Viết các số 1,2,..,100 theo một thứ tự nào đó, được dãy a1, a2,..,a100. CMR: Tổng S= |a1 - 1| + |a2 -2| + .. +|a100 -100|. Hãy tổng quát hóa bài toán
Is the function f(x) = 1/8 ^x an exponent function? If so , identify the base , if not why not ?

Yes , the base is 1/e
yes, the base is e
No, there is no base that is a positive real number not equal to 1 raised to a variable exponent.
No, the base is the reciprocal of e, a number smaller than 1.
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Answer:
(a) Yes , the base is 1/e
Step-by-step explanation:
The variable is in the exponent, so this is an exponential function.
The base is the number that has the exponent. The base is (1/e).
Answer:
Step-by-step explanation:
bvxbvxbvxbvcvbbb cv
Find the measure of angle x in the figure below:
A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 57 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 61 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 67 degrees. The interior angle on the left is labeled as x.
35°
47°
51°
62°
Your answer iss...
It is 51º
I need help completing this problem ASAP
Answer:
[tex]4\sqrt{5}[/tex]
Step-by-step explanation:
Prime factorize 20 and 45
[tex]\sqrt{20}=\sqrt{2*2*5}=2\sqrt{5}\\\\\\\sqrt{45}= \sqrt{5*3*3}=3\sqrt{5}[/tex]
[tex]\sqrt{20}-\sqrt{5}+\sqrt{45}=2\sqrt{5}-\sqrt{5}+3\sqrt{5}[/tex]
[tex]=(2-1+3)\sqrt{5}\\\\\\= 4\sqrt{5}\\[/tex]
e) Three friends were each given 25% of pie. What fraction of the pie was given altogether?
Answer:
3/4 or 75% or .75
Step-by-step explanation:
You would multiply 3 * .25 because there are three people getting 25% of a pie. All of the answers above are equivalent
Find perpendicular,hypotenuse and base
Step-by-step explanation:
In right angled triangle ABC,
Taking alpha as reference angle,
By pythagoras theorem,
p=BC,h=AB,b=AC
Taking thita as reference angle,
p=AC,h=AB,b=BC
Keep smiling and hope u are satisfied with my answer.Have a good day :)
a basketball player makes each free-throw with a probability of 0.3 and is on the line for a one-and-one free throw. (that is, a second throw is allowed only if the first is successful.) what is the probability that the player will score 0 points
Answer:
0.7 = 70% probability that the player will score 0 points.
Step-by-step explanation:
For each free throw, we have these following probabilities:
0.3 probability the player makes.
0.7 probability the player misses.
What is the probability that the player will score 0 points?
He is only allowed the second if he misses the first, thus, he ends with 0 points only if he misses the first.
For any free throw:
0.7 probability the player misses, so 0.7 = 70% probability that the player misses the first free throw, and 0.7 = 70% probability that the player will score 0 points.
the question is in the photo
9514 1404 393
Answer:
108.8 km/h at 84.3°
Step-by-step explanation:
The law of cosines can be used to find the resultant ground speed. In the attached diagram, the length of interest is OR. It will be found as ...
OR² = OP² +PR² -2·OP·PR·cos(P)
OR² = 130² +26² -2×130×26×cos(32°) ≈ 11843.19
OR = √11843.19 ≈ 108.8
__
The angle POR can be found from the law of sines.
sin(POR)/PR = sin(OPR)/OR
sin(POR) = PR/OR×sin(32°) ≈ 0.12660
∠POR ≈ arcsin(0.12660) ≈ 7.27°
Then the bearing of the ground track of the airplane is 77° +7.27° = 84.27°.
The airplane is traveling at about 108.8 km/h on a bearing of 84.3°.
define ascending and descending order by your and give one example
Answer:
ascending order} an order of numbers from least to greatest like 1 2 3 4
descending order} an order of numbers from greatest to least like 4 3 2 1
Find the value of term a14 in the sequence.
3, 1, –1, –3, –5, . . .
–23
–11
–9
–25
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Answer:
(a) -23
Step-by-step explanation:
The sequence is arithmetic with first term 3 and common difference -2. Then the general term is ...
an = a1 +d(n -1)
an = 3 -2(n -1)
and the 14th term is ...
a14 = 3 -2(14 -1) = 3 -2(13) = 3 -26
a14 = -23
Find COS Instructions: Find the value of the trigonometric ratio. Make sure to simplify the If needed
Answer:
Sin X = 12 / 37
Step-by-step explanation:
Given a right angled triangle, we are to obtain the Sin of the angle X ;
Using trigonometry, the sine of the angle X , Sin A is defined as the ratio of the angle opposite X to the hypotenus of the right angle triangle.
In the right angle triangle :
Sin X = opposite / hypotenus
Opposite = 12 ; hypotenus = 37
Sin X = 12 / 37
I NEED HELP PLEASE!!!!
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Answer:
A. 1/2
Step-by-step explanation:
The points on a unit circle are (cos(θ), sin(θ)), where θ is the angle from the +x axis to to the ray from the origin through that point.
If the point is (√3/2, 1/2), then sin(θ) = 1/2.
A trader sold 90 oranges at 3 for GHC 0.75.
How much did she get from selling all the
oranges?
Answer:
GHC22.5
Step-by-step explanation:
90/3=30
30=0.75
30×0.75
=22.5
A sample tested the claim that heights of men and heights of women have difference variances, with s=7.42388 cm for women and 7.14974 cm for men. The sample sizes are n1=144 and n2=156. When using the F test with these data, is it correct to reason that there is no need to check for normality because n1>30 and n2>30?
No. The F test has a requirement that samples be from the normally distributed populations, regardless of how large the samples are.
The F-test simply shows whether the variances that are in the numerator and the denominator are equal. The F-test can be applied on a large sampled population.
One main assumption of the F test is that the populations where the two samples are drawn are normally distributed.
Regarding the question, it's important to note that when using the F test with these data, it's not correct to reason that there is no need to check for "normality".
It should be noted that the F test has a requirement that samples are from the normally distributed populations, regardless of how large such samples are.
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Question 8 of 10
If f(x) = 4x2 and g(x) = x+1, find (f•g)(x).
A. 4X2 + 1
B. 4x2 + 4x2
C. 4(x+1)
D. 4x(x)
SURVIT
Answer:
option c is the answer for your question
the formula for finding the circumference of a circle with radius,r, is circumference= 2πr. What is the formula for the circumference of a circle with a radius r/2?
Answer:
πr
Step-by-step explanation:
radius = r/2
so circumference = 2π(r/2)
= 2πr/2
= πr
Answer:
The answer is B which is C=2πr
Step-by-step explanation:
i just did it
i need help with this question asapppppp
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Answer:
$11,680.58
Step-by-step explanation:
Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.
__
The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.
The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...
0.205×21,465 = 4400.325 ≈ 4400.33
The the total tax due on $70,000 is ...
$7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000
_____
Additional comments
The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.
__
Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.
≤ 48535 -- income × 0.15
≤ 97069 -- income × 0.205 -2669.425
≤ 150,473 -- income × 0.26 -8008.22
≤ 214,368 -- income × 0.29 -12,522.41
> 214,368 -- income × 0.33 -21,097.13
In this case, the second row of this simpler table would give the tax on $70,000 as ...
tax = 70,000 × 0.205 -2669.425
tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above
Choose the best answer from the choices below:
If a radius of a circle bisects a chord which is not a diameter, then ____.
Answer: the radius is perpendicular to the chord.
If a radius of a circle bisects a chord which is not diameter, then the radius is perpendicular to the chord.
Answered by Gauthmath must click thanks and mark brainliest
The radius is perpendicular to the chord.
Does the radius of the circle bisect the string?If the radius of the circle is perpendicular to the chord of the circle, the radius bisects the chord. The two strings are congruent only if they are equidistant from the center of the circle.
No, not all strings in a circle are diameters because the diameter passes through the center of the circle. Therefore, all the diameters of a circle are also strings, not all the strings of a circle.
