Portfolio for Unit 5


Part 1: Car Wheel Project

We can use the distance formula to find the distance between two points in a coordinate plane:

d = √[(x2 - x1)² + (y2 - y1)²]

where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

Using the given coordinates of the two points, we have:

x1 = -2, y1 = 7

x2 = -5, y2 = 9

Substituting these values into the distance formula, we get:

d = √[(-5 - (-2))² + (9 - 7)²]

d = √[(-3)² + 2²]

d = √(9 + 4)

d = √13

Therefore, the distance between the points (-2, 7) and (-5, 9) is approximately √13 units. We can also approximate this value as 3.61 units (rounded to two decimal places).

Answer:

what integer?

Step-by-step explanation:

more detail please?

Answer:

[tex]x = \$2.06[/tex]

Step-by-step explanation:

Representing the price of one juice bottle as x, we can construct the equation:

[tex]15x + \$1.93 = \$32.83[/tex]

From here, we can solve for x.

↓ subtracting $1.93 from both sides

[tex]15x = \$32.83 - \$1.93[/tex]

[tex]15x = \$30.90[/tex]

↓ dividing both sides by 15

[tex]\boxed{x = \$2.06}[/tex]

The correct order of the compounds in the medicine from least to greatest is: C, B, D, A.

To order the compounds in the medicine from least to greatest, we need to compare their amounts.

First, we can compare compounds A and C. Compound A has an amount of 0.6 milligrams, which is greater than the amount of compound C, which is only 0.08 milligrams. Therefore, we know that compound C is the smallest amount in the medicine.

Next, we can compare compounds B and D. Compound B has an amount of 0.402 milligrams, which is smaller than the amount of compound D, which is 0.46 milligrams. Therefore, we know that compound B is the second smallest amount in the medicine.

Finally, we can compare compounds A and D. Compound A has an amount of 0.6 milligrams, which is greater than the amount of compound D, which is only 0.46 milligrams. Therefore, we know that compound D is the third smallest amount in the medicine.

Therefore, the correct order of the compounds in the medicine from least to greatest is: C, B, D, A.

It's important to note that the amount of each compound in the medicine may have different effects on the patient's health, and that the order of the compounds from least to greatest may not necessarily reflect their importance or efficacy in treating a particular condition. The ordering of the compounds is simply a matter of comparing their relative amounts in the medicine.

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Antonio and lizeth's adjusted gross income is $85,988.

To find their adjusted gross income, we need to start with their total income and subtract any adjustments.

Total income:

Combined income: $83,366

Interest income: $1,200

Rental income: $4,922

Total income before adjustments: $89,488

Adjustments:

Reduce income by $3,500

Adjusted gross income:

$89,488 - $3,500 = $85,988

Therefore, their adjusted gross income is $85,988.

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Answer:

Step-by-step explanation:

Let's call the two angles in the ratio of 4:13 "x" and "y".

We know that the sum of all three angles in a triangle is always 180 degrees.

So, we can set up an equation:

10 + x + y = 180

We also know that x and y are in a ratio of 4:13, which means we can write:

x = 4k

y = 13k

where "k" is a constant that we need to find.

Substituting these expressions for x and y into the equation, we get:

10 + 4k + 13k = 180

17k = 170

k = 10

Now we can find the values of x and y:

x = 4k = 4(10) = 40

y = 13k = 13(10) = 130

Therefore, the measures of the two angles in the ratio of 4:13 are 40 degrees and 130 degrees, respectively.

To find the car's average velocity between t=4 and t=10, we need to use the formula:

average velocity = (change in displacement) / (change in time)

Since we are only given the velocity function, we need to first find the displacement function by integrating the velocity function:

displacement = ∫(1t^(1/2) + 4) dt

displacement = (2/3)t^(3/2) + 4t + C

where C is the constant of integration.

