All the statements apply on parent function are,
⇒ Reflect the graph over the x-axis
⇒ Translate the graph to the left
What is Refection?Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.
We have to given that;
The function is,
⇒ g (x) = √ - 2x + 4
And, The parent function is,
⇒ f (x) = √x
Now, The parent function is,
⇒ f (x) = √x
After reflect the graph over the x-axis,
⇒ g (x) = √ - 2x
And, After translate the graph to the left,
⇒ g (x) = √ - 2x + 4
Thus, All the statements apply on parent function are,
⇒ Reflect the graph over the x-axis
⇒ Translate the graph to the left
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Sundeep mixed 300 mL of water with 100 mL of sugar. She says "the total volume is
300 mL + 100 mL = 400 mL." Do you agree with Sundeep? Explain why or why not.
No, I don't agree with Sundeep. The mixture wont simply add up
How to show the volume will not be 400 mlWhen two liquids are mixed together, their volumes don't simply add up to equal the total volume of the mixture.
When sugar is mixed with water, the total volume of the mixture is usually slightly greater than the volume of the water alone, because the sugar particles take up space between the water molecules.
The volume of the mixture will be equal to the sum of the individual volumes only if the two liquids are completely immiscible, meaning they don't mix together at all. In this case, the total volume of the mixture will be equal to the sum of the volumes of water and sugar, which is 400 mL.
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Find sn for the arithmetic series where a1= 5 , n= 10, an= −13
Answer:
S₁₀ = - 40
Step-by-step explanation:
given the first term a₁ = 5 and the nth term [tex]a_{n}[/tex] = - 13
then the sum to n terms is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (a₁ + [tex]a_{n}[/tex] )
here n = 10 , then
S₁₀ = [tex]\frac{10}{2}[/tex] (5 + (- 13)) = 5(5 - 13) = 5 × - 8 = - 40
Suppose a spherical asteroid has a radius of approximately 8.5 × 10^2 m. Use the formula 4/3 π r^3 to find the approximate volume of the astroid.
Brainlest to anyone who answers correctly
The approximate volume of the astroid is 2.57 * 10^9 m^3
How to find the approximate volume of the astroid.From the question, we have the following parameters that can be used in our computation:
Radius = 8.5 × 10^2 m.
Using the formula 4/3 π r^3 for the volume, we get
Volume = 4/3 * (22/7) * (8.5 × 10^2)^3
Evaluate
Volume = 2.57 * 10^9 m^3
Hence, the volume is 2.57 * 10^9 m^3
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Use partial fraction decomposition to write the integrand as the sum of simpler terms: (x^3 + 2x^2 + 3x + 4)/(x^2 + x - 2) = A/(x - 1) + B/(x + 2) + Cx + D, where A, B, C, and D are constants.
Step-by-step explanation:
Here's how you can use partial fraction decomposition to write (x^3 + 2x^2 + 3x + 4)/(x^2 + x - 2) as the sum of simpler terms:
Factor the denominator to simplify the expression: x^2 + x - 2 = (x - 1)(x + 2)
Write the partial fraction decomposition of the integrand as the sum of simpler terms: (x^3 + 2x^2 + 3x + 4)/(x^2 + x - 2) = A/(x - 1) + B/(x + 2) + Cx + D, where A, B, C, and D are constants.
Multiply both sides of the equation by (x^2 + x - 2) to find the values of A, B, C, and D: x^3 + 2x^2 + 3x + 4 = A(x + 2) + B(x - 1) + (Cx + D)(x^2 + x - 2)
Substitute x = 1 and x = -2 into the equation to find two equations for A, B, C, and D:
x = 1: 4 + 2 + 3 + 4 = 9 = A(-2) + B + (C + D)(-1)
x = -2: -8 - 4 + 6 - 8 = -16 = A(1) + B(-2) + (C - 2D)(4)
Solve the system of equations to find the values of A, B, C, and D:
A = 9/3, B = 5, C = -11/3, D = 7/3
So the partial fraction decomposition of (x^3 + 2x^2 + 3x + 4)/(x^2 + x - 2) is (9/3)/(x - 1) + (5)/(x + 2) - (11/3)x + (7/3).
find the coordinates of the vertex of the following parabola algebraically. write your answer as an (x,y)(x,y) point. y
The coordinates of the vertex of the following parabola is (0,6).
