(1 point) Find all the unit vectors that are parallel to the tangent line to the curve y = 9 sin x at the point where x = 1/4. Unit vectors are (Enter a comma-separated list of vectors using either an

Sara owed $200 with terms of 2/10, n/60. She made a payment of $80 within ten days. The answer is: Sara paid $80 within ten days.

The terms "2/10, n/60" refer to a discount and a credit period. The first number, 2, represents the discount percentage that Sara can take if she pays within 10 days. The second number, 10, indicates the number of days within which she can take the discount. The letter "n" represents the net amount, which is the total amount owed without any discount. The last number, 60, represents the credit period, which is the maximum number of days Sara has to make the payment without incurring any penalty.

Since Sara paid $80 within ten days, she was eligible for the discount. To calculate the discount, we multiply the discount percentage (2%) by the net amount ($200), which gives us $4. Therefore, the discount Sara received is $4. Subtracting the discount from the net amount, Sara's remaining balance is $200 - $4 = $196.

In conclusion, Sara made a payment of $80 within ten days, received a discount of $4, and still has a remaining balance of $196.

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Answers:

==========================================================

Explanation:

Question 1

27x^6 = (3x^2)^3 which is one cube and y^3 is another cube

Therefore 27x^6+y^3 is a sum of two cubes.

It might help to think of it like A^3+B^3 where in this case A = 3x^2 and B = y.

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

Question 2

81 isn't a perfect cube since 81^(1/3) = 4.3267 approximately, which isn't a whole number. We need 81^(1/3) to be a whole number if we wanted 81 to be a perfect cube.

We don't even need to check b^15 since 81 being a non-perfect cube means the entire expression cannot be a sum of two cubes, nor a difference of cubes.

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

Question 3

64x^3 = (4x)^3 is a perfect cube

but 9z^9 is not a perfect cube

We can see this if we computed 9^(1/3) and the result is a non-whole number.

The answer here is the same as the previous question.

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

Question 4

36^(1/3) is not a whole number, so 36 isn't a perfect cube. By extension  36m^12 isn't a perfect cube either. The answer is the same as questions 2 and 3.

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

Question 5

1 is a perfect cube since 1 = 1^3

d^12 is a perfect cube because d^12 = (d^4)^3

Therefore, we have a difference of two cubes.

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

Question 6

729^(1/3) = 9 which rearranges to 9^3 = 729, showing 729 is a perfect cube.

However y^29 is not a perfect cube since the exponent 29 is not a multiple of 3.

The overall expression is "neither".

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

Question 7

343^(1/3) = 7 rearranges to 7^3 = 343, showing 343 is a perfect cube

y^6 is a perfect cube since (y^2)^3, i.e. the exponent 6 is a multiple of 3.

We have a difference of cubes.

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

Question 8

4 isn't a perfect cube since 4^(1/3) results in some decimal value that isn't a whole number. The entire expression is neither a sum nor difference of cubes.

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

Question 9

144^(1/3) isn't a whole number, so we get a similar result to problem 8.

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

Question 10

64j^6 = (4j^3)^3 is one cube

k^9 = (k^3)^3 is another cube

We have a difference of cubes

Answer:

-2.475

Step-by-step explanation:

The percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

We are given that:

Total moment of inertia of moving parts = I = 1 kgm²

Moment of inertia of air-screw = I = 18 kgm²

Outer diameter of hollow shaft = D₀ = 80 mm

Inner diameter of hollow shaft = Dᵢ = 35 mm

Length of hollow shaft = L = 0.30 m

Stiffness of the crank-throw = K = 2.5 × 10⁴ Nm/rad

Shear modulus of elasticity = G = 83000 N/mm²

We need to calculate the natural frequency of torsional vibration of the custen.

