Step-by-step explanation:
You want to use the sum of an arithmetic sequence formula.
(a1 + an) × n/2
a1 is the first term and an is the last term. n is the number of terms.
In this case: (3+24) × 8/2 = 27×8/2 = 27×4 = 108
The sum of the first 8 terms of the series 3 + 6 + 9 + ... is 108.
To find the sum of the first 8 terms of the series, we need to find the common difference (d) and then use the formula for the sum of an arithmetic series.
Given that [tex]\(a_8 = 24\)[/tex], we can see that the 8th term is 24.
The formula for the nth term of an arithmetic series is [tex]\(a_n = a_1 + (n-1) \cdot d\)[/tex], where [tex]\(a_n\)[/tex] is the nth term, [tex]\(a_1\)[/tex] is the first term, and d is the common difference.
Substitute n=8 and [tex]\(a_n=24\)[/tex] into the formula:
[tex]\(24 = 3 + (8-1) \cdot d\)[/tex]
Simplify the equation:
[tex]\(24 = 3 + 7 \cdot d\)[/tex]
Now, solve for d:
[tex]\(7d = 24 - 3\)\\\\\(7d = 21\)\\\\\(d = \frac{21}{7} = 3\)[/tex]
Now that we have the common difference d = 3, we can use the formula for the sum of an arithmetic series:
[tex]\(S_n = \frac{n}{2} \cdot (a_1 + a_n)\)[/tex]
Substitute [tex]\(n=8\)[/tex], [tex]\(a_1=3\)[/tex], and [tex]\(a_n=24\)[/tex] into the formula:
[tex]\(S_8 = \frac{8}{2} \cdot (3 + 24)\)\\\\\(S_8 = 4 \cdot 27\)\\\\\(S_8 = 108\)[/tex]
So, the sum of the first 8 terms of the series is 108.
To know more about series, refer here:
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I need help asap, please and thank you :))
Answer:
What is the value of x?
x = 40 degrees.
What is the measure of angle AFE?
Angle AFE = 140 degrees
What is the measure of angle BFD?
Angle BFD = 140 degrees.
Step-by-step explanation:
Angle AFC is 90 degrees.
To find angle x, we have to subtract angle BFC.
90 - 50 = 40 degrees.
Line BFE is 180 degrees.
To find angle AFE, we have to subtract angle x from 180 degrees.
We have solved x already.
180 - 40 = 140 degrees.
Angle BFD is just 90 degrees plus 50 degrees.
90 + 50 = 140 degrees.
Answer:
x = 40
m<AFE = 140
m<BFD = 140
Step-by-step explanation:
1. Finding X
As one can see, AD is a straight line (hence the three angles that add up to is equal 180 degrees). It is given that m<CFD is 90 degrees (signified by the box).
Given;
AD - straight line
m<AFB + m<BFC + m<CFD = 180
( m<AFB, m<BFC, m<CFD form line AD, the degree measures in al ine equal 180, hence m<AFB + m<BFC + m<CFD = 180)
m<BFC = 50
m<CFD = 90 (signified by box around it)
m<AFB + m<BFC + m<CFD = 180 parts whole postulate
x + 50 + 90 = 180 substitution
x + 140 = 180 algebra
x = 40
2. Finding m<AFE and m<BFD
When two straight lines intersect, four angles are formed. The angles that are opposite to each other are called vertical angles, and vertical angles are congruent in other words, have the same measure.
Given;
m<BFD = m< AFE
m<BFC + m<CFD = m<BFD
m<BFC = 50
m<CFD = 90
m<BFC + m<CFD = m<BFD Given (parts whole postulate)
50 + 90 = m<BFD substitution
140 = m<BFD algebra
140 = m<BFD = m<AFE substition
Use Pythagorean Theorem to determine the missing side.
How high is the end of the ladder
against the building?
h ft
13 tt
4 ft
Round to the nearest tenths place.
If 12 juice boxes cost 4.20 how much do 15 cost
Answer:
5.25
Step-by-step explanation:
4.20 ÷ 12 = 0.35
0.35 x 15 = 5.25
Ernie and Lori are playing a game. The table shows their scores for the
5 times they have played the game. Which statement is true?
