Which of the following is the correct expanded form for the series below?
A. 1+1+1/2+1/6
B.1+1/2+1/6+1/24
C.1+2/3+1/2+2/5
D.4+2+2/3+1/6
Answers
Answer: Option A is correct that is [tex]1 +1+\frac{1}{2} +\frac{1}{6}[/tex]
Explanation:
we will substitute the values of n in given expression
[tex]\sum_{n=1}^{4}\frac{n}{n!}[/tex]
when substituting n=1 we get in [tex]\sum_{n=1}^{4}\frac{n}{n!}[/tex]=[tex]\frac{1}{1!}[/tex]
when n=2 we get [tex]\frac{2}{2!}[/tex]
when n =3 we get [tex]\frac{3}{3!}=\frac{3}{6}=\frac{1}{2}[/tex] ;3 factorial that is 3! = 3 *2*1 = 6
when n=4 we get [tex]\frac{4}{4!}=\frac{4}{24}=\frac{1}{6}[/tex];4! = 4*3*2*1 = 24
Note: factorial means the product of the terms getting multiplied till 1
suppose n! will be equal to n(n-1)(n-2)(n-3).......1
The correct expanded form for the series is Option B, which represents the sum of inverse factorials up to 1/3! The other options do not accurately depict the factorial series.
Explanation:The correct expanded form for the series given would be the option that correctly represents the sum of the factorial terms in the sequence. The series in the choices seems to depict a sum of inverse factorials. Factorials are mathematical expressions that involve multiplying a series of descending natural numbers. The factorial of a number n is represented as n! and is equal to n × (n-1) × (n-2) × … × 1. Therefore, 0! and 1! are both equal to 1, while 2! is equal to 2, 3! equals 6, and 4! equals 24, and so on.
By applying this logic to the options:
Option A is incorrect because 1/6 is equivalent to 1/3! not 1/4!.Option B, 1 + 1/2 + 1/6 + 1/24, correctly represents the sum 1/0! + 1/1! + 1/2! + 1/3!.Option C is incorrect as the sequence of numbers does not represent factorials.Option D is incorrect because the numbers do not follow the pattern of the inverse factorial sequence.Therefore, the correct answer is Option B.
Related Questions
The Jonas school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table, where Low represents the fewest days attended and High represents the most days attended for a single student.
School High School M High School N High School P
Low - 128 131 140
High - 180 180 180
Range- 52 49 40
Mean- 141 159 153
Median- 160 154 165
IQR- 55.5 48.5 32.5
σ- 41.5 36.5 31.5
Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. (5 points) Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically. (5 points)
Answers
So, the answer to A) is the third High School: HS P
B) Here one looks at the central measurement: mean, median. This example is not super easy. HS N has the highest mean value, but HS P has the highest median. The median is more robust than the mean, since it is less affected by outliers. So HS P is a good candidate.
Finally, looking at the Low/High values, one can see that the high is the same: some day(s) when all students went and all HS have a maximum number of 180 students. However, the highest low is HS P.
So, I think HS P should also be awarded for the highest rate, since its median
is the highest and the lower number of students is the highest.
Median means 50% of the cases have values less than the median. Mean is an average.
What is [tex] 3\sqrt{18} [/tex] + [tex] 2\sqrt{50} [/tex] simplified?
F.[tex] 19\sqrt{2} [/tex]
G.[tex] 39\sqrt{2} [/tex]
H.[tex] 77\sqrt{2} [/tex]
I. [tex] 90\sqrt{2} [/tex]
IF THERE IS WORK PLEASE SHOW THANKS:)
Answers
A bag has five red marbles, six blue marbles, and four black marbles. What is the probability of picking a blue marble, replacing it, and then picking another blue marble?
a)1/15
b)8/75
c)4/25
d)1/9
Answers
P(picking blue) = 6/15 ...reduces to 2/5
replacing
P(picking blue) = 6/16...reduces to 2/5
P(both) : 2/5 * 2/5 = 4/25 <==
Answer:
4/15 is 100% the answer *NOT* 1/9 or anything else!
Step-by-step explanation:
a factor of the quadratic 6x2-11x-35
Answers
6x^2-11x-35
= (3x+5)(2x-7)
Answer: (3x+5)(2x-7)
6x^2-11x-35
x^2-11x-210
(x-21)(x+10)
(x-(21/6))(x+(10/6))
(x-(7/2))(x+(5/3))
(2x-7)(3x+5)
Final answer: (2x-7)(3x+5)
Lisa bought a suit on sale for 459. This price was 15% less than the original price. What was the original price?
Answers
So we have to find 15% more of 459, and to do this, we have to:
Add 100 + 15 = 115
115/100 = 1.15
1.15 x 459 = 527.85
Hope this answers your question
To find the original price of Lisa's suit, convert the discount to a decimal and divide the sale price by one minus the discount rate. The original price is calculated to be $540.
To calculate the original price of Lisa's suit, which she bought on sale for $459 at a discount of 15% less than the original price, we can use the formula:
Original Price = Sale Price / (1 - Discount Percent)
First, we convert the percentage discount to a decimal:
15% = 0.15
Then, we divide the sale price by the complement of the discount rate:
Original Price = $459 / (1 - 0.15)
Original Price = $459 / 0.85
Original Price = $540
Therefore, the original price of the suit was $540.
A photo that is 3 inches wide by 5 inches long is being enlarged so that it is 12 inches long. How wide will the enlarged photo be
Answers
12/5 = 2.4 times larger
3 x 2.4 = 7.2 inches wide
I need some more help plz
Answers
So this is why the answer is choice A
What is the solution set of the equation x^2 - 7x - 18 = 0
Answers
x=9 or x=-2
Factoring this trinomial as the product of two binomials,
we have (x - 9)(x + 2) and set that equal to 0.
So we have (x - 9)(x + 2) = 0.
So either x - 9 = 0 or x + 2 = 0.
Solving for x in each equation, we find that our solution is {9, -2}.
Best explained and correct answer gets brainliest.
Answers
3275 = x * (1+0.075/12)^(12*10)
3275 = x * (2.11206463)
x= 3275/2.11206463 = 1550.6154
x=1550.62
she needs to deposit $1,550.62
There are 10 runners in race. in how many ways can the first, second and third place finishes occur
Answers
10*9*8 = 720 ways
A plane's airspeed is 400 miles per hour on a heading of 45 degrees south of east (compass: 135 degrees, babylonian 315 degrees). if a wind is blowing from the west with a speed of 50 miles per hour, what is the ground speed and direction of the plane?
Answers
To answer this item, we take the x- and y-components of the speeds.
Airplane:
x-component = (400 mi/hr)(cos 45°) = 282.84 mi/h
y-component = -(400 mi/hr)(sin 45°) = -282.84 mi/h
Wind:
x-component = -(50 mi/hr)(sin 90°) = -50 mi/hr
y-component = 0 mi/hr
Adding up the components:
x-component = 282.84 mi/hr - 50 mi/hr = 232.84 mi/hr
y-component = -282.84 mi/hr
The resultant speed would be,
R = sqrt ((232.84 mi/hr)² + (-282.84 mi/hr)²) = 366.35 mi/h
The direction would be,
tan (∅) = -282.84 mi/hr / 232.84 mi/hr
∅ = 50.53° (south of east)
ANSWER: 366.35 mi/hr, 50.53° South of East
If the length of side a is 6 centimeters, the length of side b is 4 centimeters, and the length of side c is 7 centimeters, what is the measure of ? Round your answer to two decimal places.
Answers
Answer:
34.77
Step-by-step explanation:
The area of a triangle with sides of length 6 cm, 4 cm, and 7 cm is approximately 11.95 cm² when calculated using Heron's formula and rounded to two decimal places.
The original question appears to be incomplete as there's no clear indication of which measure is being sought for the triangle with sides of length 6 cm, 4 cm, and 7 cm. However, if the goal is to use these sides to determine the area of a triangle, we can use Heron's formula, since the lengths given do not form a right triangle.
First, calculate the semiperimeter (s):
(s) = (a + b + c) / 2
(s) = (6 + 4 + 7) / 2
(s) = 17 / 2
(s) = 8.5 cm
Now, apply Heron's formula which is Area [tex](A) = \sqrt{[ (s)((s)-a)((s)-b)((s)-c) ][/tex]:
[tex]A = \sqrt{[8.5(8.5-6)(8.5-4)(8.5-7)]}\\A = \sqrt{[8.5(2.5)(4.5)(1.5)]}\\A = \sqrt{[8.5 \times 2.5 \times 4.5 \times 1.5]}\\A \approx 11.95 cm^2 after\ calculating\ the\ square\ root[/tex]
Thus the area of the triangle is approximately [tex]11.95 cm^2[/tex] (rounded to two decimal places). Note that the question's original instructions to round to two significant figures would result in an answer of [tex]12 cm^2[/tex].
Let x+3, 2x+1, and 5x+2 be consecutive terms of an arithmetic sequence. find the absolute value of the common difference of the terms.
Answers
Difference between first and second terms,
D1 = (2x + 1) - (x + 3)
D1 = x - 2
Difference between second and third terms,
D2 = (5x + 2) - (2x + 1)
D2 = 3x + 1
Equating the differences,
D1 = D2
x - 2 = 3x + 1
Transposing the variables and constants to each of the sides of the equation,
x - 3x = 1 + 2
-2x = 3
Dividing the equation by -2,
x = -3/2
Substituting this value to either of the difference,
D1 = x - 2 = (-3/2) - 2 = -7/2
The absolute value of the difference is 7/2. Thus, the answer is 7/2.
order the group of quadratic functions from widest to narrowest graph
y=-7x^2
y=-1/5x^2
y=-1/3x^2
Answers
y=-1/3x^2
y=-7x^2
Answer:
Widest to narrowest
[tex]y=-\frac{1}{5}x^2[/tex] - [tex]y=-\frac{1}{3}x^2[/tex] - [tex]y=-7x^2[/tex]
Step-by-step explanation:
Given : Graph 1 - [tex]y=-7x^2[/tex]
Graph 2- [tex]y=-\frac{1}{5}x^2[/tex]
Graph 3 - [tex]y=-\frac{1}{3}x^2[/tex]
To find : Order the group of quadratic functions from widest to narrowest graph.
Solution :
First we plot the given graph,
Refer the attached figure below.
In the graph, we see that all graph has same vertices (0,0) and
Graph 2 with green in color [tex]y=-\frac{1}{5}x^2[/tex] is the most widest graph among all.
Then graph 3 with purple in color is the widest and then graph 1 with blue in color is the most narrowest graph.
So, The order of the graph from widest to narrowest is
Graph 2 - Graph 3 - Graph 1
[tex]y=-\frac{1}{5}x^2[/tex] - [tex]y=-\frac{1}{3}x^2[/tex] - [tex]y=-7x^2[/tex]
which equation represents the statement thirteen less then a number is forty two
Answers
x is the "variable", you're taking 13 away from that, and the answer is also given, 42.
Answer:
The equation which represents the statement thirteen less then a number is forty two is:
x-13=42
Step-by-step explanation:
Let x be any number
we are given that:
thirteen less then a number is forty two
i.e. x-13=42
Hence, the equation which represents the statement thirteen less then a number is forty two is:
x-13=42
Which of the following are the coordinates of the vertex of y=3x^2+3?
Answers
The image shown has two triangles sharing a vertex:
What is the measure of ∠WZX, and why?
A. y over 2, because Triangle UVW is congruent to triangle WXZ
B. y, because Triangle UVW is similar to triangle ZXW
C. y + 50 degrees, because Triangle UVW is similar to triangle ZXW
D. 130 degrees − y, because Triangle UVW is congruent to triangle WXZ
Answers
The measure of ∠WZX is B; y, because Triangle UVW is similar to triangle ZXW.
What is vertically opposite angles?The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
We can see that Angles UVW ad ZXW are congruent,
Then because of the vertical angle theorem; angles UWV and XWZ are congruent.
So if there are 2 angles in each triangle which are congruent to each other, then the triangle angle sum theorem state that the third angle also has to be congruent in each.
BUT congruent angles do not make the triangles congruent due to the length of the sides can change and the measures of the angles remain unchanged.
Hence, The measure of ∠WZX is B; y, because Triangle UVW is similar to triangle ZXW.
Learn more about vertically opposite angles;
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Richard has just been given a 4-question multiple-choice quiz in his history class. each question has four answers, of which only one is correct. since richard has not attended class recently, he doesn't know any of the answers. assuming that richard guesses on all four questions, find the indicated probabilities. (round your answers to three decimal places.) (a) what is the probability that he will answer all questions correctly
Answers
The probability of answering all the question correctly is [tex]\boxed{\bf \dfrac{1}{256}}[/tex]
Further Explanation:
Given:
The total number of question is [tex]4[/tex].
Each question has [tex]4[/tex] options and one is correct.
Concept used:
Probability is defined as the ratio of number of favorable outcomes to number of total outcomes.
[tex]\boxed{\text{Probability}=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}}[/tex]
Calculation:
The probability of getting the correct answer is calculated as follows:
[tex]\begin{aligned}P&=\dfrac{1}{4}\\&=0.25\end{aligned}[/tex]
The probability of getting the incorrect answer is calculated as follows:
[tex]\begin{aligned}P&=1-\dfrac{1}{4}\\&=1-0.25\\&=0.75\end{aligned}[/tex]
The formula for probability of answering all question correctly is as follows:
[tex]\boxed{P'=^nC_{r}P^{r}(1-P)^{n-r}}[/tex]
Here, [tex]n[/tex] is number of question and [tex]r[/tex] is number of correct answer, [tex]P'[/tex] is the probability of answering all question correctly.
Solve the above equation to obtain probability of answer all question correctly.
Substitute [tex]4[/tex] for [tex]n[/tex], [tex]0.25[/tex] for [tex]P[/tex] and [tex]4[/tex] for [tex]r[/tex] in above equation to obtain probability of answering all question correctly.
[tex]\begin{aligned}P'&=^4C_{4}(0.25)^{4}(1-0.25)^{4-4}\\&=\dfrac{4!}{(4-4)!\cdot 4!}\left(\dfrac{25}{100}\right)^{4}(0.75)^{0}\\&=\left(\dfrac{1}{4}\right)^{4}\\&=\dfrac{1}{256}\end{aligned}[/tex]
Therefore, the probability of the correct answer is [tex]0.25[/tex].
The probability of the incorrect answer is [tex]0.75[/tex].
The probability of answering all question correctly is [tex]\dfrac{1}{256}[/tex].
Thus, the probability of answering all question correctly is [tex]\boxed{\dfrac{1}{256}}[/tex].
Learn more:
1. Simplification: https://brainly.com/question/1602237
2. Quadratic equation: https://brainly.com/question/1332667
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Probability
Keywords: Probability, Question, Richard, multiple choice, four answer, class, attend, guesses, correctly answer, favorable outcomes, total outcomes.
The probability that Richard will answer all four questions correctly is 0.004.
Explanation:The probability that Richard will answer all four questions correctly can be determined by multiplying the probability of getting one question correct by itself for each question. Since each question has four answer choices and only one is correct, the probability of guessing the correct answer for one question is 1/4.
Therefore, the probability of Richard answering all four questions correctly is (1/4) * (1/4) * (1/4) * (1/4) = 1/256. Rounded to three decimal places, this probability is approximately 0.004.
Thus, the probability that Richard will answer all questions correctly is 0.004.
Find the value of two numbers if their sum is 12 and the difference is 4
Answers
x+y=12
x-y=4
x=y-4
y-4+y=12
2y-4=12
2y=16
y=8
x=8-4=8
8+4=12
the 2 numbers are 8 & 4
PLEASE HELP
graph and completely describe the function f (x)= 4^x
I already graphed this on desmos
Answers
Basically, whenever you have a function where there's an "x" as your exponent (f(x) = b^x), we'll categorize them as "exponential functions".
Exponential functions modify your graph in two different ways, they can either make it increase exponentially or decrease exponentially.
If you see that your graph is gradually increasing across the x-axis, then you can say that the function is making your graph exponentially increase by a factor of "4".
On a map, 1 inch equals 5 miles. two cities are 8 inches apart on the map. what is the actual distance between the cities?
Answers
The actual distance between the cities are 40 miles.
What is the scale factor?The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.
According to the question we are given that On a map, 1 inch equals 5 miles. two cities are 8 inches apart on the map.
that is, 1cm : 5 miles
Here two cities are 8 inches apart on the map.
then 8 inches equals to
5 x 8 = 40 miles.
The actual distance is 40 miles.
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Find the remaining sides of a 45°-45°-90° triangle if the longest side is 20.
Answers
All 45°-45°-90° triangles have sides that are in a unique ratio. The two legs are the exact same length, and the hypotenuse is that length times the √2.
Let a be the leg then hypotenuse = a√2.
[tex]a \sqrt{2}=20 \ \to a= \frac{20}{ \sqrt{2} } \approx 14.14 \ \text{units}[/tex]
can someone please help?
Answers
(x-1)(5x² - 7)
Answer is C.
Find the polynomial f(x) that has the roots of -2, 5 of multiplicity 2. Explain how you would verify the zeros of f(x).
Answers
similarly, if 5 is a root of f, then (x-5) is a factor of f(x).
These roots have multiplicity 2 means that there are 2 of each,
so f(x) is written as (x+2)(x+2)(x-5)(x-5)
[tex]f(x)= (x+2)^{2} (x-5)^{2} [/tex]
[the most general form is f(x)= c*(x+2)^{2} (x-5)^{2}*P(x), where c is a constant and P(x) another polynomial]
To show that -2 and 5 are zeros of f, we must prove that f(-2)=0 and f(5)=0,
Using the function we wrote:
[tex]f(-2)= (-2+2)^{2} (-2-5)^{2}=0* (-7)^{2}=0[/tex]
similarly:
[tex]f(5)= (5+2)^{2} (5-5)^{2}=0 [/tex]
What is the geometric mean of 21 and 54?
Answers
We are given two numbers: 21 and 54.
Their product is 21*54 = 1134
Because we have two numbers, their geometric mean is
√(1134) = 33.675
Answer: 33.675
Trey went to the batting cages to practice hitting. he rented a helmet for $4 and paid $0.75 for each group of 20 pitches. if he spent a total of $7 at the batting cages, how many groups of pitches did he pay for?
Answers
Which of the following statements are true for the graph shown below
Answers
The statement that is true for the graph of function shown below is option (B) both graphs have exactly one asymptote is the correct answer.
What is graph of a function?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).
For the given situation,
The diagram shows the graph that has 2 functions f(x) and g(x).
The function f(x) is increasing function and the function g(x) is decreasing function.
An asymptote of a curve y = f (x) that has an infinite branch is called a line such that the distance between the point (x, f (x)) lying on the curve and the line approaches zero as the point moves along the branch to infinity.
Here the two functions f(x) and g(x) approaches zero at asymptote of 1.
Hence we can conclude that the statement that is true for the graph of function shown below is option (B) both graphs have exactly one asymptote is the correct answer.
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WILL GIVE BRAINLIEST!! PLEASE HELP!!
Given the parent function of y=the square root of x, state the type of transformation that occured to get the function y=negative square root of x.
A.
vertical shrink
B.
vertical stretch
C.
reflection over the x-axis
D.
reflection over the y-axis
Answers
let's consider some pairs in the graph of both functions.
in [tex]y= x^{2} [/tex] we have (-2, 4), (2, 4), (3, 9), (-5, 25)
in [tex]y=- x^{2} [/tex] we have (-2, -4), (2, -4), (3, -9), (-5, -25)
so for the same values of x, we have y's of equal value, but different sign.
This means that the functions are the reflections of each other with respect to the x-axis.
Answer: C reflection over the x-axis
Identify the y-intercept of the function, f(x) = 2x 2 + x - 4. (0,-4) (0,4) (-4,0) (4,0)
Answers
so answer is
y-intercept of the function (0,-4)
Answer:
The y-intercept of the function [tex]f(x)=2x^{2}+x-4[/tex] is [tex](0,-4)[/tex]
Step-by-step explanation:
The y-intercept of a function is the intersection between the graph of the function and the y-axis.This particular point will have a ''0'' in its x-coordinate (because all points over the y-axis have a ''0'' on its x-coordinate).Therefore, we can write the y-intercept as :
[tex]y-intercept=(0,a)[/tex]
We obtain the another coordinate ''a'' replacing ''x'' by a ''0'' in the function.
In this exercise, the function is:
[tex]f(x)=2x^{2}+x-4[/tex]
If x = 0 ⇒
[tex]f(0)=2(0)^{2}+0-4=-4=a[/tex]
We find that ''-4'' is the coordinate ''a'' that we were looking for.
We conclude that the point [tex](0,a)=(0,-4)[/tex]
And [tex](0,-4)[/tex] is the y-intercept of the function.
What's the slope of the line that passes through (2,14) and (-1,-1)?