Answer:
16 is the number occurring most often in the list.
Step-by-step explanation:
Find the supremum and infimum of each of the following sets of real numbers
S = {3x 2 − 10x + 3 < 0}
Answer:
[tex]\sup(S) = 3[/tex].
[tex]\displaystyle \inf(S) = \frac{1}{3}[/tex].
Step-by-step explanation:
When factored, [tex]3\,x^{2} - 10\, x + 3[/tex] is equivalent to [tex](3\, x - 1)\, (x - 3)[/tex].
[tex]3\, x^{2} - 10\, x + 3 < 0[/tex] whenever [tex]\displaystyle x \in \left(\frac{1}{3},\, 3\right)[/tex].
Typically, the supremum and infimum of open intervals are the two endpoints. In this question, [tex]\sup(S) = 3[/tex] whereas [tex]\displaystyle \inf(S) = \frac{1}{3}[/tex].
Below is a proof of the claim that [tex]\sup(S) = 3[/tex]. The proof for [tex]\displaystyle \inf(S) = \frac{1}{3}[/tex] is similar.
In simple words, the supremum of a set is the smallest upper bound of that set. (An upper bound of a set is greater than any element of the set.)
It is easy to see that [tex]3[/tex] is an upper bound of [tex]S[/tex]:
For any [tex]x > 3[/tex], [tex]3\,x^{2} - 10\, x + 3 > 0[/tex]. Hence, any number that's greater than [tex]3\![/tex] could not be a member [tex]S[/tex]. Conversely, [tex]3[/tex] would be greater than all elements of [tex]S\![/tex] and would thus be an upper bound of this set.To see that [tex]3[/tex] is the smallest upper bound of [tex]S[/tex], assume by contradiction that there exists some [tex]\epsilon > 0[/tex] for which [tex](3 - \epsilon)[/tex] (which is smaller than [tex]3\![/tex]) is also an upper bound of [tex]S\![/tex].
The next step is to show that [tex](3 - \epsilon)[/tex] could not be a lower bound of [tex]S[/tex].
There are two situations to consider:
The value of [tex]\epsilon[/tex] might be very large, such that [tex](3 - \epsilon)[/tex] is smaller than all elements of [tex]S[/tex].Otherwise, the value of [tex]\epsilon[/tex] ensures that [tex](3 - \epsilon) \in S[/tex].Either way, it would be necessary to find (or construct) an element [tex]z[/tex] of [tex]S[/tex] such that [tex]z > 3 - \epsilon[/tex].
For the first situation, it would be necessary that [tex]\displaystyle 3 - \epsilon \le \frac{1}{3}[/tex], such that [tex]\displaystyle \epsilon \ge \frac{8}{3}[/tex]. Let [tex]z := 1[/tex] (or any other number between [tex](1/3)[/tex] and [tex]3[/tex].)
Apparently [tex]\displaystyle 1 > \frac{1}{3} \ge (3 - \epsilon)[/tex]. At the same time, [tex]1 \in S[/tex]. Hence, [tex](3 - \epsilon)[/tex] would not be an upper bound of [tex]S[/tex] when [tex]\displaystyle \epsilon \ge \frac{8}{3}[/tex].With the first situation [tex]\displaystyle \epsilon \ge \frac{8}{3}[/tex] accounted for, the second situation may assume that [tex]\displaystyle 0 < \epsilon < \frac{8}{3}[/tex].
Claim that [tex]\displaystyle z:= \left(3 - \frac{\epsilon}{2}\right)[/tex] (which is strictly greater than [tex](3 - \epsilon)[/tex]) is also an element of [tex]S[/tex].
To verify that [tex]z \in S[/tex], set [tex]x := z[/tex] and evaluate the expression: [tex]\begin{aligned} & 3\, z^{2} - 10\, z + 3 \\ =\; & 3\, \left(3 - \frac{\epsilon}{2}\right)^{2} - 10\, \left(3 - \frac{\epsilon}{2}\right) + 3 \\ = \; &3\, \left(9 - 3\, \epsilon - \frac{\epsilon^{2}}{4}\right) - 30 + 5\, \epsilon + 3 \\ =\; & 27 - 9\, \epsilon - \frac{3\, \epsilon^{2}}{4} - 30 + 5\, \epsilon + 3 \\ =\; & \frac{3}{4}\, \left(\epsilon\left(\frac{16}{3} - \epsilon\right)\right)\end{aligned}[/tex].This expression is smaller than [tex]0[/tex] whenever [tex]\displaystyle 0 < \epsilon < \frac{16}{3}[/tex]. The assumption for this situation [tex]\displaystyle 0 < \epsilon < \frac{8}{3}[/tex] ensures that [tex]\displaystyle 0 < \epsilon < \frac{16}{3}\![/tex] is indeed satisfied. Hence, [tex]\displaystyle 3\, z^{2} - 10\, z + 3 < 0[/tex], such that [tex]z \in S[/tex].At the same time, [tex]z > (3 - \epsilon)[/tex]. Hence, [tex](3 - \epsilon)[/tex] would not be an upper bound of [tex]S[/tex].Either way, [tex](3 - \epsilon)[/tex] would not be an upper bound of [tex]S[/tex]. Contradiction.
Hence, [tex]3[/tex] is indeed the smallest upper bound of [tex]S[/tex]. By definition, [tex]\sup(S) = 3[/tex].
The proof for [tex]\displaystyle \inf(S) = \frac{1}{3}[/tex] is similar and is omitted because of the character limit.
suppose that a country has approximately 3,900 cellular phones per 1000 people express the number of phones per person as a whole or mixed number. The number of phones per person is?
Answer:
40,0000000000000000000
Answer:
3 9/10
Step-by-step explanation:
PLEASE HELP
1= a-13/-6
Show your work in details if you can, I have a hard time understanding this.
Answer:a= 7
Step-by-step explanation:
Dave's favorite baseball team has won 10 fewer games than Kimiko's favorite baseball team. Write an algebraic expression for the number of games Dave's favorite team has won. Be sure to induct what variable is your expression represents.
Let x be the variable, and the unknown that gives the number of games Dave's favorite team has won.
Let y be the variable that express the number of games Kimiko's favorite baseball team has won.
Since Dave's favorite baseball team has won 10 games less than Kimiko's favorite baseball team, we can express this situation this way :
y - 10 = xy = x+10Find the equation of a line passing through the point of intersection of line 2x+y-8=0 and 3x-4y=3 and is parallel to line Y=2x-8
Step-by-step explanation:
steps are in the picture above.
Note:if you need to ask any question please let me know.Find the total amount paid on a loan when the monthly payment is $189 and the loan is paid off in 48 months. Use the formula A = MN, where A is the total amount paid, M is the monthly payment, and N is the number of payments.
9514 1404 393
Answer:
$9072
Step-by-step explanation:
Put the given numbers in the given formula and do the arithmetic.
A = MN . . . . . . M = payment = $189. N = number of payments = 48.
A = $189 × 48 = $9072
The total amount paid is $9072.
A rectangle has a height of 3 cm and width of 5cm. A proportional rectangle has a height of 12cm. What would be the width?
Step-by-step explanation:
a proportional or similar shadow uses the same factor for each line/dimension.
so, since the height of the proportional rectangle is 4 times longer than the height of the original rectangle, then also the width must be 4 times longer.
heightP = 12 cm = f × height = f × 3 cm
f = 12/3 = 4
widthP = f × width = 4 × 5 = 20 cm
66. Evaluate 4a2+3 when a=5
Given that the mean of a set of data is 25 and the standard deviation is 3,
what is the coefficient of variation?
A) 0.12
B) 12%
C) 8.33
D) 833%
in filing his income tax, raul reported annual contributions of $350 350 to a public radio station, $210 210 to a public tv station, $100 100 to a local food bank, and $294 294 to other charitable organizations what's the monthly expense?
Answer:
$79.50
Step-by-step explanation:
1. $350 + $210 + $100 + $294 = $954
2. $954 ÷ 12 = 79.50
Raul monthly expense is $79.50.
Here,
In filing his income tax, Raul reported annual contributions of $350 350 to a public radio station, $210 210 to a public tv station, $100 100 to a local food bank, and $294 294 to other charitable organizations.
