rounded to the nearest tenth, what is the area of rectangle ABCD?
Given the rectangle ABCD, you can identify that it is divided into two Right Triangles:
[tex]\begin{gathered} \Delta ACD \\ \Delta ABD \end{gathered}[/tex]• You can find the length of the rectangle by applying the following Trigonometric Function:
[tex]\cos \alpha=\frac{adjacent}{hypotenuse}[/tex]In this case, you can set up that:
[tex]\begin{gathered} \alpha=30\degree \\ adjacent=CD=AB=l \\ hypotenuse=AD=9 \end{gathered}[/tex]Then, substituting values and solving for "l", you get:
[tex]\begin{gathered} \cos (30\text{\degree})=\frac{l}{9} \\ \\ 9\cdot\cos (30\text{\degree})=l \\ \\ l=\frac{9}{2}\sqrt[]{3}ft \end{gathered}[/tex]• In order to find the width of the rectangle, you can use this Trigonometric Function:
[tex]\sin \alpha=\frac{opposite}{hypotenuse}[/tex]In this case, you can say that:
[tex]\begin{gathered} \alpha=30\degree \\ opposite=AC=BD=w \\ hypotenuse=AD=9 \end{gathered}[/tex]Therefore, substituting values and solving for "w", you get:
[tex]\begin{gathered} \sin (30\degree)=\frac{w}{9} \\ \\ 9\cdot\sin (30\degree)=w \\ \\ w=\frac{9}{2}ft \end{gathered}[/tex]• Now you need to use the following formula for calculating the area of a rectangle:
[tex]A=lw[/tex]Where "l" is the length and "w" is the width.
Substituting the length and the width of the given rectangle into the formula and evaluating, you get:
[tex]A=(\frac{9}{2}\sqrt[]{3}ft)(\frac{9}{2}ft)[/tex][tex]A\approx35.1ft^2[/tex]Hence, the answer is: Option C.
Write the conditional
statement in if-then form.
The vertices of a triangle
are not colinear.
The conditional statement for "The vertices of a triangle are not collinear" is "if the points are not collinear then they are vertices of triangle."
What is conditional statement?Conditionals are commands used in programming languages to handle choices. Particularly, conditionals carry out various calculations or actions based on whether a boolean condition defined by the programmer evaluates to true or false.
What is if-then?The hypothesis is a prediction of what will transpire in your experiment. The words "IF" and "THEN" are frequently used when writing the hypothesis. For instance, "I will fail the test if I don't study." Your independent and dependent variables are reflected in the "if" and "then" statements.
"The vertices of a triangle are not collinear" has a conditional statement that reads, "If the points are not collinear, then they are vertices of the triangle."
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help it’ll be greatly appreciated :(
In population 1:
Pattern is changing by 13.5 to 11.5 to 8.3
Which is 2 then 3.2.
In population 2:
Population is decreasing by 2.
Describe pattern.A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Given.
Pattern in which population is changing are:
In population 1:
It is changing by 13.5 to 11.5 to 8.3
Which is 2 then 3.2.
In population 2:
Population is decreasing by 2.
Completing the table:
Population 1 Population 2
42.8 29
38.6 27
33.4 25
27.2 23
Graph is mentioned below.
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The mean number of runs per game scoredby the Chicago Cubs during the 2016 World Series was 3.86 runs, with astandard deviation of 3.36 runs. Apply Chebychev’s Theorem to the datausing k = 2. Interpret the results
Chicago Cubs score between -2.86 and 10.58 runs every game, or at least 75% of their total.
The Chebyshev's Theorem calculates the minimal percentage of observations that are within a certain range of standard deviations from the mean. A wide variety of probability distributions can be used with this theorem. Another name for Chebyshev's Theorem is Chebyshev's Inequality.
Given Mean (X) = 3.86, Standard deviation (SD) = 3.36
According to Chebyshev’s Theorem,
1-1/k^2 proportion of values lies between Mean ± (k × SD )
Given k = 2.
k = x - mean /SD
1-1/k^2 =1-1/2^2
⇒1-1/4=1-0.25
⇒0.75
Therefore Proportion Value = 75%
If k= 2
75% Chebyshev’s intervals are
Lower Limit = Mean - (k × SD )
⇒3.86 - (3.36×2)
⇒3.86 - 6.72 = - 2.86
Upper Limit = Mean + (k × SD )
⇒3.86 + (3.36 × 2)
⇒3.86+6.72 = 10.58
Hence the Chicago Cubs score between -2.86 and 10.58 runs every game, or at least 75% of their total.
