PLZ HELP I WILL GIVE 20 POINTS WHOEVER ANSWERS FIRST:

To find the equation of the tangent line to the graph of y = (6x^2 − 6x + 3)(1 + 2x) at x = 1, we need to find the slope of the tangent line at that point and use the point-slope form of a line equation. Here's a summary of the solution:

Calculate the derivative of the function y = (6x^2 − 6x + 3)(1 + 2x) using the product rule and simplify the expression.

Evaluate the derivative at x = 1 to find the slope of the tangent line.

Substitute the coordinates of the point (1, f(1)) into the point-slope form of the line equation, where f(1) is the value of the function at x = 1.

Simplify the equation to obtain the equation of the tangent line.

To check the reasonableness of the answer, graph both the function and the tangent line using a graphing tool or software. Plot the function and the tangent line on the same graph to visually verify that the line is indeed tangent to the function at x = 1.

By taking the derivative of the function, evaluating it at x = 1, and applying the point-slope form, you can determine the equation of the tangent line. Graphing both the function and the tangent line together allows you to visually confirm the tangent relationship at x = 1.

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The value of k is 39.(constant)

The value of  a = -24 and b = 0. (constant)

A. To find the values of a and b, we can start by using the information about the local minimum and maximum points to set up a system of equations.

First, we know that the derivative of the function, cubic polynomial function f'(x), is equal to zero at both the local minimum and maximum points:

f'(x) = 12x^2 + 2ax + b

f'(-2) = 12(-2)^2 + 2a(-2) + b = 0  (local minimum at x = -2)

f'(0) = 12(0)^2 + 2a(0) + b = b  (local maximum at x = 0)

We also know that the second derivative of the function, f''(x), changes sign at both of these points.

f''(x) = 24x + 2a

f''(-2) = 24(-2) + 2a < 0 (concave down at x = -2)

f''(0) = 24(0) + 2a > 0 (concave up at x = 0)

Using these equations and inequalities, we can solve for the values of a and b.

From f'(-2) = 0, we have:

-48 - 2a + b = 0

From f'(0) = 0, we have:

b = 0

Substituting b = 0 into the first equation, we have:

-48 - 2a = 0

a = -24

Therefore, the values of a and b are a = -24 and b = 0.

B. To find the value of k, we can integrate f(x) from 0 to 1 and set the result equal to 32:

∫[0,1] f(x) dx = ∫[0,1] (4x^3 - 24x^2 + k) dx = [x^4 - 8x^3 + kx]_0^1

= (1^4 - 8(1)^3 + k(1)) - (0^4 - 8(0)^3 + k(0)) = 1 - 8 + k = -7 + k

Therefore, we have:

∫[0,1] f(x) dx = -7 + k = 32

Solving for k, we have:

k = 32 + 7 = 39

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The account increases in value by 1% every quarter, which is equivalent to 1/4% every month.

Savings interest is calculated on a daily basis and deposited into the account on the first day of the next quarter. The interest rate will depend on the balance in the account. Now it's between 3% and 3.5%.

To find the increase in value for an account with an APR of 4% and quarterly compounding, we'll first need to convert the APR to a quarterly interest rate.
1. Divide the APR by the number of compounding periods in a year: 4% / 4 = 1%.
2. The account increases in value by 1% every quarter.

Your answer: a. 1%

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The Formula for finding C.P., when

S.P. = Rs. 500    and Loss% = 20%   is:

CP = ( SP * 100 ) / ( 100 – percentage loss )

Putting values in the formula we get,

CP = ( 500*100) / (100 - 20)

Ans = Rs 625.

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The cost price is Rs. 625.

Cost price = 100 × selling price/100 - loss%

CP = 100 × 500/100-20

     = 100 × 500/80

     = 5000/8 = 625

Thus, the cost price is Rs.625.

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Answer:

A

Step-by-step explanation:

We want to simplify the product \((3y^{-4})(2y^{-4})\).

First, notice that both terms have a power with base y, so by the properties of exponents, we can combine the two \(y^{-4}\) into one by adding their exponents:

\(y^{-4}*y^{-4}=y^{-4+(-4)}=y^{-8}\)

Now, let's multiply the 3 and 2:

3 * 2 = 6

So far, we have \(6y^{-8}\). However, we have a negative exponent that we want to make positive. Remember another property of exponents that when we have a negative exponent, we can make it positive by taking the reciprocal of it. Thus, \(y^{-8}\) becomes \(\frac{1}{y^8}\).

Hence, our answer is \(6*\frac{1}{y^8}=\frac{6}{y^8}\), or A.

