an=a1+d(n−1) is the explicit and a recursive formula for each sequence .
What is sequence?
See the pattern
-32-(-20) = -12
-20-(-8) = -12
-8-4 = -12
By this the explicit and a recursive formula for each sequence is an=a1+d(n−1).
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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The arithmetic mean of the monthly salaries of two employees is $ 3210 . One employee earns $ 3470 per month. What is the monthly salary of the other employee?
b. What equation can you use to find the other monthly salary?
The arithmetic mean of the monthly salaries of two employees is $ 3210 . One employee earns $ 3470 per month. What is the monthly salary of the other employee.
Then $2950 is the salary of the other employee.
What is arithmetic mean?$2950 is the monthly salary of the other employee.
a. the given information = mean of two salaries = 3210
= salary of 1st employee =3470
the unknown information = salary of 2nd employee = 2950
The arithmetic mean is the most straightforward and widely used method of calculating a mean or average. It only requires adding up a group of figures, then dividing the result by the entire amount of figures in the series. Consider the numbers 34, 44, 56, and 78 as an example. It totals 212.
The mean or arithmetic average are other names for the arithmetic mean. It is determined by adding up each number in a particular data set, then dividing the result by the overall number of items in the data set. For uniformly distributed integers, the middle number serves as the arithmetic mean (AM).
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please help me I need help i have problems
Answer:
3.6cm
Step-by-step explanation:
the points lie in order like this
A.....B.....C
we know that A......B......C total spans 4cm (or 40mm)
we know that A......B spans 4mm
we need to know the length of B......C
B......C = A.......B.......C - A.....B = 40mm - 4mm = 36mm = 3.6cm
Mike wants to build a rectangular picnic area using stone tiles. he has enough money to buy 24 tiles. what are all the possible dimensions of rectangles he can make for his picnic area
Answer:
1 by 24
2 by 12
3 by 8
4 by 6
Step-by-step explanation:
We look at all the factors of 24.
1, 2, 3, 4, 6, 8, 12, 24
He can make the area:
1 by 24
2 by 12
3 by 8
4 by 6
The point A has coordinates (5, -4)
The point B has coordinates (13, 1)
a) Work out the coordinates of the midpoint of AB.
Line L has equation y = 2 - 3x
b) Write down the gradient of Line L.
Line L has equation y = 2 - 3x
c) Does the point with coordinates (100, -302) lie on line L?
You must give a reason for your answer.
The midpoint of AB has coordinates (9, -1.5), the gradient of line L is -3 and the point (100, -302) doesn't lie on L.
What is a coordinate?
Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space (3D). Mathematicians, physicists, and engineers employ a variety of coordinate schemes.
(a) Given point A (5, -4) and point B (13, 1)
Therefore, midpoint of AB is [tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
[tex]or,(\frac{5+13}{2},\frac{-4+1}{2})[/tex]
[tex]or, (\frac{18}{2},\frac{-3}{2} )[/tex]
[tex]or,(9, -1.5)[/tex]
(b) In the equation [tex]y=2-3x[/tex], -3 is the gradient of line L.
(c) The point with coordinates (100, -302) doesn't lie on L as it doesn't satisfy the equation [tex]y=2-3x[/tex]
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find the circumference of this circle
Answer:
Since the radius is 18 then the answer would be 113.1...
C=2πr=2·π·18≈113.097
Step-by-step explanation:
Hope it helps! =D
Answer:
C = 108 units
Step-by-step explanation:
using C = πd ( with π = 3 and d = 36 )
C ≈ 3 × 36 = 108 units
Solve -4(3x-7)=52 for x
Answer:
x = -2
Step-by-step explanation:
First, distribute:
-12x + 28 = 52
Then, subtract 28 on both sides:
-12x = 24
Finally, divide -12 on both sides:
x = -2
Step-by-step explanation:
hope it helps
what are the vertex and range of 7= |x +2| -3
The vertex and range are (-2, -3) and y >= -3 respectively
How to determine the vertex and range?The equation is given as:
y = |x +2| - 3
The above equation is an absolute value equation
An absolute value equation is represented as:
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
Vertex = (-2, -3)
Also, we have
a = 1
Since a is positive, then the vertex is a minimum
Hence, the vertex and range are (-2, -3) and y >= -3 respectively
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Find measure.
m ∠ 5
Measure of angle 5 i.e. m∠5 = 50°
What is measurement of an angle ?The measurement of angle is the degree of that angle or we can also say that the angles are always measured in degree. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.
How to find angle measurement ?As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360 or 180 for a straight line.
In the question,
Let given angle is ∠8.
Given, ∠8 = 50°
Now, according to vertical angle property
∠5 = ∠8
therefore, ∠5 = 50°
Thus, m∠5 = 50°
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The complete question is :
Find measure m∠5
What are the coordinates of the point on the
directed line segment from (-8, 8) to (7,-7)
that partitions the segment into a ratio of 1 to 4?
The coordinates of the point on the directed line segment is (-5,5)
In the given sum we are using the internal division formula which goes like: (x,y) = (nx₁ + mx₂)/(m+n), (ny₁ + my₂)/(m+n)
with the available data we can interpret that where m = 1 , n = 4 , (x₁,y₁) = (-8,8) , (x₂,y₂) = (7,-7)
substituting the given values in the above formulae
The coordinates of the point is :
(x,y) = (4(-8) + 1(7))/(1 + 4) , (4(8) + 1(-7))/(1 + 4)
= ( -32 + 7)/5, (32 - 7)/5
= (-25/5) , (25/5)
= (-5,5)
∴ (x , y) = (-5 , 5)
So here the coordinates are (-5 , 5) which directed line segment from (-8,8) to (7,-7) that partions the segment into a ratio of 1 to 4
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Sadie worked 14 hours last weekend at Pickles and Onions sub shop. On Saturday, her gross
income was $90 but her net income was only $77.75. On Sunday, her gross income was $120
and her net income was $101.38.
How much did Sadie pay in payroll taxes for the weekend? /PLS HELP
Answer:
$30.87
Step-by-step explanation:
Saturday
- gross: $90
- net: $77.75
Sunday
- gross: $120
- net: $101.38
Total gross: 90 + 120 = $210
Total net: 179.13
Total tax: 210 - 179.13 = 30.87
If the signs are _______, then ______ and take the sign of the number with the greatest absolute value
Answer: different and subtract go in the empty spaces
What is 2,520 divide 36
The Equation a = 1/2(8)h Represents the area a of a triangle with base of 8cm and a height of h cm. Make a table to find the areas of triangles with heights of 6 cm, 7cm, 8 cm, and 9 cm.
::::: Answer ::::::::::::::::::::::
Simplifying the Equation :
[tex]a = \frac{1}{2} \times 8 \times h[/tex]
[tex]= \frac{8}{2} \times h[/tex]
[tex]= 4 \times h[/tex]
[tex]= 4 h[/tex]
Then
[tex]\text{if h = 6} \longrightarrow a=4\times 6=24[/tex]
[tex]\text{if h = 7} \longrightarrow a=4\times 7=28[/tex]
[tex]\text{if h = 8} \longrightarrow a=4\times 8=32[/tex]
[tex]\text{if h = 9} \longrightarrow a=4\times 9=36[/tex]
Angels (LIne). I'm unsure of what to do.
Based on the linear pair theorem, the value of x is: 42°.
How to Apply the Linear Pair Theorem?A linear pair is a pair of two angles that are formed adjacent to each other on a straight line. These two angles, according to the linear pair theorem, have a sum of 180d degrees when their measures are added together.
From the image, we see that x° and 138° are a linear pair as they lie on a straight line.
Therefore:
x + 138 = 180 [linear pair theorem]
Subtract 138 from both sides of the equation
x + 138 - 138 = 180 - 138
x = 42°
Therefore, based on the linear pair theorem, the value of x is: 42°.
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The expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped. What is the distance the object falls during each time?
0.5 second
If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance of the object during 0.5 second is 4 feet
Given,
The expression model of the distance in feet that an object falls during the first t second after being dropped = [tex]16t^{2}[/tex]
Time = 0.5 second
Then the distance = [tex]16(0.5)^{2}[/tex]
=16×0.25
=4 feet
Hence, if the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance of the object during 0.5 second is 4 feet.
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The feasible solution is the best solution possible for a mathematical model.
a. true
b. false
The feasible solution is the best solution possible for a mathematical model , the statement is False.
Feasible Solution for a mathematical model is defined as the solution that satisfies all the constraints of the linear program.
Whereas an Optimal Solution is a feasible solution that minimizes or maximizes the function.
Optimal Solution is a part of feasible Solution .
So , an Optimal Solution can also satisfy all the constraints of the linear program.
Hence, The feasible solution is the best solution possible for a mathematical model statement is False .
Therefore , the correct option is (b) false.
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0.0061 Write this number in scientific notation
12.
Answer:
6.1 * 10^-3
Step-by-step explanation:
This is because 10^-3 = 0.001 so 0.0061=6.1 * 10^-3
Answer:
6,100,000,000
Step-by-step explanation:
0.0061 x 10^12 =6,100,000,000
Solve x³ = 27. A x=9. Bx = 19,683 C_x=3√3. DX = 3
Answer:
D. x = 3
Step-by-step explanation:
[tex] {x}^{3} = 27[/tex]
[tex]x = \sqrt[3]{27} = 3[/tex]
¿Cuál es el radio de un circulo de 36 centímetros de perímetro?
There is a formula that relates circumference and radius of a circle. The formula is C=2πr, where π is roughly 3.14. So if the circumference is known, the radius can then be found using this formula.
Given:
Circumference of the circle =36 cm
The formula of circumference of the circle is C=2πr
Therefore,36=2πr
36=6.28r
π=3.14
r=36/ 6028
r=5.73cm
The radius of the circle is approximately
5.73cm.
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What is 7 12/13 as a improper fraction?? I rlly need help
Answer: 103/13
Step-by-step explanation:
7 * 13 = 91
91 + 12 = 103
Jasmine wants to use her savings of $1,128 to buy video games and movies. The total price of the movies she bought was $72. The video games cost $43 each.
Choose the inequality that would be used to solve for the maximum number of video games Jasmine can buy with her savings.
The last one.
It states that "The video games cost $43 each." and the total price was $72 in movies meaning that the x would go with the 43 and 1,128 would have to be greater than the amount she's buying or she won't be able to buy it.
2. In a sale, a jacket costing $40 is reduced by 20%. What is the sale price?
Answer:
$32
Step-by-step explanation:
1.20÷100×40=8
2.$40-$8=$32
What is 5.9 × 103 in standard form?
Answer: 607 7
_
10
Step-by-step explanation:
Write in point-slope form an equation of the line through each pair of points. (1,0) and (5,5)
The equation of the line in point-slope form, which passes through the points located at (1 , 0) and (5 , 5), is y = 5/4(x - 1).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (1 , 0) and (5 , 5).
m = (y2 - y1)/(x2 - x1)
m = (5 - 0)/(5 - 1)
m = 5/4
Using the point slope form, plug in the values of the slope and one point to set up the equation.
(y - y1) = m(x - x1)
where m = 5/4 and (x1 , y1) = (1 , 0)
(y - 0) = 5/4(x - 1)
y = 5/4(x - 1)
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Pls pls help whoever gets it right gets a crown
Characteristics exhibited by continuously varying traits ________. group of answer choices are always autosomal never happen are always sex-linked are called quantitative traits always happen
Characteristics exhibited by continuously varying traits are called quantitative traits. These continuously varying traits always measure phenotypes which usually depend on the cumulative behavior of many genes.
What are continuously varying traits?
Continuous varying traits exhibit the characteristics whose traits do not fall in the discrete categories like height and weight. Different traits which come under continuous varying traits are anatomical traits, physiological traits, behavior traits as well as diseases. It shows the continuous phenotypic variation within the group of individuals.
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In a 20 -row theater, the number of seats in a row increases by three with each successive row. The first row has 18 seats.
c. Front-row tickets for a concert cost $ 60 . After every 5 rows, the ticket price goes down by $ 5 . What is the total amount of money generated by a full house?
The most commonly used explicit of an arithmetic sequence is given as,
an = a + (n - 1) d.
Each term in the sequence can easily be solved/computed without knowing the other terms in the sequence. Now by using the given information, we can say that,
First number a1 = 18
Tolerance d = 3
Now putting the values in the given formula, we will get,
an=a1+(n-1) d
=18+(n-1)3
=3n+15
20
= ∑ 3n+15
n = 1
Sn = ∑3n+15
=3∑n+15∑1
=3 n(n+1)/2+15n
Sn =3* 20(20+1)/2+15(20)
=30 (21) +300
=630+300
=930
Total Seats 930.
Now to find the number of seats on every five lines.
5 10 15 20
= ∑ 3n+15; ∑ 3n+15 ; ∑ 3n+15 ; Ticket price for each set. $55; $50; $45
= 120 * 60 + 195 * 55 + 270 * 50 + 345 * 45
= $46950
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A jar of jelly bean candies weighs
8
88 ounces. A container of caramel candies weighs
40
4040 ounces. Lúcia buys
10
1010 pounds worth of jelly bean candy jars and caramel candy containers for her big party. Given that there are
16
1616 ounces in a pound, which of the following equations correctly relates the number of jars of jelly bean candies,
j
jj, and the number of containers of caramel candies,
c
cc, that Lúcia bought?
The equation that relates the number of jars of jelly bean candies and the number of containers of caramel candies is 8/16 J + 40/16 c = 10.
How to illustrate the information?The given parameters:
Weight of jelly bean can = 8 ounces
Weight of caramel candies, = 40 ounces
Amount of Jelly bean and caramel candies bought = 10 pounds
Number of ounces in one pound = 16 ounces.
Therefore, the equation that relates the number of jars of jelly bean candies and the number of containers of caramel candies is 8/16 J + 40/16 c = 10.
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4. There is one male snake, and the rest are female. She needs one vitamin pill for every female snake. How many vitamin pills does she need if the number of snakes is:
Answer:
Is this an incomplete question?
Step-by-step explanation:
hi, 12 points available
I was just wondering if anyone knows the answer to this question?
Two numbers, Greater than 1, which have A lowest common Multiple of 48?
Answer:16 and 24
Step-by-step explanation:
