4. Prove by mathematical induction that n² +n < 2" whenever n is an integer greater than 4.
Answers
Step-by-step explanation:
n² + n < 2^n
so, let's see what happens, when I increase n by 1
(n+1)² + n + 1 < 2^(n+1) = 2×2^n
n² + 2n + 1 + n + 1 < 2×2^n
n² + 3n + 2 < 2×2^n = 2^n + 2^n
so, we added on the left and on the right side of the inequality sign compared to the original relation :
2n + 2 vs. 2^n
so, once the original relation becomes true (and we see by trying that for n = 1, 2, 3 and 4 it is not, but for n = 5 it becomes true), the next integer follows the original inequality plus the expressions mentioned above.
n² + n + (2n + 2) < 2^n + (2^n)
this inequality will remain true, if
2n + 2 <= 2^n
n + 1 <= 2^(n-1), which is true for n > 2 (and therefore also n > 4), because the "power of" function 2^n progresses much faster than a simple n+1
and therefore this relation remains true for any larger n.
Related Questions
Trayvon enters a competition to guess how many balls are in a barrel.
Trayvon’s guess is 63 balls.
The actual number of balls is 60.
What is the percent error of Trayvon’s guess?
Answers
5% error
Step-by-step explanation:
% error = (estimation - actual value)/actual value * 100%
Trayvon's estimation is 63 and the actual value is 60, so our expression is:
(63 - 60)/60 * 100
63 - 60 = 3, so we get:
3/60 * 100
And 3/60 = 0.05, so now we have:
0.05 * 100 = 5
The percent error of Trayvon’s guess is 5%
What is the absolute error?"It is the absolute difference between an observed value and the actual value."
What is the relative error?"It is the ratio of the absolute error of the measurement to the actual value."
What is the percent error?"It is the relative error multiplied by 100."
For given example.
Trayvon’s guess is 63 balls.
[tex]V_o=63[/tex]
The actual number of balls is 60.
[tex]V_A=60[/tex]
The absolute error is,
[tex]\Rightarrow A=|V_o-V_A|\\\\\Rightarrow A=|63-60|\\\\\Rightarrow A=3[/tex]
The relative error is,
[tex]\Rightarrow R=\frac{A}{V_A} \\\\\Rightarrow R=\frac{3}{60}\\\\ \Rightarrow R=0.05[/tex]
The percent error is,
[tex]\Rightarrow P=R\times 100\\\\\Rightarrow P=0.05\times 100\\\\\Rightarrow P=5\%[/tex]
Therefore, the percent error of Trayvon’s guess is 5%
Learn more about the percent error here:
https://brainly.com/question/3670306
#SPJ2
tal) In a survey of 185 college students, they were asked whether they have dogs, cats,
or birds as pets:
90 have dogs,
68 have cats,
8 have birds only,
15 have both cats and dogs only,
20 have both birds and dogs,
12 have both cats and birds, and
7 students have all three animals as pets
a). Draw a Venn diagram to represent the given information.
b). How many students have cats only?
c). What proportion of the students have exactly one type of animal as pets?
Answers
9514 1404 393
Answer:
a) see attached
b) 41
c) 56.2%
Step-by-step explanation:
a) We have drawn three circles, labeled D, C, B representing students who have dogs, cats, and birds, respectively. Based on the given information we can fill numbers in for all three animals (7), cats and dogs only (15), and birds only (8).
Then we can fill in cats and birds only by subtracting the number with all three. That will be 12 -7 = 5. Birds and dogs only is similarly filled by subtracting all three to get 20 -7 = 13 birds and dogs only.
Dogs only is found by subtracting the numbers in multiple categories from the total number of dogs: 90 -13 -7 -15 = 55. Cats only is found the same way: 68 -5 -7 -15 = 41.
The completed diagram is shown in the attachment. (We haven't figured the quantity for "none.")
__
b) 41 students have cats only
__
c) The total number with dogs only, cats only, or birds only is ...
55 +41 +8 = 104
Of the 185 total students, that is 104/185 ≈ 56.2%.
56.2% of students have exactly one type of animal as a pet.
PLEASE HELPPPP
Find m∠BXY.
Answers
Answer:
I think 30°Step-by-step explanation:
Pls make me brainliest plssssssssssssssImsureeeeeeee123
2. which of the following shows the cube of a binomial?
Answers
Answer:
Socratic app
Step-by-step explanation:
it will help you
1. Complete the problem by using your calculator. Round your answer to three decimal places.
If f(x)=x^3– 7x^2+ 3 find f(-2) and f(3/4)
a. f(-2) = 3 and f(3/4)= 2.728
b. f(-2)= 3 and f(3/4)= 10
c. f(-2)=-33 and f(3/4)=-0.516
d. f(-2)= 7 and f(3/4)= 21
e. f(-2)= 10 and f(3/4)=-0.968
nhing utility Round
Answers
Answer:
c.
Step-by-step explanation:
Plug in -2 for x ....
f(x) = -2^3 - 7(-2)^2 + 3
= -8 - 28 + 3
= -36 + 3
= -33
Plug in 3/4 for x ....
f(x) = 3/4^3 - 7(3/4)^2 + 3
= 27/64 - 63/16 + 3
The put in decimals ....
27/64 = .422
63/16 = 3.938
Put the decimals back into the equation ....
= .422 - 3.938 + 3
= -3.516 + 3
= -.516
The values of x and y which satisfy the equations
x + 2 y = 27 and 2x - y = 19 are respectively
(A) 15 and 10
(B) 10 and 15
(C) 7 and 13
(D) 13 and 7
Answers
This is because when the value of x is 13 and the value of y is 7, these equations both become true.
Write an equation in slope-intercept form of the line shown.
Answers
Answer:
y=-3/2x+5
Step-by-step explanation:
The line intersects with points (2,2) and (4,-1). Slope intercept form is y=mx+b, where m is slope and b is the y intercept. The y intercept appears to be at (0,5), so b=5. As for the line, the formula for calculating slope is y2-y1/x2-x1 (the order of the points you use actually does not matter; you just have to make sure both coordinates from the same point are placed in the same part of the formula). -1-2/4-2=-3/2. Therefore, the slope is -3/2 (or -1.5 if you want a decimal).
HELP ASAP DUE IN 5 MIN I WILL GIVE 15 POINTS QND MARK BRAINLIEST DO NOT SPAM As a kitten, Mittens weighed 2 3/4 pounds. At his 6-month check-up with the vet, Mittens weighed 6.5 pounds. How much weight did Mittens gain between the time he was a kitten and his 6-month check-up? Enter your answer as a decimal or simplified mixed number in the box.
Answers
Answer:
3.75
Step-by-step explanation:
Answer:
3.75
Step-by-step explanation:
Hope this helps
Have a great and blessed day :)
The diameter of a circle is 4 centimeters. What is the circle's circumference?
d=4 cm
Use 3.14 for .
Answers
Answer:
12.56cm.
Step-by-step explanation:
Given that the diameter of a circle is 4 centimeters
The equation to find the circumference would be C=πd
C=3.14x4
=12.56
The circumference of the circle would be 12.56cm.
Hope this helps :)
This the right one click it so you can get it right
Answers
Answer:
The one highlighted yellow is the correct option
6 liters is to 72 km as 50 liters is to x km
Find the GFC of 72 and 64
Answers
Answer:
8
Step-by-step explanation:
GCF of 64 and 72 is 8.
I hope it helps you..
A snack company makes packages of grapes and honeydew slices. The weight of an individual package of
grapes, G, is approximately Normally distributed with a mean of 3.25 ounces and a standard deviation of 0.91
ounces. The weight of an individual package of honeydew slices, H, is approximately Normally distributed with a
mean of 4.51 ounces and a standard deviation of 2.02 ounces. Assume G and H are independent random
variables. Let D=G-H. What is the probability that a randomly selected package of grapes weighs more than a
randomly selected package of honeydew slices?
O 0.127
O 0.230
0.284
0.334
Answers
Using the normal distribution, it is found that there is a 0.284 = 28.4% probability that a randomly selected package of grapes weighs more than a randomly selected package of honeydew slices.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. When two normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.In this problem, for each variable, [tex]\mu_G = 3.25, \sigma_G = 0.91, \mu_H = 4.51, \sigma_H = 2.02[/tex]
For the subtraction, we have that:
[tex]\mu_D = \mu_G - \mu_H = 3.25 - 4.51 = -1.26[/tex]
[tex]\sigma_D = \sqrt{\sigma_G^2 + \sigma_H^2} = \sqrt{0.91^2 + 2.02^2} = 2.2155[/tex]
The probability that a randomly selected package of grapes weighs more than a randomly selected package of honeydew slices is P(D > 0), which is 1 subtracted by the p-value of Z when X = 0.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - (-1.26)}{2.2155}[/tex]
[tex]Z = 0.57[/tex]
[tex]Z = 0.57[/tex] has a p-value of 0.7157.
1 - 0.715 = 0.284
0.284 = 28.4% probability that a randomly selected package of grapes weighs more than a randomly selected package of honeydew slices.
A similar problem is given at https://brainly.com/question/24663213
A rectangle has a height of 362 and a width of 464 + 26 -6 what is the area?
Answers
Answer:
175,208 square units
Step-by-step explanation:
Lets calculate the width first:
464 + 26 - 6 = 484
The area is equal to the length times the width, so
362 x 484 = the area
= 175,208 square units
need help asap PLS HURRY
Answers
Write a statement
---------------------------------------------------------------------------------------------------------------------
Answers
9514 1404 393
Answer:
C) ΔDCE ≅ ΔDQR
Step-by-step explanation:
Corresponding vertices can be identified by the number of arcs signifying congruence.
1 mark: angles D and D
2 marks: angles C and Q
3 marks: angles E and R
Corresponding angles are listed in the same order in the congruence statement:
ΔDCE ≅ ΔDQR
The step club made friendship bracelet as a fundraiser and sold them for $1.75 each. The club made a profit of $182. How many bracelets did the step club make?
Answers
Answer:
104 bracelets
Step-by-step explanation:
182 ÷ 1.75 = 104
what is 83\100 in decimal form
Answers
83 = 83.0 When you move the decimal place two places to the left you get: 0.83
Hope this helps!
The Consumer Price Index (CPI), which measures the cost of a typical package of consumer goods, was 202.2 in 2011 and 244.6 in 2016. Let x = 11 correspond to the year 2011 and estimate the CPI in 2014 and 2015. Assume
that the data can be modeled by a straight line and that the trend continue indefinitely Use two data points to find such a line and then estimate the requested quantities
Answers
Answer:
y = 8.48x + 108.92227.64236.12Step-by-step explanation:
According to given we have (x, y) pairs:
(11, 202.2) and (16, 244.6)Work out the equation of the line.
Find the slope:
m = (244.6 - 202.2)/(16 - 11) = 8.48Find the y- intercept using one pair of coordinates:
202.2 = 8.48*11 + bb = 202.2 - 93.28b = 108.92The line is:
y = 8.48x + 108.92Find the value of y when x = 14 and x = 15:
y = 8.48*14 + 108.92 = 227.64y = 8.48*15 + 108.92 = 236.12need help with identiifying slope thing i sent
Answers
Answer:
The slope is -5 and the y intercept is (0,4)
Step-by-step explanation:
The equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -5x+4
The slope is -5 and the y intercept is (0,4)
what set of angles can form a line
Answers
Answer:
Did u mean triangle? There are no angles on a line.
Or do you mean two angles of 90 degrees?
Step-by-step explanation:
Let 2m - 1 be a prime number. Prove that m is also a prime number
Answers
Answer:
False.
Step-by-step explanation:
This is false.
A Counterexample:
7 is prime.
2(4)-1 is 7.
4 is not prime.
Another Counterexample:
11 is prime.
2(6)-1 is 11.
6 is not prime.
Answer:
If m=2 (which is a prime number), then 4-1=3, 3 is a prime number.
Step-by-step explanation:
x^2+12x-20/3x-5 = x^2+8x+12/2x+3
[tex] \frac{ {x}^{2} + 12x - 20}{3x - 5} = \frac{ {x}^{2} + 8x + 12}{2x + 3} [/tex]
Solution give;;;
Answers
Answer:
In attachment I have answered this problem.
Will all rational functions have at least one vertical asymptote? Justify your response with an
explanation
Answers
Answer:
no
Step-by-step explanation:
A rational function is the ratio of two polynomials. It will have a vertical asymptote if there is a real denominator zero that is not matched by one in the numerator.
Polynomials in general may or may not have real zeros, and two polynomials may have the same zero. Hence conditions may exist for a rational function not to have any vertical asymptotes.
An example with no vertical asymptotes is ...
f(x) = (x -1)/(x^2 +1)
At a pumpkin stand, Fei bought 3 pumpkins: one large, one medium, and one small. The large pumpkin cost twice as much as the medium one, and the medium pumpkin cost three times as much as the small one. Fei spent $20 in total. How much did the large pumpkin cost?
Answers
Answer:
Step-by-step explanation:
lets put the small pumpkin as x that means medium is 3x and large is 6x
so we have a equation
x+6x+3x=20
combine them
10x=20
divide by 10
x=$2
Answer:
2
Step-by-step explanation:
you really should stop the noetic tests
The length of a rectangle is 2 in longer than its width.
If the perimeter of the rectangle is 68 in, find its length and width.
Answers
Answer:
Length: 18
Width: 16
Step-by-step explanation:
Which choices are equivalent to the expression below? Check all that apply.
4./6
O A. 96
B. 132.5
I C. 4../36
O D. 116.6
E. 196
OF V24
SUBMIT
Answers
B 32 • 3
D 16•6
E 96
Square root them and multiply to get the answer
HELP! Evaluate the line integral where C is given by the vector function r(t).
Answers
Applying the steps, the result of the line integral is 99.
The curve is:
[tex]f(x,y,z) = xy i + 9y^2 j[/tex]
The vector field is:
[tex]r(t) = (x(t), y(t)) = (16t^6, t^4)[/tex]
Applying the vector field at the curve, we have that:
[tex]f(t) = (16t^{10}, 9t^8)[/tex]
The derivative of the vector field is:
[tex]r^{\prime}(t) = (96t^5, 4t^3)[/tex]
The dot product of the vector field along the curve with the derivative is:
[tex]f(t)r^{\prime}(t) = (16t^{10}, 9t^8)(96t^5, 4t^3) = 1536t^{15} + 36t^{11}[/tex]
Hence, the line integral is:
[tex]I = \int_{0}^{1} (1536t^{15} + 36t^{11}) dt[/tex]
[tex]I = 96t^{16} + 3t^{12}|_{t = 0}^{t = 1}[/tex]
[tex]I = 96 + 3[/tex]
[tex]I = 99[/tex]
A similar problem is given at https://brainly.com/question/12666512
Which is the correct solution for the following inequality: 9 ≤ 4x + 1 < 21
2 < x < 5
2 < x < 5
2 < x < 5
2 , <, x < 5
2 < x < 5
Answers
Answer:
2<=x<5
Step-by-step explanation:
first subtract one from all pieces, then divide by four. because you never divide by a negative so switching of sides is needed. Two is less than or equal to x which is less than five.
Add and simplify. 2 3\8 + 9 1\8 =
Answers
Answer:
11 1/2
Step-by-step explanation:
So we fist should add 9 and 2 which is 11 then we should add 3/8 and 1/8 which is 4/8, which is equal to 1/2. So the answer is 11 1/2
Please help me with this question
Answers
Answer:
M: (-2,6)
M': (-2,-6)
X coordinate
M' would be (2, 6)
when it's reflected over the y-axis, the x coordinate changes signs (becomes positive)