Answer:
Step-by-step explanation:
The formula for fundung the nth term of t geometeric series is expressed as;
Tn = ar^(n-1)
a is the first term
n is the number of term
r is the common ratio
Given
a = 3
r = 21/3 = 48/12 = 4
Substitute
Tn = 3(4)^(n-1)
Tn = 3(4^n/4)
Tn = 3/4(4^n)
Tn = 0.75(4^n)
Hence the nth term of the geometric series is Tn = 0.75(4^n)
To get any term, simply substitute the value of into the equation
How do you do this question?
Answer:
∑ₙ₌₀°° (-3x)ⁿ / n!
R = ∞
Step-by-step explanation:
Maclaurin series is:
∑ₙ₌₀°° f⁽ⁿ⁾(0) xⁿ / n!
Find the nth derivative and evaluate at x=0:
f(x) = e⁻³ˣ
f⁽ⁿ⁾(x) = (-3)ⁿ e⁻³ˣ
f⁽ⁿ⁾(0) = (-3)ⁿ
The Maclaurin series is therefore:
∑ₙ₌₀°° (-3)ⁿ xⁿ / n!
∑ₙ₌₀°° (-3x)ⁿ / n!
Use ratio test to find the radius of convergence.
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-3x)ⁿ⁺¹ / (n+1)!] / [(-3x)ⁿ / n!]│< 1
lim(n→∞)│(-3x) n! / (n+1)!│< 1
lim(n→∞)│3x / (n+1)│< 1
0 < 1
The radius of convergence is infinite.
Could you please help me
Answer:
4 3/4
Step-by-step explanation:
cueluisghvreiuasghfe;ahfuiealw
Answer:
Step-by-step explanation:
[tex]4\frac{3}{4}[/tex] - [tex]\frac{1}{3}[/tex] = [tex]4\frac{9-4}{12}[/tex] = [tex]4\frac{5}{12}[/tex] feet
22. Find the slope and Y intercept of the line 3x+4y-9=0
hi there! here's my answer for you...
Answer:
slope:
m = -3/4
y-intercept:
y = −3x/4 + 9/4
hope this helped. have a good one!
Determine the solution set of (3x - 5)2 = 36.
{-1/3, 11/3}
{11/3}
{-6, 6}
Answer:
[tex]the \: solution \: set \:is \to \{{-6, 6} \}[/tex]
i need help with this ^
Answer:
23
Step-by-step explanation:
17 pluse 2 is 19
180 minus 19 is 161
add all the vs you get 7
so 161 divided by 7 is 23
Answer:
Select the correct answer.
Which path describes the movement of oxygenated blood leaving the heart? Use the standard image of the heart to guide you.
A.
left atrium → left ventricle → aorta
B.
left ventricle → left atrium → pulmonary artery
C.
right atrium → right ventricle → pulmonary artery
D.
right ventricle → right atrium → aorta
Step-by-step explanation:
A copy machine can print 48 copies every 4 minutes. A teacher printed 72 copies how long did it take to print
Answer:
6 minutes
Step-by-step explanation:
72-48 = 24
so 24 + 48 = 72
and 48 / 4=12
which means 12 copies per minute and 24 copies is 2 minutes
a leaky faucet is losing water and it is filling a 5 gallon bucket every 12 hours. At the rate, how many gallons of water will the faucet leak 48 hours
Answer:
20 gallons
Step-by-step explanation:
First start off by dividing 48 by 12 to see how many times 12 goes into 48.
48 / 12 = 4
now that you know that 12 goes into 48 4 times, multiply 4 by 5 to see how many gallons the leaky faucet will fill in 48 hours.
4 x 5 = 20
therefore the answer is 20 gallons
I hope this helps ^^
Juan is rewriting the expression 12 d minus 26 c as a product. Which statements about the expression are accurate and relevant to his rewriting the expression? Select two options.
The GCF of the numbers in each term in the expression is 2.
The GCF of the numbers in each term in the expression is 4.
The GCF of the variables in each term in the expression is cd.
The factored expression is 2 (6 d minus 13 c).
The factored expression is 2 c d (6 minus 13).
The GCF of the numbers in each term in the expression is 2.
The factored expression is 2 (6 d minus 13 c).
The accurate expression is:
The GCF is 2 as for 12 and 26 only 2 is commonSince [tex]12 = 2\times 3 \times 2[/tex] and [tex]26 = 13 \times 2[/tex]Based on this, only 2 is common between these two numbers Also, the factored expression should be 2 (6 d minus 13 c)Find out more information about the number here: https://brainly.com/question/17429689?referrer=searchResults
Answer: The GCF of the numbers in each term in the expression is 2.
The factored expression is 2 (6 d minus 13 c).
Step-by-step explanation: im not sure tho
A right triangle is shown below.
What is the value of x rounded to the nearest ten, if necessary?
Answer:
hmmmmm.... i'm only in 7th grade and to be honest i don't really know but i'll try on this. am i going to be doing this this year?
So from my logic in my empty brain: 4.2?
Step-by-step explanation:
Because i flipped the pic around and so ,
First i got "x" in my brain and turned it into 9 from 8.5
then 9 divided by 8.5
wait a sec i just realized i made the most dumb mistake by dividing welp i'll just put out what i just fixed in my head and yea here ya go.
B+ for effort ?
Z- for iq?! .-.?
Hey, we are doing a review on fractions but I don't remember how to convert fractions do decimals.
Answer:
It's quite simple, for example, 1/2 would be the same as 50%, 1/3rd would be the same as 33.333333333%, and 1/4th would be the same as 25%
dived the numerator by the denominator.
15 POINTS
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. Which ratio of gallons of blue paint to gallons of yellow paint will make the same shade of green paint?
A. 10 : 45
B. 30 : 54
C. 6 : 10
D. 27 : 15
explanation if you know how to explain
Answer:
The answer is B
Step-by-step explanation:
The problem is asking for the same ratio as 5:9
Multiply both sides by 6 to get 30:54
Use the distance formula to show that the two triangles on the coordinate plane are congruent
Answer:
Step-by-step explanation:
d = [tex]\sqrt{(x_{2} -x_{1} )^2 + (y_{2} - y_{1} )^2}[/tex]
A(- 5, - 2) , B( - 1, - 6) , C ( - 9, - 6)
AB = √[(- 5 + 1)² + (- 2 + 6)²] = 4√2
BC = √[(- 1 + 9)² + (- 6 + 6)²] = 8
AC = √[(- 5 + 9)² + (- 2 + 6)²] = 4√2
D(2, 2) , E(6, - 2) , F( 10, 2)
DE = √[(2 - 6)² + (2 + 2)²] = 4√2
EF = √[(6 - 10)² + (- 2 - 2)²] = 4√2
DF = √[(2 - 10)² + (2 - 2)²] = 8
ΔABC ≅ ΔEDF
The two triangles ABC and DEF are not congruent by SSS.
What is the distance formula between two points?The distance formula between two points is,
[tex]D = \sqrt{(x_2 - x_1_)^2 + (y_2 - y_1)^2[/tex].
Two triangles will be congruent by SSS is the distance of their corresponding sides are equal.
In ΔABC coordinates of A and B are (-5, - 2) and (-1, - 6).
[tex]D_{AB} = \sqrt{(- 1 + 5)^2 + (- 6 + 2)^2}[/tex].
[tex]D_{AB} = \sqrt{(4)^2 + (-4)^2[/tex].
[tex]D_{AB} = \sqrt{(16) + (16)[/tex].
[tex]D_{AB} = \sqrt{32}[/tex].
Similarly, the distance of DF in ΔDEF is [tex]\sqrt{64}[/tex].
hence AB ≠ DF so the triangles are not congruent.
learn more about the distance formula here :
https://brainly.com/question/28956738
#SPJ5
These reverse processes are both part of
Answer:
you forgot the picture
Step-by-step explanation:
Please put a picture
Simi bought a study table for $9000.She sold it at a profit of 20%.How much profit did she make ? What is the selling price?
Answer:
10,800
Step-by-step explanation:
9,000+ 20%= 10,800
Apples cost $0.75 per pound and bananas cost $1.05 per pound.
A baker bought a total of 12 pounds of apples and bananas for $10.20.
The system of equations {a+b=120.75a+1.05b=10.20 models this situation, where a is the number of pounds of apples, and b is the number of pounds of bananas.
How many pounds of each did the baker buy?
Aicha has 36 dress. She completes 1/2 of the dresses in 3/4 of an hour.If she continues at this rate what fraction of the dresses will she complete in one hour?
Answer:
2/3
Step-by-step explanation:
1/2 dresses = 36x1/2 = 18
18 dresses in 3/4 hr. ==> 1/4hr ==> 18/3 = 6
1hr ==> 6x4 = 24
fraction = 24/36 = 2/3
Please answer this correctly without making mistakes
Answer:
$0.31
Step-by-step explanation:
A donor gives $100,000 to a university, and specifies that it is to be used to give annual scholarships for the next 20 years. If the university can earn 4% interest, how much can they give in scholarships each year?
9514 1404 393
Answer:
$7,358
Step-by-step explanation:
Assuming the interest is compounded annually, the amortization formula is useful here.
A = Pr/(1 -(1+r)^-t)
A is the annual scholarship, P is the principal invested at rate r for t years.
A = $100,000(0.04)/(1 -1.04^-20) = $7,358.18
The university could give $7,358 in scholarships each year.
Not quite sure about the answer but it seems simple. Please answer!
Answer:
Its A
Step-by-step explanation:
Can someone please answer this, I need help?
The length of a rectangle is 3 times its width the perimeter is 92 cm find the area
Answer:
The length of a rectangle is 3 times its width.
The perimeter is 92 cm.
Length --> x
Width --> 3x
Area of the rectangle --> y
so
3x·x = y
2(3x)+2x = 92 --> 6x + 2x = 92 -> 8x = 92 --> x =11.5 cm
so
y = 3(11.5)·11.5
y = 396.75 cm²
THE AREA IS 396.75 cm²
Answer:
Step-by-step explanation:
Let Width of rectangle =X
So length of rectangle =3x
Perimeter of rectangle=92
Perimeter of rectangle =2(length +width)
2(length+width)=92
2(3x+X)=92
8x=92
X=92/8
Width X=11.5cm
So length 3x=11.5×3
=34.5cm
Area of rectangle =34.5×11.5
=396.75cm^2
Consider the feasible region in the xy-plane defined by the following linear inequalities.
x≥0
y ≥0
x ≤ 10
x +y≥ 5
x + 2y ≤ 18
Part 2 Exercises:
1. Find the coordinates of the vertices of the feasible region. Clearly show how each vertex is determined and which lines form the vertex.
2. What is the maximum and the minimum value of the function Q = 60x+78y on the feasible region?
Answer:
1. (0,5), (0,9), (10,4), (10,0), (5,0)
2. [tex]Q_{max}=912[/tex]
[tex]Q_{min}=300[/tex]
Step-by-step explanation:
1.
In order to determine the coordinates of the vertices of the feasible region, we must first graph each of the inequalities. The feasible region is the region where all the inequalities cross each other. In this case it's the region shaded on the attached picture.
The first point is the intercept between the equations x=0 and x+y=5 so in order to find this first coordinate we need to substitute x=0 and solve for y.
0+y=5
y=5
(0,5)
The next point is the intercept between the equations x=0 and x+2y=18, so again, we substitute x for zero and solve for y:
0+2y=18
[tex]y=\frac{18}{2}[/tex]
y=9
(0,9)
The next coordinate is the intercept between the lines x=10 and x+2y=18, so we substitute x for 10 and solve for y:
10+2y=18
2y=18-10
2y=8
[tex]y=\frac{8}{2}[/tex]
y=4, so the oint is
(10,4)
The next point is the intercept between the lines x=10 and y=0, so the point is:
(10,0)
The final point is the intercept between the equations: y=0 and x+y=5. We substitute y for zero and solve for x:
x+0=5
x=5
so the point is:
(5,0).
2. In order to determine the maximum and minimum value of the function Q=60x+78y on the feasible region, we must evaluate it for each of the points found on part 1.
(0,5)
Q=60(0)+78(5)
Q=390
(0,9)
Q=60(0)+78(9)
Q=702
(10,4)
Q=60(10)+78(4)
Q=912
(10,0)
Q=60(10)+78(0)
Q=600
(5,0)
Q=60(5)+78(0)
Q=300
So now we compare the answers and pick the minimum and maximum results.
We get that:
[tex]Q_{max}=912[/tex]
when x=10 and y=4
and
[tex]Q_{min}=300[/tex]
When x=5 and y=0
The feasible region is the possible set of a constraint
The vertices are: [tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex]The maximum and the minimum values are 702 and 300, respectively.(a) The coordinates of the vertices at the feasible region
The constraints are given as:
[tex]\mathbf{x \ge 0}[/tex]
[tex]\mathbf{y \ge 0}[/tex]
[tex]\mathbf{x \le 0}[/tex]
[tex]\mathbf{x + y\ge 5}[/tex]
[tex]\mathbf{x + 2y\ge 18}[/tex]
See attachment for the graph of the constraints
From the graph, the vertices are:
[tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex]
(b) The minimum and the maximum values of objective function Q
The objective function is:
[tex]\mathbf{Q=60x +78y}[/tex]
Substitute [tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex] in Q
[tex]\mathbf{Q=60(0) +78(5) = 390}[/tex]
[tex]\mathbf{Q=60(0) +78(9) = 702}[/tex]
[tex]\mathbf{Q=60(5) +78(0) = 300}[/tex]
Hence, the maximum and the minimum values are 702 and 300, respectively.
Read more about feasible regions at:
https://brainly.com/question/7243840
Answer the question in the picture please!!
Answer:
Step-by-step explanation:
take the 142 degree angle and subtract it from 180 to find value of angle n, you will get 38. then you add 38 and 90 together to get 128. Since all angles of a triangle add up to 180. You subtract 128 from 180 to get 52.
Angle M = 52
Angle L = 90
Angle N = 38
Angle LNM = 180
The local gym is charging a flat fee of $10 per month to be a member. Each time you go to the gym you are charged $3. What equation would represent
how much you paying total for the month if x is equal to the number of times you go to the gym?
Sara invested $1,500 in a bond at a simple at a simple interest rate of 3%
Answer: N/A
Step-by-step explanation:
We need more info
help please : (
convert 10.0 cm into in
Answer:
3.93700787 Inch
Step-by-step explanation:
:)
Answer:
3.93701
Step-by-step explanation:
In order to convert cm into inches you divide the cm by 2.54.
Let sets A and B be defined as follows.
A is the set of integers greater than - 7 and less than - 3
B={c, h, j, k, v, y}
(a) Find the cardinalities of A and B.
n(A) = ? n(B)= ?
(b) Select true or false.
True
False
-6E A
-14 EA
k E B
Q E B
The E is the signal used not the actual letter E
Answer:
n(A) = 3
n(B) = 6
-6 ∈ A => True
-14 ∈ A => False
k ∈ B=> True
Q∈B = >False
Step-by-step explanation:
Given
A is the set of integers greater than - 7 and less than - 3
B={c, h, j, k, v, y}
For set A:
The integers greater than -7 will be -6,-5 ....
As the set has integers less than -3, the set will be:
[tex]A = \{-6,-5,-4\}[/tex]
Cardinalities:
Cardinality is the number of elements in the set.
So,
[tex]n(A) = 3\\n(B) = 6[/tex]
Now for the statements:
-6 ∈ A True as -6 is a member of set A
-14 ∈ A False as -14 is not a member of A
k ∈ B True
Q∈B False
Hence,
n(A) = 3
n(B) = 6
-6 ∈ A => True
-14 ∈ A => False
k ∈ B=> True
Q∈B = >False
Danny bought 8 rolls of paper towels. He has 204.8 meters of paper towels in all. How many meters of paper towels are on each roll? A) 21.52 B) 25.12 C) 25.60 D) 26.52
Answer:C) 25.60
Step-by-step explanation:204.8÷8=25.60
Answer:
:C) 25.60
Step-by-step explanation:
25 percent of ____ is 6
Answer:
24
Step-by-step explanation:
1/4 of x is 6 so you multiply 6 by 4
what does x equal in the equation f(x)=17