There is a 75% chance that it will rain here or on Mars is false because there is a 25% chance that it will rain here and not on Mars.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
There is a 50% chance of rain here and a 25% chance of rain on Mars. Therefore, there is a 75% chance that it will rain here or on Mars.
The probability that it will rain here:
P(rain here) = 50%
P(rain on mars) 50%
P(not rain here) = 100 - 50 = 50%
P(not rain on mars) = 100 - 50 = 50%
P(rain here and not on mars) = 0.5×0.5 = 0.25 or 25%
Thus, there is a 75% chance that it will rain here or on Mars is false because there is a 25% chance that it will rain here and not on Mars.
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if x=-2 solve 4x^3-6x^2+x-1
Answer:
-59
Step-by-step explanation:
x = -2
4(-2)³ - 6(-2)² + (-2) - 1
= -32 - 24 - 2 - 1
= - 59
MAT 171
1. The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=-4
Find a possible formula for P(x)
2. The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at x=0 and x=-4. It goes through the point (5, 36).
Find a formula for P(x).
3. The polynomial of degree 3. P(x), has a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=-2. The y-intercept is y=-1.8.
Find a formula for P(x).
Using the Factor Theorem, the polynomials are given as follows:
1. [tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
2. [tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
3. P(x) = -0.1(x³ - 4x² - 3x + 18)
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Item a:
The parameters are:
[tex]a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4[/tex]
Hence the equation is:
P(x) = (x - 1)²x²(x + 4)
P(x) = (x² - 2x + 1)(x + 4)x²
P(x) = (x³ + 2x² - 7x + 1)x²
[tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
Item b:
The roots are:
[tex]x_1 = x_2 = 4, x_3 = 0, x_4 = -4[/tex]
Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)
[tex]P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:
[tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
Item 3:
The roots are:
[tex]x_1 = x_2 = 3, x_3 = -2[/tex]
Hence:
P(x) = a(x - 3)²(x + 2)
P(x) = a(x² - 6x + 9)(x + 2)
P(x) = a(x³ - 4x² - 3x + 18)
For the y-intercept, x = 0, y = -1.8, hence:
18a = -1.8 -> a = -0.1
Thus the function is:
P(x) = -0.1(x³ - 4x² - 3x + 18)
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What is the following answer to 2+2
Answer:
well the answer is 4 have a good day
quest
The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip. On
which day would you expect that number to be reached?
D)
10
Days People
1
26
2
30
3
34
4
38
5
42
6 46
og php?totalQuestions-10&testid-5
strand-5716&element-18789&condition-random #
Answer:
Day 5 ................
What is the approximate area of the shaded sector in the circle shown below
A.29.04 in^2
B.13.51 in^2
C.7.26 in^2
D.6.75^2
Answer:
please provide the diagram
Step-by-step explanation:
for the solution figure is necessary so provides us to solve this problem
Ashley has 100 books that she wants to give away at the rate of n books per week. Write a recursive function that represents the number of books Ashley has at any time.
The recursive function that gives the number of books Ashley has at any time is
=
, starting at
.
The recursive formula would be: 100 - XN = B.
What is Recursive formula?
When a function calls itself and uses its own previous terms to define its subsequent terms, it is called a recursive function. It is the technical recursive function’s definition, i.e., a recursive function builds on itself.
X: represents how many weeks
N: represents books per week
B: represents books she has at anytime
So the recursive formula would be: 100 - XN = B
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Recently, a random sample of 2534 year olds was asked, "How much do you currently have in savings, not including retirement savings?" The data in the table represent the responses to the survey. Approximate the mean and standard deviation amount of savings.
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
The approximations of the mean and the standard deviation are 233.3 and 229.82, respectively
How to determine the mean?The table of values is given as:
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
Rewrite the table to include the class midpoint and the frequency
x f
99.5 345
299.5 97
499.5 52
699.5 21
899.5 9
1099.5 8
1299.5 3
The mean is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{99.5* 345 + 299.5* 97 + 499.5* 52 + 699.5 * 21 + 899.5 * 9 + 1099.5 * 8 + 1299.5 * 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]
Evaluate
[tex]\bar x = 233.331775701[/tex]
Approximate
[tex]\bar x = 233.3[/tex]
Hence, the approximation of the mean is 233.3
How to determine the standard deviation?The standard deviation is calculated as:
[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]
So, we have:
[tex]\sigma= \sqrt{\frac{(99.5-233.3)^2* 345 + (299.5-233.3)^2* 97 +...... + (1299.5 -233.3)^2* 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]
Evaluate
[tex]\sigma = 229.82[/tex]
Hence, the approximation of the standard deviation is 229.82
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Evaluate.
-|a+b| 2-c when a=1 2/3 b=-1 ,and c= -3 Enter your answer as a simplified fraction in the box.
Step-by-step explanation:
-| 12/3 - 1| 2-(-3)
-|12-3/3|5
-5|9/3|
-5|3|
-5×3 & -5×-3
-15 & 15
I think it is the answer
....................
..................................
An equivalent ratio to the tape diagram shown is
to pls i need a answer
An equivalent ratio to the tape diagram shown is 1 to 2
How to determine the equivalent ratio?From the tape diagram, we have:
Red = 2
Blue = 4
Express as a ratio
Red : Blue = 2 : 4
Divide by 2
Red : Blue = 1 : 2
Hence, an equivalent ratio to the tape diagram shown is 1 to 2
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Find the nature of the graph of the function y = 9x4 + 8x - 2 using end
behavior.
the end behavior is:
as x ⇒ ∞, f(x) ⇒∞as x ⇒- ∞, f(x) ⇒∞What is the end behavior of the function?
If we have a polynomial of even degree, then the end behavior in both ends is the same one.
Particularly, in these cases (even degree) we only need to look at the leading coefficient. If it is positive, then as x tends to infinity and negative infinity, the function tends to infinity.
In this case, the polynomial is:
y = 9x⁴ + 8x - 2
Notice that the degree is 4, even, and the leading coefficient is 9 (positive).
Then the end behavior is:
as x ⇒ ∞, f(x) ⇒∞as x ⇒- ∞, f(x) ⇒∞If you want to learn more about end behaviors:
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How can the next term in the infinite sequence 1, 5, 12, 22, 35, be generated? O Square the term number, subtract the term number from the result, multiply by 3, and divide the result by 2. O Square the term number, multiply the result by 3, divide by 2, and subtract the term number from the result. O Square the term number, divide the result by 2, subtract the term number, and multiply the result by 3. O Square the term number, multiply the result by 3, subtract the term number, and divide the result by 2.
Check the forward differences of the sequence.
• first-order differences
5 - 1 = 4
12 - 5 = 7
22 - 12 = 10
35 - 22 = 13
• second-order differences (i.e. differences of the first differences)
7 - 4 = 3
10 - 7 = 3
13 - 10 = 3
The second differences are all 3 (as far as we know), so the sequence of first differences is arithmetic/linear, which means the original sequence is quadratic. Let the [tex]n[/tex]-th term be
[tex]x_n = an^2 + bn + c[/tex]
Given that [tex]x_1=1[/tex], [tex]x_2=5[/tex], and [tex]x_3=12[/tex], we have
[tex]\begin{cases} a + b + c = 1 \\ 4a + 2b + c = 5 \\ 9a + 3b + c = 12 \end{cases} \implies a=\dfrac32, b=-\dfrac12, c=0[/tex]
and so the [tex]n[/tex]-th term of the sequence is generated by the rule
[tex]x_n = \dfrac{3n^2 - n}2[/tex]
which most closely resembles the last option,
Square the term number, multiply the result by 3, subtract the term number, and divide the result by 2.
