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A company can manufacture x x hundred items for a total cost of c = 500 + 1100 x − 100 x 2 c=500+1100x-100x2. find x x if the total cost is $ 2 , 300 $2,300.
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We are given the equation:
c = 500 + 1100 x – 100 x^2
Solve for x given the value of c = 2300
Rearrange and substitute:
- 100 x^2 + 1100 x + 500 = 2300
Divide everything by -100:
x^2 – 11 x – 5 = - 23
x^2 – 11 x = - 18
Completing the square:
(x – 11/2)^2 = - 18 + (11/2)^2
x – 11/2 = ±3.5
x = 2, 9
So x is 2 or 9
Which polynomial has a factor of 3x+2?
1.) 6x²+x-2
2.) 6x²-5x-9
3.) 3x²-x-4
4.) 3x²+8x-8
Answers
You can factor 6x+x-2 in many ways-
But the right answer from factoring should come out to be (3x+2)(2x-1) because when you multiply it back out using the FOIL method, you come back to the original problem. Hope this helps:)
The circle design a class which represents a circle in the (x,y) coordinate plane. a circle object is initialized with three input arguments. the center of the circle specified as the first two inputs (x,y) and the radius of the circle. by default the circle will be centered at (0, 0) with a radius of 1. c = circle(0, 0, 1) the circle class should provide proper getters/setters for the x and y coordinates of the center as well as the radius. the circle should also have a getarea() and getperimeter() method. finally, the circle should have a method called, ispointwithincircle(x, y) which takes as augments the x and y coordinate of a point and determines whether the point lies within the circle. it should return a boolean indicating whether the point is within the circle.
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The circle design a class which represents a circle in the (x,y) coordinate plane.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
from math import dist # to calculate distance between two points
# defining class circle
class Circle:
# constructor of Circle
# with default parameters
def __init__(self, x_coord=0, y_coord=0, radius=1):
self.centre_x = x_coord
self.centre_y = y_coord
self.radius = radius
# getters
def getX(self):
return self.centre_x
def getY(self):
return self.centre_y
def getRadius(self):
return self.radius
# setters
def setX(self, x):
self.centre_x = x
def sety(self, y):
self.centre_y = y
def setRadius(self, r):
self.radius = r
# function to calculate and return area
def getArea(self):
return 3.141*(self.radius**2)
# function to calculate and return perimeter
def getPerimeter(self):
return 2*3.141*self.radius
# calculates the distance between circle centre and
# given coordinates
# returns true if distance is less than radius
def isPointWithinCircle(self, x, y):
return dist([self.centre_x, self.centre_y], [x, y]) < self.radius
c1 = Circle(3, 3, 7)
c2 = Circle()
print("First Circle perimeter: " + str(c1.getPerimeter()))
print("First Circle area: " + str(c1.getArea()))
c2.setX(3)
c2.sety(3)
c2.setRadius(2)
if c2.isPointWithinCircle(4, 3.7):
print("(4, 3.7) is within circle two")
else:
print("(4, 3.7) is not within circle two")
print("Moving second Circle")
c2.setX(3+c2.getX())
if c2.isPointWithinCircle(4, 3.7):
print("(4, 3.7) is within circle two")
else:
print("(4, 3.7) is not within circle two")
Thus, the circle design a class which represents a circle in the (x,y) coordinate plane.
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Wyatt uses 3/4 gallon of paint to paint two identical doghouses. Wyatt has 11/2 gallons of paint. Assuming that the doghouses are identical, ow many doghouses can Wyatt paint with 11/2 gallons of paint?
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1 1/2÷ 3/4 = 2
2 x 2 = 4 dh
Bryson hopes to win a three-day vacation in a drawing that is being held at his office. He purchased 40 raffle tickets. There were 500 raffle tickets sold. What is the theoretical probability of Bryson winning the trip? ANSWER ASAP
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If Bryson purchased 40 raffle tickets. There were 500 raffle tickets sold. Then 2/25 is the theoretical probability of Bryson winning the trip
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
Bryson hopes to win a three-day vacation in a drawing that is being held at his office.
Bryson purchased 40 raffle tickets
The number of raffle tickets sold were 500
We need to find the theoretical probability of Bryson winning the trip
P(win)=40/500
=4/50
=2/25
2/25 because he bought 40 out of the 500 tickets
Hence 2/25 is the theoretical probability of Bryson winning the trip
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If Adela has 12.4 L of diesel and Madison has 840 cL of diesel, how much does the pair have altogether?
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The total volume of diesel that the pair have altogether is equal to 20.8 L.
What is measurement?Measurement is a process through which the size, magnitude, volume or other physical quantities that are associated with an object or chemical substance are taken, especially for the purpose of a scientific research (experiment).
In order to determine the total volume of diesel that they have, we would convert the value in centiliter (cL) to liter (L) and then add them together as follows:
840 cL to L = 840/100 = 8.4 L.
Total = 8.4 + 12.4
Total = 20.8 L.
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A gasoline pump delivers 4 2/5 gallons of gas per minute. How many minutes will it take to fill a gas tank that holds 17 1/4 gallons?
Please show all steps and equation.
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In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. If you want to spend 1 year in the club, how much money did you spend?
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How?
Well let's first start off with the fee. It's $30, so lets add that to our total.
There are 12 months in a year, and $4 each month to stay in the club.
So 12 x 4 = 48
Then add the startup fee, $30, and you get a total of $78
recursive equation for 5,8,11,14,17
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To reduce laboratory costs, water samples from two public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sample tests positive. Based on past results, there is a 0.009 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from twotwo public swimming areas will reveal the presence of bacteria. Is the probability low enough so that further testing of the individual samples is rarely necessary?
The probability of a positive test result is _____.
Is the probability low enough so that further testing of the individual samples is rarely necessary?
A. The probability is quite low, indicating that further testing is necessary for all of the combined samples.
B. The probability is quite low, indicating that further testing is not necessary for any of the combined samples.
C. The probability is quite low, indicating that further testing of the individual samples will be a rarely necessary event.
D. The probability is quite low, indicating that further testing of the individual samples will not be a rarely necessary event.
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Answer:
The probability of a positive test result is 0.017919
Option C is correct.
The probability is quite low, indicating that further testing of the individual samples will be a rarely necessary event.
Step-by-step explanation:
Probability of finding bacteria in one public swimming pool = 0.009
We now require the probability of finding bacteria in the combined test of two swimming pools. This probability is a sum of probabilities.
Let the two public swimming pools be A and B respectively.
- It is possible for public swimming pool A to have bacteria and public swimming pool B not to have bacteria. We would obtain a positive result from testing a mixed sample of both public swimming pools.
- It is also possible for public swimming pool A to not have bacteria and public swimming pool B to have bacteria. We would also obtain a positive result from testing a mixed sample of both public swimming pools.
- And lastly, it is possible that both swimming pools both have bacteria in them. We will definitely get a positive result from this too.
So, if P(A) is the probability of the event of bacteria existing in public swimming pool A
And P(B) is the probability of the event of bacteria existing in public swimming pool B
P(A') and P(B') represent the probabilities of bacteria being absent in public swimming pool A and public swimming pool B respectively.
P(A) = P(B) = 0.009
P(A') = P(B') = 1 - 0.009 = 0.991
Since the probabilities for each public swimming pool is independent of the other.
P(A or B) = P(A n B') + P(A' n B) + P(A n B)
= P(A)×P(B') + P(A')×P(B) + P(A)×P(B)
= (0.009×0.991) + (0.991×0.009) + (0.009×0.009)
= 0.008919 + 0.008919 + 0.000081
= 0.017919
Evidently, a probability of 0.017919 (1.7919%) indicates an event with a very low likelihood. A positive result is expected only 1.7919% of the time.
Hence, we can conclude that the probability is quite low, indicating that further testing of the individual samples will be a rarely necessary event.
Hope this Helps!!!
A small train at an amusement park is carrying passengers. Half of the passengers are 4 years old, 1/10 are 5 years old, 3/10 are 6 years old, and 1/10 are 7 years old.
What is the expected age for one of the passengers on the train?
A. 5 years
B. 5.5 years
C. 6 years
D. 6.1 years
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E(x) = 4(1/2) + 5(1/10) + 6(3/10) + 7(1/10)
E(x) = 5 years
By doing this we are giving each age group a percentage of the entire population.
