11/21
b/t/w you con go on this website called calculator soup and it has fraction calculators
and the website it self has nothing to download im pretty sure it doesnt
if S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.
You can try to show this by induction:
• According to the given closed form, we have [tex]S_1=3\times2^{1-1}+2(-1)^1=3-2=1[/tex], which agrees with the initial value S₁ = 1.
• Assume the closed form is correct for all n up to n = k. In particular, we assume
[tex]S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}[/tex]
and
[tex]S_k=3\times2^{k-1}+2(-1)^k[/tex]
We want to then use this assumption to show the closed form is correct for n = k + 1, or
[tex]S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}[/tex]
From the given recurrence, we know
[tex]S_{k+1}=S_k+2S_{k-1}[/tex]
so that
[tex]S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)[/tex]
[tex]S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}[/tex]
[tex]S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)[/tex]
[tex]S_{k+1}=3\times2^k-2(-1)^k[/tex]
[tex]S_{k+1}=3\times2^k+2(-1)(-1)^k[/tex]
[tex]\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}[/tex]
which is what we needed. QED
Help plz if your good at finding the area of the compound figure plz help if you don’t know the answer your not needed but if you do plz help
Answer:
96cm^2
Step-by-step explanation:
We can divide it into two rectangles: 7x8 and 10x(12-8), arriving at the solution of 7cm*8cm + 10cm*4cm = 56cm^2 + 40cm^2 = 96cm^2
We can also divide it into two rectangles: 12x7 + (12-8)x(10-7), arriving at 12cm*7cm + 4cm*3cm = 84cm^2 + 12cm^2 = 96cm^2
We could also divide it to one big rectangle and one "negative" rectangle of 10x12 and -8x(10-7), arriving at 10cm*12cm - 8cm*3cm = 120cm^2 - 24cm^2 = 96cm^2
phil worked 5 days more than jill. together they worked 25 days. how many days did each work?
Rachel received 27 cents in change after purchasing a pet gerbil. How many different combinations of coins could she have received from the store clerk? Make a list of all the possibilities. Use the space below to write all of the possibilities. One has been done for you.
Answer:
gfddgjjjffdbbshshhshshshhshhbsbdbddbdvbd
Two variables are said to interact when ____. a. the two variables are differentially affected by a third variable b. both variables produce a change in the subjects' scores c. both variables are equally influenced by a third factor d. the effect of one independent variable depends on the levels of the second variable
Answer:
a.) the effect of one independent variable depends on the levels of the second variable
Step-by-step explanation:
In regression, an interaction effect comes to play whenever the effect that an independent variable has on a dependent variable changes, as regards to value(s) of other independent variables( one or more variables). The variables that give interaction effect as a result of interaction with each other is reffered to as "interacting variables" For instance, in a research whereby how "Male gender versus female gender" and their " dieting B and dieting D" influence their " weight loss" There would be interaction effect in a situation where by a " female gender" that operate on " diet B" shed more weight compare with " male gender" that operate on " diet B". It should be noted that two variables are said to interact when the effect of one independent variable depends on the levels of the second variable
Liz has two pieces of string; one 18cm long, the other 24cm long. She wants to cut them
up to make pieces of string that are all the same length with no string left over. What is the
greatest length she can make the pieces of string?
Answer:
6cm
Step-by-step explanation:
length of the longest string=24
length of the shortest string=18.
for both string to have the same length,
24-x=18
x=24-18
=6cm
The Pythagorean Identity states that:
(sin x)2 + (cos x)2 = 1
Given cos 0 = 8/17, find sin 0.
sin 0 =
[?]
Simplify the fraction.
Answer:
Step-by-step explanation:
cos θ=8/17
sin θ=√(1-cos²θ)=√(1-(8/17)²)=√(1-64/289)=√((289-64)/289)=√(225/289)=15/17
HELPPPPP! Tamlin collects action figures and has 2 more female action figures than male action figures. He chooses two action figures randomly. Write and simplify an expression that represents the probability that Tamlin will pick two female action figures without replacing the first action figure. Let x be the number of male action figures.
Answer:
x+2/2(2x+1)
Step-by-step explanation:
Tamlin has x male action figures and x + 2 female action figures, so a total of x + x + 2, or 2x + 2 action figures. The probability of picking two female action figures without replacement is equal to the product of the probability of
-picking 1 female action figure from the total number and
-picking 1 female action figure after 1 has been removed.
The probability of picking 1 female action figure from the total is equal to the total number of female action figures divided by the total number of action figures.
The probability of picking 1 female action figure after 1 has been removed is equal to the total number of female action figures minus 1 divided by the total number of action figures minus 1.
Multiply these two expressions and simplify.
