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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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The perimeter of the figure on the right is 40.26 yrd.  .

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object.

here, we have,

from the given figure we get,

the radius of the circle = 6 yrd.

then, the perimeter = 2*pi* 6

                                = 37.68 yrd.

now, the figure is 3/4 th of the circle,

so, perimeter = 37.68 * 3/4 + 12

                      = 40.26 yrd.

Hence, The perimeter of the figure on the right is 40.26 yrd.  .

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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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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:

I believe this is a zero polynomial since it has only one number

Answer:

3x is a monomial

Step-by-step explanation:

Monomial (One term) – 3x

Binomial (Two Term) – 7a-5

Trinomial (Three Term) – x^2-x-2

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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According to the table, the information does indeed justify using a normal model to approximation population characteristics.

The answer to the query is:

The following numbers are one standard deviation away:

= 0.33 + 0.36

= 0.69

According to the empirical rule, this value is:

= 0.68

As a result, and in accordance with the empirical rule, the quantities were always 0.95 with two standard deviations. Consequently, the data's empirical rule was followed.

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The correct question is-

The mean and standard deviation of the sample data collected on continuous variable x are −0.25 and 0.03, respectively. The following table shows the relative frequencies of the data in the given intervals.

Based on the table, do the data support the use of a normal model to approximate population characteristics?

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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The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).

The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.

here, we have,

For the graph, the domain lie across the x-axis. The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).

Note that point where the circles are shaded shows a closed interval

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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.

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.

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 95% confidence interval for the population mean is approximately (1,218, 1,271)

A 95% confidence interval for the population mean can be calculated as follows:

Calculate the standard error (SE) of the mean: SE = standard deviation/sqrt (sample size) = 38 / sqrt(16) = 12.56

Use the t-distribution to find the critical value, t*, for a 95% confidence level and degrees of freedom (df) = sample size - 1 = 15.

Calculate the margin of error (ME) as ME = t* * SE = t* * 12.56.

Calculate the lower bound and upper bound of the confidence interval: lower bound = sample mean - ME = 1,245 - ME; upper bound = sample mean + ME = 1,245 + ME.

Since the degrees of freedom for this sample size is quite small, the critical value for t-distribution can be approximated using a t-table for a 95% confidence level and df = 15. The critical value is approximately 2.131.

So, the margin of error is ME = 2.131 * 12.56 = 26.86, and the 95% confidence interval for the population mean is:

Lower bound: 1,245 - 26.86 = 1,218 (rounded to the nearest whole number)

Upper bound: 1,245 + 26.86 = 1,271 (rounded to the nearest whole number)

Therefore, the 95% confidence interval for the population mean is approximately (1,218, 1,271).

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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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The value of n from the given equation is 30.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 57,491 = 1,885n

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, n=57,491/1885

n=30.5

Therefore, the value of n is 30.5.

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"Your question is incomplete, probably the complete question/missing part is:"

Solve to find the value of n

57,491 = 1,885n

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 cost of each bag of walnut can be determined following the below steps and each bag of walnut is $1.89

Total receipt= $17.92

4 batches of chocolate chip walnut cookies requires 4 bags each of chocolate chips and walnuts if each batch requires 1 bag each of chocolate chips and walnuts

Cost of chocolate chips = $2.59

Cost of 4 bags of chocolate chips = 4($2.59)

= $10.36

Total cost of 4 bags of walnuts = Total receipt - Cost of 4 bags of chocolate chips

= $17.92 - $10.36

= $7.56

Cost of each bag of walnut= Total cost of 4 bags of walnuts / 4

= $7.56 / 4

= $1.89

Therefore, each bag of walnut cost $1.89

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Answer: Step 1: Divide 17.92 by 4

              Step 2: Subtract 2.59 from 4.48

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 missing code that can be used to replace / missing code / so that the code segment works as intended is x >= 10.

The code segment is intended to store the sum of all multiples of 10 between 10 and 100, inclusive. The value of x starts at 100 and is decremented by 10 on each iteration of the loop, until it reaches 10. The sum of all the multiples of 10 between 10 and 100 is stored in the variable total.

The missing code in the while statement determines when the loop will stop. If we use x >= 10 as a replacement for / missing code /, the loop will run as long as x is greater than or equal to 10. When x reaches 10, the loop will stop.

Here's the complete code:

int x = 100;

int total = 0;

while(x >= 10)

{

   total = total + x;

   x = x - 10;

}

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Your question is incomplete but probably the complete question is:

Consider the following code segment, which is intended to store the sum of all multiples of 10 between 10 and 100, inclusive (10 + 20 + ... + 100), in the variable total.

int x = 100;

int total = 0;

while( / missing code / )

{

total = total + x;

x = x - 10;

}

Which of the following can be used as a replacement for / missing code / so that the code segment works as intended?

A x < 100

B x <= 100

C x > 10

D x >= 10

E x != 10

Answer:

x and Y 5=(a+5)

Step-by-step explanation:

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

Answer:

  (a)  three angles: 62°, 34°, and 84°

Step-by-step explanation:

You want to know which specification can result in an infinite number of triangles.

If only the angles are specified, the sides can have an infinite number of (related) lengths.

  three angles: 62°, 34°, and 84° will create an infinite number of triangles

Assuming the side lengths can form a triangle, they will specify exactly one triangle.

Lengths 3 cm, 5 cm, and 10 cm cannot form a triangle.

When two sides are specified along with the angle between them, exactly one triangle can be formed.

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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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 dilations relation is C'D = (3/4)CD.

Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.

Its also called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.

Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).

Given;

First, we want to dilate point C using D as the center of dilation with a scale factor = 3/4.

This only means that we will have the new point C', such that:

C'D = (3/4)*CD

Where CD is the distance between points C and D

Therefore, the dilation will be C'D = (3/4)*CD.

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The solution is, the water level if today is the 5th day is 235 lit.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The expression 7w + 200 liters are the water level which drops in a particular reservoir in w days.

then, for 5 days it will be,

7*5 + 200

=35+200

= 235

Hence, The solution is, the water level if today is the 5th day is 235 lit.

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Answer:

300-20w=?

150+10w=?

Step-by-step explanation:

Answer:

Step-by-step explanation:

320

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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