Answer:
The 50th term of the sequence that begins with - 6 is 288.
Step-by-step explanation:
Definition of Arithmetic ProgressionAn arithmetic progression, also known as an arithmetic sequence, is a set of numbers in which the difference between successive terms remains constant. The sequence 5, 7, 9, 11, 13, 15,... is, for example, an arithmetic progression with a common difference of 2.
Formula -[tex]$a_{n}=a_{1}+(n-1) d$[/tex]
The given sequence is − 6, 0, 6, 12,It is in arithmetic progression as the common difference between all consecutive numbers is 6.
Let a1 be the first term and d be the common difference.
Therefore, a1 = - 6 and d = 6
For 50th term, a50 = a1 + (n - 1) d
= - 6 + (50 - 1) 6
= - 6 + 49 × 6
= - 6 + 294
= 288
Thus, the 50th term of the sequence is 288.
Learn more about arithmetic progression here-https://brainly.com/question/24462795
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Find the value of 3a+ 3b when: a = 6 and b = 4 a = 4 and b = 6 Your two answers should be the same. Look at the expression and the a and b values and explain why the answers are the same.
Answer:
The answer is 30.
Step-by-step explanation:
The given expression is :
3a+3b
Put a = 6 and b = 4 in the above expression.
3a+3b = 3(6) + 3(4)
= 18+12
= 30
Now put a = 4 and b = 6 in the above expression.
3a+3b = 3(4) + 3(6)
= 12+18
= 30
Hence, the answer in both case is same i.e. 30.
You invested $680 at 2.7% compounded monthly. How much money do you have after
8 years? Estimate your answer to two places after the decimal, if necessary.
Answer:
$843.74
Step-by-step explanation:
A = P (1 + r/n)^nt
A = 680(1 + 0.027/12)^12·8
A = 680( 1.00225)^96
A = 843.74
Andrea bought 1 2/5 pounds of avocados at $4.20 per pound and 2 1/
4 pounds of asparagus at $3.80 per pound.
What was her total cost?
Answer:
$14.43¢
Step-by-step explanation:
We are given; [tex]1\frac{2}{5}[/tex] pounds, 1 pound = $4.20 and [tex]2\frac{1}{4}[/tex] pounds,1 pound = $3.80 that Andrea bought.
Now we need to find her total cost. To do that, we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert [tex]1\frac{2}{5}[/tex] to a decimal. It is 1.4. Now we can set up a graph.
Avocados
[tex]\frac{4.2}{1}=\frac{x}{1.4}[/tex]
Switch sides
[tex]\frac{x}{1.4}=\frac{4.2}{1}[/tex]
Apply rule: [tex]\frac{a}{1}=a[/tex]
[tex]\frac{x}{1.4}=4.2[/tex]
Multiply both sides by 1.4
[tex]\frac{1.4x}{1.4}=4.2\cdot \:1.4[/tex]
Simplify
[tex]x=5.88[/tex]
So, her cost for avocados is $5.88¢
Now we must first find the cost of the avocados. To do so, let us set up a graph. But before that is done, convert [tex]2\frac{1}{4}[/tex] to a decimal. It is 2.25. Now we can set up a graph.
Asparagus
[tex]\frac{3.8}{1}=\frac{x}{2.25}[/tex]
Switch sides
[tex]\frac{x}{2.25}=\frac{3.8}{1}[/tex]
Apply rule : [tex]\frac{a}{1}=a[/tex]
[tex]\frac{x}{2.25}=3.8[/tex]
Multiply both sides by 2.25
[tex]\frac{2.25x}{2.25}=3.8\cdot \:2.25[/tex]
Simplify
[tex]x=8.55[/tex]
So, her cost for asparagus is $8.55¢
Total cost
Now that we have found out how much both of the fruits Andrea bought costs, we need to sum it up (meaning add it) to find the total cost:
$5.88¢ + 8.55¢ =
5.88 + 8.55 = 14.43
Therefore, Andrea's total cost of the fruits is $14.43¢
If you draw two cards from a standard deck of 52 cards without replacement.
Answer:
Step-by-step explanation:
a) prob(king first, Jack second)
= (4/52)(4/51) = 4/663
Ellise has 4 times as much money as her sister. If Ellise has php 10.40, how much money does her sister have?
Answer:Ellise's sister has php 2.4
Step-by-step explanation:
Let the amount of money Ellise sister has be = x
and amount Ellise has be =4x
since Ellise has php 10.40
her sister will have php 10.40/4 = php 2.4
Plz help down below is the question
Answer:
The answer would be exactly 250 messages.
0.50 × x = $125
125÷ 0.50=250
Hope this helps!
6 ( 7y - 5) simplified
Answer:
42y-30
Step-by-step explanation:
here you go
Help! How do I find AC in this equation?