The given equation of the parabola is [tex]& y=-3 x^2+6 \\[/tex]
The point where the parabola and its axis of symmetry intersect is called the vertex of a parabola. It is used to determine the coordinates of the point on the parabola's axis of symmetry where it crosses it.
The standard form of a parabola is [tex]y=ax^{2} +bx+c.[/tex]
The vertex form of a parabola is [tex]y = a(x-h)^{2} + k[/tex].
[tex]$$\begin{aligned}& y=-3 x^2+6 \\& y-6=-3 x^2 \\& y-6=-3(x-0)^2\end{aligned}$$[/tex]
The vertex formula is used to find the vertex of a parabola. The formula to find the vertex is (h, k) = (-b/2a, -D/4a), where D = [tex]b^{2} -4ac[/tex].
Now comparing the above equation by the equation of parabola
⇒[tex]$$y-b=4(x-a)^2 \cdots$$[/tex]
With vertex (a, b)
So a=0 and b=6.
So vertex of above parabola is[tex]$(\mathbf{0}, \mathbf{6})$[/tex].
Therefore, the vertex of the given parabola [tex]$\mathbf{y}=-\mathbf{3} \mathbf{x}^{\mathbf{2}}+\mathbf{6}$ is $(\mathbf{0}, \mathbf{6})$[/tex].
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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point. [tex]& y=-3 x^2+6 \\[/tex]
If a round table can seat 8 people, and a square table seats 10 people, and I have to set up tables for 124 people, using two more round tables than square tables, how many round tables will I use?
We will use six square tables and eight round tables.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's call the number of square tables used "x". Then, the number of round tables used would be x + 2.
We know that the total number of people that can be seated is represented by 8 × number of round tables + 10 × number of square tables, or 8(x + 2) + 10x = 124.
Expanding and solving for x, we get 18x + 16 = 124.
Subtracting 16 from both sides, we get 18x = 108.
Dividing both sides by 18, we find that x = 6.
So, we will use 6 square tables and 8 round tables.
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Answer:
Can you elaborate more on the question?
A polygon is shown.
4 in.
12 in.
What is the area of the polygon?
OA. 62 in²
OB. 78 in²
OC. 99 in²
OD. 120 in²
5 in.
10 in.
* diagram not drawn to scale
We have the appropriate response to the inquiry b) The polygon's area is 99 inch2.
A polygonal shape is what?A polygon is a two-dimensional, closed shape that is flat or plane and is bounded by straight sides. Its sides are not curled. The edges of a polygon are another term for its sides. The vertices (or angles) of a polygon are the places where two sides converge.
According to the diagram we have the following:
DP = 10 ₋ 4 ₋ 6inch EP = 12 ₋ 5 = 7inch
Area of rectangle = l x b
Area of Triangle = [tex]\frac{1}{2}[/tex] x base x height
Area of polygon Area MBCD + Area AMPE + Area EPD = (5x10) + (4x27) + ([tex]\frac{1}{2}[/tex]x7x6) .
= 50 + 28 + 21 = 99 inch²
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Solve for x in the drawing below.
The measure of {x} is equivalent to 18.
What is angle?In Euclidean geometry -
an angle is the figure formed by two rays known as the sides of the angle and sharing a common endpoint known as the vertex of the angle.
Given is a circle with sectors.
Now, the measure of ∠MCP = 180°. We can write -
∠MCL + ∠LCA + ∠ACP = 180°
(2x - 4) + 101 + 47 = 180
2x - 4 + 148 = 180
2x + 144 = 180
2x = 36
x = 18
Therefore, the measure of {x} is equivalent to 18.
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given a number n, return the number of ways you can draw n chords in a circle combination with 2 x n points such that no 2 chords intersect.
The number of ways you can draw n chords in a circle combination with 2 x n points such that no 2 chords intersect is n! / (2! * (n - 2)!).
Given a number n, the number of ways you can draw n chords in a circle with 2 * n points such that no two chords intersect is given by n choose 2. This is because you have 2 * n points, and for each chord, you must choose two of these points to be its endpoints.
The number of ways to choose two points out of 2 * n points is given by the binomial coefficient (n choose 2), which is equal to n! / (2! * (n - 2)!). This formula counts the number of combinations of n chords that can be drawn in a circle without any intersections.
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population of 1200 mean is 225 and standard deviation is 18 what is the population of people who scored 171
171 is 1.8 standard deviations below the mean.
Using the 68-95-99.7 rule, approximately 5.5% of the population scored 171 or lower. This translates to 66 people.
1. Calculate the z-score: z = (171 - 225) / 18 = -1.8
2. Use the 68-95-99.7 rule to calculate the percentage of the population that scored 171 or lower: 5.5%
3. Calculate the number of people that scored 171 or lower: 66 (5.5% of 1200) mean
The complete question is :
What is the population of people who scored 171 out of a population of 1200 with a mean of 225 and a standard deviation of 18?
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will give brainliest
Answer:
2
Step-by-step explanation:
y inverse 3 in mathematics
Use the distance formula to find the distance between the points S(-5,7) to V(-2,4). Round to the nearest tenth.
Edit: All good. Figured it out.
The distance between the two points S( -5, 7) to V(- 2, 4) is 3.5 units.
What is the distance formula?The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by,
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given, We have to find the distance between the points S(- 5, 7) to V(-2, 4).
Therefore, [tex]|SV| =\sqrt{(- 2 + 5)^2 + (4 - 7)^2}[/tex].
[tex]|SV| =\sqrt{(3)^2 + (-3)^2}[/tex].
[tex]|SV| =\sqrt{9 + 9}[/tex].
|SV| = √18.
|SV| = 2√3.
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In this figure, h = 3, and r = 4.
What is the exact surface area of the cone?
Enter your answer in the box.
units²
The surface area of the cone is 113.09 square units.
What is a surface area?A three-dimensional object's surface area is the sum of all of its faces. Real-world applications of the concept of surface areas include wrapping, painting, and eventually building things to achieve the best possible design.
Given that the height of the cone is 3 units and the radius of the base is 4 units.
The surface area of the cone is calculated by the formula:-
SA = πrl + πr²
Slant height will be calculated as:-
l² = h² + r²
l² = 3 ² + 4²
l² = 25
l = 5 units
The surface area will be:-
SA = πrl + πr²
SA = ( πx 4 x 5 ) + ( π x 4² )
SA = 113.09 square units
Therefore, the surface area will be 113.09 square units.
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The amount of money in Ryan's savings account can be represented by the equation y = 15x + 20,
where x is the number of weeks and y is the total amount of money. The amount of money in Lucy's savings account can be represented by the graph below.
The graph of the linear function y = 15x + 20 is given by the image presented at the end of the answer.
How to graph the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The function in this problem is defined as follows:
y = 15x + 20.
Hence the graph is constructed as follows:
Domain of x >= 0, as the number of weeks is a countable amount.When x = 0, y = 20.When x increases by one, y increases by 15.More can be learned about linear functions at https://brainly.com/question/24808124
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May I have help on This question I’ll give you brainliest
Find f(x) and g(x) such that h(x) = (f o g)(x)
Answer:
Step-by-step explanation:
The function h(x) = (f o g)(x) means that h is the composition of functions f and g, where g(x) is applied first and then the result is passed to f.
Without further information, it is impossible to determine the specific functions f(x) and g(x). The composition of functions is unique only when both f and g are specified.
write each of the following expressions in the form ca^pb^q where c, p, and q are numbers : d) ab-a/b^2-b
The given expression is not in the form of [tex]ca^{p}b^{q}[/tex], where c, p, and q are numbers.
What is simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given the equation,[tex]\frac{ab - b}{b^{2} } - b[/tex],
to find the equation in form of [tex]ca^{p}b^{q}[/tex] where c, p, and q are numbers,
dividing separately,
ab/b² - b/b² - b
using property aⁿ/aˣ = aⁿ⁻ˣ
ab/b² - b/b² - b = ab⁻¹ - b⁻¹ - b
or ab/b² - b/b² - b = (ab - b - b²)b².
so (ab - b - b²)b² ≠ [tex]ca^{p}b^{q}[/tex]
Hence the equation is not correct.
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The expression (ab - a)/b² - b in the form [tex]ca^pb^q[/tex] is ab⁻¹.
What are some rules of exponents?Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.
Given, An expression, (ab - a)/b² - b.
Now, This can be written as,
a(b - 1)/b(b - 1).
Now, (b - 1) will cancel out and we'll have,
a/b.
ab⁻¹.
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Graphing asymptotes for a rational function
Two graphs of the same rational function are shown below
On the graph below draw the horizontal asymptote and write the equation for the horizontal asymptote underneath.
F(x)=-2x/x-3
On the graph below draw the vertical asymptote and write the equation for the vertical asymptote underneath.
F(x)=-2x/x-3
The vertical asymptote and horizontal asymptote of the rational function will be x = 3 and y = -2, respectively.
What is an asymptote?An asymptote is a line that constantly reaches a given curve but does not touch at an infinite distance.
The rational function is given below.
f(x) = - 2x / (x - 3)
The vertical asymptote is given as,
x - 3 = 0
x = 3
Then the horizontal asymptote is given as,
y = lim x → ∞ f(x)
y = lim x → ∞ - 2x / (x - 3)
y = lim x → ∞ - 2
y = - 2
The vertical asymptote and horizontal asymptote of the rational function will be x = 3 and y = -2, respectively.
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2. Ricky is 35 years old. He plans to retire when he is 63. He has opened a
traditional retirement account that pays 1% interest compounded monthly. If
he makes monthly deposits of $400, how much will he have in the account by
the time he retires?
now, we're making the assumption that the monthly payments Ricky is doing are at the beginning of every month.
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]
[tex]\qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 400\\ r=rate\to 1\%\to \frac{1}{100}\dotfill &0.01\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &28 \end{cases}[/tex]
[tex]A=400\left[ \cfrac{\left( 1+\frac{0.01}{12} \right)^{12 \cdot 28}-1}{\frac{0.01}{12}} \right]\left(1+\frac{0.01}{12}\right) \\\\\\ A=400\left[ \cfrac{\left( \frac{1201}{1200} \right)^{336}-1}{\frac{1}{1200}} \right]\left(\frac{1201}{1200}\right) \implies \boxed{A \approx 155157.45}[/tex]
What is the image point of (3,3)(3,3) after the transformation D_{5}\circ T_{0,-1}D
5
∘T
0,−1
?
The coordinates of image point is (15, 20)
How to determine the image pointA dilation is a transformation that changes the size of a figure but not its shape.
In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.
The transformation is given as
T<0, 1>D5
Mathematically, this
(x, y) = 5(x, y + 1)
So the image point is
(x, y) = 5(3, 3 + 1)
(x, y) = (15, 20)
So the image point of is (15, 20)
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given the following integral and value of n, approximate the following integral using the methods indicated (round your answers to six decimal places):
The approximations using the trapezoidal rule, midpoint rule, and Simpson's rule are 0.436904, 0.439881, and 0.439363, respectively.
(a) Trapezoidal Rule:
The trapezoidal rule approximates the definite integral as the sum of areas of trapezoids under the curve, connecting the function values at evenly spaced points within the interval of integration.
The formula for the trapezoidal rule is given by:
∫_a^b f(x) dx ≈ (b - a) * [f(a) + f(b)] / 2
For n = 4 subintervals, we can find the height of each trapezoid by evaluating the function at 0, 1/4, 1/2, 3/4, and 1.
∫_0^1 e^(−6x^2)dx ≈ (1 - 0) * [e^(-6 * 0^2) + e^(-6 * 1^2)] / 2 = (1 - 0) * [1 + e^(-6)] / 2 ≈ 0.436904
(b) Midpoint Rule:
The midpoint rule approximates the definite integral as the sum of areas of rectangles under the curve, using the function value at the midpoint of each subinterval as the height of each rectangle.
