Answers
The variance of first n even natural numbers is n²-1/12. So, the correct option is (a) .
The first n even natural numbers can be represented as 2, 4, 6, ..., 2n. The mean or expected value of this sequence is given by:
mean = (2 + 4 + 6 + ... + 2n) / n
= 2(1 + 2 + 3 + ... + n) / n
= 2n(n+1)/2n
= n+1
The variance of a sequence is the average of the squared differences from the mean, so we need to calculate:
Var = [(2- (n+1))² + (4- (n+1))² + (6- (n+1))² + ... + (2n- (n+1))²] / n
Simplifying the expression inside the brackets and using the formula for the sum of the first n integers, we get:
Var = [4(1² + 2² + 3² + ... + n²) - 4(n+1)(1 + 2 + 3 + ... + n) + n(n+1)²] / n
Substituting the formula for the sum of the first n squares and the sum of the first n integers, we get:
Var = [4n(n+1)(2n+1)/6 - 4(n+1)n(n+1)/2 + n(n+1)²] / n
Simplifying and factoring out (n+1), we get:
Var = (n+1)(n² - 1) / 3
Thus, the correct option is (a) n²-1/12.
To learn more about variance click on,
https://brainly.com/question/16953345
#SPJ1
Related Questions
A parabola can be drawn given a focus of (−4,5) and a directrix of y=−9. what can be said about the parabola?
Answers
The parabola with a focus of (-4, 5) and a directrix of y = -9 is vertically oriented, opens upward, has a vertex at (-4, -2), and its equation is (x + 4)^2 = 28(y + 2).
1. The parabola is vertically oriented since the directrix is a horizontal line.
2. The vertex of the parabola is equidistant from the focus and the directrix. To find the vertex, we can calculate the midpoint between the focus and a point on the directrix with the same x-coordinate: (-4, -9 + (5 - (-9))/2) = (-4, -9 + 7) = (-4, -2).
3. The parabola opens upward because the focus is above the directrix.
4. The equation of the parabola can be found using the vertex form: (x - h)^2 = 4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and the focus or directrix. In this case, (h, k) = (-4, -2), and p = (5 - (-2)) = 7. The equation is therefore (x + 4)^2 = 28(y + 2).
In summary, the parabola with a focus of (-4, 5) and a directrix of y = -9 is vertically oriented, opens upward, has a vertex at (-4, -2), and its equation is (x + 4)^2 = 28(y + 2).
learn more about "Parabola":-https://brainly.com/question/4061870
#SPJ11
A rectangular living room measures 6 by 12 feet. At $36 per square yard, how much will it cost to carpet the room?
Answers
Area = length x width = 6 feet x 12 feet = 72 square feet
Since carpet is usually priced by the square yard, we need to convert the area from square feet to square yards. There are 9 square feet in 1 square yard, so:
Area in square yards = 72 square feet / 9 = 8 square yards
Now, we can calculate the total cost of carpeting the living room by multiplying the area in square yards by the price per square yard:
Cost = area in square yards x price per square yard = 8 square yards x $36 per square yard = $288
Therefore, it would cost $288 to carpet the living room.
Answer:
It will cost $288 to carpet the living room at $36 per square yard.
Step-by-step explanation:
First, we need to convert the room dimensions to square yards, since the carpet price is given in square yards.
The area of the living room is:
[tex]\sf:\implies 6\: ft \times 12\: ft = 72\: ft^2[/tex]
To convert this to square yards, we divide by 9 (since there are 9 square feet in a square yard):
[tex]\sf:\implies \dfrac{72\: ft^2}{9} = 8\: yards^2[/tex]
So the living room is 8 square yards in area.
To find the cost of carpeting the room, we multiply the area by the cost per square yard:
[tex]\sf:\implies 8\: yards^2 \times \$36/square\: yard = \boxed{\bold{\:\:\$288\:\:}}\:\:\:\green{\checkmark}[/tex]
Therefore, it will cost $288 to carpet the living room at $36 per square yard.
