For the given arithmetic sequence we have:
A) [tex]A_n = 20 + (n - 1)*3[/tex]B) 22 rows.C) [tex]\sum_{n = 1\ to\ 22} (20 + (n - 1)*3)[/tex]D) There are 1,133 seats in total.How to write the formula for the sequence?
We know that we have 20 seats on the front row, and then we add 3 more on each row, so the formula will be:
[tex]A_n = 20 + (n - 1)*3[/tex]
This gives the number of seats on the n-th row.
B) The last row has 83 seats, then we need to solve:
[tex]A_n = 20 + (n - 1)*3 = 83\\\\(n - 1)*3 = 83 - 20 = 63\\\\n - 1 = 63/3 = 21\\\\n = 21 + 1 = 22[/tex]
So we conclude that there are 22 rows.
C) The total number of seats will be:
[tex]\sum_{n = 1\ to\ 22} (20 + (n - 1)*3)[/tex]
D) Instead of using the sum above (we should add 22 terms) we use the general formula for the sum of N terms in an arithmetic sequence:
[tex]S_N = (N/2)*(2A_1 + (N - 1)*d)[/tex]
In this case, we replace N by 22, and d is the common difference of the sequence, which we know is equal to 3, so we wil have:
[tex]S_{22} = (22/2)*(2*20+ (22 - 1)*3) = 11*(40 + 21*3) = 1,133[/tex]
There are 1,133 seats in total.
If you want to learn more about sequences, you can read:
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When the water was 4 feet from the end of the hose, what was its height above the ground? 3.2 feet 4.8 feet 5.6 feet 6.8 feet
Answer:
Step-by-step explanation:
a. 3.2 feet
Answer:
When the water was 4 feet from the end of the hose, what was its height above the ground?
3.2 feet <<<CORRECT4.8 feet5.6 feet6.8 feetStep-by-step explanation:
2022 Edge Unit Review Test
Find the mean median mode range for the following data 89 78 91 90 89 97
Answer:
Mean would be 84, Mode would be 89, Range would be 19.
Step-by-step explanation:
Mean- 89 +78 + 91 + 90 + 89 + 97= 534
534 divided by 6= 89
Mode- There are 2 89's so thats your mode. Mode is your most frequent number.
Range- 97-78=19. For range you have to subtract your highest number by your lowest.
Happy to help you :)
Answer:
Mean: 89
median: 89.5
mode: 89
range: 19
Step-by-step explanation:
MeanMean is the total/amount of itemsthe total = 534the amount of items is 6534/6 = 89Medianthe median is the middle numberthe median for odd lists is the middle between the middle two numbersSort the list low to high : 78 89 89 90 91 97the middle numbers are 89 and 90the middle between these is 89.5ModeMode is the most common number89 appears twice, it is the most commonRangerange is the highest - lowest number97 - 78 = 192. If Ariana decides to become a CPA, she will
need to continue her education. Her master's
degree will cost $28,500, but as a CPA she will
earn $73,850 each year. How much more will
Ariana earn each year as a CPA than as an
accountant each year?
Answer:
$5,700
Step-by-step explanation:
she would earn $73,850 annualy(sry for my mistakes im in 6th Grade) and the question says how much more will she arn each year as a CPA than as an accountant each year and she would make 68,150 as an accountant so you would subtract 73,850 by 68,150 and you would get $5,700.
Can anyone help me with my homework
Step-by-step explanation:
table for y = 3x - 2 and graph
the resulting line.
*
for y = 2x + 2 and
graph the resulting
line.
.
2
- 1
0
1
2
1
-8
--5
-2.
1
Carly purchased 9 1/2 pints of ice cream for her party. If each guest will be served exactly 3/5 pints of ice cream what is the greatest number of guests that Carly can serve?
Answer: 15 guests.
Step-by-step explanation:
As the statement says that Carly has 9 1/2 of ice cream and each guest will be served 3/5 pint of ice cream, to determine the number of guests that she can serve, you have to divide 9 1/2 by 3/5:9 1/2÷3/5. 19/2÷3/5=95/6= 15According to this, the greatest number of guests that Carly can serve is 15 guests.
If f(x) = 3(x + 4), find f(2).
Answer:
18
Step-by-step explanation:
f(x) = 3(x + 4)
f(2) = 3(2 + 4)
3 x 2 = 6
3 x 4 = 12
f(2) = 6 + 12
f(2) = 18
PLS ANSWER FAST!! WILL GIVE BRAINLIEST!!
Answer:
500^1/3
Step-by-step explanation:
Since it is a cube root, the exponent is 1/3.
Find the area of each polygon each square on the grid represents 1 square centimeter the answers are mixed up at the bottom of the page cross out the answers as you complete the problems
Answer:
Step-by-step explanation:
Area of composite shapes:
13) Figure 1:
Figure1 is a rectangle.
l = 4 cm & w = 2 cm
Area of figure1 = l * w
= 4 * 2
= 8 cm²
Figure2:
Figure2 is a parallelogram
base = b = 4 cm
h = 4 cm
Area of figure2 = b * h
= 4 * 4
= 16 cm²
Area of composite shape = 8 + 16
= 24 cm²
14) Figure1:
Figure 1 is a trapezium. a & b are parallel sides and h is the height
a = 4 cm ; b = 6 cm; h = 4 -2 = 2 cm
[tex]\sf Area \ of \ figure1 =\dfrac{(a+b)*h}{2}[/tex]
[tex]= \dfrac{(4 +6)*2}{2}\\\\= 10 \ cm^{2}[/tex]
Figure2:
Figure2 is rectangle. l = 6 cm ; w = 2 cm
Area of figure2 = 6*2
= 12 cm²
Area of composite shape = 10 + 12
= 22 cm²
15) Figure 1 & figure 2:
Figure 1 and figure 2 are congruent triangles
base = b = 3 cm & h= 4 cm
[tex]\sf area \ of \ figure1 \ and \ figure 2 = 2*\dfrac{1}{2}b*h[/tex]
= b *h
= 3 * 4
= 12 cm²
Figure3:
Figure 3 is a square.
side = 3 cm
Area of figure3 = side *side
= 3 * 3
= 9 cm²
Area of composite shape = 12 + 9
= 21 cm²
Please help it’s due tonight
Answer:
SQR = 118
RQT = 62
Step-by-step explanation:
SQR + RQT = 180
10x - 22 + 3x + 20 = 180
13x - 2 = 180
13x = 182
x = 14
Answer:
m∠RQT=62°
m∠SQR=118°
Step-by-step explanation:
m∠SQT=m∠SQR+m∠RQT
180°=(10x-22°)+3x+20°
180°=13x-2°
180°+2°=13x
182°=13x
x=182÷13=14°
x=14°
So,
m∠RQT=3(14)+20°=62°
And,
m∠SQR=10(14)-22°=140°-22°
m∠SQR=118°
Write an equation in slope-intercept form for the graph shown. (1,0) (0,-2)
Answer:
y= 2x -2
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the slope and c is they y-intercept
[tex]\textcolor{violet}{\text{\textcircled{1} Find the slope}}[/tex]
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
[tex]slope = \frac{0 - ( - 2)}{1 - 0} [/tex]
[tex]slope = \frac{0 + 2}{1} [/tex]
slope= 2
[tex]\textcolor{violet}{\text{\textcircled{2} \text{Substitute value of slope into m}}}[/tex]
y= 2x +c
[tex]\textcolor{violet}{\text{\textcircled{3} Find c}}[/tex]
Given that the y-intercept occurs at (0, -2), c= -2.
[tex]\textcolor{violet}{\text{\textcircled{4} Substitute the value of c into the equation}}[/tex]
y= 2x -2
NEED HELP FAST PLEASE
Which statement correctly describes the data shown in the scatter plot?
Question 3 options:
The scatter plot shows a positive association
The point (1,1) is an outlier.
The scatter plot shows a negative association
The scatter plot shows no association.
Answer:
The scatter plot shows a positive association
Step-by-step explanation:
the points show an increasing tendency
Miss Tamika just started an art class. She had 10 children enrolled for the first class. · Before she began the art lesson, she told each of the children to shake hands with ! each of the other children and introduce I themselves. Miss Tamika did not include i herself because she had already met each i of the children. How many handshakes were there between all of the children?
Answer:
45 Handshakes.
Step-by-step explanation:
10 people shake hands.
So, each person will shake hands with 9 other people.
Total number of handshakes = 90/2 = 45
A bookcase has a mass of 20 kilograms. A book in the bookcase has a mass of 500 grams.
How many books of the same mass would it take to equal the mass of the bookcase?
Enter your answer in the box.
Answer:
Step-by-step explanation:
Remark
You have to convert one of the numbers. It doesn't matter which one, but you can't simply divide one into the other the way the numbers stand.
Conversion
20 kilograms = 20 * 1000 grams / kg
20 kilograms = 20000 grams
Formula
Number of books = mass of bookcase / mass of 1 book
Givens
number of books = ??
mass of bookcase = 20000 grams
mass of one book = 500 grams
Solution
number of books = 20000 / 500
number of books = 40
Answer: 40 books = mass of bookcase
Lincoln invested $49,000 in an account paying an interest rate of 6\tfrac{1}{8}6
8
1
% compounded daily. Eli invested $49,000 in an account paying an interest rate of 5\tfrac{5}{8}5
8
5
% compounded continuously. After 20 years, how much more money would Lincoln have in his account than Eli, to the nearest dollar?
Using compound interest and continuous compounding, it is found that Lincoln would have $15,856 more in his account than Eli.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.Hence, for Lincoln, we have that the parameters are as follows:
P = 49000, r = 0.06125, n = 365, t = 20.
Hence the amount will be of:
[tex]A_L(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A_L(20) = 49000\left(1 + \frac{0.06125}{365}\right)^{365 \times 20}[/tex]
[tex]A_L(20) = 166787[/tex]
What is continuous compounding?The amount is given by:
[tex]A(t) = Pe^{rt}[/tex]
For Eli, we have that r = 0.05625, hence the amount will be given by:
[tex]A(t) = Pe^{rt}[/tex]
[tex]A_E(20) = 49000e^{0.05625 \times 20} = 150931[/tex]
What is the difference?It is given by:
[tex]D = A_L(20) - A_E(20) = 166787 - 150931 = 15856[/tex]
Lincoln would have $15,856 more in his account than Eli.
More can be learned about compound interest at https://brainly.com/question/25781328
Which functions are linear?
A. y=x - 2
B. y=3/x + 2
C. y = 1/2x + 8
D. y = 2x - 4
E. y = 8x^2 - 2
Answer:
the linear is letter CStep-by-step explanation:
Have a great day✧◝(⁰▿⁰)◜✧Jeremy randomly selected a round tile and a square tile from the sets shown below. what is the probability that jeremy selected either two blue tiles or two white tiles? square tiles: 10 pink, 8 red, 6 blue, 12 green, 8 black, 9 white, 7 yellow.round tiles: 11 green, 5 red, 2 white, 4 black, 6 blue, 8 pink. a. 23/36 b. 4/9 c. 7/72 d. 1/40
The probability that Jeremy randomly selected a round tile and a square tile from the sets is given as 1/40 (Option D).
What is probability?
Probability in mathematics is the branch of maths that speaks to the likelihood of an event occurring. Probability is usually given or described to occur between 0 and 1.
1 is the likelihood that the event will occur while zero is the certainty that an event will NOT occur.
Taken in decimal form, the likelihood of the above event occurring will very slim, because, 1/40 = 0.025
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I will award brainliest to whoever correctly answers this!
Answer:
To find GCF we need to find what these expressions have in common
30x²=5*3*2x²
45x⁵=5*3*3x²x³
Now we can see, that GCF=5*3*x² = 15x²
Answer :
15x²
Step-by-step explanation:
[tex]30x^{2}=2\times \left( 15x^{2}\right) \\45x^{5}=3x^{3}\times \left( 15x^{2}\right)[/tex]
Then the greatest common factor is 15x²
Which equation is y = –6x2 3x 2 rewritten in vertex form? y = negative 6 (x minus 1) squared 8 y = negative 6 (x one-fourth) squared thirteen-eighths y = negative 6 (x minus one-fourth) squared nineteen-eighths y = negative 6 (x minus one-half) squared seven-halves
The vertex form of the given equation, y = -6x² + 3x + 2, is expressed as: y = -6(x - 0.25)² + 2.375.
What is an Equation in Vertex Form?The vertex form of an equation is expressed as, y = a(x - h)² + k, where:
(h, k) = vertex of the parabola.
Given the equation, y = -6x² + 3x + 2, factor the equation:
y = -6(x² - 0.5x) + 2
y = -6(x² - 0.5 + 0.0625) + 2.375
Rewriting the equation as perfect squares, we would have:
y = -6(x - 0.25)² + 2.375
The vertex form of y = -6x² + 3x + 2 is, y = -6(x - 0.25)² + 2.375.
Learn more about vertex form of an equation on:
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Answer:
c y = -6(x-1/4)^2+19/8
Step-by-step explanation:
Determine whether each quadrilateral must be a rectangle. Explain.
Answer:
All squares must be rectangles.
Step-by-step explanation:
This quadrilateral is known as a square. A square is a closed figure with four sides of equal lengths and four right angles. By definition, a rectangle is a closed figure with four straight sides and four right angles. So comparing both of these definitions, a square must be a rectangle. Rectangles sides are not all equal. This about about the only difference.
PLEASE ANSWER!
(true or false statements)
Thanks :)
What is the answer
2^12=
Answer:
2^12=2*2*2*2*2*2*2*2*2*2*2*2=4*4*4*4*4*4=16*16*16=256*16=4096
Step-by-step explanation:
Which type of data deals with causes and/or relationships?
Find the measure of an angle between 0° and 360° coterminal with the given angle.
-540°
Answer:
Los ángulos coterminales son ángulos que tienen como lado inicial el eje x y tienen el lado terminal común.
Por ejemplo un ángulo de 20º tendría un ángulo cotermiunal en 360º+20º=380º ó en 360º×2+20º= 720º+20º=740º.
a)2560º÷360º =7 ⇒ 7×360º+40º, luego 40º será su ángulo coterminal entre 0º y 360º
b) 3.600º÷360º= 10 ⇒ 10×360º+0, luego 0º será su ángulo coterminal entre 0º y 360º
c) 1.090º÷360º= 3 ⇒ 3×360º+10º, luego 10º será su ángulo coterminal entre 0º y 360º
Step-by-step explanation:
Primero lo que necesitas saber es que los ángulos coterminales son ángulos que tienen como lado inicial el eje x y tienen el lado terminal común.
Por ejemplo: un ángulo de 20º tendría un ángulo coterminal en 360º+20º=380º ó en 360º×2+20º= 720º+20º=740º.
Apartir de lo anterior, aplicamos lo siguiente:
2560º÷360º =7 ⇒ 7×360º+ 40º,
Respuesta: 40º será su ángulo coterminal entre 0º y 360º.
Laura babysat 8 nights during the month of July. She earned $22, $30, $35, $25, $25, $20, and $27 for seven nights. How much did she earn the eighth time if the mean of the data is $26.50?
Answer:
$28
Step-by-step explanation:
Given:
data = [22,30,35,25,25,20,27]
For eight night, the new list is:
new_data = [22,30,35,25,25,20,27,x]
Mean = 26.50
Mean Formula:
[tex]\displaystyle \large{m=\dfrac{x_1+x_2+x_3+...+x_n}{n} }[/tex]
Therefore:
[tex]\displaystyle \large{26.50=\dfrac{22+30+35+25+25+20+27+x}{8}}[/tex]
Multiply both sides by 8:
[tex]\displaystyle \large{26.50\cdot 8=\dfrac{22+30+35+25+25+20+27+x}{8} \cdot 8}\\\displaystyle \large{212=22+30+35+25+25+20+27+x}[/tex]
Solve for x:
[tex]\displaystyle \large{212=22+30+35+25+25+20+27+x}\\\displaystyle \large{212=184+x}[/tex]
Subtract 184 both sides:
[tex]\displaystyle \large{212-184=184+x-184}\\\displaystyle \large{28=x}[/tex]
Therefore, she will earn $28 in eighth night
The attachment below is the result of combining all eighth data as we get 26.5 through python language with numpy package.
Answer: $28.
Step-by-step explanation: To solve this problem, we should first find the mean of the data with the seven payments that are given already:
22 + 30 + 35 + 25 + 25 + 20 + 27 = 184.
184 / 7 = 26.2857142857.
In order to figure out how much she made the eighth night with the mean of the data being $26.50, we can pick a number and add it to 184 (the total of the seven payments), and divide the total by 8. The number we can try is 28. The work is done below:
184 + 28 = 212.
212 / 8 = $26.50.
Therefore, Laura's payment on the eighth night was $28.
Hope this helps! :)
Sophie earned a grade of 72% on her multiple choice history final that had a total of 200 problems. How many problems on the final exam did Sophie get wrong?
Answer:
56 questions.
Step-by-step explanation:
percent got wrong = 100% - percent got correct.
percent got correct = 72%
percent got wrong = 100%-72% = 28% or 0.28
questions got wrong = total questions * percent got wrong.
total questions = 200
questions got wrong = 200*0.28 = 56 questions
Therefore, Sophie got 56 questions wrong.
Hope this helps!
Please mark as brainliest!
The image shows Megan's checkbook register without the balance calculated after each transaction.1. What was Megan's balance after her Skate Inc purchase on 4/16?2. What was Megan's lowest balance recorded? What date did it occur?
Answer:
Step-by-step explanation:
This is a horrible credit union they charged $3, just for her to have access to her own money, then they overdraft fee charged her for $20 :/ she spent 62 dollars , that she had, but b/c they charged her 3 dollars to access her money, it made her also get the overdraft fees. This seems like usery to me and this bank should be closed. Fined , and barred from doing business. >:/
so on the 11th she was -23 dollars, she was in debt to her bank 23 dollars,
88-23=65
on the 16th she was 65-43 = 22 postive :)
Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question. A number line going from negative 9 to positive 1.
-5
-3
0
2
-5 is the solution to the inequality x < -4 and the interval is the x ∈ (-∞, -4) option first is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have inequality:
x < -4
The solutions to the above inequality will lie in the region (-∞, -4)
x ∈ (-∞, -4)
From the number line, we can mark the region for the above interval (refer attached picture)
Thus, -5 is the solution to the inequality x < -4 and the interval is the x ∈ (-∞, -4) option first is correct.
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Please tell the answer 5*25=
Answer:
5*25=125
Step-by-step explanation:
Answer:
The answer would be 125
Step-by-step explanation:
Tim has four credit cards with the balances and aprs listed in the chart below. what will tim's total monthly minimum credit card payment need to be to pay off all four credit cards in 24 months? credit card balance apr a $1,260.00 12% b $900.00 18% c $1,290.00 9% d $1,200.00 16% a. $118.24 b. $162.62 c. $163.00 d. $221.93
Answer: D) $221.93
Step-by-step explanation: that's the answer on edge.
The solution is, the minimum monthly payment is $221.93. Among the choices, the answer is D.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
Solving for the future values of the credit card balances:
1260(1 + 0.12/12)^24
= 1599.8656571502122308900(1 + 0.18/12)^24
= 1286.55253073612259711290(1 + 0.09/12)^24
= 1543.37345291648033351200(1 + 0.16/12)^24
= 1649.0625893406018547
Adding the future balances to obtain total bill:
1599.8656571502122308 + 1286.5525307361225971 + 1543.3734529164803335 + 1649.0625893406018547
= 6078.85
Solving for the annuity A (monthly payments for each account):
1599.87 = A [(((1 + 0.12/12)^24) - 1) / (0.12/12)] A = 59.31
1286.55 = A [(((1 + 0.18/12)^24) - 1) / (0.18/12)]A = 44.93
1543.37 = A [(((1 + 0.09/12)^24) - 1) / (0.09/12)]A = 58.93
1649.06 = A [(((1 + 0.16/12)^24) - 1) / (0.16/12)]A = 58.76
Adding the annuities together to obtain the minimum monthly payment:59.31 + 44.93 + 58.93 + 58.76 = 221.93
Therefore, the minimum monthly payment is $221.93. Among the choices, the answer is D.
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need some help with the question in the image
cheers
Answer:
the other candidate received 1875 votes
Step-by-step explanation:
if you add 50 and 25 percent you get 75 which leaves only 25 percent and to get the number or votes multiply 7500 by 0.25 or 7500 divided by 4