The properties of a vector space are satisfied Properties 1,2, 5(a) and 5(c) are satisfied, the relaxation of the homes aren't legitimate are if[tex]v = x ^ 2 1× v=1^ ×x ^ 2 = 1 #V[/tex]
Property three does now no longer follow: Suppose that Property three is legitimate, shall we name[tex]v = a * x ^ 2 +bx +c[/tex]the neuter of V. Since v is the neuter, then O have to be constant with the aid of using the neuted, consequently [tex]0 = O + v = (O x ^ 2 + Ox + O) + (a × x ^ 2 + bx + c) = c × x ^ 2 + b ^ 2 + a[/tex]
= 0 If O is the neuter, then it ought to restore x², but [tex]0+ x² = (0x²+0x+zero) + (x²+0x+zero) = 1.[/tex]This is a contradiction due to the fact x² isn't 1. We finish that V doesnt have a neuter vector. This additionally method that belongings four would not observe either. A set with out 0 cant
have additive inverse
[tex]Let r= v ×2x ^ 2 + v × 1x +v0 , w= w ×2x ^ 2 + w × 1x +w0 . We have that\\v+w= (vO + wO) ^ x^ 2 +(vl^ × wl)^ x+ ( v 2^ × w2)• w+v= (wO + vO) ^x^ 2 +(wl^ × vl)x+ ( w 2^ ×v2)[/tex]
Since the sum of actual numbers is commutative, we finish that v + w = w + v Therefore, belongings 5(a) is valid.
Property 5(b) isn't valid: we are able to introduce
a counter example. we could use z = 1 then[tex]v = x ^ 2 w = x ^ 2 + 1\\(v + w) + z = (x ^ 2 + 2) + 1 = 3x ^ 2 + 1[/tex]
v + (w + z) = x ^ 2 + (2x ^ 2 + 1) = x ^ 2 + 3
Since 3x ^ 2 +1 ne x^ 2 +3. then the associativity rule doesnt hold.
[tex](1+2)^ * (x^ 2 +x)=3^ * (x ^ 2 + x) = 3x + 3\\1^ × (x^ 2 +x)+2^ × (x ^ 2 + x) = (x + 1) + (2x + 2) = 3x ^ 2 + x ( ne 3x + 3 )\\(1^ ×2)^ ×(x^ 2 +x)=2^ × (x ^ 2 + x) = 2x + 2\\1^ × (2^ × (x ^ 2 + x) )=1^ × (2x+2)=2x^ 2 +2x( ne2x+2)[/tex]
Property f doesnt observe because of the switch of variables. for instance, if v = x ^ 2 1 × v=1^ × x ^ 2 = 1 #V
Properties 1,2, 5(a) and 5(c) are satisfied, the relaxation of the homes arent legitimate.
Step-with the aid of using-step explanation:
Note that each sum and scalar multiplication entails in replacing the order from that most important coefficient with the impartial time period earlier than doing the same old sum/scalar multiplication.
Property three does now no longer follow: Suppose that Property three is legitimate, shall we name v = a × x ^ 2 +bx +c the neuter of V. Since v is the neuter, then O have to be constant with the aid of using the neuted, consequently[tex]0 = O + v = (O × x ^ 2 + Ox + O) + (a × x ^ 2 + bx + c) = c × x ^ 2 + b ^ 2 + a[/tex]
= zero If O is the neuter, then it ought to restore x², but zero [tex]+ x² = (0x²+0x+zero) + (x²+0x+zero) = 1.[/tex]This is a contradiction due to the fact x² isn't 1. We finish that V doesnt have a neuter vector. This additionally method that belongings four would not observe either. A set with out 0 cant have additive inverse
Let [tex]r= v × 2x ^ 2 + v × 1x +v0 , w= w2x ^ 2 + w × 1x +w0 . \\We have thatv+w= (vO + wO) ^ x^ 2 +(vl^ wl)^x+ ( v 2^ w2)w+v= (wO + vO) ^ x^ 2 +(wl^ vl)x+ ( w 2^v2)[/tex]
Since the sum of actual numbers is commutative, we finish that v + w = w + v Therefore, belongings 5(a) is valid.
Property 5(b) isn't valid: we are able to introduce
a counter example. we could use[tex]z = 1 then v = x ^ 2 w = x ^ 2 + 1(v + w) + z = (x ^ 2 + 2) + 1 = 3x ^ 2 + 1v + (w + z) = x ^ 2 + (2x ^ 2 + 1) = x ^ 2 + 3\\Since 3x ^ 2 +1 ne x^ 2 +3.[/tex]then the associativity rule doesnt hold.
