Find an
explicit formula for the geometric sequence 120, 60, 30, 15, ....
Answers
Answer:
f(n) = 120 * (1/2)^n
Step-by-step explanation:
First the first number is 120, so we get y = 120, then 60/120 = 1/2
So we no the r, or constant rate is 1/2.
After that, we can finish our equation by doing
f(n) = 120 * (1/2)^n
or
y = 120*(1/2)^x
The explicit formula for the given geometric sequence is:
\(a_n = 120 \times 0.5^{n-1}\)
We have,
To find an explicit formula for the geometric sequence 120, 60, 30, 15, ...,
we need to determine the common ratio, denoted by 'r'.
To find the common ratio, we divide any term in the sequence by its preceding term.
Let's choose the second and first terms:
r = 60 / 120 = 0.5
Now that we have the common ratio 'r', we can express the nth term of the geometric sequence using the explicit formula:
\(a_n = a_1 r^{n-1}\)
where '\(a_n\)' represents the nth term of the sequence, '\(a_1\)' is the first term, 'r' is the common ratio, and 'n' is the position of the term we want to find.
Using the given sequence, '\(a_1\)' is 120, and 'r' is 0.5.
Plugging these values into the formula, we have:
\(a_n = 120 \times0.5^{n-1}\)
Therefore,
The explicit formula for the given geometric sequence is:
\(a_n = 120 \times 0.5^{n-1}\)
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Related Questions
Which scenario can be modeled by the linear function
y = -15x + 500?
A. The temperature on Jupiter is
15℉ and increases by 500℉ every day.
B. There is a population of 500 giraffes in Western Africa that decreases by 15 giraffes each year.
C. A carpet cleaning service charges $500 plus an additional $15 for every hour.
D. A membership fee for a movie streaming service is free, but each rental costs $15.
Answers
You guys are annoying!
Answers
the reason for the annoying behavior that you see in us is because you do not understand us. if you were a proper weirdo, you would know this.
I NEED HELP ASAP
Create an equivalent expression for \(1.3^{3}\) over \(1.2^{2}\) raised to the fourth power all raised to the power of negative six.
1.2 raised to the twenty-fourth power over 1.3 to the eighteenth power
1.2 squared over 1.3 cubed
1.3 to the eighteenth power over 1.2 to the twenty-fourth power
1.3 cubed over 1.2 squared
Answers
The equivalent expression for \([(1.3)^{3} /{(1.2)^{2}}^{4} ]^{-6}\)is \([(1.2)^{2}] ^{24}/(1.3)^{18}\).
Given an expression \([(1.3)^{3} /{(1.2)^{2}}^{4} ]^{-6}\).
We are required to find the equivalent expression of the given expression.
Expression is combination of numbers, fraction,symbols, coefficients, determinants, indeterminants or algebraic operations. It shows some relationship also. It is found without equal to form.
Expression is \([(1.3)^{3} /{(1.2)^{2}}^{4} ]^{-6}\)
It is in fraction as we know that fraction is combination of two numbers one is numerator and denominator.
First we need to multiply the powers present in numerator and denominator.
=\((1.3)^{-18} /[{(1.2)^{2}}^{-24} ]\)
We have to invert the numerator and denominator because the powers in negative.
=\([(1.2)^{2}]^{24} /(1.3)^{18}\)
Hence the equivalent expression for \([(1.3)^{3} /{(1.2)^{2}}^{4} ]^{-6}\)is \([(1.2)^{2}] ^{24}/(1.3)^{18}\).
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The Read and Feed restaurant wants to know how satisfied their customers are with their service. They printed an internet link to a survey on every receipt, and 150150150 of their customers chose to answer the survey. The data showed that 60 percent of the customers were satisfied with their service.
Answers
Answer:
a
Step-by-step explanation:
because it rite
Answer: a
Step-by-step explanation:
which of the following are in correct order from least to greatest ?
please help me outt
Answers
Answer: Last option
pie/2 = 1.570
330 = 330
5 pie/3 = 5.235
2 pie/3 = 2.094
7 pie/6 = 3.665
I got these numbers by putting them into my calculator.
A linear relationship is given in the table.
x −2 −1 0 1 2
y −12 −7 −2 3 8
What is the slope of the relationship?
A: 5
B: −5
C: one fifth
D: negative one fifth
Answers
Answer: the answer is A,5
Step-by-step explanation:
you have to do the equation to find slope y sub2 -y sub1 / x sub2 -x sub1 and i chose (-2, -12) as the sub 1's and the (-1, -7) as the y sub2's so the equation is -7+12/-1+2 that equals 5/1 or 5 so the answer is A
I HOPE THIS HELPS
simplify the given expressions and fins the value if x=1 and y=-2
Answers
Answer:
Step-by-step explanation:
1/2-9=x56
Step-by-step explanation:
1/2-9=×56
HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!1
Answers
Answer:
1/3
Step-by-step explanation:
From the given diagram of the spinner, we can infer that blue occupies 1/3 of the space and green occupies the remaining space.
Hence, the probability of spinning blue :
1/3Answer:
1/3
Step-by-step explanation:
The blue one occupied one-third of the spinner, means when it got divided into three parts, the blue get one of them.
BRAINLIEST FOR CORRECT ANSWER + 17 points
The figure shows three quadrilaterals on a coordinate grid:
Which of the following statements is true about the three quadrilaterals?
1. M and O are similar and congruent.
2. O and N are similar and congruent.
3. M and N are similar but not congruent.
4. M and O are similar but not congruent.
Answers
Answer:
D. M and O are similar but not congruent.
Step-by-step explanation:
To begin, let's eliminate some options.It can't be A. M and O are similar and congruent because M and O aren't congruent because they are different sizes. It cannot be B. O and N are similar and congruent because they aren't congruent since they're different sizes. Lastly, it cannot be C. M and N are similar but not congruent, because these two are actually congruent.
How many cubes with edge lengths of 1/2 inch are needed to fill this cube?
Answers
I need help with this question, I'm not very good at math and all help is appreciated!
Answers
Answer:
A
Step-by-step explanation:
We can solve for H by isolating it on one side of the equation, as follows:
J/H - I/H = G
Taking H as the common denominator:
(J - I)/H = G
Multiplying both sides by H:
J - I = GH
Adding I to both sides:
J = GH + I
Dividing both sides by G:
H = (J - I)/G
So the answer is
(A)
H = (J - I)/G.
Answer: A
Step-by-step explanation:
\(\frac{J}{H} = G + \frac{I}{H}\) >Since you are solving for H bring I/H to the other side
by subtracting I/H from both sides
\(\frac{J}{H}- \frac{I}{H} = G\) >There is a common denominator so you can
combine the fractions
\(\frac{J-I}{H} = G\) >Multiply both sides by H or cross multiply whichever
way your mind things about how to get H on top
\(J-I = G(H)\) >Divide both sides by G
\(\frac{J-I}{G} = H\) >Answer is A
what's the value of x in the triangle?
Answers
Answer:
I believe it 180.
Please help me create a ratio for the 2 percentages in each box. I did the first two but i need help with the other ones. Please help i need this asap
Answers
Answer:
number 3 is = 1 : 1
number 4 is = 2 ; 2 ; 1
please mark me as brainliest
Step-by-step explanation:
Number 4=2:2:1
Can you guys help me with this ?I don’t understand it.
Answers
Elaine says, “To find 6 ➗ 2/3, I can just take the value of 6 ➗ 1/3 then either multiply it by 1/2 or divide it by 2.” Do you agree with her? Explain why or why not.
Answers
Answer:
I do not agree with her
Step-by-step explanation:
You can find the answer by doing the keep change flip method. So keep the 6, chnage the sign to a multiplication sign, then flip the 2/3 to 3/2. Then you multiply and you get 18/2 which simplifies to 9.
Greg has
3 rows of stamps with 10 stamps in
each row. Greg says there are a total of
35 stamps. Use what you have learned
about multiples of 10 to explain why
Greg is incorrect.
Answers
Answer:
All multiples of 10 end with 0 only. So 35 must be wrong as it ends with 5. Therefore, Greg is incorrect.
SOMEONE HELP ME PLEZ :_)
Answers
Answer:
34.556
No hundreds, 3 tens, 4 ones, 5 tenths, 5 hundredths, and 6 thousandths.
Step-by-step explanation:
(3x10) + (4x1) + (5x1/10) + (5x1/100) + (6x1/1000)
30 + 4 + 5/10 + 5/100 + 6/1000
34.556
No hundreds, 3 tens, 4 ones, 5 tenths, 5 hundredths, and 6 thousandths.
pleace is math is test
Answers
You have a pizza with diameter 12
2
3 in., and a square box that is 12.65 in. across. Write 12
2
3 as a decimal. Can you fit the pizza inside the box?
What is the decimal expansion for 12
2
3?
A.12.6
B.12.65
C.12.6
D.12.66
pls help me
Answers
Answer:
D is the right choice and no you cannot fit the pizza inside the box.
Step-by-step explanation:
D is the answer because to turn 2/3 into a decimal you would divide 2 by 3 and the answer you would get would be 0.66666666666...You would then add 12 to the answer and get 12.6666... Once you get this answer you would round it to the hundredths to get 12.67 but since that is not an option you could use D, 12.66 inches.
Answer:
I believe the answer is D.
Step-by-step explanation:
Use the relationship between pounds and ounces shown in the example to complete the table below
Answers
Answer: 0.5, 1.25, 2.5
Step-by-step explanation:
There are 16 ounces in a pound, so 8/16 = 0.5.
20/16 = 1.25
40/16=2.5
Answer:
0.5, 1.5, 2.5
Step-by-step explanation:
You can find this answer by looking that 1 pound = 16 oz. So half of an ounce equals half of that pound.
0.5 pounds equal 8 lbs
1.5 = 20
2.5 = 40
Select ALL the statistical questions.
1 How many cups are in a gallon?
2 Which measuring spoons (tablespoon, teaspoon, half-teaspoon or quarter-teaspoon) do home bakers use most frequently?
3 On average, how much salt do professional pastry chefs use in a pie crust?
4 Which is larger, 17 ounces or 2 cups?
5 Did Walmart sell more measuring cups or measuring spoons last Tuesday?
Answers
The answer of the given questions is given below.
We have given that, the statistical questions.
We have given that,
measuring spoons (tablespoon, teaspoon, half-teaspoon or quarter-teaspoon) do home bakers use most frequently.
What is the meaning of the statistical question?
A statistical question is a question that can be answered by collecting data that vary.
The cups are in a gallon 16 cups in a gallon.
The measuring spoons (tablespoon, teaspoon, half-teaspoon or quarter-teaspoon) do home bakers use most frequently.
They use most frequently tablespoon.
On average, how much salt do professional pastry chefs use in a pie crust for one piece of Pie crust.
which has about 120 mg of sodium.
Larger, 17 ounces or 2 cups.
2 cups because FL OZ CUPS
17.00 2.125
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Washington Middle School sold 500 tickets to the annual musical production for Friday night. If the tickets sold for Friday night were only 40 percent of the total tickets sold, how many total tickets were sold for the production?
Answers
Answer:
200
Step-by-step explanation:
500x.4
Answer:
1,250 tickets
Step-by-step explanation:
-6+4q+(-6q) help me with this expression please
Answers
Answer:
-2q - 6
Step-by-step explanation:
Step 1: Rewrite expression
-6 + 4q - 6q
Step 2: Combine like terms
-6 - 2q
Step 3: Rearrange
-2q - 6
Answer:
The like terms are 4q and -6q. Since 4q + (-6q) = -2q the answer is -6 - 2q.
If angle 2 is 45 degrees, what is the measurement of angle 4?
