Determine the sum of the solutions to: 5x^2-16x+3=0
A. 3/5
B. 16
C. 8
D. 16/5
The sum of the two solutions is equal to 17/5.
How to find the solutions of the quadratic equation?Here we want to solve the quadratic equation:
5x^2 - 16x + 3 = 0
Using the quadratric formula, we will get the solutions:
[tex]x = \frac{16 \pm \sqrt{(-16)^2 - 4*3*5} }{2*5} \\\\x = \frac{16 \pm14 }{10}[/tex]
Then the two solutions of the quadratic equation are:
x = (16 + 14)/10 = 30/10 = 3
x = (16 - 14)/10 = 2/10 = 2/5
The sum is: 3 + 2/5 = 3 + 2/5 = 15/5 + 2/5 = 17/5
Learn more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ1
a sample of a radioactive substance decayed to 97% of its original amount after a year. (round your answers to two decimal places.) (a) what is the half-life of the substance? yr (b) how long would it take the sample to decay to 85% of its original amount?
a) The half-life of the substance is 22.76 years.
b) 5.34 years for the sample to decay to 85% of its original amount
A radioactive substance's half-life is the length of time it takes for half of its atoms to decay, while a drug's half-life is the amount of time it takes for half of its active ingredients to be either excreted by the body or broken down by it.
The amount of the radioactive substance after t years is modeled by the following equation:
[tex]P(t) = P(0)(1-r)^{t}[/tex]
In which P(0) is the initial amount and r is the decay rate.
A sample of a radioactive substance decayed to 97% of its original amount after a year.
This means that:
[tex]P(1) = 0.97P(0)[/tex]
Then
[tex]P(t)=P(0)(1-r)^{t}[/tex]
[tex]0.97P(0)=P(0)(1-r)^{0}[/tex]
[tex]1-r=0.97[/tex]
So
[tex]P(t)=P(0)(0.97)^{t}[/tex]
(a) What is the half-life of the substance?
This is t for which P(t) = 0.5P(0). So
[tex]P(t)=P(0)(0.97t)^{t}[/tex]
[tex]0.5P(0)=P(0)(0.97t)^{t}[/tex]
[tex](0.97)^{t} =0.5[/tex]
㏒[tex](0.97)^{t}[/tex][tex]=[/tex] ㏒[tex]0.5[/tex]
[tex]t[/tex]㏒[tex]0.97[/tex][tex]=[/tex]㏒[tex]0.5[/tex]
[tex]t=\frac{log 0.5}{log 0.97}[/tex]
[tex]t=22.76[/tex]
The half-life of the substance is 22.76 years.
(b) How long would it take the sample to decay to 85% of its original amount?
This is t for which P(t) = 0.85P(0). So
[tex]P(t)=P(0)(0.97t)^{t}[/tex]
[tex]0.85P(0) = P(0)(0.97t)^{t}[/tex]
[tex](0.97)^{t} = 0.85[/tex]
[tex]log(0.97)^{t} = log 0.85[/tex]
[tex]tlog 0.97 = log0.85[/tex]
[tex]t=\frac{log0.85}{log0.97}[/tex]
[tex]t=5.34[/tex]
5.34 years for the sample to decay to 85% of its original amount.
To learn more about radioactive decay visit:
brainly.com/question/1770619
#SPJ4
The weekly cost to produce x widgets is given by C(x)=15000 + 100x- 0. 00004x^3
and the demand function for the
given P(x): 200 -0. 005x
Determine the maginal revenue and maginal profit when 2500 widgets are sold and when 7500 widgets are sold assume that the company sells exactly what they produce
Marginal revenue and marginal profit when 2500 widgets are sold is $175 and $-17.5 respectively and when 7500 widgets are sold is $125 and $-207.5 respectively.