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a bond issue outstanding that matures in 19 years. The bonds pay interest semiannually. The bonds have a face value of $1,000 and are currently priced at $995.28. The bonds carry a coupon rate of 3.5 percent. What is the aftertax cost of debt if the total tax rate is 22 percent? Multiple Choice
The after tax cost of debt for the bond is 2.73%
Given,
The face value of the bond, FV = $1000
Present value of the bond, PV = $995.28
Maturity period = 19 years
Coupon rate = 3.5%
Total tax rate = 22%
We have to find the after tax cost of debt for the bond.
The bond pays interest semiannually ;
so coupon rate = 3.5/2 = 1.75
Coupon payment , pmt= 0.0175 x 1000 = $17.5
Maturity, nper = 19 years x 2 = 38
Compute yield rate using spreadsheet = Rate(nper,pmt,-PV, FV)
Then,
= RATE(38, 17.5, -995.28, 1000)
Rate or yield is computed as 3.5%
The present value is negative as it is a cash outflow.
The cost of debt is 3.5%
The tax rate is 22%
After tax cost of debt = 3.5 (1 - 0.22) = 2.73%
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4) Find mZUVW if mZNVW = 61° mZUVW= 15x – 5, and mZUVN= 10x – 11. 15 5x 5
Simplify by combining like terms. Type the termsin alphabetical order.-7a-2y+7+2y+5a=
-7a - 2y + 7 + 2y + 5a
Reordering:
(-7a + 5a) + (-2y + 2y) + 7 =
= -2a + 7 =
= 7 - 2a
I need help with this question but no one is helping me! Can someone please help me
Answer:
0.053
Step-by-step explanation:
the probability of taking a Boston creme first is 6/19 (19 is the total doughnuts in the box), then the probability of taking a chocolate glazed second would be 3/18 (bc there would be 18 left after taking one first). then multiply these fractions together. as a decimal you get 0.053 to 3 decimal places
21. Complete the following transactions and explain how they would appear in your register.
(5 points each - 2 points for the correct answers and 3 points for a correct explanation of your
process)
• You open your bank account on April 16 with a tax refund check of $145.00.
You pay Sell Phone $65.34 on April 18. (Check 794)
• You deposit your paycheck on April 23. ($9.76 hour for 35 hours)
• You buy $61.32 (4% sales tax not included) in clothes from BargainsRUs on April 24
using your debit card.
Be sure to include in your response:
.
• the steps you followed to complete your computations
the balance as of April 24
• the process for entering the transaction in the registry
(5 points)
After all the transaction, money left in the bank account is $15.8872.
Given that, you open your bank account on April 16 with a tax refund check of $145.00. You pay Sell Phone $65.34 on April 18.
What is a tax refund check?A tax refund is a reimbursement to a taxpayer for any excess amount paid to the federal government or a state government.
On April 16th balance in the account = $145.00 cost of phone = $65.34 on April 18.
Balance on April 18 = 145.00-65.34
= $79.66
Deposited check $9.76 on 23rd April for 35 hours
Balance on 23rd April = 79.66+9.76
=$89.42
Since, the check deposited only for 35 hours, again balance on 24th April will be $79.66
On 24th April you brought clothes from BargainsRUs for
61.32+4% of 61.32
= 61.32+2.4528
= $63.7728
So, the remaining balance in the account = 79.66-63.7728
=$15.8872
Therefore, after all the transaction, money left in the bank account is $15.8872.
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standard deviation for binomial distribution n=48 p=3/5
If a standard deviation for binomial distribution n = 48 p = 3/5 . The standard deviation is 3.39.
What is the Standard deviation?Using this formula to determine or find the standard deviation for the binomial distribution
σ =√np(1−p)
Where:
n = 48
p = 3 / 5 or 0.6
σ = ?
Let plug in the formula so as to determine the standard deviation
σ =√ (48) (0.6) ( 1 - 0.6)
σ =√ (48) (0.6) (0.4)
σ =√ 11.52
σ = 3.39
Therefore we can conclude that 3.39 is the standard deviation.
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The width of a rectangle is 4 less than the length. If the area of the rectangle is 165cm?,solve for the length and width of the rectangle.
length:15 cm
width: 14 cm
Explanation
Step 1
Let
w represents the width of the rectangle
l represents the length of the rectangle
a)The width of a rectangle is 4 less than the length,hence
write this in math terms, replace
[tex]\begin{gathered} \text{width}=length-4 \\ w=l-4\rightarrow equation\text{ (1)} \end{gathered}[/tex]b)the area of the rectangle is 165 square cm
the area of a rectangle is given by
[tex]\begin{gathered} \text{Area}=\text{length}\cdot\text{width} \\ \text{replace} \\ 165cm^2=l\cdot w\rightarrow \\ 165=l\cdot w\rightarrow equiation(2) \end{gathered}[/tex]Step 2
now, solve the equations
[tex]\begin{gathered} w=l-4 \\ 165=lw \end{gathered}[/tex]a) replace the w from equation (1) into equation(2)
[tex]\begin{gathered} 165=lw \\ 165=l(l-4) \\ 165=l^2-4l \\ \text{subtract 165 on both sides} \\ 165-165=l^2-4l-165 \\ l^2-4l-165=0 \end{gathered}[/tex]b) now, we have a quadratic equation in the form
[tex]ax^2+bx+c=0[/tex]hence, we can use the quadratic formula to solve
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]let
a=1
b=-4
c=-165
replace
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-4)\pm\sqrt[]{-4^2-4(1)(-165)}}{2\cdot1} \\ x=\frac{4\pm\sqrt[]{676}}{2}=x=\frac{4\pm26}{2} \end{gathered}[/tex]therefore
[tex]\begin{gathered} x=\frac{4\pm26}{2} \\ x_1=\frac{4+26}{2}=\frac{30}{2}=15 \\ x_2=\frac{4-26}{2}=\frac{-22}{2}=-11 \end{gathered}[/tex]as we are searchinf for a distance, the only valid answer is 15
so, the answer is length= 15 cm
[tex]l=15\text{ cm}[/tex]c) finally, replace the l value into equation (1) to find the width
[tex]\begin{gathered} w=l-4\rightarrow equation\text{ (1)} \\ w=15-4 \\ w=11 \end{gathered}[/tex]therefore, the width is 11 centimeters
I hope this helps you
If 3 gallons of paint are needed for 75 ft of fence, how many gallons are needed for 1200 ft of fence?
Answer:
48 gallons of paint are needed.
Step-by-step explanation:
Set up a proportion.
Like this: x is for the unknown number of gallons.
[tex]\frac{3}{75} = \frac{x}{1200}\\ 75(x)= 3(1200)\\ 75x=3600\\x= 3600/75\\x= 48 Answer[/tex]
What is the standard deviation for the group of data items
Check the picture below.
5x+2y=10 Does the relation represents a function
Answer:
Yes, it is a linear function. For every input there is only 1 output.
Step-by-step explanation:
A line with a slope of -2 passes through the point (3,-2). Which of the
following is the equation of the line?
The equation of the line with slope -2 and passing through the point (3,-2) is y+2x-4=0.
What is the equation of a line with a given slope and a point?The point-slope formula is used to find the equation of the line passing through a point (a,b) and having a slope of m.
A straight line equation of the form (y-b) = m(x-a), where m is the slope of the line and (a,b) are the coordinates of a given point on the line, is the standard form given for the point-slope form of the line.
A point (3,-2) and a slope -2 are given.
Use the standard Point-slope form of the line to find the equation of the line.
(y-b) = m(x-a)
Put the given values in the Point-slope equation.
y-(-2)=-2(x-3)
Simplify the equation to get the equation of the line.
y+2=-2x+6
y+2x-4=0
So, the equation of the line is y+2x-4=0.
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what is 5 to the 6 power written in expanded form
5 to the 6th power is:
[tex]5^6[/tex]This, written in expanded form, is:
[tex]5\cdot5\cdot5\cdot5\cdot5\cdot5[/tex]Simplify. DO NOT PUT ANY SPACES IN YOUR ANSWER. - 3\4 (16r-24)
Explanation
[tex]-\frac{3}{4}(16r-24)[/tex]Step 1
eliminate the parenthesis applyng distributive property
[tex]\begin{gathered} -\frac{3}{4}(16r-24) \\ \frac{-3\cdot16r}{4}+\frac{3\cdot24}{4} \\ \frac{-48r}{4}+\frac{72}{4} \\ -12r+18 \end{gathered}[/tex]I hope this helps you
Solve the inequality and graph the solution on the line provided. 9 + 3x ≥ -6
9 + 3x ≥ -6
9 is adding on the left, then it will subtract on the right
3x ≥ -6 - 9
3x ≥ -15
3 is multiplying on the left, then it will divide on the right
x ≥ -15/3
x ≥ -5
Transforming the graph of a quadratic, cubic, square root, or absolute value function
Explanation:
If we have a function g(x) = -f(x), then g(x) will be f(x) reflected across the x-axis.
