The most appropriate choice for maxima and minima of a function will be given by
Rectangle of length 72 feet and breadth 36 feet has largest area
What is maxima and minima?
Maxima of function f(x) is the maximum value of the function and minima of function f(x) is the minimum value of the function.
Here,
Let the length be x feet and breadth be y feet
The farmer has 144 feet of fencing
Three of the sides will require fencing and the fourth wall already exists.
So,
x + y + y =1 44
x + 2y = 144
Area of rectangle(A) = xy [tex]ft^2[/tex]
= (144 - 2y)y
= [tex]144y - 2y^2[/tex]
[tex]\frac{dA}{dy} = \frac{d}{dy}(144y - 2y^2)[/tex]
= [tex]144 - 2\times 2y^{2-1}\\144 - 4y[/tex]
For largest area,
[tex]\frac{dA}{dy} = 0[/tex]
[tex]144 - 4y = 0 \\4y = 144\\y = \frac{144}{4}\\y = 36[/tex]
[tex]\frac{d^2A}{dy^2} = \frac{d}{dy}(144 - 4y)\\=0-4\\=-4 < 0[/tex]
Hence area is maximum
For largest area, y = 36 feet
[tex]x = 144 - 2\times 36\\x = 144-72\\[/tex]
[tex]x = 72[/tex] feet
So length of rectangle is 72 feet, breadth of rectangle is 36 feet
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Eric and Nancy both had a successful year selling fish tanks for theirrespective employers, and so they were both given raises.Eric: Eric's base salary is still $1400, but now he makes a commission of$100 for each fish tank that he sells.Nancy: Nancy now gets a base salary of $500 per month, but her commissionhas stayed the same at $250 per fish tank.Eric and Nancy still want to make sure that they contribute the same amountto their total monthly income, and Nancy proposes using algebra to figureout how many fish tanks that they would each need to sell. She tells Ericthat he can calculate his monthly income by using the formula f(x) = 100x +1400. She says that she can calculate her own salary by using the functiong(x)=250x + 500.1 What does the variable x represent in Nancy's formulas?How do you know?
Answer:
The variable x represents the number of fish tanks he/she sells.
Explanation:
Given that Eric's base salary is still $1400, but now he makes a commission of
$100 for each fish tank that he sells and Nancy now gets a base salary of $500 per month, but her commission has stayed the same at $250 per fish tank.
Eric's total income would be;
$1400 plus $100 times the number of fish tanks he sells.
[tex]f(x)=1400+100x[/tex]and Nancy's total income would be;
$500 plus $250 times the number of fish tanks she sells.
[tex]f(x)=500+250x[/tex]Therefore, the variable x represents the number of fish tanks he/she sells.
The number of fish tanks each of them sells will determine the total commission and also determines their total income.
Find the volume and surface area of a right cone with a radius of 4 inches and a height of 7 inches
Volume of a cone =
[tex]v=\frac{1}{3}\pi r^2h[/tex]From the question;
r= 4 h=7
π is a constant and it is equal to 22/7
substitute the values into the formula;
[tex]V=\frac{1}{3}\times\frac{22}{7}\times4^2\times7[/tex][tex]V=\text{ }\frac{2464}{21}[/tex][tex]V=117.33inch^3[/tex]write the equation in standard form. identify A,B, and C
we have the following:
[tex]\begin{gathered} y=5x-8 \\ \end{gathered}[/tex]standard form
[tex]y=Ax^2+Bx+C[/tex]Therefore:
A = 0
B = 5
C = -8
Select the two values of x that are roots of this equation.
x2 + 3x – 5 = 0
The two values for the quadratic equation [tex]x^{2} +3x-5=0[/tex] is [tex]\frac{-3+\sqrt{29} }{2}[/tex] and [tex]\frac{-3-\sqrt{29} }{2}[/tex]
What is quadratic equation?
Quadratic equation is a second-order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
The solution of the x = [-b±√(b2-4ac)]/2a
where b= 3 a= 1 and c = -5.
x = -3±[tex]\sqrt{3^{2}-4(1)(-5) } /2[/tex]
x=[tex]\frac{-3-\sqrt{29} }{2}[/tex]
and x = [tex]\frac{-3+\sqrt{29} }{2}[/tex]
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9 is subtracted from the square of a number
Jay's family is moving to a new home they packed 22 boxes in 1 5/6 hours what is the average number of boxes they packed per hour Pls asap
The question to the second Image below
Q: Solving which system leads to a contradiction where there is no solution?