What is -2(x + 12y - 5 - 17x - 16y + 4) simplified?
-40x + 8y + 2
28x + 8y +2
28x + 6y + 2
-28x - 8y + 2
Answers
Answer:
Step-by-step explanation:
First, we can simplify the expression inside the parentheses by combining like terms:
-2(x + 12y - 5 - 17x - 16y + 4) = -2(-16x - 4y - 1)
Next, we can distribute the -2 to each term inside the parentheses:
-2(-16x - 4y - 1) = 32x + 8y + 2
Therefore, -2(x + 12y - 5 - 17x - 16y + 4) simplified is 32x + 8y + 2.
The simplified expression is 32x + 8y + 2.
Simplification of an algebrai expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.
The process entails collecting like terms, which implies adding or subtracting terms in an expression.
Simplify the expression -2(x + 12y - 5 - 17x - 16y + 4).
First, let's distribute the -2 to each term inside the parentheses:
-2(x) + (-2)(12y) - (-2)(5) - (-2)(17x) - (-2)(16y) + (-2)(4)
Now we'll multiply: -2x - 24y + 10 + 34x + 32y - 8
Next, we'll combine like terms:
(-2x + 34x) + (-24y + 32y) + (10 - 8)
The result is 32x + 8y + 2
Learn more about expression in math at
https://brainly.com/question/30091997
#SPJ11
what is the shape of the graph is called?
Answers
Answer:
parabola
Step-by-step explanation:
The graph shape is a parabola, opens-up type
This diagram shows an equilateral triangle and three lines, p, q, and r, that meet at the
triangle's center, T.
Select all of the transformations that map the triangle onto itself.
reflection across line q followed by 90° clockwise rotation about point T
reflection across line p followed by 240 clockwise rotation about point T
reflection across liner
270 clockwise rotation about point T
120 counterclockwise rotation about point 7
180 counterclockwise rotation about point 7 followed by reflection across
sine q
Answers
Answer:
-Reflection across line p followed by 240 clockwise rotation about point T.
-Reflection across line r.
-120 counterclockwise rotation about point T.
Step-by-step explanation:
All these transformations map the triangle onto itself.
The sales director noticed that sales in the Midwest and Northeast regions were not as expected. Additional field training is necessary for the sales representatives in these regions. After conducting a one-month training program, the sales director wants to determine the effectiveness of the training. After all, the company invested a significant amount of money in this program! So the sales director collects the sales data for the first month after the training. The sales director wants to compare the number of orders secured by those who attended the training program and those who didn't attend. This study will help the company to determine the effectiveness of the training. Part A What type of study is the sales director conducting—a survey, an observational study, or an experiment? Justify your answer
Answers
The type of study the sales director is conducting is an experiment to compare the number of orders secured by those who attended the training program and those who didn't attend.
The sales director conducted an experimented
The experiment is to do a test to see if something works or to try to improve it
Here the objective of the experiment was to see the effectiveness of the training by providing a one-month training program for employees. After that, the sales director collects the sales data for the first month. The sales director compared the number of orders secured by those who attended the training program and those who didn't attend. This experiment will help the company to determine the effectiveness of the training. If the experiment is effective or not.
To know more about experiment click here :
https://brainly.com/question/30055326
#SPJ4
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.
Answers
[tex]$x+3= \pm \sqrt{\frac{21}{2}}$[/tex] Thus, option D is correct.
What is the quadratic equation?the quadratic equation [tex]2x^2+12x-3=0$ is \ $x = \frac{-6 \pm \sqrt{42}}{2}[/tex], which simplifies to [tex]$x = -3 \pm \frac{\sqrt{42}}{2}$.[/tex]
However, the three options listed are the steps that Inga could use to solve the quadratic equation, and only three of them are correct. The correct options are:
[tex]$2\left(x^2+6 x\right)=-3$[/tex]
[tex]$2\left(x^2+6 x\right)=3$[/tex]
[tex]$x+3= \pm \sqrt{\frac{21}{2}}$[/tex]
Option 1 is the result of dividing both sides of the original equation by 2, which simplifies the coefficients.