The formula for natural frequency of torsional vibration is: f = (1/2π) [(K/L) (J/GD)]^(1/2)

Where, J = Polar moment of inertia

J = (π/32) (D₀⁴ - Dᵢ⁴)

The formula for equivalent length of hollow shaft is given by:

q₁ = q₁₁ + q₁₂

Where, q₁₁ = (π/32) (D₀⁴ - Dᵢ⁴) / L₁q₁₂ = (π/64) (D₀⁴ - Dᵢ⁴) / L₂

L₁ = length of outer diameter

L₂ = length of inner diameter

For the given shaft, L₁ + L₂ = L

Let L₁ = L₀D₀ = D = 80 mm

Dᵢ = d = 35 mm

So, L₂ = L - L₁= 0.3 - L₀...(1)

For the given crank-throw, q₁ = (π/32) (D⁴ - d⁴) / L, where D = 80 mm and d = 80 mm

Hence, q₁ = (π/32) (80⁴ - 35⁴) / L

Therefore, q₁ = (π/32) (80⁴ - 35⁴) / L₀...(2)

From the formula for natural frequency of torsional vibration, f = (1/2π) [(K/L) (J/GD)]^(1/2)

Substituting the values of K, J, G, D and L from above, f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) ((π/32) (80⁴ - 35⁴) / (83000 N/mm² (80 mm)³))]^(1/2)f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) (18.12)]^(1/2)f = 25.7 / L₀^(1/2)...(3)

Now, if we assume that the air-screw mass is infinite, then the moment of inertia of the air-screw is infinite.

Therefore, the formula for natural frequency of torsional vibration in this case is:

f = (1/2π) [(K/L) (J/GD)]^(1/2)Substituting I = ∞ in the above formula, we get:

f = (1/2π) [(K/L) (J/GD + J/∞)]^(1/2)f = (1/2π) [(K/L) (J/GD)]^(1/2)f = 25.7 / L₀^(1/2)

So, in this case also the frequency is the same.

Therefore, the percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

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Answer:

y = -5/7x + 27/7

Step-by-step explanation:

y2 - y1 / x2 - x1

1 - 6 / 4 - (-3)

-5 / 7

= -5/7

y = -5/7x + b

1 = -5/7(4) + b

1 = -20/7 + b

27/7 = b

Step-by-step explanation:

Here is the work in the middle there would be 2 because the have neither brother or sister

Answer:

2

Step-by-step explanation:

Answer:

y = 5x

Step-by-step explanation:

slope intercept form is y=mx+b

m = slope

b = the y-intercept

so you just have to plug in those values

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

From the question, we have the following parameters that can be used in our computation:

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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$1,200

Step-by-step explanation:

10 × 24 = 240

240 × 5 = 1,200

I think this is right I have no clue though

Answer:

$340

Step-by-step explanation:

10 + 10 + 24 + 24 = 68 feet. Since fencing is $5/foot, multiply the perimeter by the cost.

Since 68 x 5 =  340, the fencing will cost $340.

The equation of the tangent line at x=0 is y = x.

To find the equation of the tangent line at the given value of x, we need to find the derivative of the function y with respect to x and evaluate it at x=0.

Taking the derivative of y=∫[0 to x] sin(2t^2+π/2) dt using the Fundamental Theorem of Calculus, we get:

dy/dx = sin(2x^2+π/2)

Now we can evaluate this derivative at x=0:

dy/dx |x=0 = sin(2(0)^2+π/2)

        = sin(π/2)

        = 1

So, the slope of the tangent line at x=0 is 1.

To find the equation of the tangent line, we also need a point on the line. In this case, the point is (0, y(x=0)).

Substituting x=0 into the original function y=∫[0 to x] sin(2t^2+π/2) dt, we get:

y(x=0) = ∫[0 to 0] sin(2t^2+π/2) dt

      = 0

Therefore, the point on the tangent line is (0, 0).

Using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values, we have:

y - 0 = 1(x - 0)

Simplifying, we get:

y = x

So, the equation of the tangent line at x=0 is y = x.

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Main Answer:The events A and B are not independent.

Supporting Question and Answer:

How can we determine if two events A and B are independent using a contingency table?

To determine if two events A and B are independent using a contingency table, we need to compare the probabilities of each event occurring separately (P(A) and P(B)) with the probability of both events occurring together (P(A and B)). If the product of the individual probabilities (P(A) ×P(B)) is equal to the probability of the intersection (P(A and B)), then the events are independent.

