The total number of seats are there is row 16 is 65.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between two different arithmetic orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come along through a few specific terms in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be referred to in terms of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, as the values given in the question;
There are total 16 rows in the arena.
Thus, n = 16.
There are 20 seats present in row 1.
Consider the first term as 'a₁' = 20.
Similarly, there are 23 seats present at row 2.
Consider 'a₂' = 23 is the second term.
Now, calculate the common difference;
d = a₂ - a₁
Put the values in the 'd'.
d = 23 - 20 = 3.
Now, compute the total number of seats in 16th row bu nth formula.
n-th term: an = a + (n − 1) × d
a₁₆ = a₁ + (n - 1)d
a₁₆ = 20 + (16 - 1)3
a₁₆ = 20 + 45
a₁₆ = 65
Therefore, the total number of seats present in the 16th row is 65.
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Marianna went running and had 1/6 of a bottle of water left when she stopped to rest. She went to a water fountain and filled it until it was 2/3 full.
How much water (as a fraction of a bottle) did Marianna put in her bottle at the water fountain?
Mari put 1/2 of a bottle of water at the water fountain .
Expression in maths is outlined because the assortment of numbers variables and functions by mistreatment signs like addition, subtraction, multiplication, and division.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping will all be pictured by mathematical symbols, which might even be accustomed indicate the logical syntax's order of operations and different options.Let the capacity of the bottle holding water be 100 .
It is given that Marianna went running and had 1/6 of a bottle of water left when she stopped to rest. She went to a water fountain and filled it until it was 2/3 full.
The amount of water is given by :
2/3 of 100 - 1/6 of 100 = 2/3 × 100 - 1/6 × 100
= 100( 2/3 - 1/6)
= 100(1/2)
= 50
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16) Long John had 100 bags of silver. Each bag contained 9 3/4 lb. How much silver did he
have altogether?
Answer:
975 lbs.
Step-by-step explanation:
9 3/4 = 9.75
9.75 × 100 = 975
Which equation demonstrates the distributive property? Responses
A.(3 + 8)5 = 5(3 + 8)
B.15 x 40 = 40 x 15
C.15 + 40 = 55
D.15 + 40 = 5(3 + 8)
The option D.15 + 40 = 5(3 + 8); demonstrates the distributive property.
What is the meant by the term distributive property?To "distribute" something means to divide it or give a fraction or portion of it.The distributive property corresponds to the distributive law of multiplication over basic arithmetic operations such as addition and subtraction.This property states that multiplying a sum of two or even more addends by a number produces the same outcome as multiplying each addend separately by the number and afterwards adding the products together.In other words, the distributive property requires an expression of the form: A (B + C) can be written as AB + BC.This property also applies to subtraction: A (B - C) can be written as AB - BC.This indicates that other two operands share operand A.From the given options;
Consider option D; 15 + 40 = 5(3 + 8).
It is the case of distributive addition.
where
5(3 + 8) = 5×3 + 5×8
5(3 + 8) = 15 + 40
Thus, the option D is the correct representation of the distributive law.
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Determine whether each sequence is arithmetic or geometric. Then identify the common difference or common ratio. 1620,540,180,60,20, . . . .
The sequence 1620,540,180,60,20, . . . .. is a geometric sequence with common ratio 1/3.
To determine whether the sequence is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic sequence, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric sequence, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given sequence is:
1620,540,180,60,20, . . . .
In this sequence:
a(1) = 1620
a(2) = 540
a(3) = 180
First we check the difference between 2 consecutive terms:
a(2) - a(1) = 540 - 1620 = -1080
a(3) - a(2) = 180 - 540 = -360
Since the difference is not constant, then the sequence is not an arithmetic one.
Now we check the ratio,
a(2) : a(1) = 540 : 1620 = 1/3
a(3) : a(2) = 180 : 540 = 1/3
and so on
Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 1/3
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The turtle population on an island is increasing at a rate of 1.4% per year. The population was 3800 in the year 2009.
What is the predicted population in the year 2014?
Question
The turtle population on an island is increasing at a rate of 1.4% per year. The population was 3800 in the year 2009.
What is the predicted population in the year 2014?
Answer:
3541
What is 905.255 round to
Answer:
No decimal: 905
One decimal: 905.3
For most people, the cost of a subscription to streaming music services is definitely a
discretionary expense. Marshal researched subscription costs and found the following monthly
rates for streaming services:
$10
$5 $10 $4 $12 $5
which is?
$6 $2.75 $3
a. What is the mean subscription fee?
303
of numbers
b. What is the median subscription fee?
c. What is the mode subscription fee?
d. If Marshal is looking to add another subscription how much would it have to be so the mean
$2.0.cdcas!
subscription is exactly $7 per month?
For the given subscriptions, we have that:
a) The mean is of $6.42.
b) The median is of $5.
c) The modes are of 5 and 10.
d) Marshall would have to add a subscription of $12.25.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
For this problem, the observations are given as follows:
10, 5, 10, 4, 12, 5, 6, 2.75, 3.
Hence the mean is:
M = (10 + 5 + 10 + 4 + 12 + 5 + 6 + 2.75 + 3)/9 = $6.42.
With another observation, we want a mean of $7, hence:
(10 + 5 + 10 + 4 + 12 + 5 + 6 + 2.75 + 3 + x)/10 = 7
57.75 + x = 70
x = 12.25.
Hence, for item d:
Marshall would have to add a subscription of $12.25.
What is the median?The median of a data-set is the middle value, which is the value that 50% of the data-set is greater and 50% is lesser.
The ordered data-set in this problem is:
2.75, 3, 4, 5, 5, 6, 10, 10, 12.
The middle value is of 5, which is the median.
What is the mode of a distribution?The mode of a distribution is the observation that appears the most times in the distribution.
In this problem, those observations are 5 and 10, both of which appears twice, hence the distribution is bimodal.
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A truck can be rented from Company A for $40 a day plus $0.7 per mile. Company B charges $20 a day plus $0.9 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Answer:
100 milesStep-by-step explanation:
Let the number of miles be x.
Company ATotal amount of rental is:
A = 40 + 0.7xCompany BTotal amount of rental is:
B = 20 + 0.9xSince A = B, substitute the values and solve the equation:
40 + 0.7x = 20 + 0.9x0.9x - 0.7x = 40 - 200.2x = 20x = 20/0.2x = 100A cargo van delivers only 50-pound and 80-pound packages. for each delivery trip, the van must carry at least 20 packages, and the total weight of the packages cannot exceed 1,500 pounds. write a system of inequalities to determine the maximum number of 80-pound packages that the van can carry per trip.
If a cargo van delivers only 50-pound and 80-pound packages and the total weight of the packages cannot exceed 1,500 pounds, then a system of inequalities to determine the maximum number of 80-pound packages that the van can carry per trip is x + y ≥ 20; 80x + 50y ≤ 1,500.
A system of inequalities is a term used in mathematics that is a set of two or more than two inequalities in one or more than one variable.
Consider,
the number of 80-pound packages = x
the number of 50-pound packages = y
As the van can carry a minimum of 20 packages, the sum of x and y can be given as,
x + y ≥ 20
The weight of 80-pound boxes can be given as 80x and the weight of 50-pound boxes can be given as 50x. As the total weight of the packages cannot be more than 1500 pounds,
80x + 50y ≤ 1500
If we consider x to be 19,18 or 17 and the remaining to be y, it will exceed the limit of 1500 pounds. If x is considered to be 16,
80(16) + 50 (4) = 1480
Hence, the maximum number of 80-pound packages that the van can carry per trip is 16.
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The three sides of a triangle are n. 3n+2, and 4n - 13. If the perimeter of the triangle is 69 inches, what is the length of each side?
Separate multiple entries with a comma.
Answer:
8, 26 and 19
Step-by-step explanation:
Perimeter is the length of all sides of a polygon. It is simply the length of the boundary around a closed shape. Perimeter of a triangle = Sum of all three sides.
Hence,
[tex]\Rightarrow[/tex] n + 3n + 2 + 4n - 13 = 69 (acc. to Q)
[tex]\Rightarrow[/tex] n + 3n + 4n + 2 - 13 = 69
[tex]\Rightarrow[/tex] 8n - 11 = 69
[tex]\Rightarrow[/tex] 8n = 80
[tex]\Rightarrow[/tex] n = 80/10
[tex]\Rightarrow[/tex] n = 8
Length of all three sides:
n = 83n + 2 = 3(8) + 2 = 264n - 13 = 4(8) - 13 = 19Which one of the following is not a power equation?
p= v2/r= vxi
p= v2xi p= i2xr
The equation that is not a power equation is p = v²×i
Power equationsFrom the question, we are to determine which of the given equations is not a power equation
Where the Voltage, V, and the Current, I, are given, the power, P is given by
P = IV
When the Voltage and the Resistance, R, are given
P = V²/R
When the Current and the Resistance are given,
P = I²R
∴ P = V²/R, P = IV, and P = I²R are power equations.
Hence, the equation that is not a power equation is p = v²×i
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Here are the ingredients needed to make 8 pancakes.
250 ml milk
1 egg
140 g flour
5 g butter
Simon makes 4 pancakes.
Work out how much milk he needs.
Craig makes 12 pancakes.
Work out how much butter he needs.
Step-by-step explanation:
Simon only used 125ml milk
250÷2=125
Craig used 375ml milk
250x1.5=275
Suppose that f(1) = 4, f(4) = 8, f '(1) = 7, f '(4) = 3, and f '' is continuous. find the value of 4 xf ''(x) dx 1 .
It looks like you want to find
[tex]\displaystyle \int_1^4 x f''(x) \, dx[/tex]
Integrate by parts:
[tex]u = x \implies du = dx[/tex]
[tex]dv = f''(x) \, dx \implies v = f'(x)[/tex]
Then
[tex]\displaystyle \int_1^4 x f''(x) \, dx = x f'(x) \bigg|_{x=1}^{x=4} - \int_1^4 f'(x) \, dx[/tex]
By the fundamental theorem of calculus,
[tex]\displaystyle \int_1^4 f'(x) \, dx = f(4) - f(1)[/tex]
so that
[tex]\displaystyle \int_1^4 x f''(x) \, dx = 4 f'(4) - f'(1) - f(4) + f(1) = 12 - 7 - 8 + 4 = \boxed{1}[/tex]
In this problem, you will investigate the relationships among three points of concurrency in a triangle.
b. Draw an obtuse triangle and find the circumcenter, centroid, and orthocenter.
Construct the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter of an obtuse triangle (altitudes). Take note of how these three centers interact with one another.
What is an obtuse triangle?An obtuse-angled triangle or obtuse triangle is one in which one of the angles is an obtuse angle or greater than 90°. The sum of the obtuse triangle's interior angles is only 180°. This means that the angle sum property of any triangle remains unchanged.
An obtuse-angled triangle is one in which one of the interior angles is greater than 90°. If one angle in an obtuse triangle measures more than 90°, the sum of the remaining two angles is less than 90°.
Construct the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter of an obtuse triangle (altitudes). Take note of how these three centers interact with one another.
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Which expression correctly represents "three less than the product of a number and two, increased by five"? 2 n minus 3 5 3 minus 2 n 5 3 minus (2 n 5) 2 (n minus 3) 5
Answer: 2n+5-3
Step-by-step explanation:
Break this quote down:
"three less than the product of a number and two, increased by five"
To this:
"three less than the product" ==> product-3
Now break this quote down
Product: "product of a number and two, increased by five"
To this:
"product of a number and two" ==> 2*n
"increased by five" ==> +5
"product of a number and two, increased by five" ==> 2*n+5
Product: 2*n+5
Product-3: 2*n+5-3=2n+5-3
SOMEONE PLEASE HELP :’( Solve the equation | 4x + 7| = 9. Graph
Answer:
-4
Step-by-step explanation:
Split the problem into two cases: one positive and one negative
|4x+7| =9
4x+7=9
(4x+7) =9
Subtract 7 from both sides
4x+7 - 7 = 9 - 7
Solution
x = 1/2
x = -4
There are 5 children and 3 adults going on a trip. What fraction of the people going on the trip are ADULTS
answer=
Children =5
Adults = 3
3/8 are adults
Find the coordinates of the midpoint of a segment with the given endpoints. A(0,0), C(3,-4)
The coordinates of the midpoint of a segment with the given endpoints will be (1.5, -2).
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoints are A(0, 0) and C(3, -4).
Then the coordinates of the midpoint of a segment with the given endpoints will be
(x, y) = [(0 + 3) / 2, (0 - 4) / 2]
(x, y) = (3/2, -4/2)
(x, y) = (1.5, -2)
The coordinates of the midpoint of a segment with the given endpoints will be (1.5, -2).
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5. Points A, B, and C are collinear. AB = 5x, BC = 2x + 1, and AC = 50.
Solve for x
I would rly appreciate someones help need it by tonight
Answer:
x=7
Step-by-step explanation:
AB is 1 part of the line
BC is the other part of the line
the total length of the line is 50 units
when you add AB to BC you should get 50
5x+2x+1=50
7x+1=50
7x=49
x=7
Simplify the expression: – 8n+– 8n+– 6n
Answer:
The simplified answer would be: -22n
Please correct me if I am wrong, hope this helps! ;)
Answer:
-22n.
Step-by-step explanation:
'+-' = '-' so,
– 8n+– 8n+– 6n
= -8n - 8n -6n
= -22n.
Use the distance-rate-time formula (d = rt) to solve the following problem.
d = distance
r = rate of speed
t = time
A train carrying cattle left Miami and traveled toward New York. The train took 28 hours to arrive in
New York and traveled the distance of 1092 miles. Find the rate of speed of the cattle.
I need this answered please
The phrase "54 less than twice Chrissy's age" is translated into an algebraic expression as 2x - 54.
What is the algebraic expression in the given phrase?Given the phrase in the question;
"54 less than twice Chrissy's age"
Let variable 'c' represent Chrissy's age
Translation
Chrissy's age ⇒ x
Twice Chrissy's age ⇒ 2 × x = 2x
54 less than ⇒ -54
Now combine terms
2x and - 54
2x - 54
Therefore, the phrase "54 less than twice Chrissy's age" is translated into an algebraic expression as 2x - 54.
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what is 3 times 60? because i dont know
Answer: 180
Step-by-step explanation: 3 times 6 is 18 so just add a zero
Answer: 180
Step-by-step explanation:
3x60
60+60+60
Ann had about $2,135 in savings while her sister had double that amount in savings. what is a reasonable amount that the sisters have saved? a. $4,000 b. $4,200 c. $5,200 d. $6,400
PLEASE HELP!! The area of a square is 16 square units. Since 4^2 = 16 and (-4)^2 = 16, both 4 and -4 are square roots for 16. Explain how "both square roots for 16, the area of the square, are the length of each side of the square" is incorrect.
I will mark brainliest!
we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"
Because one of these solutions does not have a meaning in the given contest.
Why is the statement incorrect?So we have a square with an area of 16 square units, then the side length of that square will be given by:
S^2 = 16 square units
Now, there are two solutions for the above equation, these are:
S = 4 units
S = -4 units.
But being a solution of the equation does not mean that the solutions have sense in the context of the problem.
When we talk about dimensions of figures, negative numbers are not really well defined. We can't say that a square has a side length of "negative 4 units"
That does not make sense, remember that math is just a language, and it should be used to communicate things to others.
So the logical solutions (4 and -4) is not the only thing we need to look at when we state the solutions of a problem, but also the problem itself.
That is why we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"
Because one of these solutions does not have a meaning in the given contest.
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HELP ITS URGENT! AND HAVE A GOOD DAY
Answer:
the answer is D
hope this helps!
Add or Subtract.
11/12 - 7/45
Solution=0.76
How to solve 11/12 - 7/45?
[tex]\frac{11}{12} -\frac{7}{45} \\=\frac{(11*45-7*12)}{540} \\=\frac{411}{540} \\=0.76[/tex]
What is a fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size.Numerator and denominator are both natural numbers in positive common fractions. The denominator tells us how many of those equal parts there are in the numerator.The numerator tells us how many of those parts there are in the numerator. Zero pieces can never make up a whole, hence the denominator cannot be zero.Ex: 1/2 = 0.5
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Is 12/24 equivalent to 24/72?
Answer:
No
Step-by-step explanation:
12/24 = (1 * 12) / (2 * 12) = 1/2
24/72 = (1 * 24) / (3 * 24) = 1/3
1/2 ≠ 1/3
Hamburgers can be purchased from two different popular fast food restaurants. restaurant a sells 11 burgers for $14.19, and restaurant b sells 2 burgers for $2.64. which restaurant offers the best value per hamburger, and what is its amount? restaurant a for $1.29 restaurant b for $1.29 restaurant a for $1.32 restaurant b for $1.32
Restaurant A offers the best value as one hamburger is $1.29
How to calculate the Restaurant with the best value ?The first step is to calculate the price of one burger in restaurant A
11= 14.19
1= x
cross multiply
11x= 14.19
x= 14.19/11
x= 1.29
The next step is to calculate the price on one burger in restaurant B
2= 2.64
1= x
Cross multiply
2x= 2.64
x= 2.64/2
x= 1.32
Hence the price of the hamburger at Restaurant A is $1.29 and the price at Restaurant B is $1.32.
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Answer:
(A) Restaurant A for $1.29
Step-by-step explanation:
Got it right on my quiz.
in chicago, the tenperature dropped from 21 degrees to -7 degreees over the course if 6 hours, identify the rational number that represents the average temperature change per hour
Answer:
4.6667
Step-by-step explanation:
