Each sequence has eight terms. Evaluate each related series. -3.5,-1.25,1,. . . . . . , 12.25
An arithmetic progression (AP) is a sequence of numbers ordered such that the difference between any two consecutive numbers is a constant value. Also called arithmetic sequence. For example, the sequence of natural numbers: 1, 2, 3, 4, 5, 6, … is an arithmetic sequence in which the common difference between two consecutive terms (e.g., 1 and 2) is 1 (2 - 1) ... It can be seen that the tolerance of two consecutive terms is equal to 2, even for odd and even numbers.
First term a=-3.5,
Common difference d=2.25,
Number of terms n=8
Solution:
Here first term a=-3.5,
Common difference d=2.25
We know that,
f(n)=a+(n-1) d
f (8)=-3.5+(8-1)(2.25)
=-3.5+(15.75)
=12.25
We know that,
Sn=n2[2a+(n-1)d]
∴S8=82⋅[2(-3.5)+(8-1)(2.25)]
=4⋅[-7+(15.75)]
=4⋅[8.75]
=35
Hence, 8th term of the given series is 12.25 and sum of first 8th term is 35.
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HELP ASP SHOW UR WORK YOULL GET BRAINILEST I think u show work on this but if u can go ahead
Answer:
i had this question before and the correct answer was "subtract 12r from both sides of the equation" im sorry if im wrong that was my correct answer when i had this question
Step-by-step explanation:
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Perimeter: 2(7+12), 2*7+2*12, 7+12+7+12
Area: 7*12, 7*10 + 7*2
neither: 7+12
Step-by-step explanation:
perimeter is like if you want a fence all the way around your property and your yard is 7x12 feet. In that case you could use the first option because you have to count the sides and add them up. If it’s a rectangle then there are 2 12’s and 2 7’s so the first one would work. The fourth one also uses distribution. The Fourth and first one are pretty much the same and have the same answer so the fourth one would work for perimeter.
Another way to do perimeter is to instead of multiplying, is to add the sides. 7+12+7+12 is basically 7 times 2 plus 12 times 2 (the fourth ne) and the answer is still correct so this one works too,
For area you times one of the dimensions by the other so 7*12 would work for area.
7*10 + 7*2 would also work because that uses the distributive property and that’s 70 + 14 which is 84 which is still the same answer.
The only one that falls under neither is the fifth one. 7+12 is half of the perimeter because it only adds two of the sides together and has n multiplying so it’s not area either.
Use each recursive definition to write an explicit formula for the sequence. a₋₁ = 1, a n =a n ₋₁ +4
The explicit formula for the given sequence is a(n) = 1 + 4(n - 1).
What is termed as recursive definition?A recursive function is one that iterates or uses its very own previous term to determine subsequent terms, resulting in a series of terms.
The recursive formula for an arithmetic sequence is as follows.
a(1) = 1 and a(n) = a(n - 1) + 4.
Remember that this formula provides us with two types of data.
1 is the first term.Add 4 to obtain any term out of its previous term. To put it another way, this same common difference is 4.Let's look for a formal formula again for sequence.
Remember that we can use the standard explicit form to represent a sequence in which the first term is A & common difference is B: A + B(n - 1).As a result, the sequence's explicit formula is a(n) = 1 + 4(n - 1).Thus, by the use of recursive definition, the explicit formula for the sequence is a(n) = 1 + 4(n - 1).
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2(7x-7)=14x-20
with work plss and ty :)
Answer:
0=-6 (No solution)
Step-by-step explanation:
2(7x-7)=14x-20 - Distribute the 2 to 7x-7
14x -14 = 14x -20 - Subtract +14 from both sides
+ 14 +14
14x = 14x -6
-14x -14x
0=-6
In horse racing, a trifecta is a bet that the first three finishers in a race are selected, and they are selected in the correct order. Does a trifecta involve combinations or permutations? explain.
In horse racing, a trifecta, which is a bet that the first three finishers in a race are selected, and they are selected in the correct order, involves selection done in permutation.
Permutation is the method of selecting or arranging objects or numbers in order. It is used when the order or sequence of the elements selected is important. The number of permutations of n objects taken r at a time is determined by the following formula: P(n , r) = n!
