Answer:
Proved
Step-by-step explanation:
Given
[tex]a_n = 2n[/tex]
Required
Prove that [tex]S_n = n(n+1)[/tex]
The given sequence is an arithmetic sequence.
The Sn of this sequence is:
[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]
Calculate a1
[tex]a_n =2n[/tex]
[tex]a_1 =2*1[/tex]
[tex]a_1 =2[/tex]
So, we have:
[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]
[tex]S_n = \frac{n}{2}(2 + 2n)[/tex]
Factor out 2
[tex]S_n = \frac{n*2}{2}(1 + n)[/tex]
[tex]S_n = n(1 + n)[/tex]
[tex]S_n = n(n + 1)[/tex] --- Proved
Which of the following equations would have the roots -3 and 2?
Answer:
Step-by-step explanation:
The second one.
Help needed with this asap
Answer:
f(-3) = 4(-3) + 5 = -12 + 5 = -7. the answer is #2.
For the given central angle, determine the distance traveled along the unit circle from the point (1, 0).
218 degrees
a.
1.21 units clockwise
c.
7.61 units
b.
3.80 units
d.
1.90 units
Answer:
Step-by-step explanation:
radius of unit circle = 1
θ = 218° × π/180° = 109π/90 radians
arc length = rθ = 109π/90 ≅ 3.80 units
each of two equal angles is twice the third angle. find the angle of triangle.
Answer:
45 degrees each and 90 degrees
Question Help
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11.3.IP-8
John is knitting a blanket. He records the length he knits each day. How many more inches does
John need to knit so the blanket is 54 inches?
I'm not sure. Don't be angry but this is my first time on this app but it helps a lot and i would also like to help but it seems that I'm the one who needs help.
HELPPPPP!!!!!!!!!!!!!!
Answer
0.75 or 3/4 is the answer (degree)
I just solved for the angles and use a graphing calculator to find the din and cosine values and multiply them
Find the Area Please
Answer:
The area of this shape is super close/equal to 18.283 [tex]m^{2}[/tex]
Step-by-step explanation:
The area of this shape will be equal to the sum of the area of the trapezoid with the height being 4m and parallel lines being 2m and 4m long, and the area of the semi-circle with the radius of 2m. And so we get...
Let "A" be the total area of this shape, then...
[tex]A = \frac{(a + b)h}{2} +[/tex] π[tex]r^{2}[/tex]/2
[tex]A = \frac{(2 + 6)4}{2} +[/tex] π [tex]2^{2}[/tex]/2
[tex]A[/tex] ≈ 12 + 6.283
A ≈ 18.283 [tex]m^{2}[/tex]
Find x, the angle of depression from the top of a lighthouse that is 153 ft above the water level to the waterline of a ship 1071 ft off shore. Round your answer to the nearest tenth of a degree.
Answer:
x = 8.1°
Step-by-step explanation:
Reference angle = x
Opposite side = 153 ft
Adjacent side = 1071 ft
Applying trigonometric ratio (TOA), we have:
[tex] tan(x) = \frac{opp}{adj} [/tex]
[tex] tan(x) = \frac{153}{1071} [/tex]
[tex] x = tan^{-1}(\frac{153}{1071}) [/tex]
[tex] x = 8.1 degrees [/tex] (nearest tenth)
EASY MATH QUESTION Urgent pls
Answer:
I don't know that is hard
Step-by-step explanation:
You said this was an easy math question.
Answer:
I think it's b
Step-by-step explanation:
ah=b1+b2/2
h=ax(b1+b2)/2
first time taking a picture but some one help me, this is the last question and I want to die.
Answer:
Step-by-step explanation:
according to the rules of significant figures 1.25*200=300
will give brainliest pls
Answer:
It's false
Step-by-step explanation:
1.25*200=250 not 300.
When solving quadratic equation, what do the X value stand for as it relates to plotting the graph of the equation?
Step-by-step explanation:
step 1. The x values refer to the domain of the function.
step 2. if you set y = 0 and solve the quadratic equation the x values refer to the point the graph crosses the x axis.
Russ walks
7
10
mile to school.
How far has he walked when he has covered
5
8
of the distance to school?
Answer:
If he walks 7/10 miles to school, and you want to find 5/8 of that distance, you have to multiply the 2 fractions together. So he has walked 7/16 miles when he has covered 5/8 of the distance to school. thank me later
The volume of a cube, in cubic centimeters, is given by the function V(x) = x3, where x is the side length of the cube in centimeters. Write a new function for the volume of the cube in cubic millimeters.
I think we can all agree that 1 centimeter=10millimeters.
And if x is the side in centimeters then 10x will be the side in millimeters.
We just need to rewrite x^3 into (10x)^3.
Because you need to do the exponent to all part of the ( )...
(10x)^3=1000x^3
V(x)=1000x^3 cubic millimeters is the answer
Hence, a new function for the volume of the cube in cubic millimeters is [tex]V(x)=1000x^3[/tex].
What is the volume of cube?
The volume of a cube is defined as the total number of cubic units occupied by the cube completely.
A cube is a three-dimensional solid figure, having six square faces. Volume is nothing but the total space occupied by an object.
Here given that,
The volume of a cube, in cubic centimeters, is given by the function [tex]V(x) = x^3[/tex], where [tex]x[/tex] is the side length of the cube in centimeters.
As, [tex]1[/tex] centimeter=[tex]10[/tex]millimeters.
If the side is [tex]x[/tex] then the side in millimeter is [tex]10x[/tex].
So, we have [tex]x^3[/tex] which would be [tex](10x)^3[/tex]
[tex](10x)^3=1000x^3[/tex]
Then,
[tex]V(x)=1000x^3[/tex] cubic millimeters.
Hence, a new function for the volume of the cube in cubic millimeters is [tex]V(x)=1000x^3[/tex].
To know more about the volume of a cube
https://brainly.com/question/16642309
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Question 22 Noella wraps cube-shaped boxes at her gift shop. The cost of wrapping a box depends on its side length. A box with a side length, x, of at least 5 inches will cost 0.05⋅6⋅x2 dollars to wrap. A box with a side length, y, of less than 5 inches will cost 0.04⋅6⋅y2 dollars to wrap. Which of the following correctly represents the total cost to wrap each set of cube-shaped boxes? Select ALL that apply.
Answer:
D B E
Step-by-step explanation:
Can anyone help with condensing this?
Answer:
log 16x^7.
Step-by-step explanation:
log 4 + 2 log 2 + 7 log x
= log4 + log 2^2 + log x^7
= log (4*4*x^7)
= log 16x^7.
Automobiles traveling on a road with a posted speed limit of 65 miles per hour are checked for speed by a state police radar system. The following is a frequency distribution of speeds. Speed (miles per hour) Frequency 45 up to 55 50 55 up to 65 325 65 up to 75 275 75 up to 85 25 picture Click here for the Excel Data File The mean speed of the automobiles traveling on this road is the closest to ____.
Answer:
The mean speed of the automobiles traveling on this road is the closest to 64 miles per hour
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Speed} & {Frequency} & {45-55} & {50} & {55-65} & {325} & {65-75} & {275} & {75-85} & {25} \ \end{array}[/tex]
Required
Calculate the mean
First, calculate the midpoint (x)
For 45 - 55: [tex]x = \frac{1}{2}(45+55) = 50[/tex]
For 55 - 65: [tex]x = \frac{1}{2}(55+65) = 60[/tex]
For 65 - 75: [tex]x = \frac{1}{2}(65+75) = 70[/tex]
For 75 - 95: [tex]x = \frac{1}{2}(75+85) = 80[/tex]
So, we have:
[tex]\begin{array}{ccc}{Speed} & {Frequency} & {x} & {45-55} & {50} & {50} & {55-65} & {325} & {60} & {65-75} & {275} &{70} & {75-85} & {25} &{80}\ \end{array}[/tex]
The mean is then calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
[tex]\bar x = \frac{50*50+325*60+275*70+25*80}{50+325+275+25}[/tex]
[tex]\bar x = \frac{43250}{675}[/tex]
[tex]\bar x = 64.07[/tex]
[tex]\bar x = 64[/tex] --- approximated
Select the correct option from the menu.
Raj determined that the equation 3 (x+3) = 8 - 5x +7 is equivalent to 9 = 7. This means that this equation has:
no solutions
One solution
Two solutions
Infinity many solutions
Answer:
no solutions
Step-by-step explanation:
which choices are equivalent to the quotient below check all that apply √12/√6
Step-by-step explanation:
I don't see any of the choices, but I'll just give you what it's equal to. The expression is equal to: sqrt2, which is approximately 1.414.
Simplify n ⋅ n⋅ 2n
someone please help thanks
Answer:
the answer would be:
[tex]2n^3[/tex]
Hope that helps! :)
Step-by-step explanation:
equations with variables on both sides that make the answer x=8
Answer:
x/4 = x-6
Step-by-step explanation:
x/4 = x-6 makes x = 8
Hope this helps!!!
A rectangle has an area of 64 ft squared. If the length of the rectangle is x ft and the width of the rectangle is x to the 1/2 ft, find the length and width of the rectangle.
Answer:
I DONT KNOW BUT YOU HAVE TO CHECK OUT MY QUESTION NO OE CAN SOLVE IT I BET
Step-by-step explanation:
What is value of the expression below?(worth 20 points pls pls help due in 10 minutes;-;)
Answer:
1/16
2x2x2x2=16
1x1x1x1=1
Answer:
choice 4, 1/16
Step-by-step explanation:
(1/2)^4=(1/2)(1/2)(1/2)(1/2)=1/16
A) square root 6
B) 6
C) 6 square root 2
D) 12
E) 12 square root 2
Please help
sin(45degrees) or BC/AB is 1/sqrt2(that's the value of sin45 degrees I recommend you to memorize this.)
x/12=1/sqrt2
x*sqrt2=12
x=12/sqrt2
Now rationalize this fraction to make the answer more formal.
x=12sqrt2/2(I multiplied both top and bottom by sqrt2)
Now simplify
x=6sqrt2
Question done! answer is C 6 square root of 2
Hope this helped any questions just put them in the comments.
Answer:
6 square root 2
Step-by-step explanation:
12 more than the square of a number is the same as 7 times the number.
Answer: Sorry I don't know
Step-by-step explanation:
Which of the following is most likely the next step in the series ?
hey there .. here is ur answer ..
Option D is the right answer as you can see ..
If it helps u .. plz mark me as brainliest ..
follow me
Factor the following expression so it is in simplest form.
6a – 4(2a + 3)
A.
–2(a – 6)
B.
–2(a + 6)
C.
2(7a – 6)
D.
2(7a + 6)
Answer:
B) -2(a+6)
Step-by-step explanation:
6a-4(2a+3)
6a-8a-12
-2a-12
factor
-2(a+6)
A gardener wants to know if soaking seeds in water before planting them increases the proportion of seeds that germinate. To investigate, the gardener will assign 50 seeds to be soaked before planting and 50 seeds to be planted without being soaked. After two weeks, the gardener will record how many seeds in each group germinated and construct a 95 percent confidence interval for the difference in proportions. Which of the following conditions for inference should be met?
I. The seeds should be randomly assigned to a treatment.
II. The group sizes should be less than 10 percent of the population sizes.
III. The number of successful seeds and unsuccessful seeds in each group should be at least 10.
a. I only
b. II only
c. III only
d. I and III only
Answer:
d. I and III only
Step-by-step explanation:
I. The seeds should be randomly assigned to a treatment.
III. The number of successful seeds and unsuccessful seeds in each group should be at least 10.
The distribution of difference between two sample proportions :
Given :
Proportion 1 = P1 ;
Proportion 2 = P2 ;
Sample assignment for both samples 1 and 2 into the different treatment groups should be randomized, that is a simple random sampling of subjects into the treatment and control group. The sample design for difference between two sample proportions should be independent.
Finally each of the two proportions P1 and P2 should record a minimum of 10 successes and 10 non - successful Occurrences.
Given the sequence −2,−8/3,−103,−4,−14/3,... find the recursive formula.
A. a1=−2 and an+1=an+5/3
B. a1=−2 and an+1=an+1/3
C. a1=−2 and an+1=an−2/3
D. a1=−2 and an+1=an−5/3
I suppose the third term should say -10/3, not -103.
Notice that
-2 = -6/3
-4 = -12/3
so that, starting with the first term a(1) = -6/3, the every following term is obtained by subtracting 2/3.
-2 - 2/3 = -6/3 - 2/3 = -8/3
-8/3 - 2/3 = -10/3
-10/3 - 2/3 = -12/3 = -4
and so on.
So the recursive rule is
a(1) = -2,
a(n + 1) = a(n) - 2/3, for n ≥ 1
or C.
40% of x is 35.
Write an equation that shows the relationship of 40%, x, and 35.
Use your equation to find x. Show your reasoning.
i really need help