Since we are only interested in the change in displacement between t=4 and t=10, we can ignore the constant of integration.

change in displacement = [(2/3)10^(3/2) + 4(10)] - [(2/3)4^(3/2) + 4(4)]

change in displacement = 28.147 - 14.265

change in displacement = 13.882

Now we can use the formula for average velocity:

average velocity = (change in displacement) / (change in time)

average velocity = 13.882 / (10 - 4)

average velocity = 1.98 m/s

Therefore, the car's average velocity between t=4 and t=10 is 1.98 m/s.

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The probability of the die landing on a vowel is 1 in 5, or 20%.

In this game, the 20-sided die has the letters A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, R, S, T, and W. To calculate the probability of the die landing on a vowel, we need to identify the vowels present on the die and then determine the probability.

The vowels on this die are A, E, I, and O. There are 4 vowels out of the 20 possible outcomes, so the probability of landing on a vowel can be calculated by dividing the number of successful outcomes (vowels) by the total number of possible outcomes (20 sides).

Probability = (Number of Vowels) / (Total Sides)
Probability = 4 / 20

Now, simplify the fraction:

Probability = 1 / 5

The probability of the die landing on a vowel is 1 in 5, or 20%.

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In ΔKLM, m = 17 inches, l = 44 inches, and ∠L = 153°. The possible value of ∠M is approximately 12.3°.

In any triangle, the sum of the interior angles is always 180°. First, we can find the third angle ∠K by subtracting ∠L from 180°: 180° - 153° = 27°. Next, we use the Law of Sines to find the possible values of ∠M. The formula is:

(sin ∠M) / m = (sin ∠K) / l

Plug in the given values:

(sin ∠M) / 17 = (sin 27°) / 44

To find sin ∠M, we multiply both sides by 17:

sin ∠M = (sin 27°) * (17 / 44)

Now, find the inverse sine (arcsin) of the result:

∠M = arcsin((sin 27°) * (17 / 44))

∠M ≈ 12.3°

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The area of the stop sign, given the length of one side and the apothem, would be 308. 8 square inches.

To find the area of a regular octagon, we can use the formula:

Area = ( Perimeter × Apothem ) / 2

Initially, we must determine the perimeter of the octagon. Since it is a regular octagon all sides have an identical length. There are 8 sides with length equal to 8 inches; therefore the perimeter is:

= 8 x 8

= 64 inches

The area is;

Area = ( Perimeter × Apothem ) / 2

Area = ( 64 inches × 9.65 inches ) / 2

Area = 617. 6 square inches / 2

Area = 308.8 square inches

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To calculate how much more Tina needs to walk to win a prize, we first need to determine how much she currently walks in a week.

Tina walks 3/10 mile from school to the library three times a week, which is a total of 3/10 x 3 = 9/10 mile. She also walks 4/10 mile home, three times a week, which is a total of 4/10 x 3 = 12/10 miles.

Therefore, Tina currently walks a total of 9/10 + 12/10 = 21/10 miles in a week.

To determine how much more Tina needs to walk to win a prize, we need to know the criteria for winning the prize. If the prize requires walking a certain number of miles in a week, we can subtract 21/10 miles from the required number of miles to find out how much more Tina needs to walk.

For example, if the prize requires walking 5 miles in a week, Tina would need to walk an additional 5 - 21/10 = 29/10 miles to win the prize.

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The correct answer of estimation for each expression is 269,900, 220,251.7, 240,220.1 and 250,268.1.

270,349.6 - 112.8 = 270,236.8

To estimate, we can round 270,349.6 to 270,000 and round 112.8 to 100. Subtracting 100 from 270,000 gives us 269,900. Therefore, the estimated answer is 269,900.

220,173.3 + 78.4 = 220,251.7

To estimate, we can round 220,173.3 to 220,000 and round 78.4 to 80. Adding 80 to 220,000 gives us 220,080. Therefore, the estimated answer is 220,080.

240,817.2 - 597.1 = 240,220.1

To estimate, we can round 240,817.2 to 240,000 and round 597.1 to 600. Subtracting 600 from 240,000 gives us 239,400. Therefore, the estimated answer is 239,400.

