What is the explicit formula for the geometric sequence with the recursive formula?
Answers
Answer:
Option A. [tex]a_{n}=(-7)(\frac{1}{3} )^{n-1}[/tex]
Step-by-step explanation:
Recursive formula of the geometric sequence is given as [tex]a_{1}=(-7)[/tex]
and [tex]a_{n}=\frac{1}{3}(a_{n-1})[/tex]
From these formulas it is clear that first term of the sequence a1 = -7
and common ratio of the sequence = [tex]\frac{1}{3}[/tex]
Since explicit formula of any geometric sequence is represented by
[tex]a_{n}=a_{1}(r)^{n-1}[/tex]
Therefore, [tex]a_{n}=(-7)(\frac{1}{3} )^{n-1}[/tex] will be the explicit formula of the given geometric sequence.
Related Questions
Jenny charges for delivering the cakes.
Bob lives 12 miles away.
How much will Jenny charge to deliver the cakes? delivery charges £4 mixed cost + 60p per mile
Answers
To deliver the cakes to Bob, Jenny will charge £11.20.
Explanation:To calculate the delivery charges, we need to find the distance between Jenny's location and Bob's location. Since Bob lives 12 miles away, the delivery distance will be 12 miles. Jenny charges £4 as a mixed cost plus 60p per mile. So, the delivery charge will be £4 + (12 miles * 60p) = £4 + £7.20 = £11.20.
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Which of the following fractions is closest to the decimal 0.35
Answers
1/3
3/5
3/8
5/1/2
You just have to make the division and compare the results>
1 / 3 = 0.333..
3 / 5 = 0.6
3 / 8 = 0.375
5 / 12 = 0.416.....
So which is closest to 0.35? The answer is 1/3
In how many different ways can the curator of a museum arrange five of eight paintings horizontally on the wall?
Answers
There are 56 ways a curator can arrange the paintings.
The requried number of ways that 5 paintings to be chosen is 56 ways.
What are permutation and combination?In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Here,
Total number of paintings = 8
Total number of paintings to be arranged = 5
Number of ways = 8C5
= 8!/[8-5]!5! [nCr = n!/[n-r]!r!]
= 56 ways
Thus, the requried number of ways that 5 paintings to be chosen is 56 ways.
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Simplify . 4y4 4y8 8y4 8y8
Answers
Answer:
B
Step-by-step explanation:
Just did it.
Answer:
b
Step-by-step explanation:
Jody, a statistics major, grows tomatoes in her spare time. she keeps a record of the weight of each tomato she grows. what percentage of all her tomatoes will be within one standard deviation of the mean weight? choose the correct answer below.
a. 50
b. 99.7
c. 95
d. 68
e. 10
Answers
μ = the mean
σ = the standard deviation
If the weights of the tomatoes are normally distributed, then about 68% of the weights will be within one standard deviation from the mean.
That is,
P(μ-σ ≤ x ≤ μ+σ) = 0.68
Answer: c. 68
of the 30 girls who tried out for the lacrosse team at euclid Middle School, 12 were selected. Of the 40 boys who tried out but, 16 were selected. Are the ratios of the numbers of students on the team to the number of students trying out the same for both boys and girls? How do you know?
Answers
16/40 = 2/5
yes the ratio is the same, because they both simplify to 2/5
hope this helps
From a rectangular piece of cardboard having dimensions a × b, where a = 20 inches and b = 70 inches, an open box is to be made by cutting out an identical square of area x2 from each corner and turning up the sides (see the figure). Express the volume V of the box as a function of x.
Answers
The volume of the box as a function of x will be 1400x - 180x² - 4x³.
First and foremost, you should note that the volume of a rectangular prism is given as:
= Length × Width × Height
where,
Length = 70 - 2x
Width = 20 - 2x
Height = x
Volume = Length × Width × Height
Volume = (x)(20 - 2x)(70 - 2x)
Volume = 1400x - 40x² - 140x² + 4x³
Volume = 1400x - 180x² - 4x³
Therefore, the volume of the box as a function of x will be 1400x - 180x² - 4x³.
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A number and it's absolute value are equal. If you subtract 2 from the number, the new number and it's absolute value are not equal. What do you know about the number? What is a possible number that satisfies these conditions?
Answers
The absolute value is the distance away from 0 the number is.
So 1's absolute value would be 1, yet -5's absolute value would be 5.
So the number that's equal to its absolute value is positive, and the one that's not is negative.
So if you subtract 2 from the positive number, it must turn negative.
So 1 is a number that satisfies these conditions.
at a wedding dance couples have new partners nine times during a five minute song how long does one couple dance together
one couple dances toghether for _ of a minute
Answers
Final answer:
To determine how long one couple dances together, divide the total song duration by the number of times partners change plus one. With nine partner changes during a five-minute long song, each couple dances together for 0.5 minutes.
Explanation:
The question involves calculating the amount of time one couple dances together during a wedding dance if couples change partners nine times during a five-minute song. To find the answer, we need to divide the total time of the song by the number of times the partners change.
First, we find out how many times the couples will dance together. If they switch partners nine times, there will be ten different dancing intervals. Next, we divide the total length of the song by the number of intervals:
5 minutes ÷ 10 intervals = 0.5 minutes per interval.
Therefore, one couple dances together for 0.5 of a minute.
If i buy a box of candy for $30 and make $52 selling the candy what is my profit
Answers
You started on a bike trip, riding at a rate of 9 miles per hour. Your friend left one hour later and rode at the rate of 12 miles per hour. How long did it take your friend to catch up with you?
Answers
They need 3 hours to catch.
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary MethodFirst, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
riding at a rate of 9 miles per hour
the friend left at rate of 12 miles per hour
Difference between
=12-9
=3 mph
So, the time they need to take
=9/3
= 3 hours
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Solve the given initial-value problem. give the largest interval i over which the solution is defined. x dy dx + y = 6x + 1, y(1) = 8
Answers
[tex]\dfrac{\mathrm d}{\mathrm dx}(xy)=6x+1[/tex]
[tex]xy=\displaystyle\int(6x+1)\,\mathrm dx[/tex]
[tex]xy=3x^2+x+C[/tex]
Given that [tex]y(1)=8[/tex], we have
[tex]8=3+1+C\implies C=4[/tex]
so that the particular solution is
[tex]xy=3x^2+x+4[/tex]
[tex]y=3x+1+\dfrac4x[/tex]
which is valid as long as [tex]x\neq0[/tex], which in turn suggests the largest interval over which the solution may be valid is [tex](0,\infty)[/tex].
A rational number can be written as the ratio of one blank to another and be represented by a repeating or blank decimal. What are the two vocabulary for this sentence?
Answers
The answer is a rational number is one integer divided by another, and can be represented in either decimal of fraction form. The explanation behind this is visualize you are using long division to divide one number by one more. You divide, and then you acquire a remainder. Then you carry down a zero (multiply by ten) and divide again. Well, there are only so many balances you could perhaps have. For example, for 5, your choices are 0, 1, 2, 3, and 4. Sooner or later, you will replicate a remainder, at which fact you will just keep dividing the same method you did last time you saw that remainder -- and that's the reason why it repeats.
Enfaite je ne comprend pas cet exercice qui peut m'aider c'est deja la rentré et je galère merci de bien vouloir m'aider
Answers
9 680 en facteurs premier donne 9680 = 2⁴ x 5 x 11² ou 4² x 5 x 11²
Donc on peut diviser l'aire de la pizza ( au minimum) avec des carres de 4 cm de cote et au maximum avec des carres de 11 cm de cote:
Donc 9680÷ 4² = 9680 ÷ 16 = 605 carres de 4 cm chacun
et 9680 ÷ 11² = 9680 ÷ 121 = 80 carres de 11 cm chacun
if x equals 3= xequals 4 then use the equation 2x y -6 x equals 18 Z to find the value of y
Answers
"If x equals 3 and z equals 4, find the value of y in the equation: [tex]12xy-6x=18z.[/tex]"
Input the value of the variables we were given:
[tex]12(3)y-6(3)=18(4)[/tex]
Simplify.
[tex]36y-18=72[/tex]
Add 18 to both sides.
[tex](36y-18)+18=(72)+18[/tex]
Simplify.
[tex]36y=90[/tex]
Divide both sides by 36.
[tex](36y)/36=(90)/36[/tex]
Simplify.
[tex]y=5/2[/tex]
[tex]y=2.5[/tex]
The variable, y is equal to 2.5.
Hope this helps.
-Benjamin
What is the quadratic function
Answers
Joe bought 20 ounces of nuts at the store. How much is this in pounds? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answers
If Joe bought 20 ounces of nuts at the store then the nuts in pounds is 1. 25 lb
What is Unit of Measurement?
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Joe bought 20 ounces of nuts at the store.
We have to find in pounds.
As we know that 1 ounce is equal to 0.0625 pounds.
Now we have to convert 20 ounces to pounds.
To do this we have to multiply 20 with 0.0625
20×0.0625
1.25 pounds
20 oz is equal to 1. 25 lb
Hence, the nuts in pounds is 1. 25 lb if Joe bought 20 ounces of nuts at the store.
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In a recent survey, two-thirds of the 234 students in a freshman class said they watch television shows on their computer. Determine the correct arithmetic set up for determining how many students watch television on their computer
Answers
And 234 students were in that survey.
2 / 3 * 234 = 156
Answer: 156 students watch shows on their computer.
'two-thirds of the 234'.
that's all we need to know here. So let's count:
[tex] \frac{2}{3} *234=2*78=156[/tex]
so the answer is simply 156!
What is the absolute difference between 1/2 and 1/3?
Answers
1/2 - 1/3 = 3/6-2/6 = 1/6
absolute value is 1/6
Tyler used 17.04 gallons of gas.Maria used 6.2 times as many gallon of gas as Tyler. How many gallons of gas did Maria use?
Answers
Maria=6.2(T), Maria= 6.2x17.04=105.65 gallons
How do you solve step by step (-10)+14+25+(-16)
Answers
(-10) + 39 + (-16) Change 39 + (-10) to 39 - 10
(-10) + 39 - 16 Subtract 16 from 39
(-10) + 23 Change (-10) + 23 to 23 - 10
23 - 10 Subtract 10 from 23
13
*Remember, you can rearrange expressions like this as long as each number keeps its sign. Notice that (-10) had its negative sign the whole time, even though we moved it around.
what number must you add to complete the square x^2+24x=17
Answers
x² + 24x = 17 (1)
Note that
(x + 12)² = x² + 24x + 144
By adding 144 to the left side of equation (1), it becomes a perfect square.
Therefore
x² + 24x = (x+12)² - 144 (2)
Substitute (2) into (1).
(x + 12)² - 144 = 17
(x + 12)² = 17 +144
(x + 12)² = 161
Answer:
We added 144 to the left side of equation (1) in order to make it a perfect square.
Write an even number between 7 and 16. Draw a picture and then write a sentence to explain why it's an odd number
Answers
Answer:
9, 11, 13 and 15
Step-by-step explanation:
Given numbers,
7 and 16,
In the number line the numbers are arranged in ascending order from left to right,
Thus, the numbers greater than 7 are,
8, 9, 10, 11, 12, 13, 14, 15, 16, 17....
Also, the number less than 16,
.......6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
So, the numbers between 7 and 16,
8, 9, 10, 11, 12, 13, 14, 15
Now, a number with 1, 3, 5 or 7 in the ones place is an odd number.
Hence, the odd number between 7 and 16 are,
9, 11, 13 and 15
0.4 ( 8 - 0.2w ) = -4
Answers
[tex]Subtract[/tex] by the [tex]number [/tex] [tex]3.2 [/tex] to your [tex]sides [/tex]
Like → [tex]-0.08w + 3.2 - 3.2 \\ \\ = 4 - 3.2[/tex]
We get this→ [tex]-0.08w = -7.2 [/tex]
Since the [tex]-0.08 [/tex] goes into both of the number we would have to [tex]divide [/tex] by the decimal [tex]-0.08 [/tex] onto your [tex]sides [/tex]
Like → [tex] \frac{-0.08w}{-0.08} = \frac{-7.2}{-0.08} [/tex]
Now the we got those [tex]few [/tex] [tex]steps [/tex] out of the way we can solve our answer!
[tex] \frac{-0.08w}{-0.08} \\ (CancelOut) \\ \\ \\ \\ \frac{-7.2}{-0.08} \\ (Keep)[/tex]
[tex] \frac{-7.2}{-0.08} = 90 \\ \\ \\ Answer: w = 90 [/tex]
Good luck on your assignment and enjoy your day!
~[tex]MeIsKaitlyn:)[/tex]
At a local school supply store, a highlighter costs $1.25, a ballpoint pen costs $0.80, and a spiral notebook costs $2.75. Explain how you can use the Commutative Property of Addition to find the total cost if three of each item are purchased!
Answers
The addition of all costs using commutative property will be $4.8.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given,
Cost of one highlighter = $1.25
Cost of one ballpoint pen = $0.80
Cost of one spiral notebook = $2.75
The cumulative property states that the resultant of summation or multiplication does change by changing order.
Addition = 1.25 + 0.80 + 2.75
Total cost = $4.8.
Hence"The addition of all costs using commutative property will be $4.8".
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Which equation correctly applies the distributive property?
A. 50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005)
B.−1.2⋅0.57⋅0.5=−1.2⋅0.5⋅0.57
C. (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2)
D. −2.5⋅(4⋅1.045)=(−2.5⋅4)⋅1.045
Answers
hope this helps
You can take out a 0.5 from each expression
Find the average.
11,16,15,22
A.64
B.15
C.17
D.16
Answers
So:
11 + 16 + 15 + 22 = 64
64 / 4 = 16
Your answer is D. 16. Hope this helps!
Multiply or find the special product. (Simplify your answer completely.)
[(x − 8y) + z][(x − 8y) − z]
Answers
[(x − 8y) + z][(x − 8y) − z]
= (x - 8y)² - z²
= x² - 16xy + 64y² - z² ← answer
F is the midpoint EG Find the length EG given that the length FG IS10.9
Answers
that's the answer(dont forget your unit)
evaluate the expression
(4+49) - 4X10
Answers
hope this works