Answer:
[tex]T_n = 2n -3[/tex]
Step-by-step explanation:
Given
[tex]S_n = n^2- 2n[/tex]
[tex]T_n = S_n - S_{n-1[/tex]
Required
Find [tex]T_n[/tex]
[tex]S_n = n^2- 2n[/tex]
Calculate [tex]S_{n-1[/tex]
[tex]S_{n-1} = (n-1)^2- 2(n-1)[/tex]
[tex]S_{n-1} = n^2-2n+1- 2n+2[/tex]
[tex]S_{n-1} = n^2-2n- 2n+1+2[/tex]
[tex]S_{n-1} = n^2-4n+3[/tex]
[tex]T_n = S_n - S_{n-1[/tex] becomes
[tex]T_n = n^2 - 2n - (n^2 - 4n +3)[/tex]
[tex]T_n = n^2 - 2n - n^2 + 4n -3[/tex]
[tex]T_n = n^2 - n^2- 2n + 4n -3[/tex]
[tex]T_n = 2n -3[/tex]
Need help with these math problems
Answer:
1. 34 sq.m.
2. 21 sq.m
3. A square pyramid has 1 square base and 4 triangular faces.
a. 36 square centimeters
b. 48 square centimeters
c. 84 square centimeters
4. a. 248 square centimeters
b. 1240 square centimeters
5. 140.8 square centimeters
Jerry and Olivia were running a relay race. The race was 25.78 kilometers total. If Jerry ran 15.18 kilometers how far did Olivia run?
In the cylinder, the radius of the circular base is 3.5 centimeters, and the height of the cylinder is 11 centimeters. The volume of the cylinder is
Answer:
33.69[tex]\pi[/tex] or 105.83
Step-by-step explanation:
Volume for a cylinder is
V= [tex]\pi r^{2}h[/tex]
we need to find the radius from the base
B = 2[tex]\pi[/tex]r
B= 3.5/2 = 1.75
V =[tex]\pi 1.75^{2}*11[/tex]
V = 33.69[tex]\pi[/tex] or 105.83 depending if you want it in pi for or not
Hi please help me i will mark as brainiest just please help!
Answer:
B
Step-by-step explanation:
Kahlil wants it to be more than 10 seconds long, and his friend wants it 5 seconds longer than that. So it has to be at least 10 + 5 seconds long or 15 seconds. B is the only option with >15, and all the possible track lengths below satisfy the inequality.
Ms. Wolf goes shopping at Target and spends $38.75. Sales tax is 8%.
Enter the answer for question B: How much does she pay in total?
Answer:
you have to do the sales tax, times the price $3.10
then you add the $3.10 to the original price which is $41.85
Step-by-step explanation:
Select the null and the alternative hypotheses for the following claims:
a. "I am going to get the majority of the votes to win this election."
multiple choice 1
H0: μ = 0.50; HA: μ ≠ 0.50
H0: p ≤ 0.50; HA: p > 0.50
H0: p ≥ 0.50; HA: p < 0.50
b. "I suspect that your 10-inch pizzas are, on average, less than 10 inches in size."
multiple choice 2
H0: μ ≥ 10; HA: μ < 10
H0: p ≥ 10; HA: p < 10
H0: μ = 10; HA: μ ≠ 10
c. "I will have to fine the company since its tablets do not contain an average of 250 mg of ibuprofen as advertised."
multiple choice 3
H0: μ = 250; HA: μ ≠ 250
H0: p ≤ 250; HA: p > 250
H0: p = 250; HA: p ≠ 250
Answer:
a. H0: p ≥ 0.50; HA: p < 0.50
b. H0: μ ≥ 10; HA: μ < 10
c. H0: μ = 250; HA: μ ≠ 250
Step-by-step explanation:
a. "I am going to get the majority of the votes to win this election."
This sentence means that the probability of winning is more than fifty percent or more than half.The null hypothesis would be
H0: the probability of winning is more than 50 %
against the claim that
Ha: the probability of winning is less than 50%
So the best choice would be option c
H0: p ≥ 0.50; HA: p < 0.50
b. "I suspect that your 10-inch pizzas are, on average, less than 10 inches in size."
The claim is that the pizzas are less than 10 inches in size.
which can be written as alternate hypothesis
Ha: u < 10
so the best choice would be option a
H0: μ ≥ 10; HA: μ < 10
c. "I will have to fine the company since its tablets do not contain an average of 250 mg of ibuprofen as advertised."
In this statement the claim is that an average of ibuprofen do not contain 250 mg as advertised.
the alternate hypothesis would be u ≠ 250 mg
Ha: μ ≠ 250 and the null hypothesis is the reverse of the aalternate hypothesis.
so the best option would be part a
H0: μ = 250; HA: μ ≠ 250
One spring day, Jin noted the time of day and the temperature, in degrees Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 56° F. For the next 5 hours, the temperature rose 1° per hour. For the next 4 hours, it rose 2° per hour. The temperature then stayed steady until 6 p.m. For the next 3 hours, the temperature dropped 1° per hour. The temperature then dropped steadily until the temperature was 62° at midnight. On the set of axes below, graph Jin's data.
Answer:
This is how the graph will look like because I don't have a graph that why I use a note
Step-by-step explanation:
At 6am it is 56°.For the next 5hours it increases to 61° since it is 1° per hour and after 4 hours again it will increase to 69° because it is 2° per hour and it stayed steady till 6pm and it dropped the next 3 hours which the temperature now reduces to 66° and dropped steadily to 62° at midnight
The temperature variations is represented on the graph attached with the answer.
What is graph?A diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
At 6am it is 56°.For the next 5hours it increases to 61° since it is 1° per hour and after 4 hours again it will increase to 69° because it is 2° per hour and it stayed steady till 6pm and it dropped the next 3 hours which the temperature now reduces to 66° and dropped steadily to 62° at midnight
To know more about Graph follow
https://brainly.com/question/4025726
#SPJ2
I was wondering if anyone knew how to use a ti 84 to solve these. I just got one and it’s all very confusing to me.
Jayden wants to lay sod on his front yard and on half of his back yard. His front yard has a length of 50 feet and a width of 80 feet. His back yard has a length of 20 feet and a width of 30 feet. How many square feet of sod does Jayden need to purchase? OA. 4,300 square feet OB. 4,600 square feet OC. 2,600 square feet OD. 4,150 square feet
Answer:
4,300 square feet
Step-by-step explanation:
First, calculate the area of Jayden's front yard.
50 feet × 80 feet = 4,000 square feet
Next, find the area of half of Jayden's back yard.
1/2(20 feet × 30 feet) = 300 square feet
Last, add the two areas together.
4,000 feet + 300 feet = 4,300 square feet
So, Jayden needs to purchase 4,300 square feet of sod
Factorise the expressions.
Answer:
Q.1 lx²+mx
=x(lx+m)
Q.2 x² - ax - bx + ab
= x(x - a) - b(x - a)
=(x - b)(x - a)
Q.3 6ab - b²+ 12ac - 2bc
= b(6a - b) - 2a(6a - b)
=(b - 2a)(6a - b)
Which of the following examples has a unit rate of 70 miles per hour? Select all
that apply.
A) 210 miles in 3 hours
B) 420 miles in 6 hours
C) 280 miles in 5 hours
D) 560 miles in 8 hours
E) 560 miles in 7 hours
Answer:
A, B and D are the answers.
Answer:
A, B, D.
Step-by-step explanation:
giving brainliest !! *easy*
Jessica has just purchased a new purse in the shape of a rectangular box to match her favorite shoes. The purse has a length of 15 cm, a width of 6.4 cm, and a height of 8 cm. What is the volume of the purse?
Which systems of equations have the same solutions?
L (3x+y = 8
1x - 4y = -6
m{$*=*=230
NS 4x – 3y = 2
12% -8y = -12
Answer:
B. L and N
Step-by-step explanation:
Let's solve each system
✔️System L:
3x + y = 8 => Eqn. 1
x - 4y = -6 => Eqn. 2
x = -6 + 4y
Substitute x = (-6 + 4y) in eqn. 1
3(-6 + 4y) + y = 8
-18 + 12y + y = 8
-18 + 13y = 8
13y = 8 + 18
13y = 26
y = 26/13
y = 2
Substitute y = 2 into Eqn. 2
x - 4y = -6
x - 4(2) = -6
x - 8 = -6
x = -6 + 8
x = 2
Solution to system L = (2, 2)
✔️System M:
4x - 3y = 2 => Eqn. 1
5x - 4y = -30 => Eqn. 2
Multiply eqn 1 by 5, and eqn. 2 by 4
20x - 15y = 10
20x - 16y = -120
Subtract
y = 130
Substitute y = 130 into eqn. 1
4x - 3(130) = 2
4x - 390 = 2
4x = 2 + 390
4x = 392
x = 392/4 = 98
Solution to system M = (98, 130)
✔️System N:
4x - 3y = 2 =>Eqn. 1
2x - 8y = -12 => Eqn. 2
Multiply Eqn. 1 by 2, and eqn. 2 by 4
8x - 6y = 4
8x - 32y = -48
Subtract
26y = 52
y = 52/26
y = 2
Substitute y = 2 into eqn. 1
4x - 3(2) = 2
4x - 6 = 2
4x = 2 + 6
4x = 8
x = 8/4
x = 2
Solution to system N = (2, 2)
PLEASE HELP ASAP
trigonometry
Answer:
5). x = 11.9°
6). x = 27.2°
Step-by-step explanation:
5). By applying cosine rule in the given triangle,
cos(32)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
cos(32)° = [tex]\frac{x}{14}[/tex]
x = 14cos(32)°
x = 11.87
x ≈ 11.9°
6). By applying sine rule in the given triangle,
sin(54°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sin(54°) = [tex]\frac{22}{x}[/tex]
x = [tex]\frac{22}{\text{sin(54)}}[/tex]
x = 27.19°
x ≈ 27.2°
Adam is comparing the graphs of y=4x and y=8x. Which of the following statements is TRUE?
Frank bought 3.86 lbs of cherry and lime jelly beans for his birthday party. If 1.56 lbs were cherry flavor, how many pounds were lime flavor?
Answer:
2.3 lbs.
Step-by-step explanation:
Total=3.86
Cherry=1.56
3.86-1.56= 2.3
Solve | 2x - 6 | = |x| by graphing
Answer:
X=2 & X=6
Step-by-step explanation:
If you graph the equation (I recommend using desmos) you can see that X equals 2 & 6.
hi good day plss help me plssssssssss i need yoyre help now plss
Answer:
6.c 7.c 8. b 9. a 10. a
Step-by-step explanation:
6=c as 39.10-19.56
7. 89.2-78.6
8. 8.03-5.1
9. 40.98-15.6
10.55.6-47.5
8. Which of these would best measure the WEIGHT of a ship?
A. Ounces
B. Pounds
C. Tons
D. Kilograms
Answer: Tons
Step-by-step explanation: A ship is SUPER heavy.
Amy’s watch loses time at the rate of 3 minutes every 5 days. Fine the number of days before the watch loses one hour or time
Please note that this is directly proportional applications and the formula is output unit/input unit times input unit
Answer:
100 daysStep-by-step explanation:
3 min loss ⇔ 5 days60 min loss ⇔ x daysCross multiply and solve for x:
3x = 5*603x = 300x = 300/3x = 100 daysSuppose you are to select a password of size 4. The first character should be any lowercase letter or a digit, while the second should be a non-zero digit. The third should be any lower case letter, and the fourth should be any lowercase letter, which is different from the third. b. Consider a group of ten students, and six of them are boys. A committee of 3 students is expected to select from the above group. How many committees can you select with at least two girls
First question seems incomplete :
Answer:
40 ways
Step-by-step explanation:
Question B:
Number of boys = 6
Number of girls = 4
Number of people in committee = 3
Number of ways of selecting committee with atleast 2 girls :
We either have :
(2 girls 1 boy) or (3girls 0 boy)
(4C2 * 6C1) + (4C3 * 6C0)
nCr = n! ÷ (n-r)!r!
4C2 = 4! ÷ 2!2! = 6
6C1 = 6! ÷ 5!1! = 6
4C3 = 4! ÷ 1!3! = 4
6C0 = 6! ÷ 6!0! = 1
(6 * 6) + (4 * 1)
36 + 4
= 40 ways
Answer this ASAP the last question that due 5 minutes
Answer:
C
Step-by-step explanation:
If you graph the points, count boxes from the orgin (0,0).
You will have to go 3 to the right (on x), and up 6 (on y).
The number of minutes, m, of exercise, and the number of calories, c, burned during exercise. What is the independent variable?
Answer:
number of minutes
Step-by-step explanation:
Solve: 64-3x-3 .64+22=38
4.0/5
136
The answer is x = -8/9.
Hope you have a good rest of your day. :)
Answer:
B. [tex]x=-\frac{8}{9}[/tex]
Step-by-step explanation:
edge 2021
:) Good luck, loves!
Line a is parallel to line b. If the
measure of Z2 is 78°, what is the
measure of Z8?
78° =21
314
615
78
b
This is because alternate exterior angles are congruent when we have parallel lines like this.
Angle 2 and angle 8 are both outside the parallel lines, so that's what makes them exterior angles. Also, they are on alternating sides of the transversal line (angle 2 on the left, angle 8 on the right). So that's where the "alternating" comes from. The other pair of alternate exterior angles is angle 1 and angle 7.
PLEASE HELP who knows the answer to this?
Answer:
a.
Step-by-step explanation:
Can please someone help with this two problems?
Answer:
A and C
Step-by-step explanation:
20) Since the triangles are similar, you can say that 98 corresponds to 42 and 77 corresponds to 3x+6, because of this you can write an equation ((98/77)(3x-6) =42) and then simplify to get x = 13.
21) Since ABC and DFE are similar, we can say that 2x+2 corresponds to x+3 and 24 corresponds to 16. You can write this as the equation (24/2x+2)(x+3) = 16 and simplify to get x=5.
I hope this helps :)
A floor is 7 m long and 5 m wide. A square carpet of side 4 m is laid on the floor. Find
the area of the floor that is not carpeted?
Answer:
the area of the floor that is not carpeted 19 m squared
Step-by-step explanation:
7x5 =35 m squared = area of the floor
4x4 = 16 squared =(area of the carpeted floor)
35-16 = 19
Artie ate 1/5 of a box of cereal last week and 1/5 of the box more this week. How much of Arties box of cereal is left?