Answers
Answer:
16
Step-by-step explanation:
From the question given above, the following data were obtained:
Sum of N term (Sₙ) = 292
2nd term (T₂) = 8.5
5th term (T₅) = 13
Number of terms (N) =?
Next, we shall determine the first term (a) and the common difference (d) of the series. This can be obtained as follow:
T₂ = a + d
8.5 = a + d ........ 1
T₅ = a + 4d
13 = a + 4d ........ 2
Subtract equation 1 from equation 2 i.e
(2) – (1)
.. 13 = a + 4d
– 8.5 = a + d
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
4.5 = 3d
Divide both side by 3
d = 4.5 / 3
d = 1.5
Substitute the value of d into any of the equation to obtain the value of a. Here, we shall use equation 1.
8.5 = a + d
d = 1.5
8.5 = a + 1.5
Collect like terms
8.5 – 1.5 = a
a = 7
Finally, we shall determine the number of terms as follow:
Sum of N term (Sₙ) = 292
Common difference (d) = 1.5
First term (a) = 7
Number of terms (N) =?
Sₙ = n/2[2a + (n – 1)d]
292 × 2 = n[(2 × 7) + (n – 1)1.5]
584 = n[14 + 1.5n – 1.5]
584 = n[12.5 + 1.5n]
584 = 12.5n + 1.5n²
Rearrange
1.5n² + 12.5n – 584 = 0
Using formula method, the value of n can be obtained as follow:
a = 1.5
b = 12.5
c = –584
n = –b ± √(b² – 4ac) / 2a
n = –12.5 ± √(12.5² – 4 × 1.5 × –584) / 2 × 1.5
n = –12.5 ± √(156.25 + 3504) / 3
n = –12.5 ± √(3660.25) / 3
n = –12.5 ± 60.5 / 3
n = –12.5 + 60.5 / 3 or –12.5 – 60.5 / 3
n = 4 /3 or –73 / 3
n = 16 or –73 / 3
Since the number of terms can not be negative, therefore, the number of term is 16
Related Questions
HELP I WILL GIVE BRAINIEST
Answers
Answer:
sorry I can only answer no.3
[tex]4x - 2 = 180 \\ 4x = 180 + 2 \\ 4x + 3x = 182 \\ \frac{7x}{7} = \frac{182}{7} \\ x = 26[/tex]
giving brainliest! help me pls
Answers
Answer:
4 feet
Step-by-step explanation:
1 Yard = 3 feet
3 ft. + 1 ft. = 4 ft.
1 yard = 3 ft, plus 1 ft, you get 4ft
Calculate the side lengths a and b to two decimal places
Answers
Answer:
Option (a) is correct.
a = 15.68 and b = 19.58
Step-by-step explanation:
Given: A triangle with some given measurements.
We have to find the values of a and b.
For a triangle ABC , with side opposite to angle A is a , side opposite to angle B is b and side opposite to angle C is c,
Using Sine rule , we have,
For the given Δ ABC,
∠A = 50° , ∠B = 107°
AB = c = 8 , AC = b and BC = a
Using angle sum property of triangle,
Sum of angles of a triangle is always 180°
So , ∠A + ∠B +∠C = 180°
Solving for ∠C , we get,
∠C = 180° - 107° - 50°
∠C = 23°
Substitute in Sine rule , we have,
Consider first and last ratios, we have,
Solving for a, we have,
We get , a = 15.68
Consider last two ratios, we have,
and now solving for b ,
We get , b = 19.58
Thus, option (a) is correct.
a = 15.68 and b = 19.58
3. Marissa owes her parents
money for her car. She paid
them $163 for 24 months
until she finished paying her
debt. Which integer
represents how much
money she owed her
| parents?
Answers
Explanation: 163 * 24 = 3,912
please help meee!!!!!!!
Answers
Answer:
x+8 +=98
Step-by-step explanation:
x + to 90 so 98
Answer:
3 3/8 pounds.
Step-by-step explanation:
That is the one with three x's.
Total weight = 3 * 1 1/8
= 3 3/8.
Find the area. Please hurry!
Answers
Find the area of this shape
Answers
Here's the solution,
Area of rectangle :
=》
[tex]l \times b[/tex]
=》
[tex]23 \times 12[/tex]
=》
[tex]276 \: \: cm {}^{2} [/tex]
Area of trapezoid :
note : h = 18 - 12 = 6 cm
=》
[tex] \dfrac{1}{2} \times (a + b) \times h[/tex]
=》
[tex] \dfrac{1}{2} \times (23 + 15) \times 6 [/tex]
=》
[tex]38 \times 3[/tex]
=》
[tex]114 \: \: cm {}^{2} [/tex]
Area of whole figure (V) = sum of their Areas,
=》
[tex]276 + 114[/tex]
=》
[tex]390 \: \: cm {}^{2} [/tex]
Which of the following shows how to simplify 2 (4a + 6)?