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Find two power series solutions of the given differential equation about the ordinary point x = 0. Compare the series solutions with the solutions of the differential equation obtained using the method of Section 4.3. Try to explain any differences between the two forms of the solution. y'' − y' = 0 y1 = 1 − x2 2! + x4 4! − x6 6! + and y2 = x − x3 3! + x5 5! − x7 7! + y1 = x and y2 = 1 + x + x2 2! + x3 3! + y1 = 1 + x2 2! + x4 4! + x6 6! + and y2 = x + x3 3! + x5 5! + x7 7! + y1 = 1 + x and y2 = x2 2! + x3 3! + x4 4! + x5 5! + y1 = 1 and y2 = x + x2 2! + x3 3! + x4 4! +
You're looking for a solution in the form
[tex]y(x) = \displaystyle \sum_{n=0}^\infty a_nx^n[/tex]
Differentiating, we get
[tex]y'(x) = \displaystyle \sum_{n=0}^\infty na_nx^{n-1} = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1)a_{n+1}x^n[/tex]
[tex]y''(x) = \displaystyle \sum_{n=0}^\infty (n+1)na_{n+1}x^{n-1} = \sum_{n=1}^\infty (n+1)na_{n+1}x^{n-1} = \sum_{n=0}^\infty (n+2)(n+1)a_{n+2}x^n[/tex]
Substitute these for y' and y'' in the differential equation:
[tex]\displaystyle \sum_{n=0}^\infty (n+2)(n+1)a_{n+2}x^n - \sum_{n=0}^\infty (n+1)a_{n+1}x^n = 0[/tex]
[tex]\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1)a_{n+2}-(n+1)a_{n+1}\bigg)x^n = 0[/tex]
Then the coefficients of y are given by the recurrence
[tex]\begin{cases}a_0=y(0)\\a_1=y'(0)\\a_{n+2}=\frac{a_{n+1}}{n+2}&\text{for }n\ge0\end{cases}[/tex]
or
[tex]a_n = \dfrac{a_{n-1}}n[/tex]
But we cannot assume that [tex]a_0[/tex] and [tex]a_1[/tex] depend on each other; we can only guarantee that the recurrence holds for n ≥ 1, so that
[tex]a_2=\dfrac{a_1}2 \\\\ a_3=\dfrac{a_2}3=\dfrac{a_1}{3\times2} \\\\ a_4=\dfrac{a_3}4=\dfrac{a_1}{4\times3\times2} \\\\ \vdots \\\\ a_n=\dfrac{a_1}{n!}[/tex]
So in the power series solution, we split off the constant term and we're left with
[tex]y(x) = a_0 + a_1 \displaystyle \sum_{n=1}^\infty \frac{x^n}{n!}[/tex]
so that the fundamental solutions are
[tex]y_1=1[/tex]
and
[tex]y_2=x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\dfrac{x^4}{4!}+\cdots[/tex]
8 rational numbers between 3 and 4
Answer:
31/10,32/10,33/10,34/10,35/10
Step-by-step explanation:
a rational number is formed when any two integers p and q are expressed in the form of p/q
to find two two sets of rational numbers BETWEEN any two numbers
a and b we need to express a and b and rational numbers....let us express 3and4 as rational numbers 3=30/10 4=40/10
the list of rational numbers between 3and4,that is, 30/10,31/10,32/10,33/10,34/10,35/10,36/10,37/10,38/10,39/10,40/10.
therefore the five rational numbers between 3 and 4 are (31/10,32/10,33/10,34/10,35/10...
I hope that helps
Which of the following lines is perpendicular to y = -2x +3?
A. y= 2x +3
B.
1
y=-x+3
2
C. y=-2x +2
D.
1
= --X-2
2
y=1/2x-2 is perpendicular to y=2x+3
which expression is equivalent to c^2 - 4 / c + 3 /
Step-by-step explanation:
[tex] \frac{ {c}^{2} - 4 }{c + 3} [/tex]
[tex] \frac{(c - 2)(c + 2)}{(c + 3)} [/tex]
find the solution of the general equation of the differential equation:
(1-cosx)y' - ysinx =0, x ≠ k2π
Notice that the condition x ≠ 2πk for (presumably) integer k means cos(x) ≠ ±1, and in particular cos(x) ≠ 1 so that we could divide both sides by (1 - cos(x)) safely. Doing so lets us separate the variables:
(1 - cos(x)) y' - y sin(x) = 0
==> (1 - cos(x)) y' = y sin(x)
==> y'/y = sin(x)/(1 - cos(x))
==> dy/y = sin(x)/(1 - cos(x)) dx
Integrate both sides and solve for y. On the right, substitute u = 1 - cos(x) and du = sin(x) dx.
∫ dy/y = ∫ sin(x)/(1 - cos(x)) dx
∫ dy/y = ∫ du/u
ln|y| = ln|u| + C
exp(ln|y|) = exp(ln|u| + C )
exp(ln|y|) = exp(ln|u|) exp(C )
y = Cu
y = C (1 - cos(x))
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a heart.
The probability is ___.
(Type an integer or a fraction. Simplify your answer.)
Answer:
3/4
Step-by-step explanation:
There are 13 hearts in a 52 deck.
52-13=39
39/52=3/4
The probability that you are not dealt a heart from the deck of cards is 3/4.
What is the probability that you are not dealth with a heart?Probability determines the chances that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that you are not dealth with a heart = 1 - (number of hearts / total number of cards)
1 - 13/52 = 39/52 = 3/4
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What is the value of In et?
ОО
O 1
02
0 4
ASAP
The value of exponential expression ln e⁴ is 4
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an exponential expression ln e⁴ we need to simplify it,
So,
we know that,
ln aⁿ = n ln a
and =
ln e = 1
so,
ln e⁴ = 4 ln e
= 4 x 1
= 4
Hence, the value of exponential expression ln e⁴ is 4
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An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 244 of these passed the probe. Assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe. (Round your answers to three decimal places.)
Answer:
The 95% confidence interval for the proportion of all dies that pass the probe is (0.637, 0.733).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
356 dies were examined by an inspection probe and 244 of these passed the probe.
This means that [tex]n = 356, \pi = \frac{244}{356} = 0.685[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.685 - 1.96\sqrt{\frac{0.685*0.315}{356}} = 0.637[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.685 + 1.96\sqrt{\frac{0.685*0.315}{356}} = 0.733[/tex]
The 95% confidence interval for the proportion of all dies that pass the probe is (0.637, 0.733).
A regular 2016-gon with all vertices on the unit circle is given. Find its perimeter, as a decimal to the nearest hundredth. (I have been stuck on this problem for half a hour I need help asap)
Answer:
6.28 unitsStep-by-step explanation:
Interior angle opposite to each side of the polygon is:
(360/2016)°Since the circle is unit circle, its radius is 1 unit.
Let the side is a, then as per definition of sine we have:
sin ((360/2016)/2) = (a/2)/1a = 2 sin (180/2016)°a = 0.00311665811The perimeter is:
P = 2016a = 2016(0.00311665811) ≈ 6.28 unitsJacqueline will spend a fair spinner with the numbers 0 1 2 3 and 4 a total of three times if event a spinner lands on numbers are greater than 2 and event be total sum of 9 which of the following best describes event A and B
Events are said to be INDEPENDENT if the occurence of one does not rest or depend on the outcome of another. Therefore, since the outcome of event A and B does not depend on each other, then both events are INDEPENDENT
Giving a brief description of the options given :
• Dependent events are simply events where the outcome of one event affects the occurence of the other. This is usually related to selection without replacement, where the number of subjects changes after each selection.
• Mutually Exclusive events simply refers to a scenario whereby two events cannot occur simultaneously. For instance, obtaining a head and a tail simultaneously during a single coin throw.
• Complement events describes two exactly opposite events. For instance, the Complement of obtaining a 4 on a 6 - sided die roll is (1, 2, 3, 5, 6)
For the event described above , the occurrence of A does not hinder the occurrence of the other (not a dependent event ) and it is possible to have both events simultaneously (not Mutually exclusive) (If we have 3 in all throws then both events have occurred )
Therefore, the best description for events A and B is that both events are INDEPENDENT.
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Answer: the answer is dependent
Step-by-step explanation:
Events are independent if the knowledge of one event occurring does not affect the chance of the other event occurring. In this case, the chance of Event B occurring is greater if Event A occurs, so these events are dependent. Since the spinner could land on 3, 3, and 3, the events are not mutually exclusive.
1/1*2 +1/2*3+...+1/n(n+1)= n/n+1 proof by mathematical induction
I need this asap!!
Base case (n = 1):
• On the left side: 1/(1×2) = 1/2
• On the right side: 1/(1 + 1) = 1/2
Induction hypothesis: Assume the statement is true for n = k ; that is,
1/(1×2) + 1/(2×3) + … + 1/(k × (k + 1))) = k/(k + 1)
Inductive step (n = k + 1):
1/(1×2) + 1/(2×3) + … + 1/(k × (k + 1))) + 1/((k + 1) × (k + 2)))
= k/(k + 1) + 1/((k + 1) × (k + 2))
= (k × (k + 2) + 1) / ((k + 1) × (k + 2))
= (k ² + 2k + 1) / ((k + 1) × (k + 2))
= (k + 1)² / ((k + 1) × (k + 2))
= (k + 1) / (k + 2)
and this is what we wanted to show.
Find two consecutive even numbers whose sum is 758.
Answer:
378 and 380
Step-by-step explanation:
The two even consecutive numbers that add up to 758 are going to be very close to half of 758. This is because two half of 758 are going to be the most similar addends of 758. This is important because the answers will be consecutive and therefore, must also be very similar. To solve, first, divide 758 by 2. This is 379, which is not an even number. So, to find the needed addends subtract and add 1 to 379. Both of these will be even and consecutive. These two numbers are 378 and 380. Then, to check you, can add them and see that they do sum 758.
Answer:
Step-by-step explanation:
Let the first number = x
Let the second number = x + 2
x + x + 2 = 758 Collect like terms
2x + 2 = 758 Subtract 2
2x = 758 - 2 Combine
2x = 756 Divide by 2
2x/2 = 756/2
x = 378
The first number is 378
The second number 380
If your teacher is really fussy, you can do it this way.
Let the first number = 2x
Let the second number = 2x + 2
The reason for this is to guarantee that both numbers were even to start with.
2x + 2x+2 = 758 Combine like terms
4x + 2 = 758 Subtract 2
4x = 756 Divide by 4
x = 756/4
x = 189
Therefore 2x = 378
2x + 2 = 380 Just as before.