Option 2 is the result of adding $\frac{3}{2}$ to both sides of the equation to isolate the quadratic terms. Option 3 is the final step, where the equation is solved for $x$ by completing the square and taking the square root of both sides.
Therefore, it is not one of the three steps that Inga could use to solve the quadratic equation. [tex]$x+3= \pm \sqrt{\frac{21}{2}}$[/tex]
Learn more about quadratic here:
https://brainly.com/question/30098550
#SPJ1
Inga is solving [tex]$2 x^2+12 x-3=0$.[/tex] Which steps could she use to solve the quadratic equation? Select three options.
[tex]$2\left(x^2+6 x+9\right)=3+18$[/tex]
[tex]$2\left(x^2+6 x\right)=-3$[/tex]
[tex]$2\left(x^2+6 x\right)=3$[/tex]
[tex]$x+3= \pm \sqrt{\frac{21}{2}}$[/tex]
how do you know when to use the Rule of Sum or Fundamental Counting Principle for probability problems?
Answers
If the events are exclusive, use the Rule of Sum. If the events are independent, use the Fundamental Counting Principle.
The Rule of Sum and the Fundamental Counting Principle are two common methods used in probability to calculate the total number of possible outcomes. Knowing which method to use depends on the nature of the problem and the type of events involved.
The Rule of Sum is used when we have two or more exclusive events. This means that only one of the events can happen at a time. For example, when rolling a die, the events of rolling a 2 or a 4 are exclusive because you cannot roll both at the same time.
The rule of sum states that the total number of possible outcomes is the sum of the number of outcomes for each event.
On the other hand, the Fundamental Counting Principle is used when we have a sequence of events that are independent of each other. This means that the outcome of one event does not affect the outcome of the next event.
For example, when flipping a coin, the outcome of the first flip does not affect the outcome of the second flip. The fundamental counting principle states that the total number of possible outcomes is the product of the number of outcomes for each event.
To learn more about fundamental counting click on,
https://brainly.com/question/28384306
#SPJ1
Please help ASAP!! It's due VERY SOON!!!
Answers
Answer:
The answer is A. 135 cm2.
Area of a parallelogram is base * height. In this case, the base is 24 cm and the height is 9 cm. Therefore, the area is 24 * 9 = 135 cm2.
Answer: the answer would be 360
Step-by-step explanation:
the equation for area of a parallelogram is base x height.
The base is 24 as it is at the top of the shape.
The height is 15 as well since a parallelogram is congruent.
multiply the two and it gives you 360
Which statement is true about the relationship between the diameter and circumference of a circle?
A. The circumference of a circle is always two times the diameter of the circle.
B. There is an exponential relationship between the diameter and circumference of a circle.
C. The constant of proportionality between the diameter and circumference of a circle is pi.
D. The unit rate between the diameter and the circumference of a circle is a rational number.
Answers
C. The constant of proportionality between the diameter and circumference of a circle is pi.
Step-by-step explanation:The constant pi comes from the relationship between the diameter and circumference of a circle.
Constant of Proportionality
A constant of proportionality is a number that describes the ratio between 2 values. No matter the measurements of a circle, the constant of proportionality between a circumference and diameter is always the same. This means that the circumference divided by the diameter ≈ 3.14.
Pi
Pi is an irrational number that can be estimated but never completely solved. The value of pi can be used to complete many different calculations such as the area of a circle, and it is used in many different functions like sin. For this reason, pi is one of the most important constants in math.
the table shows the outputs for several inputs. use two methods to find the output for an imput of 200
imputs: 0 1 2 3 4
outputs: 25 30 35 40 45
Answers
Answer:
Method 1 (Using Slope-Intercept Form):
First, we need to find the equation of the line that passes through the given points.
