Answers
First of all, every number in each row is odd, so we can eliminate 392 and 394.
The number of elements in each row forms an arithmetic sequence:
• 1st row : 1 element
• 2nd row : 3 elements - and 3 - 1 = 2
• 3rd row : 5 elements - and 5 - 3 = 2
• 4th row : 7 elements - and 7 - 5 = 2
and so on, so that the [tex]n[/tex]-th row has [tex]1 + 2(n-1) = 2n - 1[/tex] elements.
This means that in [tex]n-1[/tex] complete rows, there is a total of
[tex]\displaystyle \sum_{i=1}^{n-1} (2i-1) = n^2 - 2n + 1[/tex]
elements, so that the first element in the subsequent [tex]n[/tex]-th row is the [tex](n^2-2n+2)[/tex]-th number in the sequence {1, 3, 5, 7, …}, i.e the [tex](n^2-2n+2)[/tex]-th odd positive integer. To compute the sum, I use the following well-known formulas.
[tex]\displaystyle \sum_{i=1}^n 1 = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = \frac{n(n+1)}2[/tex]
Now, the [tex]n[/tex]-th term of the sequence {1, 3, 5, 7, …} is simply [tex]2n-1[/tex], the [tex]n[/tex]-th odd positive integer. So the first element in the [tex]n[/tex]-th row is
[tex]2(n^2-2n+2) - 1 = 2n^2 - 4n + 3[/tex]
and hence the 1st element of the 15th row is
[tex]2\cdot15^2 - 4\cdot15 + 3 = \boxed{393}[/tex]
Related Questions
assuming 69.6 heartbeats/minutes, estimate the total number of times the heart of a human beats in an average lifetime of 89.3 y. assume 365.25 days per year. answer in units of heartbeats. your answer must be within ± 5.0%
Answers
The total number of times a human heart beats in an average lifetime of 89.3 years is estimated to be 3,268,988,688.8 heartbeats.
To calculate time:
We are to estimate the total number of times a human heart beats in an average lifetime based on the question.Based on the information provided,We will assume 69.6 heartbeats per minute.To calculate the total number of times the heart of human beats in an average lifetime of 89.3 years,
In 89.3 years, we will calculate the number of minutes.
89.3 years = 89.3 × 365.25 × 24 × 60 minutes89.3 years = 46968228 minutesBecause there are 69.6 heartbeats per minute
Then,
There are 46968228 heartbeats in 46968228 minutes.
46968228 × 69.6 = 3,268,988,688.8 heartbeatsTherefore, the total number of times a human heart beats in an average lifetime of 89.3 years is estimated to be 3,268,988,688.8 heartbeats.
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Eli, Freda and Geoff were given 800 pounds to share in the ratio of there age. Eli is 9 years old Freda is 13 years old and Geoff is 18 years old. How much should they each have?
Answers
evaluate 3(x-4)+2x-x2 for x=5
Answers
Answer:-12
Step-by-step explanation:
Im going to assume that x2 means x squared. You can just substitute "x" for 5. 3(5-4)+2(5)-5^2. First parenthesis equals 3(1)+10-5^2. Then it equals 3+10-5^2. So then it would be 13-5^2. 5^2 equals 25. so it would be 13-25. Which equals -12.
regina has five brothers who are 4, 6, 6, 9, and 15 years of age. the mean age of regina's brothers is .
Answers
The calculated mean age of Regina's brothers is 7. This is being attained by using the concept of measure of central tendency i.e. mean.
What is a mean?
Mean is interpreted as the total of all values divided by the total number of values. It is also called a mathematical average. There are three types of mean namely, arithmetic, geometric and harmonic mean.
Calculation of the mean age of Regina's brothers
Total number of Regina's brothers = 5
Sum of their ages = 4 + 6 + 6 + 9 + 10
= 35
Mean age = sum of their ages / total number
= 35 / 5
= 7
Hence, the calculated mean ages of Regina's brothers is 7
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What fraction must 7/6x be multiplied by to result in it having the least common denominator
Answers
Answer:
Step-by-step explanation:
1/6
2 tickets cost 11.00 they bought 2 drinks and used a 5.00 off coupon. the total cost was 29.18 how much was 1 drink
Answers
After buying tickets and drinks the total cost is 29.18 and using 5.00 off coupon, the cost of one drink is 11.59
As per the question statement, 2 tickets cost 11.00 and they bought 2 drinks and used a 5.00 off coupon. The total cost was 29.18. We are supposed to find out the cost of one drink.
Let the cost of one drink be "x"
Cost of 2 tickets = 11
Off coupon is of 5.00
Cost of two drinks = [tex]2x[/tex]
Total money paid = 29.18
Hence, [tex]11+2x-5=29.18\\2x=29.18+5-11=23.18\\x=\frac{23.18}{2} \\x=11.59[/tex]
Therefore the cost of one drink is [tex]x=11.59[/tex]
This question was a classic example of how to form equations when all the given conditions are in statements.
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A foreign exchange student from Denmark would like to buy gifts for her family. She finds a special deal, 7 t-shirts for $90.93, that she would like to purchase for her family. However, her family only consists of 5 people. If she wants to purchase 5 t-shirts for her family members at that special rate, what would be the cost of these t-shirts in her currency of Krona? (Currency conversion rate is 1 U.S. Dollar = 8.6964 Krona)
Answers
Using proportions, it is found that the cost of the 5 t-shirts would be of 564.83 Kronas.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for currency conversion problems, as multiplication or division operations are applied according to the rates of each coin.
For this problem, we have that 7 t-shirts cost $90.93, hence the cost of a t-shirt in U.S. dollars is given applying the proportion to find the unit rate as follows:
$90.93/7 = $12.99.
The cost of 5 t-shirts will be given by:
5 x 12.99 = $64.95.
Applying the proportion 1 U.S. Dollar = 8.6964 Krona, the cost in Kronas is:
64.95 x 8.6964 = 564.83 Kronas.
The cost of the 5 t-shirts would be of 564.83 Kronas.
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select the correct answer. which measurement is equivalent to 350 milliliters? a. 3.5 × 102 liters b. 3.5 × 101 liters c. 3.5 × 10–2 liters d. 3.5 × 10–1 liters
Answers
According to the given information the measurement is equivalent to 350 milliliters = 3.5 x 10⁻¹.
The correct option is D.
What is conversion factor?A conversion factor is a quantity that is used to multiply as well as divides one set of units by another. When converting to an equivalent value, the appropriate conversion factor must be utilized. To convert inches to feet, for example, the suitable conversion value is 12 inches equal 1 foot.
What is the significance of conversions?Conversion KPIs are critical for determining the efficacy of marketing campaigns. Only by measuring how many users convert as a result of that spend can you calculate your ROAS.
According to the given data:We are given an amount of 350 milliliters and asked to convert it to liters.
We know that :
1 liter = 1000 milliliters
We are given an amount of 350 milliliters and asked to convert it to liters.
1 liter/x liter = 1000/350
x = 350/1000
x = 3.5 x 10⁻¹
The given information the measurement is equivalent to 350 milliliters = 3.5 x 10⁻¹.
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I understand that the question you are looking for is:
Which measurement is equivalent to 350 milliliters?
A. 3.5 × 102 liters
B. 3.5 × 101 liters
C. 3.5 × 10–2 liters
D. 3.5 × 10–1 liters
Select the correct product of the exponential expression.
3^5
OA. 3.5
OB. 3.3.3.3.3
OC. 5.5.5
OD. 15
Answers
The correct product of the exponential expression 3⁵ is equal to 3.3.3.3.3.
As given in the question,
Given exponential expression is equal to 3⁵
General form of exponential expression is given by aˣ
a is the base and x is the exponent
This means 'x' times ' a ' is multiplied to ' a '
Compare 3⁵ with general form
3 is base
5 is exponent
This means '5' times ' 3 ' is multiplied to '3'
3⁵ = 3.3.3.3.3
Therefore, the correct product of the exponential expression 3⁵ is equal to 3.3.3.3.3.
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(2-y)(3y+8)=0 solve
Answers
Answer:
Step-by-step explanation:
(2 - y)(3y + 8) = 0
2 - y = 0
y = -2
3y + 8 = 0
y = -8/3
Mr. Hazel is a professional plumber. To fix a drain that is clogged, he charges a customer
$50 per hour, plus a fixed fee of $25 for the service call, as represented by the function
f(x)= 50x + 25. In the equation, what is represented by the variable "x"?
Answers
Answer:
The x is how much hours the job takes,
You can see that 25 is a fixed fee which is why there is no x attached to it, and 50 is the variable that can change, hope that made sense!
Step-by-step explanation:
^^^
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
equivalent expression to 2x7 + 2x3
Answers
Answer: 20
Step-by-step explanation:
2x7 + 2x3=
2*7 + 2*3=
14+6=20
Members of a softball team raised $2045.50 to go to a tournament. They rented a bus
for $1041.50 and budgeted $62.75 per player for meals. Which equation or tape
diagram could be used to represent the context if p represents the number of players
the team can bring to the tournament?
Answers
Answer: B
Step-by-step explanation:
Directions: Translate equation DO NOT SOLVE!
"four times the difference of a number and 7
is 32"
Number 11:
“ten increased by the quotient of a number and 2 is -15”
Answers
Sorry for taking so long :/
Step-by-step explanation:
*Four times the difference of a number and 7 is 32*
Answer-
4(x-7)=32
ten increased by the quotient of a number and 2 is 15-
Answer-
10+(x/2= -15
or
10+x/2=-15
anyone of them
what is 343250394065834698350968549846÷57547547
Answers
Answer: 5.9646399e+21
1) alice decides to take a trip from the east coast of the united states to the west coast. while planning, she chooses to drive, fly, and ride a train. her first leg of the trip is traveling by car, from sacramento, california to denver, colorado. along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. after driving for many hours, alice finally makes it to denver, colorado spending $874.80 in gas. a) let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. create an equation that models the situation.
Answers
The equation will be: 4.65r + 4.95p = 874.80
The total cost of gas will be sum of the individual costs of both the types of gas. Firstly, calculating cost of regular and premium gas followed by forming the equation.
The total cost of regular gas = Amount of regular gas × Cost of regular gas per gallon
The total cost of regular gas = 4.65 × r
The total cost of premium gas = Amount of premium gas × Cost of premium gas per gallon
The total cost of regular gas = 4.95 × p
We are given overall spending = 874.80
Forming the equation -
Total cost of regular gas + total cost of premium gas = overall spending on gas
4.65r + 4.95p = 874.80
Hence, the equation that models the situation is 4.65r + 4.95p = 874.80.
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find the equations that describe the circle of radius 3 centered at (8, 5, 6) that is parallel to the xy-plane.
Answers
The equation of the circle can be given by: (x - 8)² + (y - 5)² = 9.
What is a circle's equation?The equation for a circle in standard form is (x - x1)² + (y - y1)² = r², where (x, y) denotes arbitrary coordinates on the circle's perimeter, r denotes the circle's radius, and (x1, y1) denotes the coordinates of the circle's center.
Now,
Every point on a circle fulfills the equation describing it. A circle with radius r and a point (h, k, l) parallel to the xy plane have the following equation: (x - h)² + (y - k)² = r²We are given the values of h as 8, k as 5 and r as 3. On substituting them in the given equation, we get:=> (x - 8)² + (y - 5)² = 9
Hence, the equation that describe the circle of radius 3 centered at (8, 5, 6) that is parallel to the xy-plane is given by: (x - 8)² + (y - 5)² = 9
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Bashir is the youngest of four siblings whose ages are consecutive integers. If the sum of their ages is 66, find Bashir's age.
Answers
Answer:
15
Step-by-step explanation:
x+x+1+x+2+x+3=66
simplify into 4x+6=66
subtract 6 from both sides to get 4x=60
divide both sides by 4 to get x=15
The age of Bashir is 15 years.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the consecutive age be x, x+1, x+2 and x+3.
Now, sum of their ages is 66
So, x+ x+1 + x+2 + x+3 = 66
Simplifying for x, we get
4x+6=66
subtract 6 from both sides
4x=60
divide both sides by 4
4x /4 = 60/4
x= 15
Hence, Bashir age is 15 years.
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How many simple random samples of size 4 can be selected from a population of size 8?
a. 70
b. 32
c. 1680
d. 4
Answers
70 simple random samples of size 4 can be selected from a population of size 8
According to the question, samples of size 4 have to be selected from a population of size 8. The selection can be made in
8C4 ways.
Selection=8C4=8!(8−4)!4!
Selection=8!(8−4)!4!
Selection=8×7×6×5×4!4!×4×3×2
Selection=2×7×5
Selection=70
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Katie invested a total of $8000 part at 5% simple interest in part at 6% simple interest. at the end of one year the investments had earned $454 interest. how much was invested at each rate?
Answers
If Katie invested a total of $8000, part at 5% simple interest and part at 6% simple interest and at the end of one year the investments had earned $454 interest, then she invested $2600 at 5% and $5400 at 6% simple interest
Given,
The total invested amount = $8000
Consider the amount invested at 5% simple interest as x and the amount invested at 6% simple interest as y
Then, the equations will become
x + y= 8000
x = 8000-y
At the end of one year the investment = $454
0.05x + 0.06y =454
Substitute the value of x in the equation
0.05(8000-y) + 0.06y =454
400-0.05y+0.06y =454
0.01y+400=454
0.01y =54
y = 5400
Substitute the value of x in
x + y = 8000
x+5400=8000
x=8000-5400
x=2600
Hence, if Katie invested a total of $8000, part at 5% simple interest and part at 6% simple interest and at the end of one year the investments had earned $454 interest, then she invested $2600 at 5% and $5400 at 6% simple interest
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An angel measures 109 what is the measure of it it’s supplement
Answers
Answer:
71°
Step-by-step explanation:
A supplementary angle is the sum of two angles whom are less than 180 degrees, yet the sum will only be 180 degrees. Because we are finding the supplement angle, we must subtract.
[tex]\sf Long\:Subtraction\\9\:doesnt\:go\:into\:10,borrow\:1\\= 10\\= 10 - 9\\= 1\\8\:cant\:go\:into\:0,take\:1\:since\:you\:just\:borrowed\\= 7\\= 7 - 0\\= 7\\1 - 1\\= 0\\\\= \boxed{71}[/tex]
➲ Hope this helps.
Melina receives a chain e-mail that she forwards to 7 of her friends. Each of her friends
forwards it to 7 of their friends.
Chain E-Mail
Melina
How many people will receive the e-mail after 6 forwards?
Answers
Answer:
823543 Or 7^7
Step-by-step explanation:
M∠1=19 , m∠2 what is the answer?
Answers
Answer:
161 degrees since 180 - 19 would be 161 since they are supplementary if they are
Step-by-step explanation:
Eve is mixing paint to match a specific shade of orange. She mixes red paint and yellow paint
in different ratios. The color matches best when Eve uses 4 ounces of red paint and ounces of
yellow paint.
Eve has 1 ounce of red paint left. How many ounces of yellow paint should she add to match the
same shade of orange?
Answers
In order to get a precise orange color, Eve is mixing paint. She combines various ratios of red and yellow paint.
Eve finds that using 4 ounces of red paint and 1 ounce of yellow paint results in the best color matching. Eve still has one ounce of red paint. To get orange shade she has to add 4 ounces of yellow paint to get same shade.
Given that,
In order to get a precise orange color, Eve is mixing paint. She combines various ratios of red and yellow paint. Eve finds that using 4 ounces of red paint and 1 ounce of yellow paint results in the best color matching. Eve still has one ounce of red paint.
We have to see the ratio
4:1
extra 1 red paint that is
4+1:1
5:1
Therefore, To get orange shade she has to add 4 ounces of yellow paint to get same shade.
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how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
Answers
"Extend the domain of the trigo functions using the unit circle" Cluster A.
What is unit circle?The following steps can be used to calculate the sine and cosine of any angle thetatheta and allow us to extend the domain of sine and cosine to any real numbers:
Move counterclockwise around the unit circle starting at (1, 0), (1, 0), (1, comma, 0, right parenthesis, until the angle created by your position, the origin, and the positive xxx-axis equals thetatheta.
The yyy-coordinate of your point is equal to sin(theta)sin(theta)sine, and the xxx-coordinate is equal to cos(theta)cos(theta)cos(theta)cosine, left parenthesis, theta, right parenthesis.
There are several references to and issues with in the worlds of calculus, pre-calculus, and trigonometry.
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Please help me please help me
Answers
Answer: T (4,4)
Step-by-step explanation:
pls help! marking brainliest
Answers
Answer:
296
Step-by-step explanation:
Use long division.
296
21 |6216
-42
201
-189
126
-126
0
Hope this helps!
help with explanation!
Answers
In a heptagon, the sum of all seven angles is 900 degrees. If you add up the four given angles you will get 600 degrees. In the question it says, "the remaining interior angles are EQUAL" so therefore, the only way to get from 600 to 900 from the remaining three angles is 100. Each remaining angle is 100 degrees
Answer:
Heptagons are known to have seven interior angles that add up to 900°, so we must find the last 3. First, add the first four they gave us.
[tex]160\circ + 130\circ = 290\circ\\= 290\circ + 170\circ + 140\circ\\170\circ + 140\circ = 310\circ\\= 290\circ + 310\circ\\= 600\circ[/tex]
We now know that the remaining angles are all 100°, because the question mentions the rest of the interior angles being equal. The only reasonable 3 equal numbers to add up to 900° would be three 100s in this case.
Brainliest for correct answer
Answers
The correct symbols that complete the statements are
h(0) = g(0)
h(1) > g(1)
Graph of functionsFrom the question, we are to determine the correct symbols that complete the given statements
The given statements are
h(0) ___ g(0)
and
h(1) ___ g(1)
To complete the statements, we will find the values of the given functions from the graph
From the graph of h(x), we can observe that
h(0) = 4
and
From the graph of g(x), we can observe that
g(0) = 4
Thus,
The two functions are equal
h(0) = g(0)
Also,
From the graph of h(x),
h(1) = 3
and
From the graph of g(x),
g(1) = 2
That is, h(1) is greater than g(1)
Thus,
h(1) > g(1)
Hence, the correct symbols that complete the statements are
h(0) = g(0)
h(1) > g(1)
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So you see...
The question in my math workbook is,
45 ÷ 3 = (30 + ___) ÷ 3
= 30 ÷ 3 + ___ ÷ 3
= 10 + 5
= 15
sorry my brain is broken right now- I have a feeling this problem is really easy to solve, but as I said my brain is broken lol
Answers
The blank will be filled with 15.
The Bodmas rule is arranged according to the letters in the acronym BODMAS, which stand for brackets, position of power or roots, division, and multiplication. A stands for addition and S for subtraction. According to the BODMAS rule, multi-operator mathematical equations must be resolved in the BODMAS order from left to right.
The explanation goes like:
45 ÷ 3 = ( 30 + 15 ) ÷ 3
= 30 ÷ 3 + 15 ÷ 3
= 10 + 5
= 15
Hence the answer is 15.
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