1. Check whether the given function is a probability density function. If a function fails to be a probability density function, say why.
a) f(x) = x on [0, 7]
<1> Yes, it is a probability function.
<2> No, it is not a probability function because f(x) is not greater than or equal to 0 for every x.
<3> No, it is not a probability function because f(x) is not less than or equal to 0 for every x.
<4> No, it is not a probability function because\int_{0}^{7}f(x)dx ≠ 1.
<5> No, it is not a probability function because\int_{0}^{7}f(x)dx = 1.
b) f(x) = ex on [0, ln 2]
<1> Yes, it is a probability function.
<2> No, it is not a probability function because f(x) is not greater than or equal to 0 for every x.
<3> No, it is not a probability function because f(x) is not less than or equal to 0 for every x.
<4> No, it is not a probability function because\int_{0}^{\ln 2}f(x)dx ≠ 1.
<5> No, it is not a probability function because\int_{0}^{\ln 2}f(x)dx = 1.
c) f(x) = −2xe−x2 on (−[infinity], 0]
<1> Yes, it is a probability function.
<2> No, it is not a probability function because f(x) is not greater than or equal to 0 for every x.
<3> No, it is not a probability function because f(x) is not less than or equal to 0 for every x.
<4> No, it is not a probability function because\int_{-\infty }^{0}f(x)dx ≠ 1.
<5> No, it is not a probability function because\int_{-\infty }^{\0}f(x)dx = 1.

Yes, the triangle can be easily formed for the sides 7 cm, 5 cm and 3 cm.

According to the side side side rule of triangle, if the sum of the any two sides of triangle is more than third side, it will form a triangle. Let us check the same by assuming side a to be 7 cm, side b to be 5 cm and side c to be 3 cm.

Side a + side b > side c

7 + 5 > 3

Add the digits in Left Hand Side of the equation

12 > 3

Side b + side c > side a

5 + 3 > 7

Add the digits in Left Hand Side of the equation

8 > 7

side c + side a > side b

3 + 7 > 5

Add the digits in Left Hand Side of the equation

10 > 5

We see that the two sides of the triangle are greater than third side, hence, it is possible to form the triangle.

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The end behavior of the functions g(x) and h(x) are the same and both functions approach negative infinity as x becomes large in either direction.

Generally, The end behavior of a function refers to the behavior of the function as x approaches positive or negative infinity. To compare the end behavior of g(x) and h(x), we can look at the leading term of each function, which is the term with the highest degree.

In the function g(x) = -3x^4 + 15x^3 - 12x^2 + 3x + 20, the leading term is -3x^4, so as x approaches positive or negative infinity, the function will approach negative infinity.

In the function h(x) = -3x^4 - 16x - 1, the leading term is also -3x^4, so as x approaches positive or negative infinity, the function will also approach negative infinity.

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Answer: The exponential form should be 10⁵=9x+1 instead of 9x+1=10⁵

Step-by-step explanation:

The exponential form of a logarithm should be the other way around.

the Matrix multiplication of the given question is [tex]\left[\begin{array}{cc}-9&3\\5&-8\\\end{array}\right][/tex]

What is matrix?

The plural version of the word matrix is a matrix, which refers to the arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns. These arrays have a rectangular shape, and several operations like addition, multiplication, and transposition are specified for them. The components of the matrix are referred to as its entries or numbers. Vertical and horizontal entries in matrices are referred to as columns and rows, respectively. A matrix with m rows and n columns will contain m n entries. The uppercase letter 'A', which here stands for "matrix," Aij.

A =-1/3 [tex]\left[\begin{array}{cc}27&-9\\-15&24\\\end{array}\right][/tex]

A = [tex]\left[\begin{array}{cc}-9&3\\5&-8\\\end{array}\right][/tex]

Hence the Matrix multiplication of the given question is [tex]\left[\begin{array}{cc}-9&3\\5&-8\\\end{array}\right][/tex]

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Answer:

Below

Step-by-step explanation:

1085 miles / 31 days = 35 miles/day

The real distance by means of scales used in the map that is described in the statement is approximately equal to 72.11102550928 kilometers.