On the other hand, combination is the method of selecting or arranging objects or numbers from a group of objects or numbers where order does not matter. The number of combinations of n objects taken r at a time is determined by the following formula: C(n , r) = n!/[r!(n - r)!]
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Answer:
Step-by-step explanation:
Because the order of the first three finishers does not make a difference, the trifecta involves permutations
The current of a river flows north at a constant rate. What is the constant in the mathematical expression 3x + 5y + 3 ?
A constant is a value or number that is consistently the same regardless of how it is expressed.
In the mathematical expression 3x + 5y + 3 the constant is 3.
What is a constant in a mathematical expression?Constants are a particular kind of term that can be utilized in an equation in algebra.A constant is a value or number that is consistently the same regardless of how it is expressed.A term in an equation with a fixed value that is unaffected by variations in the variable. Constant functions can also be referred to as constants.Any input value can affect a function's output, but a constant function always produces the same result. A constant is typically represented as c to reflect a fixed value when written as a variable.Therefore, in the mathematical expression 3x + 5y + 3 the constant is 3.
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Which equation models the line that passes through points (2, 5) and (3, 1)?
Answer: y = -4x + 13
Step-by-step explanation:
Given points (2, 5) and (3, 1)
First Step find the slope given the two points:
Use the slope formula [tex]m=\frac{y2 - y1}{x2 - x1}[/tex]
[tex]m = \frac{1-5}{3-2} = -4[/tex] (Result)
Slope is equal to -4
Second step plug into y - y1 = m(x - x1) formula (Point Slope Formula)
For this I am using the first coordinate pair given (2, 5)
y - 5 = -4(x-2)
y - 5 = -4x + 8
y = -4x + 13
Simplify the expression 13. 8+(-11. 5). Use pencil and paper. How are 13. 8 + (-11. 5) and (-13. 8) +11. 5
related? Explain without computing. Using a property of operations, what can you say about their sum?
On simplifying the expression 13.8+ (-11.5) , we get 2.3 . And additions
13.8 + (-11.5) and (-13.8) + 11.5 are numbers will same value and opposite sign.
What are rules for adding a positive and a negative number?For adding a negative and a positive number, use the sign of the larger number and subtract.
For example: (–8) + 2 = -6
Given that we have to solve 13.8 + (-11.5) = 13.8-11.5 (we subtract smaller no from larger and will use the sign of lager number that is + here)
13.8+(-11.5) = 13.8-11.5 =2.3
13.8+(-11.5) simply means that 13.8 -11.5 which is subtraction of 11.5 from 13.8
but (-13.8) + 11.5 = -13.8 +11.5 = -( 13.8 -11.5) [taking -1 common from the expression]
Therefore , -13.8 + 11.5 has same value as 13.8- 11.5 but opposite in sign.
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help me please i need math
Based on the information given, the area of the trapezoid will be 89.7cm².
How to calculate the area?It should be noted that the formula for calculating the area of a trapezoid will be:
= (a + b)/2 × h
where a = 8
b = 13
h = 7.8
Area = (13 + 8)/2 × 7.8
= 21/2 × 7.8
= 11.5 × 7.8
= 89.7cm²
Therefore, based on the information given, the area of the trapezoid will be 89.7cm².
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Solve each system by substitution. Check your answers.
r + s = -12 , 4r - 6s = 12
By substitution, the solution of the system of equations, r + s = -12 and 4r - 6s = 12, is (-6 , -6).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in r and s,
r + s = -12 (equation 1)
4r - 6s = 12 (equation 2)
Using the first equation, find the value of one variable, lets say r, in terms of the other.
r + s = -12 (equation 1)
r = -12 - s
Substitute the value of r to the second equation.
4r - 6s = 12 (equation 2)
4(-12 - s) - 6s = 12
-48 - 4s - 6s = 12
Combining all terms containing the variable s on one side and the constants on the other side of the equality, and solving for s.
