Let the length of tape required be x centimeter
15centimeters to rap 5 present
x centimeters will rap 6 present
[tex]\begin{gathered} 15\operatorname{cm}=5 \\ x\text{ cm=6} \\ \text{hence} \\ 5x=15\times6 \\ 5x=90 \\ \text{divide both side by 5, we have} \\ x=\frac{90}{5} \\ x=18\operatorname{cm} \end{gathered}[/tex]H
A firm has a monthly fixed cost of $2000, and the variable cost per unit of its product is $25. a. Determine the cost function. b. The revenue R obtained by selling x units is given by R(x) = 60x - 0.01x2. Determine the number of units that must be sold each month so as to maximize the revenue. What is the maximum revenue? c. How many units must be produced and sold each month to obtain a maximum profit? What is the maximum profit?
a) We can write the cost function (in function of the units made) as the sum of the fixed cost (2000) and the variable cost (25*x):
[tex]C(x)=2000+25x[/tex]b) The revenue R(x) is:
[tex]R(x)=60x-0.01x^2[/tex]To find the value of x that maximizes R(x) we derive R(x) and equal it to 0:
[tex]\frac{dR}{dx}=60(1)-0.01(2x)=60-0.02x[/tex][tex]\begin{gathered} \frac{dR}{dx}=0 \\ 60-0.02x=0 \\ 60=0.02x \\ x=\frac{60}{0.02} \\ x=3000 \end{gathered}[/tex]We can now calculate the maximum revenue as R(3000):
[tex]\begin{gathered} R(3000)=60\cdot3000-0.01\cdot(3000)^2 \\ R(3000)=180000-0.01\cdot9000000 \\ R(3000)=180000-90000 \\ R(3000)=90000 \end{gathered}[/tex]c) The profit function P(x) can be calculated as the difference between the revenue and the cost:
[tex]\begin{gathered} P(x)=R(x)-C(x) \\ P(x)=(60x-0.01x^2)-(2000+25x) \\ P(x)=-0.01x^2+60x-25x-2000 \\ P(x)=-0.01x^2+35x-2000 \end{gathered}[/tex]In the same way as we did in b), we can calculate the number of units x that maximize the profit by deriving P(x) and making it equal to 0:
[tex]\begin{gathered} \frac{dP}{dx}=-0.01(2x)+35(1)-2000(0)=0 \\ -0.02x+35=0 \\ 35=0.02x \\ x=\frac{35}{0.02} \\ x=1750 \end{gathered}[/tex]The maximum profit can be then calculated as P(1750):
[tex]\begin{gathered} P(1750)=-0.01(1750)^2+35(1750)-2000 \\ P(1750)=-0.01\cdot3062500+61250-2000 \\ P(1750)=-30625+61250-2000 \\ P(1750)=28625 \end{gathered}[/tex]We can graph R(x) and P(x) as:
Answer:
a) C(x) = 2000 + 25x
b) x = 3000 units
R(3000) = $90000
c) x = 1750 units
P(1750) = $28625
Find the equation of line containing given points. Write the equation in slope- intercept form (0,2)(2,-3)
Answer:
[tex]y=\frac{-5x}{2}\text{ + 2}[/tex]Explanation:
Here, we want to get the equation of the line
The general equation of a line in slope-intercept form is:
[tex]y\text{ = mx + b}[/tex]where m is the slope and b is the y-intercept
We can get the equation through the following:
[tex]\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) is (0,2) and (x2,y2) is (2,-3)
Substituting the values, we have it that:
[tex]\begin{gathered} \frac{y-2}{x-0}\text{ = }\frac{-3-2}{2-0} \\ \\ \frac{y-2}{x}\text{ = }\frac{-5}{2} \\ \\ \left(y-2\right)\text{ = }\frac{-5x}{2} \\ \\ y\text{ = }\frac{-5x}{2}\text{ + 2} \end{gathered}[/tex]determine the miss term 3:5:7:?:25:
Determine algebraically ifthe function is even, odd, or neither. f(x)= -9
Background:
• Even ,functions are symmetric with respect to the ,y-axis,.
,• Odd ,functions are symmetric with respect to the origin.
,• Neither ,has no symmetry with respect to the origin or ,y-axis,.
Answer: Even
Out of 40 students, 14 are taking English composition, 29 are taking Chemistry. If 5 students are in both class how many students are in neither classes.What is the probability that a randomly chosen student from this group is taking only chemistry class.
The probability that a randomly chosen student from this group is taking only a chemistry class will be 0.60.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
Out of 40 understudies, 14 are taking English organization, and 29 are taking chemistry. Assuming 5 understudies are in both classes the number of understudies that are in neither class.
The number of students in neither class will be given as,
⇒ 40 - (29 + 14 - 5)
⇒ 40 - 38
⇒ 2
The probability that a randomly chosen student from this group is taking only a chemistry class will be
P = (29 - 5) / 40
P = 24 / 40
P = 0.60
The probability that a randomly chosen student from this group is taking only a chemistry class will be 0.60.
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find the coordinates of the ends of each latus rectum and equations of asymptotes.
For conic section of the form:
[tex](\frac{x^2}{a^2})-(\frac{y^2}{b^2})=1[/tex]The Ends of the Lactus Rectum is given as:
[tex]L=(ae,\frac{b^2}{a}),L=(ae,\frac{-b^2}{a})[/tex]The e in the equation above is the Eccentricity of the Hyperbola.
This can be obtained by the formula:
[tex]e=\frac{\sqrt[]{a^2+b^2}}{a}[/tex]Thus, comparing the standard form of the conic with the given equation, we have:
[tex]\begin{gathered} \frac{(y+8)^2}{16}-\frac{(x-3)^2}{9}=1 \\ \text{This can be further expressed in the form:} \\ \frac{(y+8)^2}{4^2}-\frac{(x-3)^2}{3^2}=1 \\ By\text{ comparing this with:} \\ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \\ We\text{ can deduce that:} \\ a=4;b=3 \end{gathered}[/tex]Then, we need to obtain the value of the Eccentiricity, e.
[tex]\begin{gathered} e=\frac{\sqrt[]{a^2+b^2}}{a} \\ e=\frac{\sqrt[]{4^2+3^2}}{4} \\ e=\frac{\sqrt[]{16+9}}{4} \\ e=\frac{\sqrt[]{25}}{4}=\frac{5}{4} \end{gathered}[/tex]Hence, the coordinate of the ends of the each lactus rectum is:
[tex]\begin{gathered} L=(ae,\frac{b^2}{a}),L=(ae,\frac{-b^2}{a}_{}) \\ L=(4\times\frac{5}{4},\frac{3^2}{4}),L=(4\times\frac{5}{4},\frac{-3^2}{4}) \\ L=(5,\frac{9}{4}),L=(5,\frac{9}{4}) \end{gathered}[/tex]help meeeeeeeeeeeeeee pleaseeeeeee
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]
pls help me wi this question
Answer:
1 block west and 8 blocks north
Step-by-step explanation:
One block east and two blocks north to the coffee shop. Subtract two blocks west from the one block east, and you get one block west. Add the six blocks north to the two blocks north, and you get eight blocks north.
if a/ b+1 = 2, what does 2b equal?
The question and the Triangle is in the same image. I'm on point 3
ANSWER
• Ratio: 2
,• Lengths of the sides of the new triangle: 6, 6√2
,• Circles: ,see explanation
,• Triangle: ,see explanation
EXPLANATION
• The ratio is the quotient between the length of segment DE and, for example, segment AB,
[tex]\frac{DE}{AB}=\frac{6}{3}=2[/tex]• Now, we have to multiply each side of triangle ABC by 2 to obtain the lengths of the sides of triangle DEF,
[tex]\begin{cases}DF=2BC=2\cdot3=6 \\ \\ EF=2AC=2\cdot\sqrt[]{3^2+3^2}=2\cdot\sqrt[]{2\cdot9}=6\sqrt[]{2}\end{cases}[/tex]• Next, draw the two circles mentioned,
• The intersection between the two circles is point F. The ,triangle is,
Gianna purchased 5\tfrac{1}{2}5
2
1
pints of ice cream for a party. If each guest will be served exactly \tfrac{1}{3}
3
1
pint of ice cream, what is the maximum number of guests Gianna can serve?
The maximum number of guests Gianna can serve will be 16.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers
From the information, Gianna purchased 5 1/2 pints of ice cream for a party. If each guest will be served exactly 1/3 pint of ice cream
The maximum number of guests Gianna can serve will be:
= 5 1/2 ÷ 1/3
= 11/2 ÷ 1/3
= 11/2 × 3
= 33/2
= 16.5
The maximum number will be 16.
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Complete question
Gianna purchased 5 1/2 pints of ice cream for a party. If each guest will be served exactly 1/3 pint of ice cream, what is the maximum number of guests Gianna can serve?