Slope (m) = (Change in y) / (Change in x) = (45 - 25) / (4 - 0) = 20 / 4 = 5
Using the slope and one point (0, 25), we can find the y-intercept:
y - y1 = m(x - x1)
y - 25 = 5(x - 0)
y = 5x + 25
Therefore, when the input is 200, the output would be:
y = 5(200) + 25
y = 1025
Method 2 (Using Linear Interpolation):
We can use the formula for linear interpolation:
y = y1 + ((x - x1) / (x2 - x1)) * (y2 - y1)
where:
x1 = 0, y1 = 25
x2 = 4, y2 = 45
x = 200
Substituting the values, we get:
y = 25 + ((200 - 0) / (4 - 0)) * (45 - 25)
y = 25 + (200 / 4) * 20
y = 25 + 500
y = 525
Therefore, when the input is 200, the output would be approximately 525.
A convenience store purchased a magazine and marked it up 100% from the original cost of $2. 30. A week later, the store placed the magazine on sale for 50% off. What was the discount price?
Answers
The discount price of the magazine was $2.30.
The convenience store purchased the magazine at an original cost of $2.30 and marked it up 100%. Find the selling price after the markup as follows.
1. Calculate the markup amount:
100% of $2.30 (Original cost * Markup percentage)
Markup amount = $2.30 * 100% = $2.30
2. Add the markup amount to the original cost to get the selling price.
Selling price = Original cost + Markup amount = $2.30 + $2.30 = $4.60
Next, the store placed the magazine on sale for 50% off.
3. Calculate the discount amount:
50% of the selling price (Selling price * Discount percentage)
1. Discount amount = $4.60 * 50% = $2.30
4. Subtract the discount amount from the selling price to get the discount price.
Discount price = Selling price - Discount amount = $4.60 - $2.30 = $2.30
Learn more about Discount price:
https://brainly.com/question/7459025
#SPJ11
helpp me with this question please
Answers
Answer:
24
Step-by-step explanation:
add all of them up
What does each angle equal?
Given : Angle 2 measures x+12 degrees
Angle 5 measures 49 degrees
Answers
Using the fact that the sum of the angles in a triangle is 180 degrees we do know that their sum is 119 degrees.
What is the measure of angle 2 and angle 5, given that angle 2 is x + 12 degrees and angle 5 measures 49 degrees?To understand why we used the fact that the sum of angles in a triangle is 180 degrees, let's take a closer look at the diagram.
We see that Angle 2 and Angle 5 are on the same side of a transversal and are therefore supplementary angles. This means that their sum is 180 degrees:
Angle 2 + Angle 5 = 180
We can substitute the value of Angle 5 (49 degrees) for Angle 5 and x + 12 for Angle 2 to get:
x + 12 + 49 = 180
Simplifying the equation, we get:
x = 119 - 49 - 12
x = 58
This gives us the value of x, but not the measure of Angle 2. To find the measure of Angle 2, we need to use the fact that the sum of angles in a triangle is 180 degrees.
We can write an equation using angles 2, 3, and 4 (which we now know is 49 degrees) as follows:
Angle 2 + Angle 3 + Angle 4 = 180
Substituting the known values, we get:
x + 12 + Angle 3 + 49 = 180
Simplifying the equation, we get:
x + Angle 3 = 119
So, we know that the sum of Angle 3 and x is 119 degrees, but we still don't know the measure of either angle on its own.
Learn more about angle
brainly.com/question/12051953
#SPJ11
If a={0,1,2} and b={-1,1,2} then what is the relation a into b
Answers
The relation a into b represent all possible combinations of elements in a and b as ordered pairs.
The relation "a into b" refers to the cartesian product of the sets a and b, which is denoted by a × b. The cartesian product of two sets is a set of all possible ordered pairs, where the first element of each ordered pair comes from the first set, and the second element comes from the second set.
In this case, a = {0, 1, 2} and b = {-1, 1, 2}. So, their cartesian product a × b is the set of all possible ordered pairs (a, b), where a is an element of a and b is an element of b. Therefore, we have:
a × b = {(0, -1), (0, 1), (0, 2), (1, -1), (1, 1), (1, 2), (2, -1), (2, 1), (2, 2)}
This means that the relation a into b consists of all possible combinations of elements in a and b as ordered pairs.
Learn more about proportional relationship at https://brainly.com/question/12303648
#SPJ11
A shipping company uses baggage tags with 3-letter city codes. The first and third letters of each code are always consonants and the middle letter is always a vowel (CVC). The English language uses 21 consonants and 5 vowels. How many different combinations of tag codes are possible? I will give brainliest to the best
(A) 105
(B)441
(C) 1,638
(D)2,205
Answers
The correct answer is (D) 2,205.
How to calculate the number of different combinations of baggage tag codes for a shipping company?To calculate the number of different combinations of tag codes, we need to consider the possible options for each position in the code.
For the first and third positions (consonants), we have 21 options for each position since there are 21 consonants in the English language.
For the middle position (vowel), we have 5 options since there are 5 vowels in the English language.
Therefore, the total number of different combinations is calculated by multiplying the number of options for each position:
21 (consonant options) * 5 (vowel options) * 21 (consonant options) = 2,205
Therefore, the correct answer is (D) 2,205.
Learn more about the number of different combinations of tag codes.
brainly.com/question/23099351
#SPJ11
Helppppp this is hard. i will give brainiest to the answer. i need it by 30 mins. please help
Answers
Of course! Please let me know what you need help with and I'll do my best to assist you within the given time frame.
To know more about assist refer here
https://brainly.com/question/12153891#
#SPJ11
If a 35 N block is resting on a steel table with a coefficient of
static friction Hs = 0,40, then what minimum force is required to
move the block.
Answers
The minimum force required to move a block of 35 N resting on a steel table with a coefficient of static friction of 0.40 is 14 N.
Friction refers to the force that resists the motion and thus the force acts in the opposite direction of the force applied.
There are the following types of friction:
1. Static Friction
2. Limiting Friction
3. Kinetic Friction
F = μN
where μ is the coefficient of friction
N is the Normal Force
When the object is resting on a table, Normal force is the weight.
N = 35 N
μ = 0.40
F = 0.4 * 35
= 14 N
Learn more about Friction:
https://brainly.com/question/24338873
#SPJ4
Here is a list of ingredients for making 16 flapjacks.
Ingredients for 16 flapjacks
120 g butter
140 g brown sugar
250 g oats
2 tablespoons syrup
jenny wants to make 24 flapjacks.
work out how much of each of the ingredients she needs.
butter
brown sugar
oats
syrup tablespoons â
Answers
Jenny needs 180g of butter, 210g of brown sugar, 375g of oats, and 3 tablespoons of syrup to make 24 flapjacks.
To make 24 flapjacks, Jenny needs to increase the amount of each ingredient proportionally.
To calculate the required amounts, we can use ratios. If 16 flapjacks require 120g of butter, then 24 flapjacks require:
Butter: (24/16) x 120g = 180g
Brown sugar: (24/16) x 140g = 210g
Oats: (24/16) x 250g = 375g
Syrup: (24/16) x 2 tablespoons = 3 tablespoons
Therefore, Jenny needs 180g of butter, 210g of brown sugar, 375g of oats, and 3 tablespoons of syrup to make 24 flapjacks.
To know more about ingredients for making, refer here:
https://brainly.com/question/24173271#
#SPJ11
Dean's family goes on a road trip every summer. This scatter plot shows the number of days
they traveled and how far they went during their last 7 road trips.
What was the most common distance?(miles)
Answers
The most common distance in miles would be = 1,200 miles.
How to determine the most common distance that was travelled?To determine the distance that is most travelled the following is considered;
The total number of road trips = 7
On day 3 the distance travelled = 600 and 1,200 miles
On day 4 the distance travelled = 1,000,1,100 and 1,200 miles
On day 5 the distance travelled = 800 miles.
On day 6 the distance travelled = 1,300 miles
Therefore the most travelled distance = 1,200 miles.
Learn more about distance here:
https://brainly.com/question/26046491
#SPJ1!
50 POINTS ASAP Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of five eighths to create polygon A′B′C′D′. If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′.
A′(5.8, −3), B′(1.6, −1.5), C′(−1.6, 3), D′(2.5, 3)
A′(−16, 24), B′(−8, 8), C′(16, −24), D′(16, 16)
A′(2.5, −3.75), B′(1.25, −1.25), C′(−2.5, 1.25), D′(−2.5, −2.5)
A′(−2.5, 3.75), B′(−1.25, 1.25), C′(2.5, −1.25), D′(2.5, 2.5)
Answers
Answer:
A′(−2.5, 3.75), B′(−1.25, 1.25), C′(2.5, −1.25), D′(2.5, 2.5)
Step-by-step explanation:
in the described situation you only need to multiply the coordinates by the scale factor (in our case the given 5/8)
A (-4, 6) turns into
A' (-4×5/8, 6×5/8) = A' (-2.4, 3.75)
and therefore we know already here that all the other answer options are wrong.
Emily brought some homemade cookies for the school bake sale. The ingredients cost her $1.50 per cookie, but she sells them for a higher price at $3.00 per cookie. What is the percent markup per cookie?
Answers
The value of the calculated percent markup of the cookie is 100%
Finding the the percent markup per cookieFrom the question, we have the following parameters that can be used in our computation:
The ingredients cost her $1.50 per cookieShe sells them for a higher price at $3.00 per cookieThe percent markup of the cookie is then calculated as
Percentage = (Selling price - cost price)/cost price
substitute the known values in the above equation, so, we have the following representation
Percentage = (3 - 1.5)/1.5
Evaluate
Percentage = 100%
Hence, the percent markup of the cookie is 100%
Read more about percentage at
https://brainly.com/question/24877689
#SPJ1
Find the derivative of the function. f(x) = (5x - 5)(Vx+3) - 1/2 O A. f'(x) = 3.33x - 1/2 - 2.5x + 15 - 1/2 OB. f'(x) = 3.33% - 1/2 - 5x + 15 O c. f'(x) = 7.5x1/2 ) - 5x - 1/2 + 15 OD/2 O D. f'(x) = 7
Answers
To get the derivative of the function f(x) = (5x - 5)(√x + 3) - 1/2, we'll first need to use the product rule and then simplify the expression. The product rule states that if you have a function g(x)h(x), its derivative is g'(x)h(x) + g(x)h'(x).
Let g(x) = 5x - 5 and h(x) = √x + 3.
Step 1: the derivatives of g(x) and h(x).
g'(x) = 5 (derivative of 5x - 5)
h'(x) = 1/(2√x) (derivative of √x + 3)
Step 2: Apply the product rule.
f'(x) = g'(x)h(x) + g(x)h'(x)
f'(x) = 5(√x + 3) + (5x - 5)(1/(2√x))
Step 3: Simplify the expression.
f'(x) = 5√x + 15 + (5x - 5)/(2√x)
This is the derivative of the function f(x) = (5x - 5)(√x + 3) - 1/2. Note that none of the given answer choices match this result, so there might be a mistake in the provided options.
Learn more about derivative here, https://brainly.com/question/12047216
#SPJ11
At what value(s) of x does cos x = 8x? X= (Use a comma to separate answers as needed. Type an integer or decimal rounded to two decimal places as needed.) Use Newton's method to obtain the third approximation, X2, of the positive fourth root of 4 by calculating the third approximation of the right 0 of f(x)= x⁴ - 4. Start with x0 = 1. The third approximation of the fourth root of 4 determined by calculating the third approximation of the right of f(x) = x⁴ - 4, starting with x0 = 1, is (Round to four decimal places.)
Answers
The third approximation of the fourth root of 4, starting with x0 = 1, is approximately 1.7321
To find the third approximation, X2, of the positive fourth root of 4 using Newton's method, we will follow these steps:
1. Define the function f(x) = x^4 - 4 and its derivative f'(x) = 4x^3.
2. Start with an initial guess x0 = 1.
3. Apply Newton's method formula to find the next approximation: x1 = x0 - f(x0) / f'(x0).
4. Repeat the process for the second and third approximations.
Step 1:
f(x) = x^4 - 4
f'(x) = 4x^3
Step 2:
x0 = 1
Step 3:
x1 = x0 - f(x0) / f'(x0) = 1 - (1^4 - 4) / (4 * 1^3) = 1 - (-3 / 4) = 1 + 0.75 = 1.75
Step 4:
x2 = x1 - f(x1) / f'(x1) = 1.75 - (1.75^4 - 4) / (4 * 1.75^3) ≈ 1.7321
The third approximation of the fourth root of 4 determined by calculating the third approximation of the right of f(x) = x^4 - 4, starting with x0 = 1, is approximately 1.7321 (rounded to four decimal places).
To know more about approximation, visit:
https://brainly.com/question/29669607#
#SPJ11
When Julie jogs she burns 255 calories I'm 15 minutes and 340 calories in 20 minutes. Which equation represents how many calories she burn pre minute?
Answers
The calories she burns per minute is 17 cal
We are given that the total calories that are burnt in 15 minutes and 20 minutes are 255 and 340 respectively.
We can use the equation
total calorie burnt = time (in minutes) * calorie burnt in one minute
here we know the total calorie that is burnt and the time, we can substitute the calorie that is burnt in a single minute with 'n'.
we can say that :
255 = 15 * x
x=255/15
x= 17.
The total calorie burn per minute is 17.
now for the verification, we know that if the total calorie burn per minute is 17 it should satisfy both the equation.
So, 340 = 20*x
340=20* 17
340 = 340
Thus it satisfies both equations.
Hence the calorie burnt per minute = 17
Learn more about Calorie at:
https://brainly.com/question/28589779
#SPJ4
Find the divergence and curl of the following vector fields. F(x, y,z) = 2y cos zi + eˣ sin zj + xe³'k.
Answers
The divergence of F is 2y cos(z) + eˣ cos(z) + 3xe³, and the curl of F is -eˣcos(z)i - 3xe³j + (eˣsin(z) + 2cos(z))k.
How to find the divergence and curl of the vector field F(x, y, z)?To find the divergence and curl of the vector field F(x, y, z) = 2y cos(z)i + eˣ sin(z)j + xe³k, we need to apply the appropriate operators.
The divergence of F is given by:
div F = ∇ · F = (∂/∂x)i + (∂/∂y)j + (∂/∂z)k · (2y cos(z)i + eˣ sin(z)j + xe³k)
where ∇ is the del operator.
Calculating the dot product, we get:
div F = 2y cos(z) + eˣ cos(z) + 3xe³
Therefore, the divergence of F is:
div F = 2y cos(z) + eˣ cos(z) + 3xe³
Now, let's find the curl of F. The curl of F is given by:
curl F = ∇ × F = ( (∂/∂y)(xe³) - (∂/∂z)(eˣsin(z)) )i - ( (∂/∂x)(2ycos(z)) - (∂/∂z)(xe³) )j + ( (∂/∂x)(eˣsin(z)) - (∂/∂y)(2ycos(z)) )k
Calculating the partial derivatives, we get:
(∂/∂y)(xe³) = 0
(∂/∂z)(eˣsin(z)) = eˣcos(z)
(∂/∂x)(2ycos(z)) = 0
(∂/∂z)(xe³) = 3xe³
(∂/∂x)(eˣsin(z)) = eˣsin(z)
(∂/∂y)(2ycos(z)) = -2cos(z)
Substituting these values, we get:
curl F = (0 - eˣcos(z))i - (0 - 3xe³)j + (eˣsin(z) - (-2cos(z)))k
Simplifying, we get:
curl F = -eˣcos(z)i - 3xe³j + (eˣsin(z) + 2cos(z))k
Therefore, the divergence of F is 2y cos(z) + eˣ cos(z) + 3xe³, and the curl of F is -eˣcos(z)i - 3xe³j + (eˣsin(z) + 2cos(z))k.