The system of equations given has infinitely number of solutions.
System of EquationA system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.
system of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
In the given question, we can solve for the equation given;
[tex]y = 4x + 5\\-8x + 2y = 10\\[/tex]
Solving for both x and y;
The solution of the equation is y = 4x + 5
The system has infinitely many solutions;
In the second system of equations;
y = 0.5x + 3, x = 2y = -16
This equation is not correct.
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Please help withstandard deviation with measurements
Answer: Standard Deviation, σ: 0.23979157616564
Count, N: 8
Sum, Σx: 33.6
Mean, μ: 4.2
Variance, σ2: 0.0575
Steps
σ2 =
Σ(xi - μ)2
N
=
(4.5 - 4.2)2 + ... + (4.1 - 4.2)2
8
=
0.46
8
= 0.0575
σ = √0.0575
= 0.23979157616564
Step-by-step explanation: but here
it isnt letting me do the fraction or the other things so yeah it will look wrong but its write for the entire graph
To win a trivia game, Nevan must score 90 points. Each correct answer is worth 134 points, and each incorrect answer is worth −14 points. If Nevan gets 58 questions correct and 22 questions incorrect how many points does he score?
Answer:7464
Step-by-step explanation:
90 is the score to get
let c represent correct and w represent wrong
if they get 134 points for it being correct, we can look at it like 134c
if they get -14 points for it being incorrect, we can look at it like -14w
now to put this in the right sense we fill in those letters with how many they got right and wrong : 134(58) -14(22)
This would get 7772 -308
after subtracting these two you'd get: 7464
Here is the imagine of the triangle ABC and it’s dilations using center D and scale factor 2
(3) The question state that we should explain the relationship between angle ACB and A'C'B' in the given diagram.
From the the diagram in the question, we can see that wa have two different triangle which are ABC and A'B'C'.
The relationship between angle ACB and angle A'C'B' is that they are corresponding angles. because they are on the same side of the line.
Corresponding angles are any pair of angles each of which is on the same side of one of two lines cut by a trasnsversal and on the same side of the transversal.
Therefore, the relationship between angle ACB and angle A'C'B' is that they are corresponding angles.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
80.58
Step-by-step explanation:
do you need an explanation or will this be fine?
how do you write 4.501795324E^-6 in simpler form
The number written in scientific notation is 1.12 × 10⁻² .
Scientific notation can be used to describe values that are either too large or too little to be conveniently presented in decimal form (typically would result in a long string of digits).
In the UK, it is also known as standard form, scientific form, and standard index form.Since it may make a number of mathematical operations simpler, this base ten notation is frequently employed by scientists, mathematicians, and engineers.Scientific notation for non-zero integers is written as m × 10ⁿ, or m times ten and raised to the power of n, where n is an integer and m is a non-zero real number.The given number is 4.501795324E⁻⁶
So simplifying we get :
4.501795324E⁻⁶ = 1.11588350 × 10⁻²
Therefore the number written in scientific notation is 1.12 × 10⁻² .
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The population of a small town in central Florida has shown a linear decline in the years 1995-2005. In 1995 the population was 24100 people. In 2005 it was 14800 people.
Part A:
Since the population is showing a linear decline, we can express the function P(t) as
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Given two points
(1995,24100), and (2005,14800)
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{IF }\mleft(x_1,y_1\mright)=\mleft(1995,24100\mright),\text{ and }(x_2,y_2)=\mleft(2005,14800\mright),\text{ THEN} \\ \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{14800-24100}{2005-1995} \\ m=\frac{-9300}{10} \\ m=-930 \end{gathered}[/tex]Now that we have solved for the slope, we can now solve for the y-intercept. We will use the point (2005,14800), but using (1995,24100) will work just as well.
[tex]\begin{gathered} \text{IF }m=-930,\text{ and }(x,y)=\mleft(2005,14800\mright),\text{ THEN} \\ \\ y=mx+b \\ 14800=(-930)(2005)+b \\ 14800=-1864650+b \\ 14800+1864650=+b \\ 1879450=b \\ b=1879450 \end{gathered}[/tex]Convert the function x into a function of time t, then the the function is
[tex]P(t)=-930t+1879450[/tex]Part 2:
What will be the population in 2007.
Substitute t = 2007.
[tex]\begin{gathered} P(t)=-930t+1879450 \\ P(2007)=-930(2007)+1879450 \\ P(2007)=-1866510+1879450 \\ P(2007)=12940 \end{gathered}[/tex]Therefore, in the year 2007, the population will be 12940.
18- A clothing store sells a shirt costing $20 for $33 and a jacket costing $60 for $93.
(i) If the markup policy of the store is assumed to be linear, write an equation that expresses retail price R
in terms of cost C.
(ii) What does a store pay for a suit that retails for $240?
(i) (a) R = 1.5C + 12
(b) R = 1.5C+3
(c) R = 3C + 1.2
(d) R = 3C +1.5
(ii) (a) 158
(b) 185
(c) 155
(d) 188
I cant solve this and I need steps while solving it.
Finding the absolute maximum and minimum of a function given the graph
Explanation
An absolute maximum point is a point where the function obtains its greatest possible value.
Similarly, an absolute minimum point is a point where the function obtains its least possible value.
Step 1
check the graph of g:
The y- coordinates (output) at the highest and lowest points are called the absolute maximum and absolute minimum
To locate absolute maxima and minima from a graph, we need to observe the graph to determine where the graph attains it highest and lowest points on the domain of the function
so, for G
[tex]\begin{gathered} \text{maximum}=\text{ None ( the graph continues raising up)} \\ \text{minimum}=-3 \end{gathered}[/tex]Step 2
Now, for h
[tex]\begin{gathered} \text{ Minimum; -5} \\ \text{ ma}\xi mum\colon5 \end{gathered}[/tex]I hope this helps you
Find the y-intercept of line on the graph.
Answer:
-3
Step-by-step explanation:
the 'y- intercept ' is ACTUALLY the 'y-axis intercept'.......this is where the graph crosses the y - axis ....for this graph this is -3
The volume of this rectangular prism is 9.044 cubic feet. What is the value of t?
The volume of a rectangular prism can be calculated with the following formula:
[tex]V=lwh[/tex]Where "l" is the length, "w" is the width and "h" is the height.
In this case, you can set up that:
[tex]undefined[/tex]Write the rule for the table, use z for the input.Input-1Output7012co woo WN3.4F(0)
Lets assume that the input values are x values and the output values are y values.
Then you will have pairs of coordinate values as shown;
(-1,7) , (0,2) , (1,-3) , (2,-8), (3,-13), (4,-18)
Using the coordinates find the slope a;
(-1,7) and (0,2) ---------slope is change in y-values/ change in x-values , (2-7) /(0--1)
= -5/ 1 = -5
Do the same for the next pair of coordinates ,(0,2) and (1,-3) , (-3-2) / (1-0) = -5/1 = -5
If you continue the procedure to the next pair which is (1,-3) and (2,-8) to get the slope as : (-8- -3) / (2-1) = -5/1 = -5
This means that the slope is -5
The relation will be represented by the equation y= mx + c where m is the slope and c is the y-intercept
First plot the points to visualize the graph
From the plot, you notice that when the points are joined, a straight graph is formed sloping to the negative side and intersecting the y-axis at point (0,2).
So to determine the rule, we apply the equation y= mx + c with m= -5 and c =2
This gives y= -5 x + 2
The rule is f(x) = -5x +2 -----------answer
Suppose the price of your dream house is $239,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30 year fixed rate mortgage at 10%. a.) Find the required down payment, b.) Find the amount of the mortgage. c.) How much must be paid for the three points at closing? d.) Find the monthly payment (excluding escrowed taxes and insurance) e.) Find the total cost of interest over 30 years.
a) The required down payment is $47,800.
b) The mortgage loan is $191,200.
c) The amount for the three points at closing is $5,736, which is 3% of the mortgage.
d) The monthly payment (excluding escrowed taxes and insurance) is $-1,677.92.
e) The total interest cost for the mortgage over its 30-year period is $412,850.06.
What is the down payment?The down payment is an upfront payment required to reduce the mortgage loan and assure the financier that the mortgagee is financially ready to engage in the mortgage transaction.
