Answer:
6,000
that is the answer to your question. hope this helps!
prove that every bounded sequence contain a convergent subsequence
Answer:
To prove that every bounded sequence contains a convergent subsequence, we will use the Bolzano-Weierstrass theorem.
Bolzano-Weierstrass theorem: Every bounded sequence in Euclidean space has a convergent subsequence.
Proof: Let (a_n) be a bounded sequence in Euclidean space, which means that there exists some M > 0 such that |a_n| <= M for all n. We will use the bisection method to construct a subsequence that converges to some limit L.
Step 1: Divide the interval [-M, M] into two subintervals, [-M, 0] and [0, M]. Since (a_n) is bounded, at least one of these intervals contains infinitely many terms of the sequence. Let's call the interval that contains infinitely many terms I_1.
Step 2: Divide I_1 into two subintervals of equal length, and again, at least one of these subintervals must contain infinitely many terms of the sequence. Let's call the interval that contains infinitely many terms I_2.
Step 3: Repeat this process for each subinterval, dividing it into two subintervals of equal length and choosing the one that contains infinitely many terms of the sequence. We obtain a sequence of nested intervals I_1 ⊃ I_2 ⊃ I_3 ⊃ ... that contain infinitely many terms of the sequence.
Step 4: Since the length of each interval is decreasing and they are nested, the intersection of all the intervals is a single point L. By construction, every term of the sequence (a_n) belongs to one of the intervals I_k, which means that there exists a subsequence (a_nk) that converges to L.
Therefore, every bounded sequence in Euclidean space has a convergent subsequence, as required.
Step-by-step explanation:
answer for -10x+18=-3(5x+6)+5x
Answer:
-10x+18=-15x-18+5x
-10x+18=-10x-18
18=-18
Since the equation is inconsistent and has no solution, there is no value of x that would make it true.
Step-by-step explanation:
If the angle -270° rotates 180° counter-clockwise, what is the new measurement of the co-terminal angle?
___°
Starting with the angle of -270°, adding 360° gives us 90° (which is a coterminal angle with -270°).
If we rotate 180° counter-clockwise from 90°, we end up at the angle of 270°. Therefore, the new measurement of the coterminal angle is 270°.
I hope this helps :)
Julia made a die for a game. It had 5 faces, labeled 1-5. Because of the shape of the die, it was biased in favor of rolling a 3. We do not know the amount of bias. She experimented to estimate how likely it was for a 3 to be rolled and her results are in the above table. Using her experimental results, find the best estimate of the probability of rolling a 3.
From the table, we see that Julia rolled the die 100 times, and the number of times she rolled a 3 was 45.
The best estimate of the probability of rolling a 3 can be found by dividing the number of times a 3 was rolled by the total number of rolls:
P(rolling a 3) = Number of times 3 was rolled / Total number of rolls
P(rolling a 3) = 45 / 100
P(rolling a 3) = 0.45 or 45%
Therefore, based on Julia's experimental results, the best estimate of the probability of rolling a 3 on her biased die is 0.45 or 45%.
A game Is played using one die. If the die is rolled and shows 3, the player wins $15. M the die shows any number other than 3, the player wins nothing. Complete parts (a) through (0)
a. If there is a charge of $3 to play the game, what is the game's expected value?
Answer:
0
Step-by-step explanation:
Expected Value = (Probability of winning) x (Amount won) + (Probability of losing) x (Amount lost)
In this case, the probability of winning is 1/6 (since there is only one way to roll a 3 out of six possible outcomes), and the probability of losing is 5/6 (since there are five other outcomes that do not result in a win).
The amount won is $15, and the amount lost (i.e., the cost of playing the game) is $3.
Therefore, the expected value is:
Expected Value = (1/6) x $15 + (5/6) x (-$3)
Expected Value = $2.50 - $2.50
Expected Value = $0
There were 8500 patients in total last month in the trust. 25% of these are smokers. How many patients smoke? *
Answer:
To find out how many patients smoke, you can multiply the total number of patients by the percentage of smokers:
8500 x 25% = 2125
Therefore, there were 2125 patients who smoke last month in the trust.
Step-by-step explanation:
2125 of the patients are smoker.
What is percentage?Percentages are fractions with 100 as the denominator. It is the relation between part and whole where the value of whole is always taken as 100.
Given that, there were 8500 patients in total last month in the trust. 25% of these are smokers.
We need to find the number of the patients who smoke.
So,
25% of 8500
= 0.25 × 8500
= 25 × 85
= 2125
Hence, 2125 of the patients are smoker.
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Graciela needs to design a can with radius 2
inches and surface area as close to 100
square inches as possible. What is the height of the can? (Use π=3.14
, and round your answer to the nearest inch.)
The height of the can should be approximately 7 inches to have a surface area as close to 100 square inches as possible.
What is cylinder?
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases.
The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrhwhere r is the radius of the base, h is the height, and π is approximately 3.14.
In this case, the radius is given as 2 inches, and we want to find the height that will give us a surface area as close to 100 square inches as possible. So we need to solve for h in the equation:
100 = 2π(2)² + 2π(2)h
Simplifying this equation:
100 = 8π + 4πh
92 = 4πh
h = 23/π
h ≈ 7.32
Rounding this answer to the nearest inch, we get:
h ≈ 7 inches
Therefore, the height of the can should be approximately 7 inches to have a surface area as close to 100 square inches as possible.
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please help me.............
The Tοtal number οf tickets tο play will be 15.
What is inequality?Mathematical expressiοns with inequalities οn bοth sides are knοwn as inequalities. In an inequality, we cοmpare twο values as οppοsed tο equatiοns. In between, the equal sign is changed tο a less than (οr less than οr equal tο), greater than (οr greater than οr equal tο), οr nοt equal tο sign.
At a schοοl fair, there are different games tο play that each require 5 tickets tο play.
Jοrdan wants a bag οf pοpcοrn that requires 26 tickets and tο use the rest οf the tickets tο play games.
Jοrdan has 101 tickets.
Fοr tickets tο play will be 101-26 = 75
Sο the Tοtal number οf tickets tο play will be 75/5 = 15.
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After grading the take-home assignments, Mr. Montes randomly selects 5 take-home
assignments to analyze. He considers the student's responses to the three multiple choice
questions, which are as shown.
Student 1:
(C, A, C)
a. Set 1n Set 2
Student 2:
{C, B, B}
b. Set 2 U Set 3
Student 3:
{C, B, C)
7. The correct responses for the multiple choice questions are, in order, C, B, and A. If Set 1
represents the subset of these students who answered C for number 1, Set 2 represents the subset
of these students who answered B for number 2, and Set 3 represents the subset of students who
answered A for number 3, find each of the following. Explain what each notation means in
context of this scenario.
c. The complement of Set 1
Student 4:
{C, B, A}
Student 5:
{C, A, A}
8. Amisha was too tired to work on the take home assignment Mr. Montes gave her, so she
randomly selected answers without reading any of the questions. Suppose that you wanted to
find the odds that Amisha answered at least 3 of the 5 questions correctly. Do you think you
would use a permutation or a combination? Why?
Answer:
b
Step-by-step explanation:
my brain
The height of a ball thrown in to the air is given by the formula
y= s(t) = 16t^2 + 50t + 2 where s(t) is in feet and t in seconds
A. Find the average velocity of the object over the interval [1,2] and include units.
B. Find a simplified expression that gives the average rate of change of s(t) on the interval [1, 1 + h]. Your answer will be an expression involving h.
Part II: According to the tax tables below, how much would Melvin pay in federal
income taxes if filing separately? How much would Sylvia pay if filing separately?
How much would Melvin and Sylvia pay combined if filing separately?
According to the tax tables below, Melvin would have to pay in federal income taxes if filing separately $5,131 and Sylvia $6,750. The total would be $11,881
How to identify how much tax Melvin and Sylvia have to pay?To identify how much Melvin and Sylvia have to pay in taxes, we must look carefully at the table. In this, the different incomes are classified and on the right side are shown how much the tax is depending on the condition of the citizen. These options are: single, married filling jointly, married filling separately and head of a household.
In accordance with the above, we must look at which number coincides in the row of married filling separately with the value of the income of each one of them. According to the above, Melvin has to pay 5,131 in taxes while Sylvia has to pay 6,750.
Note: This question is incomplete. Here is the complete information:
Melvin and Sylvia are married with no children, and they're filing their federal income tax return. Melvin had a gross income of $35,750 last year, while Sylvia had a gross income of $41,700.
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Maureen drove for 1.5 hours at an average speed of 62 mph and then for another half hour at an average speed of 24 mph. How far did she drive altogether?
Answer:
105 mi
Step-by-step explanation:
distance = speed x time
total distance = (62 mi/hr)(1.5 hr) + (24 mi/hr)(0.5 hr) = 105 mi
30 min = 0.50 hr
Can I please get some help???
Answer: B) 2
Step-by-step explanation:
In the image, we see a box and whisker plot. The middle line represents the median. Looking at the numbers on the side, and the placement of the middle line, we can see that the median in this situation is 2.
F’ G’ H’ is a dilation of F G H with the center of dilation at the origin
What is the scale factor of the dilation?
what is the value of X when 7=3x_2
Answer:
7+2=3x-2+2
9/3=3x/3
3=x
NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6
. In an earlier study, the population proportion was estimated to be 0.41
.
How large a sample would be required in order to estimate the fraction of people who black out at 6
or more Gs at the 95%
confidence level with an error of at most 0.04
? Round your answer up to the next integer.
EASY MATH POINTS!
Answer from the screenshot.
The rate of change is $1.25 per premium movie watched.
A. $1.25 / 1 premium movie
How to find the rate of changeThe rate of change in this scenario is the increase in cost for each additional premium movie watched.
In this case, the rate of change is constant, since the cost per premium movie remains the same regardless of the number of premium movies watched.
Therefore, the rate of change is simply the additional cost per premium movie, which is $1.25.
So, for example, if you watched 10 premium movies, the total cost would be:
$35 + (10 * $1.25) = $47.50
And if you watched 20 premium movies, the total cost would be:
$35 + (20 * $1.25) = $60.00
rate of change = (60 - 47.5) / (20 - 10) = 1.25
In both cases, the rate of change is still $1.25 per premium movie watched.
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PLEASEEEE HELP!!!!
Enter your answer and show all the steps that’s you used to solve this problem in the space provided.
How do the graphs of y = 1/x and y = 5/x+6 compare?
The transformations that compares the functions y = 1/x and y = 5/(x + 6) are
The second function is shifted 6 units to the left and Dilated by 5 unitsWhat are transformations?
Transformations are mathematical operations that are performed to change the shape or value of a graph, function or image.
Since we have the functions
y = 1/x and y = 5/(x + 6),We want to see how the graphs of
y = 1/x and y = 5/x+6 compare?We proceed as folows.
Looking at the functions
y = 1/x and y = 5/(x + 6),We compare the transformations and see that
The second graph is shifted 6 units to the left since it has x + 6 units denominatorAlso, since we have 5 in the numerator, it is dilated by 5 units.So, the functions compare by
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Will give brainliest if correct!
When x = 5, y = 9 / 11
When x = 0, y = -1 / 6
when x = -6, y = -13
How to solve for the value of yWhen x = 5
we would have
[tex]y = \frac{2(5) - 1}{5 + 6}[/tex]
y = 10 - 1 / 11
y = 9 / 11
when the value of x = 0
[tex]y = \frac{2(0) - 1}{0 + 6}[/tex]
y = -1 / 6
When the value of x = -6
[tex]y = \frac{2(-6) - 1}{-6 + 6}[/tex]
y = -12 - 1 / 0
y = -13 / 0
y = -13
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1. The sum of the angles of a triangle is 180. Find the three angles of the triangle if one
angle is four times the smallest angle and the third angle is 36 greater than the smallest
angle.
Answer: they small angel is 12
Step-by-step explanation:because the third angle is 36 and 12 times three is 36
Perform the indicated operations 9√64 3 − 2√125
Answer: We can simplify the given expression as follows:
9√64 - 2√125
Since √64 = 8, we can substitute to get:
9(8) - 2√125
Since √125 = √(25 × 5) = √25 × √5 = 5√5, we can substitute again to get:
9(8) - 2(5√5)
Simplifying further:
72 - 10√5
Therefore, the expression 9√64 3 − 2√125 simplifies to 72 - 10√5.
Step-by-step explanation:
x.cot a. tan (90°+a) = tan (90°+a). cot (180°-a) + x.sec (90°+a).
Marley's car gets 25 miles per gallon, and they expect to drive 1350 miles for their next vacation. If the average price of gasoline is $2.549, how much should they budget for gas for the trip?
A. $63.73
B. $54
C. $137.65
D. $337.50
Find the Area.
12 ft
12 ft
Answer:
144ft^2
Step-by-step explanation:
Answer:
144^2 feet
Step-by-step explanation:
To find the area you would multiply length x width for your answer. I hope this helps!
An item is marked down to 9/10 of its original value and then further marked down to 7/10 of that. What portion of the value of item remains
Answer:
I think the answer is 63%
Step-by-step explanation:
9/10 * 7/10 = 63/100 = 63%
(I am not fully sure.)
Find x. Round your answer to the nearest tenth of a degree.
The measure of angle x to the nearest tenth of a degree is 51.8°
What is the measure of angle x?The figure in the image is a right triangle.
From the image;
Angle x = ?Opposite to angle x = 11 unitsHypotenuse = 14 unitsTo solve for the measure of angle x, we use one of the six (6) trigonometric ratio.
Sine = Opposite / Hypotenuse.
Plug in the given values and solve for angle x.
sin( x ) = 11 units / 14 units.
Take the sine inverse.
x = sin⁻¹( 11/14 )
x = 51.7867
x = 51.8 degrees.
Therefore, the value of x is 51.8 degrees.
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A 6 foot 2 man casts a shadow of 5 feet. What size shadow will a 5
foot 5 lady cast?
The 5 foot 5 tall lady will cast a shadow of approximately 4.4 ft.
What size shadow will the 5 foot 5 lady cast?Given that, a 6 foot 2 man casts a shadow of 5 feet. Also, a lady is 5 foot 5 and we find the shadow she casted.
We can solve this problem by setting up a proportion:
The height and shadow length are proportional, so we can write:
6 feet 2 inches : 5 feet = 5 feet 5 inches : x
where x is the length of the shadow cast by the lady.
To solve for x, we can cross-multiply:
(6 feet 2 inches) × x = (5 feet) × (5 feet 5 inches)
To simplify the calculation, we can convert all the lengths from feets to inches:
Note: 1 ft = 12 in
(74 inches) × x = (60 inches) × (65 inches)
Now we can solve for x:
x = (60 inches) × (65 inches) / (74 inches)
x = 3900/74
x = 52.70 inches
Convert back to ft
x = 4.4 ft
Therefore, the lady will cast a shadow of approximately 4.4 ft.
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a section of an exam contains four true false questions. A completed exam paper is selected at random, and four answers are recorded.
the probability that all answers are False?
the probability that exactly three or four answers is false?
the probability that at lastt answer is true is ?
We can use the binοmial distributiοn tο mοdel this situatiοn, where each questiοn is a Bernοulli trial with a prοbability οf success (getting the cοrrect answer) οf 0.5.
A prοbability simple definitiοn is what?A prοbability is a numerical representatiοn οf the likelihοοd οr chance that a specific event will take place. Bοth prοpοrtiοns ranging frοm 0 tο 1 and percentages ranging frοm 0% tο 100% can be used tο describe prοbabilities.
Let X be the number οf False answers in the cοmpleted exam paper.
Prοbability that all answers are False:
[tex]P(X = 4) = (0.5)^4 = 0.0625[/tex]
Prοbability that exactly three οr fοur answers are False:
P(X = 3 οr X = 4) = P(X = 3) + P(X = 4)
[tex]= 4C3(0.5)^3(0.5)^1 + (0.5)^4[/tex]
= 0.25 + 0.0625
= 0.3125
Prοbability that at least οne answer is True (which is the cοmplement οf the event that all answers are False):
P(at least οne True) = 1 - P(all False) = 1 - 0.0625 = 0.9375
Prοbability that the last answer is True:
This prοbability can be calculated using cοnditiοnal prοbability, where we find the prοbability that the last answer is True given that we knοw that at least οne answer is True:
P(last answer is True | at least οne True) = P(last answer is True and at least οne True) / P(at least οne True)
P(last answer is True and at least οne True) = P(last answer is True) = 0.5
P(at least οne True) = 0.9375 (calculated in part 3)
Sο, P(last answer is True | at least οne True) = 0.5 / 0.9375 = 0.5333 (rοunded tο fοur decimal places).
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A bug is moving along the right side of the parabola y = x at a rate such that its distance from the origin is increasing at 9 cm/min. a. At what rate is the x-coordinate of the bug increasing when the bug is at the point (4, 16)? dy dx b. Use the equation y=x² to find an equation relating to dt dt c. At what rate is the y-coordinate of the bug increasing when the bug is at the point (4, 16)? 2 a. Let D=√x + y terms of only x. 4 2 D = √x +X Differentiate both sides of the equation with respect to t. dD dt 2 2x + 1 be the distance the bug is from the origin. Considering the bug is moving along y = x, rewrite D in 1 2 dx dt (x²+1) At what rate is the x-coordinate of the bug increasing when the bug is at the point (4, 16)? The x-coordinate of the bug is increasing at a rate of (Type an exact answer, using radicals as needed.)
Answer:
Step-by-step explanation:
a. To find the rate at which the x-coordinate of the bug is increasing when the bug is at the point (4, 16), we need to differentiate the equation y=x with respect to time t:
dy/dt = dx/dt
Since the bug is moving along the right side of the parabola y=x, the bug's position can be described by the equation y=x^2. Taking the derivative of both sides with respect to time t, we get:
2y(dy/dt) = 2x(dx/dt)
Simplifying and plugging in the given values for y and dy/dt:
2(16)(9) = 2(4)(dx/dt)
dx/dt = 36 cm/min
Therefore, the x-coordinate of the bug is increasing at a rate of 36 cm/min when the bug is at the point (4, 16).
b. The equation y=x^2 can be rewritten as x=sqrt(y). Differentiating both sides with respect to time t, we get:
dx/dt = 1/(2sqrt(y)) * dy/dt
Substituting y=16 and dy/dt=9, we get:
dx/dt = 1/(2sqrt(16)) * 9
dx/dt = 9/8 cm/min
c. We can use the same equation from part (a) to find the rate at which the y-coordinate of the bug is increasing when the bug is at the point (4, 16):
2y(dy/dt) = 2x(dx/dt)
Substituting y=16, x=4, and dx/dt=36, we get:
2(16)(dy/dt) = 2(4)(36)
Solving for dy/dt:
dy/dt = 18 cm/min
Therefore, the y-coordinate of the bug is increasing at a rate of 18 cm/min when the bug is at the point (4, 16).
d. Let D be the distance the bug is from the origin. We can use the Pythagorean theorem to relate D to x and y:
D^2 = x^2 + y^2
Substituting y=x^2, we get:
D^2 = x^2 + x^4
Taking the derivative of both sides with respect to time t, we get:
2D(dD/dt) = 2x(dx/dt) + 4x^3(dx/dt)
Simplifying and substituting x=4, dx/dt=36, and y=16:
2sqrt(16+16^2)(dD/dt) = 2(4)(36) + 4(4^3)(36)
Solving for dD/dt:
dD/dt = (836 + 44^3*36) / (2sqrt(16+16^2))
dD/dt = 72/(sqrt(17))
Therefore, the distance between the bug and the origin is increasing at a rate of 72/(sqrt(17)) cm/min when the bug is at the point (4, 16).
Sonja's house is 4 blocks west and 1 block south of the center of town. Her school is 3 blocks east and 2 blocks north of the center of town.
Which graph represents this scenario?
(Hint: The center of town should be the origin, and north is up.)
The answer is [tex]\sqrt{58} = 7.62[/tex]
So, if you draw this down, you will see that the direct distance is hypotenuse c of a right triangle which sides are 3 blocks (1 south and 2 north) and 7 blocks (4 west and 3 east).
Use the Pythagorean theorem:
[tex]c^2 = a^2 + b^2[/tex]
[tex]a = 3[/tex]
[tex]b = 7[/tex]
[tex]c^2 = 3^2 + 7^2[/tex]
[tex]c^2 = 9 + 49[/tex]
[tex]c^2 = 58[/tex]
[tex]c = \sqrt{58}[/tex]
[tex]c = 7.62[/tex]