Answer:
33
Step-by-step explanation:
add 25 & 8 together
Answer:
SEE IMAGE FOR SOLUTION
Hope it helps
Have a great day
PLEASE HELP! ( no random links )
“How many servings of fruit did you eat yesterday?” Is this a statistical question or non-statistical question?
Answer:
This is not a statistical question
Step-by-step explanation:
A statistical question is a question the gathers varying data
what if a man has 19 cows and he wants to give Half of them to his brother 1/4th to Son and 1/5th to daughter?
9.5 for the brother 19/4 for the son and 19/5 for the daughter I think
Step-by-step explanation:
So 9.5 would be 10. 19/4 would be 5 and 19/5 would be 4
SO the brother would get 10 the son would get 5 and the daughter would get 4
Answer:
Brother-9.5
Son-19/4
Daughter-19/5
Step-by-step explanation:
Also, pls help me on my phsyics Q3 work on graduation alliance. PLEASE PLEASE.
Find the number exactly halfway between 1/5 and9/10
I am not pretty sure of the answer but maybe it's 5/10
Answer:
the number half way between 1-5 is 3. and the number half way between 9/10 is 9.5
Step-by-step explanation:
to find the number half way between 1/5 just write out all the numbers (1 2 3 4 5) and 3 is the halfway point because there are two numbers on the right and to numbers on the left
the number halfway between 9 and 10 is 9.5. all you do is add 9 +10 then divide by 2
9+10=19
19÷2= 9.5
Write a system of linear inequalities represented by the graph.
Answer:
Alright so youd havee to right the terms in order which should be easy then your done! Hope this helped!
Step-by-step explanation:
Simon lost his library card and has an overdue library book. When the book was 5 days late, he owed $2.25 to replace his library card and pay the fine for the overdue book. When the book was 21 days late, he owed $6.25 to replace his library card and pay the fine for the overdue book. Suppose the total amount Simon owes when the book is n days late can be determined by an arithmetic sequence. Determine a formula for an, the nth term of this sequence. Use the formula to determine the amount of money, in dollars, Simon needs to pay when the book is 60 days late.
Answer:
[tex](a)\ y = 0.25n +1[/tex]
[tex](b)\ \$16[/tex]
Step-by-step explanation:
Given
[tex]n \to days[/tex]
[tex]y \to amount[/tex]
[tex](n_1,y_1) = (5,2.25)[/tex]
[tex](n_2,y_2) = (21,6.25)[/tex]
Solving (a): Formula that represents the scenario.
Calculate slope (m)
[tex]m = \frac{y_2 - y_1}{n_2 -n_1}[/tex]
[tex]m = \frac{6.25-2.25}{21-5}[/tex]
[tex]m = \frac{4}{16}[/tex]
[tex]m = 0.25[/tex]
The equation is calculated using:
[tex]y = m(n - n_1) + y_1[/tex]
This gives:
[tex]y = 0.25(n - 5) + 2.25[/tex]
[tex]y = 0.25n - 1.25 + 2.25[/tex]
[tex]y = 0.25n +1[/tex]
Solving (b): Amount after 60 days late.
This means that:
[tex]n = 60[/tex]
So:
[tex]y = 0.25 * 60 + 1[/tex]
[tex]y = 15 + 1[/tex]
[tex]y = 16[/tex]
Pls answer quick 45 points :))
Answer:
5
Step-by-step explanation:
140.23 < 140.203 what is the answer true or false.
Answer:
true
Step-by-step explanation:
Answer:
false because 140.23 is not less then 140.203
Isaac earns $15 per hour when he babysits. Let A be the amount he earns in dollars after babysitting for H hours.
Answer:
A= 15(H)
Step-by-step explanation:
A is the total amount he is going to get, And H is the hours. If he gets 15 an hour. it means however many hours he works multiplied by 15 is the total amount he gets.
PLS HELP WILL MARK BRAINLEST IF UR CORRECT
Answer:
52. (0,-3)
53. Slope= 4
54. Y=4x-3
Mr. Cobb is carpeting a 17.7 m long hallway. He has a piece of carpet 22 m long. How much does Mr. Cobb need to cut off the length of the piece of carpet?
Answer:5.7
Step-by-step explanation:
Good morning, can someone help me solve this problem? I already did some of it but I need help, thank you
Answer: (-4, -1)
This means x = -4 and y = -1 pair up together.
======================================================
You're on the right track. You'll replace the 'x' with 3y-1, but you made a typo. I think you meant to write the subtraction symbol instead of the equal sign.
Here's what your steps could look like
-2x + 5y = 3
-2(3y-1) + 5y = 3
-6y + 2 + 5y = 3
-y + 2 = 3
-y = 3-2
-y = 1
y = -1
x = 3y-1
x = 3(-1) - 1
x = -3-1
x = -4
Therefore, (x, y) = (-4, -1) is the solution
-------------------
As the steps above show, I replaced each copy of x in the second equation with (3y-1). This is due to x = 3y-1. From there, we isolate y. Once you determine that y = -1, it's plugged into the first equation to find x.