The price of a dream house = $239,000
Down payment = 20% = $47,800 ($239,000 x 20%)
Mortgage loan = $191,200 ($239,000 - $47,800)
Three points at closing = 3% of $191,200
= $5,736
Periodic Payment:N (# of periods) 360 months (30 years x 12)
I/Y (Interest per year) = 10%
PV (Present Value) = $191,200
FV (Future Value) = $0
Results:
PMT = $-1,677.92
Sum of all periodic payments = $-604,050.06
Total Interest = $412,850.06
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the mass of a car is 1990kg rounded to the nearest kilogram. the mass of a person is 58.7kg rounded to one decimal place. write the error interval for the combined mass, m, of the car and the person in the form _______
The error interval for the combined mass (m) of the car and the person is 2047.7 ≤ m < 2049.7
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).The error interval for the mass of car is given by:
Mass of car = 1990 ± 0.5;
Mass of car = 1990 + 0.5 = 1990.5
Mass of car = 1990 - 0.5 = 1989.5
The error interval for the mass of a person is given by:
b = 1990 ± 0.5;
b = 58.7 + 0.5 = 59.2
b = 58.7 - 0.5 = 58.2
For the value of a and b, we have:
a = 1989.5 + 58.2 = 2047.7
b = 1990.5 + 59.2 = 2049.7
Next, we would calculate the combined mass (m):
m = 1990 + 58.7
m = 2048.7
Now, we can write the error interval for the combined mass (m) of the car and the person as follows:
a ≤ m < b
2047.7 ≤ m < 2049.7
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which expression is a factor xsquared - 5x-6
The Factors of x² - 5x + 6 are (x-3) (x-2)
Step 1: Add the constant term to the first term's coefficient. i.e (6 x 1) = 6
Step 2:Find the two factors of 6 whose total matches the middle term's coefficient., i.e -5.
Thus, the factors are -3 and -2 as,
-3 × (-2) = 6 (Product)
-3 + (-2) = -5 (Sum)
The polynomial may be expressed as follows after dividing the middle term by the two components, -3 and -2:
x² - 3x - 2x + 6 = 0
⇒ x(x-3) -2(x-3) = 0
⇒ (x-3)(x-2) = 0
Thus, the Factors of x² - 5x + 6 are (x-3) (x-2).
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Kelly downloaded 195 pictures from her cell phone to her computer. These pictures took up 585 megabytes of space on her computer. Each picture took up the same amount of space. How many megabytes do 39 of these pictures take?
The amount of space taken by 39 of these pictures is 117 megabytes.
What is the unitary method?The unitary approach is a problem-solving process that begins by identifying the value of a single unit and then multiplying that value by the needed value.
Given:
Number of pictures downloaded by Kelly from her cell phone to her computer = 195
Amount of space taken by the pictures = 585 megabytes
Now, an equal amount of space is taken by each picture.
To determine, the megabytes taken by 39 of these pictures.
By the unitary method,
195 pictures = 585 megabytes
39 pictures = ? megabytes
Divide 585 megabytes by the number of pictures 195 and then multiply it by 39.
= (585/195) × 39
= 117 megabytes
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Let the graph of g be a vertical stretch by a factor of 2 followed by a translation 3 units down of the graph of f(x) = x^2 Write a rule for g.
The equation for the function after the transformation is f'(x) = 2x^2 - 3
How to write the image for the function?The initial equation is given as
f(x) = x²
The above represents the parent function
The sequence of transformations is given as
Vertically stretched by a factor of 2Shifted a distance of 3 units downThe rules of the above sequence of transformations are
Vertically stretched by a factor of 2: (x, 2y)Shifted a distance of 3 units down: (x, y - 3)When the rules are applied, we have
Stretch: f(x) = 2x^2Shifted: f'(x) = 2x^2 - 3Hence, the equation in its final position is f'(x) = 2x^2 - 3
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can you please answer my homework, its about sets.
The value of the set (A∪C)'∩B is {9 , 12} .
A subfield of mathematical logic called set theory examines sets, which are essentially collections of objects.