Learn more about divergence and curl of the vector fields
brainly.com/question/7964566
#SPJ11
Find the missing dimension for the triangle. The area is 256. 5 cm sq and the base is 27 cm
Answers
The missing dimension of the triangle is the height, which is 19 cm.
To find the missing dimension of the triangle, we can use the formula for the area of a triangle:
Area = (1/2) x base x height
We know that the area is 256.5 cm^2 and the base is 27 cm. Therefore, we can plug in these values into the formula and solve for the height:
256.5 = (1/2) x 27 x height
256.5 = 13.5 x height
height = 256.5 / 13.5
height = 19
Therefore, the missing dimension of the triangle is the height, which is 19 cm.
To know more about triangle refer here:
https://brainly.com/question/2773823
#SPJ11
If you multiply each value in the data set below by 3, what are the mean, median, mode, and range of the resulting data set?
2 3 9 0 5 8 3
Answers
Answer: range=9 mode=3 mean=9
Step-by-step explanation:
The table shows the results of a survey of 150 students.
Use the table to find the probability of a student participating
in each sport.
1. Football
2. Tennis
Answers
Probability of a student participating in football: 0.4 or 40%
Probability of a student participating in tennis: 0.2 or 20%
Assuming that the table lists the number of students who participate in each sport out of a total of 150 students, we can find the probability of a student participating in each sport by dividing the number of students who participate in each sport by the total number of students:
Probability of a student participating in football:
Number of students who participate in football / Total number of students = P(Football)
Probability of a student participating in tennis:
Number of students who participate in tennis / Total number of students = P(Tennis)
For example, if the table shows that 60 students participate in football and 30 students participate in tennis out of a total of 150 students, then the probabilities would be:
Probability of a student participating in football:
60/150 = 0.4 or 40%
Probability of a student participating in tennis:
30/150 = 0.2 or 20%
To know more about probability, refer to the link below:
https://brainly.com/question/13515204#
#SPJ11
Position vector = 3 ti + tj + 1/4t^2k
Time = 2
Find the velocity vector, speed, and acceleration vector of the object.
Answers
the velocity vector of the object is v(2) = 3i + j + k, the speed is sqrt(11), and the acceleration vector is a(t) = (1/2)k.
We're given the position vector and time and asked to find the velocity vector, speed, and acceleration vector of the object. Let's solve this step-by-step.
1. Differentiate the position vector with respect to time (t) to find the velocity vector:
Position vector: r(t) = 3ti + tj + (1/4)t^2k
Velocity vector: v(t) = dr(t)/dt = d(3ti)/dt + d(tj)/dt + d((1/4)t^2k)/dt
v(t) = 3di/dt + dj/dt + (1/2)tk
v(t) = 3i + j + (1/2)tk
2. Plug in the given time (t = 2) into the velocity vector to find the velocity at that time:
v(2) = 3i + j + (1/2)(2)k
v(2) = 3i + j + k
3. Find the speed by calculating the magnitude of the velocity vector:
Speed = |v(2)| = sqrt((3^2) + (1^2) + (1^2))
Speed = sqrt(9 + 1 + 1)
Speed = sqrt(11)
4. Differentiate the velocity vector with respect to time (t) to find the acceleration vector:
Acceleration vector: a(t) = dv(t)/dt = d(3i)/dt + d(j)/dt + d((1/2)tk)/dt
a(t) = 0i + 0j + (1/2)k
So, the velocity vector of the object is v(2) = 3i + j + k, the speed is sqrt(11), and the acceleration vector is a(t) = (1/2)k.
to learn more about velocity vectors click here:
https://brainly.com/question/28491008
#SPJ11