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
Sarah went to a basketball game. She bought a ticket to the game and a bag of
popcorn spending a total of $15.00. Tyler went to a basketball game. He bought a
ticket to the game and 3 bags of popcorn spending a total of $30.00. How much is a
ticket to the game?
o $4.75
o $10.50
O $7.50
O $5.25
Answers
Answer:
10.5
Step-by-step explanation:
Help pleas I need help
Answers
Answer:
3.05
Step-by-step explanation:
Answer:
3 3/4 inches
Step-by-step explanation:
Rewrite the expression without parentheses. 13m−(3+8m)
Answers
Answer:
13m-3+8m
Step-by-step explanation:
need help with area for solving this
Answers
Answer:
Step-by-step explanation:
First find the area of total rectangle which equals 20 * 12 = 240
Second find the area of triangle which equals 0.5 * 4 * 6 = 12
The required area = total rectangle - triangle = 240 - 12 = 228
Answer:
NEEEEEGARRRRR
Step-by-step explanation:
Kevin and Ornella entered a fun run. Their times for completing the course totaled 1 hour 52 minutes. Kevin's time was 4 minutes less than Ornella's. How many minutes did it take Ornella to complete the course?
Answers
Answer:
58 minutes
Step-by-step explanation:
Kelvin and Ornella completed the course in 1 hour 52 minutes
60 minutes + 52 minutes
= 112 minutes
Kelvin time is 54 minutes
Kelvin time is 4 minutes less than ornella
Hence Ornella time is 58 minutes
Solve for m:
M
_ - 23 = 109
6
Answers
Answer:
132
Step-by-step explanation:
I'm assuming the six is not supposed to be there so here's what I did:
M - 23 = 109 - all you need to do is add 23 to both sides
M = 132 - doing this cancels out the -23 on the left
In which set do all values make the inequality 3x+5<26 true?
Answers
2x - 1 < 10
Add 1 to both sides:
2x < 11
Divide both sides by 2:
x < 5.5
Answers must be smaller than 5.5, therefore option (D) is the answer.
Answer: D. {2, 3, 4}
<3 - Bee
express (x-1)(2x-8) as a trinomial
Answers
Answer:
the answer is 2x²-10x+8
The trinomial equation is A = 2x² - 10x + 8
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ( x - 1 ) ( 2x - 8 ) be equation (1)
On simplifying the equation , we get
A = x ( 2x - 8 ) - 1 ( 2x - 8 )
A = x ( 2x ) - x ( 8 ) - 2x + 8
On further simplification , we get
A = 2x² - 8x - 2x + 8
A = 2x² - 10x + 8
Therefore , the value of A is 2x² - 10x + 8
Hence , the equation is A = 2x² - 10x + 8
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
A survey of a random sample of juniors shows that 12% are not planning to attend homecoming, and 88%
are planning to attend. The survey has a margin of error of t8%. What is the range for the percentage of juniors who are
going to homecoming?
F 4% to 20%
G 4% to 12% H 80% to 96%
J. 4% to 96%
Answers
Answer:
i would guess
Step-by-step explanation:
Lin has a die with 6 sides, each labeled 1, 2, 3, 4, 5, and 6. What is the probability that she will roll a 3? *
Answers
Answer:
Probability of rolling number 3 = [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Lin has a die with 6 sides.
Each side of the die is labeled with 1, 2, 3, 4, 5 and 6.
Since, probability of rolling any number = [tex]\frac{\text{Favorable event}}{\text{Total number of events}}[/tex]
Therefore, probability of rolling number 3 = [tex]\frac{\text{Favorable event}}{\text{Total number of events}}[/tex]
Favorable event of getting 3 in single roll = 1
Total events that can happen in one roll = 6
Therefore, probability of rolling number 3 = [tex]\frac{1}{6}[/tex]
A lighthouse can light up to 40 miles away through an angle of 125 degrees. What area can the lighthouse light? Round your answer to the nearest tenth.
Answers
Answer: 12
Step-by-step explanation:
Which of the following best explains why cosine StartFraction 2 pi Over 3 EndFraction not-equals cosine StartFraction 5 pi Over 3 EndFraction
Answers
Answer:
B.)- Cosine is negative in the second quadrant and positive in the fourth quadrant.
Step-by-step explanation:
Answer:
B.) Cosine is negative in the second quadrant and positive in the fourth quadrant. i just took the quiz
Step-by-step explanation:
I hope this helped ;)
Help me please please please please
Answers
pi is 3.15 so I think its pi time radius to get the area which is 3.15 times 9. that equals to 28.35
HELPPPPP PLSSSS IT IS DUE AT 3:15 PM
If the diameter of the circle above is 22 in, what is the circumference of the circle?
A.
11 in
B.
22 in
C.
44 in
D.
121 in
Answers
Answer:
B. 22 in ?
Step-by-step explanation:
circumference of the circle: 2πr
2 × π × 11 = 22π in
A CD manufacturer wanted to determine which of two different cover designs for a newly released CD will generate more sales. The manufacturer chose 70 stores to sell the CD. Thirty-five of these stores were randomly assigned to sell CDs with one of the cover designs and the other 35 were assigned to sell the CDs with the other cover design. The manufacturer recorded the number of CDs sold at each of the stores and found a significant difference between the mean number of CDs sold for the two cover designs. Which of the following gives the conclusion that should be made based on the results and provides the best explanation for the conclusion?
A. It is NOT reasonable to conclude that the difference in sales was caused by the different cover designs because this was not an experiment.
B. It is NOT reasonable to conclude that the difference in sales was caused the different cover designs because there was no control group for comparison.
C. It is NOT reasonable to conclude that the difference in sales was caused the different cover designs because the 70 stores were not randomly chosen.
D. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores.
E. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the sample size was large.
Answers
Answer:
The statement that gives the best conclusion that should be made based on the results and provides the best explanation for the conclusion is option D;
D. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores
Step-by-step explanation:
The data given in the question are presented as follows;
The particulars the CD manufacturer wants to determine = The CD cover design that will generate more sales
The mode of selection of the stores for the test = Random selection
The number of stores in each group of stores, n = 35 stores
The number of sets of stores tested = 2 sets of stores
Let [tex]\overline x_1[/tex] represent the mean number CDs sold at one set of stores and [tex]\overline x_2[/tex] represent the mean number CDs sold at the other set of stores
The null hypothesis, H₀; [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]
The alternative hypothesis, H₀; [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]
Given that the statistical analysis shows that the difference in mean between the two sets of randomly selected stores is significant, we therefore should reject the null hypothesis and accept the alternative hypothesis that there is a significant difference in CD sale attributable to the difference in cover design as the CDs having on of two cover design where assigned randomly to the stores.
Judah deposited $450 into an account that earns simple interest, and after 4 years, the interest in the account was 90$. What was the simple interest rate?
Answers
Answer:
$22.50 I think I'm not 100% sure, Im sorry
Step-by-step explanation:
90/4 is 22.5 a year
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answers
Answer and Step-by-step explanation:
To find the range, we must plug in the values 0 to 15 into the function to find the values of f(x), which are the range.
When plugging in the values, we see that the answer should be the last one.
We start with a pay of $15.50, and it increases each time by $10, until it reaches $165.50.
So, D is the answer.
#teamtrees #PAW (Plant And Water)
Type of angle:
Angle measures:
Answers
measurement: 85°
find endpoint T, given an endpoint S (-2, 9) and Midpoint M (8, 0)
Answers
How do you find the cube root of a number?
I am literally confused, it would be appreciated if someone explained to me. Thank you :)
Answers
Answer:
How to Cube A Number
To cube a number, just use it in a multiplication 3 times .
A cube root goes the other direction:
3 cubed is 27, so the cube root of 27 is 3
Let f(x)=x^2+2 and g(x)=1-3x. Find each function value: f(g(-1))
Answers
Answer:
g(-1)=4 ,f(g(-1))=18
Step-by-step explanation:
g(-1):
1-3(-1)=4
f(g(-1)):
sub in g(-1) as x
(4)^2+2=18
The diameter of a circle is 18m . Find its circumference in terms of pi?
Answers
Answer:
The circumference of a circle =πd = π×18 =18π m
The diameter of a circle is 18 m. Find its circumference in terms of π.
Solution:-Diameter of a circle = 18 m. (Given)
Radius (r) of a circle = 18/2 = 9 m.
We know,
[tex] \dag [/tex] Circumference of a circle is 2πr.
So, It's circumference is (2 × π × 9) m.
It's circumference is 18π m.
It's circumference in terms of π is 18π m. [Answer]help, thank youu
A: 75
B: 61
C: 48
D: 80
Answers
Answer:
The answer is C, 48
Step-by-step explanation:
Its the only answer that makes sense
Answer:
75
Step-by-step explanation:
1. Eliminate wrong answers
a. (boys 5 & girls 4) meaning the boys should have a higher number than girls (which is 60) this meaning that 48 and 61 can not be the correct answer.
5/4=x/60
x=(5/4)*60
x=75
Math rocks
Leaving it to the obvious chose(The answer is 75)
Hope this helps
José and Wally install windows. Each day, José installs 5 more than 2 times as many windows
as Wally installs. If José installs 15 windows each day, which equation can be used to
determine the number of windows, w, that Wally installs?
A: 2w-5= 15
B: 2w +5= 15
C: 5w+2 = 15
D: 5w-2= 15
Answers
4
Select the correct answer.
Shania's test scores in 8 subjects were 88, 91, 85, 74, 69, 72, 80, and 87. Shanla found the middle number of her scores. W
did she find?
O A.
a measure of center
OB.
a measure of variation
Ос.
a measure of neither variation nor center
OD.
a measure of both variation and center
Reset
Next
Answers
Answer:
A: Measure of center, also known as the Median.
find the volume of the sphere. either enter an exact answer in terms of pie or use 3.14 for pie and round your final answer to the nearest hundredth.
someone please help asap i’ll give u brainliest
Answers
Answer:
Step-by-step explanation:
volume = [tex]\frac{4}{3}*pi*r^3[/tex]
= 4/3pi
x=
A. 100
B. 50
C. 25
Answers
Answer:
b=50 central angle equal to the arc
Help me please I don’t understand this
Answers
Answer:
D) 159°
Step-by-step explanation:
[tex]10x+9+90+34+6x-13=360[/tex]
→[tex]16x=240[/tex] →[tex]x=15[/tex]
∠[tex]YZU=10*15+9=159[/tex]
[tex]---------[/tex]
hope it helps...
have a great day!!
Answer:
159°
Step-by-step explanation:
A circle measures 360°. We can use this knowledge to find the unknown angles.
(10x + 9) + (6x - 13) + 34 + 90 = 360
Combine like terms and solve for x.
16x + 120 = 360
16x = 240
x = 15
So, we have found the value of x, and can now find m∠YZU.
10(15) + 9 = m∠YZU
m∠YZU = 159°
We can ascertain that this is the answer by plugging in x for the initial equation we created.
(10(15) + 9) + (6(15) - 13) + 34 + 90 = 360
159 + 77 + 34 + 90 = 360 It works!
Sal buys y pens and some pencils. He buys 10 more pencils than pens. How many pens and pencils does he buy
altogether?
Answers
Answer:
20
Step-by-step explanation:
GIVING BRANLIEST 5 STARS AND A LIKE PLS HELP IM SOOOOO STUCK
b) If the base of the panel is 31.2 inches and the height is 18 inches, what is the area of one triangular section?
What is the formula with these numbers plugged in? --
Answer --
Answers
Answer:
280.8 and the formula is Base x Height = ? x.5
Step-by-step explanation:
(31.2 x 18) x 0.5 =280.8