We have to find Raul's monthly expense.
What is total amount?
A total is a whole or complete amount.
Now,
Raul's annual expense = $350 + $210 + $100 + $294
= $954
Hence,
Raul's monthly expense = 954/12
= 79.50
So, Raul monthly expense is $79.50.
Learn more about the total amount visit:
https://brainly.in/question/45320943
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how do you write 2 4/9 as a decimal
please help
4
2 --
9
Answer:
2.4 put a bar over the 4 because it is repeating
Step-by-step explanation:
22/9 =
22 divided by 9
equals
can anyone plz with steps
[tex]\boxed{\sf \displaystyle{\lim_{x\to a}}(x^n)=a^n}[/tex]
[tex]\\ \sf\longmapsto \displaystyle{\lim_{x\to \infty}}(\sqrt{3x}-\sqrt{x-5})[/tex]
[tex]\\ \sf\longmapsto \displaystyle{\lim_{x\to \infty}}\sqrt{3x}-\displaystyle{\lim_{x\to \infty}}\sqrt{x-5}[/tex]
[tex]\\ \sf\longmapsto \infty^{\dfrac{1}{2}}-\sqrt{\infty-5}[/tex]
[tex]\\ \sf\longmapsto \infty-\sqrt{\infty}[/tex]
[tex]\\ \sf\longmapsto\infty-\infty[/tex]
[tex]\\ \sf\longmapsto\infty[/tex]
A ray extends forever. True or false
false
false
false........
false
Answer:
it extends forever in one direction. so false i guess
Step-by-step explanation:
Is 9 a rational or non-rational number
Answer: 9 is a rational number.
Step-by-step explanation:
it is a Rational number
.
9
.
.
.
.
what is 0.112 times 7.2 and how to solve the problem
Answer:
0. 8064
Step-by-step explanation:
Look at the Image
Lines k and I are parallel and the measure of angle ABC is 22 degrees. Find the measure of the other angles.
What is the measure of angle DCE?
Α. 158
B. 73
C. 124
D. 22
Answer:
A. 158
Step-by-step explanation:
Angle ABC and Angle ECF have the same tick mark(little line over the angle). The means they are congruent, the same. Since Angle ECF + Angle DCE = 180 degrees, 180 - 22 is the measure of angle DCE, or 158. You're welcome, and brainliest me.
Wanted to add that this is not at all college math. This like middle school lvl bro.
If a= 2,b= -1,c= -3 and d = -2 evaluate the following Q1. ab-3b+4d , Q2. 5abd+3bc-2ax and Q3. 2(ab)^2+bc^2
Answer:
the answer for question 1 is -7
Question 3 of 20
A rectangular school gym has a length of x + 14 and a width of x - 20. Which
measure does (x + 14)(x-20) represent?
A. The perimeter of the gym
B. The area of the gym
C. The height of the gym
D. The volume of the gym
SUBMIT
in this case, we are looking at a length × width equation. this equation gives you the area of the gym. so the answer is B.
Answer:
B
Step-by-step explanation:
L× w = area of a rectangle
PLS HELP!! Will give brainliest!
Angle AOC measures 84 degrees. Angle AOB = 3x and BOC is x
First, write the equation you would use to find the answer then find the value of x
Answer:
∠AOB + ∠BOC = ∠AOC we will be using this equation
x = 21 this is the value of x
Step-by-step explanation:
Angle AOC = 84
Angle AOB = 3x
Angle BOC = x
it is given that Angle AOC = 84so we just need to add Angle AOB and Angle BOC
now lets make the equation we that we will be using
∠AOB + ∠BOC = ∠AOC
3x + x = 84
4x = 84
x = 84 ÷ 4
x = 21
Step-by-step explanation:
Here, we have,
AOC=84°
AOB=3x
BOC=x
Now, the required equation will be;AOC=AOB+BOC[whole part axiom]
or, 84°=3x+x
or, 84°=4x
or, 84°÷4=x
or, x=21°
Thus, the equation to find the answer is AOC=AOB+BOC and the value of x is 21°.
Integral of x"2+4/x"2+4x+3
I'm guessing you mean
[tex]\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx[/tex]
First, compute the quotient:
[tex]\displaystyle \frac{x^2+4}{x^2+4x+3} = 1 + \frac{4x-1}{x^2+4x+3}[/tex]
Split up the remainder term into partial fractions. Notice that
x ² + 4x + 3 = (x + 3) (x + 1)
Then
[tex]\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52[/tex]
So the integral becomes
[tex]\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}[/tex]
We can simplify the result somewhat:
[tex]\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}[/tex]
brainiest to whoever right
does anybody know how to do the rest of this? also I'll give brainliest ;p
Answer:
I what you gotta do is this where they say subtract previous temperature from current temperature all you have to do is on that row subtract the temperature written there from the one directly above it that is all I can advise you to do that is what it means also in the other one that says the same thing that's all you have to do nothing more nothing less
One angle of a triangle measures 136º. The other two angles are congruent.
Enter and solve an equation to find the measure x of the congruent angles.
Answer:
22°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , then
x + x + 136° = 180°
2x + 136° = 180° ( subtract 136° from both sides )
2x = 44° ( divide both sides by 2 )
x = 22°
In ΔRST, m < R = 104°, r = 20, and t = 10. Find the m < S, to nearest degree.
9514 1404 393
Answer:
47°
Step-by-step explanation:
The law of sines helps you find angle T. From there, you can find angle S.
sin(T)/t = sin(R)/r
sin(T) = (t/r)sin(R) = (10/20)sin(104°)
T = arcsin(sin(104°)/2) ≈ 29°
Then angle S is ...
S = 180° -R -T = 180° -104° -29°
∠S = 47°
If
a
=
−
5
x
a=−5x and
b
=
−
x
+
4
i
b=−x+4i, then find the value of
a
2
b
a
2
b in fully simplified f
Answer:
what to do which lesson of ath
Help me in math please this is my last question btw
Answer:
A) y=-7
Step-by-step explanation:
we talking about the better pond right?
The data below represent the per capita (average) disposable income (income after taxes) for 25 randomly selected cities in a recent year.
Frequency distribution allows finding the occurrence of events: 12, 9, 0, 1
The frequency distribution is a grouping of data in exclusive categories, where the number of occurrences of each event is indicated
In this case the categories and their occurrences are
Categories Occurrence Frecuencie relative (%)
30,000 - 36,000 12 54.5%
36000 - 42000 9 40.9%
42000 - 48000 0 0%
48000 - 54000 1 4.5%
With these data, bar graphs can be built where the category is placed on the x-axis, an independent variable, and the occurrences on the y-axis, a dependent variable.
With these distributions, relative frequency is defined, which is the number of times a category appears among the total number of events.
fr = occurrence /n
Where fr is the relative frequency and n is the number of events, sometimes it is given as a percentage by multiplying by one hundred
In this case the number of events is n = 22
Category 30000- 36000
fr₁ = 12/22
fr₁ = 0.5454
fr₁% = 54.5%
Category 36000 - 42000
fr₂ = 9/22
fr₂ = 0.4090
fr₂% = 40.9%
Category 42000-48000
fr₃ = 0
fr₃% = 0%
Category 48000 - 54000
fr₄ = 1/22
fr₄ = 0.04545
fr₄% = 4.5%
The frequency distribution allows finding the occurrence of the events:
12, 9, 0, 1
Learn more about frequency distribution here: brainly.com/question/17008997
. What is the total cost of 6 books at N8.50k each?
Answer:
51
Step-by-step explanation:
1 book= N8.50
therefore 6 books= N8.50 × 6 = N51
) Find the value of 'x' and 'y' if ( 2x+3y,4) = ( 5 , 2y).
Answer:
x = -0.5
y = 2
Step-by-step explanation:
(2(-0.5)+3(2), 4) = (5, 2(2))
(-1 + 6, 4) = (5, 4)
(5, 4) = (5, 4)
Express the terms of the following geometric sequence by giving an explicit formula. 8 , -32 , 128 , -512 , 2,048 , ...
Answer:
8*(-4)^(n-1)
Step-by-step explanation:
The common ratio is - 32/8 = - 4, the first term being 8. The formula will be 8*(-4)^(n-1).