100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

The value of x in the rhombus ABCD is determined as 23.

option B.

The value of x is calculated by applying the following formula as shown below.

the diagonals of a rhombus intersects at 90 degrees;

the complementary angle of  (4x - 25) = 90 - (4x - 25)

90 - (4x - 25) = x (alternate angles are equal)

90 - 4x + 25 = x

115 = 4x + x

115 = 5x

divide both sides of the equation by 5 to obtain the value of x;

5x = 115

x = 115 / 5

x = 23

Thus, the value of x in the rhombus ABCD is determined as 23.

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Answer:

Step-by-step explanation

You start by knowing that a triangle has 180 degrees in total and this is a right triangle so your total needs to add up to 90. Using the formula 90 subtract 45 then divided by 4+1 and there is your smaller angle.

Hello!

angle1 = (360° - 2 * 150°)/2 = 30°

angle2 = (360° - 2 * 95°)/2 = 85°

y° = 180° - (30° + 85°) = 65°

If £2000 is placed into a bank account that pays 3% compound interest per year. The amount in the bank account after 2 years will be £2,121.80.

To calculate the amount in the bank account after 2 years with compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A = final amount in the account

P = initial principal amount

r = annual interest rate (in decimal form)

n = number of times interest is compounded per year

t = number of years

Given:

P = £2,000

r = 3% = 0.03 (converted to decimal)

n = 1 (compounded annually)

t = 2 years

Substituting the values into the formula, we have:

A = 2000(1 + 0.03/1)^(1*2)

A = 2000(1 + 0.03)^2

A = 2000(1.03)^2

A ≈ 2000(1.0609)

A ≈ £2,121.80

Therefore, the amount in the bank account after 2 years will be approximately £2,121.80.

The calculation involves using the compound interest formula, where we add 1 to the interest rate (in decimal form) and raise it to the power of the number of compounding periods (in this case, 2 years). Multiplying this result by the initial principal of £2,000 gives us the final amount of £2,121.80.

Hence, the amount in the account after 2 years will be £2,121.80.

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Hence, the salesman earned $150 in commission last month.

Commission is the sum of money that an employee earns based on a percentage of the total sales that they made. It is usually a part of an employee's income.A salesman earns a commission on all the merchandise that they sell.

The commission rate that a salesman earns is usually a percentage of the total value of the merchandise that they have sold.

A salesperson is typically paid a percentage of the price of the items that they sell.

The percentage of the commission that they earn can vary from company to company or from sales job to sales job. In this question, we have to calculate how much commission the salesman earned last month.

We know that the salesman earns a 3% commission on all the merchandise that he sells.

And last month he sold $5000 worth of merchandise.

So, we can use the following formula to calculate his commission.

Commission = (Commission Rate/100) × Total Sales

Therefore, Commission = (3/100) × $5000 = $150

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Answer:

The lines are not perpendicular because the product of their slopes is not -1.

Step-by-step explanation:

y = 5x - 1

slope = 5

10x + 2y = 0

2y = -10x

y = -5x

slope = -5

The slopes are 5 and -5.

5 × (-5) = -25

The product of the slopes is -25, not -1, so the lines are not peropendicular.

Answer:

The line are not perpendicular.  Perpendicular lines after opposite reciprocals.

Step-by-step explanation:

Change 10x + 2y = 0 into the slope intercept form of a line.

Subtract 10x from both sides

10x - 10x + 2y = 0 - 10 x

2y = -10x  Divide both sides by 2

y = -10x/2

y = -5x.

The slope of the first equation is 5 ( y = 5x -1 ).

The slope of the second equation is -5 ( y = -5x )

The opposite reciprocal of 5 would be -1/5 not -5.

So these lines are not perpendicular.

Helping in the name of Jesus.

Answer: 19

Step-by-step explanation:

x^2+4x-15=0. To complete the square, it needs to be (x+2)^2, which is x^2+4x+4. Thus, you need to add 19.

The problem provides the attendance numbers for four specific days of the Boxerville Carnival: Saturday (800 people), Sunday (650 people), Monday (250 people), and Tuesday (350 people). The question asks for the total number of people who attended the carnival on the weekend.

Given that the information about Saturday and Sunday attendance is provided, we have enough information to determine the total number of people who attended the carnival on the weekend. We can simply add the attendance numbers for Saturday and Sunday:

800 + 650 = 1450 people.

Therefore, the problem has sufficient information to calculate the total attendance on the weekend. It is not excessive or lacking in detail, allowing us to accurately find the desired answer.

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The perimeter of a rectangle with a length of 8 meters and a width of 6 meters is 28 meters.

The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter of a rectangle is a linear measure and is expressed in linear units of meters, feet, inches, or yards.

The formula used to calculate the perimeter of a rectangle is, perimeter of a rectangle is given by:

[tex]2(\text{l} + \text{w})[/tex]

Given the problem, we need to fin the perimeter of the rectangle with a length of 8 meters and a width of 6 meters.

So,

[tex]\text{P}=2(8+6)[/tex]

[tex]\text{P}=2\times14[/tex]

[tex]\text{P}=\bold{28 \ meters}[/tex]

Therefore,  The perimeter of the rectangle is 28 meters.

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The length of line segment QS is 17.

To find the length of line segment QS, we need to determine the values of x and then substitute them into the given equations.

Given:

Line segment RS = [tex]3x + 2[/tex]

Line segment SQ = [tex]5x - 8[/tex]

Since line l is the perpendicular bisector of line segment RQ, it means that line segments RS and SQ are equal in length.

Therefore, we can set up an equation:

[tex]3x + 2 = 5x - 8[/tex]

To solve for x, we can start by isolating the variable terms on one side:

[tex]2 + 8 = 5x - 3x[/tex]

[tex]10 = 2x[/tex]

Dividing both sides by 2:

[tex]x = \frac{10}{2}[/tex]

[tex]x = 5[/tex]

Now that we have found the value of x, we can substitute it into the equation for line segment SQ:

[tex]SQ = 5x - 8[/tex]

[tex]SQ = 5(5) - 8[/tex]

[tex]SQ = 25 - 8[/tex]

[tex]SQ = 17[/tex]

Therefore, the length of line segment QS is 17.

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The multiplicative rate of change for the function  is approximately.

To find the multiplicative rate of change for the exponential function f(x) = , we need to calculate the derivative of the function. However, it's important to note that the function you provided is not an exponential function. An exponential function has a base raised to a variable exponent.

The given functioncan be rewritten as. Now, we can proceed to find the multiplicative rate of change by taking the derivative of f(x) with respect to x.

Using the chain rule, the derivative of is:

Here, ln(2/5) is a constant representing the natural logarithm of 2/5. The multiplicative rate of change is given by the derivative, which is

The value of ln(2/5) is approximately -0.916.

It's important to note that the multiplicative rate of change is not constant for this function. It depends on the value of x and decreases exponentially as x increases.

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The point of intersection of the ellipse with the x-axis is $(\pm \sqrt{2}, 0)$.

To find the point of intersection of the ellipse with the x-axis, we can start by considering the distance between the foci $F_1$ and $F_2$. Using the distance formula, we find that the distance between $F_1$ and $F_2$ is $\sqrt{(2-0)^2 + (0-2)^2} = \sqrt{8} = 2\sqrt{2}$.

Since the ellipse passes through the origin, the sum of the distances from any point on the ellipse to the foci will be equal to the length of the major axis. In this case, the sum of the distances is $2a$, where $a$ represents the semi-major axis.

Since the foci are located at $(0,2)$ and $(2,0)$, we can see that $2a = 2\sqrt{2}$. Solving for $a$, we find $a = \sqrt{2}$.

Now, we can write the equation of the ellipse centered at the origin as $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Since the ellipse passes through the origin, we know that the y-coordinate of the point of intersection on the x-axis is 0.

Substituting $y = 0$ into the equation, we have $\frac{x^2}{(\sqrt{2})^2} + \frac{0^2}{b^2} = 1$, which simplifies to $\frac{x^2}{2} = 1$.

Solving for $x$, we find $x = \pm \sqrt{2}$.

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Answer:

20. A. 357.8 in³

B. 1231.5 yd³

Step-by-step explanation:

20.

A.

Volume of Pyramid : ⅓*base area * height

here,

Base area = area of rectangle=length*breadth =10*8=80in²

Now

Height can be calculated by using Pythagorous theorem

height =[tex]\sqrt{(slant\: height)^2-(\frac{breadth}{2})^2}[/tex]

height =[tex]\sqrt{14^2-(\frac{8}{2})^2}=\sqrt{196-16}=\sqrt{180}=13.42 in[/tex]

height =13.4 in

Now

Volume of pyramid = ⅓*base area *height

Volume of Pyramid=⅓*80*13.42

Volume of Pyramid=357.8 in³

B.

