Answer: No, the orders are not independent.
Step-by-step explanation:
If event 1 has some possible outcomes, suppose that we choose a given outcome 1 with a probability P1, and event 2, also with different possible outcomes, we can select an outcome 2, that has a probability P2, and the two events are independent (meaning that the outcome in event 1 does not affect the outcome in event 2, and vice versa)
Then the probability of outcome 1 and outcome 2 happening at the same time is equal to the product of their individual probabilities.
P = P1*P2.
In this case, event 1 is the selection of the pizza, and outcome 1 is the selection of the square pizza, with a probability of 55%.
Event 2 is the selection of the drink, outcome 2 is the order of a soft drink, with a probability of 72%.
If those two events were independent, then the probability that a customer orders a square pizza and a soft drink would be:
P = 0.55*0.72 = 0.396 (or 39.6%)
But we know that the actual probability is 48%.
So this is larger, which means that the outcomes are not independent.
A portion of the quadratic formula proof is shown. Fill in the missing reason.
Answer:
Find a common denominator on the right side of the equation
Step-by-step explanation:
The equation before the problem is
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
The next step in solving the above equation is to fibd tge common denominator on the right side of the equation.
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
X² + b/a(x) + (b/2a)²= -4ac/4a² + b²/4a²
X² + b/a(x) + (b/2a)²=( b²-4ac)/4a²
The right side of the equation now has a common denominator
The next step is to factorize the left side of the equation.
(X+b/2a)²= ( b²-4ac)/4a²
Squaring both sides
X+b/2a= √(b²-4ac)/√4a²
Final equation
X=( -b+√(b²-4ac))/2a
Or
X=( -b-√(b²-4ac))/2a
A report states that the mean yearly salary offer for students graduating with a degree in accounting is $48,722. Suppose that a random sample of 50 accounting graduates at a large university who received job offers resulted in a mean offer of $49,870 and a standard deviation of $3900. Do the sample data provide strong support for the claim that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722? Test the relevant hypotheses using α = 0.05. State your conclusion.A. Reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.B. Do not reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.C. Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.D. Do not reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Answer:
Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Step-by-step explanation:
First of all let's define the hypothesis;
Null hypothesis;H0; μ = $48,722
Alternative hypothesis;Ha; μ > $48,722
Now, let's find the test statistic for the z-score. Formula is;
z = (x' - μ)/(σ/√n)
We are given;
x' = 48,722
μ = 49,870
σ = 3900
n = 50
Thus;
z = (49870- 48722)/(3900/√50)
z = 2.08
So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526
This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722
Can someone please help me?
Negative Integers are :
Less than zeroTo the left of zero on a number line.What is credit?
an arrangement in which you receive money, goods, or services now in exchange for the promise of payment later
an arrangement in which you receive goods or services in exchange for other goods and services
an arrangement in which you receive money now and pay it bulk later with fees?
HELP NEED PRECALC HELP WILL GIVE BRAINLIEST PLEASE HELP
From your earlier questions, we found
[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]
so the wave has amplitude √29. The weight's maximum negative position from equilibrium is then -√29, so you are solving for t in the given interval for which
[tex]\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)=-\dfrac{\sqrt{29}}2[/tex]
Divide both sides by √29:
[tex]\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)=-\dfrac12[/tex]
Take the inverse sine of both sides, noting that we get two possible solution sets because we have
[tex]\sin\left(\dfrac{7\pi}6\right)=\sin\left(\dfrac{11\pi}6\right)=-\dfrac12[/tex]
and the sine wave has period 2π, so [tex]\sin x=\sin(x+2\pi)=\sin(x+4\pi)=\cdots[/tex].
[tex]\implies 4\pi t+\tan^{-1}\left(\dfrac52\right)=\dfrac{7\pi}6+2n\pi[/tex]
OR
[tex]\implies 4\pi t+\tan^{-1}\left(\dfrac52\right)=\dfrac{11\pi}6+2n\pi[/tex]
where n is any integer.
Now solve for t :
[tex]t=\dfrac{\frac{7\pi}6+2n\pi-\tan^{-1}\left(\frac52\right)}{4\pi}[/tex]
OR
[tex]t=\dfrac{\frac{11\pi}6+2n\pi-\tan^{-1}\left(\frac52\right)}{4\pi}[/tex]
We get solutions between 0 and 0.5 when n = 0 of t ≈ 0.196946 and t ≈ 0.363613.
How can a company use a scatter plot to make a future sales decision?
Answer:
Hope this helps :)
Step-by-step explanation:
A scatter plot is a two-dimensional diagram that displays individual data points based on the intersection of two variables, shown as vertical and horizontal axes. Individual data points or values are plotted at particular coordinates of the two variables being studied. Patterns of data points provide a visual representation of relationship between the two variables. A wide range of jobs and careers use this valuable analytical tool for data analysis and decision making.
My conclusion,
They help organize important data for future occurences.
What is f ( 1/3)? When the function is f(x) =-3x+7
Answer:
f(1/3) = 6
Step-by-step explanation:
f(x) =-3x+7
Let x = 1/3
f(1/3) =-3*1/3+7
= -1 +7
= 6
Answer:
f(1/3) = 6
Step-by-step explanation:
The function is:
● f(x) = -3x+7
Replace x by 1/3 to khow the value of f(1/3)
● f(1/3) = -3×(1/3) +7 = -1 +7 = 6
Help pleaseeeee!!!!!!
Answer:
0.05m^2
Step-by-step explanation:
5 divided by 100
if the nth term is , then the (n+1)st is: Sorry if formatting is off, check the image to see the equation better!
Answer:
5
----------
( n+1)(n+2)
Step-by-step explanation:
5
----------
n ( n+1)
Replace n with n+1
5
----------
(n+1) ( n+1+1)
5
----------
( n+1)(n+2)
We replace every 'n' with n+1 and simplify
[tex]\frac{5}{(n+1)(n+1+1)} = \frac{5}{(n+1)(n+2)}[/tex]
For each ordered pair, determine whether it is a solution to y=-9.
Is it a solution?
Yes or No
(1, -9)
(7,3)
(-9,4)
(0, -9)
Answer:
(1, -9) yes
(7,3) no
(-9,4) no
(0, -9) yes
Step-by-step explanation:
The y value must be -9
The x value can be any value to satisfy the equation y = -9
In this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ
Answer:
2.7 in²
Step-by-step explanation:
Given that ∆BAC ~ is similar to ∆EDF, the ratio of the area of ∆BAC to the area of ∆EDF = the square of the ratio of their corresponding sides.
Thus, let x be the area of ∆EDF
[tex] \frac{6}{x} = (\frac{3}{2})^2 [/tex]
[tex] \frac{6}{x} = \frac{9}{4} [/tex]
Cross multiply
[tex] x*9 = 4*6 [/tex]
[tex] 9x = 24 [/tex]
[tex] \frac{9x}{9} = \frac{24}{9} [/tex]
[tex] x = 2.67 [/tex]
Area of ∆EDF = 2.7 in²
Mark has a collection of 80 coins. There are only nickels and dimes in the collection. The total value of the coins is $5.00. How many dimes does Mark have?
Answer:
number of nickel = 60
number of dimes = 20
Step-by-step explanation:
1 nickel = 5 cents
1 dimes = 10 cents
$1 = 100 cents
we will use these value to solve the questions
_______________________________
Total no of coins = 80
let the number of nickels be x
let the number of dimes be y
thus,
x+y = 80
y = 80-x equation 2
value of x nickels = 5x
value of y dimes = 10y
Total value of x nickels and y dimes = 5x+10y
The total value of the coins is $5.00
total value of the coins in cents = 5*100 = 500
thus
5x+10y = 500
using y = 80-x from equation 2
5x + 10(80 - x) = 500
5x + 800 - 10x = 500
-5x = 500 - 800 = -300
x = -300/-5 = 60
Thus,
number of nickel = 60
number of dimes = 80-60 = 20
A tin of tennis balls costs $6.99, and each tin contains 4
tennis balls.
If the tennis balls were sold individually, then
approximately how much would one tennis ball cost?
$
Answer:
About $1.75 per tennis balls
Step-by-step explanation:
A tin of 4 tennis balls costs $6.99. We are asked to find the price of one tennis ball.
We need to find the unit price, or price per ball.
Divide the cost by the number of tennis balls.
cost / tennis balls
cost = $6.99
tennis balls = 4 tennis balls
$6.99 / 4 tennis balls
Divide 6.99 by 4.
$1.7475 / 1 tennis ball
Round to the nearest cent or hundredth. The 7 in the thousandth place tells us to round the 4 to a 5 in the hundredth place.
$1.75 / 1 tennis ball
It would cost approximately $1.75 for one tennis ball.
A) Which of triangle A, B, C and D is congruent to triangle E.? B) Which other two triangles (from A, B, C and D) are congruent to each other? Please help!