Set theory is a discipline of mathematics that largely addresses problems that are pertinent to mathematics as a whole, despite the fact that any kind of object can be constructed into a set.Set theory is founded on a simple binary relationship between an object o and a set A.It is written as o A if o is a part (or member) of A. Members of a set are enumerated with commas to denote separation when describing them, or a property of those parts is enclosed in braces.Sets can be associated by the membership relation since they are objects.The given sets are:
U ={1,2,3,4,5,6,7,8,9,10,11,12,13}
A = {3,7,11,13}
B = {3,6,9,12,13}
C = {2,3,5,6,7,8}
Now B' = {1,2,4,5,7,8,10,11}
b) B'∩C = {2,5,7,8,}
c) A∪C = {2,3,5,6,7,8,11,13}
(A∪C)' = {1,4,9,10,12}
(A∪C)'∩B = {9 , 12}
Hence the value of the set (A∪C)'∩B is {9 , 12} .
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A side mirror of a small pick up truck is similar to that of a larger full size pickup truck. If the smaller truck has a rectangular side mirror of width 5.0 in. and height 6.0 in., what is the height in inches of the larger mirror if the width is 10.0 in.?
If the width of larger full size pickup truck is 10.0 in. then its height is equal to 12inches.
As given in the question,
Side mirror of a small pick up truck is similar to larger full size pick up truck.
Smaller truck has rectangular side mirror
Width = 5.0 in.
Height = 6.0 in.
Larger mirror
Width = 10.0 in.
Let h be the height of the larger mirror
Both the mirrors are similar and rectangular in shape.
Hence, sides are in proportion
5 /6 = 10 /h
⇒h = (6 ×10) / 5
⇒ h = 12 in.
Therefore, if the width of larger full size pickup truck is 10.0 in. then its height is equal to 12inches.
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line m and n are parallel when x=
we have those angles must measure the same so
[tex]\begin{gathered} 4x-6=150 \\ 4x=156 \\ x=\frac{156}{4}=39 \end{gathered}[/tex]so x=39
That is just the chart. Disregard question 6. 7. A survey of 381 adult females produced a mean height of 65.2 inches with a standard deviation of 2.8 inches. Construct a confidence interval based on a 95% confidence level.O (64.92, 65.48)© (64.83, 65.57)O (65.19, 65.21)© (64.96, 65.44)
Step 1
Given;
[tex]\begin{gathered} n=381\text{ adults} \\ Mean\text{ \lparen}\mu)=65.2 \\ \sigma=2.8 \end{gathered}[/tex]Step 2
The confidence interval is given as follows;
[tex]CI=\mu\pm t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n}})[/tex]The test statistic for a 95% confidence interval with α = 0.05, the degrees of freedom, df= n-1 = 381-1=380
[tex]t_{\frac{\alpha}{2},df}=t_{\frac{0.05}{2},380}[/tex][tex]t_{\frac{\alpha}{2},df}=t_{\frac{0.05}{2},380}=1.97[/tex][tex]\begin{gathered} C.I=65.2\pm1.97(\frac{2.8}{\sqrt{381}})=65.2\pm0.2825932406 \\ C.I=(64.92,65.48) \end{gathered}[/tex]Answer;
[tex]C.I=(64.92,65.48)[/tex]Which is the area of the circle shown? Use 3.14 for π.
1. 18.84 m^2
2. 37.68 m^2
3. 113.04 m^2
4. 354.95 m^2
Answer:
3: 113.04 m^2
Step-by-step explanation:
pi r^2
3.14 x 36
= 113.04 m^2
:]
Determine weather the sequence 6,12,24,48 could be an an arithmetic sequence.
Answer:
The sequence cannot be arithmetic.
Explanation:
Given the sequence: 6,12,24,48
We want to determine if the sequence is arithmetic.
An arithmetic sequence is a sequence made in which the next term is obtained by the addition of a constant term called the common difference.
In the given sequence:
[tex]\begin{gathered} 12-6=6 \\ 24-12=12 \\ 48-24=24 \end{gathered}[/tex]The difference between the terms is not constant.
Therefore, the sequence cannot be arithmetic.
Penny is selling candles for $3 each at a fundraiser.
If she starts selling with $4 to help her make change, how many candles, x, will she
have to sell to end up with $19?
Answer: x=5
Step-by-step explanation: Based on the given conditions formulate:: 4+3[tex]x[/tex]x=19
Rearrange variables to the left side of the equation: 3x=19-4
Calculate the sum or difference: 3x=15
Divide both sides of the equation by the coefficient of the variable: x=[tex]15/3[/tex]
Cross out the common factor: x=5