O 8a + 12
O 12a + 8
O 2a + 3
Answers
You have to work out between 2 x 4a = 8a
Then you work out between 2 x 6 = 12
8a + 12
PLEASEEEE HELPPP SOMEONEEE
The number of texts Lee and John received each day for 8 days is shown. Lee's Text messages: (36, 31, 33, 35, 40, 29, 34, 34)
John's Text messages: (20, 15,45,5,23,22, 12, 18)
Lee's mean number of texts per day is 34 and John's mean number of texts per day is 20.
What statement involving MAD (mean absolute deviation) is true?
A. Lee has less variation in the number of text messages per day than John because Lee's MAD of texts per day is less than John's.
B. Lee has less variation in the number of text messages per day than John because Lee's MAD of texts per day is greater than John's.
C. Lee has greater variation in the number of text messages per day than John because Lee's MAD of texts per day is less than John's.
D. Lee has greater variation in the number of text messages per day than John because Lee's MAD of texts per day is greater than
John's
Answers
Answer:
a
Step-by-step explanation:
We in the same boat sis
What is the area of this figure?
Answers
The answer to this problem is A) 760.27 in^2
Help me please. :) :) :)
Answers
Answer:
c
Step-by-step explanation:
c is the right one
PLEASE HELP I HAVE TEST!! Find the measure of the arc or angle indicated
Answers
Answer:
Step-by-step explanation:
<JKL = 90 ( being inscribed angle in semi circle )
< JKP = 38 ( Inscribed angles on same arc are equal )
So now
<PKL = <JKL - < JKP
= 90 - 38
= 52
FINALLY
ARC PL = 2 * < PKL (Relation between arc and inscribed angle )
ARC PL = 2 * 52
= 104
hope it helps :)
Write a math problem that includes multiplying decimals.Explain how you know where to place the decimal in the product.
Answers
Answer:
0.1 x 2 = 0.2
Step-by-step explanation:
when you multiply, you move the decimal once because there is one decimal place.
Help please!!! I’ll name you brainliest!!
Answers
Answer:
0,1,2,6,8,11,13,15,20
Step-by-step explanation:
cuanto es 1+1
respuestas originales
gracias
Answers
Answer:
Step-by-step explanation:
It’s 2
Answer:
[tex]1 + 1 = 2[/tex]
[tex]espero \: haberte \: ayudado[/tex]
Carl has $25.00 to spend o six packs of soda for the dance. If the cost of one-six pack is $2.50, which inequality could be used to represent this relationship?
Answers
Answer:
25 ≤ 2.5n
Step-by-step explanation:
Total budgeted amount = $25
Cost per pack of = $2.50
To represent the relationship using inequality :
Let the Total number of packs purchased = n
Hence,
Total budgeted amount ≤ (cost per pack * number of packs)
25 ≤ 2.5n
This means the total actual purchase made should be less than or equal to the budgeted amount.
help me pls
5x^2-45=0
Answers
Step-by-step explanation:
5x²-45=05x²=45x²=9x=√9x=3hope it helps.
Answer:
x=±√9 or x= 3, x=-3
Step-by-step explanation:
The problem requires us to find the x.
So we must isolate the variable, as so-
[tex]5x^2-45=0\\5x^2=45[/tex] (add 45 to both sides)
Now we can divide both sides by -
[tex]5x^2=45\\x^2=9[/tex]
Now we must square root both sides to find the root of x.
[tex]\sqrt{x^2} =\sqrt{9}[/tex]
x=±√9
or x= 3, x=-3
17. Michaela and Aleah play on the same basketball team. In one game Michaela scored one fifth of the
team's points and Aleah scored one tenth's of the team's points. Together the scored a total of 42
points. How many points did the team score?
Answers
Answer:
Michaela scored 140/5 = 28 points; Aleah scored 140/10 = 14 points.
Step-by-step explanation:
There is a classic game called “Rock, Paper, Scissors.” Two people play by counting to 3 together, then making a hand gesture to resemble paper (hand flat, palm down), rock (fist), or scissors (two fingers extended).
• When paper and rock are shown, paper wins the round.
• When paper and scissors are shown, scissors wins the round.
• When rock and scissors are shown, rock wins the round.
• When both players show the same thing, the round is a tie.
Using the site: Rock, Paper, Scissors to play Rock, Paper, Scissors. You will scroll down until you see the hand. Then click on Generate to begin game.
Play 3 rounds of 10, using the same gesture for each round. Record what gesture was used by you, the gesture used by the computer, and the result.
Round 1:
My Option: Rock
Computer Scissors Paper Scissors Scissors Rock Scissors Scissors Rock Rock
Winner? Win Lost Win Win Tie Win Win Tie Tie
Round 2:
My Option: Paper
Computer Scissors Paper Scissors Rock Rock Rock Paper Rock Rock
Winner? Lost Tie Lost Win Win Win Tie Win Win
Round 3:
My Option: Scissors
Computer Rock Paper Rock Rock Scissors Paper Rock Rock Paper
Winner? Lost Win Lost Lost Tie Win Lost Lost Win
1. Is the event “win the round” dependent on another event? Explain your reasoning.
2. Create a graph of your data. Make sure to label your graph and that the graph is appropriate for the type of data you have.
3. Choose an event that you think might influence the probability of winning, then analyze the data using probability to determine whether the event you chose to study is independent of winning. Provide evidence to support your claim.
Answers
Answer:
Round 1: rock
Round 2: scissors
Round 3: paper
Step-by-step explanation:
YOUR DATA TABLES
Round 1: TIE
Round 2: LOST
Round 3: WIN
(4, 11), (10, 11), and (9, 7) is reflected over the y-axis .
PLEASE HELP THIS IS DUES TO DAY
Answers
Answer:
The new coordinates would be (-4, 11)
(-10, 11) (-9, 7) Hope this helps!
1) ABC is a right-angled triangle.
AB = 50 cm.
Angle ABC= 24°
Work out the length of BC.
Give your answer correct to 1 decimal place.
Answers
Answer:
112.3
Step-by-step explanation:
Write an equation in slope-intercept form of the line that passes through the given points.
Answers
Answer:
y = 1/3x -3
Step-by-step explanation:
How do you find the percentage of 70.9 of 100
Answers
70.9/100=0.709=70.9%
answer for brainilest 11 points
Answers
Answer:
729 is 3 to the power of 6
Step-by-step explanation:
Answer:729
Step-by-step explanation: 3x3x3x3x3x3=729
lauren spent $3.26 for lunch on Tuesday she spent $1.98 on Wednesday and $2.74 on Thursday list the price in ascending order
Answers
Answer:
1.98, 7.74, 3.26
Step-by-step explanation:
I listed them from Smalest to largest 1.98 being samller than 2.74 and 2.74 being smaller than 3.26.
Hope this helped :)
OKAY, guys give me a really brilliant explanation on how 2+2=4. It should be 22. It doesn't make sense.
Answers
Answer:
It does make perfect sense... Count with ya fingers and see 4 yourself.
Step-by-step explanation: Go back to kindergarten buddy...
~ thx 4 the points my dude!~
compare the numbers with
>, <, =
- 3.5 ____ 2.8
7.4 ____ - 9
Answers
Answer:
-3.5 < 2.8
7.4 > -9
Step-by-step explanation:
If you have a negative number and a positive number the positive number is always greater.
When you have a negative number and another negative, the smallest number is greater.
For example: -2.5 -3.7
-2.5 is greater than -3.7 because it is less negative.
-2.5 > -3.7
When you have a positive number and a positive number, the biggest number is greater.
For example: 8.3 4.2
8.3 is greater than 4.2 because it is a bigger number.
8.3 > 4.2
A box in the shape of a rectangular prism has the dimensions shown. What is the length of the interior diagonal of the box? Round to the nearest tent
Enter your answer in the box.
Answers
Answer:
141.4 cm
Step-by-step explanation:
Refer to the notations in the attached photo,
AG = d
Using Pythagoras Theorem:
In triangle ABC,
AC
=[tex] \sqrt{ {60}^{2} + {80}^{2} } [/tex]
=[tex] \sqrt{3600 + 6400} [/tex]
=[tex] \sqrt{10000} [/tex]
= 100 cm
∴ AC is 100 cm.
In triangle ACG,
d
=[tex] \sqrt{ {100}^{2} + {100}^{2} } [/tex]
=[tex] \sqrt{10000 + 10000} [/tex]
=[tex] \sqrt{20000} [/tex]
= 141.4 cm (cor. to the nearest tenth)
I don't know this questions so pls help
Answers
Answer:
The distance between the two points is 6.3 units
Step-by-step explanation:
Here, we want to find the distance between the two points
We have the equation to find this as follows;
D = √((x2-x1)^2 + (y2-y1)^2
where (x1,y1) = (-4,2) and (x2,y2) = ((2,4)
so we have the length calculated as follows;
D = √(2-(-4))^2 + (4-2)^2
D = √6^2 + 2^2
D = √36 + 4
D = √40
D = 6.3 units
GUYS SINCE YOU ARE SMART AND IM NOT HELP PLEASE