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You're very close. The answers you've selected are correct, but there's one third series that's also alternating. Choice C is also an answer due to the [tex](-1)^n[/tex] term.
Any alternating series is in the form [tex]\displaystyle \sum (-1)^n*a_n[/tex] or [tex]\displaystyle \sum (-1)^{n+1}*a_n[/tex] where [tex]a_n[/tex] is any sequence.
Choice E comes close, but the 2n being the exponent means that we don't have alternating signs (positive, negative, positive negative, etc). Why is this? Well notice how 2n is even regardless of what integer n we pick. Raising any negative number to an even power results in a positive value.
Eg: (-7)^2 = 49 and (-3)^4 = 81
This means that all of the terms of sequence E are going to be positive. The terms do not bounce back and forth between positive and negative.
Put another way, [tex](-1)^{2n} = \left((-1)^2\right)^n = 1^n = 1[/tex]
So [tex]\displaystyle \sum_{n=0}^{\infty} (-1)^{2n}\frac{1}{n+3} = \sum_{n=0}^{\infty} \frac{1}{n+3}[/tex]
And it's why choice E is not one of the answers.
-------------------------
To summarize:The 3 answers are A, C, and DRelated Questions
Could someone help with this math??!
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Answer:
1. what I the square root of negative 4
2. one is minusing the square root of 4
18x-(3x+9) expression and equations
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Answer:
15x−9
Step-by-step explanation:
HELPPP PLEASE!!!! SHOW ALL WORK!!!
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Answer:
x=54
Step-by-step explanation:
these two angles are supplementary to each other. this is because alternate interior angles are congruent, and 2x+42 degrees is supplementary to the alternate interior angle of x-24 degrees. so, we can add these two numbers up and set it equal to 180.
2x+42+x-24=180
3x+18=180
3x=162
x=54
if this question is asking for x, 54 is the answer. if it is asking for the angle measures, plug in 54 for x for each angle and solve.
Please help me ASAP help
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f (x) = (x + 5)^3(x - 9)(x + 1)
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Answer:
F (x) = (x + 5)^3(x - 9)(x + 1) = 5
Step-by-step explanation:
Hope this helps! :)
Answer:
3
Step-by-step explanation:
edge
Each square in the periodic table contains the element's atomic number, chemical symbol, name, and atomic mass.
True or false?
Answers
Answer:
True...
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
A hot air balloon was rising at a rate of 474 feet per minute (ft/min). convert this speed to meters per second (m/s).
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HELPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!
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Answer:
so
Step-by-step explanation:
the first goes 3rd
the 2nd goes 1
3rd goes 4
Geometry sucks I need help im really behind
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Answer:
26°
Step-by-step explanation:
[tex]m\angle WXZ = 78\degree... (given) \\\\
m\angle 2 = 2m\angle 1...(given)... (1)\\\\
\because m\angle 1 + m\angle 2=m\angle WXZ \\\\
\therefore m\angle 1 + m\angle 2=78\degree... (2)\\\\
\therefore m\angle 1 + 2m\angle 1=78\degree\\ [From\:equations\: (1)\: \&\:(2)] \\\\
\therefore 3m\angle 1=78\degree\\\\
\therefore m\angle 1=\frac{78\degree}{3}\\\\
\therefore m\angle 1=26\degree \\[/tex]
Simplify 16x^3 - 8x^2 + 4x^4 / 2x
A) 8x^2 - 4x + 2x^3
B) 8x^2 - 4 + 2x^3
C) 8x^3 - 4x + 2x^3
D) 8x^2 - 4x + 2x
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Answer:
2 x ^3 + 8 x ^2− 4 x
Step-by-step explanation:
Just simplify!
8)Find a point R on segment ST such that the length of TR is 2/3 the length of ST. *
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What is five to the second power in expanded form and standard
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Step-by-step explanation:
Answer:
5x5 and 5^2
Step-by-step explanation:
hope this helps.
Which binomial is a factor of the following quadratic? K2-12k+36
Answers
9514 1404 393
Answer:
(k -6)
Step-by-step explanation:
The given quadratic is a perfect square, so has one repeated binomial factor:
k^2 -12k +36 = (k -6)^2
Calories consumed by members of a track team the day before a race are normally distributed, with a mean of 1,600 calories and a standard deviation of 100 calories. If a normal curve is sketched using these data, what is the range for 3 standard deviations to the right and to the left of the mean?