If g(x) = f(x) - c, g(x) will be f(x) shifted c units down
If g(x) = f(x + c), g(x) will be f(x) shifted c units to the left.
In this case, the initial function is f(x) = |x| and g(x) = -|x + 3| - 2, then
g(x) = -f(x + 3) - 2
Therefore, g(x) will be the initial function reflected across the x-axis, shifted 3 units to the left and 2 units down.
Answer:
So, the graph for y = -|x + 3| - 2 will be:
Describe a series of transformations Matt can perform to device if the two windows are congruent
Combining the three different transformations—rotations, reflections, and translations—will result in congruent shapes. Actually, any pair of congruent shapes can be matched to one another using a combination of one or more of these three transformations.
What are transformation ?There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.
We now know that during rigid transformations, the size and shape of the figures are maintained (reflections, translations, and rotations). The pre-image and the image are always in agreement.
Matt has the following transformational abilities:
Reflection (Flip)
A reflection keeps its original shape because the comparable points from the pre-image to the image stay at the same distance from the line of reflection.
Rotations as a Congruence Transformation
Rotations as a Congruence Transformation
A figure twists when it rotates. The figurine looks to have fallen over, although being the same size and shape. A great illustration of a rotation in the actual world is a clock. The connecting arms of a clock rotate around its axis every hour or every day. A rotation is defined by its degree; common rotations include 90 degrees, 180 degrees, and 270 degrees. The figure completes a full 360-degree rotation before returning to its starting point. A rotation must include indicate the clockwise or counterclockwise direction. This information can be used to calculate the degree, quantity, and direction of a revolution.
Translational congruence transformation
We refer to a movement as a translation when an object or shape is moved from one place to another without changing its size, shape, or orientation. Every point on an item or shape is moved by the same amount and in the same direction during a translation, sometimes referred to as a slide.
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What are the X and Y intercepts for the graph shown in the picture?
Based on the given figure, you can conclude:
x-intercepts:
x = 0
x = number in between 100 and 125, approximately 105
x = number greater than 175, approximately 180
y-intercepts:
y = 0
For the second and third x-intercepts there is no possible to specifiy the exact numbers due to the scale units of the graph.
Given: Q R ≅ S T
Q T ≅ R S
Prove: Q R S T is a parallelogram
The proof that Q R S T is a parallelogram is given and enumerated in the following paragraph.
What is mathematical proof?A mathematical proof is a deductive argument for a mathematical declaration that demonstrates that the provided assumptions logically ensure the conclusion.
The proof that the above-named geometrical shape is a parallelogram goes thus:
Statements Reasons
1. [tex]\overline{QR}[/tex] ≅ [tex]\overline{ST}[/tex] Given
2. [tex]\overline{RS}[/tex] ≅ [tex]\overline{QT}[/tex] Given
3. [tex]\overline{RT}[/tex] ≅ [tex]\overline{TR}[/tex] Reflexive Property
4. [tex]\Delta QRS[/tex] ≅ [tex]\Delta STQ[/tex] SSS Congruence Theorem
5. A 1 ≅ A 4 CPCTC Property
6. A 2 ≅ A3 CPCTC Property
7. QR | ST Alternate Interior Angles Converse
8. QT | RS Alternate Interior Angles Converse
9. Q R S T is a parallelogram Definition of parallelogram
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The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks plus $125 for each ton of sugar transported. The total cost, C (in dollars), for transporting n tons is given by the following function.
C (n) = 6500 + 125n
(a). What is the total cost of transporting 12 tons?
(b). If the total cost is $9375, how many tons is the company transporting?
The total cost of transporting 12 tons is $8000 and number of tons the company transporting is 23.
The total cost of transporting 12 tons can be calculated by keeping the value of number of tons in the formula.
Total cost = 6500 + 125×12
Performing multiplication on the Right Hand Side of the equation
Total cost = 6500 + 1500
Performing addition on the Right Hand Side of the equation
Total cost = 8000
The number of tons can be calculated by keeping the total cost in the formula.
9375 = 6500 + 125n
125n = 9375 - 6500
Performing subtraction on Right Hand Side of the equation
125n = 2875
n = 2875 ÷ 125
Performing division
n = 23
So, the total cost is $8000 and number of tons is 23.
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Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)
Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. The tax rate t that maximizes revenue for the government is 66.992%.
Tax rate that maximizes revenueRevenue can be defined as the amount or the income a person or an organization generated from the sales of goods and services.
