simplify
3x^2 - 2x+ 1=
X=2

The definite integral represents the area of the region ∫(x²-3x)dx.

The definite integral is the region beneath the curve of y1 = x2 - 3x between its first intersection with y2 = 0 and its subsequent intersection with y2 = 0. The curve looks like this:

In order to find their intersection, we equalize them:

x2 - 3x = 0

x(x - 3) = 0

x = 0 and x = 3.

Thus, the integral is:

∫(x²-3x)dx

The area lies below the x-axis, hence the result will be negative (see graph). I would argue that we should take this integral's absolute value in order to arrive at the correct answer for the region's area as we are asked to calculate it. Just place absolute value indications all around the integral.

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The magnitude of the vector is shown by the length of the vector and the angle it makes with the positive x-axis is shown by the direction of the vector.

The magnitude of vector v is 2 and the angle it makes with the positive x-axis is given as θ = 3.

The component form of vector v can be found by using the following formula:

V = ||V|| (cosθi + sinθj)

Therefore, the component form of vector v is given by:

V = 2 (cos3i + sin3j)

We can calculate the components by substituting the values for ||v|| and θ in the above formula.

Therefore, the x component of vector v is given by:

Vx = 2 cos3

Vx = 1.86

The y component of vector v is given by:

Vy = 2 sin3

Vy = 3.42

Therefore, the component form of vector v is given by:

V = 1.86 i + 3.42 j

This can be represented graphically as shown in the figure.

The magnitude of the vector is shown by the length of the vector and the angle it makes with the positive x-axis is shown by the direction of the vector.

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Answer:

62.5 square feet

Step-by-step explanation:

Let's call the width of the rectangle w. Since the ratio of the length to the width is 5 to 2, the length can be expressed as 5/2 times the width:

l = 5/2 * w

We know the length is 12.5 feet, so we can use that information to solve for the width:

12.5 = 5/2 * w

w = 12.5 * 2/5

w = 5

The width of the rectangle is 5 feet.

The perimeter of the rectangle is calculated by adding up the lengths of all four sides:

p = 2 * (l + w)

p = 2 * (12.5 + 5)

p = 2 * 17.5

p = 35

The perimeter of the rectangle is 35 feet.

The area of the rectangle is calculated by multiplying the length and width:

a = l * w

a = 12.5 * 5

a = 62.5

The area of the rectangle is 62.5 square feet.

The mean net worth of the 42 national corporations is approximately 31.5 million dollars. The modal class is the class with the highest frequency, which is the class with class limits of 10-15 and a frequency of 14.

To find the mean, we add up all the net worth values and divide by the total number of corporations. However, since we only have the frequency of each class, not the actual net worth values, we need to estimate the mean using the midpoint of each class and the frequency as the weight. The midpoint of a class is calculated by averaging the lower and upper-class limits.

In this case, the midpoint for a class with class limits of 10-15 is 12.5 million dollars and the midpoint for a class with class limits of 40-45 is 42.5 million dollars. By multiplying the midpoint of each class by its frequency and summing up the results, we can estimate the mean net worth of the corporations.

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Complete Question:

Net Worth of Corporations These data represent the net worth (in millions of dollars) of 42 national corporations. Find the mean and modal class for the data.

Class limits     Frequency

10-15                   14

16-21                   2

22-27                 4

28-33                 8

34-39                 3

40-45                 11

The horizontal velocity of a bullet right before it hits the ground is 10 m/s.

The horizontal velocity of a bullet remains constant throughout its flight, as it is only affected by gravity. This means that the horizontal velocity of the bullet right before it hits the ground will be the same as the initial horizontal velocity when it was fired.

In this case, the bullet was fired at an angle of 60 degrees above the horizontal, but the horizontal velocity remains constant, so it will still be 10 m/s right before it hits the ground. To determine the vertical velocity, we would need to know the time of flight and use the equations of motion to calculate the vertical acceleration due to gravity.

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There are 8 nickels does Richard have.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Richard has 17 coins with a value of 76 cents.

And, The coins are nickels, dimes, and pennies. He has twice as many pennies as dimes.

Now, Let p = number of pennies

n = number of nickels

d = number of dimes

Hence, We can formulate;

⇒ p(1) + n(5) + d(10) = 76

⇒ p + 5n + 10d = 76  .. (i)

Here, He has twice as many pennies as dimes.

⇒ p = 2d

And, Richard has 17 coins.

⇒ p + d + n = 17 .. (ii)

Substitute p = 2d in equation (i) and (ii),

⇒ p + 5n + 10d = 76  

⇒ 2d + 5n + 10d = 76  

⇒ 5n + 12d = 76  .. (iii)

⇒ p + d + n = 17

⇒ 2d + d + n = 17

⇒ n + 3d = 17  .. (iv)

Solve equation (iii) and (iv), we get;

⇒ d = 3

⇒ n = 8

Hence, There are 8 nickels.

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The  probability density function (pdf) of X can be written as fx(x) = 3x, where 0 < x < 1.

The given probability density function (pdf) is fx(x) = cx, where 0 < x < 1 and c is a constant. To find the value of c, we can use the property that the integral of the pdf over the entire sample space must equal 1, as the sum of all probabilities in the sample space must equal 1. Thus, the equation to find c is:

[tex]\int\limits^1_0{cx} \,dx = 1[/tex]

Solving for c, we have:

c = 3.

Therefore, the pdf of X can be written as fx(x) = 3x, where 0 < x < 1. This function can be used to find probabilities and other statistical measures related to the random variable X.

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Equations (a) and (c) are linear, while equation (b) is nonlinear.

(a) This is a second order linear differential equation. The order of the equation is 2, and the independent variable used is t. There are no nonlinear terms.

(b) This is a nonlinear differential equation. The order of the equation is 2, and the independent variable used is y. The nonlinear terms are y and y'.

(c) This is a first order linear differential equation. The order of the equation is 1, and the independent variable used is t. There are no nonlinear terms.

Equations (a) and (c) are linear, while equation (b) is nonlinear.

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1. To compute the probability that we have picked exactly n cards, we need to consider the number of ways to pick n cards out of 52 such that all 4 shades are represented, and divide that by the total number of possible n-card combinations from the deck of 52.

The number of ways to pick n cards such that all 4 shades are represented is given by the number of combinations of n items taken 4 at a time, with repetition allowed (denoted as C(n-1,3) or C(n+3-1,n)). This is because there are 4 shades, and we need to pick one card from each shade.

The total number of possible n-card combinations from the deck of 52 is given by C (52, n).

Therefore, the probability that we have picked exactly n cards is given by:

P(n) = C(n-1,3) / C(52, n)

2. To verify that the probability sums up to 1, we need to take the summation over all possible values of n, from n=4 to n=52:

P = sum(P(n)) from n=4 to n=52

If P is equal to 1, then the probability of picking exactly n cards over all possible values of n adds up to 1, which means that the event of picking all 4 shades is certain to occur at some point.

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The functions are 1. f(x) = x⁴ and g(x) = cos (x), 2. f(x) = cos x and g(x) = cos x and 3. f(x) = cos (x) and g(x) = x⁴.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

The composition of two functions f(x)  and g(x) can be defined as the new function h(x) such that h(x) = f(g(x)).

1. cos^4 (x) = f(g(x))

cos⁴ (x) can be written as (cos x)⁴

f(g(x)) = (cos x)⁴

Let g(x) = cos (x)

f(g(x)) = (g(x))⁴

Substitute x in place of g(x).

So, f(x) = x⁴

2. cos(cos(x)) = f(g(x))

Let g(x) be cos x

f(g(x)) = cos (g(x))

Substitute x in place of g(x),

f(x) = cos x

3. cos (x⁴) = f(g(x))

Let g(x) = x⁴

f(g(x)) = cos (g(x))

Substitute x in place of g(x),

f(x) = cos (x)

Hence each of the functions is found from the composition of functions.