Answers
Answer:
600 calories
Step-by-step explanation:
John has consumed 1600 calories out of which he has burned off 400. So the total calories for the day so far are:
1600-400
=1200 calories
He has to keep the count of calories upto 1800 per day and the consumed calories so far are 1200
So he needs to burn:
= 1800 - 1200
= 600 calories
He has to consume 600 calories more..
Hence 1000 is not a viable solution to the problem as the remaining count of calories that need to be consumed are 600 ..
Answer:
The Answer is A.
Step-by-step explanation:
Hope this helps!
HELP PLS I GIVE ALL MY MONEY
Suppose the linear cost function C(x) = 6x gives the cost for buying x items. If the items are sold in packages of 10, and no one can buy more than 5 packages, then the RANGE of the function C is
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Answer:
The range of C is :60≤C≤300
Now I need all your money like you said you would give me :)
Step-by-step explanation:
And i need brainliest
Hello! Please help with this fill in the blank, thanks!
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Triangle ABC is rotated 180 degrees around point E, therefore, A maps to D, B maps to C, and C maps to B.
===================================================
Explanation:
If you were to rotate triangle ABC 180 degrees around point E, then it would line up perfectly with triangle DCB
Point A lands on point DPoint B lands on point CPoint C lands on point BNote how in the sequence ABC we have A first, B second, then C third
Then for the sequence DCB we have D first, C second, then B third
This order matters so we can pair up the points properly
A goes to D (A is first of ABC; D is first of DCB)B goes to C (B is second in ABC; C is second in DCB)C goes to B (C is third in ABC; B is third in DCB)A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 90% of the time when the person has the virus and 15% of the time when the person does not have the virus. (This 15% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive." (a) Using Bayes' Theorem, when a person tests positive, determine the probability that the person is infected. (b) Using Bayes' Theorem, when a person tests negative, determine the probability that the person is not infected.
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Answer:
a) P[A/B] = 0,019 or P[A/B] = 1,9 %
b) P[A- /B-] = 0,9996 or P[A- /B-] = 99,96 %
Step-by-step explanation:
Bayes Theorem :
P[A/B] = P(A) * P[B/A] / P(B)
The branches of events are as follows
Condition 1 real infection 1/300 and not infection 299/300
Then
1.- 1/300 299/300
When the test is done (virus present) 0,9 (+) 0,15 (-)
2.- 299/300
When the test is done ( no virus ) 0,15 (+) 0,85 (-)
Then:
P(A) = event person infected P(B) = person test positive
a) P[A/B] = P(A) * P[B/A] / P(B)
where P(A) = 1/300 = 0,0033 P[B/A] = 0,9
Then P(A) * P[B/A] = 0,0033*0,9 = 0,00297
P(B) is ( 1/300 )*0,9 + (299/300)*0,15
P(B) = 0,0033*0,9 + 0,9966*0,15 ⇒ P(B) = 0,1524
Finally
P[A/B] = 0,00297 /0,1524
P[A/B] = 0,019 or P[A/B] = 1,9 %
b) Following sames steps:
P[A- /B-] = (299/300) * 0,85 / (299/300) * 0,85 + (1/300 * 0,1)
P[A- /B-] = 0,8471 /0,8474
P[A- /B-] = 0,9996 or P[A- /B-] = 99,96 %
The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 71.5 miles/hour and a standard deviation of 4.75 miles/hour. The speed limit on this stretch of the freeway is 70 miles/hour. (a) A highway patrol officer is hidden on the side of the freeway. What is the probability that 5 cars pass and none are speeding? Assume that the speeds of the cars are independent of each other. (Round your answer to four decimal places.) .0074 (b) On average, how many cars would the highway patrol officer expect to watch until the first car that is speeding? (Round your answer to two decimal places.) What is the standard deviation of the number of cars he would expect to watch? (Round your answer to two decimal places.)
