quarterly, how much money will you have after the 5 years? Round your answer to the nearest cent.
Answers
Answer:
$2122.17 (correct to the nearest cent).
Explanation:
To find the amount after 5 years, we use the compound interest formula below:
[tex]\begin{gathered} A=P(1+\frac{i}{k})^{nk} \\ \text{Principal, P}=1500 \\ Interest\text{ Rate, i =7\%} \\ \text{Period, k=4 (Quarterly)} \\ \text{Number of years, n=5} \end{gathered}[/tex]Substitute the given values:
[tex]\begin{gathered} A=1500(1+\frac{0.07}{4})^{4\times5} \\ =1500(1+0.0175)^{20} \\ =1500(1.0175)^{20} \\ =\$2122.17 \end{gathered}[/tex]After 5 years, you will have $2122.17 (correct to the nearest cent).
Enter your answer and show all the steps that you use to solve this problem in the space provided. Convert the map scale to a unit rate. How many inches represent one mile? Show your work. Interpret the meaning of the unit rate. 3/ 10 in . = 7 /8 mi . please fast i dont have much time
Answers
The map, every 1-inch drawing represents 2.917 miles in reality, using conversation.
What is conversation ?
A unit's use depends on the context; for example, a room's area is expressed in metres, yet a pencil's length and thickness are expressed in centimetres and millimetres, respectively.
Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion.
When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.
In the map, every 1 inch drawing represents 2.917 miles in reality.
the meaning of the unit rate. 3/ 10 in. = 7 /8 mi
1 in = (7/8) mi ÷ (3/10)
= 7/8 * (10/3) = 70/24
1 in = (70/24) mi
Hence the map, every 1-inch drawing represents 2.917 miles in reality.
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Help me please I haven't been able to understand his stuff
Answers
This pattern is additive because when we add 6 to x we get y
12+6=18
24+6=30
48+6=54
60+6=66
so the answer is D
Graph the linear inequality & find the coordinates 2x-y<2
Answers
Answer:
(1,0) (0,-2)
Step-by-step explanation:
Which list shows all the factors of 16? 1,4, 16 1, 2, 8, 16 1, 2, 4, 8, 16 1,2,4,6,8,16
Answers
evaluate the expression [tex]{ - 4}^{2} [/tex]
Answers
Step 1: Let's evaluate the following expression
[tex](-4)^2[/tex]Step 2: Solve the exponent expression:
[tex](-4)^2\text{ = -4 }\ast\text{ - 4 = 16}[/tex]The correct answer is 16.
For the second case, we apply the same principle:
[tex]-5^2\ast4\text{ = -5}\ast\text{ -5 }\cdot\text{ 4 = 25 }\ast4\text{ = 100}[/tex]Find the area of the polygon. (hint: you need to solve for missing apothem or sides).Also round the area to the nearest whole number
Answers
Solution
The hexagon given is a regular hexagon. With apothem of 15 in
Area of a hexagon =
[tex]\begin{gathered} =\frac{1}{2}\times a\times P \\ \text{where a = apothem} \\ p=\text{perimeter of the hexagon} \end{gathered}[/tex]Let us calculate the perimeter of the hexagon
From the triangle above,
[tex]\begin{gathered} \text{tan 60=}\frac{15}{x} \\ x\text{ tan 60 = 15} \\ x=\frac{15}{\tan 60} \\ x=5\sqrt[]{3} \end{gathered}[/tex][tex]\text{The side length of the hexagon = 2x = 2(5}\sqrt[]{3})\text{ = 10}\sqrt[]{3}\text{ in}[/tex][tex]\text{The perimeter of the hexagon = 6 x 10}\sqrt[]{3}\text{ = 60}\sqrt[]{3}\text{ in}[/tex][tex]\begin{gathered} \text{Area of the hexagon = }\frac{1}{2}\times a\times P \\ =\frac{1}{2}\text{ x 15 x 60}\sqrt[]{3} \\ =779.42in^2 \\ \\ Hence,\text{ the area of the polygon is }779in^2\text{ (to nearest wholw number)} \end{gathered}[/tex]Lucy needs to memorize words on a vocabulary list for Korean class. She has memorized 20 of the words, which is four-fifths of the list. How many words are on the list?
Answers
Given:
Lucy needs to memorize words on a vocabulary list for Korean class.