Answer:
c is congruent to e congruent means to be the same
Step-by-step explanation:
Write the expression as a single term, factored completely. Do not rationalize the denominator. 54x2+1−−−−−−√+20x4x2+1√ Select one: a. 5(4x2+4x+1)4x2+1√ b. 20x2+20x+1)5x+1 c. 20x2+20x+1)4x2+1√ d. 5(4x2+4x+1)5x+1
When we write expression 5√(4x² + 1) + 20x / √(4x² + 1) as singled term factorised completely, we have 5(4x² + 4x + 1) / √(4x² + 1) (Option A)
Data obtained from the question5√(4x² + 1) + 20x / √(4x² + 1)Factorised =?How to factorised 5√(4x² + 1) + 20x / √(4x² + 1)5√(4x² + 1) / 1 + 20x / √(4x² + 1)
Least common multiple (LCM) is √(4x² + 1)
[(5√(4x² + 1) × √(4x² + 1) + 20x] / √(4x² + 1)
[5(4x² + 1) + 20x] / √(4x² + 1)
[20x² + 5 + 20x] / √(4x² + 1)
[20x² + 20x + 5] / √(4x² + 1)
5(4x² + 4x + 1) / √(4x² + 1)
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Complete question
See attached photo
Factor this trinomial completely. -6x^2 +26x+20
Answer:
Step-by-step explanation:
-6x²+26x+20
=-2(3x²-13x-10)
=-2(3x²-15x+2x-10)
=-2[3x(x-5)+2(x-5)]
=-2(x-5)(3x+2)
What is the value of b.
C=25
s=9
B=4c-s2
Answer:
82
Step-by-step explanation:
Plug in the variables into the equation and solve for B but remember your order of operations when solving multiplication/division before addition/subtraction.
B = 4*25-9*2
B = 100-18
B = 82
Which of these functions could have been the graph shown below?
Answer:
B
Step-by-step explanation:
we take the only point we know
(0,20)
in A when x =0
[tex]f(x)=e^{20x} =e^{20*0}=1[/tex]
in B when x=0
[tex]f(x)=20e^x=20e^0=20*1=20[/tex]
fits
in C
[tex]f(x)=20^x=20^0=1[/tex]
in D
[tex]f(x)=20^{20x}=20^{20*0}=20^0=1[/tex]
so the only choice is B
Multiply: (x−5)(x−7) A x2−12x+35 B x2+2x+35 C x2+35 D x2+35x−12
Answer:
x^2 -12x+35
Step-by-step explanation:
(x−5)(x−7)
FOIL
first x*x = x^2
outer -7x
inner -5x
last -7*-5 = 35
Add them together
x^2 -7x-5x +35
x^2 -12x+35
Answer:
Step-by-step explanation:
x*x=2x
x*-7=-7x
-5*x=-5x
-5*-7=+35
2x-12x+35
A
The manager of the video department at a department store plans to purchase a large number of DVDs of a recent movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling boxes of 14 DVD movies for $170. Only complete boxes of DVD movies can be purchased. Complete part a) and b) below. a)
a) If the manager can purchase boxes of DVD movies from either or both suppliers, determine the maximum number of DVD movies that can be purchased for $415. Indicate how many boxes of 20 and how many boxes of 14 will be purchased.
— box(es) of 20 and — box(es) of 14
b) How much will the DVD movies cost?
They will cost $—
Answer:
1 box of 20 and 1 box of 14
They will cost $410
Step-by-step explanation:
1. Find how many boxes of 20 DVD movies can be bought
415 - 240 = 175
1 box of 20 DVD movies can be sold
2. Find how many boxes of 14 DVD movies can be bought from $175
175 - 170 = 5
1 box of 14 DVD movies can be bought
3. Find the cost
240 + 170 = 410
Why is f (x) = (3x + 1/3)^2 + 8/9 not the vertex form of f (x)
not the vertex form of f (x) = 9x^2 +2x +1?
O The expression has a constant outside of the squared term.
O Some of the terms are fractions instead of integers.
O The expression is not the product of two binomials.
O The variable x has a coefficient.
Answer:
The Variable has a coefficient.
Step-by-step explanation:
The diameter of steel rods manufactured on two different extrusion machines is being investigated. Two random samples of sizes n1"=15 and n2"=17 are selected, and the sample means and sample variances are x1 =8.73, s2=0.35, x =8.68, and s2=0.40, respectively. Assume that σ1^2 = σ2^2 that the data are drawn from a normal distribution.
Required:
a. Is there evidence to support the claim that the two machines produce rods with different mean diameters? Use alpha=0.05 in arriving at this conclusion.
b. Find the P-value for thet-statistic you calculated in part (a).
c. Construct a 95% confidence interval for the difference in mean rod diameter. Interpret this interval.