Note that each expressions are same because of the distributive rule of actual numbers. Also, you could be aware that his assets holds due to the fact in each instances we 'switch variables twice.
[tex]· (1+2)^ * (x^ 2 +x)=3^ * (x ^ 2 + x) = 3x + 31^ * (x^ 2 +x)+2^ * (x ^ 2 + x) = (x + 1) + (2x + 2) = 3x ^ 2 + x ( ne 3x + 3 )(1^ * 2)^ * (x^ 2 +x)=2^ * (x ^ 2 + x) = 2x + 21^ * (2^ * (x ^ 2 + x) )=1^ ×* (2x+2)=2x^ 2 +2x( ne2x+2)[/tex]
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if the area of the vegetable garden is 170 square feet, which equation could be use to find the length of the tomato patch? select the correct answer.
a triangle has altitudes of length 21, 28, and 60 and perimeter 420. find the length of the shortest side of the triangle. (a) 70 (b) 75 (c) 84 (d) 90 (e) 105
A triangle field has sides that are 6:7:8 and a perimeter of 420 meters.
What is the Perimeter of a Triangle?The total of a triangle's three sides is the perimeter. The Greek words "peri" (which means around) and "metron," which means measure, are combined to get the English word perimeter. The perimeter of any 2D shape is the total distance encircling it. Since a shape's perimeter indicates how long its boundary is, it is stated in linear units.Triangle's perimeter in Real Life: Consider that we need to fence the below-shown triangle park. We now add the lengths of the park's three sides to determine the fence's size. The perimeter of a triangle refers to the length or distance of the triangle's edge.Hence, A triangle field has sides that are 6:7:8 and a perimeter of 420 meters.
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A garden measuring 1515 by 2424 feet is to be completely bordered by a fence. Fencing costs $2$2 per foot. What is the total cost to fence the entire garden?$360.00$360.00$78.00$78.00$39.00$39.00$156.00
The entire garden needs to be fence for a total of $156.
Given that,
A fence is required to entirely enclose a garden that is 15 by 24 feet in size. Each foot of fencing costs $2.
To find : The overall cost of fencing the garden?
Dimensions are given by 15 feet and 24 feet
Cost per foot is $2
Total perimeter of garden is given as 2(l+b)
P = 2(l+b)
P= 2(15+24)
P = 78 feet
1 feet = $2
78 feet = 78 * 2 = $156
Therefore, the total cost required to fence the entire garden is $156
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calculated. If the net force on the body is not zero, as is true for most of the beams in this part, then the torque will depend on the point about which you calculate the torque. Part F Consider (Figure 2) in Part E. For which diagrams is the angular momentum constant? Type alphabetically the letters corresponding to the correct diagrams. For instance, if you think that only diagrams A, B, and C answer the question, type ABC. You may have noticed that nearly every translational Figure 2 of 2 > View Available Hint(s) Α Hint 1. Determining when angular momentum is constant 6N 1/4 /4, 1/4, 1/4 1/4, 1/4 1/4, 1/4 CD 6N 14N 20 N Submit Previous Answers Request Answer с 120 Nf20N L 4 L/4 20N 12 N X Incorrect; Try Again; One attempt remaining 1/4 1/4 L4L/4, 1/4 6N4N 2N Part G Complete previous part(s)
The correct answer is that B and C both have constant torque.
a)The torque about the left side (i.e -1)
T = (8-28-3)c/4= -232/4.
b)The torque about the left side (i.e -1)
T = (8+24-12-20)c/4 = 0
c) The torque about the left side (i.e -1)
T = (20+60-80)c/4 = 0
d)The torque about the left side (i.e -1)
T = (24-6-12-8)c/4 = -2c/4
The net force is the vector sum of forces appearing on a particle or object. The net pressure is a single force that replaces the impact of the unique forces on the particle's movement. It gives the particle equal acceleration as all the one's real forces together as described by Newton's second law of motion.
The internet pressure is whilst a body is in motion and plenty of forces are energetic on it like gravitational force [tex]F_{g}[/tex], frictional pressure [tex]F_{f}[/tex], and the everyday force. consequently, the net force formula is given by way of.[tex]F_{Net}[/tex] = [tex]F_{a}[/tex]+ [tex]F_{g}[/tex] + [tex]F_{f}[/tex] + [tex]F_{N}[/tex].The net force is the vector sum of all the forces appearing on an item. while an object is in equilibrium (either at rest or shifting at a regular pace), the net pressure acting on its miles is 0. The greater the net force performing on the object, the greater its acceleration will be. Newton's second law of movement summarizes those relationships. The equation for acceleration above can be rewritten to solve for net force as internet pressure = Mass ×Acceleration, or F = m × a.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The total cheese production in 2006 was about 7.7 billion pounds and the total cheese production in 2014 was about 9.7 billion pounds
The total cheese production in 2006The equation of the function is given as
y = 7(1.03)ˣ
From the question, we understand that:
x represents the number of years after 2003
So, we calculate x when the year is 2006 using
x = 2006 - 2003 = 3
Substitute x = 3 in the equation y = 7(1.03)ˣ
y = 7(1.03)³
Evaluate the equation
y = 7.7 (approximately)
The total cheese production in 2014We calculate x when the year is 2014 using
x = 2014 - 2003 = 11
Substitute x = 11 in the equation y = 7(1.03)ˣ
y = 7(1.03)¹¹
Evaluate
y = 9.7 (approximately)
Hence, the amount of cheese is 9.7 billion pounds
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What doubles fact can help you find 7 8?.
The doubles fact for 7 8 is 7+7+1=15.
In simple words, Double Plus One Fact is a strategy for adding two consecutive numbers . To get final result then simply add a smaller number to itself or double it then and add 1.
The numbers that are added together are known as doubles. For example, 5+5=10, 3+3=6, so the doubles plus one fact are simply adding 1 to the resultant of the double fact.
For given, the doubles fact is 7+7=14, then add 1 to get 15.
As a result, 7+7+1=15 is the doubles fact for 7 8.
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Niamh carrie out an experiment dropping piece of toat to ee if they land jam up or jam down. Here are her reult. Complete the miing relative frequency value in the table. (1 mark)
Using Relative frequency formula ,
We can easily compute the relative frequency missing terms in given table.
the missing terms in relative frequency are 0.14,0.2,0.26
Relative frequency:
Relative frequency can be defined as the number of occurrences of an event divided by the total number of events occurring in a given scenario.
To calculate the relative frequency,
Relative frequency = f / n
Creating a relative frequency table is a two-step process:
Create a table with category names and counts.Add a second column called "relative frequency". I shortened it to rel. freq. here for space.Determine your first relative frequency by dividing the count by the total count.Complete the rest of the table by determining the remaining relative frequencies.we have given a table of values of experiment results carried by Nimah .
we have to find out the relative frequency for given data .
total frequency= 10+11+15+17+20 = 75
dropping
toat piece frequency relative frequency
3 10 10/75 = 0.13
4 13 11/75= 0.14
5 15 15/75= 0.2
6 17 17/75 = 0.22
7 20 20/75 = 0.26
Hence, we computed the relative frequency table for given data.
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Complete question:
Niamh carrie out an experiment dropping piece of toat to ee if they land jam up or jam down. Here are her reult. Complete the miing relative frequency value in the table. (1 mark)
total frequency terms are 75 .
given data :
dropping
toat piece frequency relative frequency
3 10 0.13
4 13
5 15
6 17 0.22
7 20
Which congruence theorem can be used to prove that the triangles are congruent?.
Side Angle Side(SAS) , theorem can be used to prove that ABC is congruent to DCA.
What is congruency?Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them.Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another. We will see that they will superimpose, or be positioned entirely on top of, one another. This demonstrates the congruence of the two circles.The circles below may be put perfectly over one another and have the same radius, hence they are considered to be congruent. The congruence of figures is represented by the symbol "". Circle A and circle B are congruent, hence we may say the following: A + B = Circle A.According to our question-
The SAS congruency theorem,
two triangles are congruent if any pair of corresponding sides and their included angles are identical in both triangles. In this scenario,
the pair of corresponding sides AB with DC and AD with DA
and their included angles BAD with CDA are equal.
Hence, Side Angle Side(SAS) , theorem can be used to prove that ABC is congruent to DCA.
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Dole Pineapple, Inc., is concerned with the 16-ounce can of sliced pineapple is being overfilled. Assume the standard deviation of the process is .03 ounces. The quality control department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounces. At the 5% level of significance, can we conclude that the mean is greater than the 16 ounces? Determine the p-value.
The required value Z = 11.792 >1.96 at a 0.05 level of significance.,he null hypothesis is rejected,the alternative hypothesis is accepted at a 0.05 level of significance.
As the mean weight is less than 16 ounces.
How to solve the P-value ?Given that the mean of the Population = 16
Given that the standard deviation of the process
σ = 0.03 ounce
Given that the mean of the sample = 16.05 ounces
Null hypothesis: H₀:μ > 16 ounces
Alternative HypothesisH₁: μ <16 ounces
According to given data:Z = x-mean/SD/√n
Z = 16.05-16/0.03/√50
Z = 11.792
Level of significance = 0.05
Z₀.₀₅ = 1.96
The required Z = 11.792 >1.96 at 0.05 significant level,null hypothesis is rejected and alternate hypothesis is accepted.
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What 2 numbers make 22 but have a range of 5
Range = 12
■ Maximum value = 10.
■ Minimum value = -2
■ Count of numbers within the set = 13
if a confidence interval for the difference between a pair of treatment means includes 0, then we reject the null hypothesis that there is no difference in the pair of treatment means. group startstrue or false true, unselected false, unselected group ends
We reject null hypothesis in which there is no difference here between pair of treatment means if the confidence interval for that difference contains zero; this is a "true" statement.
Define the term null hypothesis?A statistical conjecture known as a null hypothesis asserts that certain features of such a population or content process are not different from one another.
Any variation between the selected attributes that you observe in a collection of data is thought to be the result of chance, according to the null hypothesis. Because rejecting the null hypothesis is a firm conclusion, analysts aim for it. Strong evidence for this is needed in the form of just an observed difference that cannot be explained by chance alone. Failure to reject the null hypothesis, which states that outcomes can only be explained by chance, is a weak conclusion since it acknowledges that there may be forces at play that the statistical test is not sensitive enough to detect.Thus, we reject null hypothesis in which there is no difference here between pair of treatment means if the confidence interval for that difference contains zero; this is a "true" statement.
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help, I've been stuck on this for forever... rise/run
The slope of the line in the simplest form is 1 / 2.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
The slope is rise over run.
The slope of the line can be found as follows:
m = slope = y₂ - y₁ / x₂ - x₁
Therefore, using (7, 0) and (3, -2)
Hence,
x₁ = 7
x₂ = 3
y₁ = 0
y₂ = -2
Therefore,
slope = - 2 - 0 / 3 - 7
slope = - 2 / -4
slope = 1 / 2
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What does it mean for whole numbers to be closed?.
The outcome of the operation belongs to the same set of domains emphasizing the mean for whole numbers to be closed.
A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.
Here,
Closure occurs when an operation on members of a set, such as real numbers, always results in a member of the same set. As a result, the result remains in the same set.
Thus, the outcome of the operation belongs to the same set of domains emphasizing the mean for whole numbers to be closed.
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dave and martin have sweets in the ratio of 2:3 martin gives dave 15 sweets how many sweets does dave have now
The number of sweets that Dave have equals to 18 sweets.
What is the meaning of ratio?In mathematics, a ratio is a metric that shows how many times one number contains another. For instance, if we have 8 oranges and 6 lemons in a bowl of fruit, then, the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.
Given data
Dave and martin ratio = 2:3
Dave is given 15 sweets.
The number of sweets that dave have now is computed as follows:
2/5 = 0.4= 40%
3/5 = 0.6 = 60%
Dave sweets will equals to:
= 15 sweets + (15 sweets * 1/5)
= 15 sweets + 3 sweets
= 18 sweets.
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What are the three steps for finding the mean absolute deviation?.
The three steps for finding the mean absolute deviation are - i)Find the mean of the given observations, ii)Find difference between each observation and calculated mean, iii)Evaluate the mean of the differences obtained in the second step.
Absolute deviation is somewhat same with mean deviation in some extent. The measurement of spread represents the amount of dispersion in a data-set, that is how spread-out are the values of data-set around the central value(example- mean/mode/median).It tells how far away the data points to fall from the central value.
The lower is the value of the measure of spread reflects that the data points are close to the central value. In this case, the values in a data-set are considered as more consistent.Further, the distance of the data points from the central-value, although spread of data points are greater in amount, the values are still not much consistent.To know more about absolute deviation, visit here:
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In triangle def, if m∠d = (4x)°, m∠e = (2x − 3)°, and m∠f = (x 8)°, what is the value of x? 51 29 26 25
Answer:
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180°.
m<D + m<E + m<F = 180°
4x + 2x + m<F = 180
What is the measure of <F? It's not clear in the post.
What is the nature of the roots of the quadratic equation if the discriminant is negative?.
If discriminant is negative then the nature of roots is imaginary.
For a general quadratic equation, [tex]ax^2+bx+c=0[/tex]
the roots of the equation are [tex]\alpha=\frac{-b-\sqrt{b^2-4ac}}{2a}\ and\ \beta=\frac{-b+\sqrt{b^2-4ac}}{2a}[/tex]
Where, [tex]b^2-4ac[/tex] is known as discriminant.
If
Case i) [tex]b^2-4ac > 0[/tex]
then discriminant is positive and the roots α and β of the quadratic equation are real and unequal.
Case ii) [tex]b^2-4ac =0[/tex]
then discriminant is zero and the roots α and β of the quadratic equation are real and equal.
Case iii) [tex]b^2-4ac < 0[/tex]
then discriminant is negative and the roots α and β of the quadratic equation are unequal and not real, it means imaginary.
Case iv) [tex]b^2-4ac > 0[/tex] and perfect square
then discriminant is positive and perfect square and the roots α and β of the quadratic equation are real, rational and unequal.
Hence, if discriminant is negative then the nature of roots is imaginary.
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What are some examples of parallel lines in real life?.
Parallel lines Examples from Real Life
The railway tracks run parallel to each other.The edges of a ruler are parallel to each other.Cricket bats have parallel stumps.On ruled paper, the lines are parallel.White lines run parallel at the zebra crossing.Parallel lines are straight lines that never meet each other no matter how long we extend them. Observe the following figure that shows parallel lines.
Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are complementary, others are congruent (equal).
Hence we get the required answer.
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suppose we observe an unending sequence of days on which the umbrella appears. show that, as the days go by, the probability of rain on the current day increases monotonically towared a fixed point. calculate this fixed point.
The computed probability is computed as <0.8967, 0.1033> which shows that as the days 90 by, the probability of rain on the current day increases monotonically towards a fixed point.
Chance is the branch of arithmetic concerning numerical descriptions of how probable an event is to occur, or how probable it is that a proposition is proper. The chance of an event is a range between zero and 1, wherein, roughly speaking, 0 indicates the impossibility of the occasion and 1 shows actuality. The higher the chance of an occasion, the much more likely it's miles that the event will occur. A simple example is the tossing of a truthful (impartial) coin. because the coin is truthful, the two outcomes ("heads" and "tails") are both similarly possible; the chance of "heads" equals the possibility of "tails"; and on account that no different effects are feasible, the possibility of either "heads" or "tails" is half off (that could additionally be written as zero.5 or 50%).
these standards had been given an axiomatic mathematical formalization in chance ideas, that are used extensively in areas of observation which include records, arithmetic, technology, finance, gambling, artificial intelligence, gadget studying, computer science, sport idea, and philosophy, for example, draw inferences about the expected frequency of events. possibility concept is likewise used to describe the underlying mechanics and regularities of complex structures.
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work out the value of m in the equation below.
give your answer as a decimal.
3(2m+5)=4(9-m)
(pls help with this!!!)
Answer:
Step-by-step explanation:
6m+15=36-m
Plus m to both sides
7m+15=36
Minus 15 from both sides
7m=14
Divide by 2
m=2
f + 8 = b5q could you guys help me i don't understand at all
Answer:
Step-by-step explanation:
are there values for f or b or q? What are we trying to solve?
What is the answer? Please help!!!!
Answer:
a) 14
b) 13
Step-by-step explanation:
P= Purse W= Watch
1P + 1W = 27 (So think about different combinations that make 27)
2P + 1W = 41 (Multiply this by negative 1)
So now you have
1P + 1W = 27
-2P - 1W = -41
You can subtract them
-1P = -14 or 1P = 14
So 1 purse = 14
Now plug it in
14 + 1W = 27 (Subtract 14 from both sides)
1W = 13
So 1 watch = 13
Furthermore, 1 watch = 13 and 1 purse = 14
Is quadratic function non-linear?.
Quadratic functions are one type of non linear function.
Given,
We have to find whether quadratic function non-linear;
The graph is not a straight line if it is non-linear. A non-linear function has a curved line as its graph. A line that continuously changes in direction is said to be curved.
These are the so-called nonlinear functions, and they can take many various shapes. A quadratic function is one of these nonlinear functions, and its typical form is y = ax2 + bx + c. A parabola represents the graph of a quadratic function.
Therefore,
Quadratic functions are one type of non linear function.
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V/7 = 8
One step equation
Help me get the answer?
which of the following would be the scatterplot for the given data? x 1 4 7 12 14 18 y 24 29 30 40 31 44
Answer:
Below is a picture
Step-by-step explanation:
Demos is a free calculator that can do things like this for you.
what is the inductive hypothesis in the proof by strong induction that every integer greater than 1 can be written as the product of primes?
Using the Induction hypothesis,
strong induction that every integer greater than 1 can be written as the product of primes
Induction Hypothesis:
This is the assumption that given a general element a[n], if something is true about the elements of an ordered set, we can show that it is also true for a[n+1]. is. This means it must be true for all elements. A classic example is the proof that the sum of the natural numbers is triangular.
Induction Has Strong and Weak Versions
This is a case where strong induction is needed because factoring n gives no information about the factorization of n+1.
For brevity, we say that even prime numbers are products of prime numbers. So the statement is: "Every number n≥2 is a product of primes". So the steps are:
base case, where we prove n=2.
If n>2 and every number m with 2≤m prove that n is also a product of primes. The
base case is because 2 is prime.
Let n>2. If n is prime, we are done. Otherwise, n=ab and 1 products of prime numbers.
Strong Induction: Base Case: n=2 and n has a factor of 1.2 n is prime:
Assume k is prime or can be expressed as the product of sets of prime factors for all k≤n To do.
We need to show that n+1 is prime or that n+1 can be expressed as the product of a set of prime factors.
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What are the 5 steps to solve a linear equation?.
Answer:
1. Distribute
2. Combine like terms
3. Get all variable on one side and everything else on the other (Inverse operations: Add / subtract)
4. Solve for one of your variables (inverse operation: Multiple / Division
5. Simplify
each of two teams has seven players numbered 1 to 7. in the first game, the two players numbered 1 play each other. the loser of each game is eliminated and replaced by the next player of the same team, until all players from one team have been eliminated. let be the number of possible sequences of games. find the remainder when is divided by 1000.
Remainder formula helps us to find the remainder when total number of possible sequence of games (i.e 3452) is divided by 1000.
The Remainder is 432.
We have given that
Number of players in team A = 7
Number of players in team B = 7
This problem is the same as the number of combinations problem. Let's assume team A is the winner (and we must remember to multiply our final result by 2 to account for the possibility that B is the winner).
A can win exactly 6 of the first k+6 games, and then Game k+7 (ending the series in exactly k+7 games), in (k+66) = (k+6k) ways, so we want
2∑k=06(k+6k).
This is 2⋅(1+7+28+84+210+462+924)= 3432.
Conversely, given a permissible series, allow the losing team to win all of the remaining (unplayed because superfluous) games, and you end up with a 7-7 tie.
Now, we calculate the remainder when 3432 is divided by 1000.
Using Remainder Formula ;
Dividend = Divisor × Quotient + Remainder
3432 = 1000× 2 + 432
so, remainder is 432 .
Hence , toatal number of possible sequence of games is 3432.
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What is SSS AAS SAS ASA?.
Answer:
SSS: Side-Side-Side
AAS: Angle-Angle-Side
SAS: Side-Angle-Side
ASA: Angle-Side-Angle
Step-by-step explanation:
These are all used for triangles and proofs :)
Can you pls do this fast
3x² - 7x + 9 is x² - 11x + 17 less than 2x² + 4x - 8.
The value of the expression, x² - 11x + 17, when x = 2 is: -1.
How to Find the Value of an Expression?To find the value of an expression, simply replace the given value of the variable and solve to simplify.
To find how much less the expression, 3x² - 7x + 9 is less than 2x² + 4x - 8, subtract 2x² + 4x - 8 from 3x² - 7x + 9:
(3x² - 7x + 9) - (2x² + 4x - 8)
3x² - 7x + 9 - 2x² - 4x + 8
Combine like terms
x² - 11x + 17
Substitute x = 2 into the expression:
2² - 11(2) + 17
= -1.
Learn more about value of an expression on:
https://brainly.com/question/625174
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