The cost function is given by:
C(x)\ =\ 15000\ +\ 100x\ -\ 0.03x^2\ +\ 0.000004x^3
The demand function is given by:
p\left(x\right)=200-0.005x
The marginal revenue and marginal profit are determined by differentiating revenue function R(x) and profit function P(x) respectively. The relationship between cost function C(x), revenue function R(x) and profit function P(x) is:
P(x)\ =\ R(x)\ -\ C(x)
The revenue function is determined by multiplying demand function p(x) and number of widgets x, hence
R(x)\ =xp(x)\ =\ x(200\ -\ 0.005x)\ =\ 200x\ -\ 0.005x^2
The profit function is given by:
P(x)\ =\ (200\ -\ 0.005x^2)\ -\ (15000\ +\ 100x\ -\ 0.03x^2\ +\ 0.000004x^3)
P(x)\ =\ -0.000004x^3\ -\ 0.025x^2\ +\ 100x\ -\ 15000
Differentiating profit function to determine marginal profit:
P\left(x\right)=-0.000004x^3-0.025x^2+100x-15000
P'(x)\ =\ -0.0000012x^2\ -\ 0.05x\ +\ 100
Differentiating revenue function to determine marginal revenue:
R(x)\ =\ 200x\ -\ 0.005^2
R'(x)\ = 200 – 0.01x
Evaluating these differentials when x = 2500 and x = 7500
P'(x)\ =\ -0.0000012x^2\ -\ 0.05x\ +\ 100
P'(2500)\ =\ -0.0000012(2500)^2\ -\ 0.05(2500)\ +\ 100\ =\ -17.5
P'(7500)\ =\ -0.0000012(7500)^2\ -\ 0.05(7500)\ +\ 100\ =\ -207.5
R'(x)\ = 200 – 0.01x
R'(2500)\ = 200 – 0.01(2500) = 175
R^\prime\left(7500\right)=200-0.01\left(7500\right)=125
Hence, marginal revenue and marginal profit when 2500 widgets are sold is $175 and $-17.5 respectively and when 7500 widgets are sold is $125 and $-207.5.
Note: The question is incomplete. The complete question probably is: Question: The weekly cost to produce x widgets is given by: C(x)\ =\ 15000\ +\ 100x\ -\ 0.03x^2\ +\ 0.000004x^3 and the demand function for the widgets is given by: p(x) = 200 - 0.005x. Determine the marginal revenue and marginal profit when 2500 widgets are sold and when 7500 widgets are sold assume that the company sells exactly what they produce.
Learn more about Marginal revenue:
https://brainly.com/question/12231343
#SPJ4
Determine if line AB is tangent to the circle.
22)
10.9
9.1
B
6
A
Yes we can say that the line AB of the given diagram is a tangent to the given circle.
How to find a tangent line to a circle?For the line to be tangent to the circle it means that the line must be perpendicular to the diameter line that divides the circle into 2. Thus, we will make use of Pythagoras theorem;
AB = √(10.9² - 9.1²)
AB = √(118.81 - 82.81)
AB = √36
AB = 6
This length of AB corresponds with the given length and as such AB is perpendicular to the line of length 9.1 and is therefore a tangent to the circle.
Read more about Circle Tangent Line at; https://brainly.com/question/28035740
#SPJ1
What is 5/7 times 10/11 as a fraction in simplest form
Answer: 50/77
Step-by-step explanation:
EASY 100 POINTS, WILL MARK BRAINLEST TO FIRST ANSWER,
Data was collected on the weight, in ounces, of kittens for the first three months after birth. A line of fit was drawn through the scatter plot and had the equation w = 3.25 + 0.3d, where w is the weight of the kitten in ounces and d is the age of the kitten in days.
What is the w-intercept of the line of fit and its meaning in terms of the scenario?
A, 3.25; a kitten who is just born is predicted to weigh 3.25 ounces
B,0.3; a kitten who is just born is predicted to weigh 0.3 ounces
C, 3.25; for each additional day after the kitten is born, its weight is predicted to increase by 3.25 ounces
D, 0.3; for each additional day after the kitten is born, its weight is predicted to increase by 0.3 ounces
Answer:
The correct answer is A, 3.25; a kitten who is just born is predicted to weigh 3.25 ounces. This means that according to the line of fit, a kitten who is just born is predicted to weigh 3.25 ounces.
On what interval is the parametric curve defined by x(t) = e^{-t} and y(t) = cos(t) for 0 ≤ t≤ π concave down?
A. (0, 3π/4)
B. (3π/4, π)
C. (0, π)
D. (0, π/2)
The parametric curve defined by x(t) = e^{-t} and y(t) = cos(t) for 0 ≤ t≤ π is concave down in the interval (c) (0, π) .
