The proof using Bolzano-Weierstrass Theorem is suggestive of the fact that the bounded sequence that is given has a subsequence that is convergent.
What is Bolzano-Weierstrass Theorem?The Bolzano-Weierstrass theorem, is a key conclusion regarding convergence in a finite-dimensional Euclidean space in mathematics, notably in real analysis.
According to the theorem above, each bounded sequence in Rⁿ has a convergent subsequence.
***See proof in the attached document.
Hence the given sequence is bounded. It is safe therefore to state that given Bolzano-Weierstrass theorem, the stated real bounded sequence has a convergent subsequence.
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11. Let f(x) = 2x² + 7x + 5
Answer:
(x+1)(2x+5)
Step-by-step explanation:
f(x) = 2x² + 7x + 5
Factor the expression by grouping. First, the expression needs to be rewritten as 2x²+ax+bx+5. To find a and b, set up a system to be solved.
a+b=7
ab=2×5=10
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 10.
1,10
2,5
Calculate the sum for each pair.
1+10=11
2+5=7
The solution is the pair that gives sum 7.
a=2
b=5
2x²+7x+5 as (2x²+2x)+(5x+5).
(2x²+2x)+(5x+5)
Factor out 2x in the first and 5 in the second group.
2x(x+1)+5(x+1)
Factor out common term x+1 by using distributive property.
(x+1)(2x+5)
please help me asap!!
Answer:
3
Step-by-step explanation:
If it is 10 on the big one and 5 on the small ones it is half. So half of 6 is 3
Answer:
f=3
Step-by-step explanation:
5/10=x/6
10x=30
x=3
PLEASE ANSWER QUICKLY I NEED AN ANSWER PLEASE ;0;
Answer:
infinitely many solution......
HELP ME I NEED SOMEONE TO SHOW WORK AND AWNSER QUESTION ITS TIMED PLEASE HURRY 60 POINTS FOR IT!
Answer:
Hope this helps, thank you !!
Find the length of the hypotenuse if a = 5 and b = 7. Round to the nearest tenths.
Answer:
8.6
Step-by-step explanation:
To find the length of a hypotenuse, use the formula a²+b²=c² where c is the hypotenuse. In this case, it's 5²+7²=c². Then do the calculations and take the square root to find c. 25 + 49 = c². 74=c². The square root of 74 to the nearest 10th is 8.6
si la cantidad de nacimientos es de 19 bebes por día, Cuántos nuevos habitantes existieran en 300 días
la respuesta correcta es: 5,700
Answer:
5700
Step-by-step explanation:
Vi en la calculadora yo xd
Determine the missing card value that will result in a product of -324.
-6 3 -9
Answer:
-2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
-324 ÷ -6 ÷ 3 ÷ -9 = 162
-324 ÷ 162 = -2
From an airplane flying over the ocean, the angle of depression to a submarine lying under the surface if 24 degrees 10 minutes. At the same moment, the angle of depression from the airplane to a battleship is 17 degrees 30 minutes. The distance from the airplane to the battle ship is 5120 ft. Find the distance between the battleship and the submarine.
Evalua la siguiente
expresión algebraica si
X=3 Y=2
3x + 4y =
Answer:
3x + 4y = 17
Step-by-step explanation:
Espero y te haiga ayudado :)
The cost (C) for P pounds of apples can be represented by the equation c=4p. Graph the proportional relationship between the number of pounds of apples and the total cost.
HELP ASAP PLEASE
A rectangle has a width of 9 km and a length of 6 km. How does the area change when each dimension is multiplied by 3? The area is increased by a factor of 3. The area is increased by a factor of 6. The area is increased by a factor of 9. The area is increased by a factor of 18.
Answer:
The answer is increased by 9
Step-by-step explanation:
Simplify this expression.
(2 - 5/6) 3/2
O 6V2 - 1576
62 - 15/12
O 672-876
O 672-30/3
Answer:
The second one is correct
Answer:
b
Step-by-step explanation:
can someone please help me
Step-by-step explanation please
Answer:
x=3
Step-by-step explanation:
AB+BC>AC
2x + 3 + x + 1 > x + 10
we correct like terms
2x + x + 3 + 1> x+ 10
3x + 4> x + 10
3x - x > 10-4
2x > 6
divide both sides by 2
2x÷2 > 6÷2
x = 3
Does anybody know how to do this?
Answer:
hajajajanannanssjaiwowi
A dozen of oranges costs P288.50. About how much is the cost of 5.75 dozen?
A.$2,800
B.$1,900
C.$1,800
D.$900
Answer:
A is the correct answer, hope this helps
8.652
10)
1.2
Help please
Answer:
1.921
Step-by-step explanation:
Pls help me with this
Answer:
the third one!
Step-by-step explanation:
Because it says, the SUM of the number, x (or z I can't really see it well) and 1/2, you must add those two together:
1/2 + x
Then it says those two numbers equal to 4, so it would look like this:
1/2 + x = 4
Because you are trying to isolate, and solve for x, you must SUBTRACT 1/2 from both sides of the equal sign:
1/2 + x = 4
-1/2 -1/2
1/2 minus 1/2 would result 0, so there would be x by itself. and 4 minus 1/2 would be 3 and a half ( 3 1/2), so x would be 3 1/2
x = 3 1/2
Hope this helped. If this is incorrect please specify so I can help :)
Mary buys a pair of jeans for $24.99, a skirt for $32.99 and a pair of shoes for $49.99. She has a coupon for 15% off the most expensive item. If the tax is 7.5%, what is the total cost?
no lm not sure but lm sure$107.97
Step-by-step explanation:
okieee
The total cost is $108.01.
What is a percentage?
A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Mary buys a pair of jeans for $24.99, a skirt for $32.99 and a pair of shoes for $49.99.
She has a coupon for 15% off the most expensive item.
And the most expensive item costs $49.99.
That means, 15% of 49.99
15 x 49.99 = $7.4985
So, the total amount 24.99 + 32.99 + 49.99 - 7.4985
= 100.4715
The tax is 7.5%.
That means,
7.5% of 100.4715
7.5 x 100.4715 / 100 = 7.5353625
Now the total cost = 100.4715 + 7.5353625 = 108.0068625
Therefore, $108.01 is the total cost.
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What is the probability of drawing an even numbered card keeping it then drawing another even numbered card from a stack of 24 card numbered 1-24
Answer: I think
Step-by-step explanation:
1/12
Which of the following is not a characteristic of both experiments and
surveys?
A. The researcher exercises direct control over at least one variable.
B. Subjects should be randomly selected.
C. Data are collected about a population.
D. The data collected might be studied for patterns.
The researcher exercise direct control over at least one variable.
Answer:
C?correct me if I'm wrong
The length is 8 1/3 yd the width is 6 3/4 yd what is the area
Answer:
56 and 1/4 square yds
Step-by-step explanation:
The 59th and 4th team of an Ap are - 61 and 64 respectively. Show that the common differences is - 2.5 and 23rd term is 16.5
Answer:
See answers below
Step-by-step explanation:
T59 = a+58d = -61
T4 = a+3d = 64.
Subtract
58d-3d = -61-64
-55d = -125
d =125/55
d = 25/11
Get a;
From 2
a+3d = 64
a+3(25/11) = 64
a = 64-75/11
a = 704-75/11
a = 629/11
T23 = a+22d
T23 = 629/11+22(25/11)
T23 = 1179/11
‼️ANSWER QUICKLY THIS IS A TIMED TEST ‼️The community garden in your neighborhood has three
different types of vegetable plants: peppers, tomatoes, and
cucumbers. The ratio of the number of peppers to tomatoes
to cucumbers is 1:5:3. If there are 48 cucumber plants in the
garden, how many total vegetable plants are there in the
garden?
The data given below contain the state cigarette tax​ (in $) for all 20 regions of a country.
1.36
1.70
2.50
0.45
1.18
0.64
3.46
0.57
2.00
0.80
1.60
0.98
0.36
2.24
4.35
0.62
2.70
1.78
1.53
0.84
Required:
a. Compute the population mean and population standard deviation for the regional cigarette taxes.
b. The population standard deviation is σ=_______
c. Interpret the parameters in​ (a).
1. The population mean is the average amount of regional cigarette tax. The population standard deviation represents the amount of spread in the regional cigarette tax around the median.
2. The population mean is the most common regional cigarette tax. The population standard deviation represents the amount of spread in the regional cigarette tax around the median.
3. The population standard deviation is the average amount of regional cigarette tax. The population mean represents the amount of spread in the regional cigarette tax around the standard deviation.
4. The population mean is the average amount of regional cigarette tax. The population standard deviation represents the amount of spread in the regional cigarette tax around the mean.
Answer:
(a) [tex]\bar x= 1.583[/tex] -- Population Mean
(b) [tex]s = 1.032[/tex] --- Population standard deviation
(c) See Explanation
Step-by-step explanation:
Given:
Cigarette tax for 20 regions
Solving (a): The population mean
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\sum x = 1.36 + 1.70 + 2.50 + 0.45 + 1.18 + 0.64 + 3.46 + 0.57 + 2.00 + 0.80 + 1.60 +0.98 + 0.36 + 2.24 + 4.35 + 0.62 + 2.70 + 1.78 + 1.53 + 0.84[/tex]
[tex]\sum x = 31.66[/tex]
[tex]n = 20[/tex]
So, we have:
[tex]\bar x= \frac{31.66}{20}[/tex]
[tex]\bar x= 1.583[/tex]
Solving (b): The population standard deviation
This is calculated as:
[tex]s = \sqrt{\frac{\sum( x - \bar x)^2}{n}[/tex]
[tex]\sum (x -\bar x)^2 = (1.36 - 1.583)^2 + (1.70 - 1.583)^2+ (2.50 - 1.583)^2+ (0.45 - 1.583)^2+ (1.18 - 1.583)^2+ (0.64 - 1.583)^2+ (3.46 - 1.583)^2+ (0.57 - 1.583)^2+ (2.00 - 1.583)^2+ (0.80 - 1.583)^2+ (1.60 - 1.583)^2+(0.98 - 1.583)^2+ (0.36 - 1.583)^2+ (2.24 - 1.583)^2+ (4.35 - 1.583)^2+ (0.62 - 1.583)^2+ (2.70 - 1.583)^2+ (1.78 - 1.583)^2+ (1.53 - 1.583)^2+ (0.84- 1.583)^2[/tex]
[tex]\sum (x -\bar x)^2 = 21.29222[/tex]
So:
[tex]s = \sqrt{\frac{21.2922}{20}[/tex]
[tex]s = \sqrt{1.06461}[/tex]
[tex]s = 1.032[/tex]
Solving (c):
Population mean tells the average amount while the standard deviation represents the spread from the calculated mean
Option (4) is correct
Whats the equation in slope-intercept form -y - 3x = 4
Answer:
y = -3x - 4
Step-by-step explanation:
Using algebra we solve for solely y
-y = 3x + 4
y = -3x - 4
Help me answer question 1
Answer:
The answer is option
3 and 4
Help plz:)))I’ll mark u Brainliest
Answer:
28ft
Step-by-step explanation:
Pls help im an idiot and cant solve this first gets brainliest
Answer:
1. 6 x 7/2 = 21
2. 6 x 10/3 = 20
3. 6 x 25/6 = 25
Step-by-step explanation:
Keith has saved 12 quarters from washing cars how many cents does Keith have
Answer:300
Step-by-step explanation:25 cents each quarter so the equation would be 12 times 25.
Answer: 300 cents
Step-by-step explanation: 12 quarters saved, 1 quarter = 25 cents, 12 x 25 = 300
PLEASE HELP! WILL MARK BRAINLIEST
Answer:
I don't know Im sorry
Step-by-step explanation: