Helpp me which one is correct

The equation of the tangent AB is y = (1/2)x + 3/2. The equation of the normal AC is y = -2x + 4.

To find the equation of the tangent AB and the equation of the normal AC, we'll start by finding the derivative of the curve y = [tex](6x + 2)^{(1/3).[/tex]

Step 1: Find the derivative of the curve

Let's differentiate y = [tex](6x + 2)^{(1/3)[/tex] with respect to x using the chain rule:

[tex]dy/dx = (1/3)(6x + 2)^{(-2/3)} * d(6x + 2)/dx[/tex]

[tex]dy/dx = (1/3)(6x + 2)^{(-2/3)} * 6[/tex]

Simplifying:

[tex]dy/dx = 2(6x + 2)^{(-2/3)[/tex]

Step 2: Find the slope of the tangent at point A

To find the slope of the tangent at point A (1, 2), substitute x = 1 into the derivative:

m = dy/dx |(x=1)

[tex]m = 2(6(1) + 2)^{(-2/3)[/tex]

[tex]m = 2(8)^{(-2/3)[/tex]

m = [tex]2/(2^3)^{(2/3)[/tex]

m = [tex]2/2^2[/tex]

m = 1/2

So, the slope of the tangent at point A is 1/2.

Step 3: Find the equation of the tangent AB

Using the point-slope form of a line, we have:

y - y₁ = m(x - x₁)

Substituting the values x₁ = 1, y₁ = 2, and m = 1/2:

y - 2 = (1/2)(x - 1)

y - 2 = (1/2)x - 1/2

y = (1/2)x + 3/2

Therefore, the equation of the tangent AB is y = (1/2)x + 3/2.

Step 4: Find the slope of the normal at point A

The slope of the normal is the negative reciprocal of the slope of the tangent. So, the slope of the normal is -2.

Step 5: Find the equation of the normal AC

Using the point-slope form of a line and substituting x₁ = 1, y₁ = 2, and m = -2:

y - 2 = -2(x - 1)

y - 2 = -2x + 2

y = -2x + 4

Therefore, the equation of the normal AC is y = -2x + 4.

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Answer:

Step-by-step explanation:

The surface area of each net is 60 square inches.

The area of a triangle is given by :

1/2*(Base)*(Height)

In this problem :

Base = 6 inches

Height = 5 inches

Area of each triangle is 1/2*(6)*(5) = 15 square inches

Net comprises 4 triangles.

Surface Area of Net = 4*(15)

Surface Area of Net = 60 square inches.

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It will take Maria and the new clerk approximately 156/25 hours = 6 hours 14 mins to fill the order when working together.

To determine how long it will take Maria and the new clerk to fill the order when working together, we can use the concept of their combined work rates.

Let's first find the individual work rates of Maria and the new clerk:

Maria's work rate = 1 order / 12 hours = 1/12 orders per hour

New clerk's work rate = 1 order / 13 hours = 1/13 orders per hour

When working together, their work rates will add up:

Combined work rate = Maria's work rate + New clerk's work rate

= 1/12 + 1/13 orders per hour

Now, to find the time it will take them to fill the order together, we can invert the combined work rate and multiply it by the number of orders:

Time = 1 / (Combined work rate)

Time = 1 / (1/12 + 1/13)

= 1 / (13/156 + 12/156)

= 1 / (25/156)

= 156 / 25

≈ 6 hours 14 mins

So, 6 hours 14 mins

Therefore, it will take Maria and the new clerk approximately 156/25 hours = 6 hours 14 mins to fill the order when working together.

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The sample space of the two digit numbers is 11, 14, 15, 19, 41, 44, 45, 49, 51, 54, 55, 59,  91, 94, 95, 99

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

Digits = 1, 4, 5 and 9

The sample size of the above digits is

Sample size = 2⁴

Where

2 = the count of digits in each number

4 = the count of 1, 4, 5 and 9

So, we have

Sample size = 16

using a table, we have the sample space to be

           1         4         5        9

1         11         14         15       19

4         41       44        45       49

5        51        54         55       59

9         91         94         95       99

So, the sample space is 11, 14, 15, 19, 41, 44, 45, 49, 51, 54, 55, 59,  91, 94, 95, 99

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The value of vertical asymptotes is, x = 9

And, The value of Horizontal asymptotes is,

y = - 4

We have to given that;

Expression is,

⇒ j (x) = 1/(x - 9) - 4

Now, We can simplify as,

⇒ j (x) = 1/(x - 9) - 4

⇒ j (x) = (1 - 4(x - 9)] / (x - 9)

⇒ j (x) = [1 - 4x + 36] / (x - 9)

⇒ j (x) = (- 4x + 37) / (x - 9)

Hence, For vertical asymptotes make denominator zero.

As, x - 9 = 0

x = 9

And, Here degree of numerator and denominator both are one.

Hence, Horizontal asymptotes is,

y = - 4 / 1

y = - 4

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The sequence of transformation that can take your car are

Translation:

The car starts from point (3, 1). Translation up 2 units, takes the car to (3, 3).

Then going left 7 units will take the car to point (-4, 3).

The last move to the "Reserved to student" spot is moving down 2 units and this takes the car to ((-4, 1)

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Jared will have to wait for 59.5 years to be able to withdraw money without

penalty. option B

Jared will have to wait until he is 59.5 years old to be able to withdraw money from his traditional IRA without penalty. This is because withdrawals from traditional IRAs before age 59.5 are generally subject to a 10% early withdrawal penalty, in addition to any taxes owed on the amount withdrawn.

There are some exceptions to the early withdrawal penalty, such as for certain medical expenses or the purchase of a first home, but in general, it is best to wait until age 59.5 to avoid the penalty.

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Answer:

Step-by-step explanation:

Number sense includes tactics such as rounding off numbers, using practical reasoning in math problem solving, and checking correctness of answers by substituting them back into equations. The use of acronyms, though beneficial in remembering procedures or facts, is not a direct part of number sense.

Number sense typically encompasses a range of competencies including rounding off numbers, using common sense in mathematics, and putting answers back into equations to verify their correctness. These are all tactics that help improve and test our understanding of numbers and their relationships. However, the use of acronyms is not generally included in the concept of number sense.

Acronyms are more often used as an educational tool in various subjects, including mathematics, to help students remember procedures, facts, or rules. They may contribute indirectly to building number sense, by helping students remember mathematical processes for instance, but they are not themselves a part of number sense.

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If the rectangle is rotated about a line perpendicular to its plane and passing through one of its sides, it will generate a rectangular prism.

The solid generated when the rectangle is rotated about a line depends on the line of revolution chosen. There are three main possibilities:

1. If the rectangle is rotated about one of its sides, it will generate a cylindrical shape. In particular, if the rectangle is rotated about a shorter side, the resulting cylinder will have a height equal to the length of the longer side of the rectangle, and a radius equal to the length of the shorter side.

2. If the rectangle is rotated about one of its corners, it will generate a cone. The height of this cone will be equal to the distance between the corner of the rectangle and the opposite side. The radius of the cone will be equal to the length of the adjacent side of the rectangle.

3. In particular, if the rectangle is rotated about a longer side, the resulting prism will have a height equal to the length of the shorter side of the rectangle, and a depth equal to the length of the longer side.

In general, when rotating a flat shape about an axis, the resulting solid will be a three-dimensional shape with a circular cross-section. The specific shape of this cross-section will depend on the shape of the original flat shape and the axis of rotation chosen.

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Step-by-step explanation:

The time it takes to complete a course depends on various factors such as the student's learning style, motivation, and the complexity of the material. Some students may complete a course in a shorter time than others by working on it for long hours, focusing on the material, and using the resources provided.

Answer:

22 is the  answer

Step-by-step explanation:

The combined taxes will reduce bi-weekly paycheck by $49.53.

Data:

Earns $8.75 per hour

Work for 37 hours per week.

We will multiply hourly rate by weekly hours:

= $8.75 * 37 hours

= $323.75.

We will multiply weekly pay by 2:

= $323.75  * 2

= $647.50

The FICA tax rate is 6.2% and Medicare tax rate is 1.45%. The total tax rate is:

= 6.2% + 1.45%

= 7.65%

The Bi-weekly tax amount is:

= $647.50 * 7.65%

= $49.53

The net bi-weekly pay will be:

= $647.50 - $49.53

= $597.97.

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Answer:

Step-by-step Suppose Emily randomly turns on 2 of the 7 computers. Which expression could you use to determine the probability that both computers will be infected with a virus?

The Fraction that represents the probability is: P = C(m, 2) / C(n, 2)

The probability that Emily will randomly select the 2 computers that have viruses, we need more information. Specifically, we need to know the total number of computers and the number of computers that have viruses. Once we have this information, we can calculate the probability using the concept of combinations.

Let's assume there are a total of n computers and m computers that have viruses. The probability of randomly selecting the 2 computers that have viruses can be calculated as follows:

The numerator of the fraction represents the number of favorable outcomes, which is the number of ways to choose 2 computers from the m computers that have viruses. This can be calculated using the combination formula:

C(m, 2) = m! / (2! * (m - 2)!)

The denominator of the fraction represents the total number of possible outcomes, which is the number of ways to choose 2 computers from the total n computers. This can also be calculated using the combination formula:

C(n, 2) = n! / (2! * (n - 2)!)

Therefore, the fraction that represents the probability is: P = C(m, 2) / C(n, 2)

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The equations that represent the relationship between the two angles is:

x = 2(y + z) - 60

x = 2z + 20

We are given the parameters as:

x is the largest angle.

y is the next largest angle

z is the smallest angle.

The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles. Thus:

x = 2(y + z) - 60

The largest angle is twice the smaller angle plus 20 degrees. Thus:

x = 2z + 20

x + y + z = 180

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The least common multiple of the given pair of polynomials is 3(z - 5)(z + 5).

The least common multiple (LCM) of the given pair of polynomials: 3z^2 - 75 and z + 5.
Step 1: Factor the polynomials
First, we need to factor both polynomials if possible.
For the first polynomial, 3z^2 - 75:
- Factor out the greatest common divisor (GCD), which is 3: 3(z^2 - 25)
- Recognize that (z^2 - 25) is a difference of squares, so it can be factored further: 3(z - 5)(z + 5)
For the second polynomial, z + 5:
- There is no need to factor further, as it's already in simplest form.
Step 2: Find the LCM
Now that we have factored forms of the polynomials, we can find the LCM.
- The LCM must have all the factors from both polynomials.
- For the first polynomial, we have factors 3, (z - 5), and (z + 5).
- For the second polynomial, we have the factor (z + 5).
- Combine the factors, without repeating any common factors: 3(z - 5)(z + 5)
Therefore, the least common multiple of the given pair of polynomials is 3(z - 5)(z + 5).

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The figure that is symmetrical by the figure is given in the image

Symmetry is a core principle in mathematics and physics which denotes the property of a particular system or entity that remains unaltered even after undergoing specific transformations like translation, rotation, or reflection.

To put it differently, a symmetric entity retains its fundamental shape unchanged despite experiencing specific alterations. The utilization of this notion is prevalent across various disciplines such as art, architecture, biology, and chemistry, as it facilitates comprehension of frameworks, arrangements, and mechanisms.

The concept of symmetry holds significant importance in both the principles of natural laws and doctrines of physics.

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Answer:

f(- 1) = 10

Step-by-step explanation:

using the rule of exponents

[tex](\frac{a}{b}) ^{-1}[/tex] = [tex](\frac{b}{a}) ^{1}[/tex] = [tex]\frac{b}{a}[/tex]

to find f(- 1) substitute x = - 1 into f(x)

f(- 1) = 5[tex](\frac{1}{2}) ^{-1}[/tex] = 5 × [tex]\frac{2}{1}[/tex] = 5 × 2 = 10

Answer:

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

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

London needs to invest approximately $91,461.41 to reach a value of $281,000 in 19 years with an interest rate of 5.7% compounded continuously.

To calculate how much London needs to invest to reach a value of $281,000 in 19 years with an interest rate of 5.7% compounded continuously, we can use the formula A = Pe^(rt),

where A is the final amount, P is the principal amount (what London needs to invest), e is Euler's number, r is the interest rate, and t is the time period.

Plugging in the values, we get:

281000 = Pe^(0.057*19)

Solving for P, we get:

P = 281000/e^(0.057*19)

Using a calculator, we get:

P ≈ $91,461.41

It's important to note that this is an approximation and the actual amount may vary slightly due to rounding.

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Answer:

x = -3

Step-by-step explanation:

Step 1:  First, let's find the greatest common factor (GCF) of 4, -8, and -60 and factor it out.  

4/4 = 1, -8/4 = -2, and -60/4 = -15.  

Thus, the equation we can now use is 4(x^2 - 2x - 15).

Step 2:  We can by find the zeroes by factoring.  

Step 3:  Setting 4(x - 5) equal to 0:

4(x - 5) = 0

x - 5 = 0

x = 5

Setting (x + 3) equal to 0:

x + 3 = 0

x = -3

Thus, the smallest zero is -3

Tina's total fees for the month were $21.24.

Based on the information given, Tina had a basic charge of $5.84, 6 service charges at $0.40 each, a lost card replacement fee of $4.00, out-of-network ATM fees of $3.00, and a cash advance fee of 3 percent of $200. To calculate the total fees, we need to add all of these charges together.

First, let's calculate the service charges: 6 x $0.40 = $2.40.

Next, let's calculate the cash advance fee: 3% of $200 = $6.00.

Now we can add up all of the charges:

$5.84 + $2.40 + $4.00 + $3.00 + $6.00 = $21.24

It's important to keep track of these fees when using online banking to ensure that they don't add up and become too costly over time.

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Answer:

11:4 (I think)

Step-by-step explanation:

First, you have to figure out the number balance in each side of the ratio. I divided 280 by 7 (by adding 5 and 2) which gave me 40. Then, I did 40 x 5 (to get to 5) and then 40 x 2 (to get to 2).

This now makes the ratio 5:2 = 200:80

To get the 10% for potatoes, I figured out that 10% of 200 is 220.

Now, with the numbers 220: 80, you keep on dividing the numbers until you can't anymore, which leaves us with 11:4

Hope this helped! :)

Answer:

Step-by-step explanation:

[tex]\frac{3x^4}{(\frac{1}{x^2})^2} \\= 3x^8[/tex]

Answer:

[tex]3x^{8}[/tex]

Step-by-step explanation:

[tex](x^{-2})^{2}[/tex] is equal to [tex]x^{-4}[/tex]. Whenever an x has a negative exponent, it means that you can put it to the other side, whether it be from denominator to numerator or numerator to denominator. In this case, because it is in the bottom it goes from denominator to numerator. You will end up with something like [tex]3x^{4} x^{4}[/tex] but you can add the X's and end up with the answer.

Answer:

1,900seconds 2,120hours 3,5hours 4,2months 5,720days

Step-by-step explanation:

1,15*60=900seconds

2,5*24=120hours

3,1day=24h

? 120h

120/24=5hours

4,2months

5,360*2=720days

If the plant produces 53 seeds, the model predicts that approximately 57.5% of the seeds will sprout.

To predict the percent of seeds that sprout if the plant produces 53 seeds, we can try to establish a relationship between the number of seeds produced and the sprout percentage based on the given data points.

We can create a scatter plot of the given data points to visualize the relationship.

Seeds Produced: 65, 55, 56, 70, 44, 63, 51

Sprout Percent: 51, 54, 67.6, 49, 70.4, 49.8, 72.6

Based on the scatter plot, we can see if there is a clear pattern or trend. Let's assume that there is a linear relationship between the number of seeds produced and the sprout percentage.

Using the data points provided, we can perform linear regression to estimate the relationship and predict the sprout percentage for 53 seeds produced.

After performing linear regression on the given data points, the estimated equation for the relationship between the number of seeds produced (x) and the sprout percentage (y) is:

y = -0.3933x + 79.2133

Using this equation, we can plug in x = 53 to predict the sprout percentage for 53 seeds produced:

y = -0.3933 * 53 + 79.2133

Calculating this expression, we find:

y = 57.5

Therefore, if the plant produces 53 seeds, the model predicts that approximately 57.5% of the seeds will sprout.

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The regression equation is y = 28.0 + 0.0510x.

The best predicted temperature at a time when the cricket chirps 3000 times in 1 minute, based on the regression equation is 181°F.

What is wrong with this predicted temperature: B. It is unrealistically high. The value 3000 is far outside of the range of observed values.

In this scenario, the chirps in 1 min would be plotted on the x-axis (x-coordinate) of the scatter plot while the temperature would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

From the scatter plot (see attachment) which models the relationship between the chirps in 1 min and the temperature, a regression equation or an equation for the line of best fit is given by:

y = 28.0 + 0.0510x

When x = 3000, the temperature can be calculated as follows;

y = 28.0 + 0.0510(3000)

y = 181°F

In conclusion, a temperature of 181°F is unrealistically too high because a chirps of 3000 times in 1 min is an outlier.

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Step-by-step explanation:

To calculate the volume of the bucket, we can use the formula for the volume of a frustum (a truncated cone):

V = (1/3)πh (r₁² + r₂² + r₁r₂)

where h is the height of the frustum, r₁ and r₂ are the radii of the top and bottom circles respectively.

In this case, the height (h) of the frustum is 4 cm, the top radius (r₁) is half of the top diameter, which is 12 cm / 2 = 6 cm, and the bottom radius (r₂) is half of the bottom diameter, which is 8 cm / 2 = 4 cm.

Substituting these values into the formula, we get:

V = (1/3)π(4) (6² + 4² + 6*4)

= (1/3)π(4) (36 + 16 + 24)

= (1/3)π(4) (76)

= (4/3)π(38)

= 50.265 cm³ (approx)

Therefore, the volume of the bucket is approximately 50.265 cm³.

Answer:

A

Step-by-step explanation:

To solve the equation 7x-3(x-6)=30, we need to use the distributive property to simplify the left-hand side of the equation:

7x - 3(x-6) = 30

7x - 3x + 18 = 30

4x + 18 = 30

Next, we need to isolate the variable term on one side of the equation. To do this, we can subtract 18 from both sides:

4x + 18 - 18 = 30 - 18

4x = 12

Finally, we can solve for x by dividing both sides by 4:

4x/4 = 12/4

x = 3

Therefore, the solution to the equation 7x-3(x-6)=30 is x = 3. Answer A is correct.