The probability that at most 5 of these lights are red is 0.971.
To calculate this probability, we can use the binomial distribution with n = 7 and p = 0.4, since we want to know the probability of getting at most 5 red lights out of 7. We can use the formula:
P(X ≤ 5) = ΣP(X = k) for k = 0 to 5
Using this formula, we can calculate the probability as follows:
P(X = 0) = (0.5)^7 = 0.0078
P(X = 1) = 7(0.5)^7 = 0.0547
P(X = 2) = 21(0.4)(0.6)^6 = 0.2028
P(X = 3) = 35(0.4)^2(0.6)^5 = 0.322
P(X = 4) = 35(0.4)^3(0.6)^4 = 0.2458
P(X = 5) = 21(0.4)^4(0.6)^3 = 0.0907
Therefore, the probability of getting at most 5 red lights out of 7 is:
P(X ≤ 5) = 0.0078 + 0.0547 + 0.2028 + 0.322 + 0.2458 + 0.0907 = 0.971.
So the probability that at most 5 of these lights are red is 0.971.
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Find the area and the circumference of a circle with radius 9km.
Write your answers in terms of π, and be sure to include the correct units in your answers.
Answer:
Area: 81*pi
Circumference: 18*pi
Step-by-step explanation:
Area: 9^2= 81
So it would be 81*pi
Circumference: 9*2= 18
So it would be 18*pi
If you want the full area then it's 81*pi= 254.34
If you want the full circumference it's 18*pi= 56.55
in an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. what is the sum of the first $20$ terms of this sequence?
The sum of the first $20$ terms of the arithmetic sequence is $420$.
In an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. The sum of the first $20$ terms of this sequence can be calculated using the following formula:
Sum of the first $20$ terms = $20$/2($a_1 + a_{20})$, where $a_1$ is the first term of the sequence and $a_{20}$ is the twentieth term of the sequence.
Therefore, we need to find the first term of the sequence and the twentieth term of the sequence. To find the first term, we use the following equation:
$5 = a_2 + a_8$, where $a_2$ is the second term and $a_8$ is the eighth term.
To find the twentieth term, we use the following equation:
$5 = a_4 \times a_5$, where $a_4$ is the fourth term and $a_5$ is the fifth term.
Solving both equations, we get $a_2 = 1$ and $a_{20} = 40$. Then, we can calculate the sum of the first $20$ terms of the sequence:
Sum of the first $20$ terms = $20$/2($1 + 40$) = $420$.
Therefore, the sum of the first $20$ terms of the arithmetic sequence is $420$.
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a rectangle has an area that is decreasing at a rate of 541 square inches per hour with the width being held constant. determine the rate of change of the length if the width is 3 square inches.
The length is therefore shrinking at a rate of -541/3, or around -180.33 square inches per hour.
what is rectangle ?A rectangle is a flat, four-sided shape with parallel, equal-length opposite sides on each side. There are four right angles (90-degree angles). The distance between the two longer sides, also known as the longer sides or the longer edges, is the rectangle's length. The distance between the two shorter sides, also known as the shorter sides or the shorter edges, determines the rectangle's width. The perimeter of a rectangle is equal to the total of the lengths of all of its sides, and the area of a rectangle is equal to the product of its length and width.
given
Let A represent the rectangle's area, l its length, and w its width. So, we are aware of:
A = lw
By applying the derivative to time t, we obtain:
(d/dt) = dA/dt (lw)
l(dw/dt) + w(dl/dt) = dA/dt
dw/dt = 0 since the width is kept constant, which results in:
w(dl/dt) = dA/dt
We are informed that w = 3 in and that dA/dt = –541 in2/hour. By replacing these values, we obtain:
-541 = 3(dl/dt)
By calculating dl/dt, we obtain:
dl/dt = -541/3
The length is therefore shrinking at a rate of -541/3, or around -180.33 square inches per hour.
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A box contains eight cards labeled P,Q ,R ,S ,T ,U ,V , and W. One card will be randomly chosen. What is the probability of choosing a letter from P to R?
