Answer:
189
Step-by-step explanation:
The difference between consecutive terms of an arithmetic sequence, known as the common difference is given by
d = a(k) - a(k-1) where k = 1,2,3 ....n
We have the 5th term as a(5) = 9
The 6th term is 9 + d
The 7th term is 9 + 2d
The 8th term is 9 + 3d
Each successive term adds a d to the previous term
We have 8th term = 27
So 9 + 3d = 27
3d = 27 - 9 (subtract 9 from both sides)
3d = 18
Divide above by 3 on both sides to get
d = 18/3 = 6
So the common difference is 6
Let's figure out how to calculate the 31st term
We can see that the 5th term can be expressed as
9 + 0d = 9 + 0.6 = 9
The sixth term is
9 + 1d = 9 + 1(6) = 9 + 6 = 15
The seventh term is 9 + 2d = 9 + 12 = 21 and so on
Therefore the general equation for the nth term, given the 5th term
is
a(n) = a(5) + (n - 5)(6) 9 + 6(n - 5)
So the 31st term is
a(31) = 9 + 6(31-1) 9 + 6 x 30 = 9 + 180 = 189
Answer: 31st term is 189
2/5d+4/9e=-2d+7/18e-1
solve for e
Answer:
[tex]e=\frac{-5e-90}{216}[/tex]
Step-by-step explanation:
[tex]\frac{2}{5}d+\frac{4}{9}e=-2d+\frac{7}{18}e-1[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}=-2d+\frac{7}{18}e-1 < - Muiltiply[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}=-2d+\frac{7e}{18}- < - Muiltiply Again\\[/tex]
[tex]\frac{2}{5}d+\frac{4e}{9}-\frac{4e}{9}=-2d+\frac{7e}{18}-1-\frac{4e}{9} < - Subtract BothSides[/tex]
[tex]\frac{2}{5}d=-2d-\frac{e}{18}-1 < - Simplify[/tex]
[tex]\frac{2}{5}d+2d=-2d-\frac{e}{18}-1+2d < - AddToBothSides[/tex]
[tex]\frac{12}{5}d=-\frac{e}{18}-1 < - Simplify[/tex][tex]\frac{12d}{12}=-\frac{\frac{5e}{18}}{12}-\frac{5}{12} < - DivideBothSides[/tex]
[tex]e=\frac{-5e-90}{216}[/tex]
4. Solve x - 2 = 1.
Which statement shows the correct justification for the step used to solve the
equation?
O Add 1 to each side.
O Add 2 to each side.
O Subtract 1 from each side.
O Subtract 2 from each side
Answer:
x=3
Step-by-step explanation:
or,x-2=1
or,x=2+1
or,x=3
A standard train ticket in a certain city costs 3 per ride. people who use the train also have the option of purchasing a frequent-rider pass for 18.75 each month. with the pass, a ticket costs only 2.25 per ride. how many train rides in a month make the frequent-rider pass a better deal than standard train tickets?
a. 26 or more rides
b. 24 or more rides
c. 25 or more rides
d. 27 or more rides
Number of train rides to make the frequent-rider pass a better deal than standard train tickets is 26 or more rides.
As given,
Cost of standard train ticket = 3 per ride
Price of frequent rider pass= 18.75 each month
Cost of ticket using rider pass = 2.25 per ride
let x be the number of rides
Equation:
18.75 + 2.25x < 3x
⇒ 0.75x > 18.75
⇒ x > 25
Therefore, number of train rides to frequent-rider pass a better deal than standard train tickets is 26 or more rides.
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Brian rolls a fair dice 12 times.
How many times would Brian expect to roll a number greater than 4?
Answer:
I times the 12 by 5 and divided by 2 and subtract by 12
I get 18 and I thought it is 18
Answer:
Step-by-step explanation:
If a fair dice is rolled 6 times, 2/6 times the number would be greater than 4
If rolled 12 times, then 4/12 times the number would be greater than 4
4/12 = 1/3
4.51X3=
SHOWN WORK 13.53
Multiplication is the opposite of division. When we multiply 4.15*3 we get 13.53.
What do you mean by multiplication?Multiplication is one of the four basic arithmetic operations, alongside the addition, subtraction, and division. In math, multiply means the repeated addition of groups of the equal sizes.
The symbols for multiplication are cross (x), asterisk (*), and dot (.). You seem to utilize the cross a lot when you write in your notebooks. In both algebra and computer languages, the asterisk and dot are symbols (higher mathematics).
Commutative Property: According to this property, when we multiply two numbers, the result will not change depending on the order.
Associative property: It states that if we multiply three or more numbers consecutively, the order is irrelevant.
4.51
X 3
-----------
13.53
-----------
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A 19-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than five times the length of the first piecefind the lengths of the pieces. 3 + 5x
Using algebraic expressions and equations to solve this problem, a 19- inch piece of steel is cut into three pieces measuring 2 inches, 4 inches, and 13 inches.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
If the second piece is twice as long as the first piece, we can write this as an algebraic expression "2x" where x is the length of the first piece.
If the third piece is three inches more than five times the length of the first piece, we can write this as an algebraic expression "3 + 5x" where x is the length of the first piece.
If the three pieces were cut from a single piece of steel 19-inches long, we can write the equation for the sum using the algebraic expressions.
let x = length of first piece
2x = length of second piece
3 + 5x = length of third piece
x + 2x + 3 + 5x = 19 inches
Solving for x,
8x = 19 -3
8x = 16
x = 2 inches
length of first piece = 2 inches
Substitute the value of x in the expressions for the second and third piece.
length of second piece = 2x
length of second piece = 2(2)
length of second piece = 4 inches
length of third piece = 3 + 5x
length of third piece = 3 + 5(2)
length of third piece = 3 + 10
length of third piece = 13 inches
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what is 1408 rounded to the nearest hundredth
Answer:
It would still be 1408
Step-by-step explanation:
There are no decimal points to round to the nearest hundreth
Answer:
1408.00
Step-by-step explanation:
1408.00 ==>the underlined digit which is 1 digit away from the decimal is the hundredth digit.
Angle DEF is an inscribed angle on a circle, and m
O 48°
O 96°
O 132°
O 24°
∠24°
What is an inscribed angle in a circle?
Inscribed angles are angles whose vertices are on a circle and that intersect an arc on the circle. The measure of an inscribed angle is half of the measure of the intercepted arc and half the measure of the central angle intersecting the same arc.
given that intercepted arc = ∠48°
The intercepted arc is the arc that is inside the inscribed angle and whose endpoints are on the angle.
If the intercepted arc is twice the size of the inscribed angle, then the inscribed angle is half the size of the intercepted arc. So if the intercepted arc is 48 degrees, the inscribed angle is 48 / 2 = 24 degrees.
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4. (03.01)
Is the following relation a function? (1 point)
Yes
No
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
No, The given relation isn't a function.
[ For a relation to be a function, every value that lies in the domain ( set A ) should have only one corresponding value in its Range ( set B ) but here, -1 has two corresponding values that are : (-1) and (2) ]
Therefore, conclusion can be made that the given relation isn't a function.
Answer:
Not a function.
Step-by-step explanation:
Functions
A function is a special type of relation where each input (x-value) has a single output (y-value).
One-to-one: Each value in the range (y-values) corresponds to exactly one value in the domain (x-values).Many-to-one: Some values in the range (y-values) correspond to more than one (many) value in the domain (x-values).The given function is not a function as the input value of x = -1 has multiple output values of y = 2 and y = -1.
please help! i can’t figure this out I’ve somebody help QUICKKKK !!!!
Answer: A
Step-by-step explanation:
are 8x and 2x^3 like terms ??
Answer:
No they are not 'like' terms
Step-by-step explanation:
8x and 2x WOULD be 'like' terms
8x and 2x^2 are not
8x and 2x^3 are not either
Use the picture to solve for Y.
Answer:
y=2x+5
y=-1.5x+9
3y=-2x+10
Step-by-step explanation:
2x+y=5
y=2x+5
9-y=1.5x
-y=1.5-9
y=-1.5x-9
2x=-3y+10
3y=-2x+10
Need help asap
will give u brainliest
. Write a variable expression that represents the following word phrase:
Four less than half the difference of 3 and x
Answer: [tex]\frac{3-x}{2}[/tex]-4
Step-by-step explanation:
(3-x)/2 -4=[tex]\frac{3-x}{2}[/tex]-4
how many 1/3 cups are in 2 cups
Answer:
6 1/3 cups are in 2 cups
Step-by-step explanation:
1/3 + 1/3 + 1/3 = 3/3 = 1 cup
+
1/3 + 1/3 + 1/3 = 3/3 = 1 cup
1 cup + 1 cup = 2 cups
Therefore it is 6 1/3 cups.
How many 7 digit phone number combinations are possible, except now assume that the phone number is not allowed to start with 911?
9990000 are 7 digit phone number combinations are possible.
what is permutation and combination?
In mathematics, there are two additional methods for dividing a set of components into subsets: combination and permutation. The elements of the subset may be mixed in any order. The subset's elements are listed in a permutation in a certain order.Find every 7-digit phone number combination that exists first.
Given that the digit can be repeated, a total of 107 combinations are available.
The next step is to identify all conceivable combination of seven-digit numbers that begin with "911."
since it begins with "911" Therefore, there are just 4 digits left. 104 combinations are thus feasible in total.
The total number of potential combinations that begin with "911" is then subtracted.
We finally get
10⁷ - 10⁴
= ( 10³ - 1 ) × 10⁴
= 999 × 10⁴
= 9990000
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a) down payment, b) amount of the loan, c) monthly payment, and d) finance charge.
Shelly Lemony obtains a small business equipment loan for $120,000. Her down payment is 20% and the APR is 8% for 12 months.
a) Shelly Lemony's down payment is $24,000.
b) The loan amount is $96,000.
c) The monthly payment is $8,350.89.
d) The finance charge is $4,210.68.
What is the down payment?The down payment represents the initial up-front partial payment for the purchase of the equipment on loan.
The down payment reduces the cost of the equipment to the loan amount. Finance companies demand a down payment to ascertain the buyer's willingness and ability to proceed with the loan arrangement.
It is a sign of commitment to meet the loan contract obligations.
Data and Calculations:Monthly Pay: $8,350.89
Total Loan Amount = $96,000.00
Upfront Payment $24,000.00
Equipment loan = $120,000
Number of periods = 12 months
APR = 8%
Total of 12 Loan Payments = $100,210.68
Total Loan Interest = $4,210.68
Total Cost (price, interest, tax, fees) = $124,210.68
Thus, Shelly will make a down payment of $24,000 or 20% of the equipment loan.
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ZA and ZB are vertical angles. If m/A = (4x − 8)° and m/B = (3x + 18)°,
then find the value of x.
For the given vertical angles that is angle A = (4x-8) and angle B=(3x+18) the value of x = 26
We have been given that angle A and angle B are both vertical angles. Therefore both the angles will be equal as vertical angles are equal.
Thus, angle A = angle B
Now we will put the value of the respective angles and solve for x, we will get,
angle A = angle B
(4x-8)° = (3x+18)°
4x – 3x = 18 + 8
x = 26
hence the value of x = 26
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A traditional unit of length in japan is the ken (1 ken = 1.97 m). what are the ratios of (a) square kens to square meters?
The ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88
For given question,
We have been given the unit conversion.
A traditional unit of length in Japan is the ken
and 1 ken = 1.97 m
We need to find the the ratios of (a) square kens to square meters.
First we find the square of 1 ken.
⇒ 1 square kens = (1.97 m)²
⇒ 1 square kens = 1.97 × 1.97 m²
⇒ 1 square kens = 3.88 m² ..................(1)
And 1 square meters = 1 m² ................. (2)
Now we take the ratio of square kens to square meters.
From (1) and (2),
⇒ 1 ken² / 1 m² = 3.88 / 1
⇒ 1 ken² / 1 m² = 3.88
Therefore, the ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88
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Continuation of Qn on part ii)
Answer:
Step-by-step explanation:
below is a sequence of numbers:
0.5, 3, 5.5, 8, …
Calculate:
(a) the 8th term,
Answer: ______________
(b) the 100th term,
Answer: ______________
(c) which term has a value of 148.
Answer:
a) 18
b)248
c) 58
Step-by-step explanation:
The formula is:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1)d
[tex]a_{n}[/tex] Is the number at the n term
[tex]a_{1}[/tex] Is the first number in the sequence
n Is the number for the term
d is the common difference. How much is added each time in the sequence. In this case, 2.5
Put in the numbers that you know and solve for the unknown.
A:
[tex]a_{8}[/tex] = 0.5 + (8 -1)(2.5)
[tex]a_{8}[/tex] = 0.5 +(7)(2.5)
[tex]a_{8}[/tex] = 0.5 + 17.5
[tex]a_{8}[/tex] = 18
B:
We follow the same pattern, but we are now looking for [tex]a_{100}[/tex].
[tex]a_{100}[/tex] = 0.5 + (100-1)(2.5)
[tex]a_{100}[/tex] = 0.5 + 247.5
[tex]a_{100}[/tex] = 248
C:
This time we know the value of the number in the sequence, we do not know which term it is.
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d Put in what we know
148 = 0.5 + (n -1)2.5 Distribute the 2.5
148 = 0.5 + 2.5n - 2.5 Combine like terms
148 = 3 + 2.5n Subtract 3 from both sides of the equation
145 = 2.5n Divide both sides by 2.5
58 = n
If you are examining a function over an interval ( a , b ) , for a and b finite, is it possible not to have an absolute maximum or absolute minimum?
Yes, it is not possible to have an absolute maximum or absolute minimum.
Here,
We are examining a function over an interval ( a , b ) , for a and b finite,
We have to find, is it possible not to have an absolute maximum or absolute minimum.
What theorem indicates the existence of absolute maxima or absolute minima of a function?
If f is continuous on a closed interval [a, b] (that is: on a closed and bounded interval), then, the Extreme Value Theorem indicates the existence of an absolute maximum or minimum value of f on the interval [a, b].
Now,
The function is define over an interval (a, b).
Hence, the function is define on open interval.
So, it is not possible to have an absolute maximum or absolute minimum.
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PLEASE SOLVE ITS FOR A TEST I NEED IT
Answer:
The answer is Option C
Answer:
I think the answer would be C
Step-by-step explanation:
graph the inequlity
y > |x-7| + 1
Answer:
D.
Step-by-step explanation:
The inequality graphed matches the graph on the answer choice D.
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If a+b+c =9 and a²+ b²+c²=35,find the value of a³+b³+c³-3abc
Here is your Answer
step by step explanation
Hit thanks, if it's help full
Solve the simultaneous equation
-4x+3y=1
6x-y=2
Answer:
x = 1/2 or 0.5, y = 1
Step-by-step explanation:
it just means a system of equations.
-4x + 3y = 1
6x - y = 2
let's multiply the second equation by 3 and add both resulting equations :
-4x + 3y = 1
18x - 3y = 6
-------------------
14x 0 = 7
14x = 7
x = 7/14 = 1/2 = 0.5
6x - y = 2
6×1/2 - y = 2
3 - y = 2
-y = -1
y = 1
I need Help please :(
Step-by-step explanation: See attached step by step
Filip is inviting 6 friends to a party. Each friend wants 5 cookies and each box has 8 cookies. How many boxes should Filip get?
Complete the table.
Answer:
-1, 2
Step-by-step explanation:
Plug the "x" on the top row into the "x" on the equation.
y = 3(0) - 1 = -1
y = 3(1) - 1 = 2
Hayfa does 336 jumping jacks in 8 minutes. How many does Hayfa do in 1 minute?
Answer:42
Step-by-step explanation:
Hayfa dose 336 jumping jacks in 8 mins so you divide 336 by 8 and that equals 42
Answer:
42 jumping jacks
Step-by-step explanation:
To find how many Hayfa does in a minute divide 336 by 8
➟ 336/8
➟ 42
∴ Hayfa can do 42 jumping jacks in a minute