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Answer:30

Step-by-step explanation:

64-4=60

60/2 = 30

The measure of the j of triangle ΔHIJ is given by the law of sine and is given by j = 2.3 inches

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ΔHIJ

Now , the equation will be

The measure of i = 2.8 inches

The measure of ∠I = 68°

The measure of j = j

The measure of ∠J = 50°

Now , from the law of sines , we get

a / sin A = b / sin B

Substituting the values in the equation , we get

2.8 / sin ( 68 )° = j / sin ( 50 )°

On simplifying the equation , we get

2.8 / 0.92718 = j / 0.766044

Multiply by 0.766044 on both sides of the equation , we get

j = 3.0198972 x 0.766044

On further simplification , we get

j = 2.3 inches

Hence , the measure of j of triangle is 2.3 inches

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Answer: Based on the information given, it seems like the crow is unable to break open the walnut in its current location without it being stolen. To overcome this problem, the best solution would be for the crow to fly away to another location where it can safely break open the walnut. With a take-off speed of 19 feet per second, the crow should be able to quickly reach a new location where it can safely open the walnut.

Step-by-step explanation:

The additive inverse of an integer n can be expressed mathematically as Vn e Z+, Im E Z, m < n | m + n = 0, which states that if an integer m exists such that m + n = 0, then m is the additive inverse of n.

The formal statement can be expressed mathematically as:

Vn e Z+, Im E Z, m < n | m + n = 0

This statement translates to: Given an integer n, if there exists an integer m such that m + n = 0, then m is the additive inverse of n.

To understand this statement more clearly, we can use an example. Let's say n = 5. This means that we are looking for an integer m such that m + 5 = 0. In this case, m = -5, which is the additive inverse of 5. We can also calculate this mathematically. We know that m + n = 0, so we can rearrange and solve for m: m = -n. Therefore, the additive inverse of n is -n.

In summary, given an integer n, the additive inverse of n is -n. This can be expressed mathematically using the statement Vn e Z+, Im E Z, m < n | m + n = 0.

The additive inverse of an integer n can be expressed mathematically as Vn e Z+, Im E Z, m < n | m + n = 0, which states that if an integer m exists such that m + n = 0, then m is the additive inverse of n.

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This is  referred to Fermat's Little Theorem, which states that if p is a prime number and a is an integer such that 0 < a < p, then a^(p-1) ≡ 1 (mod p).

In other words, if we raise a to the power of p-1 and divide by p, the remainder will always be 1. This theorem can be used to efficiently test the primality of a number or to find modular inverses in modular arithmetic.

Fermat's Little Theorem is a fundamental result in number theory and has important applications in cryptography and computer science. The theorem states that if p is a prime number and a is an integer such that 0 < a < p, then a^(p-1) ≡ 1 (mod p). This can be expressed as:

a^(p-1) = 1 + kp where k is an integer.

This theorem is a direct consequence of the fact that the set of integers from 1 to p-1 (mod p) form a group under multiplication (mod p). This group is known as the group of units modulo p, and the order of this group is p-1. Hence, a^(p-1) must be congruent to 1 (mod p) since it is the product of all elements in the group.

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Answer:

Step-by-step explanation:

The cost of the labor per hour will be $35.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Ella needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4 hours and charged her $85 for parts. The total was $225.

The expression will be formed as below to get the value of x.

4x+85 =225

x =35

Therefore, the cost of the labor per hour will be $35.

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Thresholding is the simplest method of image segmentation. It is a non-linear operation that converts a gray-scale image into a binary image where the two levels are allowed to pixels that are below or above the specified threshold value.

In other words, if the pixel value is greater than a threshold value, it is assigned one value (maybe white), or else it is assigned another value (maybe black). In OpenCV, we use cv2.threshold() function.

cv2.threshold(src, thresh, maxval, type[, dst])

This function put fixed-level thresholding to a single-channel array. The function is used to get a binary image out of a grayscale image or for removing noise, that is, filtering out pixels with too small or too large values.

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The value of x is 94/13 approximately equal to 7.23.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Line segment described in the question is given below.

Given that,

Length of XY = 7x

Length of YZ = 6x - 11

Length of XZ = 83

We have the equation,

XY + YZ = XZ

7x + 6x - 11 = 83

13x = 83 + 11

13x = 94

x = 94/13 ≈ 7.23

Hence the value of x is 94/13.

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Step-by-step explanation:

The circumference of the can is 22/7 * 4 = 88/7 cm.

Since the label needs to touch end-to-end with no overlap, the length of the label is equal to the circumference of the can, so it is 88/7 cm.

The journal entries to record the receipt of the application money and its allotment to share capital and Allotment Account are as follows:

Debit Cash Rs. 300,000

Credit Share Application Account Rs. 300,000

(To record the receipt of the money on application)

Debit Share Application Account Rs. 300,000

Credit Share Capital Rs. 150,000

Credit Share Allotment Account Rs. 150,000

(To record the transfer of the application money to the Share Capital and the Allotment accounts, respectively.)

Journal entries are the initial records kept of business transactions.

Journal entries are made as transactions occur on a daily basis.

Authorized capital = Rs. 1,000,000

The number of shares issued = 5,000

The par value = Rs. 100

The premium = Rs. 10 (Rs. 100 x 10%)

The issuance price per share = Rs. 110 (Rs. 100 + Rs. 10)

The expected amount to be received on application = Rs. 30 per share

The number of applications received = 10,000

Application money = Rs. 300,000

Excess Application = Rs. 150,000

Cash Rs. 300,000

Share Application Account Rs. 300,000

Share Application Account Rs. 300,000

Share Capital Rs. 150,000

Share Allotment Account Rs. 150,000

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Answer:

300-20w=?

150+10w=?

Step-by-step explanation:

Answer:

Step-by-step explanation:

320

Answer:

(f + g)(x) = 3x² + x + 1

Step-by-step explanation:

[tex]\displaystyle{(f+g)(x) = f(x)+g(x)}[/tex]

Substitute f(x) = 3x² - 1 and g(x) = x + 2 in:

[tex]\displaystyle{f(x)+g(x) = (3x^2-1)+(x+2)}\\\\\displaystyle{f(x)+g(x)=3x^2-1+x+2}\\\\\displaystyle{f(x)+g(x) = 3x^2+x+1}\\\\\displaystyle{\therefore (f+g)(x) = 3x^2+x+1}[/tex]

The equation is linear, with the independent variable (CORE STRENGTH) being multiplied by 12 and the constant term being -178. The constant term represents the estimated age in months of a unit with a core strength of 0, which is not likely to occur in reality.

The age in months of a unit with a core strength of 100 can be calculated by plugging the value into the equation

AGE in months = -178 + 12 * 100

AGE in months = 12 * 100 - 178

AGE in months = 1200 - 178

AGE in months = 1022

So, the estimated age in months of a unit with a core strength of 100 would be 1022 months.

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The value of the variable x is 72 degrees

A supplementary angle is simply defined as a  pair of angles that sum up to 180 degrees.

The properties of supplementary angles includes;

From the information given, we have that;

108 degress + x = straight line

But we know that angles on a straight line is 180

Then,

108 + x = 180

collect like terms

x = 180 - 108

subtract the values

x = 72 degrees

Hence, the value is  72 degrees

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Since the y-intercept of the estimated line of best fit is at (0, b), the appropriate value of b is 360.

The appropriate slope of the estimated line of best fit is -30

In Mathematics, the y-intercept is also referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0). Therefore, the y-intercept is at (0, 360).

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (360 - 0)/(0 - 12)

Slope, m = -30.

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Answer:

x and Y 5=(a+5)

Step-by-step explanation:

...................

The expression of the given composite functions is; (f ∘ g)(x) = 75x² - 150x + 78

We are given the functions as;

f(x) = 3x²+3

g(x) = 5x - 5

We know that the expression of the composite function (f ∘ g)(x) is;

(f ∘ g)(x) = f(g(x)

Thus;

f(g(x) = 3(5x - 5)² + 3

= 3(25x² - 50x + 25) + 3

= 75x² - 150x + 75 + 3

= 75x² - 150x + 78

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The simple three-period moving average forecast for period 6 is 68.33.

The simple three-period moving average is a method for smoothing out fluctuations in a time series data by taking the average of the three most recent data points. To find the forecast for period 6, we calculate the average of the demand in periods 4, 5, and 6. In this case, the forecast for period 6 is 68.33. To find this, we sum the demand in periods 4, 5, and 6 and divide by 3. (70 + 69 + ?)/3 = 68.33, where the '?' represents the demand in period 6.

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