Hope this helps!
I have a bag of trail mix. half of the bag contains peanuts, 1/4 of the bag is chocolate candies, and 1/4 of the bag is dried fruit. what is the probability that i will select a peanut?
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0.5 chance
1/2 chance
Reason:
Half the bag is peanuts therefore there is half a chance you will pick one out
which number is halfway between 1/2 and 5/6
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The fraction which is halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is equal to [tex]\frac{2}{3}[/tex].
What is a fraction ?
A fraction is used to represent a portion or component of a whole. The numerator and denominator are its two parts.
The two fractions are given which are [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex].
We know that numerator is the top value of the fraction whereas the denominator is the bottom value of the fraction. We need to add the given fractions and then divide it by 2 to find the halfway between the two given functions.
To add the fractions we need to equal denominator firstly. The common denominator of 2 and 6 will be 6 because 6 is a multiple of both 2 and 6.
So ,
Halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is :
= ( [tex]\frac{1}{2}[/tex] + [tex]\frac{5}{6}[/tex] ) / 2
= [tex]\frac{3 + 5}{6}[/tex] / 2
= [tex]\frac{8}{6}[/tex] × [tex]\frac{1}{2}[/tex]
= [tex]\frac{4}{6}[/tex]
or
[tex]\frac{2}{3}[/tex]
Therefore , the fraction which is halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is equal to [tex]\frac{2}{3}[/tex].
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PLEASE HELP ME!
Diana made a recipe that yields 6 and 1 over 2 cups. If each serving is 1 over 4 cup, which expression will help Diana determine the number of servings her recipe will yield?
Answers
6 1/2 divided by 1/4
6.5 /0.25 =26 servings
In traveling across flat land, you see a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive 15 miles closer to the mountain, the angle of elevation is 9° (see figure). Approximate the height of the mountain. (Round your answer to one decimal place.)
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[tex]\bf tan(3.5^o)=\cfrac{y}{15+x}\implies 15+x=\cfrac{y}{tan(3.5^o)}\\\\\\ \boxed{x=\cfrac{y}{tan(3.5^o)}-15} \\\\\\ tan(9^o)=\cfrac{y}{x}\implies x\cdot tan(9^o)=y\\\\\\ \left[ \cfrac{y}{tan(3.5^o)}-15 \right]tan(9^o)=y \\\\\\ \left[ \cfrac{y-15tan(3.5^o)}{tan(3.5^o)} \right]tan(9^o)=y \\\\\\[/tex]
[tex]\bf \cfrac{y\cdot tan(9^o)-15tan(3.5^o)tan(9^o)}{tan(3.5^o)}=y \\\\\\ y\cdot tan(9^o)-15tan(3.5^o)tan(9^o)=y\cdot tan(3.5^o) \\\\\\ ytan(9^o)-ytan(3.5^o)=15tan(3.5^o)tan(9^o) \\\\\\ \stackrel{common~factor}{y}[tan(9^o)-tan(3.5^o)]=15tan(3.5^o)tan(9^o) \\\\\\ y=\cfrac{15tan(3.5^o)tan(9^o)}{tan(9^o)-tan(3.5^o)}[/tex]
make sure your calculator is in Degree mode.
the amount is small, but bear in mind that is mile units.
To solve such problems we must know about Tangent (Tanθ).
What is Tangent (Tanθ) ?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
The height of the mountain is 1.495 miles.
Given to us
AB = 15 miles∠CAD = 3.5°∠CBD = 9°In ΔCAD,[tex]\rm{ tan(\angle A) = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]
[tex]tan(3.5^o) = \dfrac{CD}{15+x}[/tex]
[tex]CD=tan(3.5^o) \times(x+15)[/tex]
In ΔCBD,[tex]\rm{ tan(\angle B) = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan(\angle B) = \dfrac{CD}{BD}[/tex]
[tex]tan(9^o) = \dfrac{CD}{x}[/tex]
[tex]CD=tan(9^o) \times(x)[/tex]
Equating CD,
[tex]tan(3.5^o) \times (x+15) = tan(9^o) \times x\\\\(x+15)= \dfrac{tan(9^o) }{tan(3.5^o) }\times x\\\\x+15=2.59\ x\\15 = 2.59x-x\\15= 1.59x\\x = 9.44[/tex]
Substituting the value of x
[tex]CD=tan(9^o) \times(x)[/tex]
[tex]CD=tan(9^o) \times(9.44)\\CD= 1.495[/tex]
Hence, the height of the mountain is 1.495 miles.
