Variance and standard deviation are measures of variability that are appropriate and possible to calculate for variables measured on an interval or ratio scale of measurement.
Interval scales have a true zero point, meaning that a difference of zero on the scale represents a lack of the characteristic being measured (e.g. temperature measured in degrees Celsius). Ratio scales are similar to interval scales, but also have a meaningful zero point, meaning that a value of zero on the scale represents a complete absence of the characteristic being measured (e.g. height measured in meters).
Variance and standard deviation can be calculated for interval and ratio variables because these scales provide meaningful differences and ratios between values. The calculation of variance involves finding the average squared difference between each value and the mean of the values, while standard deviation is the square root of the variance. Both variance and standard deviation provide information about how spread out the values of a variable are and are useful in statistical analysis.
On the other hand, nominal and ordinal scales only provide categories or rank order for values, without any meaningful differences or ratios between values. As such, it is not appropriate or possible to calculate variance or standard deviation for variables measured on nominal or ordinal scales.
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C is equidistant to which of the following points?
If you guys answer you get 10 points
C is equidistant to the following points: CL=CM=CN
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
One of the triangle's centers where the bisectors of the inner angles converge is known as the incline
The circumcenter of a triangle, which is equal distances from all the vertices, is where the perpendicular bisectors of the triangle meet.
so, C is equidistant to the following points: CL=CM=CN
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please help me will give u extra points :)
•
The compound inequality for the graph shown above include the following:
x < -2.
x > 5.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.
Generally speaking, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
Since the point is at -2 and the arrow points to the left of the number line, it represents the less than (<) inequality symbol and should be written as x < -2.
Additionally, the second point is at 5 and the arrow points to the right of the number line, it represents the greater than (>) inequality symbol and should be written as x > 5.
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my bowl of easter candy has colorful foil-wrapped chocolate eggs. there are 5 gold, 7 blue, and 10 pink. when callie brooke raids the candy bowl, what is the probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil? give your answer as a percent (including the percent sign) rounded to the nearest 0.01%.
If my bowl of easter candy has colorful foil-wrapped chocolate eggs. there are 5 gold, 7 blue, and 10 pink. The probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil is 0.45.
How to find the probability?Total color = 5 gold + 7 blue + 10 pink
Total color = 22
Now let find the probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil
Probability (pink) = 10/22
Probability (pink) = 0.45
Therefore the probability of Callie Brooke getting a pink foil-wrapped chocolate egg is 10/22, or approximately 0.45.
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pls help I really need this ASAP
Use the general slicing method to find the volume of the following solid. The solid with a semicircular base of radius 11 whose cross sections perpendicular to the base and parallel to the diameter are squares
The volume of the solid is 1789.33
For a circle of radius 11, we have the following equation:
x²+y²=11²
x²+y²=121
Now, making it explicit for x:
[tex]x=\sqrt{121-y^2}[/tex]
Then, if we consider that for a height y, the length x is double, we have that the length of each cross-section is given by:
[tex]s=\sqrt[2]{81-y^2}[/tex]
With this, we can propose the following integral to obtain the volume that they are asking us:
[tex]\int\limits^1_0 {s^2} \ \, dy \\\int\limits^1_0 ({\sqrt[2]{121-y^2})^2 } \, dy\\\\\int\limits^1_0 {4*(121-y^2)} \, dy\\\\4*(121y-\frac{y^3}{3} )[/tex]
Finally, calculating, we have that the volume is V=1789.33
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can someone just try to answer this ?:(
Ima fail
Answer:
-2 <n>5 I believe? that's all I know
Answer:
below
Step-by-step explanation:
For the LEFT part
n < -2 or -2 > n
for the RIGHT part
n>5
combine these two to get -2 > n > 5
there are n given points (numbered from 0 to n-1) on a plane maximum number of points inside the circle
Circle Detection Algorithm is a highly efficient and effective solution to finding the most number of points that lie on any one circle in a 2D real plane.
The algorithm to solve this problem is known as the "Circle Detection Algorithm." This algorithm starts by considering three points randomly selected from the given N points.
Next, the algorithm checks the number of points that lie on this circle. If this number is greater than the current maximum, then this circle becomes the new candidate for the circle that contains the most number of points.
To ensure that the algorithm is efficient, it is important to choose the points randomly, as this reduces the chances of getting stuck in a local maximum.
The mathematical formula to calculate the center and radius of the circle that passes through three points (x₁, y₁), (x₂, y₂), and (x₃, y₃) is given by:
x = ( (y₂ - y₁)(y₃² - y₁² + x₃² - x₁²) - (y₃ - y₁)(y₂² - y₁² + x₂² - x₁²) ) / (2 * (x₃ - x₁)(y₂ -y₁) - 2 * (x₂ - x₁)(y₃ - y₁) )
y = ( (x₂ - x₁)(x₃² - x₁² + y₃² - y₁²) - (x₃ - x₁)(x₂² - x₁² + y₂² - y₁²) ) / (2 * (y₃ - y₁)(x₂ -x₁) - 2 * (y₂ - y₁)(x₃ - x₁) )
r = √(x₁ - x)² + (y₁ - y)²
Once the center and radius have been calculated, the algorithm can easily check the number of points that lie on the circle by calculating the distance of each point from the center and checking if it is equal to the radius.
Complete Question:
Given N points on the 2D real plane, what is the most efficient algorithm to find the most number of points that lie on any one circle?
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Solve x^2-7x=-12
Need help
Answer:
x=4 and x=3
Step-by-step explanation:
Modeling with Composite Functions
A boutique prices merchandise by adding 80% to its cost. It later decreases by 25% the price of items that don't sell quickly.
a. Write a function f(x) to represent the price after the 80% markup.
b. Write a function g(x) to represent the price after the 25% markdown.
c. Use a composition function to find the price of an item after both price adjustments that originally the boutique $150.
d. Does the order in which the adjustments are applied make a difference? Explain.
a. f(x) = 1.8x.
b. f(x) = 1.35x.
c. f(150) = 1.35×150 ⇒ f(150) = 202.5.
d. The order in which the adjustments are applied doesn't make any difference.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A department store has marked down its merchandise by 25%. It later decreases by $5 the price of items that have not sold.
Let, 'x' be the price of the merchandise.
So, After adding 80% to its cost it becomes [(100 + 80)/100]×x = 1.8x.
Later it decreases by 25% the price of items that don't sell quickly.
So, It has a value of (75/100)×1.8x = 1.35x.
a. A function f(x) to represent the price after the 80% markup is.
f(x) = 1.8x.
b. A function g(x) to represent the price after the 25% markdown is,
f(x) = 1.35x.
c. A composition function to find the price of an item after both price adjustments that originally the boutique $150 is,
f(150) = 1.35×150.
f(150) = 202.5.
d. Let, The price of the item be $100, after 80% makeup it would be
$180 and after 25% markdown it would be $135.
Again 25% markdown on $100 is $85 and an 80% markup is
75×1.8 = $135 hence no difference.
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A semi trailer is being packed with boxes that are 1 1/2 feet on each edge,
the cargo space of the trailer is 28 ft long, 8 1/2 ft wide, and 9 1/6 ft hight.
what is the maximum number of boxes that will fit in the trailer?
HELP PLSSSSSS!!
Answer:614
Step-by-step explanation:
The maximum number of boxes that can fit in the trailer can be calculated by dividing the volume of the trailer by the volume of each box.
First, we need to convert the dimensions of the boxes and the trailer to the same unit, such as cubic feet. The volume of each box is given by:
V_box = (1 1/2 ft)^3 = (1.5 ft)^3 = 3.375 ft^3
Next, we calculate the volume of the trailer:
V_trailer = 28 ft * 8 1/2 ft * 9 1/6 ft = 2070 ft^3
Finally, we divide the volume of the trailer by the volume of each box to find the maximum number of boxes:
N_boxes = V_trailer / V_box = 2070 ft^3 / 3.375 ft^3 = 614.07 boxes
Since we can only fit whole boxes in the trailer, the maximum number of boxes that will fit is 614.
The article "Determination of Most Representative Subdivision" gave data on various characteristics of subdivisions that could be used in deciding whether to provide electrical power using overhead lines or underground lines. Data on the variable x = total length of streets within a subdivision are as follows.
1280 5320 4390 2100 1240 3060 4770 1050 360 3330 3380 340 1000 960 1320 530 3350 540 3870 1250 2400 960 1120 2120 450 2250 2320 2400 3150 5700 5220 500 1850 2460 5850 2700 2730 1670 100 5770 3150 1890 510 240 396 1419 2109
(a) Fill in a stem-and-leaf display for these data using the thousands digit as the stem. Do not truncate numbers. For example, number 2380 has stem-"2" and leaf-"380". (Enter solutions from smallest to largest. Separate the numbers with spaces.)
0 100 240 340 360 396 396 450 500 510 530 540 960 960
(b) Fill in the table below. (Round your answer to four decimal places if needed.)
Class Interval Frequency Relative Frequency
0 - <1000
2000 - < 3000
4000 - < 5000
5000 - < 6000
(c)
What proportion of subdivisions has total length less than 2000?
What proportion of subdivisions has total length between 2000 and 4000? (Round your answer to four decimal places if needed.)
a) The data is not symmetric
b) The complete table:
Class interval Frequency Relative Frequency
0-1000 12 0.255319151000-2000 11 0.234042552000-3000 10 0.212765963000-4000 7 0.148936174000-5000 2 0.04255319 5000-6000 5 0.10638298c) Proportion of subdivisions has total length less than 2000 is 0.49
Proportion of the subdivisions has total length between 2000 and 4000 is 0.36
a) To draw the stem and leaf plot we take the thousandth place digit as stem and the leaf is obtained by remaining digits.
Stem Leaf
0 360, 340, 960, 530, 540, 960, 450, 500, 100, 510, 240, 3961 280, 240, 050, 000, 320, 250, 850, 670, 890, 4192 100, 400, 120, 250, 320, 400, 460, 700, 730, 1093 060, 330, 380, 350, 870, 150, 1504 390, 7705 320, 700, 220, 850, 770The data is not symmetric
b) To draw the histogram first we form the frequency distribution and the relative frequency using the formula
Relative Frequencies are given by
Relative frequency = Frequency / Total frequency
Class interval Frequency Relative Frequency
0-1000 12 0.255319151000-2000 11 0.234042552000-3000 10 0.212765963000-4000 7 0.148936174000-5000 2 0.04255319 5000-6000 5 0.10638298= 47
Histogram attached at end of solution
The histogram is approximately positively skewed.
c) Proportion of lengths less than 2000 = sum of relative frequency from 0 to 2000
= 0.26 + 0.23
Proportion of subdivisions has total length less than 2000 = 0.49
Proportion of length between 2000 and 4000 = sum of relative frequency between 2000 and 4000
= 0.21 + 0.15
Proportion of the subdivisions has total length between 2000 and 4000 = 0.36
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A phone company offers two monthly plans. Plan A costs s12 plus an
additional s0.14 for each minute of calls. Plan B costs s28 plus an additional
50.12 for each minute of calls.
The plan cost same for 800 minutes.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Plan A costs $12 plus an additional $0.14 for each minute of calls.
Plan B costs $28 plus an additional $0.12 for each minute of calls.
let the number of minutes for which two plans are equal be x.
so, 12 + 0.14x = 28 + 0.12 x
12 - 28 = 0.12x - 0.14x
-16 = -0.02x
x= 800 minutes
and, the plan cost
y = 12 + 0.14x
y = 12 + 0.14(800)
y = $124
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Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. ln(6)/6 + ln(7)/7 + ln(8)/8 + ln(9)/9 + ln(10)/10 + ... integral_1^infinity ln(x + 5)/x + 5 dx = O converges O diverges
The infinite series, [tex]ln(6)/6 + ln(7)/7 + ln(8)/8 + ln(9)/9 + ln(10)/10 + ... = \int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx\\ [/tex] is diverges as the integral diverges.
We know that the Integral test : Suppose that f(x) is a continuous, positive and decreasing function on the interval [ k,∞) and that f(n)= a, then
If [tex] \int_{k}^{ \infty } f(x)dx[/tex] is convergent then the series, [tex] \sum_{n = 1}^{ \infty } a_{n}[/tex]
If [tex] \int_{k}^{ \infty } f(x)dx[/tex] is divergent so is [tex]\sum_{n = 1}^{ \infty } a_{n}[/tex].
We have an integral equals to an infinite series [tex] \frac{ln(6)}{6} + \frac{ln(7)}{7} + \frac{ln(8)}{8} + \frac{ln(9)}{9} + \frac{ln(10)}{10} + ... = \int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx \\ [/tex]
[tex]\int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx = {\lim_{k-> \infty } \\}\int_{1}^{k} \frac{ln(x + 5)}{ (x + 5 )}dx [/tex]
[tex]= {\lim_{k-> \infty } \\}[ \frac{ {(ln(x+5))}^{2} }{2} ]_{1}^{k}\\ [/tex]
[tex] = \infty [/tex]
This implies that the integral diverges, so by integral test the series also diverges.
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3. What is a Cartesian plane?
A. A graph used in mathematics to only compare linear planes.
B. A graph used in mathematics to calculate positive and negative multiplication tables.
C. A graph used in mathematics to create 3-dimensional shapes.
D. A graph used in mathematics to plot points.
The Cartesian, or rectangular, coordinate system is composed of an x-axis that runs horizontally and a y-axis that goes vertically.
What is meant by Cartesian plane?The rectangular coordinate system of the Cartesian plane, which bears Rene Descartes' (1596–1650) name, assigns each point in the plane a pair of integers.
An x-axis that runs horizontally and a y-axis that runs vertically make up the Cartesian, or rectangular, coordinate system. The origin is the place where the two axes meet. Any point can be characterized by its distance from the origin along the x-axis and along the y-axis, and this distance is represented by the symbol (x, y).
A two-dimensional coordinate plane produced by the intersection of the x- and y-axes is known as the cartesian plane in mathematics. At the location known as the origin, the x- and y-axes cross perpendicularly.
Therefore, the correct answer is option D. A graph used in mathematics to plot points.
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false or true the square roor of 361 is 19
The answer to your question is true
Answer:
true, the square root of 361 is 19
Step-by-step explanation:
( ﾟｰﾟ)ﾉ
1. You have a system of K equations in two variables, k >= 2. Explain the geometric significance of there being no solution.
If there is no solution to the system of equations, it signifies that the equations describe two parallel lines in the two-dimensional plane. This indicates that the lines will never meet because they have the same slope but separate y-intercepts. This signifies that the two lines are geometrically distinct and will never intersect.
What is a geometric significance?A geometric significance is a geometric aspect or quality of a form or item. This encompasses the object's size and orientation, as well as its symmetry and proportions. Several areas, including architecture, engineering, graphic design, and mathematics, rely on geometric importance. In architecture, for example, the size and direction of a structure may be utilised to decide how much light it receives and how much shade it casts. The geometry of an item can be used to determine its strength, stiffness, and durability in engineering. The symmetry and dimensions of an object may be employed in graphic design to produce an appealing and balanced design.
The given question states that when there are no solutions to a system of K equations in two variables, it means that the lines associated with those equations are either parallel or coincident. Geometrically, this means that the lines are not intersecting, which implies that the two variables cannot simultaneously satisfy all of the equations.
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A triangle is formed by the building's height
and shadow. Another triangle is formed by
the flagpole's height and shadow. Using the
following diagram, find the height of the
building.
Answer: 400 ft
Step-by-step explanation:
Since the triangles are Congruent Triangles (similar)
x/40 = 50/5
Cross multiply
5x = 2000
divide both sides by 5
5x/5 = 2000/5
x = 400 ft
What is the product of x(x+1)?
the model shows that there are 9 picecs that are ft long i ready
Answer:
The model shows that there are 9 pieces that are each ft long.. The model shows that there are 9 pieces that are - 1.
 How many solutions will this equation have?
7(5x + 2) = 5x + 2
O
0000
0
a
b
d
=
f
There is no way to know
Two solutions
Three solutions
No solution
Infinite solutions
One solution
Answer:
[tex]\Huge \boxed{\textbf{F. One solution}}[/tex]
Step-by-step explanation:
To find the number of solutions for the given equation, we can start by simplifying and solving the equation.
First, distribute the 7 on the left side of the equation:
[tex]\tt{35x + 14 = 5x + 2}[/tex]Now, subtract 5x from both sides:
[tex]\tt{30x + 14 = 2}[/tex]Next, subtract 14 from both sides:
[tex]\tt{30x = -12}[/tex]Finally, divide by 30:
[tex]\tt{x = -12/30}[/tex]Simplifying the fraction, we get:
[tex]\tt{x = -2/5}[/tex]Since we found a unique value for x, the equation has only one solution.
Therefore, the correct answer is option F.
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________________________________________________________
Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. Which statement best describes the meaning of one of the bars in the histogram? O 110 snacks have between 100 and 120 mg of sugar O 110 snacks have 7 mg of sugar. O 7 snacks have about 110 mg of sugar. O The largest number of snacks have 12 mg of sugar
The correct answer is option A. 110 snacks have between 100 and 120 mg of sugar.
A bar in a histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar. So, the statement that best describes the meaning of one of the bars in the histogram is: 110 snacks have between 100 and 120 mg of sugar.
In summary, the bar in the histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar.
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Please help me with this question.
Answer:
a) 4
b) 2
Step-by-step explanation:
I use this sentence to remember quadrants:
All Students Take Coffe
- All trigs are positive in 1 Quadrant
- Sin and (cosine) is positive in 2 quadrant
-Tan and (Cotan) are positive in 3 quadrant
- Cos and (Sec) are positive in 4 quadrant
all other trigs other than those are negative.
a) cos is positive in 1 and 4 quadrant. Csc is reciprocal of Sin and is negative in 3 and 4 quadrant. 4th quadrant satisfies both conditions.
b) csc is reciprocal of Sin and is positive in 1 and 2 quadrants. Sec is reciprocal of Cos and is negative in 2 and 3 quadrant. 2nd quadrant fulfills both conditions.
Ian has $28 in his checking account if he writes a check for $12 how much money is left in his account?
Ian would have $16 left in his checking account.
Here is the working:
$28 (starting amount) - $12 (check written)
= $16 (remaining amount)
Find an equation of the sphere with center (4, −12, 8) and radius 10.Use an equation to describe its intersection with each of the coordinate planes. (If the sphere does not intersect with the plane, enter DNE.)intersection with xy-plane intersection with xz-plane intersection with yz-plane
The equation of the sphere with center coordinates (4, −12, 8) and radius 10 is x² -8x + y² + 24y + z² -16z + 124 =0 .
And different plane equations are :
Intersection with xy-plane : ( x - 4 )² + ( y + 12 )² = 6²
Intersection with yz plane :( y + 12 )² + ( z - 8 )² = (√84)²
Intersection with zx plane :( x - 4 )² + ( z - 8 )² = -44
Equation of the sphere with center coordinates (4, −12, 8) and radius 'r' = 10 is :
( x - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²
⇒ x² -8x + y² + 24y + z² -16z + 224 = 100
⇒x² -8x + y² + 24y + z² -16z + 124 =0
Intersection with xy-plane
z = 0
( x - 4 )² + ( y + 12 )² + ( 0 - 8 )² = 10²
⇒( x - 4 )² + ( y + 12 )² = 6²
Circle with center ( 4,-12) and radius 6.
Intersection with yz-plane
x = 0
( 0 - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²
⇒( y + 12 )² + ( z - 8 )² = (√84)²
Circle with center ( -12, 8) and radius √84.
Intersection with zx-plane
y = 0
( x - 4 )² + ( 0 + 12 )² + ( z - 8 )² = 10²
⇒( x - 4 )² + ( z - 8 )² = -44
Not possible as radius cannot be negative.
Therefore, the equation of the sphere with the given center and radius is equal to x² -8x + y² + 24y + z² -16z + 124 =0 and equation of the intersection of different planes are:
xy-plane : ( x - 4 )² + ( y + 12 )² = 6²
yz plane :( y + 12 )² + ( z - 8 )² = (√84)²
zx plane :( x - 4 )² + ( z - 8 )² = -44
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Como se calcula un ángulo de referencia?
The method to calculate the reference angle is discussed below.
What is reference angle?Reference Angle is the acute angle between the terminal side and the
x - axis.
Given is reference angle.
You determine a reference angle by looking at the terminal side of the angle you're working with and its relation with the positive or negative x-axis (depending on which quadrant the terminal side is in).
Therefore, the method to calculate the reference angle is discussed above.
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{Question in english -
How is a reference angle calculated?}
Find the point of intersection of the lines given below and then find the plane determined by these lines x=3t+1, y=4t+4, z = 6t + 2, 0
The point of intersection of the lines given is (1,4,2) and the plane determined is -3y +2z+8 = 0.
Let us first define the lines as -
L1 = x=3t+1, y=4t+4, z = 6t + 2
L2 = X=s+2 y=2s+6, z = 3s - 1
We have to find the intersection so -
= 3t+1 = s+2 ⇒ 3t - s - 1 = 0
= 4t+4 = 4t+4 ⇒ 4t - 2s - 2 = 0
= 6t + 2 = 3s - 1 ⇒ 6t - 3s + 3 = 0
Now, if we input the values of t and s as given in the question i.e., t = 0 and s = -1, we get -
= x = 1
= y = 4
= z = 2
These are the points of intersections of the given lines.
Now, the direction vector of L1 = (3,4,6) and L2 = (1,2,3)
So, the normal vector to the plane can be calculated using the determinant method.
[tex]\left[\begin{array}{ccc}i&j&k\\3&4&6\\1&2&3\end{array}\right][/tex]
On solving this, we get = -3j + 2k
The equation of the plane is -
= 0(x-1) - 3(y-4) + 2(z-2) = 0
= -3y +2z+8 = 0
The complete question that you might be looking for is given below -
Find the point of intersection of the lines given below and then find the plane determined by these lines x=3t+1, y=4t+4, z = 6t + 2, 0<t< 0 X=s+2 y=2s+6 2 = 3s - 1 , C < 5 < 0
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determine if b is in the span of the other given vectors. if so, express b as a linear combination of the other vectors. (if b cannot be written as a linear combination of the other two vectors, enter dne in both answer blanks.) -1 -2 -6
a1 = 3 a2 = -3 b= 9
-1 6 2
Yes, b(-6, 9, 2) is in the span of the other given vectors [tex]a_1[/tex] = (-1, 3, -1), [tex]a_2[/tex] = (-2, -3, 6).
b as a linear combination of the other vectors [tex]a_1[/tex] and [tex]a_2[/tex]
b = c [tex]a_1[/tex] + d [tex]a_2[/tex]
A vector is a quantity that has magnitude and direction.
We say that a vector u spans vectors v, w if u = av + bw where a and b are scalars.
As per the given data:
[tex]a_1[/tex] = (-1, 3, -1), [tex]a_2[/tex] = (-2, -3, 6), b = (-6, 9, 2)
We need to write vector b as a linear combination of vectors [tex]$a_1[/tex] and [tex]a_2$[/tex].
Let c and d be scalars.
b = c [tex]a_1[/tex] + d [tex]a_2[/tex]
(-6, 9, 2) = c(-1, 3, -1) + d(-2, -3, 6)
(-6, 9, 2) = (-c - 2d, 3c - 3 d, -c + 6d)
-6 = -c - 2d........(i),
9 = 3c - 3d ...... (ii),
2 = -c + 6d .......(iii)
b = c [tex]a_1[/tex] + d [tex]a_2[/tex]
On solving equations (i) and (ii), we get c = 4, d = 1
Now, we will check if c = 4, and d = 1 satisfy equation (iii).
= - c + 6d
= -4 + 6(1)
= -4 + 6
= 2
As it satisfies this equation, so b is a linear combination of [tex]$a_1[/tex] and [tex]a_2[/tex]
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Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors. (if b cannot be written as a linear combination of the other two vectors, enter done in both answer blanks.) a1=[-1 3 -1],a2=[-2 -3 6],b=[-6 9 2]
SAVINGS If $10,000 is deposited into a savings account that pays 1.8% annual interest, how much more would the account be worth if interest were compounded monthly rather than annually over a period of 30 years?
Round to Nearest Dollar
The amount of money that is compounded monthly for 30 years will be $17,153.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
If $10,000 is deposited into a savings account that pays 1.8% annual interest.
Then the rate is given as,
r = 1.8% / 1200
r = 0.0015
Then the number of years is given as,
n = 30 x 12
n = 360
Then the amount of money that is compounded monthly for 30 years is given as,
A = $10,000 × (1 + 0.0015)³⁶⁰
A = $10,000 × (1.0015)³⁶⁰
A = $10,000 × 1.715
A = $17,153
The amount of money that is compounded monthly for 30 years will be $17,153.
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Please help me with this question.
A sales presentation aims to attract and compel the audience to whom the presentation is made.
How do you create a sales presentation?Creating a sales presentation involves several steps:
Define the goal and audience of the presentation: Before creating the presentation, it is important to understand the goal of the presentation, and the target audience it is meant for. This will help you tailor the content of the presentation to the specific needs and interests of the audience.
Research the product or service: Understand the product or service you are selling inside and out. This will help you answer any questions that may come up during the presentation and show that you are an expert on the subject.
Create an outline: Once you have a clear understanding of your audience and the product or service, create an outline for the presentation. This will help you organize your thoughts and stay on track during the presentation.
Create compelling content: Use persuasive language and storytelling to create content that is engaging and easy to understand. Use statistics, testimonials, and visual aids to support your points.
Design the visual aids: Use charts, graphs, images, and other visual aids to supplement the text of your presentation. Make sure that the visual aids are clear and easy to understand, and that they support the points you are making.
Rehearsal: Practice the presentation several times before delivering it. This will help you build confidence and ensure that the presentation flows smoothly.
Delivery: During the presentation, engage with the audience and be responsive to their questions and feedback. Make sure that you are well-prepared and that you stay on track.
Follow-up: After the presentation, make sure to follow up with the audience and address any remaining questions or concerns they may have.
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Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it
The axis of symmetry for the function f(x) is x = 8 , and h(x) is x = 3
What is the axis of symmetry of a quadratic function?The axis of symmetry is a hypothetical straight line that splits a form into two identical halves, making one half the mirror image of the other. Both pieces are overlaid when folded along the axis of symmetry.
A straight line called the axis of symmetry is what gives an object its symmetrical form and exactly the same reflections are produced on each side of the axis of symmetry on the graph.
From the given information:
f(x) = -4(x - 8)² + 3
Use the vertex form, y = a ( x − h )² + k, to determine the values of a, h, and k.
a = -4, h = 8, k = 3Since the value of a is negative, the parabola opens down, and the vertex (h, k) is (8, 3).
The distance (p) from the vertex and the focus of the quadratic equation can be calculated by using the formula:
P = 1/4a
Replacing the value of a from above:
P = 1/4(-4)
P = -1/16
The focus of a parabola can be determined by adding the p to the y-coordinate k if the parabola opens up or down. Thus, (h, k + p) = (8, 47/16).
Thus, the axis of symmetry is finally estimated by finding the line that passes through the vertex and the focus;
Axis of symmetry x = 8
For the graphical function of h(x); we use the following points on the graph to determine the equation of the parabola: (1,-2), (3,2), (5,-2)
Thus, h(x) = -x² + 6x - 7
Rewriting the function in its vertex form, we have:
y = - (x - 3)² + 2
Using the vertex form;
a = -1, h = 3, k = 2The vertex (h,k) = (3,2). The axis of symmetry (x) is the line that passes through the vertex and the focus, x = 3.
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