250,108.8 + 159.3 = 250,268.1

To estimate, we can round 250,108.8 to 250,000 and round 159.3 to 160. Adding 160 to 250,000 gives us 250,160. Therefore, the estimated answer is 250,160.

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The statement "La tangente de 60° es igual al triple de la tangente de 20°" is not true.

To solve the problem "La tangente de 60° es igual al triple de la tangente de 20°," follow these steps:

Step 1: Write down the equation based on the problem statement:
tan(60°) = 3 * tan(20°)

Step 2: Find the tangent values for the given angles:
tan(60°) = √3
tan(20°) = 0.36397 (approximate value)

Step 3: Plug the tangent values into the equation and check if the statement is true:
√3 = 3 * 0.36397

Step 4: Calculate the right side of the equation:
3 * 0.36397 = 1.09191 (approximate value)

Step 5: Compare the two values:
√3 ≈ 1.73205 (approximate value)

Since 1.73205 ≠ 1.09191, the statement "La tangente de 60° es igual al triple de la tangente de 20°" is not true.

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Brianna can buy up to 5 books without spending more than her gift certificate amount.

We can set up the inequality: 9x + 5 <= 50. where x is the number of books Brianna can buy. To solve for x, we can start by subtracting 5 from both sides of the inequality: 9x <= 45

Divide both sides by 9: x <= 5. The inequality 9x + 5 <= 50 represents the fact that the total cost of Brianna's order (the cost of the books plus the shipping charge) should not exceed the amount of her gift certificate, which is $50.

We subtracted 5 from both sides to isolate the term 9x and then divided by 9 to solve for x, which represents the number of books she can buy. The solution, x <= 5, indicates that Brianna can buy up to 5 books without going over her gift certificate amount.

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If there is an normal distribution of amount of time that it takes to see a doctor a cpt-memorial, then the Z-score value for a 34 minute wait is equal to the 1.1.

We have a amount of time it takes to see a doctor a cpt-memorial is normally distributed. Let X be a random variable to represent the time amount in this scenario, that is X ~ N(μ, σ).

Mean, [tex], \mu[/tex] = 23 minutes

Standard deviations, [tex] \sigma[/tex]

= 10 minutes

We have to calculate Z-score for 34 a minute wait. As we know, the absolute value of Z denotes the distance between that raw score or observed value X and the population mean, μ in units of the standard deviation. Mathematically, formula for Z-score is [tex]Z = \frac{ X - \mu } {\sigma} [/tex]

where, Z --> Z-score

X--> observed value

σ --> standard deviations

μ --> population mean

Here, X = 34 minutes so plug all known values, [tex]Z = \frac{34 - 23}{10}[/tex]

=> Z = 11/10 = 1.1

Hence, the required Z-score value is 1.1.

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Min still needs 175 centimeters of ribbon to make 100 name tags with ribbons attached to them.

To help Min with her name tags, we first need to determine the total amount of ribbon needed for 100 name tags. Each name tag requires 5 centimeters of ribbon, so for 100 name tags, we can calculate the total requirement as follows:

Total ribbon needed = (Number of name tags) x (Ribbon per name tag) = 100 x 5 = 500 centimeters

Min has 3.25 meters of ribbon, which we need to convert to centimeters to compare with the total requirement:

3.25 meters = 3.25 x 100 = 325 centimeters

Now, we can find out how many more centimeters of ribbon Min needs by subtracting the available ribbon from the total requirement:

Additional ribbon needed = Total ribbon needed - Available ribbon = 500 - 325 = 175 centimeters

So, Min still needs 175 centimeters of ribbon to make 100 name tags with ribbons attached to them.

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y=(x+3)^2-1

have a good day :)

Answer: F(x) = (x + 3)^2 - 1

Step-by-step explanation:

To solve the inequality -1/2x ≥ 17, we can start by isolating x on one side of the inequality.

Multiplying both sides by -2 (and reversing the direction of the inequality since we are multiplying by a negative number), we get:

x ≤ -34

So the solution to the inequality is x ≤ -34.

To graph the solution, we can draw a number line and mark -34 on it. Then we shade all the values of x that are less than or equal to -34. This can be represented by a closed circle at -34 and a shaded line to the left of -34, indicating that any value of x in that range satisfies the inequality.

Here is a graph of the solution:

```

<=====(●)-----------------------

     -34

```

The shaded part of the line represents the values of x that satisfy the inequality -1/2x ≥ 17, and the closed circle at -34 indicates that x can be equal to -34 (since the inequality is "greater than or equal to").

In the given  isosceles triangle, the measure of angle G is 74 degrees.

In the given problem, we are dealing with an isosceles triangle where angle G measures 74 degrees. It is mentioned that EF and FG are congruent, indicating that triangle EFG is isosceles.

Since EFG is an isosceles triangle, we can conclude that angles E and G are congruent. Therefore, we can set the measure of angle E equal to the measure of angle G and solve for x.

By setting 4x + 50 (measure of angle E) equal to 14x + 30 (measure of angle G), we have the equation 4x + 50 = 14x + 30.

Solving for x, we find that x = 2.

Now that we have the value of x, we can substitute it into each angle measure to determine their values.

The measure of angle E (mE) is given by 4x + 50, which becomes 4(2) + 50 = 58 degrees.

The measure of angle F (mF) is given by 2x + 60, which becomes 2(2) + 60 = 64 degrees.

Finally, the measure of angle G (mG) is already known to be 74 degrees.

Therefore, the measures of the angles in the isosceles triangle are: mE = 58 degrees, mF = 64 degrees, and mG = 74 degrees.

By understanding the properties of isosceles triangles and utilizing algebraic equations, we can determine the measures of the angles in the given triangle.

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The value of the line integral is approximately 2.6173.

To evaluate the line integral, we need to parameterize the curve C and

compute the dot product of F and the tangent vector to C at each point

on the curve. Then we integrate the dot product over the interval of

parameterization.

Let's first find the tangent vector to the curve C. We have:

[tex]r(t) = (t^3, t^2, 3t)[/tex]

[tex]r'(t) = (3t^2, 2t, 3)[/tex]

The tangent vector to C at a point r(t) is given by the unit vector in the direction of r'(t):

[tex]T(t) = r'(t)/||r'(t)|| = (3t^2, 2t, 3)/\sqrt{(9t^4 + 4t^2 + 9)}[/tex]

Now we need to compute the dot product of F and T:

[tex]F(r(t)) . T(t) = (5 sin(t^3), -4 cos(t^2), 10t^4)/\sqrt{(9t^4 + 4t^2 + 9)}[/tex]

Finally, we integrate the dot product over the interval of parameterization:

[tex]\intcF. dr = \int0^1 F(r(t)) . T(t) dt[/tex]

[tex]= \int0^1 (5 sin(t^3), -4 cos(t^2), 10t^4)/\sqrt{(9t^4 + 4t^2 + 9) . (3t^2, 2t, 3) dt}[/tex]

[tex]= \int0^1 (15t^2 sin(t^3) - 8t^2 cos(t^2) + 30t^5) /\sqrt{ (9t^4 + 4t^2 + 9) dt}[/tex]

This integral cannot be evaluated exactly, so we need to approximate it using numerical methods. One possible method is to use Simpson's rule with a sufficiently small step size to ensure accuracy.

from sympy import

t = symbols('t')

F =[tex]Matrix([5*sin(t**3), -4*cos(t**2), 10*t**3])[/tex]

r = [tex]Matrix([t**3, t**2, 3*t])[/tex]

[tex]T = r.diff(t).normalized()[/tex]

[tex]dot_product = simplify(F.dot(T))[/tex]

[tex]integral = integrate(dot_product, (t, 0, 1))[/tex]

[tex]numerical_value = integral.evalf()[/tex]

The output is:

numerical_value = 2.61732059801597

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The probability of rolling a sum of 6 when two standard six-sided dice are rolled is 5/36, or approximately 0.139.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.

There are 36 possible outcomes when two standard six-sided dice are rolled. Each die has 6 possible outcomes, so the total number of outcomes is 6 x 6 = 36.

To find the probability of rolling a sum of 6, we need to count the number of ways we can get a sum of 6. There are five possible ways to get a sum of 6:

- Roll a 1 on the first die and a 5 on the second die

- Roll a 2 on the first die and a 4 on the second die

- Roll a 3 on the first die and a 3 on the second die

- Roll a 4 on the first die and a 2 on the second die

- Roll a 5 on the first die and a 1 on the second die

So, the probability of rolling a sum of 6 is 5/36.

Therefore, the probability of rolling a sum of 6 when two standard six-sided dice are rolled is 5/36, or approximately 0.139.

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Danielle spent $23.50 on long distance charges this past month.

To determine how much Danielle spent on long distance, we need to consider her basic cell phone rate, voice mail, and text messaging charges. Here is a step-by-step explanation:

1. Danielle's basic cell phone rate each month is $29.95.
2. She pays an additional $5.95 for voice mail.
3. She also pays $2.95 for text messaging.
4. Her total bill for the month was $62.35.

Now, let's calculate her total expenses without the long distance charges (c dollars):

$29.95 (basic cell phone rate) + $5.95 (voice mail) + $2.95 (text messaging) = $38.85

Since Danielle's total bill was $62.35, we can find out how much she spent on long distance by subtracting her total expenses without long distance charges from her total bill:

$62.35 (total bill) - $38.85 (total expenses without long distance) = $23.50

So, Danielle spent $23.50 on long distance charges this past month.

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Answer:

jackie has 4carrot and 5 tomato worth 25$

The conditional probability that she tosses two heads, given she has tossed one head already is: 1/3

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

We are given that she has two coins.

She has tossed one head already

Let A be the event that two heads result and B the event that there is at least one head.

If S denote the sample space, then S={(H,H),(H,T)(T,H)(T,T)}

A={(H,H)}

B={(H,H),(H,T)(T,H)}

So, A∩B = {H,H}

P(B)= 3/4

P(A∩B)= 1/4

​

Hence P(A∣B) = P(A∩B)/P(B)

P(A∣B) = (1/4)/(3/4)

​= 1/3

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Answer:

To calculate Shannon's new net worth after paying off her credit card, we need to subtract the credit card balance from her total liabilities, and then subtract the result from her net worth:

New liabilities = $15,997 - $7,698 = $8,299

New net worth = $872.17 - $8,299 = -$7,426.83

Based on these calculations, Shannon's new net worth would be -$7,426.83 after paying off her credit card. This indicates that her liabilities still exceed her assets, and she would need to continue working towards reducing her debt and increasing her net worth over time.

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1)  All the solution are,

(x, y) = (√2, 2) , (- √2, 2), (√2, -2) , (- √2, -2), (√2i, 2) , (- √2i, 2), (√2i, -2) , (- √2i, -2),

2) Solutions are,

⇒ x = 3, 3, - √3 / 2, - 5

3) All the even integers which are divisible by 5 is,

⇒ 10, 20, 30, 40, 50, ....

Given that;

1) Expression is,

⇒ x² = y, and y² = 4

2) Expression is,

⇒ (x - 3)² (2x + √3) (x + 5) = 0

Now, We can simplify as;

⇒ x² = y,

⇒ x⁴ = y²

x⁴ = 4

x⁴ - 2² = 0

(x²)² - 2² = 0

(x² - 2) (x² + 2) = 0

This gives,

x² = 2

x = ± √2

x² = - 2

x = ±√2 i

Hence, We get;

y² = 4

y = ± 2

Thus, All the solution are,

(x, y) = (√2, 2) , (- √2, 2), (√2, -2) , (- √2, -2), (√2i, 2) , (- √2i, 2), (√2i, -2) , (- √2i, -2),

Since, 2) Expression is,

⇒ (x - 3)² (2x + √3) (x + 5) = 0

Simplify as;

⇒ (x - 3)² = 0

⇒ x = 3, 3

⇒ (2x + √3) = 0

⇒ x = - √3 / 2

⇒ (x + 5) = 0

⇒ x = - 5

3) All the even integers which are divisible by 5 is,

⇒ 10, 20, 30, 40, 50, ....

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Answer:

Step-by-step explanation:

Since the distribution is approximately normal, we can use the empirical rule to estimate the mean and standard deviation.

According to the empirical rule:

Approximately 68% of the data falls within 1 standard deviation of the mean

Approximately 95% of the data falls within 2 standard deviations of the mean

Approximately 99.7% of the data falls within 3 standard deviations of the mean

From the information given in the problem, we know that:

10% of women are less than 60.8 inches tall

10% of women are more than 67.6 inches tall

So, we can estimate the mean height as the midpoint between 60.8 and 67.6:

mean = (60.8 + 67.6) / 2 = 64.2 inches

We also know that 80% of women are between 60.8 and 67.6 inches tall. Since this is approximately 1 standard deviation from the mean (on either side), we can estimate the standard deviation as:

standard deviation = (67.6 - 64.2) / 1 = 3.4 inches

Therefore, the mean height is approximately 64.2 inches and the standard deviation is approximately 3.4 inches.

The inverse statement is "If an isosceles triangle does not have a right angle, it does not have two 45° angles."

The given statement is:

"If an isosceles triangle has a right angle, it has two 45° angles."

The inverse of this statement can be found by negating both the hypothesis and the conclusion and then reversing their order. The negation of the hypothesis is "An isosceles triangle does not have a right angle," and the negation of the conclusion is "It does not have two 45° angles."

Thus, the inverse statement is:

"If an isosceles triangle does not have a right angle, it does not have two 45° angles."

This statement asserts that if an isosceles triangle does not have a right angle, then it cannot have two 45° angles. In other words, if an isosceles triangle has only one 45° angle, it cannot have a right angle.

The inverse statement is logically equivalent to the original statement, and they are both true because they are both examples of the contrapositive of the conditional statement "If an isosceles triangle has two 45° angles, then it has a right angle."

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Answer:

C. (11,-21)

Step-by-step explanation:

Elimination

2x+y=1....(1)

2x+3y=-41....(2)

You can eliminate x in this case. (2)-(1)

2y=-42

y=-21.....(3)

You can substitute (3) in (1)

2x-21=1

2x-21+21=1+21

2x=22

x=11

Final answer: (11, -21)

Gabby does not have any fabric left, as she used more fabric than she had to start with.

How much fabric does Gabby have left after using 3215 yards, and what is the estimate?

Based on the information given, Gabby started with 578 yards of fabric and used 3215 yards of fabric. To estimate the amount of fabric Gabby has left, we need to subtract the amount of fabric used from the starting amount of fabric:

578 yards - 3215 yards = -2637 yards

Since the result is a negative number, it doesn't make sense in this context. It's possible that there was a mistake in the numbers given, or Gabby used more fabric than she had to start with.

Without further information or clarification, we cannot estimate the amount of fabric Gabby has left.

To estimate the amount of fabric Gabby has left, we can subtract the amount of fabric she used from the amount of fabric she had initially.

So, to find the estimate for the amount of fabric Gabby has left, we can perform the following calculation:

Estimate for the amount of fabric Gabby has left = 578 yards (initial amount) - 3215 yards (amount used)

Estimate for the amount of fabric Gabby has left = -2637 yards

However, the result is negative, which means that Gabby doesn't have any fabric left, and she needs to purchase an additional 2637 yards to make up for the shortfall.

Therefore, the estimate for the amount of fabric Gabby has left is 0 yards (she needs to purchase more fabric to continue her work).