Let the number of words on the list = x
She has memorized 20 of the words, which is four-fifths of the list.
So, we can write the following equation:
[tex]\frac{4}{5}x=20[/tex]Solve the equation for (x), multiply both sides by 5/4
[tex]\begin{gathered} \frac{5}{4}*\frac{4}{5}x=\frac{5}{4}*20 \\ \\ x=\frac{100}{4}=25 \end{gathered}[/tex]So, the answer will be:
The number of words on the list = 25
A cylindrical well has a radius of 8 feet and a height of 13 feet. What is the volume of the well? Use 3.14 for pi round your answer to the nearest hundredth
Answers
The volume of A cylindrical well has a radius of 8 feet and a height of 13 feet will be 2612.48 feet³ as the definition of volume says, "The space occupied within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's capacity."
What is volume of cylinder?Each object in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's capacity.
Here,
Volume=πr²h
r=8 feet
h=13 feet
Volume=π*8²*13
π=3.14
volume=3.14*64*13
volume=2612.48 feet³
According to the definition of volume, a cylindrical well with a radius of 8 feet and a height of 13 feet will have a volume of 2612.48 feet³ "The volume of an object is the area occupied within its three-dimensional boundaries. It is additionally known as an object's capacity."
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Malena is in a book club. The graph shows a proportional relationship between the number of the books Malena has read and the number of the years she has been in the club.
Answers
Given:
There are given the graph to find the slope:
Explanation:
To find the slope, we need to select two intersecting points.
So,
The two points are:
[tex](2,30),(4,60)[/tex]Now,
From the formula to find the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then,
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{60-30}{4-2} \\ m=\frac{30}{2} \\ m=15 \end{gathered}[/tex]So,
The slope of the given line is 15.
Final answer:
Hence, the correct option is D.
The Senate in a certain state is comprised of 59 Republicans, 39 Democrats, and 2 Independents. How many committees can be formed if each committee musthave 3 Republicans and 2 Democrats?
Answers
Given:
There are given that the Senate in a certain state is comprised of 59 Republicans, 39 Democrats, and 2 Independents.
Explanation:
According to the question, the committees must have 3 Republicans and 2 democrats
That means,
Choose 3 Republicans from 59 Republicans and 2 democrats from 39 Democrats.
The,
[tex](59\text{ choose 3)(39 choose 2)}[/tex]So,
[tex](59C_3)(39C_2)_{}[/tex]Then,
From the formula of combination:
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]Then,
[tex](59C_3)(39C_2)_{}=(\frac{59!}{3!(59-3)!})(\frac{39!}{2!(39-2)!}[/tex]Then,
[tex]\begin{gathered} (59C_3)(39C_2)_{}=(\frac{59!}{3!(59-3)!})(\frac{39!}{2!(39-2)!} \\ =(\frac{59!}{3!(56)!})(\frac{39!}{2!(37)!}) \\ =(\frac{59\times58\times57\times56!}{3!(56)!})(\frac{39\times38\times37!}{2!(37)!}) \\ =(\frac{59\times58\times57}{3!})(\frac{39\times38}{2!}) \end{gathered}[/tex]Then,
[tex]\begin{gathered} (\frac{59\times58\times57}{3!})(\frac{39\times38}{2!})=(\frac{59\times58\times57}{3\times2\times1})(\frac{39\times38}{2}) \\ =(\frac{59\times58\times57}{6})(\frac{39\times38}{2}) \\ =\frac{289070028}{12} \\ =24089169 \end{gathered}[/tex]Final answer:
Hence, 24089169 committees can be formed.
solve the system of equations by the addition method3x - 7y = 45x - 5y = 4
Answers
List all numbers from given set that are a. Natural numbers, b. Whole numbers, c. Integers, d. Rational numbers, e. Irrational numbers, f. Real numbers {-6,-3/5,0,0.25,2.4}
Answers
(a) Natural Numers: root 81 = 9
(b) Whole Numbers: 0, root 81 = 9
(c
g(x) = 5x? – 9x - 7x + 12) What is the degree of the following polynomial?
Answers
Leading coefficient means the number that goes multiplicating the bigger exponent ,in this case is -9 because -9 multiplies x^3
Leading coefficient is the bigger exponent in a polynomial. In this case is 3 ,because -9x^3 is the biggest number in exponent.
So finally is a third degree equation.