The Concavity of a parametric curve is determined by the second derivative of the curve.
To find the second derivative of a parametric curve, we need to differentiate each component of the curve with respect to the parameter t, then differentiate those expressions with respect to t again.
For x(t) = e^{-t} and y(t) = cos(t),
the first derivative w.r.t "t" is x'(t) = -e^{-t} and y'(t) = -Sin(t) ;
the second derivative with respect to t of x''(t) = e^{-t} and y''(t) = -Cos(t),
Since , y''(t) = -Cos(t) is negative over the interval (0, π), we can conclude that the curve is concave down over that interval.
Therefore, the curve is concave down over that interval (0, π).
Learn more about Parametric Curve here
https://brainly.com/question/15585522
#SPJ4
What is 3/18 written in simplest form? Explain how you found you answer.
Answer:
1/6
Step-by-step explanation:
You have to divide both the numerator and denominator by the greatest common factor to get simplest form. In this case, the gcf(Greatest Common Factor) is 3. 3/3 is 1 and 18/3 is 6
Therefore, the answer is 1/6
How many liters of 20% apple cider vinegar solution must be added to 5 liters of a 5%
Gena needs to add 2.5 liters of the 20% solution. Option B is correct.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Let's call the amount of 20% solution that Gena needs to add "x". Then the total amount of solution will be 5 + x liters. The total amount of apple cider vinegar in the solution will be:
0.20x + 0.05(5 + x) = 0.10(5 + x)
Expanding the right side:
0.20x + 0.05 * 5 = 0.10 * 5 + 0.10x
Solving for x:
0.20x - 0.10x = 0.10 * 5 -0.05 * 5
0.1x = 0.25
x = 2.5
So, Gena needs to add 2.5 liters of the 20% solution. Option B is correct.
Learn more about models here:
https://brainly.com/question/22591166
#SPJ1
Giselle enjoys playing chess and Scrabble. She wants to play a total of at least 10 games (condition a) but she has only 6 hours to do it (condition b)
Giselle can play at most 6 games in the 6 hours she has available, which meets her second condition but not her first.
To determine the maximum number of games Giselle can play, we need to balance the time available with the number of games she wants to play. Let's assume that each game takes x hours to complete.
Condition a: 10 games = x * 10
Condition b: 6 hours = x * 10
From these two equations, we can solve for x, which represents the time it takes for Giselle to play one game. To do this, we'll divide both sides of the first equation by 10:
10 games / 10 = x * 10 / 10
x = 1 hour
So, it takes Giselle 1 hour to play one game. Knowing this, we can determine how many games she can play in the 6 hours she has available:
6 hours / 1 hour per game = 6 games
Therefore, Giselle can play at most 6 games in the 6 hours she has available, which meets her second condition but not her first.
To learn more about the unitary method, refer to the link:brainly.com/question/28276953
#SPJ4
Giselle can play at most 6 games in the 6 hours she has available, which meets her second condition but not her first.
To determine the maximum number of games Giselle can play, we need to balance the time available with the number of games she wants to play. Let's assume that each game takes x hours to complete.
Condition a: 10 games = x * 10
Condition b: 6 hours = x * 10
From these two equations, we can solve for x, which represents the time it takes for Giselle to play one game. To do this, we'll divide both sides of the first equation by 10:
10 games / 10 = x * 10 / 10
x = 1 hour
So, it takes Giselle 1 hour to play one game. Knowing this, we can determine how many games she can play in the 6 hours she has available:
6 hours / 1 hour per game = 6 games
Therefore, Giselle can play at most 6 games in the 6 hours she has available, which meets her second condition but not her first.
To learn more about equations,
https://brainly.com/question/28276953
#SPJ4
Choose the best graduated cylinder to make each measurement in a single use. 36 mL of water A 50 ml graduated cylinder with markings every 10 mL 5.75 ml of a sucrose solution A 10 ml graduated cylinder with markings every 0.1 mL - 18.5 mL of a NaCl solution A 25 ml graduated cylinder with markings every 1 ml
The best-graduated cylinder to make each measurement in a single use would be:
a) 36 mL of water - A 50 ml graduated cylinder with markings every 10 mL
b) 5.75 ml of a sucrose solution - A 10 ml graduated cylinder with markings every 0.1 mL
c) 18.5 mL of a NaCl solution - A 25 ml graduated cylinder with markings every 1 ml.