Answer:
The answer is x+2/2(2x+1)
Jon is taking a 625 mile trip, on the first day he drove 183 miles. How many more miles does he need to drive???
Answer:
442
Step-by-step explanation:
624-183= 442 he needs to drive 442 miles more
Anthony's hourly rate increased from $16.00 to $20.90 in January 2019. Find the
percent change in her hourly rate.
Answer:
30.6%
Step-by-step explanation:
Use the rule of three
A certain brand of all-purpose plant food is sprinkled evenly over the soil surface at a rate of 4.8 ounces per 10
square feet. What is the unit rate of ounces per square feet?
A)0.48
B)21
C)48
D) 2.08
Answer:
48(c)
Step-by-step explanation:
4.8=48 as move 10 will change 4.8 as 48A TV has a listed price of $751.98 before tax. If the sales tax rate is 8.75%, find the total cost of the TV with sales tax included.
Round your answer to the nearest cent, as necessary.
Answer:
$817.78
Step-by-step explanation:
To find the tax you must do the equation:
751.98 x 0.0875
(Btw, 0.0875 is decimal form of 8.75%. Always turn the percentage into a decimal before finding the tax or sale amount)
751.98 x 0.0875 = 65.80.
Now, add the sale tax amount and the original price:
751.98 + 65.80 = 817.78
Therefore, the answer is 817.78.
Find the circumference of the circle P. Find the length of arc AB.
Answer:
A) 56.549
B) 9.425
Step-by-step explanation:
2(pi)r=56.54867
60/360x56.54867=9.425
A number between 0 and 1, expressed as one number over another, is called a
Answer:
its called a frcaction
Step-by-step explanation:
Can someone help me daughter I just wanna see who helps her
Answer:
Yes.
Step-by-step explanation:
The total amount needed is the amount per teacher x the volume of the water bottles.
16 x 9 = 144
since one gallon is 128 ounces,
144/128 = 1.125 = 1 1/8
Since 1 1/8 is less than 1 1/2, there is enough water.
Liam and Michael are going to play video games this afternoon. Together, they have 38 video games. If they decide to randomly choose two video games, what is the probability that the two they choose will consist of each of their favorite video games? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that the Liam and Michael are 0.001422 as a fraction in lowest terms or a decimal rounded to the nearest millionth is 5 decimal.
Liam and Michael are going to play video games this afternoon.
Then, Liam going to play video games = 38
Michael going to play video games = 2
In 38 video games and 2 video games are exactly what Liam and Michael need.
So,
We can write,
Probability = [tex]\frac{2C_{2} }{38C_{2} }[/tex]
As only one case is possible,
That is, [tex]2C_{2}[/tex] = 1
Probability = 1/(38!/(38-2)!2!)
= 1/(38!/36!2!)
=( 2! * 36! )/38!
= (2! * 36! )/38!*37!*36!
= 2!/38!37!
= 1/19!37!
= 1/703
= 0.001422
Rounding to nearest million ( 5 decimal )
Required probability = 0.001422
Therefore,
The probability 0.001422 as a fraction in lowest terms or a decimal rounded to the nearest millionth is 5 decimal.
To learn more about information visit Probability :
brainly.com/question/28730701
#SPJ1
The equal sides of an isosceles triangle are 2 cm shorter than the length of the third side. If the perimeter of the triangle is 35 cm, find the length of the third side.
with the formula plsssss
• Equal sides of an isosceles triangle = 2cm shorter than the length of the third side.
To calculate :• Length of the third side.
Calculation :Let the third side be c.
Also, two equal sides be a and b.
According to the question,
[tex] \longmapsto [/tex] a = ( Third side - 2 ) cm
[tex] \longmapsto [/tex] a = ( c - 2 ) cm
Similarly, length of b(second side) will also be same as a and b are two equal sides of an isosceles triangle.
[tex] \longmapsto [/tex] b = ( c - 2 ) cm
Now, we know that :
★ Perimeter of ∆ = Sum of all sides
Perimeter = 35 cm.[tex] \longmapsto [/tex] 35 = a + b + c
[tex] \longmapsto [/tex] 35 = (c - 2) + (c - 2) + c
[tex] \longmapsto [/tex] 35 = c - 2 + c - 2 + c
[tex] \longmapsto [/tex] 35 = c + c + c - 2 - 2
[tex] \longmapsto [/tex] 35 = 3c - 4
[tex] \longmapsto [/tex] 35 + 4 = 3c
[tex] \longmapsto [/tex] 39 = 3c
[tex] \longmapsto [/tex] [tex] \sf \dfrac{39}{3} [/tex] = c
[tex] \longmapsto [/tex] 13 = c
So, third side of the triangle is 13 cm.
If ΔABC is similar to ΔDEFand EF = 6y, which represents the length of DF ?
Options
3y + 3
3y + 9
4y + 7
4y + 16
Answer:
Length of DF = 3y + 9
Step-by-step explanation:
Given:
ΔABC is similar to ΔDEF
Line EF = 6y
Find:
Length of DF
Computation:
Given that ΔABC is similar to ΔDEF
So,
Line BC similar to Line EF
Line BA similar to Line ED
Line AC similar to Line DF
Common factor = EF/BC
Common factor = 6y/2y
Common factor = 3
So,
Line AC similar to Line DF
So,
DF = 3[AC]
Length of DF = 3[y+3]
Length of DF = 3y + 9
expand the square of a binomial (y^7-11)^2
Answer:
[tex]y^{14} -22y^7+121[/tex]
Step-by-step explanation:
This equation should help:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](y^{7}-11)^2\\\\=y^{14} +2*y^7*-11+11^2\\\\=y^{14} -22y^7+121[/tex]
Answer:
[tex] {y}^{14} - 22 {y}^{7} + 121[/tex]
Step-by-step explanation:
[tex](y {}^{7 } - 11)( {y}^{7} - 11)[/tex]
First terms,
[tex]{y}^{14} [/tex]
Outer,
[tex] {y}^{7} \times - 11 = - 11 {y}^{7} [/tex]
Inner,
[tex] {y}^{7} \times - 11 = - 11 {y}^{7} [/tex]
Last,
[tex] - 11 \times - 11 = 121[/tex]
Add all terms up
[tex] {y}^{14} - 22 {y}^{7} + 121[/tex]
Type your answer into the box.
240 people are going to a charity event.
3/5 of the guests have ordered chicken for their meals.
Of the remaining guests, 12.5% have ordered gluten-free meals
How many people haven't ordered their meals yet?
Answer:
84 people
Step-by-step explanation:
1
Type the correct answer in the box.
5 units
2 units
2 units
3 units
2 units
The area of the figure is
square units
Reset
Next
Answer:
Is there any more information to this so I can try and help
Let A and B be two events. Suppose the probabilities P(A) = 0.5, P(
A and B) = 0.2
and P((AUB)') = 0.4. What is P(B)?
Answer:
[tex]P(B) = 0.3[/tex]
Step-by-step explanation:
We use the following formula for Venn probabilities to solve this question.
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
P((AUB)') = 0.4
This means that:
[tex]P(A \cup B) = 1 - P(A \cup B)' = 1 - 0.4 = 0.6[/tex]
We also have that:
[tex]P(A) = 0.5, P(A \cap B) = 0.2[/tex]
What is P(B)?
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
[tex]0.6 = 0.5 + P(B) - 0.2[/tex]
[tex]0.3 + P(B) = 0.6[/tex]
[tex]P(B) = 0.3[/tex]
Solve the following inequality
4 + 6x ≤ x + 6x
Select one:
A. x ≤ 4
B. x ≥ 4
C. x > 4
D. x < 4
Answer:
x ≥ 4
Step-by-step explanation:
The given inequality is :
4 + 6x ≤ x + 6x
Subtract 6x from both sides,
4 + 6x-6x ≤ x + 6x -6x
4≤ x
or
x ≥ 4
Hence, the correct option is (b) i.e. x ≥ 4.
Alex's pig weighs under 220 pounds.
Let p = the weight of the pig
Answer:
p > 220
Explanation:
This inequality says, "p (the weight of the pig) is less than 220." This describes the situation shown. So, the answer is p > 220.
Good luck ^^
*10 POINTS *
find the value of x
x = ___??
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
You can create a proportion with the sides and solve for x:
[tex]\frac{SR}{QR} =\frac{TR}{UR}[/tex]
[tex]\frac{20}{24}=\frac{15}{-4x+10}[/tex]
[tex]\frac{5}{6}=\frac{15}{-4x+10}[/tex]
[tex]-20x+50=90[/tex]
[tex]-20x=40[/tex]
[tex]x=-2[/tex]
Order the numbers from least to greatest.
= –1.5
- (-2)
2.5
8/3
HELPP
Answer:
-1.5, -(-2), 2.5, 8/3
Step-by-step explanation:
pretty sure this is right
After basketball practice, 8 players equally shared 3 large bottles of water. What fraction of a bottle did each player get?
if the submarine travels 518 kilometers in 14 hours, how many kilometers does the submarine travel in 1 hour
Answer:
37 km
Step-by-step explanation:
Answer:
37kph
Step-by-step explanation:
518/14=37
someone please help me answer this!!
Answer:
-5 63/100
Step-by-step explanation:
Plz help if correct ill give Brainlyest
Answer:
x=21
Step-by-step explanation:
x=(16.8 * 2.5) /2=21