Find the 10th term of the geometric sequence whose common ratio is 3/2 and whose first term is 8
Answer: 19683/64
Step-by-step explanation:
[tex]a_{n}=8\left(\frac{3}{2} \right)^{n-1}\\\\\implies a_{10}=8 \left(\frac{3}{2} \right)^{10-1}=\boxed{\frac{19683}{64}}[/tex]
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. what is the value of this function
The range of y will be all real numbers such that 0≤y≤40
The complete question is:
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. What is the range of this function? all real numbers such that y ≤ 40 all real numbers such that y ≥ 0 all real numbers such that 0 ≤ y ≤ 40 all real numbers such that 37.75 ≤ y ≤ 40
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute.
The amount of water remaining in the bathtub = y
The function of time in minutes, that it has been draining = x
At 0 minutes the amount of water is 40 gallons.
The highest volume of water is 40 which is decreasing at the rate of 1.5 gallons per minute.
The given function is a linear function
y = 0
However, the volume of water can be 0 but cannot ever be negative.
Therefore the range of y will be all real numbers such that 0≤y≤40
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x(x - 5) = -4
Solve the equation, using the quadratic formula.
The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Find the range, sample variance, and sample standard deviation of the numbers of medals won by these countries. 1 2 3 3 4 9 9 11 11 11 14 14 19 22 23 24 25 29
The range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.
What is a Range?A range is given to a parameter to allow maximum leverage to the parameter. for example, if a vendor wants a rod of diameter 20 cm, then he may give a range of ±1 cm., which means he will accept the rod of 19(20-1) cm to 21(20+1) cm.
The range of the numbers of medals won by these countries is,
Range = Max - Min = 29 - 1 = 28
To find the standard deviation we need to know the following details,
Sum of the number of medals = ∑x = 234Sum of the square of the number of medals = ∑x² = 4372Number of observations = n = 18Now, the standard deviation of medals won by these countries is,
[tex]\sigma = \sqrt{\dfrac{\sum x^2 - \frac1n (\sum x)^2}{n-1}}\\\\\sigma = \sqrt{\dfrac{\4372 - \frac{234^2}{18}}{18-1}}\\\\\sigma = 8.845[/tex]
The variance of the numbers of medals won by these countries is,
v = σ²
v = 78.2353
Hence, the range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.
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Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
The area of the region bounded by the line y =3x -6 and line y=-2x+8 is 12/5 units
How to find the area?y = 3x - 6
y = -2x + 8
Set these two equations equal to each other.
3x - 6 = -2x + 8
Add 2x to both sides of the equation.
5x - 6 = 8
Add 6 to both sides of the equation.
5x = 14
Divide both sides of the equation by 5.
x = 14/5
Find the y-value where these points intersect by plugging this x-value back into either equation.
y = 3(14/5) - 6
Multiply and simplify.
y = 42/5 - 6
Multiply 6 by (5/5) to get common denominators.
y = 42/5 - 30/5
Subtract and simplify.
y = 12/5
These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.
Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.
Set both equations equal to 0.
(I) 0 = 3x - 6
Add 6 both sides of the equation.
6 = 3x
Divide both sides of the equation by 3.
x = 2
Set the second equation equal to 0.
(II) 0 = -2x + 8
2x = 8
x = 4
The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.
The height of the triangle is 12/5 units.
A = 1/2bh
Substitute 2 for b and 14/5 for h.
A = (1/2) · (2) · (12/5)
A = 12/5
The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.
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Rob bought a pair of jeans at 30% off the original price. If the original price was $55, how much did he pay for the jeans?
Answer:
$38.50
Step-by-step explanation:
(100-30)% of $55
= 70% of $55
= $38.50
Hope this helps :)
A bag of 20 marbles consists of 5 blue marbles, 4 red marbles and 9 yellow marbles. You draw a marble out of the bag, put it back then draw out another marble. Calculate the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw? Write your answer a percentage to the nearest hundredth.
The probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total marbles = 20
Number of blue marbles = 5
P(blue) = 5/20
P(blue∩blue) = P(blue)×P(blue)
= (5/20)(5/20)
= 25/400
= 1/16
= 0.0625 ≈ 0.063
Thus, the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.
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Find the parametric equation of the line that passes through P(1, 0, −3) and is parallel to the line with parametric equations x = −1 + 2t , y = 2−t, and z = 3+3t.
Which is the equation for y?
Answer:
y = -t
Step-by-step explanation:
Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.
⇒ parametric equation of line passing through a point (a₁, b₁, c₁)
and parallel to a vector <a, b, c> is given by :
x =a₁ + at , y = b₁ + bt , z = c₁ + ct
now according to question:
given -
point, P(1, 0, -3)
line, x = −1 + 2t , y = 2−t, and z = 3+3t.
so from the line the vector is= <2, -1, 3>
now using above formula,
equation of line is = x = 1 + 2t , y = −t, and z = -3+3t.
we have to solve for 'y' only,
⇒ y = -t (answer)
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For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.21 probability of failure. Complete parts (a) through (c) below.
Would it be unusual to observe one component fail? Two components?
It
▼
would not
would
be unusual to observe one component fail, since the probability that one component fails,
enter your response here, is
▼
less
greater
than 0.05. It
▼
would not
would
be unusual to observe two components fail, since the probability that two components fail,
enter your response here, is
▼
greater
less
than 0.05.
Using the probability concept, we have that:
a) It would not be unusual to observe one component fail, since the probability that one component fails is greater than 0.05.
b) It would be unusual to observe two components fail, since the probability that two components fail is less than 0.05.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. If a probability is less than 0.05, the event is considered unusual.
In this problem, the probabilities are given as follows:
0.21 probability that one component fails, hence not unusual.(0.21)² = 0.0441 probability that two components fail, hence unusual.More can be learned about probabilities at https://brainly.com/question/14398287
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simplify completely 12x^2 -4x^2+8x over -2x
Answer:
-4*(x+1)
Step-by-step explanation:
Simplify
⇒ 8x2 + 8x/-2x
2: Pulling out like terms
4.1 Pull out like factors :
8x2 + 8x = 8x • (x + 1)
Canceling Out :
4.2 Canceling out x as it appears on both sides of the fraction line
Final result :
-4 • (x + 1)
Answer:
-4(x+1)
Step-by-step explanation:
factor out -2x
-2x(-6x + 2x - 4) / -2x
the -2x in numerator and denominator cancel out
-6x + 2x - 4
-4x - 1
-4(x+1)
is y=6x-3 a function
Yes it is
Step-by-step explanation:
it is a linear function as it is written in the standard form Y=MX+C
A greedy hamster hoarded 2 piles of sunflower seeds. Yesterday the ratio of the seeds in these piles 3:4; but today the greedy hamster placed another 2 pounds of seeds in the bigger pile. He also ate 1/4 pound from the smaller pile and now the quantities of seeds in those piles is in the ratio of 5:16. What was the weight of each pile yesterday
The weight of each pile yesterday will be 6 and 8 pounds.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
It is Given that Yesterday the ratio of seeds in these piles was 3:4.
Let 3x and 4x represent the seeds.
If the 2 pounds of seeds are added in the bigger pile, then
4x + 2
He also ate 1/4 pound from the smaller pile,
3x - 1/4
The quantities of seeds in those piles is in the ratio of 5:16.
So, 4x + 2 = 5x
3x - 1/4 = 16x
Solve;
So, 4x + 2 = 5x
2 = 5x - 4x
x = 2
The weight of each pie will be
3x = 6 pound
4x = 8 pound
Hence, The weight of each pile yesterday would be 6 and 8 pounds.
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y - wy = m (solve for w)
I need an answer ASAP.
answer:
w = (-m+y)/y
Step-by-step explanation:
y-wy = m
-wy = m-y
y = -(m-y)/w
wy= -m + y
w = (-m+y)/y
.
rewrite the equation y-8=2 into slope form
Answer:
y=2x+16 is the slope intercept form
Step-by-step explanation:
sorry if its wrong tried!!!
Larry Mitchell invested part of his $36,000 advance at 7% annual simple interest and the rest at 2% annual simple interest. If his total yearly interest from both
accounts was $1,970, find the amount invested at each rate.
The amount invested at 7% is $
The amount invested at 2% is $
The amount invested at each rate
Investment at 7% = $25000
Investment at 2% = $11,000
What is investment?Investment definition is an asset acquired or invested in to build wealth and save money from the hard earned income or appreciation.
Given:
Larry Mitchell invested = $36,000 at 7% annual simple interest
the rest at 2% annual simple interest.
Total investment = 36000
let the investment at 7% is x
then, invested at 2% = 36000 - x
Total interest earned = $1,970
Simple interest = principal * rate * time
Investment at 4%:
(x * 0.07) + [(36000 - x) * 0.02] = 1970
0.07x + 720 - 0.02x= 1970
0.05x = 1970-720
0.05x = 1250
x= 25000
Hence,
Investment at 7% = $25000
Investment at 2% = $36,000 - $25000 = $11,000
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A few years ago, Sarah acquired a parcel of land valued at $13,800. Today, that same parcel of land has a value of $14,766. Find the percent increase in the property's value. Round your answer to the nearest hundredth, if necessary.
Answer:
7%
Step-by-step explanation:
[tex] \frac{14766 - 13800}{13800} \times 100 = 7 [/tex]
The percent increase in the property's value is 7% if the parcel of land is valued at $13,800. Today, that same parcel of land has a value of $14,766.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
A few years ago, Sarah acquired a parcel of land valued at $13,800. Today, that same parcel of land has a value of $14,766
Percentage increase:
[tex]= \rm \dfrac{14766-13800}{13800}\times 100[/tex]
= 7%
Thus, the percent increase in the property's value is 7% if the parcel of land is valued at $13,800. Today, that same parcel of land has a value of $14,766.
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College students (ages 18-26) tend to make decisions which are
tentative (more short-range) and support a desire for autonomy.
a result of a greater sense of commitment and stability.
more permanent choices.
College students (ages 18-26) tend to make decisions that are tentative (more short-range) and support a desire for autonomy. This depicts more permanent choices.
How to illustrate the information?
It should be noted that values are a compass that helps us make decisions and choices.
Choices characterize the stage of life we are in. For example 18-26 ages tend to make tentative choices, later 27-31 ages tend to make permanent choices, and ages 32-42 people make stable choices.
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Find and prove an inequality relating 100n and n^{3} .
An inequality relating 100n and n³ is 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.
What is inequality?An inequality is comparison of two values, showing if one is less than, greater than, or simply not equal to another value.
Since 100n and n³ for n = 1, 2, 3, . . . 9, 10, 11 are 100, 200, 300, . . . 900, 1000, 1100 and 1, 8, 27, . . . 729, 1000, 1331 respectively.
Therefore, an inequality relating 100n and n³ will be 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.
Induction hypothesis:
Suppose 100n ≤ k³ for some positive integer k ≥ 10.
We need to show that 100( k + 1 ) ≤ ( k + 1 )³ = k³ + 3k² +3k + 1.
Note 100( k + 1 ) = 100k + 100 ≤ k³ + 100
≤ k³ + 3k² (∵ k ≥ 10 )
≤ k³ + 3k² + 3k
≤ k³ + 3k²+3k + 1
So 100( k + 1 ) ≤ ( k + 1 )³, which is true.
Hence by the principle of mathematical induction, 100n ≤ k³ for every integer k ≥ 10.
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