A graduated cylinder is a laboratory glassware used to measure the volume of a liquid. It is a tall, narrow container with a straight cylindrical shape, marked with precise volume measurements on the side. Graduated cylinders are typically made of glass or plastic, and come in various sizes, with the most common sizes ranging from 10 mL to 2000 mL. The cylinder is calibrated to a specific volume, and the volume of a liquid can be measured by reading the scale at the bottom of the meniscus, the curved surface of the liquid. Graduated cylinders are used in a wide range of scientific applications, including chemistry, biology, and physics experiments. They are an essential tool in any laboratory setting as they allow for precise measurement of liquids, which is crucial in many experiments.
Thus, the best-graduated cylinder to make each measurement in a single use would be:
a) 36 mL of water - A 50 ml graduated cylinder with markings every 10 mL
b) 5.75 ml of a sucrose solution - A 10 ml graduated cylinder with markings every 0.1 mL
c) 18.5 mL of a NaCl solution - A 25 ml graduated cylinder with markings every 1 ml.
To learn more about measurements, visit brainly.com/question/4725561
#SPJ4
A graduated cylinder is a piece of lab equipment used to gauge a liquid's volume. It is a tall, slender container with a straight cylindrical shape that is labeled on the side with exact volume measurements. Graduated cylinders can be found in a variety of sizes and are normally made of glass or plastic. The most popular sizes range from 10 mL to 2000 mL. The cylinder is calibrated to a particular volume, and the liquid's volume can be determined by looking at the scale at the base of the meniscus, the liquid's curved surface. Applications for graduated cylinders in science are numerous and include studies in physics, biology, and chemistry. They are a necessary instrument in every laboratory setting since they make it possible to measure liquids precisely, which is important for many investigations.
To learn more about cylinder, refer:-
https://brainly.com/question/16134180
#SPJ4
how many terms does the sequence, 2, 5, 8, …, 332 have?
As per the details given, the sequence 2, 5, 8, …, 332 has 111 terms.
The formula for the nth term of an arithmetic series can be used to find the number of terms in the given sequence:
nth term = a + (n - 1) * d
Here,
nth term is the value of the term at position n
a is the first term of the sequence
n is the position of the term
d is the common difference between consecutive terms
In this case, the first term (a) is 2, and the common difference (d) is 3, as each term increases by 3.
We need to find the value of n when the nth term is 332. Plugging the values into the formula:
332 = 2 + (n - 1) * 3
Simplifying the equation:
330 = (n - 1) * 3
Dividing both sides by 3:
110 = n - 1
n = 111
Therefore, the sequence has 111 terms.
For more details regarding arithmetic series, visit:
https://brainly.com/question/30214265
#SPJ12
The vertices of a rectangle are at (−1, −5), (3, −5), (3, −7), and (−1, −7). What is the length of the shorter side of the rectangle? Enter your answer in the box
Answer:
4 units
Step-by-step explanation:
The length of the shorter side is equal to the difference in y-coordinates of two vertically opposite vertices. The y-coordinates of the vertices (-1, -5) and (3, -5) are both -5, so the vertical side between them is not the shorter side. The y-coordinates of the vertices (3, -7) and (-1, -7) are both -7, so the vertical side between them is the shorter side. The difference in the x-coordinates of these two vertices is 3 - (-1) = 4, so the length of the shorter side is 4 units.
Answer: Your answer is 2
Step-by-step explanation: I did the k12 quiz here's proof
Midterm-exam scores and final-exam scores. We expect that students who do well on the midterm exam in a course will usually also do well on the final exam. Gary Smith of Pomona College looked at the exam scores of all 346 students who took his statistics class over a 10-year period The least-squares line for predicting final-exam score from midterm-exam score was
Octavio scores 10 points above the class mean on the midterm. How many points above the class mean do you predict that he will score on the final? (Hint: What is the predicted final-exam score for the class mean midterm score x?) This is an example of regression to the mean, the phenomenon that gave "regression" its name: students who do well on the midterm will, on the average, do
Aug 27 2021| 12:13 PM |
So, if Octavio scores 10 points higher than the class mean on the midterm, we may anticipate that he will score final = a + b * (x + 10) points higher on the final.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.