~ an aesthetics lover

To compute the expected revenue from a single trip of a small ferry that can accommodate cars and buses, you need to know the joint distribution of x (number of cars) and y (number of buses) as described in question 1.

Once you have the joint distribution, calculate the expected revenue by multiplying the probabilities of each combination of cars and buses by the corresponding tolls, and then sum up the results. In mathematical terms:

Expected Revenue = Σ (Probability(x, y) * ($3x + $10y))

Please provide the joint distribution from question 1 to compute the expected revenue accurately.

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Given the system of equations:

The solution of the system will be as follows:

Substitute with y into the first equation to find x:

So, the solution of the system is:

Answer:

See below

Step-by-step explanation:

-4x -8y = 8

3x-5y = 16    <===== multiply this equation by   4/3 to get

4x - 20/3 y = 64/3      <=====add to first equation...this will eliminate 'x'

      -8y - 20/3 y = 8 + 64/3       solve for y = -2

   use this value of y in any of the equations to compute x

        -4x - 8(-2) = 8

         -4x = 8-16      shows x = 2

Answer:

200 m

Step-by-step explanation:

\(v = 60 km/h \times\frac{1000m}{1km}\times\frac{1h}{3600sec}}=\frac{60}{3.6}m/s\)

For the passenger, the other train moves at a rate of 2v

Time t = 6 sec

The length = (2v) x t = \(2\times\frac{60}{3.6}\times 6=200 m\)

Answer:

12

Step-by-step explanation:

to find the answer, divide 6 by 0.5. you will get 12

Answer:

AB = 4

Step-by-step explanation:

AB + BC = AC

Substitute the line segments for their given values:

AB + 38 = 42

Subtract both sides by 38:

AB = 42 - 38

AB = 4

Check your work:

4 + 38 = 42

42 = 42

Correct!

Answer:

none of these are correct

Answer:

  1/20 g/mL

Step-by-step explanation:

You want the fraction form of the ratio in grams per mL of 50 g in 1000 mL.

The word "per" in this context means "divided by." That is, "grams per mL" means "grams divided by milliliters." That ratio looks like ...

  \(\dfrac{50\text{ g}}{1000\text{ mL}}=\boxed{\dfrac{1}{20}\text{ g/mL}}\)

The group given the treatment being studied during an experiment, such as medication, fertilizer, or exposure to some other variable, is called the (A) test group.

Therefore, the group given the treatment being studied during an experiment, such as medication, fertilizer, or exposure to some other variable, is called the (A) test group.

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The correct question is given below:

The group given the treatment being studied during an experiment, such as medication, fertilizer, or exposure to some other variable, is called the _____?

(A) test group

(B) placebo group

(C) control group

(D) variable group

Answer:

It's 38.

Step-by-step explanation:

the sum of three consecutive even integers is 108, the largest number in the sequence would be 38.

I hope this helps you!

Answer:

We can use algebra to solve this problem. Let's call the smallest of the three consecutive even integers x. Since the integers are consecutive and even, the next two integers will be x+2 and x+4.

The problem states that the sum of three consecutive even integers is 108, so we can write an equation:

x + (x+2) + (x+4) = 108

We can simplify this equation by combining like terms:

3x + 6 = 108

3x = 102

x = 34

So, the smallest of the three consecutive even integers is 34.

The next two integers will be x+2 = 34+2 = 36 and x+4 = 34+4 = 38

The largest number of the three consecutive even integers is x+4 = 38.

Answer:

How to graph it

Step-by-step explanation:

First, put the y-intercept (when it crosses the up- and-down line) at the whole number, and for every one x unit, put three y units up.

=) Hope this helps.

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The 25-lb weight stretched by 0.2 inches.

According to the question, Hooke's law states that the spring can be stretched directly with a force F. Therefore, the expression for the Hooke's law can be written as: F(Force) = extension(d). constant(k)

If a spring is stretched 0.8 inches by 40-lb weight:

40 = 0.8k ⇒k = 50

Now: the stretched inches be:

25 = 50d ⇒ d = 0.2 inches

Hence, the 25-lb weight stretched by 0.2 inches.

What is Hooke's law?

The Hooke's law states that the force produced by the spring is directly proportional to the weight of the spring. And the work done can be done either in the form of stretching or compressing.

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Given the data set of the number of miles that Monica walked each day, the summary is :

First sort the numbers into ascending order:

3. 2, 3. 8, 4. 1, 4. 2, 4. 7, 5, 5. 8

Min is smallest value in the data set.

Min = 3.2

Max is the largest value in the data set.

Max = 5.8

The median is the middle number which we can see to be 4. 2 .

