Answer:
The sequence converges
Step-by-step explanation:
Given the sequence Un = 10n-6/2n-3
To determine whether the sequence converges or diverges, we will have to take the limit of the sequence as n goes large.
[tex]\lim_{n \to \infty} \left\{\frac{10n-6}{2n-3}\right}\\[/tex]
Divide through by n
[tex]= \lim_{n \to \infty} \left\{\frac{10n/n-6/n}{2n/n-3/n}\right}\\= \lim_{n \to \infty} \left\{\frac{10-6/n}{2-3/n}\right}\\= \left\{\frac{10-6/\infty}{2-3/\infty}\right}\\= \frac{10-0}{2-0}\\= 10/2\\= 5[/tex]
Since the limit of the sequence gives a finite value, hence the sequence converges
Logan saved $35 from cutting the neighbor’s yard. He earns $10 a week from washing dishes, which he also saves. Which function can be used to find s, the amount of money Logan will have saved at the end of w, weeks of washing dishes?
the answer is “s = 10w + 35” since he already has 35 but needs to find out how many weeks he washed the dishes :))
Чу- 8х + 5x - Зу
OOoO
im gonna assume that ur just simplifying this equation so here it is
y-3x
hope this helped!!
If A=[1 0 -1 7] find K such that A^2-8A-ki-KI=0
Answer:
K = -7
Step-by-step explanation:
If A=[1 0 -1 7] find K such that A^2-8A-ki-KI=0
Given the 2×2 matrices
A = [tex]\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right][/tex]
We are to find K if =0
A² = [tex]\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right][/tex]
A² = [tex]\left[\begin{array}{ccc}1&0\\-8&49\\\end{array}\right][/tex]
8A = 8[tex]\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right][/tex]
8A = [tex]\left[\begin{array}{ccc}8&0\\-8&56\\\end{array}\right][/tex]
Since [tex]I = \left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right] \\[/tex]
[tex]KI = \left[\begin{array}{ccc}K&0\\0&K\\\end{array}\right][/tex]
Substitute the resulting matrices into the expression above:
A^2-8A-KI = [tex]\left[\begin{array}{ccc}1&0\\-8&49\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}8&0\\-8&56\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}K&0\\0&K\\\end{array}\right][/tex] =[tex]\left[\begin{array}{ccc}0&0\\0&0\\\end{array}\right][/tex]
From the expression, we have the equations;
1 - 8 - k = 0
-7 - k = 0
-7 = k
k = -7
Hence the value of K is -7
2.3.2: Michael Myers predicts that SAT scores predict college graduation rates in a linear fashion. U of M has an average SAT of 1450 and a graduation rate of 90%. GVSU has an average SAT of 1110 and a graduation rate of 69.6%. Write an equation to represent the linear relationship . Be sure your equation is in slope-intercept form
Answer:
[tex]y = \frac{5000r}{3} -50[/tex]
Step-by-step explanation:
Represent the SAT score with y and the rate with r.
So, we have:
[tex](r_1,y_1) = (90\%,1450)[/tex]
[tex](r_2,y_2) = (69.6\%,1110)[/tex]
Required
Determine the equation in slope intercept form
First, we calculate the slope
[tex]m =\frac{y_2 - y_1}{r_2 - r_1}[/tex]
This gives:
[tex]m =\frac{1110 - 1450}{69.6\% - 90\%}[/tex]
[tex]m =\frac{-340}{-20.4\%}[/tex]
Convert percentage to decimal
[tex]m =\frac{-340}{-0.204}[/tex]
[tex]m =\frac{340}{0.204}[/tex]
Multiply by 1000/1000
[tex]m =\frac{340*1000}{0.204*1000}[/tex]
[tex]m =\frac{340000}{204}[/tex]
[tex]m = \frac{5000}{3}[/tex]
The equation is then calculated as:
[tex]y - y_1 = m(r - r_1)[/tex]
This gives:
[tex]y - 1450 = \frac{5000}{3}(r - 90\%)[/tex]
Open Bracket
[tex]y - 1450 = \frac{5000r}{3} - \frac{5000}{3}*90\%[/tex]
Convert percentage to decimal
[tex]y - 1450 = \frac{5000r}{3} - \frac{5000}{3}*0.90[/tex]
[tex]y - 1450 = \frac{5000r}{3} - 5000*0.30[/tex]
[tex]y - 1450 = \frac{5000r}{3} - 1500[/tex]
Make y the subject
[tex]y = \frac{5000r}{3} - 1500+1450[/tex]
[tex]y = \frac{5000r}{3} -50[/tex]
What is the average of 139 and 78?
Answer:
108.5
Step-by-step explanation:
(139 + 78)/2 = 217/2 = 108.5
Answer:
108.5
Step-by-step explanation:
add 139 and 78 then divide by 2
2x+5+3x+6= combine like terms to simplify each expression
Answer:
5x +11
Step-by-step explanation:
Answer:
5x+11
Step-by-step explanation:
Please give brainliest
The number of entertainment websites in 1995 was 54. By 2004 there were 793 entertainment websites. Approximately what was the rate of change for the number of websites for this period of time?
A. 82 websites per year
B. 739 websites per year
C. 12.18 websites per year
D. 424 websites per year
Answer:
Step-by-step explanation:
2004 - 1995 = 9 years
793 - 54 = 739 new sites
739 / 9 = 82.1111111111
approx 82 websites per year change.. ( delta is change )
r!×p(5,r)=40....r=??
What’s is the solution to the equation x to the power of 2 =16/25
Answer:
[tex]x=\dfrac{4}{5}[/tex]
Step-by-step explanation:
The given equation is :
[tex]x^2=\dfrac{16}{25}[/tex]
We need to find the value of x.
When the exponent 2 removes from LHS, it will shift to RHS as square root as follows :
[tex]x=\sqrt{\dfrac{16}{25}}[/tex]
We know that, 4×4= 16 and 5×5 = 25
So,
[tex]x=\sqrt{\dfrac{4\times 4}{5\times 5}}\\\\x=\dfrac{4}{5}[/tex]
So, the solution of the given equation is 4/5.
good night dears...❤️❤️❤️
Answer:
gn
Step-by-step explanation:
Answer:
Good Night! :)
how many 3 element subsets of {1, 2, 3, 4, 5, 6, 7, 8, ,9, 10, 11} are there for which the sum of the elements in the subset is a multiple of 3
Answer:
There are 155 ways in which these elements casn occur.
Step-by-step explanation:
We want 3 element subsets whose sum are multiples of 3
1+2+3= 6
1+2+6= 9
1+2+9= 12
1+9+11=21
1+3+5=9
1+4+8=12
1+5+6=12
1+6+8=15
1+7+10=18
1+8+9=18
1+9+11=21
2+3+7=12
2+4+6=12
2+4+9=15
2+5+11=18
2+6+7=15
2+7+9=18
2+8+5=15
2+8+11=21
2+9+10=21
3+6+9= 18
3+9+11=21
3+10+11=24
6+9+10=27
6+8+11=27
6+7+11=24
7+8+9= 24
8+9+10=27
7+9+11=27 .........
We have 11 elements
We need a combination of 3
The combinations can be in the form
even+ even+ odd
odd+odd+odd
even + odd+odd
So there are 3 ways in which these elements can occur
Total number of combinations with 3 elements =11C3= 165
There are 6 odd numbers and 5 even numbers.
Number of subsets with 3 odd numbers = 6C3= 20
Number of two even numbers and 1 odd number = 5C2*6C1=10*6= 60
Number of 2 odd and 1 even number = 6C2* 5C1= 5*15= 75
So 20+60+75=155
There are 155 ways in which this combination can occur
can someone please help me :(
Answer:
41/3 - 14 - Square root of 200
Step-by-step explanation:
41/3 is between 13 and 14
14 is 14
Square root of 200 is between 14 and 15
what is 17 / 20 as a decimal
please help.
also, i hope you enjoyed you holidays !
Answer:
1. angle AXB
2. 52
Step-by-step explanation:
1.supplementary is 180⁰
2.90-38=52
Please help I’m so confused, I’ve been doing testes all day so my brain is fried. Pleaseee
Answer: 40%
Step-by-step explanation: 20 hours jogging/ 50 total hours gives you .4 which is 40%
is anyone able to answer this?
Step-by-step explanation:
(59,76) , (65,100)
independent variable 76times per minute and 100 per minute dependent variable 65°F and 59°F
[tex] m = \frac{y2 - y1}{x2 - x1} = \frac{100 - 76}{65 - 59} = 4[/tex]
y = mx + b
76 = 4(59)+b
b = -160
y= 4x -160
How many times does 20 go into 168?
Answer:
8.4
Step-by-step explanation:
How many times 20 goes into 168 = 168/20
= 8.4
Pls mark as brainliest <3
Can somebody help me
Answer:
AB ≈ 3.14 ft
Step-by-step explanation:
The arc AB is calculated as
AB = circumference of circle × fraction of circle
= πd × [tex]\frac{45}{360}[/tex] ( where d is the diameter )
= 8π × [tex]\frac{1}{8}[/tex]
= π
≈ 3.14 ft ( to 2 dec. places )
Y=x2+2x+5
Write each function in vertex form.
Farmer John can till his field 1.5 times faster than Farmer Bob. If they work together, they can till the field in 6 hours. How long would it take Farmer John on his own
Answer:
It would take Farmer John 10 hours on his own to till his field.
Step-by-step explanation:
Let;
J = Time spent by John alone
B = Time spent by Bob alone = 1.5 * J = 1.5J
Time spent by both = 6
Using reciprocal, time spent by John alone can be calculated as follows:
(1 / J) + (1 /1.5J) = 1 / 6
Multiply through by 6J and solve for J, we have:
(6J / J) + (6J / 1.5J) = 6J / 6
6 + (6 / 1.5) = J
J = 6 + 4 = 10
Therefore, it would take Farmer John 10 hours on his own to till his field.
What is the solution to the system below?
x + y = 5
x - y = 3
( x, y ) = ( 4, 1 )
hope it helps!
Answer:
x= 4
y= 1
Step-by-step explanation:
by adding 2 equations
2x = 8
x= 4
by sub. in Equation 1
4+y=5
y = 5-4
y= 1
Jerome's sister told him to multiply both the amount of water and the amount of drink
mix by the same number to keep the ratio of water to drink mix the same and still
increase the total amount of energy drink.
a) Complete the table below. (2 points)
Original
Ratio
X1
x2
*3
X4
Drink mix help me plz fast
(cups)
3
Water (cups)
8
Answer:
See below
Step-by-step explanation:
a) Completing table:
×1 column: 3×1 = 3, 8×1 = 8 ⇒ numbers 3 / 8×2 column: 3×2 = 6, 8×2 = 16 ⇒ numbers 6 / 16×3 column: 3×3 = 9, 8×3 = 24 ⇒ numbers 9 / 24×4 column: 3×4 = 12, 8×4 = 32 ⇒ numbers 12 / 32b) Yes, Jerome's sister is correct because 3/8 ratio is same as 3n/8n where n is the number both numerator and denominator are multiplied to, it keeps the ratio as is but helps to increase the amount of drink
Switch the rule 2(x - 5) + 12 into simplified (or standard) form.
Please show the work aswell
Answer:
6x + 9
Step-by-step explanation:
2(3x + 1) + 7, distribute 2 through the parentheses
↓
6x + 2+7
↓
6x + 9
Hope this helps!:)
([tex]\sqrt{\frac{2}{3}[/tex]) plsexplain and solve hurry
Answer:
√6/3
Step-by-step explanation:
Answer:
srry i need points
Step-by-step explanation:
Given a mean of 518, a standard deviation of 22, and a sample size of 200, calculate a 95% confidence interval.
Answer:
do you want me to look it up for you?
solve the equation A = P + Prt for r. Solve the equation A = P + prt for p.
Answer:
b
Step-by-step explanation:
can someone please help me with this question?
Answer:
BA ≈ 1.88
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesTrigonometry
[Right Triangle Trig] sin∅ = opposite over hypotenuseStep-by-step explanation:
Step 1: Define
We are given a right triangle. We can use trig to find the missing length
Step 2: Identify Variables
POV from angle C
Angle = 28°
Adjacent = BA
Hypotenuse = 4
Step 3: Solve for BA
Substitute [sine]: sin28° = BA/4Isolate BA: 4sin28° = BAEvaluate: 1.87789 = BARewrite: BA = 1.87789Round: BA ≈ 1.88I need help with this question!!!
Answer: B. positive 6
Step-by-step explanation: Addomg the positive number to a negative number would turn it to a positive eventually. So u covert your factions to decimals to better see the resemblance. And 1 1/2 is the same as 1.5, and 2 1/10 is the same as 2.1 but it’s easier to deal with decimals. So then just add the positive to the negative sense 1 1/2 is closer to zero. I hope this helps I’m not the best at explaining things
Describe how to transform the graph of f into the graph of g. (2 points)
f(x) = x2 and g(x) = -(-x)2
The graph shifts left one unit.
Reflect the graph of f across the y-axis and then reflect across the x-axis.
Reflect the graph of f across the y-axis.
Reflect the graph of f across the x-axis.
Answer:
Reflect the graph across the x-axis from the positive Quadrant of x-axis to the negative quadrant of x-axis while maintaining the coordinates.
(x⁴ + 8x³ - 45x + 30) ÷ (x + 7)
Topic is Polynomials. Find the answer using long division. Please, provide detailed steps.
Answer:
Step-by-step explanation:
I added 3 images labelled Synthetic division 1 , 2 , 3 . I hope you understand this. It's really hard to type the method in the format so I used an online calculator symbolab.
Answer:
The quotient is: [tex]x^3+x^2-7x+4[/tex]
The remainder is: 2
Step-by-step explanation:
We need to solve the polynomials [tex](x^4 + 8x^3 - 45x + 30) \div (x + 7)[/tex]
by using long division.
The long division is done in figure attached.
The quotient is: [tex]x^3+x^2-7x+4[/tex]
The remainder is: 2