Answers
Answer:
a
[tex]G = 0.007523 [/tex]
b
The number of cars the highway patrol officer would watch before a car that is seen is [tex]E(X) = 1.6027 [/tex]
The standard deviation is [tex]s = 0.9829 [/tex]
gg
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 71.5 \ miles/hour[/tex]
The standard deviation is [tex]\sigma = 4.75 \ miles/hour[/tex]
The speed limit is [tex] x = 70 \ miles /hour[/tex]
Generally the probability of getting a car that is moving with speed greater than the speed limit is mathematically represented as
[tex]p =P(X > x ) = P(X > 70) = P(\frac{X - \mu }{\sigma } > \frac{70 - 71.5 }{4.75})[/tex]
=> [tex] p= P(X > 70) = P(\frac{X - \mu }{\sigma } > \frac{70 - 71.5 }{4.75})[/tex]
=> [tex] p= P(X > 70) = P(\frac{X - \mu }{\sigma } > -0.31579 )[/tex]
Here
[tex]\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of X )[/tex]
So
=> [tex] p= P(X > 70) = P(Z > -0.31579 )[/tex]
From the z-table
[tex]p = P(Z > -0.31579 ) = 0.62392[/tex]
So
[tex] p = P(X > 70) = 0.62392 [/tex]
Generally the probability of getting a car that is not moving with speed greater than the speed limit is mathematically represented as
[tex]q = 1 - p[/tex]
=> [tex]q = 1 - 0.62392 [/tex]
=> [tex]q = 0.37608 [/tex]
Generally the probability of getting 5 cars that are not speeding is mathematically represented as
[tex]G = q^5[/tex]
=> [tex]G = (0.37608)^5[/tex]
=> [tex]G = 0.007523 [/tex]
Generally the number of cars that the highway patrol officer is expected to watch until the first car that is speeding is gotten is mathematically represented as
[tex]E(X) = \frac{1}{p}[/tex]
=> [tex]E(X) = \frac{1}{0.62392}[/tex]
=> [tex]E(X) = 1.6027 [/tex]
Generally the standard deviation is mathematically represented as
[tex]s = \sqrt{\frac{1 - p }{ p^2} }[/tex]
=> [tex]s = \sqrt{\frac{1 -0.62392 }{ (0.62392)^2} }[/tex]
=> [tex]s = 0.9829 [/tex]
The probability that 5 cars pass and none are speeding is 0.007523 and the number of cars the highway patrol officer would watch before a car that is seen is E(X) = 1.6027
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The distribution of passenger vehicle speeds traveling on a certain freeway in California is nearly normal with a mean of 71.5 miles/hour and a standard deviation of 4.75 miles/hour.
The speed limit on this stretch of the freeway is 70 miles/hour.
Generally, the probability of getting a car that is moving with speed greater than the speed limit is mathematically represented as;
[tex]p = P(X > x) = P(X > 70) = P(z = \dfrac{X - \mu}{\sigma } > \dfrac{70 - 71.5}{4.75})\\\\p = P(X > 70 ) = P(\dfrac{X -\mu}{\sigma} > -0.31579)[/tex]
From the z-table
[tex]p = P(X > 70)= P(z > -0.31579) \\\\p = 0.62392[/tex]
Generally, the probability of getting a car that is not moving with speed greater than the speed limit will be
q = 1 - p
q = 1 - 0.62392
q = 0.37608
Generally, the probability of getting cars that are not speeding will be
G = q⁵
G = 0.37608⁵
G = 0.007523
The number of cars that the highway patrol officer is expected to watch until the first car that is speeding is gotten will be
[tex]\rm E(X) = \dfrac{1}{p}\\\\E(X) = \dfrac{1}{0.62392}\\\\E(X) = 1.6027[/tex]
The standard deviation will be
[tex]\sigma = \sqrt{\dfrac{1-p}{p}}\\\\\\\sigma = \sqrt{\dfrac{1-0.63292}{0.62392}}\\\\\\\sigma = 0.9829[/tex]
More about the normal distribution link is given below.
https://brainly.com/question/12421652
PERCENTAGE of 7.50 OF ₹6
Answers
Answer:%80 or 0.8
Step-by-step explanation:
Total = 7.50
Part of 7.50 is 6
The percentage of 6 in 7.50 is 6*100/7.50
0.8* 100
80%
Or you could do it this way:
6/7.5
x10 on both
60/75
by 5 times
12/15
4/5
=0.8
Write an equation of the line passing through each of the following pairs of points. c (4, 0), (−2, 8)'
Answers
Answer:
Step-by-step explanation:
First, you must find the slope of the line using the formula (y2-y1/x2-x1). For your problem that would be (8-0/-2-4)= -4/3.
Then, you would plug in the slope and the y-intercept into the slope-intercept formula (y=mx+b), where m is the slope and b is the y intercept (4).
Your answer would be y=-4/3x+4
The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the measure of the third angle of the triangle is 45° more than nbsp the measure of either of the other two angles, find the measure of each angle of the triangle. (Recall that the sum of the measures of the angles of a triangle is 180°.)
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Please I need help 20 POINTS!
The question States: come up with a story problem that matches the above representations. (There all apart of the same problem)
Answers
Answer: 9
Solving Steps:
A hockey player strikes a hockey puck. The height of the puck increases until it reaches a maximum height of 3 feet, 55 feet away from the player. The height y (in feet) of a second hockey puck is modeled by y=x(0.15−0.001x), where x is the horizontal distance (in feet). Compare the distances traveled by the hockey pucks before hitting the ground.
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The total distance travelled by the first and second hockey pucks before hitting the ground is 110 feet and 150 feet, respectively.
We are given that there are two hockey pucks.The height of the first hockey puck increases until it reaches a maximum height of 3 feet when it is 55 feet away from the player.This hockey puck will travel an additional 55 feet after it reaches its maximum height before it hits the ground.The total distance travelled by the first hockey puck before hitting the ground is 110 feet.The height y (in feet) of the second hockey puck is modelled by y=x(0.15−0.001x), where x is the horizontal distance (in feet).When it hits the ground, its height will be zero.0 = x(0.15−0.001x)x(0.15−0.001x) = 0A value of "x" is 0 when it is just hit by the player.When it hits the ground, the value of "x" is :0.15−0.001x = 00.001x = 0.15x = 150The total distance travelled by the second hockey puck before hitting the ground is 150 feet.To learn more about distance, visit :
https://brainly.com/question/15172156
#SPJ1
The Perimeter of a triangle is 90 cm. The triangle has side lengths of 2x + 5, 4x - 10, and x + 4. Find the value of x and the length of each side.
Answers
Answer:
This makes no sense as you dont say what type of triangle it is
Step-by-step explanation:
If its a equallateral its x = 89/7
What would make the following equation true?
5m+(2m+8)=__+8
Answers
Answer:
7m
Step-by-step explanation:
Answer: 7m
Step-by-step explanation: 5m + 2m = 7m, so 5m+2m+8 = 7m+8
Please help, explain and correct the mistake on the picture below, marking brainliest!
Answers
Answer:
see below
Step-by-step explanation:
2/3 x = -6
Multiply each side by the reciprocal to isolate x
3/2 * 2/3x = -6 * 3/2
x = -9
In a week, 12 hens laid 84 eggs. What is the unit rate for eggs per hen?
Answers
Answer:
7 eggs per hen
Step-by-step explanation:
There were 84 eggs laid between the 12 hens. That means the 84 eggs are split among the 12 hens. 84 divided by 12 = 7.
Dexter got a raise in his hourly pay, from $12.75 to $16.30. Find the percent change. Round to the nearest tenth of a percent.
Answers
Answer:
27.8
Step-by-step explanation:
16.3 - 12.75 = 3.55
3.55 ÷ 12.75 = 27.8
solve for the variable. b^2 = 100
Answers
Answer:
b = ±10
or
b = -10, 10
Step-by-step explanation:
Step 1: Write equation
b² = 100
Step 2: Solve for b
Square root both sides: b = ±10Step 3: Check
Plug in x to verify it's a solution.
(-10)² = 100
(10)² = 100
Answer:
b=-10 or b=10
Step-by-step explanation:
They would both work because negative times negative is also positive so it would also work.
*someone deleted my answer to this question saying it was incorrect but it was correct :/
The column headers of a formal proof are _____________ and ____________.
statements and reasons
definitions and examples
givens and conclusions
conjectures and counterexamples
Answers
Answer:
Statements and reasons
Step-by-step explanation:
Answer:
statements and reasons
Step-by-step explanation:
These headers are standard and are used on every formal proof.