Here,
Given the regression equation for predicting final-exam score from midterm-exam score:
final = a + b * midterm
where a and b are the regression coefficients, we can use the class mean midterm score x as a reference point to predict the final exam score for a student who scored 10 points above the class mean on the midterm.
First, we need to find the class mean midterm score, which can be represented as x:
x = mean(midterm_scores)
Next, we find the predicted final exam score for the class mean midterm score:
final = a + b * x
Finally, we find the predicted final exam score for a student who scored 10 points above the class mean midterm score:
final = a + b * (x + 10)
So, if Octavio scores 10 points above the class mean on the midterm, we can predict that he will score final = a + b * (x + 10) points above the class mean on the final.
To know more about equation,
https://brainly.com/question/2228446
#SPJ4
How to Use the X-Intercept Calculator?
Press second, then CALC (above the TRACE key). Select option 2: 0You'll be required to enter an x-intercept guess, a left bound, and a right bound into the calculator.
What is the X-Intercept Calculator Used For? Press second, then CALC (above the TRACE key). Select option 2: 0You'll be required to enter an x-intercept guess, a left bound, and a right bound into the calculator.By dragging the cursor to the correct x-value with your left and right arrows, then pressing ENTER, you can enter them.When y = 0, we solve the equation for x to determine the x-intercept.The line crosses the x-axis at y=0, explaining this.If an equation isn't in the y = mx + b form, we can still find the intercepts by substituting 0 where necessary and solving for the remaining variable.With x = 0, solve for y to determine the y-intercept.To learn more about X-Intercept Calculator refer
https://brainly.com/question/26838456
#SPJ4
Blake puts eight marbles in the bag cold puts nine marbles in the bag then Blake takes out seven marbles from the bag how many marbles are in the bag now
Answer: 10 marbles are still in the bag.
Step-by-step explanation:
(8+9)-7
17-7
10
A town's population has been declining in recent years. The table shows the population since 1980. Is this data consistent with an exponential function? Explain. If so, predict the population for 2010 assuming the trend holds.
Year | Population
1980 | 5000
1990 | 4000
2000 | 3200
2010 | ____
The predicted population for 2010 is approximately 2782.7.
The data is consistent with an exponential function. An exponential function decays at a constant rate, which corresponds to the table's decreasing population trend.
To forecast the population for 2010, use the equation y = abx, where y is the population, an is the initial population, b is the decay factor, and x is the number of years elapsed. We can use the logarithm:
log(y2/y1) = log (b)
log(y2/y1) / log(x2/x1) = log (b)
Using data from 1980 to 1990:
log(4000/5000) / log(1990/1980) = log (b)
log(b) = -0.2231 b = 0.796
So the equation is: y = 5000 * 0.796x, where x is the number of years since 1980.
To find the population in 2010, enter x = 30:
y = 5000 * 0.796^30
y = 2782.7
So the predicted population for 2010 is approximately 2782.7.
To learn more about exponential function.
https://brainly.com/question/28596571
#SPJ4
The kid went to the park to play 1/3 played on the eeaw 2/6 played on the lide and the remaining of the kid played occer what fraction of the kid played occer?
The fraction of the kid played soccer is 0
What is a fraction in math?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categories its types based on these two terms.Given data :
2/6 - 1/3 =
2 / 6 - 1*2 / 3*2
= 2/6 - 2/6 = 0/6 = 0
Learn more about fraction refer to :
https://brainly.com/question/78672
#SPJ4
Jane needs a short-term loan to buy a new washing machine. She needs to borrow $1500 at 20% compounded annually and plans to have it paid off in 1 year. Jane writes the formula 1500(1. 2)t and finds out that this loan will cost her $1800. Which equation shows how Jane can rewrite the formula to find the annual percentage rate that would cost her the same amount if it compounded semi-annually?
A≈1500(1. 095)2t
A≈1500(1. 2)^1/2t
A≈1500(1. 095)^1/2t
A≈1500(1. 2)2t
The that shows how Jane can rewrite the formula to find the equivalent semi-annual interest rate is Option (a) A ≈ [tex]1500(1.095)^{2t}[/tex].
The formula [tex]1500(1.2)^t[/tex] shows the amount Jane will have to pay after t years if the loan is compounded annually at an interest rate of 20%. To find the equivalent semi-annual interest rate, we need to rewrite the formula so that it represents the amount she would have to pay if the interest was compounded semi-annually.
First, let's find the equivalent semi-annual interest rate. If the annual interest rate is 20%, the semi-annual interest rate would be:
[tex]r = 20\% / 2 = 10 \%[/tex]
Next, let's raise (1 + r) to the power of 2 to find the equivalent annual interest rate when compounded semi-annually:
[tex](1 + r)^2 = (1 + 10\%)^2 =( 1.1)^2 = 1.21[/tex]
So, the equivalent annual interest rate when compounded semi-annually is 21%.
Finally, let's substitute the equivalent semi-annual interest rate into the formula to find the amount Jane would have to pay if the interest was compounded semi-annually:
[tex]A = 1500(1 + r)^{2t} = 1500(1.095)^{2t}[/tex]
So, the equation that shows how Jane can rewrite the formula to find the equivalent semi-annual interest rate is:
A ≈ [tex]1500(1.095)^{2t}[/tex]
This equation represents the amount Jane would have to pay after t years if the loan is compounded semi-annually at an interest rate of 21%.
Learn more about interest rate :
https://brainly.com/question/13324776
#SPJ4
suppose p and q are polynomial functions. if and q(0), find p(0).
The value of p(0) is the same as the value of q(0) since p and q are both polynomials.
Polynomials are mathematical expressions that are composed of variables and constants and involve only non-negative integer powers of the variables. In this case, p and q are both polynomials. This means that they have the same degree, or highest power of the variable, and the same coefficients. As a result, p(0) will have the same value as q(0). To find the value of p(0), substitute 0 into the function for p. This will give the value of p(0). For example, if p(x) = 3x2 + 2x + 1, then p(0) = 3(0)2 + 2(0) + 1 = 1. This means that p(0) = 1.
Learn more about value here
https://brainly.com/question/6975587
#SPJ4
is 40% bigger than 1/4
Answer:
40% is bigger
Step-by-step explanation:
40% ⇒ 40/100
1/4 ⇒ 25/100
40>25
∴ 40% is bigger
what are the roots of 2x^4-26x^2-28
Answer: To find the roots of a polynomial equation, we can use various methods, such as factoring, synthetic division, or the quadratic formula. One common method to find the roots of a quartic polynomial (degree 4) is to use the factor theorem, which states that if a polynomial equation has a root "r", then "r" is a factor of the polynomial.
In this case, we can factor 2x^4-26x^2-28 as:
2x^4 - 26x^2 - 28 = 2(x^2 - 7)(x^2 + 4)
So, the roots of 2x^4-26x^2-28 are x = ±√7 and x = ±i√2.
These are the solutions to the equation 2x^4-26x^2-28 = 0.
Step-by-step explanation:
What is a representative sample? What is its value? Choose the correct answer below A. A representative sample is a sample that is selected at random from the population of interest. It is valuable because its unbiased nature allows descriptive B. A representative sample is a sample that exhibits characteristics typical of those possessed by the population of interest. It is valuable because these C. A representative sample is a sample that is selected at random from the population of interest. It is valuable because its unbiased nature allows inferential statistics D. A representative sample is a sample that exhibits characteristics typical of those possessed by the population of interest. It is valuable because these statistics to be applied.
A representative sample is randomly selected from a population, and its unbiased nature allows for inferential statistics to be applied, making it a valuable tool for research.
Option C. A representative sample is a sample that is selected at random from the population of interest. It is valuable because its unbiased nature allows inferential statistics to be applied.A representative sample is a sample that is randomly selected from a population, and that is representative of that population in terms of characteristics such as demographics, attitudes, and behaviors. This type of sample is valuable because it is unbiased, meaning that it does not favor any particular group within the population, and this allows for inferential statistics to be used to draw conclusions about the population as a whole.
Learn more about representative sample: https://brainly.com/question/16037112
#SPJ4
Given nonzero vectors u, v, and w, use dot product and cross product notation, as appropriate, to describe the following.(a) The projection of u on v.(b) A vector orthogonal to u and v.(c) A vector orthogonal to u X v and w.(d) The volume of the parallelepiped determined by u, v, and w.(e) A vector orthogonal to u X v and u X w.(f) A vector of length |u| in the direction of v.
The solution to all the components of this question are as follows:
a) The projection of u on v is given by the dot product of u and the unit vector in the direction of v, scaled by the magnitude of v:
proj(u,v) = (u . v/|v|) * v/|v|
b) A vector orthogonal to u and v can be found by taking the cross product of u and v:
u x v
c) A vector orthogonal to u X v and w can be found by taking the cross product of u X v and w:
(u x v) x w
d) The volume of the parallelepiped determined by u, v, and w is given by the magnitude of the scalar triple product of u, v, and w:
|u . (v x w)|
e) A vector orthogonal to u X v and u X w can be found by taking the cross product of u X v and u X w:
(u x v) x (u x w)
f) A vector of length |u| in the direction of v is given by the projection of u on v scaled by the magnitude of u:
|u| * proj(u,v) = |u| * (u . v/|v|) * v/|v|
Therefore, all the answers are given above.
To learn more about vectors,
Visit; brainly.com/question/29740341
#SPJ4
if x and y are independent random variables does it mean x^2 and y are also independent random variables?
No, the independence of x and y does not necessarily mean the independence of [tex]x^2[/tex] and y.
Independence means that the values of one random variable do not affect the values of the other random variable. In other words, knowing the value of one random variable does not give us any information about the value of the other random variable.
However, squaring a random variable changes its distribution and can affect its independence from another random variable.
For example, if x is a normally distributed random variable with a mean of 0 and a standard deviation of 1, then [tex]x^2[/tex] will follow a chi-squared distribution with 1 degree of freedom. The distribution of [tex]x^2[/tex] and y may not be independent, even though x and y are independent.
Hence, just because x and y are independent random variables does not mean that [tex]x^2[/tex] and y are also independent random variables. Independence must be established based on the joint distribution of the random variables.
Read more about variables:
brainly.com/question/25223322
#SPJ4
AXYZ was reflected over a vertical line, then dilated by a
scale factor of Ź, resulting in AX'YZ. Which must be
true of the two triangles? Select three options.
O AXYZ - AX'Y'Z'
O ZXZY - ZY'Z'X'
OYXY'X'
OXZ = 2X Z
=
OmZYXZ = 2mZY'X'Z'
The true options for the triangles are :
ΔXYZ [tex]\sim[/tex] ΔX'Y'Z'
∠XYZ ≅ ∠X'Y'Z'
XZ = 2X'Z'
What is meant by reflection and dilatation?Flipping a figure over a line is called reflection. Rotation is the process of turning a figure a specific amount around a point. Dilation is when we enlarge or reduce a figure.
A triangle can change due to reflection and dilatation.
Triangle XYZ exists reflected over a vertical line.
Then dilated by 1/2 to form X'Y'Z'
The above highlights mean that:
ΔX'Y'Z' = 1/2 × XYZ
i.e., the triangle X'Y'Z"s side lengths are half that of the original triangle XYZ.
This means that:
The triangles exists similar then option (a) exists true
The angles are congruent then option (b) exists true
The side lengths of XYZ are twice the side lengths of X'YZ' then option (d) exists true.
To learn more about transformation refer to:
https://brainly.com/question/11352944
#SPJ4
Pablo generates the function f (x) = three-halves (five-halves) superscript x minus 1 to determine the xth number in a sequence.
The equation represent to determine the [tex]x^n[/tex] number in a sequence is this function f( x+1) = 5/2 f(x). This is the equation used to determine the xth number in a sequence.
Here, these values are given,
f(x) = 3/2 [5/2] x-1 [ After putting the values of f(x)}
So,here from this ,the equation will become ,
f(x+1) = 3/2 [ 5/2] x+1-1
f(x+1) = 3/2 [5/2] x
Here, 5/2 f(x)= 5/2×3/2 [5/2] x-1
5/2 f(x) = 3/2 [5/2] x-1+1
5/2 f(x) = 3/2 [5/2] x
So, f(x+1) =[ 5/2]f (x)
So, this will be the equation for this function .