Answer:
ernie has the greater range.
Step-by-step explanation:
Ernie and Lori are playing a game. the table shows their scores for 5 times they have played the game.
Answer:2
Step-by-step explanation:
What’s the answer????
HELPPPP!!!
(WILL MARK BRAINLIEST)
Answer:
y÷8
Step-by-step explanation:
quotient is just a fancy word for division
A number is first decreased by 40% and then again decreased by 60%. Find the percentage increase or decrease in the whole sum...please tell quickly
Answer:
It is decreased by 76 percent.
Step-by-step explanation:
The key skills are percentage and multiplication with percentages.
You first have to get a variable. Let's use the letter o as a variable (o For orginial cost). Then we have to find out how much it is when o is decreased by 40 percent. 100% (or the whole) - 40% is 60%. Therefore, with a 40 percent decrease, It would be 60% of o, or 0.6o. Then, if it decreases by 60 percent, the final number would be 100% - 60 % or 40% of 0.6o. This means itbwould be 0.4 × 0.6o which is 0.24o0.24o means that o is 24 percent of its orginial number, which is 100% - 24% or a 76 percent decrease.Hope you understood and have a nice day!
Sushi was thinking of a number. Sushi doubles it,then adds 20 to get an answer of 27.7 what was the original number
Answer:
3.85
Step-by-step explanation
7.7 divided by 2 = 3.85
So if you double 3.85 you get 7.7 and then add 20 to 7.7 then you get 27.7
Let the number they are thinking of be X.
They double x , which would be 2x.
They then add 20, which would be 2x +20
So you have 2x + 20 = 27.7
Now we can solve for x:
Subtract 20 from both sides:
2x = 7.7
Divide both sides by 2:
x = 7.7 / 2
x = 3.85
The original number was 3.85
What is the slope of the equation y = 5x – 7?
A. 32
B. 23
C. 3
D. 2
where x is the value, 4 is the mean,
The formula for a z-score is z =
(x-0)
44
and o is the standard deviation.
A. True
B. False
Answer:
False
[tex]Z = \frac{x-mean}{S.D}[/tex]
Z = x - μ /σ
Step-by-step explanation:
Explanation
The given mean of the Population= μ
Given the standard deviation of the Population(S.D) = σ
Let 'X' be the random variable in a normal distribution
Z-score
[tex]Z = \frac{x-mean}{S.D}[/tex]
Z = x - μ /σ
Answer:
true
Step-by-step explanation:
WILL GIVE BRAILIEST IF YOU ANSWER!! The MTC Theater holds 250 people, and last night’s performance sold out! Students under the age of 16 paid $2.50 per ticket, while everyone else paid $4.00 per ticket. Last night’s show brought in $910.
Write a system to represent the given equations.
How many adult tickets were sold?
How many under the age of 16 tickets sold
Answer:
Adult Tickets: 190
16 and less: 60
Step-by-step explanation:
190 x 4.00 + 60 x 2.5 = 910
Thirty-two of 50 marbles are blue. What percent of the marbles are blue?
Answer:
64%
Step-by-step explanation:
Thirty-two of 50 marbles = 32/50[tex]\frac{32}{50} = \frac{64}{100}[/tex] 64/100 = 64%I hope this helps!
11. 3/4 of 12=
12. 6/7 of 49
15. 2/3x27
16. 3/8 x 16
Step-by-step explanation:
3/4 of 12
3/4 × 12 = 9
6/7 of 49
6/7 × 49 = 42
2/3 × 27 = 18
3/8 x 16 = 6
if 12% = £54
what does 100% =
Brainliest to first correct answer :)
Answer:
£450
Step-by-step explanation:
12%=£54
100%=?
we will criss cross it then 12%×?=100%×£54÷12
=£450
A recipe for baba ghanoush cause for twice as much olive oil as lemon juice
Which expression represents the amount of olive oil needed for 4 tablespoons of lemon juice choose ALL that apply
A). 4•4
B). 4+2
C). 4•2
D). 4+4
Please Help
Answer:
4•2 and 4+4
Step-by-step explanation:
What is the
lcm of 4, 7, and 8?
Answer:
56
Step-by-step explanation:
4, 7 and 8 all go into 56
Determine the measure of the angle in ?
Answer:
? = 30°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
48° is an exterior angle of the triangle, then
? + 18° = 48° ( subtract 18° from both sides )
? = 30°
Melanie wrote an equivalent expression to the one shown. Which expression could Melanie have written?
6a+6(2a−3)+3
A
18a
B
18a + 15
C
3(6a - 5)
D
3(4a - 5)
Answer:
c.
Step-by-step explanation:
3(6a-5)
is the answer of question given above
Answer:
It is C.
Step-by-step explanation:
By using the distributive property and combining like terms, the expression becomes eighteen a minus fifteen. Three can then be factored from both terms to write the expression as three times the quantity six a minus five.
0.002347 written to three significant figures is
Answer:0.00234
Step-by-step explanation:
Boba cost $4.00 and left a tip. The total was $4.36. What % did you tip?
4.36 - 4 = 0.36
for finding tip percentage=
0.36/4 x 100
= 9%
Hope this helps and please mark me as brainliest.
I need help on this question
my teacher didn't teach me anything about scale factors and then assigned it to me- pls show work so that I can understand this hhhhhhhh
Answer:
x = 9 cm
y = 30 cm
Step-by-step explanation:
Here, we want to get the lengths of the missing sides
Mathematically if two shapes are similar, the ratio of their corresponding sides are equal
Thus, we have that:
15/50 = x/30
50 * x = 15 * 30
x = (15 * 30)/50
x = 450/50
x = 9 cm
Also;
y/50 = 18/30
30 * y = 50 * 18
y = (50 * 18)/30
y = 30 cm
guys im freaking out right now help meeee please
Answer:
are u ok
Step-by-step explanation:
27 is 76% of what number?
Answer:
36
Step-by-step explanation:
i think im right about this
Answer:
35.53
Step-by-step explanation:
100% of 35.53 is 35.53 so 76% of 35.53 is 27
simplify: 2(3x-2)-(2x-4)
Answer:
4x
Step-by-step explanation:
2(3x-2)-(2x-4)
6x-4-2x+4
4x
Solve the expression (-3) (-2)(3)(4)
Answer:
The answer to the question provided is 72.
Which of the following will always be true of a graph that is non-proportional?
please help.
Given:
Consider any graph that is non-proportional.
To find:
The correct statement that is true of a graph that is non-proportional.
Solution:
We know that, if y is proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex]
where, k is constant of proportionality.
In these cases if x=0, then y=0. It means the graph always pass through the origin, i.e., (0,0).
So, if a graph is not passes through (0,0), then it is non-proportional.
Thus, non-proportional graph will not pass through (0,0).
Therefore, the correct option is A.
Task 4
Shelly started driving her own car for Uber. She
charges a flat fee of $5.00 and $0.50 for every
kilometer.
Q: How many kilometers were travelled if she
charges $32.50?
Answer:
5 and 10/11 kilometers
Step-by-step explanation:
if she gets $5.50 per 1 kilometer the she gets $33 dollars per 6 kilometers but she got 32.50 there are $0.50 missing which equals to 10/11 the actual price so she went 5 kilometers and 10/11 killometer
PLEASE HELP WILL MARK BRAINLIEST!! I put math because I don’t know what this goes under but PLEASE HELP
Answer:
1. 8-10
2. oven
3. 200-220
4 dampen the surface of the bread
5. no allow it to cool
Isaiah is working two summer jobs, making $16 per hour tutoring and $10 per hour clearing tables. Isaiah must earn at least $110 this week. Write an inequality that would represent the possible values for the number of hours tutoring, tt, and the number of hours clearing tables, cc, that Isaiah can work in a given week.
Answer:
16t + 10c > 110
Step-by-step explanation:
Cost of tutoring per hour = $16
So, cost of tutoring t hours = $16t
Cost of clearing tables per hour = $10
So, cost of clearing tables c hours = $10c
Since, Isaiah must earn at least $110 this week.
Therefore, the required inequality will be given as:
16t + 10c > 110