In the given contingency table, we can calculate the probabilities P(A), P(B), and P(A and B) by dividing the number of observations in each category by the total number of observations.

Body of the Solution:To find the probabilities A|B, A|B', and A'|B', we need to use the given contingency table:

Table: B B'

A 30 40

A' 40 20

a. A|B represents the probability of event A occurring given that event B has occurred. In this case, A|B can be calculated as:

A|B = P(A and B) / P(B)

P(A and B) is the number of observations in both A and B (30 in this case), and P(B) is the total number of observations in B (30 + 40 = 70).

A|B = 30 / 70 = 3/7

Therefore, A|B is 3/7.

b. A|B' represents the probability of event A occurring given that event B has not occurred. In this case, A|B' can be calculated as:

A|B' = P(A and B') / P(B')

P(A and B') is the number of observations in both A and B' (40 in this case), and P(B') is the total number of observations in B' (40 + 20 = 60).

A|B' = 40 / 60 = 2/3

Therefore, A|B' is 2/3.

c. A'|B' represents the probability of event A not occurring given that event B has not occurred. In this case, A'|B' can be calculated as:

A'|B' = P(A' and B') / P(B')

P(A' and B') is the number of observations in both A' and B' (20 in this case), and P(B') is the total number of observations in B' (40 + 20 = 60).

A'|B' = 20 / 60 = 1/3

Therefore, A'|B' is 1/3.

To determine if events A and B are independent, we need to compare the probabilities of A and B occurring separately to the probability of their intersection.If the probabilities are equal, the events are independent.

Let's calculate these probabilities:

P(A) = (observations in A) / (total observations) = (30 + 40) / (30 + 40 + 40 + 20) = 70 / 130 = 7/13

P(B) = (observations in B) / (total observations) = (30 + 40) / (30 + 40 + 40 + 20) = 70 / 130 = 7/13

P(A and B) = (observations in A and B) / (total observations)

= 30 / 130 = 3/13

Since P(A) ×P(B) = (7/13)× (7/13) = 49/169, and P(A and B) = 3/13, we can see that P(A) × P(B) ≠ P(A and B).

Therefore, events A and B are not independent.

Final Answer: Thus, events A and B are not independent.

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The events A and B are not independent. To determine if two events A and B are independent using a contingency table, we need to compare the probabilities of each event occurring separately (P(A) and P(B)) with the probability of both events occurring together (P(A and B)).

If the product of the individual probabilities (P(A) ×P(B)) is equal to the probability of the intersection (P(A and B)), then the events are independent.

In the given contingency table, we can calculate the probabilities P(A), P(B), and P(A and B) by dividing the number of observations in each category by the total number of observations.

Body of the Solution: To find the probabilities A|B, A|B', and A'|B', we need to use the given contingency table:

Table: B B'

A 30 40

A' 40 20

a. A|B represents the probability of event A occurring given that event B has occurred. In this case, A|B can be calculated as:

A|B = P(A and B) / P(B)

P(A and B) is the number of observations in both A and B (30 in this case), and P(B) is the total number of observations in B (30 + 40 = 70).

A|B = 30 / 70 = 3/7

Therefore, A|B is 3/7.

b. A|B' represents the probability of event A occurring given that event B has not occurred. In this case, A|B' can be calculated as:

A|B' = P(A and B') / P(B')

P(A and B') is the number of observations in both A and B' (40 in this case), and P(B') is the total number of observations in B' (40 + 20 = 60).

A|B' = 40 / 60 = 2/3

Therefore, A|B' is 2/3.

c. A'|B' represents the probability of event A not occurring given that event B has not occurred. In this case, A'|B' can be calculated as:

A'|B' = P(A' and B') / P(B')

P(A' and B') is the number of observations in both A' and B' (20 in this case), and P(B') is the total number of observations in B' (40 + 20 = 60).

A'|B' = 20 / 60 = 1/3

Therefore, A'|B' is 1/3.

To determine if events A and B are independent, we need to compare the probabilities of A and B occurring separately to the probability of their intersection. If the probabilities are equal, the events are independent.

Let's calculate these probabilities:

P(A) = (observations in A) / (total observations) = (30 + 40) / (30 + 40 + 40 + 20) = 70 / 130 = 7/13

P(B) = (observations in B) / (total observations) = (30 + 40) / (30 + 40 + 40 + 20) = 70 / 130 = 7/13

P(A and B) = (observations in A and B) / (total observations)

= 30 / 130 = 3/13

Since P(A) ×P(B) = (7/13)× (7/13) = 49/169, and P(A and B) = 3/13, we can see that P(A) × P(B) ≠ P(A and B).

Therefore, events A and B are not independent.

Thus, events A and B are not independent.

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Answer:

- 8

Step-by-step explanation:

Given

x² - 64 = 0 ( add 64 to both sides )

x² = 64 ( take the square root of both sides )

x = ± \(\sqrt{64}\) = ± 8

Solutions are x = 8 and x = - 8

The topologies {∅, {x}, {y}, {z}, {x, y, z}} and {∅, {x}, {y}, {z}, {x, y}, {y, z}, {x, z}} satisfy both the Frechet and Hausdorff properties.

To find all possible topologies of the space  = {x, y, z}, we need to consider all the possible subsets of this set. Since the set has three elements, there are 2^3 = 8 possible subsets.
The possible topologies are as follows:
1. {∅, {x, y, z}}: This is the trivial topology, where the whole set and the empty set are the only open sets.
2. {∅, {x}, {y}, {z}, {x, y, z}}: This is the discrete topology, where every subset of the set is open.
3. {∅, {x}, {y}, {z}, {x, y}, {y, z}, {x, z}, {x, y, z}}: This is the indiscrete or trivial topology, where only the whole set and the empty set are open.
4. {∅, {x}, {y}, {z}, {x, y}, {y, z}, {x, z}}: This is a topology that is not discrete or indiscrete.

To determine which of these topologies satisfy the Frechet property and the Hausdorff property, we need to consider the limit points and the ability to separate points, respectively.
The Frechet property states that for every point x in a set A, there exists a sequence of points in A that converges to x. In other words, every point is a limit point.
The Hausdorff property states that for any two distinct points x and y in a set A, there exist disjoint open sets U and V such that x is in U and y is in V. In other words, every pair of distinct points can be separated by open sets.

Let's analyze each topology:
1. {∅, {x, y, z}}: This topology does not satisfy the Frechet or Hausdorff property because it does not have any limit points or allow for the separation of points.
2. {∅, {x}, {y}, {z}, {x, y, z}}: This topology satisfies both the Frechet and Hausdorff properties. Any point x can be approached by the sequence (x), and any two distinct points can be separated by open sets.
3. {∅, {x}, {y}, {z}, {x, y}, {y, z}, {x, z}, {x, y, z}}: This topology does not satisfy the Frechet or Hausdorff property because it does not have any limit points or allow for the separation of points.
4. {∅, {x}, {y}, {z}, {x, y}, {y, z}, {x, z}}: This topology satisfies both the Frechet and Hausdorff properties. Any point x can be approached by the sequence (x), and any two distinct points can be separated by open sets.

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Answer:

? equals 80

Step-by-step explanation:

Answer: 5.657

Step-by-step explanation:

Split it into two right triangles, with the hypotenuse being the diagonal.

Then, a square plus b square = c square

So, 4 square + 4 square = c square

16 + 16 = c square

32 = c square

square root of 32 = c

square root of 32 = ~5.657

c = ~5.657

Answer:

i think it is 262

Step-by-step explanation:

If to renew the policy the insurance company charges an extra 40% to her premium rate: b. Even with the extra charge for renewal, Eva’s plan is the least expensive.

Premium rate can be defined as the additional money a person pay  instalmentally for an insurance policy.

Based on the given scenario Eva plan is the least expensive plan due to the fact that despite the  insurance company  charge her  the   additional 40% to her premium rate before they can renew her insurance policy,  her plan will be the  least expensive plan which inturn means that she can often renew the plan because it will cost her less.

Therefore If to renew the policy the insurance company charges an extra 40% to her premium rate: b. Even with the extra charge for renewal, Eva’s plan is the least expensive.

The missing option are:

a.Eva would have been better off selecting the 20-year term policy.

b.Even with the extra charge for renewal, Eva’s plan is the least expensive.

c.Given that Eva plans to renew, she should have selected the whole life policy.

d.Eva ends up paying the same amount for each policy.

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Answer: B

Step-by-step explanation:

A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. Therefore, option B is the correct answer.

A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. This is because the electron microscope requires a vacuum environment to function properly, which would kill any live specimen. Additionally, electron microscopes can only see surface details and do not have a very high power of resolution. Lastly, electron microscopes can only be used by doctors or trained technicians, so they are not as widely available as light microscopes.

Therefore, option B is the correct answer.

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A disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens (option b). Electron microscopes use a beam of electrons to create an image, which requires a vacuum environment. This means that living organisms cannot survive in the vacuum and therefore cannot be observed with electron microscopes.

I hope this helped! :)

Greetings from Brasil...

Here we have supplementary angles, that is, the sum of both results in 180. Therefore,

A + B = 180 ⇔ ∠1 + ∠2 = 180

∠1 + ∠2 = 180     by defining supplementary angles

143 + ∠2 = 180

∠2 = 180 - 143

the 90% confidence interval for the true average number of alcoholic drinks all UF non-Greek students have in a one-week period is approximately 3.2424 to 4.0776 drinks.

To construct a 90% confidence interval for the true average number of alcoholic drinks all UF non-Greek students have in a one-week period, we can use the following formula:

Confidence interval = sample mean ± (critical value) * (standard deviation / √n)

Where:

- The sample mean is 3.66 (average number of alcoholic drinks consumed in the past week).

- The standard deviation is 2.82.

- The sample size is 124 (random sample of non-Greek UF students).

First, we need to find the critical value corresponding to a 90% confidence level. Since the sample size is large (n > 30), we can use the z-distribution. For a 90% confidence level, the z-value is approximately 1.645 (looked up from the standard normal distribution table).

Plugging the values into the formula, we have:

Confidence interval = 3.66 ± (1.645) * (2.82 / √124)

Calculating the values within the formula:

Confidence interval = 3.66 ± (1.645) * (0.2536)

Simplifying:

Confidence interval = 3.66 ± 0.4176

The lower bound of the confidence interval is 3.66 - 0.4176 = 3.2424.

The upper bound of the confidence interval is 3.66 + 0.4176 = 4.0776.

Therefore, the 90% confidence interval for the true average number of alcoholic drinks all UF non-Greek students have in a one-week period is approximately 3.2424 to 4.0776 drinks.

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The limit of the given function is  π/2.

What is a limit?

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.

Here, we have

Given: \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

We have to find the limit of the given function.

=  \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

Now, we substitute the value of each variable.

x = π and y = π/2

= y sin(x-y)

= π/2sin(π-π/2)

= π/2sinπ/2

= π/2sin(90°)   (∴sin90° = 1)

= π/2×1

= π/2

Hence, the limit of the given function is  π/2.

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Answer:

9.93 liter approximately 10 liter

Step-by-step explanation:

3 days = 3/2 quart

3 week = 3/2/3 × 21 quarts

= 1/2×21

=21/2 quarts

now

1 quart = 0.946 liter

21/2 quart = 0.946×21/2 liter

21/2 quart = 9.93 liter

Answer:

245,008.60

Step-by-step explanation:

3 div/ 450,000 = 150000     7%150000= 10500 10500x20=210000 150000x2 =30000  210000+30000 =245000

Answer:

3:23

Step-by-step explanation:

The water fight ended at 4:28 and lasted for 32 minutes so

4:28 - 32 minutes = 3:56

3:56 - 33 minutes = 3:23

Answer: 96 servings.

Step-by-step explanation:
There are 16 cups in 1 gallon, so 3 gallons of punch would be equal to:

3 gallons x 16 cups/gallon = 48 cups

If each serving size is 1/2 cup, then the number of servings in 3 gallons of punch would be:

48 cups / (1/2 cup/serving) = 96 servings

Therefore, 3 gallons of punch would provide 96 servings, assuming each serving size is 1/2 cup.