Write your answer as a fraction in simplest form.
Answer:3/7
Step-by-step explanation:
PLEASE HELPP I NEED HELP WITH THIS MATHS PLEASE
1. It will take about 8 years for the tithe to double in value if invested at 7.75% APR compounded monthly.
2. An annual interest rate of 4.84% compounded semi-annually would be required for $22,500 to accumulate to $50,000 in 14 years.
3 A principal of $26,512.18 invested in a GIC at 4% APR compounded quarterly would return $40,000 in 9 years.
How to solve the questionsa. Using the TVM Solver function in Excel, we can input the following information:
Present value (PV): -$35,000 (since it's an outgoing cash flow)
Future value (FV): $70,000 (since we want the tithe to double in value)
Interest rate per period (Rate): 7.75%/12 (since the APR is compounded monthly)
Number of periods (Nper): unknown (what we're solving for)
Payment (Pmt): 0 (since there are no recurring payments)
Solving for Nper, we get 96.16 months, or approximately 8 years.
Therefore, it will take about 8 years for the tithe to double in value if invested at 7.75% APR compounded monthly.
b. Present value (PV): -$22,500 (since it's an outgoing cash flow)
Future value (FV): $50,000
Interest rate per period (Rate): unknown (what we're solving for)
Number of periods (Nper): 14*2=28 (since the interest is compounded semi-annually, we need to double the number of years)
Payment (Pmt): 0
Solving for Rate, we get 4.84% APR.
Therefore, an annual interest rate of 4.84% compounded semi-annually would be required for $22,500 to accumulate to $50,000 in 14 years.
c. Using the TVM Solver function in Excel, we can input the following information:
Present value (PV): unknown (what we're solving for)
Future value (FV): $40,000
Interest rate per period (Rate): 4%/4 (since the APR is compounded quarterly)
Number of periods (Nper): 9*4=36 (since the interest is compounded quarterly, we need to multiply the number of years by 4)
Payment (Pmt): 0
Solving for PV, we get $26,512.18.
Therefore, a principal of $26,512.18 invested in a GIC at 4% APR compounded quarterly would return $40,000 in 9 years.
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which of the following fractions are equivalent to 15/21 ? select all that apply. a. 5/7 b. 30/42 c. 21/15 d. 25/31 e. 45/84
The fractions a. 5/7 b. 30/42 e. 45/84 are equivalent to 15/21.
When it comes to fractions, equivalent means that both fractions show the same part of a whole. The numerator and denominator of equivalent fractions may be multiplied or divided by the same number or the number multiplied by the numerator and denominator should be the same.
The following are steps to simplify fractions:
First, find the greatest common factor (GCF) of both numbers.
And then divide both numbers by the GCF. The result is the simplified fraction.
The greatest common factor of 15 and 21 is 3. By dividing both 15 and 21 by 3, the simplified fraction will be found.
15/21 = 5/7
By dividing both 30 and 42 by 6, the simplified fraction will be found.
30/42 = 5/7
By dividing both 45 and 84 by 3, the simplified fraction will be found.
45/84 = (5/12)21/15 and 25/31 are not equivalent to 15/21.
Therefore, the correct options are a. 5/7 b. 30/42 e. 45/84
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in a standard deck of 52 cards (4 suits, 13 numbers per suit), how many hands can we be dealt 5 cards that do not share a number
Answer: 1287
Step-by-step explanation:
sixty percent of 800 students in a business statistics class are female. if you want to make probability estimates of the sample proportion of female students without applying the finite population correction factor, what minimal sample size of the random sample should be used?
Sixty percent of 800 students in a business statistics class are female. if you want to make probability estimates of the sample proportion of female students without applying the finite population correction factor, 368 is the minimal sample size of the random sample should be used
The appropriate sample size for probability estimates of the sample proportion of female students in the business statistics class is determined by the margin of error (m) and the level of confidence (Z).
The formula for sample size calculation is as follows:
N = [tex](Z^2\times p \times q) / m^2[/tex]
where
N is the sample size
Z is the z-score that corresponds to the level of confidence
p is the estimated proportion of female students
q is 1 - p (proportion of male students)m is the margin of error.
Since we don't have any margin of error, we can assume it to be a standard value of 5%. And a z-score of 1.96 is appropriate for a 95% level of confidence.
As a result, the sample size for estimating the sample proportion of female students in the business statistics class is given by
N = [tex](1.96^2\times0.60\times0.40) / (0.05^2)[/tex]
N = 368 students
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WILL MAKE U BRAINLIST! HELPS PLS AND SHOW ALL STEPS
Answer:
................
Step-by-step explanation:
.................
if i have four boxes arranged in a $2 \times 2$ grid, in how many distinct ways can i place the digits $1$, $2$, and $3$ in the boxes, using each digit exactly once, such that each box contains at most one digit? (i only have one of each digit, so one box will remain blank.)
If i have four boxes arranged in a [tex]2 \times 2[/tex] grid, in 6 distinct ways can i place the digits 1, 2, and 3 in the boxes, using each digit exactly once, such that each box contains at most one digit
If a student has four boxes arranged in a 2 × 2 grid, the distinct ways to place the digits 1, 2, and 3 in the boxes, using each digit exactly once, such that each box contains at most one digit are six in number.
There are two possibilities for which box is left blank, so let's consider them separately:
Case 1: The top left box is left blank. In this case, the other three boxes must contain the digits 1, 2, and 3. There are three choices for what digit goes in the top right box, and then two choices for what digit goes in the bottom left box, and then one choice for what digit goes in the bottom right box.
This gives a total of 3·2·1 = 6 ways to place the digits in the boxes when the top left box is left blank.
Case 2: A different box is left blank. In this case, one of the digits must be left out. There are three choices for which digit is left out, and then three choices for which box is left blank. Once the digit and the blank box have been chosen, the remaining two digits can be placed in the other two boxes in any order, giving 2 ways.
This gives a total of 3·3·2 = 18 ways to place the digits in the boxes when a different box is left blank.
Therefore, the distinct ways to place the digits 1, 2, and 3 in the boxes, using each digit exactly once, such that each box contains at most one digit are six in number.
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an online buying club offers a membership for $245, for which you will receive a discount of 10 percent on all brand-name items you purchase. how much would you have to buy to cover the cost of the membership?
You would have $2,450 to buy to cover the cost of the membership.
An online buying club offers a membership for $245, for which you will receive a discount of 10 percent on all brand-name items you purchase.
We have to determine how much you would have to buy to cover the cost of the membership.
You have to buy to cover the cost of the membership = An online buying club offers a membership/Receive a discount
You have to buy to cover the cost of the membership = $245/10%
You have to buy to cover the cost of the membership = $245/0.10
You have to buy to cover the cost of the membership = $2,450
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Eric owns and operates the Hot Ham food truck. The expression 3. 25b+2h3. 25b+2h3, point, 25, b, plus, 2, h gives the cost of bbb burgers and hhh hot dogs. What is the cost of 444 burgers and 666 hot dogs?
\$
As per the expression, the cost of 444 burgers and 666 hot dogs from Eric's Hot Ham food truck would be $2773.
In this case, Eric's expression is 3.25b + 2h, where b represents the number of burgers and h represents the number of hot dogs. The expression tells us how much it costs to buy a certain number of burgers and hot dogs from Eric's truck.
To find the cost of 444 burgers and 666 hot dogs, we can substitute b = 444 and h = 666 into the expression. So the cost would be:
3.25(444) + 2(666)
Now we just need to simplify this expression by using the order of operations.
First, we multiply 3.25 by 444 to get 1441. Then, we multiply 2 by 666 to get 1332.
Next, we add these two values together:
1441 + 1332 = 2773
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find the measure of the marked arc
2) A man spent 58% of his income and the amount of money left was GH210.00. Find his income.
Answer: Let x be the man's income.
He spent 58% of his income, which is 0.58x.
The amount of money left is the remaining 42% of his income, which is 0.42x.
According to the problem, 0.42x = GH210.00.
Solving for x, we get:
x = GH210.00 / 0.42
x = GH500.00
Therefore, the man's income is GH500.00.
Step-by-step explanation:
Helppp!!! i’m having a really hard time figuring this out:
Therefore , the solution of the given problem of unitary method comes out to be the composite shape's overall size is 30 square units.
What is a unitary method?Utilizing previously well-known variables, this uniform convenience, or all crucial elements from a prior flexible study that followed a particular methodology event can all be used to achieve the goal. It will be possible to contact the entity again if the anticipated assertion outcome actually happens; if it doesn't, both important systems will surely miss the statement.
Here,
We must divide the composite shape into smaller shapes and sum up their areas in order to determine the area of the composite shape.
We can see that the composite form is made up of a triangle with a base of four and a height of three, and a rectangle with dimensions of six by four.
=> length times breadth equals six by four, or 24 square units, for a rectangle.
Triangle's area is equal to
=> (1/2) x base times height, or (1/2) x 4 times 3, or 6 square units.
As a result, the composite shape's overall size is:
=> 24 + 6 = 30 square units.
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Which equation can be used to find x, the measure of angle M in AAMP?
A = 180 +95 + 54
B x = 180 - 95 + 54
C x = 180- 149
D x = (95 +54) - 180
the correct equation to find x, the measure of angle M in AAMP is: [tex]x = 149[/tex]. Thus, option C is correct.
What is the equation for measure of angle?To find the value of x, we need to know the angles of triangle AMP.
Assuming that AAMP is a quadrilateral, we know that the sum of its angles is [tex]360[/tex] degrees.
Thus, we can write:
Angle AMP + Angle M + Angle A [tex]= 360[/tex]
We know that Angle AMP is [tex]180 - 95 - 54 = 31[/tex] degrees (since the sum of the angles in triangle AMB is 180 degrees, and we are given that Angle BAM = 95 degrees and Angle ABM = 54 degrees).
Substituting this value and the given value of Angle A (which is 180 degrees) into the equation above, we can solve for Angle M:
[tex]31 + Angle M + 180 = 360[/tex]
Angle [tex]M = 149[/tex] degrees
Therefore, the correct equation to find x, the measure of angle M in AAMP is: [tex]x = 149[/tex]
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Find the value of each variable with step by step explanation
The length of the missing side of the geometric system of right triangles is equal to 2√29 units.
How to determine the missing length of the right triangle
In this problem we find a geometric system formed by two right triangles, in which we must determine the length of a missing side. The length can be found by means of Pythagorean theorem, whose formula is now introduced:
r² = x² + y²
Where:
x, y - Legsr - Hypotenuser = 30, x = 28
30² = 28² + y²
y = √(30² - 28²)
y = 2√29
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There are 20 Skittles in a bag. Five of them are orange and three of them are blue. Find the probability that you would choose an orange Skittle, replace it, and then choose a blue Skittle.
Answer:
There is a 1 in 4 chance that you would choose an orange Skittle, replace it, and then choose a blue Skittle.
A student was asked to factor
Answer:
Step-by-step explanation:
1) [tex]6x^4 \times 6x^4 = 36x^8[/tex] (needs to be [tex]36x^{16}[/tex] )
2) [tex](4y^2) \times (4y^2) =16y^4[/tex] (needs to be [tex]25y^4[/tex] )
1) Change both [tex]6x^4 \text{ terms to } 6x^8.[/tex]
2) Change both [tex]4x^2 \text{ terms to } 5y^2.[/tex]
Bonus:
Need to change a minus to a plus,
[tex]36x^{16}-25y^4=(6x^8+5y^2)(6x^8-5y^2)[/tex]
Can you please answer this question
Answer:
9/14
Step-by-step explanation:
add them
Only 2 fairly short word problems about solving systems.
The ages of Paige, Quiana, and Ryan, given their relationship to each other's ages are:
Paige - 12 years Quiana - 24 years Ryan - 21 yearsThe amount of each type of coin that Uncle Ralph has are:
Quarter - 5 Dime - 4 Nickel - 9How to find the ages and coin types ?The equations we have are:
Paige is half as old as Quiana: P = 0.5 x Q
Quiana is three years younger than Ryan: Q = R - 3
Ryan is nine years older than Paige: R = P + 9
Now we can substitute for R from the second equation into the new equation: Q - 3 = (0.5 x Q) + 9
Now, let's solve for Q: 0.5 x Q = Q - 12 => 0.5 x Q = 12
Now we can find Q: Q = 24
Now that we have Quiana's age, we can find Paige's and Ryan's ages:
P = 0.5 x Q = 0.5 x 24 = 12
R = P + 9 = 12 + 9 = 21
Uncle Ralph has 18 coins in total: Q + D + N = 18
The number of quarters and dimes combined is the same as the number of nickels: Q + D = N
He has $2.10 worth of coins: 0.25 x Q + 0.10 x D + 0.05 x N = 2.10
Now we have two equations:
Q + D = 9
0.25 x Q + 0.10 x D + 0.05 x (Q + D) = 2.10
We can solve the system of linear equations. Multiply the first equation by 0.15 and subtract it from the second equation:
0.30 x Q + 0.15 x D - (0.15 x Q + 0.15 x D) = 2.10 - 1.35 => 0.15 x Q = 0.75
Substitute the value of Q back into the first equation to find the number of dimes: 5 + D = 9 => D = 4
Now we can find the number of nickels using the second equation: N = Q + D = 5 + 4 = 9
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Follow the instructions in the image Pt. 1
1. The perimeter of triangle JKL is the sum of the three sides of the triangle, which is JK + KL + LJ is 37.
2. The measure of arc ZWX is 136.
3. Length of AB is 48
4. The value of x is 30π.
What is Pythagorean Theorem?It states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
1. The perimeter of triangle JKL is the sum of the three sides of the triangle, which is JK + KL + LJ.
As JA = 14, AL = 17, and
CK = 6,
then the perimeter of JKL is 14 + 17 + 6 = 37.
2. To find the measure of arc ZWX, we can use the formula for the circumference of a circle, which is 2πr, where r is the radius.
As WZ and AR are diameters of the circle, they each have a length of 2r. The measure of arc ZWX is the same as the measure of angle WCX plus the measure of angle YCZ, which is
42 + 94 = 136.
Therefore, the measure of arc ZWX is 136.
3. To find the length of AB, we can use the Pythagorean Theorem.
OC is given as 12. and Radius is given as 30.
So, length of OC=30-12
=18
As OB is also the radius of the circle, its length is 30.
By using the Pythagorean Theorem,
OB²=BC²+OC²
BC²=OB²-OC²
BC=√30²-12²
BC=24
As we know a perpendicular divides a line into 2 equal parts, thus, AB=BC+AC
AB=48
4. To find the value of x, we can use the formula for the measure of an arc, which is
2πr × (angle/360).
As the measure of arc AB is 60 degrees and the measure of arc CD is 20 degrees, then x can be calculated as
2πr × (60/360) + 2πr × (20/360) = 30π.
Therefore, the value of x is 30π.
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how would i graph my question when the x and y intercept is (10,140) when the slope is -14
The given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.
What is point-slope form?When you know the slope of the line to be investigated and the given point is also the y-intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b).
The y value of the y-intercept point is denoted by the symbol b in the formula.
The general form of a linear equation is y-y1=m(x-x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
So, in the given situation:
The point-slope form is: y = mx + b
Then y is y and b is the x value and m is the slope.
Now, insert values as follows:
y = mx + b
140 = -14x + 10
Graph the equation as follows:
(Refer to the graph attached below)
Therefore, the given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.
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If f(x) = 3x + 2, find f(2).
a. 2
b. 5
c. 8
d. 9
e. 12
Answer:
C
Step-by-step explanation:
Since the number in the parenthesis is treated as "x", for f(2), replace "x" with 2. So the equation will be f(2) = 3(2) + 2. Then multiply. f(2) = 6 + 2. Lastly add them up. f(2) = 8. The answer is 8.
which value of n makes the equation true
[tex]-\frac{1}{2}n=-8[/tex]
Answer:
Step-by-step explanation:
nothing makes it true
PLEASE HELP - WORTH 60 POINTS! Ella's school choir is singing two songs for their school's Artist Showcase. The choir director put these song choices on the board.
Answer:9%
Step-by-step explanation:
Sorry for taking so long i didn't understand it at first
math is too hard for me help
Answer:
Step-by-step explanation:
1/5(-25) + 16/8
-5 + 2 = -3
Option A
A quadrilateral is on a coordinate plane at points A(-3, 1) B(1, 4) C(5, 1) D(1, -2).
Which sides of the quadrilateral are parallel? Select all that apply!
Responses
A. AB and BC
B. BC and CD
C. AB and CD
D. There are no parallel sides
E. BC and AD
The correct option is E. BC and AD, are the two parallel sides of the quadrilateral ABCD.
Explain about the quadrilateral?Quadrilaterals are geometric figures with four sides and four vertices. Frequently, two of something like the sides are parallel, meaning implies that no matter how far they stretch, their distance from one another remains constant.quadrilateral on coordinate plane had points:
A(-3, 1) B(1, 4) C(5, 1) D(1, -2).
Find distance between points using distance formulae:
d = √(x2 - x1)² + (y2 - y1)²
AB = √(1 + 3)² + (4 - 1)²
AB = √(4)² + (-3)²
AB = √16 + 9
AB = √25
AB = 5
CD = √(5 - 1)² + (1 + 2)²
CD = √(4)² + (3)²
CD = √16 + 9
CD = √25
CD = 5
As, sides Ab and CD are both equal of 5 units each, , then the sides in between them BC and AD will be parallel.
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Clark is 8 years older than John. In 5 years, Clark will be twice as old as John. How old are they now?
Step-by-step explanation:
Let the John age be x
Clark is 8 years older than John will be written as :
x+8 = x
In 5 years, Clark will be twice as old as John will be written as :
(x+8)+5 = 2(x+8)
Simplify it
x+13 = 2x+16
x-2x = 16-13
-x = 3
x = -3
Their current age :
Clarke:= x+8
= -3+8 ( x = -3)
= 5
John:=2(x+8)
=2(-3+8)
=-6+16
=10
Present age John and Clark are 3 and 11 years respectively .
Let the John present age be J and Clark present age be C
Clark is 8 years older than John will be written as :
C= J + 8
In 5 years, Clark will be twice as old as John will be written as :
C+ 5 = 2(J + 5)
Substitute,
C = J + 8
Simplify it
J + 8 + 5 = 2J + 10
J = 3
C = J + 8
C =11
Thus their present ages are :
Clark = 11 years
John = 3 years
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Write the equation of the trend line. Use the points (4, 12) and (12, 8).
The equation of the trend line is y = (-1/2)x + 14.
What is trend line?The overall pattern or trend in a collection of data is represented by a trend line, sometimes referred to as a regression line. In statistics, it is frequently used to illustrate the connection between two variables, one of which is the independent variable and the other the dependant variable. Regression analysis, which determines the line that most accurately fits the data points based on their connection, is used to compute the trend line. In order to anticipate or estimate future values of the dependant variable based on the independent variable, the equation of the trend line may then be utilised.
The slope of the line can be found using the formula:
slope = (change in y) / (change in x)
slope = (8 - 12) / (12 - 4)
slope = -4 / 8
slope = -1/2
Using the point slope form:
y - y1 = m(x - x1)
y - 12 = (-1/2)(x - 4)
y = (-1/2)x + 14
Hence, the equation of the trend line is y = (-1/2)x + 14.
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