Answer:
a) No sufficient evidence to support the claim that the two machines produce rods with different mean diameters.
b) P-value is 0.80
c) −0.3939 <μ< 0.4939
Step-by-step explanation:
Given Data:
sample sizes
n1 = 15
n2 = 17
sample means:
x1 = 8.73
x2 = 8.68
sample variances:
s1² = 0.35
s2² = 0.40
Hypothesis:
H₀ : μ₁ = μ₂
H₁ : μ₁ ≠ μ₂
Compute the pooled standard deviation:
[tex]s_{p} = \sqrt{\frac{(n_{1} - 1)s_{1}^{2} + (n_{2} - 1)s_{2}^{2}}{n_{1} +n_{2} -2} }[/tex]
[tex]= \sqrt{\frac{(15-1)0.35+(17-1)0.40}{15+7-2}}[/tex]
[tex]= \sqrt{\frac{(14)0.35+(16)0.40}{30}}[/tex]
[tex]= \sqrt{\frac{4.9+6.4}{30}}[/tex]
[tex]= \sqrt{\frac{11.3}{30}}[/tex]
[tex]= \sqrt{0.376667}[/tex]
= 0.613732
= 0.6137
Compute the test statistic:
[tex]t = \frac{x_{1} -x_{2} }{s_{p} \sqrt{\frac{1}{n_{1} }+\frac{1}{n_{2} } } }[/tex]
[tex]= \frac{8.73-8.68}{0.6137\sqrt{\frac{1}{15}+\frac{1}{17} } }[/tex]
[tex]= \frac{0.05}{0.6137\sqrt{0.06667+0.05882} } }[/tex]
[tex]= \frac{0.05}{0.6137\sqrt{0.12549} } }[/tex]
[tex]= \frac{0.05}{0.6137(0.354246)} } }[/tex]
[tex]= \frac{0.05}{0.6137(0.354246)} } }[/tex]
= 0.05 / 0.217401
= 0.22999
t = 0.230
Compute degree of freedom:
df = n1 + n2 -2 = 15 + 17 - 2 = 30
Compute the P-value from table using df = 30
P > 2 * 0.40 = 0.80
P > 0.05 ⇒ Fail to reject H₀
Null hypothesis is rejected when P-value is less than or equals to level of significance. But here the P-value = 0.80 and level of significance = 0.05. So P-value is greater than significance level. Hence there is not sufficient evidence to support the claim that population means are different.
Construct a 95% confidence interval for the difference in mean rod diameter:
confidence = c = 95% = 0.95
α = 1 - c
= 1 - 0.95
α = 0.05
Compute degree of freedom:
df = n1 + n2 -2 = 15 + 17 - 2 = 30
Compute [tex]t_{\alpha /2}[/tex] with df = 30 using table:
t₀.₀₂₅ = 2.042
Compute confidence interval:
= [tex](x_{1}-x_{2})-t_{\alpha/2} ( s_{p} )\sqrt{\frac{1}{n_{1} }+\frac{1}{n_{2} } }[/tex]
= (8.73 - 8.68) - 2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]
= 0.05 - 2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]
= 0.05 - 1.253175 [tex]\sqrt{0.06667+0.05882} } }[/tex]
= 0.05 - 1.253175 [tex]\sqrt{0.12549} } }[/tex]
= 0.05 - 1.253175 (0.35424))
= 0.05 - 0.443925
= −0.393925
= −0.3939
[tex](x_{1}-x_{2})+t_{\alpha/2} ( s_{p} )\sqrt{\frac{1}{n_{1} }+\frac{1}{n_{2} } }[/tex]
= (8.73 - 8.68) + 2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]
= 0.05 + 2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]
= 0.05 + 1.253175 [tex]\sqrt{0.06667+0.05882} } }[/tex]
= 0.05 + 1.253175 [tex]\sqrt{0.12549} } }[/tex]
= 0.05 + 1.253175 (0.35424))
= 0.05 + 0.443925
= 0.493925
= 0.4939
−0.3939 <μ₁ - μ₂< 0.4939
Officer Jacobi drove 180 miles in his patrol car during part of May. The distance represents 40% of May. How many miles did he drive all of May? a) 710 miles b) 420 miles c) 720 miles d) 450 miles Need Help on How to work this problem out, what formula would I use?
Answer:
D: 450 miles
Step-by-step explanation:
So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):
[tex]0.4D=180[/tex]
This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:
[tex]0.4D=180\\D=450[/tex]
So the answer is D or 450 miles.
Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.
What number is the opposite of -3?
Explain your reasoning
Yo help me real quick?
Answer:
1,2 and 6
Step-by-step explanation:
pie symbol
2/3
0.333333....
Janine and Thor are both running for class president. Janine goes down a hallway in the school and puts a sticker on every fourth locker. Thor goes down the same hallway, putting one of his stickers on every fifth locker. If there are 130 lockers in the hallway, how many have both students' stickers?
Answer:
6 lockers have both students' stickers
Step-by-step explanation:
There are 130 lockers in the hallway
Janine goes down a hallway in the school and puts a sticker on every fourth locker.
Janine= 4th, 8th, 12th, 16th, 20th, 24th, 28th, 32nd, 36th, 40th, 44th, 48th, 52nd, 56th, 60th, 64th, 68th, 72nd, 76th, 80th, 84th, 88th, 92nd, 96th, 100th, 104th, 108th, 112th, 116th, 120th, 124th, 128th.
Thor goes down the same hallway, putting one of his stickers on every fifth locker
Thor= 5th, 10th, 15th, 20th, 25th, 30th, 35th, 40th, 45th, 50th, 55th, 60th, 65th, 70th, 75th, 80th, 85th, 90th, 95th, 100th, 105th, 110th, 115th, 120th, 125th, 130th.
Common multiples of Janine fourth locker and Thor fifth locker= 20, 40, 60, 80, 100, 120
Therefore,
6 lockers have both students' stickers
(08.01 MC)
The volume of a pyramid that fits exactly inside a cube is 9 cubic feet. What is the volume of the cube? (5 points)
Select one:
a. 3 cubic feet
b. 6 cubic feet
c. 18 cubic feet
d. 27 cubic feet
Answer:
d. 27 cubic feet
Step-by-step explanation:
volume of cube = s^3 = B * s
volume of pyramid = (1/3) * B * h
The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.
volume of pyramid = 9 cu ft
volume of cube = 3 * 9 cu ft = 27 cu ft
Answer: d. 27 cubic feet
Answer:
27 ft^3 (Answer d)
Step-by-step explanation:
Here the volume of the pyramid is (1/3) the volume of the cube:
Letting s represent the length of one side of the base,
(1/3)(s)^2(s) = 9 ft^3, equivalent to s^3 = 27.
Solving for s, we get s = 3 ft.
Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)
True or False. The statistician should use Printout C to perform a t-test on the GROUP variable in the regression model. g
Answer:
False
Step-by-step explanation:
Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.
Which is an infinite arithmetic sequence? a{10, 30, 90, 270, …} b{100, 200, 300, 400} c{150, 300, 450, 600, …} d{1, 2, 4, 8}
Answer:
C
Step-by-step explanation:
An arithmetic sequence has a common difference d between consecutive terms.
Sequence a
30 - 10 = 20
90 - 30 = 60
270 - 90 = 180
This sequence is not arithmetic
Sequence b
200 - 100 = 100
300 - 200 = 100
400 - 300 = 100
This sequence is arithmetic but is finite, that is last term is 400
Sequence c
300 - 150 = 150
450 - 300 = 150
600 - 450 = 150
This sequence is arithmetic and infinite, indicated by ........ within set
Sequence d
2 - 1 = 1
4 - 2 = 2
8 - 4 = 4
This sequence is not arithmetic
Thus the infinite arithmetic sequence is sequence c
9. Marvin Gate bought some fencing from a wholesaler for $6,000. The wholesaler offered a trade discount of 35%. What was the original price?
(Round to the nearest cent.)
A. $6,230.77
O B. $9.230.77
O C. $6,930.77
D. 55,930 77
Mark for review (Will be highlighted on the review page)
Answer:
B - %9230.77
Step-by-step explanation:
the original price of the fencing before the trade discount was approximately $9,230.77.
To find the original price of the fencing before the trade discount, we need to calculate the amount that corresponds to a 35% decrease from the discounted price.
Let's denote the original price as "P". The discounted price is given as $6,000.
The discounted price is calculated by subtracting the discount amount from the original price:
Discounted price = Original price - Discount amount
The discount amount is determined by multiplying the original price by the discount rate:
Discount amount = Original price × Discount rate
Given that the discount rate is 35% (or 0.35), we have:
Discount amount = P × 0.35
Substituting the discounted price of $6,000, we can write the equation as:
$6,000 = P - (P × 0.35)
Simplifying the equation:
$6,000 = P(1 - 0.35)
$6,000 = P(0.65)
To solve for P, we divide both sides of the equation by 0.65:
P = $6,000 / 0.65
P ≈ $9,230.77
Therefore, the original price of the fencing before the trade discount was approximately $9,230.77.
The correct answer is B. $9,230.77.
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