The total cost function for a product is given by C(x)=3x3−9x2−243x+1229, where x is the number of units produced and C is the cost in hundreds of dollars. Use factoring by grouping and then find the number of units that will give a total cost of at least $50,000. Verify the conclusion with a graphing utility.
Answers
C(x) = 3x³ − 9x² − 243x + 1229
500 = 3x³ − 9x² − 243x + 1229
Subtract 500 on each side, as follows:
0 = 3x³ − 9x² − 243x + 729
(3x³ − 9x²) - (243x - 729) = 0
3x² (x - 3) - 243 (x - 3) = 0
(x - 3)(3x² - 243) = 0
x = 3, x = 9, x = -9; in the context of this problem, where x is the number
of units produced, negative values of x must be omitted, so x = 3 and x = 9
So we can say that if either 3 units or 9 units are produced the total cost
for the product will be at least $50000
[0, 3] U [9,∞)
Related Questions
A house addition is in the shape of a semicircle (a half-circle) with a radius of 9 ft. What is itsarea?
Answers
We find its area as follows:
[tex]A=\frac{1}{2}\pi r^2[/tex][This is the equation for the area of a circle divided by 2] Now, we replace the radius:
[tex]A=\frac{1}{2}\pi(9)^2\Rightarrow A=\frac{81}{2}\pi\Rightarrow A\approx127.23[/tex]So, the area of the semi-circle is approximately 127.23 squared feet.
which of the following are accurate of the distribution below
Answers
A: An outlier is a point that is an exception compared to the distribution of the data. In a histogram, it would appear as a bar away from the distribution with a lower height. We can't observe this in this distribution.
A do not apply.
B: A cluster is an accumulation of point in a certain interval. The interval given is 0 to 39. In the distribution, there are no points for this interval, so no cluster.
B do not apply.
Since A and B do not apply, C do apply.
Suppose the main income of firms in the industry for a year is $80 million with a standard deviation of $13 million. If incomes for the industry are distributed normally what is the probability that a randomly selected firm will earn less than $96 million? Round your answer to four decimal places
Answers
Given that
The mean income of firms in the industry for a year is $80 million with a standard deviation of $13 million. and we have to find the probability that a randomly selected firm will earn less than $96 million.
Explanation -
We have to find the probability that a firm will earn less than $96 million.
The mean is $80 and the standard deviation is $13.
Then, it is written as
[tex]\begin{gathered} P(x<96)=P(z<\frac{96-80}{13}) \\ \\ The\text{ formula to find the z is \lparen here z is the z value\rparen} \\ z=\frac{x-\mu}{\sigma} \\ \mu\text{ is mean and }\sigma\text{ is the standard deviation.} \\ \\ P(<96)=P(z<\frac{16}{13})=P(z<1.2) \end{gathered}[/tex]The table to find the z value is
According to the z table, the value will be
[tex]\begin{gathered} P(x<96)=P(z<1.2)=0.8849 \\ P(x<96)=88.49\% \end{gathered}[/tex]Hence, 88.49% of the randomly selected firms will earn less than $96.
So the probability will be 0.8849.
Final answer -
The final answer is 0.8849 or 88.49%.One sample t for means You want to know if the average customer rating fro your store is about a 7.0 on a 1-10 scale. Your collect a sample of 100 customers. Their average rating was 7.3, with a standard deviation of 2.0.
Answers
Given:
A sample of 100 customers.
Are the pair of lines y = 1/3x - 1 and y = 3x parallel, perpendicular, or neither?
Answers
A line with slope m and y-intercept b has the following slope-intercept form equation:
[tex]y=mx+b[/tex]If two lines have the same slope, they are parallel. If they have slopes that are the negative reciprocal of each other, then they are perpendicular.
If none of the above cases happen, then they are neither parallel nor perpendicular.
The line y = (1/3)x - 1 has slope 1/3.
The line y = 3x has slope 3.
As we see, the slopes are different, so the lines are not parallel. Also, the negative reciprocal of 3 is -1/3, not 1/3.
Therefore, the given lines are neither parallel nor perpendicular.
identify the correct trigonometry formula to use to solve for the given anglea. sin-¹(1.41)b. cos-¹(1.41)c. sin-¹(.71)d. tan-¹(.71)
Answers
The definition of arctan is opposit side by adjesent side.
[tex]\begin{gathered} \text{Angle}=tan^{-1}(\frac{Oppos\text{ side}}{\text{Adjesent side}}) \\ =\tan ^{-1}(\frac{34}{48}) \\ =\tan ^{-1}(0.71) \end{gathered}[/tex]Thus, the correct option is option d.
a chemical company makes two brands of antifreeze. the first brand is 45% pure antifreeze and the second brand is 70% pure antifreeze. in order to obtain 170 gallon of a mixture that contains 65% pure antifreeze how many gallons of each brand of antifreeze mudt be used
Answers
Answer:
The first brand is 34 gallons
The second brand is 136 gallons
Explanation:
Let x represent the first brand, and
y represent the second brand
The total number of gallons of mixture to be obtained is 170, so
x + y = 170 .................................................................................(1)
And
45% of x + 70% of y = 65% of (x + y)
0.45x + 0.7y = 0.65(x + y)
0.45x - 0.65x = 0.65y - 0.7y
0.2x = 0.05y
Divide both sides by 0.05
4x = y ...........................................................................................(2)
Solving (1) and (2) simultaneously
Using (2) in (1)
x + 4x = 170
5x = 170
Divide both sides by 5
x = 170/5 = 34
Put x = 34 in (2)
4(34) = y
y = 136
CWhich of the following is the inverse of F(x)=2x+3?COAa 4520-19B.0 с.OD.103765PREVIOUSG Search or type URI(3,0)(15,0)3YSUBMIT
Answers
We have to find the inverse of the function f(x) = 2x + 3.
We can find the inverse function as:
[tex]\begin{gathered} f(f^{-1}(x))=x \\ 2f^{-1}(x)+3=x \\ 2f^{-1}(x)=x-3 \\ f^{-1}(x)=\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]From the options we can see that the slope has to be positive, so we can discard optiosn B and C.
Then, we can check option A:
- It has a y-intercept of -1.5, which is equal to -3/2.
- The x-intercept is (3,0), what indicates that it increases 0.5 units of y per unit increase in x. This corresponds to a slope of 0.5 or 1/2.
Then, as both characteristics match with the equation of the inverse, the right representation is option A.
Answer:
The inverse is f^-1(x) = 1/2*x - 3/2 [Option A]
Give the slope and the Y intercept of the line represented by y-7=-7x
Answers
Answer:
• m=-7
,• b=7
Explanation:
Given the line:
[tex]y-7=-7x[/tex]To determine the slope and y-intercept, first, express the line in the slope-intercept form (y=mx+b).
[tex]\implies y=-7x+7[/tex]You can then compare:
• Slope, m = -7
,• y-intercept, b =7
The slope of the line is -7 and the y-intercept is 7.
For the data shown in the plot below identify a point apart from the main cluster
Answers
(8, 7) or (8.5, 7.5)
See explanation below
Explanation:From the graph, there are two points away from the main clusters.
This is because their distance compared to other points is far apart. The main cluster is where most of the points are located
The two points are (x, y): (8, 7) and (8.5, 7.5)
In the absence of options, you can pick any of the points as the point that is apart from the cluster.
FIRST ANSWER WILL GET BRAILIEST! AND 50 PTS!
Which division problem is represented with this model?
Responses
1/5÷6
1/6÷2
1/2÷5
1/5÷2
Answers
Answer: Choice B
1/6÷2
Reason:
We have 6 slips of paper side by side. Shading one of those 6 represents the fraction 1/6.
Then split that shaded piece of paper in half as shown in the diagram. The blue region in that diagram represents 1/6÷2 which simplifies fully to 1/12.
If you were to do this to all 6 pieces of paper, then we'd have 2*6 = 12 smaller pieces. One of which is shaded, so that explains how we get 1/12.
In other words:
[tex]\frac{1}{6} \div 2 = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}[/tex]
For which graph is the parent function y = x2
Answers
Answer:
Answer d
Step-by-step explanation:
Make sure to get another answer + can you make sure if there is answer choices, please and thx
Rushdoors,
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change these to decimals. 7%, 200%, .3%
Answers
the 7% means
7/100 = 0.07
[tex]7\text{ \% =}\frac{7}{100}=0.07[/tex]200 % means
200/100 = 2
and 0.3 % means
0.3/100 = 0.003
What plus Ten equals thirty two
Answers
What plus Ten equals thirty two is equivalent to
x + 10 = 32
10 is adding on the left, then it will subtract on the right
x = 32 - 10
x = 22
I'm confused about how to solve this using the special right triangles method
Answers
ANSWER:
[tex]x=4\sqrt[]{2}[/tex]STEP-BY-STEP EXPLANATION:
We can calculate the value of x, by means of the trigonometric function sine
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \text{opposite = }4 \\ \theta\text{ =60\degree} \\ \text{hypotenuse = x} \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} \sin 45=\frac{4}{x} \\ x=\frac{4}{\sin45} \\ \sin 45=\frac{\sqrt[]{2}}{2} \\ x=\frac{4}{\frac{\sqrt[]{2}}{2}} \\ x=\frac{8}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ x=\frac{8\sqrt[]{2}}{2} \\ x=4\sqrt[]{2} \end{gathered}[/tex]how does a to the 4 b to -5 over c to -3 d to the 6th get simplified?
Answers
Given the expression
[tex]\frac{a^4b^{-5}}{c^{-3}d^6}[/tex]To simplify the expression above, we convert all negative indices to positive indices
Applying the rule of indices
[tex]a^{-x}=\frac{1}{a^x}[/tex]Applying the rule to the given expression gives
[tex]\begin{gathered} \text{Where b}^{-5}=\frac{1}{b^5}\text{ and} \\ c^{-3}=\frac{1}{c^3} \end{gathered}[/tex]Substitute the above deduction into the given expression
[tex]\begin{gathered} \frac{a^4b^{-5}}{c^{-3}d^6}=a^4\times\frac{1}{b^5}\times\frac{1}{\frac{1}{c^3}}\times\frac{1}{d^6} \\ \text{Where }\frac{1}{\frac{1}{c^3}}=c^3 \\ =a^4\times\frac{1}{b^5}\times\frac{1}{\frac{1}{c^3}}\times\frac{1}{d^6}=a^4\times\frac{1}{b^5}\times c^3\times\frac{1}{d^6} \\ =\frac{a^4c^3}{b^5d^6} \\ \frac{a^4b^{-5}}{c^{-3}d^6}=\frac{a^4c^3}{b^5d^6} \end{gathered}[/tex]Hence, the simplified form is
[tex]\frac{a^4c^3}{b^5d^6}[/tex]What is the value of t? 76 T
Answers
Those are vertical angles, which are two non-adjacent angles formed by intersecting two lines. The intersection forms two pair of vertical angles. So:
[tex]m\angle t=76[/tex]The circle is inscribed in the square. Find the area of the shaded region.
Answers
We can solve this by calculating the area of the square and subtracting the area of the inscribed circle. The area of the square is:
[tex]Square=10\cdot10=100cm^2[/tex]The formula for the area of a circle is:
[tex]A=\pi r^2[/tex]The radius of the inscribed circle is half the length of the side of the square, then, the radius is r = 5 cm
[tex]Circle=\pi5^2=25\pi\text{ }cm^2[/tex]Now, we rest:
[tex]Square-Circle=100cm^2-25\pi cm^2\approx21.46cm^2[/tex]The answer is 21.46cm²
Edward deposited 9,000 into a savings account 2years ago tthe simple interest is 2% how much money did edward earn in intrest
Answers
We just need to use the simple interest formula:
[tex]I=PV\cdot r\cdot t[/tex]Where:
I = Interest
PV = Principal or initial investment = 9000
r = interest rate = 0.02
t = time = 2
[tex]\begin{gathered} I=9000\times0.02\times2 \\ I=360 \end{gathered}[/tex]$360
Find the equation of the line containing the point (3,5) and having slope: 4A. y=4x+24B. y=4x+7C. y=4x+17D. y=4x
Answers
Data
Point = (3, 5)
slope = 4
Equation of a line
y - y1 = m(x - x1)
m = slope = 4
x1 = 3
y1 = 5
Substitution
y - 5 = 4(x - 3)
Simplifying
y - 5 = 4x - 12
y = 4x - 12 + 5
Result
y = 4x - 7
Type the correct answer in each box. Use numerals instead of words. If necessary, use/ for the fraction bar(s).The equation of a circle is given.2+ y²+6x+10y+18=0Determine the center and radius of the circle.) and the radius of the circle isunits.The center of the circle is at (ResetNext
Answers
ANSWER
[tex]\begin{gathered} center=(-3,-5) \\ r=4 \end{gathered}[/tex]EXPLANATION
Given;
[tex]x^2+y^2+6x+10y+18=0[/tex]The standard equation of circle of a circle centered at (h,k) with radius r is;
[tex](x-h)^2+(y-k)^2=r^2[/tex]Re-write the given equation in the standard form, we have;
[tex]\begin{gathered} x^{2}+y^{2}+6x+10y+18=0 \\ x^{2}-6x+(\frac{6}{2})^{2}+y^{2}+10y+(\frac{10}{2})^{2}=-18+9+25 \\ (x-3)^2+(y-5)^2=4^2 \end{gathered}[/tex]Hence, h=-3, k=-5, radius is 4
Solve the following quadratic equation using the quadratic formula in the picture: Problem: -3y^2 - 2y - 6 = 0
Answers
The given equation is,
[tex]-3y^2-2y-6=0[/tex]Here, a = -3, b = -2, c = -6. Therefore, y can be calculated as,
[tex]\begin{gathered} y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{2\pm\sqrt[]{4-(4)(-3)(-6)}}{-6}=-\frac{1\pm\sqrt[]{-68}}{3} \\ =\frac{-1+\sqrt[]{68}}{3},\frac{-1-\sqrt[]{68}}{3} \end{gathered}[/tex]The problem is:The area of a square picture frame is 55 square inches. Find the length of one side of the frame. explain.Part A. Part B To the nearest whole inch. To the nearest 10th of an inch
Answers
Part A
area = 55 in²
The area of a square is given by:
area = side x side
So
55 in² = side x side
55 in² = side²
Taking the square root of both sides of the equation we get:
√55 in² = side
7 in = side
Part B
side = 7.4 in
which equation doesn't represent a linear function? [tex]a. \: y = \frac{1}{2}x \: + 2[/tex][tex]b . \: y = {x}^{2} \\ c . \: y = 2x \\ d. \: y = x - 2[/tex]
Answers
The general equation for linear equation is,
[tex]y=mx+b[/tex]The equation y = x^2, consist of power term on the variable x. So this equation does not follow the linear equation and is a quadratic equation.