-48 - 4s - 6s = 12
-4s - 6s = 12 + 48
-10s = 60
s = -6
Substitute the value of s in the equation of r and solve for r.
r = -12 - s
r = -12 - (-6)
r = -12 + 6
r = -6
Hence, the solution of the given system of equations is (-6 , -6).
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4. Point A has coordinates (3, 4). After a translation 4 units left, a reflection
across the x-axis, and a translation 2 units down, what are the coordinates
of the image? (Lesson 1-6)
5. Here is triangle XYZ:
After a translation 4 units left, a reflection across the x-axis, and a translation 2 units down, the coordinates of the image are (-1, 2).
What is translation?In mathematics, a translation is the movement of a shape to the left or right, and/or up or down. The translated shapes appear to be the same size as the original shape, implying that the shapes are congruent.
They have simply been moved in one or more directions. There is no change in the shape because it is simply moving from one location to another.
According to transformation rule in graph, when moving it to the right, you add the x value And when moving to the left, you subtract the x value,
Value of x = 3
Here the reflection of x has translated 4 units left, which implies
3 - 4 = -1
And, when moving up you add to the y value and when moving down you subtract to the y value,
Value of y = 4
Here the reflection of y has translated 2 units down, which implies
4 - 2 = 2
Thus, the coordinates of the image formed by the reflection are (-1, 2)
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Divide 7/15 by 3/5.
A.7521
B. 21/75
c.7/9
D.7/25
Answer: C. 7/9
Step-by-step explanation:
Below are the decimal expansions for some fractions with a denominator of 12. When you look at the
numbers, you might notice that the decimal expansion in the first row always ends in three; the decimal
expansion in the second row always ends in six; and the third row "comes out even". Now explore the decimal
expansions for the 9ths and describe the pattern you find. Start with finding the decimal for 1/9, then 2/9, and
so on
If we find the decimal values of 1/9,2/9 and so on then we will get 1/9=0.11,2/9=0.22,3/9=0.33,4/9=0.44,5/9=0.55,6/9=0.66,7/9=0.77,
8/9=0.88,9/9=1.
Given some values in which the denominator is 12 and we are required to find the values of numbers whose denominator is 9.
Decimal expansion is basically representation of a non-negative real number r is its expression as a sequence of symbols consisting of decimal digits traditionally written with a single separator.
1/9=0.11
2/9=0.22
3/9=0.33
4/9=0.44
5/9=0.55
6/9=0.66
7/9=0.77
8/9=0.88
9/9=1
Hence if we find the values of 1/9,2/9 and so on then we will get decimals of 1/9=0.11,2/9=0.22,3/9=0.33, 4/9=0.44,5/9=0.55,6/9=0.66, 7/9=0.77, 8/9=0.88,9/9=1.
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I don’t really understand this can someone please help me I have to find the tangent ratios for
The tangent ratio for the ΔABC is tanФ = 1.
What is defined as the trigonometric ratios?The values of all trigonometric functions derived from the ratio of sides inside a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of such a right-angled triangle with respect to that acute angle.Some of the trigonometric ratios are-
sin = perpendicular/hypotenusescos = base/hypotenusestan = perpendicular/basecosec = 1/sinsec = 1/coscot = 1/tanFor the given right angles triangle ABC.
The sides AC = CB = 15
As, the angle ACB is the right angle i.e, ∠ACB = 90°, so, AB is the hypotenuses of the triangle.
For finding the value of tangent ratio;
tan = perpendicular/base
tan B = AB/ CB
tan B = 15/15
tan B = 1/1
tan B = 1
Thus, the value of tangent ratio = 1.
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Solve without graphing. Find the slope and the y-intercept for the graph of each equation in the given system. Use this information (and not the equations' graphs) to determine if the system has no solution, one solution, or an infinite number of solutions.
For equation (1), we get the Slope as 3 / 4 and y intercept as - 9 and for equation (2), we get the Slope as 3 / 4 and y intercept as - 4.
We are given 2 equations:
y = 3 / 4 x - 9 ...(1)
and y = 3 / 4 x - 4 ... (2)
Slope for equation (1) will be
slope = m1 = 3 / 4
Slope for equation (2) will be
Slope = m2 = 3 / 4
Y intercept for equation (1) will be:
= - 9
Y intercept for equation (2) will be:
= - 4
Also, since the Slope of equation are equal, so, it has no solutions as they are parallel to each other.
Therefore, for equation (1), we get the Slope as 3 / 4 and y intercept as - 9 and for equation (2), we get the Slope as 3 / 4 and y intercept as - 4.
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the thermometer reads 6 degrees the temperature drops 15 degrees overnight the it rises 25 degrees at 9:00am what temperature is it at 9:00pm
When the thermometer reads 6 degrees the temperature drops 15 degrees overnight, the temperature at 9:00pm will be 16°.
How to illustrate the information?From the information, the thermometer reads 6 degrees the temperature drops 15 degrees overnight the it rises 25 degrees at 9:00am.
Therefore, the temperature at 9:00pm will be:
=6° - 15° + 25°
= 16°
Therefore, the temperature at 9:00pm will be 16°.
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A rock climber descends 94 feet into a canyon, and then climbs up 52 feet. What is his final position?
find the value of (8x^6)^2/3
Answer: 4x^4
Step-by-step explanation:
from the law of indices,
( a^x)^y = a^xy
Now from the question
( 8x^6)^2/3
8^2/3X^6x2/3
From another law of indices,
a^x/y = ( y cube root of a)^x
8^2/3 = 2^2 = 4 ——— 1
Now X^6*2/3
= X^4 ——————-2
Now combine 1 & 2 together gives the answer
= 4x^4
Sarah paid for 6 bags of sand to be delivered. Each bag of sand costs $114.95. Sarah paid $54.55 for delivery. What is the total amount Sarah paid?
Answer: $744.25
Step-by-step explanation:
6 * 114.95 = 689.7
689.7 + 54.55 = 744.25
Caroline walks Nine and a half inches per second. Rou d to the nearest tenth.
The speed of Caroline in miles per hour is 0.5 miles/hour.
Given that, Caroline walks 9 1/2 inches per second.
How do you convert the inches to miles formula?How to convert inches to miles. To convert an inch measurement to a mile measurement, divide the length by the conversion ratio. The length in miles is equal to the inches divided by 63,360.
Now, 9.5 inches/second
We know that 1 inch/second=0.0568182 miles/hours
So, 9.5 × 0.0568182=0.5397729 miles/hours
≈0.5 miles/hours
Therefore, the speed of Caroline in miles per hour is 0.5 miles/hour.
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Your question is incomplete, probably the complete question/missing part is:
Give the rate in miles per hour. Round to the nearest tenth. Caroline walks 9 1/2 inches per second.
Find the slope of the line passing through the pair of points. (If an answer does not exist, enter DNE.) (0, 15), (9, 0)
The required slope of the line through the points (0, 15), (9, 0)
is -5 / 3.
Given that,
To determine the slope of the line passing through the pair of points (0, 15), (9, 0).
The slope of the line is a tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.
Here,
Slope of line ( m ) = [ y₂ - y₁ ] / [x₂ - x₁]
We have points (0, 15), (9, 0).
y₂ = 0 y₁ = 15 x₂ = 9 x₁ = 9
now,
m = 0 - 15 / 9 - 0
m = -15 / 9
m = -5 / 3
Thus, the required slope of the line is -5 / 3.
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Which expression is equivalent to sum of quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity? negative twenty nine sixths times n minus one twelfth negative twenty nine sixths times n plus one twelfth negative eleven sixths times n minus one twelfth negative eleven sixths times n plus five twelfths
The expression "quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity" or (-3 1/3n + 1/6) + (1 3/6n - 3/12) is equivalent to "negative eleven sixths times n minus one twelfth" or -11/6n - 1/12.
An algebraic expression is a number, variable, or the combination of both and operational symbols.
To determine the equivalent of the expression "quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity" or simply (-3 1/3n + 1/6) + (1 3/6n - 3/12), combine all like terms and perform necessary operations.
(-3 1/3n + 1/6) + (1 3/6n - 3/12)
⇒ -3 1/3n + 1 3/6n + 1/6 - 3/12
⇒ (-3 1/3 + 1 3/6)n + 1/6 - 3/12
⇒ (-10/3 + 9/6)n + 2/12 - 3/12
⇒ (-20/6 + 9/6)n - 1/12
⇒ -11/6n - 1/12
Hence, the equivalent expression is negative eleven sixths times n minus one twelfth" or -11/6n - 1/12.
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Here are five number cards.
2
5
7
8
One of the cards is removed and the mean aver
of the remaining four number cards is 6
Which card was removed?
The card with the number 7 was removed.
What are equations?An equation, in its most basic form, is a mathematical statement that shows that two mathematical expressions are equal.For example, 3x + 5 = 14 is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.So,
The sum of all the numbers on the cards is 2+5+7+8+9=31.One card is removed, for example, with the number x.Now the sum new would be =31-x. ... (1)6 is the average of the remaining four cards.So the sum of the remaining four cards is 6(4) = 24. ...(2)The sum of the remaining four cards is represented by(1) and (2). As a result, they should be equal to 31 - x = 24.Subtraction 31 from both sides yields -x = -7 or x = 7.Therefore, the card with the number 7 was removed.
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the tuition for a private college is currently 18000 for each semester. The college will raise tuition by 500 dollars per semester per year How much is tuition per year. By how much will tuition increase each year.
Based on the calculation below, we have:
The tuition per year is $36,000; and
The amount of increase in the tuition each year is $1,000.
How do we calculate tuition and an increase in tuition?The tuition per year and the amount of increase in the tuition each year can be calculated as follows:
Number of semesters in a year = 2
Tuition per semester = $18,000
Amount of increase in the tuition each semester = $500
Therefore, we have:
Tuition per year = Number of semesters in a year * Tuition per semester = 2 * $18,000 = $36,000
Amount of increase in the tuition each year = Number of semesters in a year * Amount of increase in the tuition each semester = 2 * $500 = $1,000
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If P(A | B) is the same as P(A) , and P(B \mid A) is the same as P(B) , what can be said about the relationship between events A and B ?
When P(A | B) = P(A) and P(B ∩ A) = P(B). Then, the given events A and B are independent events.
What is defined as the independent events?Independent events are those where the occurrence is unrelated to any other event.
For example, suppose we toss a coin as in air and the result Head, then we throw the coin again and get the result Tail. Both events occur independently of one another in both cases.Now, as for the given question.
There are two events given as A and B.
The probability of occurrence of event A is P(A).
The probability of occurrence of event B is P(B).
The occurrence of the event A when B is already happened is denoted by P(A | B).
The intersection of events A and B are given as; P(B ∩ A).
Now, it is given in the question that;
P(A | B) = P(A) and P(B ∩ A) = P(B)
And, we already know that, the formula of the conditional probability for event A when event B has already occurred is;
P(A | B) = P(B ∩ A)/P(B)
This can also be written as;
P(B ∩ A) = P(A | B).P(B)
Now, P(A | B) = P(A), replace in the obtained equation.
P(B ∩ A) = P(A).P(B)
The obtained result is the condition for independent events.
Therefore, the events A and B are found to be independent events.
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How many solutions are there to this equation?
7x3(x - 1) = 2(2x + 3)
A. no solution
B. exactly one solution
C. at least two solutions
D. infinitely many solutions
Answer:
at least two solution so c
Use the Distance Formula to calculate the distance between points A (-4, 2) and D (1, 7). Round your answer to 1 decimal place.
Step-by-step explanation: I hope this helps.
Answer: 7.07 units
Solve the application problem.
In one day a baker used 2/3 of a pound of flour, then 3/4 of a pound of flour, then 5/12 of a pound of flour. How much flour was used that day?
Answer:
1 5/6 or 11/6
Step-by-step explanation:
2/3+3/4+5/12 = 11/6
Answer:
22/12
Step-by-step explanation:
Add all 2/3 + 3/4 +5/12
=take LCM of 3 , 4, 12
=
12/8 +9 + 5
= 22/12
Write an equation that represents a horizontal translation 10 units left of the graph of g(x) = |x|.
h(x) =_____