The area between y = x² and y = -2 for x in [-1, 1] is 10/3 square units. To find the area of the region between y = x² and y = -2 for x in [-1, 1], we need to calculate the integral of the difference between the two functions over the given interval.

In this case, the function y = -2 is above y = x² on the interval [-1, 1].

The integral representing the area between the two curves is:

Area = ∫[-1,1] (-2 - x²) dx

To find the area, we calculate the antiderivative of the integrand and evaluate it at the given interval limits:

Area = [-2x - (x³/3)] (from -1 to 1)

Now, evaluate the antiderivative at the limits:

Area = [(-2(1) - (1³/3)) - (-2(-1) - (-1³/3))] = [-2 - 1/3 - 2 + 1/3] = -4 + 2/3 = -10/3

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The solutions to the equation 3x^2+10x=8 is 2/3 and -4.

To find the solutions to the equation 3x^2 + 10x = 8, we need to resolve it by means of factoring, finishing the square, or the usage of the quadratic formulation. Let's undergo the procedure of fixing it.

3x^2 + 10x = 8

First, let's rearrange the equation to carry the whole lot to 1 side:

3x^2 + 10x - 8= 0

Now, we can clear up this quadratic equation by using factoring. However, it can not element properly. So allow's use the quadratic components, which states that for an equation in the form ax^2 + bx + c = zero, the answers are given with the aid of:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = 3, b = 10, and c = -8. Substituting those values into the quadratic components:

x = (-10 ± √(10^2 - 4 * 3 * -8)) / (2 * 3)

x = (-10 ± √(100 + 96)) / 6

x = (-10 ± √196) / 6

x = (-10 ± 14) / 6

Now we've got  feasible solutions:

x1 = (-10 + 14) / 6 = 4 / 6 = 2/3

x2 = (-10 - 14) / 6 = -24 / 6 = -4

Therefore, the solutions to the equation 3x^2 + 10x = 8 are:

2/3 and -4.

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The solutions to the equation 3x^2 + 10x = 8 are 2/3 and -4. Hence, the correct answer is 1) 2/3 and -4.

To find the solutions to the equation 3x^2 + 10x = 8, we can start by rearranging the equation to bring all the terms to one side:

3x^2 + 10x - 8 = 0

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation 3x^2 + 10x - 8 = 0, we have a = 3, b = 10, and c = -8.

Plugging these values into the quadratic formula, we get:

x = (-10 ± √(10^2 - 4 * 3 * -8)) / (2 * 3)

x = (-10 ± √(100 + 96)) / 6

x = (-10 ± √196) / 6

x = (-10 ± 14) / 6

This gives us two possible solutions:

x = (-10 + 14) / 6 = 4/6 = 2/3

x = (-10 - 14) / 6 = -24/6 = -4

Therefore, the solutions to the equation 3x^2 + 10x = 8 are 2/3 and -4.

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Answer:

A. The fraction 1\(\frac{1}{6}\) would negative, since she is cutting off/losing hair rather than gaining it.

B. (this is just an improper fraction converted to have the same denominator as the second fraction, and is equivalent to  -1\(\frac{1}{6}\) )--> - \(\frac{14}{12}\) + \(\frac{5}{12}\) = - \(\frac{9}{12}\) or - \(\frac{3}{4}\)

The longest list of numbers that an average person can remember without any repetition is around 7 ± 2, according to Miller's Law.

Miller's Law suggests that the capacity of human short-term memory is limited to around 7 ± 2 items, or "chunks" of information. This means that if the professor reads a list of numbers to you without giving you a chance to repeat them, the longest list you are likely to remember is around 7 ± 2 numbers.

However, this capacity can be increased through the use of various memory strategies such as chunking, which involves grouping pieces of information into meaningful units. Additionally, the ability to remember numbers or any other type of information can vary greatly between individuals depending on factors such as age, cognitive ability, and previous experience with the material.

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