Given function :
Total sale = S(t) = 7−6∛t
Hence,
Expression for Revenue rate = r(t) = tS(t)
Now let substitute and solve expression
r(t) = t (7−6∛t)
= 7t−6(t)^4/3
Differentiate the expression
d[r(t)] dt = r′(t)
r′(t) = 7− (4/ 3) 6(t)^1/3
=7−8(t) ^1/3 ........ expression (1)
Maximum revenue
r′(t) = 0
Substitute and solve expression (1)
0 =7−8(t)^1/3
(t) = (7/8)^3
= 0.66992 × 100
= 66.992%
Therefore we can conclude that the tax rate t that maximizes revenue is 66.992%.
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The complete question is :
Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)
S(t)=7−6∛t
c) 2.5-1.4 x 1.4 x 1.4 2.5 x 2.5 x (2.5)² + 2.5 x 1.4+ (1.4)²
We will have the following:
[tex]\begin{gathered} \frac{2.5\ast2.5\ast2.5-1.4\ast1.4\ast1.4}{(2.5)^2+2.5\ast1.4+(1.4)^2}=\frac{15.625-2.744}{6.25+3.5+1.96} \\ \\ =1.1 \end{gathered}[/tex]So, the simplification is equal to 1.1.
***Explanation***
[tex]\frac{2.5\operatorname{\ast}2.5\operatorname{\ast}2.5-1.4\operatorname{\ast}1.4\operatorname{\ast}1.4}{(2.5)^2+2.5\operatorname{\ast}1.4+(1.4)^2}[/tex]First, we multiply all the values that are asked to be multiplied, and we also operate all the exponents. [We recall that a value at the power of a number is the number of times the value is multiplied by itself], then we get that:
[tex]\frac{2.5\ast2.5\operatorname{\ast}2.5-1.4\operatorname{\ast}1.4\operatorname{\ast}1.4}{(2.5\ast2.5)+2.5\operatorname{\ast}1.4+(1.4\ast1.4)}=\frac{15.625-2.744}{6.25+3.5+1.96}[/tex]Finally we operate the simpler and lower in the hierarchy of operations expressions:
Please help solve this.
Answer:
C
Step-by-step explanation:
[tex]x^2 - 2x - 1 = 0\\x^2 = 2x + 1\\x^4 = 4x^2 + 4x + 1\\x^4 = 4(2x + 1) + 4x + 1\\x^4 = 8x + 4 + 4x + 1\\x^4 = 12x + 5[/tex]
the temperature (in degrees Fahrenheit) x hours after 5 p.m. is represented by t(x)=-4+72. The temperature x hours after 10 a.m. is represented by d(x)=4x+72. Describe the transformation from the graph of t to the graph of d.
The graph of function d is a reflection across the y-axis of the graph of function t.
The types of transformation.In Geometry, there are different types of transformation and these include the following:
DilationRotationTranslationReflectionWhat is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Geometry, a reflection across the y-axis (y = x) of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, function t(x) = -4x + 72 would be transformed to function d:
d(x) = -(-4x) + 72.
d(x) = 4x + 72.
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Complete Question:
The temperature (in degrees Fahrenheit) x hours after 5 p.m. is represented by t(x) = -4x + 72. The temperature x hours after 10 a.m. is represented by d(x) = 4x + 72. Describe the transformation from the graph of t to the graph of d.
So what's in the photo is what I need help with.
Answer:
1 == B No Solutions
2 == A One Solution
3 == C Infinitely Many Solutions
Explanation:
We first find go through each system and see which has one solution, no solutions, and infinitely many solutions.
1.
x
Question is in the photo.
The derivative of y = [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
What is a derivative of a function?The derivative of a function f(x) represents its rate of change.
We have,
y = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex]
Putting log on both sides.
[ log a² = 2 log a ]
log y = 1/2 log [tex]\frac{x(x+4)}{(5x+1)(3x+7)}[/tex]
log y = 1/2 [ log x(x+4) - log (5x +1)(3x + 7) ]
log y = 1/2 [ log x(x+4) - log(5x + 1) - log (3x + 7) ]
Derivation on both sides.
[ d(logx)/dx = 1/x ]
d (log y) / dx = d [ {1/2 log x(x+4) - log(5x + 1) - log (3x + 7)} ] / dx
1/y y' = 1/2[ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]
y' = y/2 [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ]
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
Thus,
The derivative of y = [ 1/x(x+4) - 1/(5x + 1) - 1/(3x + 7) ] is
y' = [tex]\sqrt{\frac{x(x-4)}{(5x+1)(3x+7)} }[/tex] x 1/2 [1/x(x+4) - 1/(5x + 1) - 1/(3x + 7)]
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At the market, 5 light bulbs cost $9
How much do 7 light bulbs cost?