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Does anyone know this??
The range of the following relation R {(3, −2), (1, 2), (−1, −4), (−1, 2)} is
A {−1, 1, 3}
B {−1, −1, 1, 3}
C {−4, −2, 2, 2}
D {−4, −2, 2}
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Manny and Emma are both competing in a long jump competition at their school .mang can jump for fifths of the distance that Emma can jump . many can jump 40 inches how far can Emma jump
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divide 40 by 4/5 =
40*5/4 = 200/4 =50
Emma can jump 50 inches
A business owes $8000 on a loan. Every month, the business pays 12 of the amount remaining on the loan.
How much will the business pay in the sixth month?
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Answer:
$125 on the 6th month
If i flip a coin 4 times what is the probability of one tail
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Probability means occurrence of chance.
You have two sides in a coin: heads and tails.
so when you flip the coin 4 times the probability on getting one tail is one. If you had to find the probability of 2 tails then the answer would be [tex]2/4[/tex].
P = (of one tail) = [tex]1/4[/tex]
It cannot be simplified further, as it is in its simplest form already.
Hope I helped (:
Have a great day!
CAN someone please check this i will give out brainliest !
its proofs and theorems in geometry
check the ones in red
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Reason 3 should be "angle congruence postulate" leading us from the congruent notation shown in statement 2 to the equality notation in statement 3.
In short, you have reason 2 and reason 3 swapped. Reason 5 is in the proper place.
Please help it’s due tomorrow! I’m in a hurry!! Omg pls help! :( ahhhhhhhhhhh
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In the problem 17- 8= 9, the number 9 is the ____________
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In the subtraction problem 17 - 8, the number 9 is the difference, which is the result obtained after subtracting 8 from 17.
In the problem 17 - 8 = 9, the number 9 is the difference. In subtraction, the difference is the result of subtracting one number from another. Here, when we subtract 8 from 17, we get the difference of 9. This is because 17 is the minuend (the number from which another number is subtracted), 8 is the subtrahend (the number that is to be subtracted), and 9 is the difference (the result of the subtraction).
There are 3 people who work full time and are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full time. if one of the people is budgeted for 1/2 of the time and the other person is budgeted for 1/3, what part od the third workers time should be budgeted to this project
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5/6 + x = 1
x = 1/6
x being the amount of time for the third person. YOU'RE WELCOME :D
Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency.
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Answer: The length of the chord AB is √2 r units.
Step-by-step explanation: Given in the question that Circle P is tangent to the X-axis at the point A and tangent to the Y-axis at the point B.
Also, the co-ordinates of centre of the circle P are C(r, r). See the attached image below.
We are to find the length of the chord AB, with end-points A and B as the points of tangency.
From the figure, we note that
the co-ordinates of the points A and B are (0, r) and (r, 0) respectively.
As the X-axis and Y-axis are perpendicular to each other, so the lines parallel to them, OB and OA are also perpendicular to each other.
That is, ∠ACB = 90°.
This implies that the triangle ACB is a right-angled triangle.
Now, using Pythagoras theorem in ΔACB, we have
[tex]AB^2=CA^2+CB^2~~~~~~~~~~~~~~~~~~~~~(i).[/tex]
The lengths of the line segments CA and CB are calculated, using distance formula, as follows:
[tex]CA=\sqrt{(0-r)^2+(r-r)^2}=\sqrt{r^2}=r,\\\\CB=\sqrt{(r-r)^2+(0-r)^2}=\sqrt{r^2}=r.[/tex]
From equation (i), we get
[tex]AB^2=r^2+r^2\\\\\Rightrarrow AB^2=2r^2\\\\\Rightarrow AB=\sqrt2r~\textup{units}.[/tex]
Thus, the length of the chord AB is √2 r units.
A circle, tangent to the x-axis and y-axis, forms a square where its radius r is the side length. The chord, which is the diagonal, can be found using the Pythagorean theorem resulting to r√2.
Explanation:In the given problem, a circle P is tangent to the x-axis and y-axis at two points. This means that the radius of the circle is the distance from the center to either axis, which are both r, as the coordinates of the center are (r,r). We are asked to find the length of the chord whose endpoints are the points of tangency.
The chord is actually the diagonal of a square that has sides of length r. So, its length can be found using the Pythagorean theorem (a^2 + b^2 = c^2), where a and b are the lengths of the sides of the square and c is the diagonal. Hence the length of the chord can be found as √(r^2 + r^2) = √(2r^2) = r√2.
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How do you think business owners determine how much of each of their products to make?
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Answer: First - Add your costs to your mark-up. (Costs + Mark-up Amount = Baseline Price), Next - If you want to find the price percentage, (Costs x Mark-up Percentage = Mark-up Amount) (Mark-up Amount + Costs = Baseline Price) Next - Multiply your baseline price by your overhead percentage and figure out what is the amount that you must add to the baseline prices so that the overhead expenses can be covered. (Price x Overhead Percentage = Overhead Contribution)Now you must finally add your overhead contribution to your baseline price: (Overhead Contribution + Baseline Price = Final Price)
Solve the system of equations by graphing [tex] \left \{ {{y=- \frac{3}{2}x+2 } \atop {y=3x-7}} \right.[/tex] *Show all work
Answers
That is a straightline with slope -3/2 and y-intercept 2
If you do not know how to graph it, you can make a table like this:
x y = (-3/2)x + 2
-1 3/2 + 2 = 7/2
0 0 + 2 = 2
2 - 3 + 2 = -1
4 - 6 + 2 = - 4
2) Graph of y = 3x - 7
That is a straight line with slope 3 and y intercept -7
If you do not know how to graph it you can make a table like this:
x y = 3x - 7
-1 - 3 - 7 = - 10
0 0 - 7 = - 7
1 3 - 7 = - 4
2 6 - 7 = - 1
3 9 - 7 = 2
3) When you draw the two lines you will see that the intersect at x = 2, with the correspondant y = - 1.
That point of intercection is the solutions of the system (2, -1)
PB is a line segment on a number line. It has endpoints at -2 and 12. What is the coordinate of its midpoint?
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This can be done by adding the absolute values.
|12| + |-2| = 14.
mid = half
so what is half of 14? 7 is half of 14.
So, it is 7 less than the last point and 7 more than the first
-2 + 7 = 5
12 - 7 = 5
so, the midpoint is 5.
Hope this helps!
Can you pease help me find all the zeroes of the polynomial function f(x)=x^3-5x^2+6x-30 using synthetic devision?
thank you!
Answers
| 1 - 5 6 - 30
|
|
5 | 5 0 30
----------------------------------------------
| 1 0 6 0 <------ the resiude is 0.
Resiude 0 means that the polynomial is divisible by x - 5, and that means the root is x = 5.
That is the only rooto because the quotient is x^2 + 6, which does not have real roots.
Answer: x = 5
what is 10 1/2 divided by 2 1/4
Answers
The solution of the expression '' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] '' will be [tex]4 \frac{2}{3}[/tex].
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The mathematical expression is;
'' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] ''
Now, Solve the mathematical expression by using division method as;
The mathematical expression is,
[tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] = [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]
Change the mixed fraction into improper fraction as;
⇒ [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]
⇒ [tex]\frac{21}{2}[/tex] ÷ [tex]\frac{9}{4}[/tex]
It can be solve as;
⇒ 21/2 ÷ 9/4
⇒ 21/2 × 4/9
⇒ 14/3
Change into mixed fraction as;
⇒ [tex]\frac{14}{3} = 4 \frac{2}{3}[/tex]
So, [tex]10\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex] = [tex]4 \frac{2}{3}[/tex].
Therefore,
The solution of the expression '' [tex]10\frac{1}{2}[/tex] divided by [tex]2\frac{1}{4}[/tex] '' will be [tex]4 \frac{2}{3}[/tex].
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1/2 of 6 is what percentage of 1/4 of 60 options: A 16 2/3 B 8 1/3 C 37 1/2 D 8 E 12 1/2 Show work