Thus, equation y = x^2 is not a linear function. Option B is correct answer.
complete the function table for the given domain and plot the points on the graph f(x)=2^x-7x. 0. 1. 2. 3. 4. f(x) . . . . graph
Answers
we have the following:
[tex]f(x)=2^x-7[/tex]replacing:
[tex]\begin{gathered} f(0)=2^0-7=1-7=-6;(0,-6)^{} \\ f\mleft(1\mright)=2^1-7=2-7=-5;(1,-5) \\ f\mleft(2\mright)=2^2-7=4-7=-3;(2,-3) \\ f(3)=2^3-7=8-7=1;(3,1) \\ f(4)=2^4-7=16-7=9;(4,9) \end{gathered}[/tex]x 0 1 2 3 4
f(x) -6 -5 -3 1 9
Dan is a software salesman. His base salary is $2200, and he makes an additional $120 for every copy of History is Fun he sells.Let P represent his total pay (in dollars), and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 23 copies of History is Fun.
Answers
We will have the following:
The equation in this case is:
[tex]P=120N+2200[/tex]So, if he sells 23 copies, he will make:
[tex]P(23)=120(23)+2200\Rightarrow P(23)=4960[/tex]So, he would make $4960.
62 - 12 ÷ 3 + (15-7)
Answers
62 - 12 ÷ 3 + (15-7)
First, solve the parenthesis:
62-12÷ 3 + 8
Then, solve the division:
62-4+8
Add And subtract
66
The school band brought cheese and pepperoni pizzas in ratio represented in the tape diagram for their end of year party.
Answers
ANSWER
2 pepperoni pizzas
EXPLANATION
From the tape diagram, the ratio of cheese pizzas to pepperoni pizzas is:
3 : 1.
They bought 6 cheese pizzas.
Let the number of pepperoni pizzas be x.
So, by comparison, we have that:
3 : 1 = 6 : x
or
[tex]\begin{gathered} \frac{3}{1}\text{ = }\frac{6}{x} \\ \text{Cross multiply to find x:} \\ 3\cdot\text{ x = 6 }\cdot\text{ 1} \\ \text{Divide through by 3:} \\ x\text{ = }\frac{6}{3} \\ x\text{ = 2} \end{gathered}[/tex]Therefore, they bought 2 pepperoni pizzas.
solve y=f(x) for x. then find the inputs when the output is -3
Answers
Answer:
Given that,
[tex]f(x)=-7x-2[/tex]To find the inputs when the output is -3
that is, when f(x)=-3, to find the value of x
Put f(x)=-3 in the above equation we get,
[tex]-3=-7x-2[/tex][tex]-7x=-3+2[/tex][tex]\begin{gathered} -7x=-1 \\ x=\frac{1}{7} \end{gathered}[/tex]Answer is: x=1/7.
7-Which beans are the better deal? O Kidney Beans $1.18 per Ib Lima Beans $2.13 for 2 lbs 7b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 07 00, so if answer is 43 cents, its 043 or 43, if there is a dollar amount ke 1.50, do not add zeros in front) Your answer
Answers
Kidney $1.18 per 500g
Lima. $ 2.13. Per 2 lbs= 1000g
Then
Kidney = 1.18 x 1 lb
Lima = 2.13/2= 1.065 x 1 lb
So ANSWER IS :Better deal Is LIMA BEANS
Part 7b
UNIT PRICE for better deal is
LIMA BEANS , At $1.065 per lb