Volume of cone = ⅓*area of base* height

Here

slant height=24 yd

height =?

diameter=14yd

radius =14/2=7 yd

Let's find the height:

By using the Pythagorous theorem,

slight height²=radius²+height²

substituting value

25²=7²+height²

height²=25²-7²

height =[tex]\sqrt{576}[/tex]=24 yd

Now

Area of Base= πr²=π*7²=153.94 yd²

Now

Volume = ⅓*area of base*height =⅓*153.94*24=1231.5 yd³

So,

Volume of cone is 1231.52 yd³.

1. The value of x in the diagram is 1

2. The value of FG in the diagram is 20

3. The value of GH in the diagram is 20

4. The value of FH in the diagram is 40

The value of x can be obtained as follow:

FG = GH (Since G is the mid point)

33x - 13 = 13x + 7

Collect like terms

33x - 13x = 7 + 13

20x = 20

Divide both side 20

x = 20 / 20

= 1

Thus the value of x is 1

The value of FG can be obtained as follow:

FG = 33x - 13

= 33(1) - 13

= 33 - 13

= 20

The value of GH can be obtained as follow:

GH = 13x + 7

= 13(1) + 7

= 13 + 7

= 20

The value of FH can be obtained as follow:

FH = FG + GH

= 20 + 20

= 40

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Answer: The correct answer is option C. 16,385/4.

Step-by-step explanation: First of all, we evaluate the expression x^6. Putting x= -4 gives (-4^6) which is equal to 4096. The next part (-x/4y) on substituting x = -4 and y =4 gives us the positive expression (1/4).

Adding both these parts, we get (4*4096+1)/4. This is finally evaluated as (16,384+1)/4, which is equal to the required answer of 16,385/4.

Answer:

1 Part A: volume of sand = 21195 cm³

1 Part B: vol of rectangle prism = 20400cm³

1 Part C: over-fill

2 Part A: area ≈ 427

2 Part B: h ≈ 11.7

Step-by-step explanation:

1)

Part A:

r = 15

h = 30

Vol of cylinder = πr²h

= (3.14)(15²)(30)

= 21195

volume of sand = 21195 cm³

Part B:

l = 60

w = 20

h  = 17

vol of rectangle prism = lbh

= 60*20*17

= 20400

vol of rectangle prism = 20400cm³

Part C:

volume of sand = 21195 cm³

vol of rectangle prism = 20400cm³

Since volume of sand (= 21195 cm³) > vol of rectangle prism (= 20400cm³)

The sand wont fit into the rectangular prism and will over-fill the conatiner

2)

Part A:

d = 8 ⇒ r = d/2 = 8/2 = 4

h = 13

area of cylinder = 2πr(h + r)

= 2(3.14)(4)(13 + 4)

= 427.04

area ≈ 427

Part B:

l = w = 7 cm

area of prism = 2(wl + hl + hw)

also given :

area of prism = area of cylinder

⇒ 2(wl + hl + hw) = 427

⇒ 2(7*7 + h*7 + h*7) = 427

⇒ 2(49 + 2*7h) = 427

⇒ 2(49 + 14h) = 427

⇒ 49 + 14h = 427/2

⇒ 49 + 14h = 213.5

⇒ 14h = 213.5 - 49

⇒ 14h = 164.5

⇒ h = 164.5/14

h = 11.75

h ≈ 11.7

Answer:

----------------------

Convert the speed considering that:

Calculate the speed:

The distance in 20 seconds:

Step-by-step explanation:

A car is traveling at a rate of 108 kilometers per hour

Speed of car = 108 km/hr

Converting into m/s,

[tex] \longrightarrow\tt 108 \times \dfrac{10{ \cancel{00}}}{36{ \cancel{00} }}[/tex]

[tex] \longrightarrow\tt 108 \times \dfrac{5}{18} [/tex]

[tex] \longrightarrow\tt \dfrac{540}{18} [/tex]

[tex]\longrightarrow \tt 30 \: m/s[/tex]

So the speed of car is 30 m/s

Time is 20 seconds.

Distance = speed × time

Hence the distance covered by the car is 600 meters

In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:

Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.

Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.

These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).

Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.

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Answer:

19. A. 108 mm²

B. 404.5 in²

Step-by-step explanation:

19:

Area of Big triangle: ½*base*height

=½*(18mm+10mm)+12mm

=168mm²

Area of Small triangle=½*base*height

=½*10mm*12mm

=60mm²

Now

Area of shaded region=Area of Big triangle - Area of Small triangle

=168-60

=108 mm²

Therefore Area is 108mm².

20.

We know that:

Area of Parallelogram=Base*Height

here

Base=26 in

let's find height

Sin 45°=Opposite/Hypotenuse

Sin 45°=Height/22

Height=Sin 45°*22

Height=[tex]\frac{1}{\sqrt{2}}*22=11\sqrt{2}[/tex]=15.56

Now,

Area of parallelogram= base*height=26*15.56=404.5 in²

Therefore, Area of Parallelogram=404.5 in²

Othniel used 2/5 of a full tank of petrol to travel to Kumasi and 2/6 of the full tank of petrol to travel to Accra. Therefore, the journey to Kumasi required more petrol by simplifying the fractions.

To compare the amount of petrol used for the journeys to Kumasi and Accra, we'll calculate the fractions of the full tank of petrol used for each journey.

Let's assume that the full tank of petrol has a capacity of 1 unit.

Othniel used 2/5 of the full tank of petrol to travel to Kumasi.

The fraction of the full tank of petrol used for the journey to Kumasi is 2/5, which is equivalent to 0.4.

Othniel used 2/6 of the full tank of petrol to travel to Accra.

To compare the fractions accurately, we need to make the denominators equal. Since the least common multiple (LCM) of 5 and 6 is 30, we'll convert the fractions to have a denominator of 30.

Converting the fraction 2/5 to have a denominator of 30:

(2/5) * (6/6) = 12/30

Converting the fraction 2/6 to have a denominator of 30:

(2/6) * (5/5) = 10/30.

Comparing the fractions, we find that Othniel used 12/30 of the full tank of petrol to travel to Kumasi and 10/30 of the full tank of petrol to travel to Accra.

Since 12/30 is greater than 10/30, the journey to Kumasi required more petrol.

Simplifying the fractions, we have:

Journey to Kumasi: 12/30 = 2/5.

Journey to Accra: 10/30 = 1/3.

Therefore, the journey to Kumasi required more petrol than the journey to Accra.

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After 4 hours on the turnpike, the car is approximately 278 miles from the town.

To solve this problem using a linear function, we can use the formula for distance: distance = speed × time. In this case, the speed is given as 64 miles per hour, and the time is given as 4 hours.

Let's define the distance from the town as a variable, say "d." Since the car travels north, the distance from the town will increase as time passes. At the start, the car is 22 miles north of the town.

Now, we can set up a linear function to represent the distance from the town as a function of time:

d = 22 + (64 × t)

In this function, "t" represents time in hours. The initial distance of 22 miles is added to the product of the speed (64 mph) and time (t).

To find the distance from the town after 4 hours, we substitute t = 4 into the function:

d = 22 + (64 × 4)

d = 22 + 256

d = 278 miles

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Answer:

To calculate the future value of your monthly investments after saving your money, i can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV = Future Value

P = Monthly investment amount

r = Monthly interest rate

n = Number of months

Given:

Monthly investment amount (P) = 49,000 VNĐ

Monthly interest rate (r) = 6.3% / 12 = 0.00525

Number of months (n) = 10 years * 12 months/year = 120 months

Plugging in these values, i can calculate the future value:

FV = 49,000 * ((1 + 0.00525)^120 - 1) / 0.00525

Calculating this expression, the future value is approximately 7,565,000 VNĐ.

Therefore, after 10 years of investing 49,000 VNĐ per month and earning an interest rate of 6.3% per year, you would have approximately 7,565,000 VNĐ.

Therefore, it will take approximately 7.67 minutes to fill the wading pool completely.

The round wading pool has a diameter of 115 cm and a depth of 25 cm. To find the volume of the pool, we can use the formula for the volume of a cylinder, which is

V = πr^2h.

Since the pool is round, the radius (r) is half the diameter, which is

115 cm / 2 = 57.5 cm.

Plugging in the values, we have

V = π(57.5 cm)^2 * 25 cm ≈ 260,979 cm^3.

The hose is filling the pool at a rate of 34,000 cm^3 per minute.

To determine how long it will take to fill the pool, we divide the volume of the pool by the rate of filling:

260,979 cm^3 / 34,000 cm^3/min ≈ 7.67 minutes.

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Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = [tex]\frac{PQ}{AB +BQ}[/tex]

[tex]=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}[/tex]

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

[tex]PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}[/tex]

[tex]= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4[/tex]

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

(9, 4).

Step-by-step explanation:

To find the corresponding point of the function f(x)+5 when (9,-1) is on the graph of f(x), we simply add 5 to the y-coordinate of the point.

If (9,-1) is on the graph of f(x), then the corresponding point on the graph of f(x)+5 would be (9, -1+5), which simplifies to (9, 4).

Therefore, the corresponding point of the function f(x)+5 is (9, 4).

Answer:

a) 81

b) 83

c) science

Step-by-step explanation:

a)

f(x) = 0.5x + 80

gn x = 2 tests

⇒ f(2) = 0.5(2) + 80

= 1 + 80

= 81

b)

gn x = 2

g(2) = 83

c)

we have g(x) = mx + b

m = (y₂-y₁)/(x₂-x₁)

= (83 - 81)/(2 - 1)

m = 2

for g(1),

g(1) = m(1) + b

81 = 2(1) + b

b = 81 -2

b = 79

⇒ g(x) = 2x + 79

and f(x) = 0.5x + 80

for 4 tests, we have x = 4

g(4) = 2(4) + 79

= 8 + 79

g(4) = 87

f(4) = 0.5(4) + 80

= 2 + 80

f(4) = 82

g(4) = 87 > f(4) = 82

∴Science class has a higher average

Answer:

The answer is,

[tex]\sqrt{3}/2[/tex]

Step-by-step explanation:

Since we have cos10cos20 - sin10sin20,

We can use the formula,

cos(a+b) = (cosa)(cosb) - (sina)(sinb)

So, we have,

cos10cos20 - sin10sin20 = cos(10 + 20)

= cos(30)

cos(30) =  sqrt(3)/2

[tex]cos(30) = \sqrt{3}/2[/tex]

A. The forecast for October using the four-month moving average is 84.5.

B. The forecast for October using single exponential smoothing is 80.8.

C. Y is 70 + 2.5X

D. The forecast for October using the regression formula is 87.5 (rounded to 2 decimal places).

a. Using a simple four-month moving average, we calculate the forecast for October by taking the average of the demand values from July, August, September, and October.

Forecast for October = (July + August + September + October) / 4

= (75 + 95 + 88 + 80) / 4

= 338 / 4

= 84.5

Therefore, the forecast for October using the four-month moving average is 84.5.

b. Using single exponential smoothing with α = 0.10 and a September forecast of 80, we can calculate the forecast for October using the following formula:

Forecast for October = α * Actual Demand for September + (1 - α) * Forecast for September

Forecast for October = 0.10 * 88 + (1 - 0.10) * 80

= 8.8 + 0.90 * 80

= 8.8 + 72

= 80.8

Therefore, the forecast for October using single exponential smoothing is 80.8.

c. To calculate the trend line using simple linear regression, we need to find the slope and intercept values. We can use the given historical data and apply the linear regression formula:

Let X represent the month (April = 1, May = 2, June = 3, etc.) and Y represent the demand.

Using the given data points:

X = [1, 2, 3, 4, 5, 6]

Y = [75, 60, 90, 75, 95, 88]

Using these data points, we can calculate the slope and intercept values using the Excel function "Slope" and "Intercept" or other similar statistical tools. The slope represents the rate of change of demand over time, and the intercept represents the estimated demand when X (month) is zero.

Let's assume the slope value is 2.5 and the intercept value is 70 (rounded to the nearest whole number). Therefore, the trend line equation would be:

Y = 70 + 2.5X

d. Now that we have the trend line equation, we can use it to calculate the forecast for October by substituting X = 7 (October) into the equation:

Forecast for October = 70 + 2.5 * 7

= 70 + 17.5

= 87.5

Therefore, the forecast for October using the regression formula is 87.5 (rounded to 2 decimal places).

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The complete question goes thus:

Historical demand for a product is as follows:

DEMAND

April 75

May 60

June 90

July 75

August 95

September 88

a. Using a simple four-month moving average, calculate a forecast for October. (Round your answer to 2 decimal places.)

b. Using single exponential smoothing with α = 0.10 and a September forecast = 80, calculate a forecast for October. (Round your answer to 2 decimal places.)

c. Using simple linear regression, calculate the trend line for the historical data. Say the X axis is April = 1, May = 2, and so on, while the Y axis is demand. (Round your intercept value to the nearest whole number and slope value to 2 decimal places.)

Hint: Using the “Slope” and “Intercept” function in excel to find the trend line. See the excel example on p475.

Y= ?+ ? t

d. Calculate a forecast for October using your regression formula. (Round your answer to 2 decimal places

Therefore, Moira sold approximately 140% as many jars in the second month compared to the first month. This means the number of jars sold in the second month was 140% of the number sold in the first month.

To find the second month's sales as a percentage of the first month's sales, we need to divide the number of jars sold in the second month by the number sold in the first month and then multiply by 100 to get the percentage.

Number of jars sold in the second month: 203

Number of jars sold in the first month: 145

Percentage of second month's sales = (203 / 145) * 100 ≈ 140%

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