The formula for the midpoint rule is given by:
∫_a^b f(x) dx ≈ (b - a) * ∑ f(a + (b - a) * i / n) / n, where i = 1, 2, ..., n
For n = 4 subintervals, we can find the midpoints by evaluating the function at 1/8, 3/8, 5/8, and 7/8.
∫_0^1 e^(−6x^2)dx ≈ (1 - 0) * [e^(-6 * 1/8^2) + e^(-6 * 3/8^2) + e^(-6 * 5/8^2) + e^(-6 * 7/8^2)] / 4 ≈ 0.439881
(c) Simpson's Rule:
Simpson's rule approximates the definite integral as the sum of areas of parabolic curves under the curve, connecting the function values at three evenly spaced points within each subinterval.
The formula for Simpson's rule is given by:
∫_a^b f(x) dx ≈ (b - a) * [f(a) + 4 * ∑ f(a + (b - a) * i / (2n)) + 2 * ∑ f(a + (b - a) * i / n) + f(b)] / (6n)
For n = 4 subintervals, we can find the points by evaluating the function at 0, 1/4, 1/2, 3/4, and 1.
∫_0^1 e^(−6x^2)dx ≈ (1 - 0) * [e^(-6 * 0^2) + 4 * (e^(-6 * 1/4^2) + e^(-6 * 3/4^2)) + 2 * (e^(-6 * 1/2^2)) + e^(-6 * 1^2)] / (6 * 4) ≈ 0.439363
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The complete question is :
Given the following integral and value of n, approximate the following integral using the methods indicated (round your answers to six decimal places):
[tex]\int\limits {e^{(-6x^2)}} \, dx[/tex] ,n=4.(ps: b =1, a = 0)
(a) Trapezoidal Rule
(b) Midpoint Rule
(c) Simpson's Rule
Graph the function y = (1/2)x-3-10 using the given table of values and following
the instructions below.
X
-10
-9
-8
-7
-6
-5
-4
y
8182
4086
2038
1014
502
246
118
X
-3
-2
-1
0
1
2
3
Y
54
22
6
-2
-6
-8
-9
X
4
5
6
7
8
9
10
y
-9.5
-9.75
-9.875
-9.9375
-9.96875
-9.984375
-9.9921875
Equation of asymptote:
y =
The graph of function y = 1/2 (x - 3) - 10 is shown in figure.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation of function is,
⇒ y = 1/2 (x - 3) - 10
Now, The equation of function is,
⇒ y = 1/2 (x - 3) - 10
Clearly, This represent the equation of line.
Hence, By using tool;
The graph of function y = 1/2 (x - 3) - 10 is shown in figure.
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detecting unusual numbers or outliers in a data set is important in many disciplines, because the outliers identify interesting phenomena, extreme events, or invalid experimental results. a simple method to check if a data value is an outlier is to see if the value is a significant number of standard deviations away from the mean of the data set. for example, is an outlier if
Important to detect outliers in data set, Z-score (3 std dev from mean) and IQR methods are commonly used, choosing right method and threshold crucial for accurate data analysis.
it is more than 3 standard deviations away from the mean. This method is known as the Z-score method or the standard deviation method for detecting outliers. It provides a way to quantify how far away a data point is from the mean in terms of standard deviations. However, it is important to note that the 3 standard deviation threshold is just a general guideline and may not always be appropriate. Other methods, such as the interquartile range (IQR) method, can also be used to detect outliers in a data set.
It's essential to detect outliers as they can greatly impact the analysis and interpretation of data, so choosing the appropriate method and threshold for identifying outliers is crucial.
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According to her doctor, Carrie is under-weight. For health reasons her doctor advises that she gain weight before her next appointment in 3 months.
He said she should gain at least 10 pounds, but less than 30 pounds to move into a healthy weight range.
The weight range is 10 ≤ x < 30.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
For health reasons her doctor advises that she gain weight before her next appointment in 3 months.
She should gain at least 10 pounds but less than 30 pounds.
let her weight is x pounds then the range for her weight to be healthy.
10 ≤ x < 30.
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1. Let X denote the life of a semiconductor laser (in hours) with the following probabilities: P(X ≤ 5000) = 0.05 and P(X > 7000) = 0.45. a. What is the probability that the life is less than or equal to 7000 hours? b. What is the probability that the life is greater than 5000 hours? c. What is P(5000 < X ≤ 7000)? 2. Suppose that f(x) = 1.5x2 for -1 < x < 1 and f(x) = 0 otherwise. Determine the following probabilities. a. P(0 < X). b. P(-0.5 ≤ X ≤ 0.5). c. P(X < -2). d. Determine x such that P(x < X) = 0.05. 3. Assume that X is normally distributed with a mean of 6 and a standard deviation of 3. Determine the value for x that solves each of the following. a. P(X > x) = 0.5 b. P(X > x) = 0.95 c. P(x < X < 9) = 0.2 d. P(3 < X < x) = 0.8
1. a. Probability (X ≤ 7000) = 0.40; b. P(X > 5000) = 0.95; c. P(5000 < X ≤ 7000) = 0.40.
2. a. P(0 < X) = 1; b. P(-0.5 ≤ X ≤ 0.5) = 1; c. P(X < -2) = 0; d. x = -1.645.
3. a. x = 9; b. x = 12; c. x = 7; d. x = 6.
1. a. The probability that the life of a semiconductor laser is less than or equal to 7000 hours can be calculated by subtracting the probability that it is less than or equal to 5000 hours from 1: P(X ≤ 7000) = 1 - 0.05 = 0.40. b. The probability that the life is greater than 5000 hours can be calculated by subtracting the probability that it is less than or equal to 5000 hours from 1: P(X > 5000) = 1 - 0.05 = 0.95. c. The probability that the life is between 5000 and 7000 hours can be calculated by subtracting the probability that it is less than or equal to 5000 hours from the probability that it is less than or equal to 7000 hours: P(5000 < X ≤ 7000) = 0.40 - 0.05 = 0.35.
2. a. The probability that X is greater than 0 can be calculated by subtracting the probability that X is less than or equal to 0 from 1: P(0 < X) = 1 - 0 = 1. b. The probability that X is between -0.5 and 0.5 can be calculated by subtracting the probability that it is less than or equal to -0.5 from the probability that it is less than or equal to 0.5: P(-0.5 ≤ X ≤ 0.5) = 1 - 0 = 1. c. The probability that X is less than -2 can be calculated by simply looking at the upper limit of the function: P(X < -2) = 0. d. The value x such that P(x < X) = 0.05 can be found by solving the equation: x = -1.645.
3. a. The value x such that P(X > x) = 0.5 can be found by solving the equation: x = 9. b. The value x such that P(X > x) = 0.95 can be found by solving the equation: x = 12. c. The value x such that P(3 < X < x) = 0.2 can be found by solving the equation: x = 7. d. The value x such that P(3 < X < x) = 0.8 can be found by solving the equation: x = 6.
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Let X denote the number of unique vsitors to library in a month with following probabilities: P0X9)-04, P0X19)-07, P(0 X 29)-0.8, P(0≤x≤39)=0.9, P(0sX<49)-1. Determine the following probabilities: [4]a. P(X 50)b. P(10≤x≤19)P(205X≤29)d. More than 39 unique visitors.
The number of unique visitors to library in a month with following probabilities: P0X9)-04, P0X19)-07, P(0 X 29)-0.8, P(0≤x≤39)=0.9, P(0sX<49)-1 are;
a. P(X=50) = 0, since X can't be greater than 49 (according to the given information) and the probability of X being exactly 49 is 1.
b. P(10≤X≤19) = P(X=10) + P(X=11) + ... + P(X=19) = 0.07 - 0.04 = 0.03
c. P(20≤X≤29) = P(X=20) + P(X=21) + ... + P(X=29) = 0.8 - 0.07 = 0.73
d. P(X>39) = 1 - P(0≤X≤39) = 1 - 0.9 = 0.1
Library Unique Visitor ProbabilitiesI determined the probabilities in the way I did by using the cumulative distribution function of a discrete random variable.
The cumulative distribution function (CDF) of a discrete random variable X is defined as:
CDF(x) = P(X≤x) = ∑P(X=x'), for all x' such that x' ≤ x
So, for each of the given ranges, I calculated the cumulative probability up to that range using the CDF definition and the individual probabilities of X being exactly each value within the range.
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a coin is flipped 5 times. for each of the events described below, express the event as a set in roster notation.
The probability of the event is calculated by taking the probability of the event occurring 0.53, or about 0.03125.
A coin being flipped five times is an example of a Bernoulli trial, which is a type of experiment where the outcome can be either success or failure. The probability of success (a heads) is equal to the probability of failure (a tails). So, for this experiment, the probability of a heads is 0.5 and the probability of a tails is 0.5.
The event of a coin being flipped five times can be expressed as a set in roster notation as {HHHHT, HHHTH, HHTHH, HTHHH, THHHH, HHHTT, HHTTH, HTHHT, THHHT, HTTHH, TTHHH, HHTTT, HTTHT, THHTT, TTHHT, TTTHH, HTTTT, THTTT, TTHTT, TTTHT, TTTTH, TTTTT}.
The probability of the event is calculated by taking the probability of the event occurring (in this case, 0.5 for a heads and 0.5 for a tails) and multiplying it by the number of trials (in this case, 5). This gives us a probability of 0.53, or about 0.03125.
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are a type of qualitative method seeking unrestricted comments or opinions and asking questions to help better understand the various dimensions of opinions.
Open-ended questions are often used in market research, customer satisfaction surveys, and other social sciences research to gather in-depth information from respondents.
Open-ended questions are a type of qualitative research method that seeks to gather unrestricted comments or opinions from respondents. These questions are usually framed in a way that allows the respondent to express their thoughts and feelings without being limited by pre-determined response options. This method can provide valuable insights into the perspectives, experiences, and motivations of the individuals being studied. Open-ended questions are often used in market research, customer satisfaction surveys, and other social sciences research to gather in-depth information from respondents.
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2. Birat tea packaging company was established last year in eastern part of Nepal. From the last years data, it was found that the cost of buying a packaging machine, factory set up and the cost of land and house was Rs. 8,000,000. The cost price of raw tea was Rs. 80 per Kg, cost of packaging material along with a hologram of the company was Rs. 15 per Kg., cost of labor was Rs. 10 per kg and the transportation cost was Rs 20 per Kg. After investing the above mentioned cost, the owner of the company was able to sell his product at Rs. 160 per Kg at the different part of Nepal as well as some part of India such as West Bengal, Sikkim, Bihar and some part of Uttar Pradesh. Find the a. Total cost function. b. Total revenue function. C. Total profit function. you d. If you were the owner of the company, how many units should have to sell in order to reach neither loss nor profit? e. What strategy will you apply if the market is very competitive and there are lots of substitute products?
Answer:
a. Total Cost Function: The total cost function for Birat tea packaging company is given by: Total Cost = 8,000,000 + 80x + 15x + 10x + 20x = 8,360,000 + 125x
b. Total Revenue Function: The total revenue function for Birat tea packaging company is given by: Total Revenue = 160x
c. Total Profit Function: The total profit function for Birat tea packaging company is given by: Total Profit = Total Revenue - Total Cost = 160x – 8,360,000 - 125x = 7,225,000 - 125x
d. If you were the owner of the company, you would need to sell at least 58,000 Kgs of tea in order to reach neither loss nor profit.
e. If the market is very competitive and there are lots of substitute products, the Birat Tea Packaging Company can use a variety of strategies to stay competitive. These strategies can include offering discounts, loyalty programs, promotional campaigns, product diversification, and improved marketing efforts. The company should also focus on providing superior customer service to build and maintain customer loyalty. Additionally, the company should stay up-to-date on the latest trends in the industry and explore opportunities to collaborate with other companies to gain a competitive advantage.
Step-by-step explanation: