The limits of the function as x approaches infinity and negative infinity are 0 and negative infinity, respectively, and the horizontal asymptote is y = 0.
A function is a mathematical rule that assigns a unique output for each input.
For the function
=> f(x) = 3x²+2/x³√4x⁶+1,
we will evaluate the limits as x approaches infinity and negative infinity. We will also determine the horizontal asymptote of the function.
When x approaches infinity, the denominator
=> x³√4x⁶+1
becomes very large, so the value of the function becomes very small. Thus, the limit of the function as x approaches infinity is 0.
To determine the horizontal asymptote, we need to look at the degree of the numerator and denominator.
The numerator has a degree of 2 and the denominator has a degree of 3. Since the denominator has a higher degree, the horizontal asymptote is y = 0.
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-3 = -2(h-1) + 5
h =
Answer:
h = 5
Step-by-step explanation:
-3 = -2(h-1) + 5
-3 = -2h + 2 + 5
-3 = -2h + 7
-10 = -2h
h = 5
Let's check
-3 = -2(5-1) + 5
-3 = -2(4) + 5
-3 = -8 + 5
-3 = -3
So, h = 5 is the correct answer.
How long does it take for a deposit of $1400 to double at 5% compounded continuously?
Deposit of $1400 will be double in 14.2 years.
What is compound interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
Given,
Deposited Principal Amount P = $1400
Rate of interest r = 5% = 0.05
Amount A = double the deposit = 2× $1400 = $2800
Let the number of years = n
Amount A = P(1 + r)ⁿ
$2800 = $1400(1 + 0.05)ⁿ
(1 + 0.05)ⁿ = 2
Taking log on both side
n log(1.05) = log2
n = log2 / log(1.05)
n = 0.3010/0.0212
n = 14.2
Hence, It will take 14.2 years to double the deposit of $1400.
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Maria is planting a row of flowers in a bed 37 feet long. The instructions say to space the plants 1 foot apart. The flowers come in flats containing 6 plants per flat
Maria has 6.33 flower plants remaining.
A word problem is a short passage presenting a "real-life" situation where an issue has to be solved using math.
Word problems are seen as an essential component of learning in the elementary curriculum because they require students to apply their understanding of various concepts to situations that are representative of "real-life" situations.
Given that the length of the bed is = 37 feet long
The space between plants is = 1 foot
Finding the number of plant flowers to be planted along this bed = 37/1 + 1 = 38 flower plants
Given that
6 flower plants= 1 flat
38*1/6= 6.33
The remaining flower plants are 6.33.
Complete question:
Maria is planting a row of flowers in a bed 27 feet long. The instructions say to space the plants 1 foot apart. The flowers come in flats containing 6 plants per flat.
How many flats will she need?
How many plants will she have left over?
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Cost of a theater ticket is an example of O a) O quantitative data. b) nominal data. O c) categorical data. d) either categorical or quantitative data.
The correct option: a) O quantitative data; defines the cost of the theater ticket.
Define the term quantitative data?Data that expresses a definite quantity, amount, or range is known as quantitative data.
In most cases, the data is accompanied with measuring units, such as metres with in case of a person's height. Setting boundaries for such data makes sense, and performing mathematical operations on the data has significance.Specifically, this phrase should refer to data that is composed of numerical quantities like measurements or counts, as opposed to qualitative data. Sometimes, less precisely, it is used to describe things when the variables are quantities instead of data derived from qualitative qualities, like height, weight, or price.Thus, the cost of any theater ticket defines an example of quantitative data.
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find the z-score for which the area under the standard normal curve to its left is 0.96. round to two decimal places
The z-score for which the area under the standard normal curve to its left is 0.96 is approximately 1.75.
The z-score for which the area under the standard normal curve to its left is 0.96 can be found using a standard normal table or a calculator with a standard normal cumulative distribution function (CDF).
Using a standard normal table, we find that the z-score that corresponds to an area of 0.96 to its left is approximately 1.75.
Alternatively, using a calculator with a standard normal CDF, we can calculate the inverse CDF of 0.96:
z = invNorm(0.96)
This gives us a z-score of approximately 1.75.
Therefore, the z-score for which the area under the standard normal curve to its left is 0.96 is approximately 1.75, rounded to two decimal places.
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which process occurs between steps (iii) and (iv) in the diagram shown below?
Answer: Diploid cells divide to form four haploid daughter cells during mitosis.
Step-by-step explanation:
The answer is: Sister chromatids separate to form haploid daughter cells during meiosis.
What is chromatids?One of a chromosome's two identical halves that has undergone replication in order to facilitate cell division is referred to as a chromatid. A chromosomal region known as the centromere is where the two "sister" chromatids are fused.
One of the two identical copies of a duplicated chromosome is called a chromatid. At the centromere, a portion of the chromosome, the twin copies of the DNA join together during cell division. Sister chromatids are those that are joined. A chromosome is a protein and DNA-based structure that resembles a thread. It contains an organism's whole genetic makeup. Parents pass this on to their children. One of a chromosome's halves is called a chromatid. There is just one chromatid per chromosome.
The chromatids in each thread-like structure in the chromosome are the result of the chromosome's DNA replicating itself. Haploid cells are produced as a result of the segregation of the chromatids during meiosis II.
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The complete question is as follows:
Find all real values of x that satisfy the equation (x^2 - 82)^2 = 324
The real values of x are -10 and 10
How to determine the real values of xFrom the question, we have the following parameters that can be used in our computation:
(x^2 - 82)^2 = 324
Take the square roots of both sides
So, we have
x^2 - 82 = 18
Add 82 to both sides of the equation
So, we have the following representation
x^2 = 100
Take the square root of both sides
x = -10 and x =10
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i need help on this I don't understant this.
Answer:
a line
Step-by-step explanation:
2 points make a line
Answer A Line
Step-by-step explanation:
a student in a statistics class decided to analyze the number of candies per package for a project. a dot plot of the counts of candies in one package is shown below. what was the most common number of candies in a package?
To determine the most common number of candies in a package, the student would need to examine the dot plot and identify the value(s) with the highest frequency.
A dot plot is a type of graph that can be used to display the distribution of data by plotting individual observations as dots on a number line. To determine the most common number of candies in a package, the student would need to look at the dot plot and identify which value appears most frequently.
Typically, the most common number of candies in a package, also known as the mode, would be the value that has the highest number of dots plotted on the number line. If there are multiple values that have the highest frequency, then the data set is considered to have multiple modes. If all values in the data set appear with equal frequency, then the data set is considered to have no mode.
Thus, In conclusion, to determine the most common number of candies in a package, the student would need to examine the dot plot and identify the value(s) with the highest frequency.
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The most common number of candies in a package is 60
To analyze the number of candies per package for the project
60 candidates make up the majority of packages.
For a project in statistics class, a student chose to examine how many candies are contained in each container.
The maximum number of dots in a dot plot of the candy counts in one package is 60.
60 are the maximum limit of candies that can be placed in each and every package so these are the maximum number of candies that can be placed
The average candidate package has 60
So the most number of candies in each package are 60
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The midpoint of AB is (−2,1) M(−2,1). If the coordinates of A are (1,−2) (1,−2), what are the coordinates of B?
By definition of midpoint, the coordinates of B is (- 5, 4).
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
We have to given that;
The midpoint of AB is M (-2, 1).
And, The coordinates of A are (1,−2).
Now, Let the coordinate of B = (x, y)
Then, By definition of midpoint we get;
⇒ (1 + x) / 2 = - 2
⇒ 1 + x = - 4
⇒ x = - 4 - 1
⇒ x = - 5
⇒ (- 2 + y) / 2 = 1
⇒ - 2 + y = 2
⇒ y = 2 + 2
⇒ y = 4
Thus, The coordinate of B = (- 5, 4)
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Riggoletto's Portraits specializes in making circular portraits of people. A large portrait is 18 in. In diameter. A medium portrait is 6 in. In diameter. Estimate the difference between the areas of the two sizes of portraits. Use 3. 14 for T. Round your answer to the nearest whole number.
The estimated difference between the areas of the two sizes of portraits is 226.
First, find the area of the large portrait:
A = πr^2 = π(9)^2 = 3.14 * 81 = 253.94
Next, find the area of the medium portrait:
A = πr^2 = π(3)^2 = 3.14 * 9 = 28.26
Finally, subtract the area of the medium portrait from the area of the large portrait to find the difference:
253.94 - 28.26 = 225.68
Rounding to the nearest whole number, the difference is 226.
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HURRY UP NOW I DON'T HAVE TIME TO WAIT
The area of the pool is 113.04 ft².
How to find the area of the pool?The diagram shows a circle inside a square. The circular surface is the pool and it is surrounded by the square deck. The diameter of the pool can be chosen from 12 to 24 feet.
The blue shaded region is the area of the pool. Therefore, let's find the area of the pool as follows:
area of the pool(area of a circle) = πr²
where
r = radius of a circleTherefore,
r = diameter / 2 = 12 / 2 = 6 feet
Hence,
area of the pool(area of a circle) = 3.14 × 6²
area of the pool(area of a circle) = 3.14 × 36
area of the pool(area of a circle) = 113.04 ft²
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common core prec-calc answers
The output of the function can be calculated by plugging in 2 for x and evaluating the equation:[tex]f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.[/tex]
The Common Core standards for Pre-Calculus focus on the study of functions and their applications, as well as the development of a deeper understanding of the algebraic and geometric principles in the mathematical field. One of the core concepts covered in Pre-Calculus is the concept of polynomial functions. A polynomial function is an expression made up of terms that involve only constants, variables, and exponents. It is represented by the equation [tex]f(x) = ax^n + bx^n-1 + cx^n-2 + … + z[/tex], where a, b, c, …, z are constants and n is a non-negative integer. To find the value of a polynomial function at a given value of x, the equation can be evaluated by plugging in the x value and calculating the output. For example, if a polynomial function is represented by the equation f(x) = 2x^3 + 5x^2 - 7x + 4, and the x value is 2, then the output of the function can be calculated by plugging in 2 for x and evaluating the equation: [tex]f(2) = 2(2^3) + 5(2^2) - 7(2) + 4 = 16 + 20 - 14 + 4 = 26.[/tex]
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Complete question:
What is the output of the polynomial function f(x) = 2x^3 + 5x^2 - 7x + 4 when x = 2?
write the following symbolically 'Triangle is equilateral or isosceles'.
Answer: Let p: Triangle is equilateral. Let q: Triangle is isosceles. Then the symbolic form of the given statement is p ∨ q.
Step-by-step explanation:
what is the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal and 8th octagonal numbers?
The sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
What is triangle ?
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.
The nth triangular number is given by the formula: n(n+1)/2
The nth square number is given by the formula: n^2
The nth pentagonal number is given by the formula: n(3n-1)/2
The nth hexagonal number is given by the formula: n(2n-1)
The nth heptagonal number is given by the formula: n(5n-3)/2
The nth octagonal number is given by the formula: n(3n-2)
So, the sum of the 3rd triangular number, 4th square number, 5th pentagonal number, 6th hexagonal number, 7th heptagonal number and 8th octagonal number can be calculated as follows:
Triangular number: 3 * (3 + 1) / 2 = 6
Square number: 4^2 = 16
Pentagonal number: 5 * (3 * 5 - 1) / 2 = 35
Hexagonal number: 6 * (2 * 6 - 1) = 91
Heptagonal number: 7 * (5 * 7 - 3) / 2 = 98
Octagonal number: 8 * (3 * 8 - 2) = 128
The sum of these numbers is: 6 + 16 + 35 + 91 + 98 + 128 = 384.
So, the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
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The sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.
The nth triangular number is given by the formula: n(n+1)/2
The nth square number is given by the formula: n^2
The nth pentagonal number is given by the formula: n(3n-1)/2
The nth hexagonal number is given by the formula: n(2n-1)
The nth heptagonal number is given by the formula: n(5n-3)/2
The nth octagonal number is given by the formula: n(3n-2)
So, the sum of the 3rd triangular number, 4th square number, 5th pentagonal number, 6th hexagonal number, 7th heptagonal number and 8th octagonal number can be calculated as follows:
Triangular number: 3 * (3 + 1) / 2 = 6
Square number: 4² = 16
Pentagonal number: 5 * (3 * 5 - 1) / 2 = 35
Hexagonal number: 6 * (2 * 6 - 1) = 91
Heptagonal number: 7 * (5 * 7 - 3) / 2 = 98
Octagonal number: 8 * (3 * 8 - 2) = 128
The sum of these numbers is: 6 + 16 + 35 + 91 + 98 + 128 = 384.
So, the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
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Which is the graph of f(x) = 2(3)?
The graph of the exponential function:
f(x) = 2*(3)^x
Is the first one.
Which one is the graph of f(x) = 2*(3)^x?We want to find the graph of the exponential function:
f(x) = 2*(3)^x
To identify it, you can evaluate the function in some different values of x.
if x = 0
f(0) = 2*(3)^0 = 2
if x = 1
f(1) = 2*3^1 = 6
if x = 2
f(2) = 2*(3)^2 = 18
So we have the 3 points:
(0, 2), (1, 6), (2, 18)
The only graph that passes through these points is the first one, so that is the correct option.
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draw a curve through these points that illustrates the relationship between balloon rides and price when the temperature is constant at 50 degrees.
The curve for the relationship between balloon rides and price when the temperature is constant at 50 degrees is illustrated below.
The term constant in math is defined as a value or number that never changes in expression it's constantly the same.
When the temperature is constant, it means that one of the variables that can affect the demand for balloon rides is eliminated. This allows us to focus on the relationship between balloon rides and price. The relationship between these two variables can be represented by a curve. The curve can show us how the price of a balloon ride changes as the number of rides changes.
Then table for the relationship between balloon rides and price when the temperature is constant at 50 degrees is attached below.
when the temperature is constant, the relationship between balloon rides and price can be shown by a curve. The shape of the curve will depend on the relationship between the two variables, which can be upward-sloping, downward-sloping, or remain constant. The constant temperature allows us to focus on the relationship between balloon rides and price without the interference of other factors that can affect the demand for rides.
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How to convert ounces (oz) to pints?
1 fluid Pint (U.S.) = 16 fluid Ounces (US)
How to convert ounces to pints?We assume you are converting between ounce [US, liquid] and pint [US, liquid].You can view more details on each measurement unit:The ounce is any of several different units of mass, weight or volume and is derived almost unchanged from the uncia, an Ancient Roman unit of measurementThe avoirdupois ounce is 1⁄16 avoirdupois pound; this is the United States customary and British imperial ounceThe pint is a unit of volume or capacity in both the imperial and United States customary measurement systems. In both of those systems it is traditionally one eighth of a gallon. The British imperial pint is about 20% larger than the American pint because the two systems are defined differently.To learn more about ounces to pints refers to:
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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
y=4x, y=5x2
Answer:
Step-by-step explanation:
y=0,16/5
Find the general solution of the given differential equation. dy/dx + y = e^7x y = Give the largest interval I over which the general solution is defined.
The largest interval I over which the general solution is defined is (-∞, ∞).
What do you mean by differential equation?A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.
A differential equation can be thought of as an equation that describes how a function changes over time. For example, the velocity of an object is the derivative of its position with respect to time. If the position of the object is modeled by a function, then its velocity can be described by a differential equation.
ODEs deal with functions of a single variable and their derivatives, while PDEs deal with functions of multiple variables and their partial derivatives.
The given differential equation is a first-order linear ordinary differential equation with constant coefficients:
dy/dx + y = e⁷ˣ
This equation can be solved using the method of integrating factors. The integrating factor is given by e^∫1 dx = e^x. Multiplying both sides of the equation by the integrating factor, we get:
eˣ(dy/dx) + eˣ y = e⁸ˣ
Integrating both sides, we get:
eˣ y = e⁸ˣ - eˣ + C, where C is an arbitrary constant of integration.
Dividing both sides by eˣ, we get the general solution:
y = e⁷ˣ + Ce⁻ˣ
The largest interval I over which the general solution is defined is (-∞, ∞).
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A 2-column table with 4 rows. Column 1 is labeled statement with entries tangent (2 x), = tangent (x + x), = startfraction tangent (x) + tangent (x) over 1 minus tangent (x) tangent (x) endfraction, = startfraction 2 tangent (x) over 1 minus tangent squared (x) endfraction. Column 2 is labeled reason with entries given, 1, 2, 3. The table shows the derivation of tan(2x). Select the correct reason for each step. Reason 1 is. Reason 2 is. Reason 3 is.
The application of the identity tan(a+b) = (tan(a)+tan(b))/(1-tan(a)tan(b)).the result tan(2x) = 2*tan(x)/(1 - tan²(x)).
Statement | Reason
Tangent (2x) | Given= tangent (x + x) | 1= startfraction tangent (x) + tangent (x) over 1 minus tangent (x) tangent (x) endfraction | 2= startfraction 2 tangent (x) over 1 minus tangent squared (x) endfraction | 3.Reason 1 is the application of the identity tan(a+b) = (tan(a)+tan(b))/(1-tan(a)tan(b)). Reason 2 is the application of the identity tan(2x) = 2*tan(x)/(1 - tan²(x)). Reason 3 is the result of the two previous steps, which is the solution to tan(2x). By applying the identities, we have derived the result tan(2x) = 2*tan(x)/(1 - tan²(x)).
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Answer:
Reason 1 is - Addition
Reason 2 is - Tangent Sum Identity
Reason 3 is - Simplify
Step-by-step explanation:
edge
There are 13 yellow and 7 pink flowers in The garden Jacob picks 9 flower hóquei mano flawer are in The garden nos?
Find an equivalent fraction for each fraction using 12 as a common denominator of 4/6
The equivalent fraction to 4/6 with a denominator of 12 is:
4/6 = 8/12
How to find an equivalent fraction?If we have any fraction a/b, to find a equivalent fraction we just need to multiply both numerator and denominator by the same number (different than zero)
Here we want to find an equivalent fraction to 4/6, such that the new denominator is 12, then we can multiply both numerator and denominator by 2.
We will get:
4/6 = (2*4)/(2*6) = 8/12
So these two are equivalent fractions:
4/6 = 8/12.
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there are 36 possible outcomes for rolling two dice (6 outcomes for the first dice times 6 outcomes for the second dice.) what is the probability of both dice coming up with the same number?
The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences.
What is meant by probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability. Calculating a result or an event's likelihood is known as simple probability. To calculate the likelihood of having to pay out a claim, insurance firms employ probability statistics. A simple probability is computed by dividing a particular result by all potential results.
There are now 36 distinct ways the dice can land when two of them are rolled. This amount is calculated by multiplying the first die's possible outcomes (six) by the second die's possible outcomes (six). 6 x 6 = 36.
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let -1 4 4 , 2 -7 -12 , and -2 6 . for what value of is in the plane spanned by and ?
Value of is in the plane spanned will be -2[1,2,-1] - 3[-2,-1,1] = [4,-1,-1].
If y is on the plane covered by v1 and v2, v1 and v2 can be combined linearly to form y.
Y is equal to av1 plus bv2, where a and b are constants.
[4,-1,h] = a[1,2,-1] + b[-2,-1,1]
According to the laws of vector addition and multiplication, [4,-1,h] = [a - 2b,2a - b, -a + b]. A vector is equal if each of its components is equal.
4 = a - 2b
-1 = 2a - b
h = -a + b
From the first two equations, we can solve for a and b to obtain h:
a = -2
b = -3
h = -1
As we can see, -2[1,2,-1] - 3[-2,-1,1] = [4,-1,-1].
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Full Question:
For what value of h is y in the plane spanned by v1 and v2?
write 6x+3y=24 in slope-intercept form
Answer:
the answer to it is y = -2x + 8
Step-by-step explanation:
Answer:
6x-3y=12 equals -3y=-6x+12 equals y=2x-4. In slope-intercept form; y=mx+c, m is slope and c is the y-value of the intercept; (0,y). So the slope is 2, and the y-intercept is -4 or (0,-4). answer.
Step-by-step explanation:
pls, tell me if wrong have a good day/night<3
Find The Slope Of The Graph Of The Function At The Given Point F(T) = 5 - 3/5t (1/4, 13/5)
Answer:
The slope of a graph at a point can be found by computing the derivative of the function at that point. The derivative of the function f(t) = 5 - 3/5t is:
f'(t) = -3/5
So the slope of the graph of the function at the point (1/4, 13/5) is -3/5.
determine whether the set s spans r2. if the set does not span r2, then give a geometric description of the subspace that it does span. s = {(−1, 4), (4, −1), (3, 3)}
After solving the set we get three unknowns and two equation. So the set S does not spans r^2.
A geometric description of the subspace:
s = {(−1, 4), (4, −1), (3, 3)}
Let the element of R^2 be (x, y).
(x, y) = [tex]c_{1}[/tex](-1, 4) + [tex]c_{2}[/tex](4, −1) + [tex]c_{3}[/tex](3, 3)
(x, y) = (-1[tex]c_{1}[/tex] + 4[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex], 4[tex]c_{1}[/tex] - 1[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex],)
Now the value of
x = -1[tex]c_{1}[/tex] + 4[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex]
y = 4[tex]c_{1}[/tex] - 1[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex]
x - y = -1[tex]c_{1}[/tex] + 4[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex] - (4[tex]c_{1}[/tex] - 1[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex])
x - y = -1[tex]c_{1}[/tex] + 4[tex]c_{2}[/tex] + 3[tex]c_{3}[/tex] - 4[tex]c_{1}[/tex] + 1[tex]c_{2}[/tex] - 3[tex]c_{3}[/tex]
As we can see that there have three unknown and two equations. So we can not solve them. So the set S does not span R^2.
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an urn contains 5 red, 6 blue, and 8 green balls. if a set of 3 balls is randomly selected, what is the probability that each of the balls will be
The probability that each of the balls will be of a different color is approximately 0.084.
To calculate the probability that each of the balls will be of a different color, we need to consider all possible combinations of 3 balls from the urn. There are a total of 19 balls in the urn, so there are 19 choose 3, or 19!/(3! * (19-3)!) = 191817/3! = 969 possible combinations.
Of these 969 combinations, there are
5 choose 1 * 6 choose 1 * 8 choose 1 = 5 * 6 * 8 = 240 combinations where each of the 3 balls is of a different color. So, the probability that each of the balls will be of a different color is 240/969 = 0.084, or approximately 0.084.
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5. Parallelogram AB'C' D' was obtained by dilating parallelogram ABCD using A as
the center of dilation.
B
В'
A
D
a. What was the scale factor of the dilation?
b. How many congruent copies of ABCD have we fit inside AB'C' D'?
c. How does the area of parallelogram AB'C' D' compare to parallelogram
ABCD?
D'
d. If parallelogram ABCD has area 12 square units, what is the area of
parallelogram AB'C' D'?
A parallelogram is a two-dimensional shape with four straight sides that are parallel to one another and with opposite sides that are of equal length. The parallel and equal lengths of the opposing sides give the shape its name.
What is the dilating parallelogram?A rectangle that has been extended or contracted in one direction, or two congruent adjacent rectangles combined, can be used to describe a parallelogram.
a. The scale factor, when a dilation is carried out with centre of dilation A, is the ratio of the lengths of the corresponding sides of the pre-image and image. If the parallelograms ABCD and AB'C'D' have equivalent sides with lengths of AB and AB', respectively, the scaling factor is AB'/AB.
b. Set n equal to the total number of parallelograms ABCD that can fit inside parallelogram AB'C'D'.
Then, by multiplying the area of the parallelogram AB'C'D' by the area of the parallelogram ABCD, the area of the parallelogram AB'C'D' is equal to n times the area of the parallelogram ABCD.
c. The area of the parallelogram AB'C'D' is exactly proportional to the area of the parallelogram ABCD; as a result, if the scale factor of the dilation is k, the area of the parallelogram AB'C'D' is equal to k2 times the area of the parallelogram ABCD.
d. If the area of parallelogram ABCD is 12 square units, then the area of parallelogram AB'C'D' is equal to k2, or k2 times, the area of parallelogram ABCD.
Therefore, A parallelogram's adjacent sides and opposite sides combine to form a pair of neighbouring angles and two parallel lines, respectively.
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