The Q1 is the first quartile which would be:

lower half is 3.2, 3.8, and 4.1 = 3 . 8

The Q3 is the third quartile and would be the upper half is 4.7, 5, and 5.8. Q3 = 5

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1. For Joshua's triangle; the distance of the green side of the triangle d₃ is 5.

2. For Murney's triangle, the perimeter of the triangle is 12.

3. For Grace, Abby and Chris's triangle, the perimeter of the triangle is 5 + √17 +  4√2.

4. For Chloe's triangle, the perimeter of the triangle is 11 + √65.

The distance of the triangles is calculated as follows;

For Joshua's triangle;

The length of d₁, d₂, and d₃ is calculated as follows;

d₁ = √ [(3 - 2)² + (2 - 0)²] = √5

d₂ = √ [(-1 - 3)² + (4 - 2)²] = 2√5

d₃ = √ [(-1 - 2)² + (4 - 0)²] = 5

The distance of the green side of the triangle d₃ = 5

For Murney's triangle, the perimeter of the triangle is calculated as;

BC = √ [(4 - 4)² + (6 - 2)²] = 4

AC = √ [(1 - 4)² + (2 - 2)²] = 3

AB = √ [(4 - 1)² + (6 - 2)²] = 5

Perimeter = 4 + 3 + 5 = 12

For Grace, Abby and Chris's triangle, the perimeter of the triangle is calculated as;

AC = √ [(-3 - 2)² + (2-2)²] = 5

BC = √ [(1 - 2)² + (2 + 2)²] = √17

AB = √ [(1 + 3)² + (2 + 2)²] = 4√2

Perimeter = 5 + √17 +  4√2

For Chloe's triangle, the perimeter of the triangle is calculated as;

AC =  √ [(-3 - 4)² + (2-2)²] = 7

BC =  √ [(4 - 4)² + (6-2)²] = 4

AB =  √ [(4 + 3)² + (6-2)²] = √65

Perimeter = 7 + 4 + √65 = 11 + √65

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Given: 15 different shirts with 5 different colours

To Determine: The bar chart represent the different colours

Solution

Let us get the frequecy table representing the number of the different colors

Answer:

a=2.4

b=13.9

c= -8.1

Step-by-step explanation:

a= 3-0.6= 2.4

b= 12.5-(-1.4)= 13.9

c= -5.2-2.9= -8.1

Answer:

(0, 5)

Step-by-step explanation:

The solution is the point of intersection of the lines.

(0, 5)

The ratio of the number of circles to the number of triangles in simplest form is 3:4. The number of circles that need to be added to make the ratio 1 : 1 is 3.

First of all, we would have to determine the total number of circles and the number of triangles based on the information provided in the chart (see attachment) as follows;

Total number of circles, C = 9 circles.

Total number of triangles, T = 12 triangles.

Therefore, the ratio of the number of circles to the number of triangles is given by

C:T = 9:12

Dividing both sides of the ratio by 3, we have the following ratio in simplest form:

C:T = 3:4

In order to make the ratio 1:1, the number of circles that need to be added can be calculated as follows;

9 + x:12=1:1

(9 + x)/12 = 1/1

9 + x = 12

x = 12 - 9

x = 3 circles.

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The total square footage (area) of the apartment is 337 square feet.

It is given in the question that, In a small apartment:-

Dimensions of the bedroom = 10 ft by 10ft

Dimensions of the bathroom = 5 ft by 5 ft

Dimensions of the living room/kitchen = 14 ft by 18 ft

We have to find the total square footage (area) of the apartment.

We know that,

Area of square = \(side^2\)

Hence,

Area of the bedroom = 100 square feet

Area of the bathroom = 25 square feet

Area of the living room/ kitchen = 212 square feet

Hence,

Total square footage of the apartment = 100 + 25 + 212 = 337 square feet.

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Answer:

The first one would be 82.5

Step-by-step explanation:

Answer:

82.5 for the first one,

Step-by-step explanation:

you take the base and the height for the trapezoid, multiply it together, and then for the square you take base and width for the rectangle, after you multiply you add

The specific gravity of the combined product is 1.22

Specific gravity is the ratio of the density of a substance to the density of some substance (such as pure water) taken as a standard when both densities are obtained by weighing in air.

Given,

The total quantity of portion= 50 ml

Specific gravities of the three syrups = 1.10,1.25 and 1.32

Then,

The specific gravity of the combined product= \(\frac{1.10+1.25+1.32}{3}\)

= 1.22

Hence, the specific gravity of the combined product is 1.22.

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Answer:

Step-by-step explanation:

The mean of the dataset is:

Increased mean is:

The sum of the numbers in the larger data set is:

The difference of sums is:

We need a combination of 3 different numbers with the sum of 54.

One option would be: