Answer:
Step-by-step explanation:
This is an arithmetic sequence because each term subtracted by the previous term is a constant called the common difference.
an=a+d(n-1) where a is the initial term and d is the common difference
a=-20 and d=-16+20=4 so
an=-20+4(n-1)
an=4n-24
The sum of an arithmetic sequence is the average of the first and last terms times the number of terms
sn=(a1+an)(n/2)
s30=(-20+4(30)-24)(30/2)
s30=1140
The sum of the first 30 terms of the sequence –20, –16, –12, –8, –4, . . . is obtained being 1140
What is the sum of terms of an arithmetic sequence?Arithmetic sequence is a sequence where each consequtive term has a common constant difference.
An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.
Let the starting term be 'a' and common difference be 'd', then we get the arithmetic sequence as:
[tex]\rm a, a+d, a+2d, \cdots[/tex]
The sum of the first 'n' terms of that sequence is is:
[tex]\rm a + (a+d) + (a+2d) + \cdots + (a+(n-1)d) = \dfrac{n}{2}[2a + (n-1)d ][/tex]
For this case, the series –20, –16, –12, –8, –4, . . . starts from a = -20,
and each next term is obtained by adding d = 4 in previous term.
Thus, the sum of the first n = 30 terms of that sequence is evaluated as:
[tex]S_n = \dfrac{n}{2}[2a + (n-1)d ]\\\\S_{30} = \dfrac{30}{2}[2(-20) + (30-1)(4) ] = 15(-40 +116) = 15 \times 76 = 1140[/tex]
Thus, the sum of the first 30 terms of the sequence –20, –16, –12, –8, –4, . . . is obtained being 1140
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how many people in the town of summit have jobs if there are 9,255 people in the town and 1/3 of them are employed? simplify the fraction if possible
Answer:
divide 9,255 divide 1/3 and you will get your answer hope this helps :)))
Step-by-step explanation:
In the town of Summit, 3,085 people have jobs. If there are 9,255 people in the town and 1/3 of them are employed.
To find the number of people in the town of Summit who have jobs, we can multiply the total population by the fraction representing the employed individuals.
Total population = 9,255 people
Fraction employed = 1/3
Number of people employed = Total population * Fraction employed
Number of people employed = 9,255 * (1/3)
To simplify the fraction (1/3), we can divide both the numerator and denominator by their greatest common divisor, which is 1 in this case.
Dividing 1 and 3 by 1, we get:
1/1 = 1
3/1 = 3
So, the simplified fraction is 1/3.
Continuing the calculation:
Number of people employed = 9,255 * (1/3)
Number of people employed = 9,255 / 3
Number of people employed = 3,085
Therefore, in the town of Summit, 3,085 people have jobs.
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need help very badly i do not understand geometry lol
Answer:
Step-by-step explanation:
sin 63 = JK/8
sin = opposite/hypotenuse
answer is C
Write an equation of the line that passes through the points (1, 2) and (4, 8)
Answer:
y = 2x
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, 8)
m = [tex]\frac{8-2}{4-1}[/tex] = [tex]\frac{6}{3}[/tex] = 2 , then
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 2 )
2 = 2 + c ⇒ c = 2 - 2 = 0
y = 2x ← equation of line
Answer:
2x-y=0 / y=2x
Step-by-step explanation:
6x-3y=0, 2x-y=0
need help can't figure it out
Answer:
415
Step-by-step explanation:
Please help me (Trig) and show your work in the answer
Answer:
30.24 mStep-by-step explanation:
Find the length of one of the braces b, use sine:
sin 55° = 6.2 / bb = 6.2 / sin 55° b = 7.56 mTotal length:
7.56*4 = 30.24 mPls help...................
Starbucks customers are complaining that a small cup of coffee at a local Starbucks coffee shop does not contain as much coffee as it should. On average, Starbucks claims that a small cup of coffee contains 360 grams of coffee. The customers decide to order 20 cups of coffee at random times; on average their cups contained 356 grams, and a standard deviation of 9 grams.
Required:
What is the null hypothesis?
you have 4 ice cubes in your cup of lemonade. each ice cube has a length of 7 3/4 cm, a width of 4 5/8 cm and a height if 2 4/5 cm. what is the total volume of all ice cubes? explain how you used math to come to your decision.
Answer:
how is this Spanish
Step-by-step explanation:
(90 POINTS SHOW YOUR WORK!!!) Determine the equation of the line that goes through points (-2, 1) and (1, -1)
Answer:
we have
(y-y1)/(x-x1)=(y2-y1)/(x2-x1)
(y-1)/(x--2)=(-1-1)/(1--2)
(y-1)/(x+2)=(-2)/3
3(y-1)=(-2(x+2))
3y-3=-2x-4
2x+3y-3+4=0
2x+3y+1=0 is a required equation
I need help please in my homework 100 point question
Answer:
5,000? what does it want me to find
Step-by-step explanation:
Solve x - 9 = 3 + y for y.
Step-by-step explanation:
[tex]x - 9 - 3 = y \\ y = x - 12[/tex]
The given equation solved for y as x-12.
The given equation is x-9=3+y.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved as follows:
x-9=3+y
⇒y=x-9-3
⇒y=x-12
Therefore, the given equation solved for y as x-12.
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A fraction is shown. 8/16 Which expression is equivalent to this fraction?
Answer:
1/2
Step-by-step explanation:
PLEEEEEEEEAAAAAAAAAAAASEEEEEEE HELP
What is 1/7 as a decimal rounded to the nearest 100th
Triangle Inequalities part 2 help please
Answer:
The perimeter can not be 26 inches
Step-by-step explanation:
Given
[tex]Side\ 1 =19[/tex]
[tex]Side\ 2 =16[/tex]
Required
Is a perimeter of 26 possible?
First, calculate the possible side 3
[tex]Side\ 3 = Perimeter - Side\ 1 - Side\ 2[/tex]
[tex]Side\ 3 = 26 - 16 - 19[/tex]
[tex]Side\ 3 = -9[/tex]
The side length can not be negative.
So, the perimeter can not 26 inches
Mr. Robinson has raised $900 for his St. Baldricks campaign to fund childhood cancer research. This is 60% of his fundraising goal. What is Mr. Robinson's fundraising goal? pls give answer asap! :)
Answer:
1500
Step-by-step explanation:
STEP 1 900 = 60% × Y
STEP 2 900 =
60
100
× Y
Multiplying both sides by 100 and dividing both sides of the equation by 60 we will arrive at:
STEP 3 Y = 900 ×
100
60
STEP 4 Y = 900 × 100 ÷ 60
STEP 5 Y = 1500
which property justifies the statement below?
a(2b+c)=a(c+2b)
a. commutative property of addition
b. commutative property of multiplication
c. associative property of addition
d. distributive property
a
asta e raspunsul
gyyy
Divide the given polynomial by the given monomial.
Answer:
Here are the answers. Need to have 20 characters for answer. Phew
A certain disease has an incidence rate of 0.7%. If the false negative rate is 5% and the false positive rate is
3%, compute the probability that a person who tests positive actually has the disease.
Give your answer accurate to at least 3 decimal places
Find the missing length of the triangle.
Answer:
89
Step-by-step explanation:
Hypotenuse = sqrt[ (Leg a)2 + (Leg b)2 ]
Hypotenuse = sqrt[ (39)2 + (80)2 ]
Hypotenuse = sqrt[ 1521 + 6400 ]
Hypotenuse = sqrt[ 7921 ]
Hypotenuse = 89
Answer:
45 is your answer c=45 13
What equation can be used to find the earnings
6.62 X 0.7= 2.68 X 1.35
Answer:
3.934 = 3.634; hope this helps........
Step-by-step explanation:
Solve:
Multiply the numbers
5.62 ⋅ 0.7 = 2.68 ⋅ 1.35
3.934 = 2.68 ⋅ 1.35
Multiply the numbers
3.934 = 2.68 ⋅ 1.35
3.934 = 3.618
Result
3.934 = 3.618
The input is a contradiction: it has no solutions
Pls help! How do i Graph 4y = -3x - 8. explain the steps
Answer:
Step-by-step explanation:
to make a graph, when you have the equations, as you do, just make up a table of some x coordinates, you get to choose which ever ones you want so pick some easy ones, like - 2,-1 , 0, 1, 2 .. then put each of those numbers into your equations as the x ... one at a time, ofc, and see what you get out for y. then you have the y coordinate of your table
when you have your table then you can plot each of the points, if you use the Demos web site graphing tool you can make the graph on your computer , or use a graph paper.
:)
Is(x+6)>8 is equation (with variable) give reason for your answer
Answer:
it's a non equation if x=2 is given then we get a proper line of the equation bur x is greater than 2 the we find a region that go far from origin
a sphere of radius 10cm is to be turned out on a lathe. If the radius is made 0.1cm too long, what is the precentage of error made in the surface area of the sphere
Answer:
The percentage error is 8%
Step-by-step explanation:
Given
[tex]r = 10cm[/tex]
[tex]\triangle r =0.1cm[/tex]
Required
% error in the surface area
The surface area of a sphere is:
[tex]S = \4\pi r^2[/tex]
Differentiate
[tex]dS \approx 8\pi r\ dr[/tex]
Rewrite as:
[tex]\triangle S =8\pi r \triangle r[/tex] --- This represents the relative error
The percentage error is then calculated as:
[tex]\% Error = \frac{Relative\ Error}{Surface\ Area}[/tex]
[tex]\% Error = \frac{\triangle S}{S} * 100\%[/tex]
[tex]\% Error = \frac{8\pi r \triangle r}{\pi r^2} *100\%[/tex]
[tex]\% Error = \frac{8 \triangle r}{r} * 100\%[/tex]
[tex]\% Error = \frac{8 *0.1}{10} * 100\%[/tex]
[tex]\% Error = \frac{0.8}{10} * 100\%[/tex]
[tex]\% Error = 0.08 * 100\%[/tex]
[tex]\% Error = 8\%[/tex]
Help! I need to answer this on edge
your answer will be A
The function y=3x is growing slower than y=3^x
Step-by-step explanation:
hope it helps you
have a great day!!
Write a story problem for the equation 7z+4=32
Answer:
z=4
Step-by-step explanation:
7z+4=34
7x=32-4
7z=28
7z/7=28/7
z=4
Which is proportional
Answer:
B
Step-by-step explanation:
It goes up the same amount ($0.75) for every bar you get.
Please help- will give brainlist
Which proportion can be used to find 20% of 17?
Answer:
8.5
Step-by-step explanation:
Convert the percent to a decimal.
20% ÷ 100 = 0.2.
X = 17 ÷ 0.2.
X = 8.5
So 20% of 17 is 8.5.
The cashier determines that the customer's groceries total $156.75. If the sales tax is four percent, how much will the customer have to pay for their groceries, including tax?