Find the domain of the piecewise function and evaluate it for the given values. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters. f(x) = \left\lbrace \begin{array}{cc} x+1 & x<-2 \\ -2x-3 & x\ge -2 \end{array}\right. The domain is:AnswerAnswer,AnswerAnswerf(-3)=Answerf(-2)=Answerf(-1)=Answerf(0)=Answer
SOLUTION
Let us make a graph of the function
[tex]\begin{gathered} f(x)=x+1\mleft\{x<-2\mright\} \\ f(x)=-2x-3\mleft\{x\ge-2\mright\} \end{gathered}[/tex]This is shown below
(a) The domain is usually determined from the x-axis. From the graph, the domain is all real numbers, that is, it is infinite for both positive and negative values for x, as you can see that if the graph is extended, there is no limit for x-values that it can contain. So the domain is (-infinity, infinity)
Hence the answer, Domain is
(-inf, inf)
(b)
[tex]f(-3)[/tex]In
[tex]\begin{gathered} f(x)=x+1\{x<-2\} \\ -3\text{ is less than -2, so -3 is valid here, so } \\ f(-3)=-3+1 \\ f(-3)=-2 \end{gathered}[/tex]Hence, the answer is -2
(c)
[tex]f(-2)[/tex]In
[tex]\begin{gathered} f(x)=-2x-3\{x\ge-2\} \\ -2\text{ is equal to -2, so we will put -2 for x here, so } \\ f(-2)=-2(-2)-3 \\ f(-2)=4-3 \\ f(-2)=1 \end{gathered}[/tex]Hence, the answer is 1
(d)
[tex]f(-1)[/tex]In
[tex]\begin{gathered} f(x)=-2x-3\{x\ge-2\} \\ -1\text{ is greater than -2, hence, it is valid, so we will put -1 for x here, so } \\ f(-1)=-2(-1)-3 \\ f(-1)=2-3 \\ f(-1)=-1 \end{gathered}[/tex]Hence, the answer is -1
(e)
[tex]f(0)[/tex]In
[tex]\begin{gathered} f(x)=-2x-3\{x\ge-2\} \\ 0\text{ is greater than -2, so we will put 0 for x here, so } \\ f(0)=-2(0)-3 \\ f(0)=0-3 \\ f(0)=-3 \end{gathered}[/tex]Hence, the answer is -3
Write an equation in slope-intercept form for the line that passes through (0,4) and is parallel to the line described by y=3x-7
slope-intercept form of a line (L1): y = mx + b; where m is the slope and b the y - intercept.
If two lines are parallel, that means the slope of both equations are equal.
L2: y = 3x - 7, m = 3
So, m for L1 is m = 3.
Now we just need to find y - intercept, as follows:
L1 passes through (0,4), then:
4 = 3(0) + b
4 = 0 + b
b = 4
The equation for the line is y = 3x + 4
Please help me with this problem it’s 1 question of 3 please help me I will leave good feedback for you(((
tan T = 8/8 = 1
tan ^-1 T = 45°
angle T = 45°
2) angle J = tan J = 2/4
tan J = 1/2
tan^-1 J = 26.57
rounded J = 26.6
Andrea labels ten cards with the numbers 1 through 10. She places the cards with prime numbers (2,3,5,7) in one box, and places the rest of the cards in another box. If Andrea draws one random card from the box of prime numbers and then one random card from the other box, how many different pairs of numbers are possible outcomes?
Box with prime numbers = 2, 3, 5, 7
Box with the other numbers = 1, 4,6,8,9, 10
Possible pairs
12 13 15 17 Four pairs
42 43 45 47 Four pairs
62 63 65 67 Four pairs
82 83 85 87 Four pairs
92 9 3 95 97 Four pairs
102 103 105 107 Four pairs
Total numbers of pairs 24 pairs
A fish descends 4 meters per minute for 2 minutes. Then it ascends 3 meters per minute for 3 minutes. What is the total distance, in meters, the fish traveled?
Answer:
1 meter of dispalcement,
17 meters of path distance
Step-by-step explanation:
-4meters/min * 2min = -8meter
3 m/m * 3m = 9meters
-8+9 = 1 meter of displacement, it's looking for the total path's distance, then that is just |-8|+|9|=17 meters
I hope this helps
Answer:
The fish ascended a total of meter.
Step-by-step explanation:
distance= rate x time
D= -4(2)= -8m
A= 3(3)= 9m
-8m+9m= 1m
;)
3. A car originally cost $16,000. The owner reduced the price of the car by 20%. After a few
weeks, the owner reduced the price of the car by another 20%, Belinda then purchased the
If a 3% sales tax was added, how much did Belinda pay for the car?
A. $9,600.80
B. $9,888,20
C. $10,240.00
D. $10,547.20
Answer:
the answer is D: $10547.20
The sale price of women's wool coats is $ ____question attached below
By '70% off' the text means that there is a discount of 70% on the item, in other words we are only paying 30% of the original value of the item. Therefore if we multiply 30% by the value of the item, we will find the price. This is done below:
[tex]\begin{gathered} \text{price}=220\cdot30\text{ \%} \\ \text{price}=220\cdot\frac{30}{100} \\ \text{price}=220\cdot0.3 \\ \text{price}=66 \end{gathered}[/tex]The price of the with discount coat is $66
Proof Practice
Given: ∠ PQR and ∠ XYZ are complementary
m ∠ XYZ = 10 degrees
Prove: m ∠ PQR = 80 degrees
5 statements and Reasons needed
Answer:
1. Given (angle PQR and angle XYZ are complimentary)
2. Definition of complimentary angles (Complimentary means they are added to 90 degrees)
3. Definition of Complimentary angles (Complimentary angles only include two angles)
4. Subtraction postulate (90 degrees - 10 degrees= 80 degrees which proves they are complimentary)
5. Complimentary angles theorem (angle XYZ is 80 degrees)
Sorry if that's too vague, but I really hope this helps you! I bet someone elses answer would clear it up better, so more research or finding a different answer would probably help, just to confirm. I tried to explain as much as I could, I'm not good at teaching what I know.
I’m not sure how to solve 3d. College calculus 1
Step 1
Given;
[tex]f(x)=(x^2+5)^3[/tex]Required; To simplify
[tex]\frac{f(x)-f(0)}{x},\text{ x}\ne0[/tex]Step 2
[tex]\frac{(x^2+5)^3-(0^2+5)^3}{x}[/tex][tex]\mleft(a+b\mright)^3=a^3+3a^2b+3ab^2+b^3---(apply\text{ p}\operatorname{erf}ect\text{ cube formula)}[/tex][tex](x^2+5)^3=(x^2)^3+3(x^2)^2(5)+3x^2(5^2)+5^3[/tex][tex](x^2+5)^3=x^6+15x^4+75x^2+125[/tex][tex]\frac{(x^6+15x^4+75x^2+125)-125}{x}[/tex][tex]\begin{gathered} \frac{x^6+15x^4+75x^2+125-125}{x} \\ \frac{x^6+15x^4+75x^2}{x} \\ \frac{f(x)-f(0)}{x}=x^5+15x^3+75x \end{gathered}[/tex]Hence if we factorize we get;
[tex]x(x^4+15x^2+75)[/tex]Therefore;
[tex]\frac{f(x)-f(0)}{x}=x(x^4+15x^2+75)[/tex]Answer:
See below
Step-by-step explanation:
f(x) = ( x^2 + 5)^3 f(0) = 5^3 = 125
(x^2+5)^3 = x^6 + 15x^4 + 75 x^2 + 125
so you have (x^6 + 15x^4 + 75x^2 + 125 - 125) /x
= x^5 + 15x^3 + 75x = x ( x^4 + 15x^2 + 75)
how do I find a triangle congruence postulate that can be used to prove that the triangles are congruent if any with the options below?
First figure
we have that the triangles
ABC is congruent with triangle DCB by HL (hypotenuse leg)
Second figure
The triangles are congruent by Angle-Side- Angle
Third figure
The triangles are congruent by Side-angle -side
y=-x^2-2x+3 what is the vertex of the graph? Answer an order pair.
Given:
[tex]y=-x^2-2x+3[/tex]a) To find the vertex:
Here, a=-1, b=-2, and c=3
We know that the formula to find the x- coordinate of the vertex is given by,
[tex]\begin{gathered} -\frac{b}{2a}=-\frac{(-2)}{2(-1)} \\ =-1 \end{gathered}[/tex]Substitute x=-1 in the given equation we get,
[tex]\begin{gathered} y=-(-1)^2-2(-1)+3 \\ =-1+2+3 \\ =4 \end{gathered}[/tex]Hence, the vertex of the graph is (-1, 4).
b) To find the range of the graph:
Let us find the y-intercept.
Put x=0, we get
[tex]\begin{gathered} y=-(0)^2-2(0)+3 \\ =3 \end{gathered}[/tex]From the figure, we observe that
The range of the graph is
[tex]\lbrack0,4\rbrack[/tex]c) To find the domain of the graph:
Let us find the x-intercept.
Put y=0, we get
[tex]\begin{gathered} -x^2-2x+3=0 \\ (x+3)(x-1)=0 \\ x=-3,1 \end{gathered}[/tex]From the figure, we observe that,
The domain of the graph is,
[tex]\lbrack-3,0)[/tex]the circle graph shows how a family budgets its annual income. if the total annual income is $90,000 what amount is budgeted for clothing?
Answer:
$11700
Step-by-step explanation:
comment if u need the explanantion ;D
Kyle can was the car in 30 minutes. Michael can wash the car in 40 minutes. Working together, can they wash the car in less than 16 minutes?
No, they can not wash the car in less than 16 minutes while working together.
Given, Kyle can wash the car in 30 minutes.
Michael can wash the car in 40 minutes.
Now, we are asked that working together, can they wash the car in less than 16 minutes.
So, Kyle wash the car = 30 min
Kyle can wash (1/30)th part of the car in 1 min.
Michael wash the car = 40 min
Michael can wash (1/40)th part of the car in 1 min.
Kyle and Michael can together wash the ( 1/30 + 1/40 )th part of the car in 1 min.
Kyle and Michael = 1/30 + 1/40
Kyle and Michael = (4 + 3)/120
Kyle and Michael = 7/120
So, Kyle and Michael can together wash the 7/120th part of the car in 1 min.
and both can together wash the car in 120/7 min i.e. 17.14 min
So, working together both can wash the car in 17.14 min.
Hence, No, they can not wash the car in less than 16 minutes while working together.
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pls help I was taught this concept today and I can't understand or get it right!! Find the measure of the arc or angle indicatedFind the measure of mPSQa) 53°b) 248°c) 72°d) 65°
Step 1:
Find the value of x
Using secant theorem
[tex]<\text{PQR =}\frac{1}{2}\text{ }\timesStep 2:If x = 9
Then 6x+2 = 6(9) + 2 = 54+2 = 56 degrees
The measure of arc PQ = 14(9) - 14 = 126 - 14 = 112 degrees
Step 3:
The total angle in a circumference is 360 degrees
Therefore ,
mPQ + mPSQ = 360
mPSQ = 360 - mPQ
mPSQ= 360 - 112 = 248degrees
The answer is option B
start new workings.
What value of x makes the two expressions
below equal? Give your answer as a
decimal.
5x-8
First expression
3x+5
Second expression give ur answer as a decimal maths
The value of x that makes both expressions equal is 6.5.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.So, the value of x that makes both the expression equal.
So, we can write the expression as:
5x - 8 = 3x + 5
Now, solve for x as follows:
5x - 8 = 3x + 5
5x - 3x = 5 + 8
2x = 13
x = 13/2
x = 6.5
Therefore, the value of x that makes both expressions equal is 6.5.
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find the slope of 4x + 3y equals to
find the slope of 4x + 3y equals to
I will assume a value of a
so
4x+3y=a
Isolate the variable y
3y=-4x+a
y=-(4/3)x+a/3
therefore
the slope is -4/3Note: the value of the slope not depend of the value of a
Translate and solve. Twice a number plus 6 is -14
translation 2x + 6 = -14
2x = -14 - 6
2x = -20
x = -20/2
x = -10
Please I need you to help me and show the steps please so I can understand it better
I will mark brainliest
Answer:
LM = √34
Step-by-step explanation:
L is at (-7, 4), and M is at (-2, 1).
LM
[tex] \sqrt{ {( - 7 - ( - 2))}^{2} - {(4 - 1)}^{2} } [/tex]
[tex] \sqrt{ {( - 5)}^{2} + {3}^{2} } = \sqrt{25 + 9} = \sqrt{34} [/tex]
pls help mepls pls pls pls pls pls
The expression with a coefficient of 10 and a constant of 5 is given by 10x + 5.
What is an equation? What is a coefficient?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.
We have a expression with a coefficient of 10 and a constant of 5.
The expression with a coefficient of 10 and a constant of 5 is given by -
10x + 5
Therefore, the expression with a coefficient of 10 and a constant of 5 is given by 10x + 5.
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