Answer:
The function is f(n) = 10n - 13 ⇒ answer A
Step-by-step explanation:
* Lets revise the arithmetic sequence
- There is a constant difference between each two consecutive
numbers
- Ex:
# 2 , 5 , 8 , 11 , ……………………….
# 5 , 10 , 15 , 20 , …………………………
# 12 , 10 , 8 , 6 , ……………………………
* General term (nth term) of an Arithmetic sequence:
# U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d
# Un = a + (n – 1)d, where a is the first term , d is the difference
between each two consecutive terms, n is the position of the
term in the sequence
* Now lets solve the problem
- The sequence is -3 , 7 , 17 , 27 , .........
∵ 7 - (-3) = 7 + 3 = 10
∵ 17 - 7 = 10
∵ 27 - 17 = 10
∴ The sequence is arithmetic with constant difference 10
∴ f(n) = a + (n - 1)d
∵ a = -3
∵ d = 10
∴ f(n) = -3 + (n - 1)(10) ⇒ lets simplify it
∴ f(n) = -3 + n(10) + (-1)(10) = -3 + 10n - 10 ⇒ add like terms
∴ f(n) = 10n - 13
* The function is f(n) = 10n - 13
Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.
To determine which function could be used to define and continue the given sequence (-3, 7, 17, 27...), we need to analyze the pattern of differences between consecutive terms and see which option best represents this pattern. The sequence increases by 10 each time, as can be seen from the differences (7 - (-3) = 10, 17 - 7 = 10, 27 - 17 = 10).
Looking at the functions provided:
Option A: f(n) = 10n - 13If we put n=1, f(1) = 10*1 - 13 = -3; If we put n=2, f(2) = 10*2 - 13 = 7; and so on. The pattern matches.Option B: f(n) = -3n + 10 If we put n=1, f(1) = -3*1 + 10 = 7, which does not match the first term of our sequence.Option C: f(n) = 10n - 3 If we put n=1, f(1) = 10*1 - 3 = 7, which does not match the first term of our sequence.Option D: f(n) = -3(n - 1) + 10 If we put n=1, f(1) = -3*(1 - 1) + 10 = 10, which does not match the first term of our sequence.Therefore, Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.
What is the slope of the line shown below?
A. 2/3
B. -3/2
C. 3/2
D. -2/3
Answer:
A
Step-by-step explanation:
The line passes through the points (-3,-7) and (9,1).
The slope of the line can be calculted using formula
[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]
Thus, the slope of the given line is
[tex]\dfrac{1-(-7)}{9-(-3)}=\dfrac{8}{12}=\dfrac{2}{3}.[/tex]
Answer:
A
Step-by-step explanation:
slope is given by the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We need 2 points to find a line's slope.
The first point is (-3,-7) hence x_1 = -3 & y_1 = -7.The second point is (9,1) hence x_2 = 9 & y_2 = 1.Plugging these into the slope formula, we will get the slope:
[tex]\frac{1--7}{9--3}\\=\frac{1+7}{9+3}\\=\frac{8}{12}\\=\frac{2}{3}[/tex]
correct answer is A
HELP PLEASE
A stadium is charging $45 per ticket for a big concert, and through a special promotion,
there is no service fee. What are the parameters in this scenario?
a. x and f(x)
b. 7 and 45
c. 0 and 45
d. 1 and 52
Answer:
c
Step-by-step explanation:
Since there's no service fee, Answer c is correct. Here, 0 represents the zero service fee and 45 represents the $45 cost of each ticket.
A density curve for all the possible ages between 0 years 50 years is in the shape of a triangle,what is the height of the triangle
Answer: The answer is 0.04
Step-by-step explanation:
To determine the height of a triangle-shaped density curve spanning from 0 to 50 years, we use the fact that the area under the density curve must equal 1. The equation (50 * height) / 2 = 1 allows us to solve for the height, which is 0.04 on the probability density scale.
Explanation:To determine the height of the triangle representing a density curve for possible ages, we need some information about the properties of that triangle and density curves in general. A density curve shows how the proportion of a particular measurement (in this case, ages) is spread out over a range. The area under a density curve must equal 1 (or 100%) since it represents the total probability distribution.
In this scenario, we have a triangle as a density curve stretching from 0 to 50 years, which suggests that 0 and 50 are the bounds of our variable (age). The base of the triangle spans these 50 years. If we assume a right-angled triangle for simplicity's sake (which isn't specified in the question but is a common assumption), then the area of the triangle, which represents the probability, would be (base * height) / 2.
To ensure that the total area under the curve equals 1, we set up the following equation: (50 * height) / 2 = 1. Solving this equation for height gives us height = 2 / 50, which simplifies to height = 0.04. Therefore, the height of the density triangle is 0.04 on whatever scale is being used for probability density (e.g., per year).
In a certain college, 33% of the physics majors belong to ethnic minorities. find the probability that, from a random sample of 10 physics majors, exactly 4 do not belong to an ethnic minority.
If a random student has a 33% probability of belonging to a minority, then there is a 67% chance that they do not. In a sample of 10 students, the probability that exactly 4 do not belong to a minority is
[tex]\dbinom{10}40.67^4(1-0.67)^{10-4}\approx0.0547[/tex]
The diameter of an open parachute is 15 ft. if the distance from the parachute to the center of the diameter is 8 ft, what is the length of the suspension line (from the harness to the edge of the open chute)?
The length of the suspension line from the harness to the edge of the open chute is approximately 10.97 ft.
Explanation:To find the length of the suspension line, we can use the Pythagorean theorem. The distance from the parachute to the center of the diameter is the radius of the parachute, which is half the diameter. Therefore, the radius is 15 ft / 2 = 7.5 ft. The suspension line is the hypotenuse of a right triangle with one leg being the radius and the other leg being the distance from the parachute to the edge of the open chute. Using the Pythagorean theorem, we can calculate the length of the suspension line as follows:
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What is the difference of 21x / 3x^2 - 2 and 7 / 3x^2 - 2. Show steps
Answer:
Final answer is [tex]\frac{21x-7}{3x^2-2}[/tex]
Step-by-step explanation:
We have been given two terms [tex]\frac{21x}{3x^2-2}[/tex]
and [tex]\frac{7}{3x^2-2}[/tex]
Now we need to find their difference. So let's subtract them
[tex]\frac{21x}{3x^2-2}-\frac{7}{3x^2-2}[/tex]
Denominators are equal so we can easily subtract numerators
[tex]=\frac{21x-7}{3x^2-2}[/tex]
We may factor the numerator but we won't get any factor in denominator that can be cancelled with numerator.
Hence final answer is [tex]\frac{21x-7}{3x^2-2}[/tex]
which is a rule that describes the translation of a point from 4, -8 to 7, -10
(x, y) > (x + 3, y - 2)
(x, y) > (x + 3, y + 2)
(x, y) > x - 3, y - 2
(x, y) > (x - 3, y + 2)
Answer:
[tex]\large\boxed{(x,\ y)\to (x+3,\ y-2)}[/tex]
Step-by-step explanation:
[tex](4,\ -8)\to(7,\ -10)\\\\4\to7\Rightarrow4+3=7\\\\-8\to-10\Rightarrow-8-2=-10\\\\\text{Conclusion}\\\\(x,\ y)\to (x+3,\ y-2)[/tex]
Answer:
first choice: (x, y) ------> (x + 3, y - 2)
Step-by-step explanation:
The x-coordinate started as 4. Then it became 7. To change from 4 to 7, you add 3. The rule for x is to add 3.
The y-coordinate started as -8. Then it became -10. To go from -8 to -10, you subtract 2. The rule for y is to subtract 2.
Look at the choices, and pick the one that adds 3 to x and subtract 2 from y.
The answer is the first choice: (x, y) ------> (x + 3, y - 2)
What is the limit of e^x, as x approaches pi.
Answer:
[tex]\lim_{x \to \pi } e^x=e^\pi[/tex]
Step-by-step explanation:
Jocelyn invests $1,600 in an account that earns 2.5% annual interest. Marcus invests $400 in an account that earns 5.4% annual interest. Find when the value of Marcus's investment equals the value of Jocelyn's investment and find the common value of the investments at that time. If necessary, enter the year to the nearest tenth and the value to the nearest cent.
Answer:
Total = Principal * (1 + rate) ^ years
We have to solve this for years:
Years = {log(total) -log(Principal)} ÷ log(1 + rate)
Jocelyn: Years = {log(total) -log(1,600)} ÷ log(1.025)
Marcus: Years = {log(total) -log(400)} ÷ log(1.054)
We know the years must be equal but we won't know the total so we'll call that "x".