Scales are a useful resource to represent any system in a size different than real. Maps are usually created from application of scales. Mathematically speaking, scales are described by following mathematical ratio:

r = s / R

Where:

If we know that r = 0.1 centimeters per kilometers and s = 7.211102550928 centimeters, then the real distance derived from the distance shown in the map that is described in the statement is:

R = s / r

R = (7.211102550928 cm) / (0.1 cm / km)

R = 72.11102550928 km

By using scales on the map, the real distance is approximately equal to 72.11102550928 kilometers.

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The advice I will give Kenny that was using division to write a fraction equivalent to 30/100 after she tried to divide the numerator and denominator by three, is to also  divide them by factor of 10.

The concept that will be used is division,

The given values is  30/100, if we divide the numerator and denominator by three, we have 10/100.

Then we can also divide the  numerator and denominator  of  10/100 by factor of 10, then we will have 1/10.

It should be noted that Division in mathematics is the process of dividing an amount into equal parts.

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Answer:

d = 24

Step-by-step explanation:

d/4 - 9 = -3

d/4 - 9 + 9 = -3 + 9

d/4 = 6

d/4 * 4 = 6*4

d = 24

Check:

(24)/4 - 9 = -3

6 - 9 = -3

-3 = -3 (Correct)

Hope this helps!

Each friend will get 48 books. The solution is obtained using arithmetic operations.

What are arithmetic operations?

There are four basic operations which are listed as follows:

Now, Tara has 3 boxes of books and each box contains 48 books.

So, the total books that Tara has is equal to 3×48= 144.

Thus, Tara has total 144 books.

Tara divides the books among 3 friends.

So, the number of books that each friend will get is equal to 144÷3= 48

Hence, each friend of Tara will get 48 books.

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The mathematical concepts used to calculate insurance premiums include probability, actuarial science, risk assessment, pricing models, financial models, and statistical analysis.

Probability:

To calculate premiums, insurance companies use statistical data to determine the likelihood of a claim occurring. Probability is used to estimate the likelihood of certain events happening, such as accidents, illnesses, or natural disasters, and to determine the likelihood of a claim being made.

Actuarial Science:

Actuarial science is the application of mathematical and statistical methods to assess risk and uncertainty in insurance, finance, and other industries. Actuaries use mathematical models to analyze data and make predictions about future events, which is crucial in determining insurance premiums.

Risk Assessment:

Insurance companies use risk assessment to determine the level of risk associated with insuring a particular individual or group. Factors such as age, health, occupation, and location are considered when assessing risk, and premiums are adjusted accordingly.

Pricing models:

Pricing models are used to determine the cost of insurance based on the perceived level of risk. Pricing models like Loss Ratio, Pure Premium, and Captive pricing are used to arrive at the insurance premium.

Financial Models:

Financial models are used to determine the long-term financial stability of an insurance company and to ensure that the company has enough funds to pay out claims. Actuaries use financial models to calculate the amount of money an insurance company needs to set aside in order to pay claims and to determine the long-term financial health of the company.

Statistical Analysis:

Insurance companies use statistical analysis to evaluate data on claims and losses, and to identify patterns that can be used to predict future claims and losses. This analysis is used to identify trends in claims, to identify high-risk groups, and to set premiums.

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Answer:

cos(T) = 5/11

Step-by-step explanation:

cos = adjacent(5)/hypotenuse(11)

So whatever "cosine" of something to choose, the adjacent side to the angle needs to be five. It cannot be the right angle, therefore only the option "T" remains, as eleven would always be the hypotenuse for any angle.

The number of the cans that is produced is 5832.

We know that the term direct proportion has to do with a case in which one of the variables is increasing and the other is also increasing along side. This implies that the two variables can be seen to increase at the same time.

We have that the relationship of the process can be given as shown in question in simple format as; y = 243x where;

x = Number of hours

y = Number of cans

After 24 hours, we have;

y = 243(24)

y = 5832

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The following statements are true:

Segment DEF is parallel to ABC

The line segment  AB is parallel to DE

Line FC is parallel to AD

the line that is skewed to DE is BC

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)

Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;

DEF is parallel to ABC

CADF is parallel to CBEF

For the lines, the lines that are parallel to each other are:

AD is parallel to BE

AB is parallel to DE

FC is parallel to AD

Skew lines are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC

The missing image is attached with the answer below.

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A 3-dimensional vector is a line segment running from a point called head to the point called tail in 3-Dimensional space.

Vectors are mathematical or geometrical quantity that has two independent properties i.e., direction and magnitude. There are many types of vectors like unit vectors, equal vectors, etc.

The magnitude of the vector is the length of the line segment without it the direction has no power, Similarly unit vectors help us to find the direction of vectors and their magnitude is 1.

A 3-dimensional vector has majorly 3 components i.e., it has projections in the x, y, and z axes. For a three-dimensional vector A(a1,a2,a3), the formula for its magnitude is ∥a∥=√a21+a22+a23.

Along with magnitude and directions, the 3-D vectors also have angles and they are formed from the vector directly to each of the 3 positive axes.\ i.e., x, y, z axes. The formula used to calculate angle  is θ = cos-1 [ (a · b) / (|a| |b|) ]

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Answer:

A. -1

Step-by-step explanation:

imma human calculator and no one can stop me

Answer:

1/2

Step-by-step explanation:

6 x __ = 3

We divided by 6 into both sides

x  = 3/6 = 1/2

So, the missing number is 1/2

The correct option is 1/(n+1).The upper bound for the integral is 1/(n+1).

To determine the upper bound, we can use the fact that the integrand is bounded by its maximum value on the interval. The maximum value of the integrand on the interval [0, 1] is:

f(x) = 5x(1 + x)^(0.5)

At x = 1, f(x) = 5(1 + 1)^(0.5) = 5√2.

Therefore, an upper bound for the integral is:

In ≤ 5√2∫x^n dx

             0

Using integration by parts, we obtain:

In ≤ 5√2[x^(n + 1)/(n + 1)]_0^1

= 5√2/ (n + 1)

Therefore, the upper bound for the integral is 1/(n+1).

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A corollary is a theorem that connects to an established theorem in mathematics with a brief proof. As opposed to statement or theorem, the term "corollary" is inherently arbitrary.

A corollary may be unquestionably true if the idea or theory it is founded on is correct. Any triangle's internal angles, for instance, add up to 180 degrees in all cases. Each interior angle of an equilateral triangle is 60 degrees, which is a corollary of the aforementioned theorem.

A triangle is equiangular if it is equilateral, which is a corollary to the Base Angles Theorem. Converse of Base Angles Theorem Corollary: If a triangle is equiangular, it is also equilateral.

The sum of the measurements of the two distant interior angles determines how large an exterior angle of a triangle must be. the triangle's angle-sum Corollaries: A right triangle's acute angles are complimentary. A theorem whose proof naturally follows from another theorem is called a corollary.

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The corollary interior angles theorem is a mathematical result that relates to the number of sides in a polygon and the sum of the interior angles of that polygon.

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Polygonal Modeling: a type of 3D modeling that uses points, lines, and polygons to create a 3D object. NURBS Modeling: a type of 3D modeling that uses mathematical equations to create smooth curves and surfaces. Subdivision Modeling: a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes.

1. Polygonal Modeling: This type of 3D modeling uses points, lines, and polygons to create a 3D object. The polygons are connected together to create the 3D shape, and then textures and colors can be applied to the shape. This type of modeling is often used to create characters and environments for video games and animations.

2. NURBS Modeling: NURBS stands for Non-Uniform Rational B-Splines. This type of 3D modeling uses mathematical equations to create smooth curves and surfaces. NURBS modeling is often used for creating organic shapes such as cars and furniture.

3. Subdivision Modeling: Subdivision modeling is a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes. This type of modeling is often used for creating characters and creatures for video games and animations.

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143x11

=1573 cherries

One bag holds 11 cherries and there are 143 bags. To find out how many cherries there are, we would need to multiply the amount of cherries by the number of bags.

[tex]11\times143[/tex]

[tex]=\fbox{1573 total cherries}[/tex]

The slope of -6 means that the battery reduces by 6% each hour

What is the linear equation?

Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.

The slope of -6 means that, the battery reduces by 6% each hour and the equation is B = -6t + 48

The points

The points on the graph are represented using the following ordered pair (1, 42) and (5,18)

The slope

Start by calculating the slope (m) using:

m = (B2 - B1)/(t2 - t1)

So, we have:

m = (18 -42)/5-1

m = -24/4

m = -6

The equation

The equation is then calculated as:

B = m(t - t1) + B1

This gives

B = -6(t - 1) + 42

B = -6t + 6 + 42

B = -6t + 48

Hence, The slope of -6 means that the battery reduces by 6% each hour

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(1, 1) is not  solution of system of equations.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

We need to check the  point (1, 1) is a solution to the system of equations.

graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one.

y = 3x + 2

g = |x-1| +1

We obtain the intersection point

(0,2)

The only point of intersection of the graphs is (0, 2).

The point of intersection is the solution to the system of equations. (1, 1) is not the point of intersection

Hence, (1, 1) is not  solution of system of equations.

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By using the ratio formula, the number of doughnuts that will be consumed of 8 students in the time period of 9 minutes is 24 doughnuts.

The ratio formula compares the connection between two quantities or numbers. In this case, we are given that:

2 students can eat 4 doughnuts in 6 minutes

By using the ratio formula, 1 student can eat = 4/2 = 2 doughnuts in 6 minutes

It takes an average student about 3 minutes to consume a doughnut using the formula= 6/2 = 3 minutes

In one minute, the amount of doughnut can be consumed by a student is 1/3 of a doughnut

This method can be used to predict how many doughnuts 8 students can consume in 9 minutes:

X = 8 x 9 x (1/3) = 24 doughnuts

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Answer:

Step-by-step explanation:

44/4= 11

44-24/2=12

20/2=10

The room is 10 x 12' long

Answer:

n + 2 + 3m

Step-by-step explanation:

[tex]\frac{1}{2} (2n+4+6m) = (\frac{1}{2}*2n)+(\frac{1}{2}*4)+(\frac{1}{2}*6m)\\ =n+2+3m[/tex]

The functions differ from functions that we have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.

An output variable and one or more input variables are the minimum number of variables in a function.

An equation can have any number of variables and declares that two expressions are equal (none, one, or more). Although not all equations are functions, a function is frequently expressed as an equation.

It should be recalled that a function is merely an equation in which the x inserted produces precisely one from the equation.

In this instance, the functions are different from the ones we have used in algebra in the past since they may be coupled and focus more on rotation than on where they travel.

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The equation of perpendicular line that bisects the line segment is y = - (1 / 3) · x + 4 / 3.

In this problem we must determine the equation of the line that is perpendicular to a line segment and partitions the line segment in two parts of equal length, it happens when the perpendicular line passes through the midpoint of the line segment.

The equation of the line in explicit form is shown below:

y = m · x + b

Where:

In addition, two lines are perpendicular to each other when the following relationship is observed:

m · m' = - 1

Where:

Besides, the slope of a line can be determined by secant line formula:

m = Δy / Δx

Where:

And lastly, the midpoint of a line segment is determined by this formula:

M(x, y) = 0.5 · A(x, y) + 0.5 · B(x, y)

First, find the midpoint of the line segment:

M(x, y) = 0.5 · (3, 7) + 0.5 · (- 1, - 5)

M(x, y) = (1.5, 3.5) + (- 0.5, - 2.5)

M(x, y) = (1, 1)

Second, determine the slope of the line related to line segment:

m = (- 5 - 7) / (- 1 - 3)

m = (- 12) / (- 4)

m = 3

Third, calculate the slope of the perpendicular line:

3 · m' = - 1

m' = - 1 / 3

Fourth, find the intercept of the equation of perpendicular line:

b = y - m · x

b = 1 - (- 1 / 3) · 1

b = 1 + 1 / 3

b = 4 / 3

Fifth, write the equation of perpendicular line:

y = - (1 / 3) · x + 4 / 3

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Answer:

The measure of the third side of a triangle, when the measures of the other two sides are 18 ft and 23 ft, must be greater than the difference between the measures of the other two sides (which is 18 ft - 23 ft = -5 ft) and less than the sum of the measures of the other two sides (which is 18 ft + 23 ft = 41 ft).

This is because according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the measure of the third side must be between the difference of the two given sides and the sum of the two given sides.

Therefore the range of the measure of the third side of a triangle with side lengths 18 ft and 23 ft is:

(-5 ft < x < 41 ft)

or

[x > -5 ft and x < 41 ft].

It is also important to note that any value of x within this range will produce a valid triangle, however, any value less than -5 or greater than 41 will not.

Step-by-step explanation:

To obtain how fast the ball traveling 2 seconds after it is thrown, we differentiate the position equation with respect to time once;

dh(t) =  d  (-16[tex]t^{2}[/tex] + 40t +5 )

dt        dt

dh(t) = -32t  + 40

dt

with t= 2:

h'(2) =-32 (2) +40

h'(2) =-24 ft/s.

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