Answers
Answer:
angle 4 = angle 2{opposite angles are equal} =45 degrees
Step-by-step explanation:
Answer:
Step-by-step explanation:
Angle 4 is an exterior angle which corresponds to the remote interior angles of 33 degrees and 75 degrees. Through the remote interior angle theorem, we can add the remote interior angles to get the exterior angle So we simply add 33 and 75 to get 33+75 = 108 If you chose not to use this theorem, then you can find angle three by using the fact that all three angles of the triangle must add to 180 degrees. So, 33+75+(angle 3) = 180 108+(angle 3) = 180 108+(angle 3) - 108 = 180 - 108 angle 3 = 72 degrees Then use the fact that angle 3 and angle 4 are supplementary (angle 3) + (angle 4) = 180 72 + (angle 4) = 180 72 + (angle 4) - 72 = 180 - 72 angle 4 = 108 degrees either way, we get the same answ
i'm so confuzzled, please help
Answers
Step-by-step explanation:
0.5% of w is 12 is what they are asking
0.5% of w = 12. Only the first answer has the equation equal to 12, so the first part is
\(12 = 0.005 \times w\)
Now to solve it, we want to get W alone, we can do that by dividing 0.005 on both sides. Since right now it's being multiplied we must do the opposite
\(w = \frac{12}{0.005} = 2400\)
Answer:
0.5% of w is 12 is what they are asking0.5% of w = 12. Only the first answer has the equation equal to 12, so the first part isNow to solve it, we want to get W alone, we can do that by dividing 0.005 on both sides. Since right now it's being multiplied we must do the opposite
Step-by-step explanation:
What is the value of x?
Answers
Explain: Hope this helps!
1.) In a the heavy weight division boxing match, Mike throws 270 punches in 9 rounds. What is the unit rate of punches per round by Mike?
Answers
i think :)
just divide the punches by the rounds hope this helps
Debra sold t-shirts at a festival. She made $5 for each t-shirt she sold. Her expenses were $22. If she made a profit of $83, how many t-shirts did she sell?
Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 5, 22, and 83. Let x represent the number of t-shirts.
answer options:
_x+_=_
_x-_=_
Answers
Answer:
Step-by-step explanation:
she sold 22
please write a function for the points (1/3,0) (-2 3/4,0) and (0,-5) and explain the steps.
thank you!
Answers
The function for the points are y = -15x - 5
How to determine the functionFrom the information given, we have that;
The points are;
(1/3,0) (-2 3/4,0) and (0,-5)
Using the point-slope form of a linear equation, we have;
y - y₁ = m(x - x₁)
Such that;
m is the slope of the liney - y₁ and (x - x₁) are the pointsUsing (1/3, 0) and (0, -5), we have that the slope is;
m = (0 - (-5))/0 -1/3)
expand the bracket
= 5 / (-1/3)
= -15
Now, take any of the given points and substitute the values
Using (1/3, 0), we get;
y - 0 = -15(x - 1/3).
y = -15x - 5.
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The function for the points solved by (1/3,0) (-2 3/4,0) and (0,-5) solved by point slope form is \(a=-15b-5\)
We have given the points:
(1/3,0) (-2 3/4,0) and (0,-5)
Using the formula of linear equation
\(a-\)\(a_{1}\)\(=x[b-b_{1}]\)
Where we will consider (1/3,0) = \(a-a_{1}\) and (0,-5) = \(b-b_{1}\)
that is 1/3 = \(a\), 0 = \(a_{1}\) and
0 = \(b\), -5 = \(b_{1}\)
\(x\) refers to the slope of line (take any variable)
Now for finding the value of \(x\),
\(x=a-a_{1}/b-b_{1}\)
inserting the values,
\(x=[0-[-5]]/[0-1/3]\\x= -15\)
Substitute the value of \(x\) in the equation
\(a-0=-15[b-1/3]\)
By simplifying the equation, we get
\(a=-15b-5\)
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Please help me with this question! Thank you
Answers
Answer:
Step-by-step explanation:
Well it would be true for f. because all people would want orange juice or lemonade.