If you were to graph x = 3y-1 and -2x+5y = 3 on the same xy coordinate grid, then the two lines would intersect at (-4, -1)
Also, note how plugging x = -4 and y = -1 into the second equation leads to...
-2x+5y = 3
-2(-4)+5(-1) = 3
8 - 5 = 3
3 = 3
We get the same value on both sides, so that verifies the second equation. I'll let you verify the first equation.
A recipe calls for 1 ¾ cups of flour. If the recipe is tripled, how much flour is needed?
Answer:
5 and 1/4 cups
Step-by-step explanation:
Break it down
.75 times 3 = 2.25
1 times 3 = 3
2.25 +3 = 5.25 or 5 1/4 cups
Answer:
5 and 1/4 = 5.25
Step-by-step explanation:
I converted 5 and 3/4 to 5.75. Then i just multiplied 5.75*3=5.25. 5.25 is equal to 5 and 1/4
Hope this helps :)
pls help me with these and can you do them all and mitch you show me how to and I don't care if you use photo math thank you and use give me the best will be thank and brainlist.
The 2nd term of an arithmetic progression is (1/2) and the sum of the first 14th terms is -70. Find
(a) the common difference
(b) the last term.
Answer:
The common difference is -1.
The last term (the 14th term) is -11.5.
Step-by-step explanation:
In an arithmetic sequence, the second term is 0.5 and the sum of the first 14 terms is -70.
We want to determine the: (a) common difference and (b) the last term.
We can write an explicit formula to represent the sequence. An arithmetic sequence can be modeled by the formula:
[tex]\displaystyle x_n=a+d(n-1)[/tex]
Where a is the initial term, d is the common difference, and n represents the nth term.
Since the second term is 0.5:
[tex]x_2=0.5=a+d(2-1)[/tex]
Simplify:
[tex]x_2=0.5=a+d[/tex]
The sum of an arithmetic sequence is given by the formula:
[tex]\displaystyle S=\frac{k}{2}\left(a+x_k\right)[/tex]
Where k is the number of terms and x_k is the last term.
Since the sum of the first 14 terms is -70, S = -70 and k = 14:
Using our explicit formula, the last term is:
[tex]x_{14}=a+d(14-1)=a+13d[/tex]
Substitute:
[tex]\displaystyle -70=\frac{14}{2}(a+(a+13d))[/tex]
Simplifiy:
[tex]-10=2a+13d[/tex]
Rewrite the equation for the second term:
[tex]a=0.5-d[/tex]
Substitute:
[tex]-10=2(0.5-d)+13d[/tex]
Simplify:
[tex]-10=1-2d+13d[/tex]
Solve for d:
[tex]d=-1[/tex]
Hence, our common difference is -1.
Solve for a, the initial term:
[tex]a=0.5-(-1)=1.5[/tex]
So, our explicit formula is now:
[tex]x_n=1.5-1(n-1)=1.5-n+1=2.5-n[/tex]
So, the last term (which is 14) is:
[tex]x_{14}=2.5-(14)=-11.5[/tex]
help! (equivalent fractions)
it has three questions, please awnser the three! thank you!!!
Answer:
1. answer is 12
2. answer is 18
3. answer is 2
Can you answer the question in the picture please?
Answer:
D)
Step-by-step explanation:
5x5+5=30
8x9+7=79
24x3+28=100
Which radio costs 150% as much as Radio D?
*How are the ordered pairs used to create the sine and cosine graphs?
Answer:
The graphs of sine and cosine have the same shape: a repeating “hill and valley” pattern over an interval on the horizontal axis that has a length of . The sine and cosine functions have the same domain—the real numbers—and the same range—the interval of values
Order the following in ascending order.
1,2,3,5 and 7 are all common factors of two numbers. Write down the digit that the two numbers must end in?
What are the adjacent and vertical pairs in this picture
Answer:
Step-by-step explanation:
Two line segments AD and CE intersects at a point B.
Two angles which represent the pair of adjacent angles are,
∠ABC and ∠DBC
Pair of vertical angles (Opposite angles between two intersecting lines) is,
∠ABE and ∠CBD
A library labels each book with a six-character code to identify the book in its computer system. The first character is either a letter or digit, and this is followed by three digits, then two letters. How many different codes are possible
Answer: There are 24336000 different codes that are possible.
Step-by-step explanation:
We know that,
Total alphabets = 26
Total digits = 10
Choices for First place = 26+10=36
Choices for next 3 places = 10 x 10 x 10 = 1000
Choices for last 2 places = 26 x 26 = 676
Total different codes are possible = 36 x 1000 x 676
=24336000
Hence, there are 24336000 different codes that are possible.