[log(x) -log(1,600)] ÷ log(1.025) = [log(x) -log(400)] ÷ log(1.054)
EDITED TO ADD
Time is about 49 Years 8 Months and total is about 5,454.00
We know the years must be equal
Step-by-step explanation:
Kari wants to measure the height of a tree. She walks exactly 105 feet away from the base of the tree and looks up to the top of it. The angle from the ground to the top of the tree is 33 degrees. This particular tree grows at an angle of 86 degrees with respect to the ground rather than vertically. How tall is the tree to the nearest tenth of a foot?
Answer:
68.2 feet
Step-by-step explanation:
The angle of elevation, the one from the ground up, is given as 33 degrees. If Kari is 105 feet from the tree, that serves as the measure of the base of the right triangle. We are looking for the height of the tree, which is the side opposite the angle. What we have, then, is the angle (33 degrees), the side adjacent to the angle (105 ft), and we are looking for the side opposite the angle (x). What we need to use is the tangent ratio, which relates the side opposite the angle to the side adjacent to the angle, as follows:
[tex]tan33=\frac{x}{105}[/tex]
To solve for x we multiply both sides of the equation by 105 to get 105tan33°=x. Plug that into your calculator in degree mode to get 68.18779729. Round from there to get 68.2 feet.
I really need help on this I have no clue how to do this and my new teacher have a foreign accent so I can’t understand her
Answer:
sinθ = 12/15 -> 4/5
cosθ = 9/15 -> 3/5
tanθ = 12/9 -> 4/3
cscθ = 15/12 -> 5/4
secθ = 15/9 -> 5/3
cotθ = 9/12 -> 3/4
Step-by-step explanation:
The theta is where you would use to identify the numbers for the trig functions. The adjacent side is the one closest to the theta (but not the diagonal line, that is the hypotenuse), and the opposite line is the line next to the adjacent line.
For the first three trig functions, would use the method Soh Cah Toa.
Sin = opp/hypotenus, Cosine = adjacent/hypotenuse, and Tangent = opposite/adjacent. Then, there is cosecant(csc) = hyp/opp, secant = hyp/adj, and cotangent = adj/opp.
Which graph shows the correct solution for y=-3 x-y=8
Answer:
"Third graph" in the attached picture.
Step-by-step explanation:
The correct graph would be the "intersection" of the lines:
y = -3, and
x - y = 8
We know, y = -3 is a horizontal line at y = -3 and the next is a line. By looking at the first equation, we can eliminate 2 graphs and thus find the correct graph.
y = -3 is a horizontal line at y = -3, the first graph has the line y = 3, so we can eliminate this even without looking at the graph of 2nd equation.
The second graph has a vertical line, no horizontal, so we can eliminate this choice as well.
The third graph has y = -3 (horizontal line at y = -3) and thus this is the correct choice. Also, x - y = 8 means y = x -8, which is the other graph shown.
correct answer is the "third graph".
Answer: last option.
Step-by-step explanation:
The equation of the line in slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b the intersection with the y-axis.
The line [tex]y=-3[/tex] is a line with slope 0 that cut the y-axis at (0,-3)
Solve for y from the second equation:
[tex]x-y=8\\x-8=y[/tex]
The line [tex]y=x-8[/tex] is a line with slope 1 that cut the y-axis at (0,-8)
You can identify these lines in the last graph, where the point of intersection between them is the solution of the system of equations.
Help me find the mean of this data set.
74
67
74.25
64
72
67.75
73
66
68
72
68
68
69
70
72
76
70
68
68
72
74
71
66
71
67
70
71.5
71
72
70
71.5
74
69
70.5
72
75.5
71.5
72
69.5
71
74
74
72
74
75
Answer:
Finding the mean is very simple, add them all together and divide that sum by the number of data points you have; in this case there are 45
Step-by-step explanation:
[tex]\frac{74+67+74.25+64+72+...}{45}[/tex] = mean
A factory makes 12 bags in three hours making both at the same rate how many bags would have made an eight hours
Known: 12 bags in 3 hours
Question: X bags in 8 hours
1) Find the amount of bags made in 1 hour
12/3 = 4 bags per hour
2) If each hour makes 4 bags, and the factory is running for 8 hours then multiply the rate of bag production by the time running
8*4=32
Final Answer = 32 bags
I tried to personal message you but it didn't work. I have a question about your question it says "making both at the same rate". My question is both what?
Solve. 10x^2 = 6 + 9x10x 2 =6+9x10, x, start superscript, 2, end superscript, equals, 6, plus, 9, x Choose 1 answer: Choose 1 answer: (Choice A) A x =\dfrac{5 \pm \sqrt{65}}{-2}x= ?2 5± 65 ? ? x, equals, start fraction, 5, plus minus, square root of, 65, end square root, divided by, minus, 2, end fraction (Choice B) B x =\dfrac{9 \pm \sqrt{321}}{20}x= 20 9± 321 ? ? x, equals, start fraction, 9, plus minus, square root of, 321, end square root, divided by, 20, end fraction (Choice C) C x =\dfrac{4 \pm \sqrt{26}}{10}x= 10 4± 26 ? ? x, equals, start fraction, 4, plus minus, square root of, 26, end square root, divided by, 10, end fraction (Choice D) D x =\dfrac{-1 \pm \sqrt{109}}{18}x= 18 ?1± 109 ? ?
Answer:
Option B.
Step-by-step explanation:
If a quadratic equation is defined as
[tex]ax^2+bx+c=0[/tex] .... (1)
then the quadratic formula is
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The given equation is
[tex]10x^2=6+9x[/tex]
It can rewritten as
[tex]10x^2-9x-6=0[/tex] .... (2)
On comparing (1) and (2) we get
[tex]a=10,b=-9,c=-6[/tex]
Using quadratic formula we get
[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(10)(-6)}}{2(10)}[/tex]
[tex]x=\dfrac{9\pm \sqrt{81+240}}{20}[/tex]
[tex]x=\dfrac{9\pm \sqrt{321}}{20}[/tex]
Therefore, the correct option is B.
Answer:
B
Step-by-step explanation:
I got it right
If sin x = -3/5 and x is in quadrant 3, then tan2x
Answer:
i think it should be tan2x = 24/7, i hope i am not wrong
Step-by-step explanation:
If sin x = -3/5 and x is in quadrant 3, then tan 2x = 24/7.
How to estimate the value of tan 2x?
Given:
[tex]$Sin x = \frac{-3}{5}[/tex]
To estimate cos x by identity
[tex]$Cos^{2} x=1-Sin^{2} x[/tex]
[tex]$Cos^{2} x =1-\frac{9}{25}[/tex]
[tex]$=\frac{16}{25}[/tex]
cos x = ±(4/5)
Since x exists in Quadrant III, then cos x exists negative.
tan x = Sin x/Cos x
= (−35)/(−54) = 3/4
By using the trigonometric identity, we get
tan 2x = 2 tan x / [tex]$1-tan^{2} x[/tex]
tan 2x = (6/4) / (1−9/16)
= (6/4)(16/7)
= 24/7
Therefore, tan 2x = 24/7.
To learn more about trigonometric identity
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Can someone please help with NUMBER 7?!! It’s my last one I will mark brainliest to the best answer
Answer:
1, 3, 9, 27
Step-by-step explanation:
[tex] a_n = 3^{n - 1} [/tex]
You need the first 4 terms, so let n = 1, and evaluate the expression. Then do the same for n = 2, n = 3, and finally n = 4.
n = 1
[tex] a_1 = 3^{1 - 1} = 3^0 = 1 [/tex]
n = 2
[tex] a_2 = 3^{2 - 1} = 3^1 = 3 [/tex]
n = 3
[tex] a_3 = 3^{3 - 1} = 3^2 = 9 [/tex]
n = 4
[tex] a_4 = 3^{4 - 1} = 3^3 = 27 [/tex]
Explain how to solve this, step by step?
Together, a chair, a table, and a lamp cost $562. The chair costs 4 times as much as the lamp, and the table costs $23 less than the chair. Calculate the cost of the chair, the table, and the lamp.
Answer:
The cost of chair is [tex]\$260[/tex]
The cost of a lamp is [tex]\$65[/tex]
The cost of a table is [tex]\$237[/tex]
Step-by-step explanation:
Let
x----> the cost of chair
y----> the cost of lamp
z----> the cost of table
we know that
[tex]x+y+z=562[/tex] ----> equation A
[tex]x=4y[/tex] -----> [tex]y=x/4[/tex] -----> equation B
[tex]z=x-23[/tex] ------> equation C
substitute equation C and equation B in equation A and solve for x
[tex]x+(x/4)+(x-23)=562[/tex]
[tex](9/4)x=562+23[/tex]
[tex](9/4)x=585[/tex]
[tex]x=585*4/9=\$260[/tex]
Find the value of y
[tex]y=260/4=\$65[/tex]
Find the value of z
[tex]z=260-23=\$237[/tex]
therefore
The cost of chair is [tex]\$260[/tex]
The cost of a lamp is [tex]\$65[/tex]
The cost of a table is [tex]\$237[/tex]
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
A number generator was used to simulate the percentage of students in a town who enjoy playing video games. The process simulates randomly selecting 100 students from the town and was repeated 20 times. The percentage of students who play video games is shown in the dot plot. Which statement is true about the student population of the town?
Answer:
Step-by-step explanation:
Notice that the greatest number of dots is over the '70,' indicating that 70% of the students in the town enjoy playing video games.
This problem has to do as much with your ability to interpret graphs as to apply statistics concepts correctly.
Explain the steps used to convert a temperature from Celsius to Fahrenheit.
For this case we have that by definition, to move from Celsius to Fahrenheit we must apply the following formula:
[tex]F = \frac {9} {5} C + 32[/tex]
Example, we want to convert 45 degrees Celsius to Fahrenheit:
[tex]F = \frac {9} {5} (45) +32\\F = 9 * 9 + 32\\F = 81 + 32\\F = 113[/tex]
Thus, 45 degrees Celsius equals 113 degrees Fahrenheit.
ANswer:[tex]F = \frac {9} {5} C + 32[/tex]
For anyone who still needs this:
1. Multiply your Celsius measurement by 9/5 (or 1.8)
2. Add 32 to the result
Formula: F = (9/5)°C + 32
PLEASE HELP WITH THESE!!
THANK U SOOO MUCH!!
Answer:
Step-by-step explanation:
One
Since you are asked to solve this using a graphing tool, here is the results as graphed by Desmos.
The point you want is (3,2)
The answer is 2.
Two
Multiply the second equation by 2
2[0.5x - y = 10]
x - 2y = 20 Add the first equation
x + 2y = 16
2x = 36 Divide by 2
x = 36/2
x = 18
Since this is all you are asked for, x = 18 is the answer.
Three
y is an exterior angle.
It is the sum of the two (given) remote interior angles.
y = 35 + 105
y = 140
x and y are supplementary (they add up to 180o
x + y = 180
x + 140 = 180
x = 180 - 140
x = 40
y - x = 140 - 40
y - x = 100
TIMED!!!
Marlon built a ramp to put in front of the curb near his driveway so he could get to the sidewalk more easily from the street on his bike.
If the ramp includes the flat piece as well as the angled piece and is made entirely out of concrete, what is the total amount of concrete in the ramp?
768in^3
936in^3
984in^3
1,080in^3
Answer: Last option.
Step-by-step explanation:
The total amount of concrete in the ramp ([tex]V_t[/tex]) will be the sum of the volume of the rectangular prism ([tex]V_{rp}[/tex]) and the volume of the triangular prism ([tex]V_{tp}[/tex])
[tex]V_t=V_{rp}+V_{tp}[/tex]
The formulas are:
[tex]V_{rp}=lwh[/tex]
Where "l" is the lenght, "w" is the width and "h" is the height.
[tex]V_{tp}=\frac{bhl}{2}[/tex]
Where "l" is the lenght, "b" is the base and "h" is the height.
Substituting, we get:
[tex]V_t=V_{rp}+V_{tp}\\\\V_t=lwh+\frac{bhl}{2}\\\\V_t=(18in)(6in)(6in)+\frac{(8in)(6in)(18in)}{2}\\\\V_t=1,080in^3[/tex]
Answer:
The guy above me is correct lol
Step-by-step explanation:
Henry gargles with mouthwash. Which is a responsible amount of mouthwash for Henry to use? 2 fluid ounces, 8 fluid ounces, 12 fluid ounces, or 20 fluid ounces.
Answer:
2 fluid ounces
Step-by-step explanation:
8 is a lot of mouthwash to use and anything aove that is a just alot...
Rachel is making nachos for a party. The recipe calls for 2/3 cups of cheese for each plate of nachos. How many plates can she make with five cups of cheese
Answer:
[tex]7\frac{1}{2}\ plates[/tex]
Step-by-step explanation:
we know that
The recipe calls for 2/3 cups of cheese for each plate of nachos
so
using proportion
Find out how many plates can she make with five cups of cheese
let
x ----> the number of plates
[tex]\frac{1}{(2/3)}\frac{plate}{cups} =\frac{x}{5} \frac{plates}{cups}\\ \\x=5/(2/3)\\ \\x=7.5\ plates[/tex]
Convert to mixed number
[tex]7.5=\frac{14}{2}+\frac{1}{2}=7\frac{1}{2}\ plates[/tex]
She can make 7.5plates with 5 cups of cheese
Ratios and proportionsAccording to the question, we are told that the recipe calls for 2/3 cups of cheese for each plate of nachos. This is expressed as:
2/3 cups of cheese = 1 plate of nachos
In order to calculate the number of plates she can make with five cups of cheese
5 cups = x
Cross multiply
2/3x = 5
2x = 15
x = 7.5 plates
Hence she can make 7.5plates with 5 cups of cheese
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PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The owner of a chain of dance studios releases a report to the media. The report shows that participation in dance classes has increased by 5% in each of the past three years.
Which statement describes the most likely reason the owner releases the report?
Answer:
B
Step-by-step explanation:
I would say that the owner wants people to believe that dance classes are a good form of exercise.
20 points!!! Hurry hurry hurry!! Distance between points
Answer:
This is just a guess so I'm sorry if its wrong but I'd guess that it's A
Answer:
It is A
Step-by-step explanation:
You can use the Pythagorean Theorem a^2+b^2=c^2
3^2+5^2=c^2
9+25=c^2
34=c^2
square root of 34=c
The variables x and y vary inversely with a constant variation of 6. Find y when x=12.
Answer:
y = 1/2
Step-by-step explanation:
If two variables x and y vary inversely, then:
xy = k
where k is the constant variation.
In this case:
xy = 6
When x = 12:
12y = 6
y = 1/2
The value of y when x is 12 is 2 (option C)
What is inverse variation?Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases. Example is the price of a commodity and the quantity acquired, the higher the price, the lower of commodity bought and vice- versa.
here, we have,
Inverse relationship between two quantities x and y is expressed as:
x= ky
where k is the constant
k = 6
when x = 12
12 = 6y
divide both sides by 6
y = 12/6
y = 2
therefore the value of y when x is 12 is 2
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The second term of an arithmetic sequence is 7. The sum of the first 4 terms of the arithmetic sequence is 12. Find the first term, and the common difference, d, of the sequence.
*Please help*
Answer:
15 is the answer
Step-by-step explanation:
4Σn=! n/n!
I understand what the denominator, n! is by definition. I just don't understand what to put for the numerator when n = !
Can anyone help me figure this out?
I think the sum is supposed to be
[tex]\displaystyle\sum_{n=1}^4\frac n{n!}=\sum_{n=1}^4\frac1{(n-1)!}[/tex]
since [tex]n!=n\cdot(n-1)![/tex]. Then
[tex]\displaystyle\sum_{n=1}^4\frac1{(n-1)!}=\frac1{0!}+\frac1{1!}+\frac1{2!}+\frac1{3!}[/tex]
and [tex]0!=1[/tex] by definition so that the sum has a value of [tex]\dfrac83[/tex].
Which pair of angles are coterminal with 120°?
240°, 600°
-240°, -600°
180°, -360°
-60°, 300°
Answer:
-240°, -600°
Step-by-step explanation:
Coterminal angles are angles that land in the same spot around a circle.
So, that means they do full turns of the circle to reach each other.
To find coterminal angles of a given angle (here 120 degrees), you add or subtract 360 (the number of degrees in a full circle). That can go in both positive or negative directions.
So, from 120 degrees, let's find the coterminal angle that is 1 rotation above and one rotation below:
120 + 360 = 480
120 - 360 = -240
You see that 480 isn't among the possible answers, so one part of the answer is -240. If you subtract another 360 degrees, you end up with -600 degrees... so the answer is -240°, -600°