Learn more about function here:
https://brainly.com/question/12431044
#SPJ4
[tex]f(x) = (3/2)^(5/2)^(x - 1)[/tex] this function can be used to calculate the xth number in the sequence for any given value of x.
f(x) is the function that will generate the xth number in the sequence.
The function is written as:
[tex]f(x) = (3/2)^(5/2)^(x - 1)[/tex]
This can be read as:
Take 3/2 (three halves) to the power of 5/2 (five halves) to the power of x minus 1.
This will generate the xth number in the sequence.
The function f(x) is used to determine the xth number in a sequence. It is written as: f(x) = [tex](3/2)^(5/2)^(x - 1)[/tex]. This means that we take the number 3/2 (three halves) and raise it to the power of 5/2 (five halves) and then to the power of x minus 1. This will generate the xth number in the sequence, where x is the position in the sequence. For instance, if x is 5, then the fifth number in the sequence will be generated using the function f(x). Therefore, this function can be used to calculate the xth number in the sequence for any given value of x.
learn more about function here
https://brainly.com/question/12431044
#SPJ4
what is the probability that the mean weight is less than 23 pounds
The probability of the sample mean weight is more than 3 pounds away from the 26:
P(x(bar) < 23) + P(x(bar) > 29) = 0.0030
Now, According to the question;
Sampling Distribution:
As per the central limit theorem, the sampling distribution is approximately normal if the sample is random and the sample size is at least 30, or the population from which the sample is selected, is normally distributed.
We have,
Population mean, μ = 26 pounds
Population standard deviation , σ = 3 pounds
Sample size, n = 9
P(x(bar) < 23) = 0.0015
P(x(bar) > 29) = 0.0015
The probability of the sample mean weight is more than 3 pounds away from the 26:
P(x(bar) < 23) + P(x(bar) > 29) = 0.0015 + 0.0015
= 0.0030
Learn more about Probability at:
https://brainly.com/question/11234923
#SPJ4
The given question is incomplete, complete question is:
The weights of 1-year-old male children are fairly normal with mean 26 pounds, a standard deviation of 3 pounds. If we randomly sample nine 1-year-old boys, the probability of their sample mean weight being less than 23 pounds is 0.0015, and the probability of being greater than 29 pounds is also 0.0015. What is the probability of the sample mean weight being more than 3 pounds away from 26?
in this situation is it possible that lim x → 1 f(x) exists? explain.
Yes, in this situation is it possible that lim x → 1 f(x) exists.
A horizontal/vertical oblique line that approaches 0 but never reaches it is known as an asymptote. Its distance from the graph of the function keeps becoming smaller.
What's the vertical asymptote rule?
Vertical asymptotes happen when a factor from a rational expression's denominator does not cancel out with a factor from the numerator.
The existence of a vertical asymptote occurs when a factor does not cancel, as opposed to creating a hole at that number. Using a dotted vertical line, the vertical asymptote is shown.
if f(x) has a vertical asymptote at x = 1,
it can be defined such that lim x→1− f(x) = 6,
lim x→1+ f(x) = 3,
and lim x→1 f(x) exists.
Learn more about Vertical asymptotes
brainly.com/question/4084552
#SPJ4
A bicycle wheel has a diameter of 26 inches. What is the circumference?
Note: Use 3. 14 for pi (Tt) rather than the pi (Tt) key on a calculator,
*
The bicycle that has a diameter of 26 inches has a circumference of 81.64 inches
What is perimeter?The perimeter is the total length of the edge of a geometric figure.
To solve this geometry exercise the equation and procedure we will use is:
P = 2*pi*r
Where:
pi = constantr = radiusP = Length of a circleInformation about the problem:
pi = 3.14d = 26 inchesP = ?Applying the perimeter equation of a circumference, we have:
P = 2*pi*r
P = 2*3.14*(26 inches/2)
P = 3.14*26 inches
P = 81.64 inches
Learn more about perimeter at brainly.com/question/397857
#SPJ4