Which is a recursive formula for this geometric sequence?
-18
, -14
, -12
, -1, . . .
Answers
The recursive formula for the geometric sequence is given as follows:
\(a_1 = -\frac{1}{8}\)\(a_n = 2a_{n - 1}\)What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The first term of the sequence is given as follows:
\(a_1 = -\frac{1}{8}\)
Each term is the previous term multiplied by two, hence the common ratio is given as follows:
q = 2.
Then each term is the previous term multiplied by two, and the recursive rule is given as follows:
\(a_n = 2a_{n - 1}\)
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Related Questions
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
A) 1/5 + 3/10
B) 7/8 - 1/4
Work out then simplify
Answers
Answer:
please follow me and take thanks
35 POINTS WILL MARK BRAINLIEST!!!
Please solve it from the picture below!!
Answers
Good luck!!!
If the opposite of g(x) is –g(x),
then –g(x) =
Answers
Answer:
g(x) not negitive
Step-by-step explanation:
List the first 5 terms of the geometric sequence with a₁ = -6 and r= -2.
Answers
Answer:
See below
Step-by-step explanation:
-6
times -2
12
times -2
-24
times -2
48
times -2
- 96
You are installing a rectangular pool in your backyard. The pool measures 24 feet by 16 feet. You also would like to build a concrete walkway around the pool. You have allocated 560 ft? of your backyard for both the pool and the walkway around it. How wide should you make the walkway?
Answers
Answer:
The walkway should be 2ft wide.
Step-by-step explanation:
Let x be the width of the walkway surrounding the pool.
The area including the pool is 560ft².
Let's solve for the value of x.
The length plus twice the width of the pool is multiplied by the width plus twice the width of the pool. This makes up the whole area.
A = lw
560 = (24 + 2x)(16 + 2x)
560 = 384 + 48x + 32x + 4x²
4x² + 80x + 384 - 560 = 0
4x² + 80x - 176 = 0
Divide the whole equation by 4
x² + 20x - 44 = 0
(x + 22)(x -2) = 0
x = -22; x = 2
Since we are dealing with dimensions, take the one with the positive value.
x = 2ft
Let's check
560ft² = (24ft + 2x)(16ft + 2x)
560ft² = (24ft + 2(2ft)) (16ft + 2(2ft))
560ft² = (24ft + 4ft)(16ft + 4ft)
560ft² = (28ft)(20ft)
560ft² = 560ft² ✔
Solve the system of equations using the substitution or elimination method.
y = 4x - 7
4x + 2y = -2
.
Show your work
Correct x and y
Answers
The solution to the system of equations is x = 1 and y = -3.
To solve the system of equations using the substitution or elimination method, let's start with the substitution method.
Given equations:
y = 4x - 7
4x + 2y = -2
We'll solve equation 1) for y and substitute it into equation 2):
Substituting y from equation 1) into equation 2):
4x + 2(4x - 7) = -2
4x + 8x - 14 = -2
12x - 14 = -2
Now, we'll solve this equation for x:
12x = -2 + 14
12x = 12
x = 12/12
x = 1
Now that we have the value of x, we can substitute it back into equation 1) to find y:
y = 4(1) - 7
y = 4 - 7
y = -3
Therefore, the solution to the system of equations is x = 1 and y = -3.
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Explain how you use a net to find the surface area of a prism.
Answers
Answer:
Hello, Here is your answer.
Finding the areas of each of the rectangles and squares of the net of a rectangular prism and adding up those areas gives the surface area or total surface area of the prism. For example, if the length of one side of the cube 4 units then the area of one its face is 4 × 4 = 16 square units.
Answer:
Step-by-step explanation:
By drawing a net, you can see each face of the prism. You can find the areas of each face and then add them together to find the total surface area.
this is my warmup can you please help me out with it
Answers
Answer:,
the answer is (4,2)
Step-by-step explanation:
is you look at the 2 equations and plug in the points where the lines intercets you would get the answer soo examples
4+2=6
the first one checks out
the second one
4+(2*2)=8
so the parinthises go first 2 times 2 = 4 plus 4 = 8
PLEASE HELP !
You go to a store to buy sneakers. You have a coupon for $15 off. Write a function f(d) that models this discount on an item that costs d dollars
Answers
The function f(d) that models this discount on an item that costs d dollars is f(d) = d - 15
How to write a function f(d) that models this discount on an item that costs d dollars?The given parameters are
Discount = $15
Value = d
The function f(d) that models this discount on an item that costs d dollars is
f(d) = Value - Discount
This gives
f(d) = d - 15
Hence, the function f(d) that models this discount on an item that costs d dollars is f(d) = d - 15
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find the gradient of y=x³ + 6, using the
a) first principle formula
b) general gradient function formula
Answers
Answer:
B Hope this helps you out!
PLEASE HELP
For the infinite geometric series below, identify whether the series is convergent or divergent. If convergent, find the number where the sum converges
5 + 10 + 20 +.....
Answers
The series 5 + 10 + 20 +..... is divergent
How to find if the series diverges or converges?The sequence is given as:
5 + 10 + 20 +.....
The above sequence has the following parameters
First term, a = 5
Common ratio, r = 2
As a general rule:
If the common ratio of a geometric series is between -1 and +1, then the series is convergent.
Otherwise, it is divergent
The above means that the series is divergent
This is so because the common ratio is outside the range -1 to +1
Hence, the series 5 + 10 + 20 +..... is divergent
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0,0,0,2,3,4,7,7,8,12,14,15,15,16,18 quartile 1 = quartile 2= interquartile range=
Answers
The IQR describes the middle 50% of values when ordered from lowest to highest.
Given a dataset, to find the interquartile range first find the median (middle value) of the lower(first quartile) and upper half of the data(third quartile), and then find their difference.
Our dataset is
\(\lbrace0,0,0,2,3,4,7,7,8,12,14,15,15,16,18\rbrace\)We have 15 elements on this dataset. The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. Since we have 15 elements, the middle element is the 8th element(this way we have 7 elements below and 7 elements above our median). The 7 elements below are
\(\lbrace0,0,0,2,3,4,7\rbrace\)The median of those points are the first quartile. The median of this dataset is 2.
For the upper half of the data, we have
\(\lbrace8,12,14,15,15,16,18\rbrace\)The median is 15, therefore, the third quartile is 15.
The interquartile range is the difference between those values.
\(15-2=13\)The IQR of our dataset is 13.
QUESTION 1 Determine the general solution of: 2 sin x. cos x = COS X
Answers
Starting with the given equation: 2 sin x cos x = cos x
By dividing both sides by cos x, we may simplify: 2 sin x = 1
Dividing both sides by 2:
sin x = 1/2
The values of x that fulfil sin x = 1/2 must now be found, and they are:
x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.
Therefore, the general solution is:
x = π/6 + 2πn or
x = 5π/6 + 2πn, where n is any integer.
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If the tree grows an additional 10 feet, what is the new angle of
elevation from the point 25 feet from the base of the tree to the top of the tree?
A) 42.30
B) 47.1°
C) 49.8°
D) 54.6
Answers
Answer:
B) 47.1°
Step-by-step explanation:
The tangent relation is useful here.
Tan = Opposite/Adjacent
The original height of the tree is the side of the triangle that is opposite the angle of elevation:
Opposite = Adjacent × Tan
original height = (25 ft)×tan(34°) ≈ 16.863 ft
__
After growing an additional 10 ft, the tree has a height of ...
16.863 ft + 10 ft = 26.863 ft
Then the angle of elevation is found from ...
tan(angle) = (26.863 ft)/(25 ft) ≈ 1.07451
angle of elevation = arctan(1.07451) ≈ 47.057°
The angle of elevation to the top of the tree is about 47.1°.
In the decimal 3.0874, what numeral is in the thousandths place?
A: 0
B: 4
C: 8
D: 7
Answers
Answer:
7
Step-by-step explanation:
:)
Answer:
D: 7
Explanation: after the decimal, its tenths, hundredths, thousandths
I need this to be explained
Answers
Answer:
Step-by-step explanation:
So, the perimeter of a square means the total length or the sum of it's lenghts(four equal lengths )which means the formula for the perimeter is 4*l where l is a lenght
The area means the total area inside the square so jut imagine taking the length as a line, copy pasting it till the square turns black, that's the area.
The formula for the area is l*l which means a length multiplied by itself as I said above.
Calculate the answers by yourself.
The table below shows Amadou's earnings on the job.How long does it take him to make \$255.45$255.45?
Answers
The time taken to make an amount of $255.45 is 9.75 hours
How to determine the time taken to make the amount?From the table, we have the following representations:
x=Time
y = Earnings
Using a point from the table, we have
x = 3 and y = 78.60
Express as ratio
This gives
x : y = 3 : 78.60
When the earning is $255.45, we have
x : 255.45 = 3 : 78.60
Express as fraction
x/255.45 = 3/78.60
So, we have
x = 255.45 * 3/78.60
Evaluate
x = 9.75
Hence, it will take 9.75 hours
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What is the simplified form of the inequality below? S - 7 < 3
Answers
Answer:
s-7<3
in order to find the value adding 7 on both sides
s-7+7<3+7
s<10
Step-by-step explanation:
i hope this will help you :)
Answer:
s-7<3
in order to find the value adding 7 on both sides
s-7+7<3+7
s<10
Step-by-step explanation:
Jared writes a multiplication expression with eight rational factors. Half of the factors are positive and half are negative.
Is the product positive or negative? Why?
Answers
The multiplication expression with eight rational factors are ''positive''.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
Jared writes a multiplication expression with eight rational factors. Half of the factors are positive and half are negative.
Since, Multiplication of four positive numbers are always gives a positive number and multiplication of four negative numbers are always gives a positive number.
Hence, The multiplication expression with eight rational factors are positive.
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Ver en español
Pam, the CEO of Zettabyte Tek, set up a $750,000 education fund. She wants to give each employee who takes a computer security class a $350 reimbursement toward the cost of the class. You can use a function to describe the amount of money left in the fund after x employees receive the reimbursement.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x.
Answers
The formula for this linear function is f(x) = mx + b, where m is the slope (in this example, -350), and b is indeed the y-intercept (750,000 in this case).
What does a simple equation represent?An equation expressing the connection between the expressions on either side of a sign. Normally, it has an equal sign and just one variable. such as: 2x - 4 is equal to 2. The variable x is present in the example above.
Workers who complete the computer security course will each receive a reimbursement of $350.
We deduct $350x from of the initial $750,000 to determine how much money will remain inside the education fund once x employee gets the reimbursement.
Thus, f(x) = 750,000 - 350x is the equation again for function that describes that amount of money still in the fund when x employees receive the refund.
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what is 13,899 rounding to the thousands
Answers
Answer: 14,000
...............................
Answer:
Step-by-step explanation:
round 13,899 to the nearest thousands which would be
14,000
If UVWX is a parallelogram, what is the value of y?
Answers
Answer:
y=39
Step-by-step explanation:
according to question;
13=1/3×y
or;13/y=1/3
or;13×3/y=1
or;39/y=1
or;39=y
PLZ HELP
You decide to deposit $5000 in a savings account that earns 3% interest. How much money will you have in 10 years?
Answers
Answer:
$6500
Step-by-step explanation:
First you find 3% of 5,000. You get 150. Then you would multiply 150 by 10 since it was in the bank for 10 years. You get 1500. Then you add 5000 and 1500 to get 6500.
Find all the zeros of f(x) = 2x^4 − 5x^3 − 5x^2 + 20x − 12
Answers
Answer:
x=-2 x=2 x = 1/2 x=3
Step-by-step explanation:
f(x) = 2x^4 − 5x^3 − 5x^2 + 20x − 12
Graph
We see that there is a zero at -2
Using synthetic division
-2 2 -5 -5 20 -12
-4 18 -26 12
------------------------------
2 -9 13 -6 0
This gives us ( x+2) ( 2x^3 -9x^2 +13x -6)
We see that there is a zero at 2
Using synthetic division ( 2x^3 -9x^2 +13x -6)
2 2 -9 13 -6
4 -10 6
------------------------------
2 -5 3 0
This gives us ( x+2) ( x-2) ( 2x^2 -5x+3)
We can factor ( 2x^2 -5x+3)
( x+2) ( x-2) ( 2x -1) ( x-3)
Using the zero product property
( x+2)=0 ( x-2)=0 ( 2x -1)=0 ( x-3)=0
x=-2 x=2 x = 1/2 x=3
QUICK! 40 points. Consider this cone with the diameter measure of 17 inches.
A cone with diameter 17 inches and slant height of 22 inches.
What is the surface area of the cone?
SA = Pir2 + Pirl
A. 204Pi in.2
B. 259.25Pi in.2
C. 446.25Pi in.2
D. 663Pi in.2
Answers
259.25π in² is the surface area of the cone
The surface area of a cone can be calculated using the formula SA = πr² + πrl
where r is the radius and l is the slant height.
Given that the diameter is 17 inches, the radius (r) is half of the diameter, which is 17/2 = 8.5 inches.
The slant height (l) is given as 22 inches.
Substituting these values into the formula:
Surface Area = π(8.5)² + π(8.5)(22)
= 72.25π + 187π
= 259.25π
Therefore, the surface area of the cone is 259.25π in²
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
Answers
The standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.
How to illustrate the information?From the information given, it was stated that the students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury.
Based on the information given, it should be noted that the appropriate thing to do is to find the z score for the 75th percentile.
This will be looked up in the distribution table. In this case, the value is 0.674. Therefore, standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.
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List the terms of the polynomial. Give the coefficient of the second term. -4y5 + 6x4 +9w³ - 4w - 1 Separate terms using commas. Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c . Make sure your variables match those in the question. Terms Coefficient
Answers
The coefficient of the second term, 6x⁴, is 6.
The terms of the polynomial are:
-4y⁵, 6x⁴, 9w³, -4w, -1
The coefficient of the second term, which is 6x⁴, we look at the number in front of the variable term.
The coefficient is 6.
Therefore, the list of terms is:
-4y⁵, 6x⁴, 9w³, -4w, -1
Each term represents a separate component of the polynomial, where the variable is raised to a certain power and multiplied by its coefficient.
The coefficients indicate the scalar value by which each term is multiplied.
The polynomial's terms are -4y5, 6x4, 9w3, -4w, and -1.
Looking at the number in front of the variable term, we can determine the second term's coefficient, which is 6x4.
There is a 6 coefficient.
As a result, the terms are as follows: -4y5, 6x4, 9w3, -4w, and -1.
Each term represents a different part of the polynomial, where the variable is multiplied by its coefficient and raised to a given power.
The scalar value by which each phrase is multiplied is shown by the coefficients.
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Richard took his time looking around for a tuxedo to wear to his sister's wedding. He found that buying a tuxedo would cost the same as renting one and he would own it. He bought a tuxedo for $250. He wore the tuxedo to his sister's wedding and when he was asked to be the "padrino" for his best friend's baby, he wore it again. What is the cost per wear of the tuxedo?
Answers
$125 per wear
1) Gathering the data
Bought a Tuxedo for $250
2) As Richard has used his Tuxedo 2 times then we can write this ratio on the numerator the price, and on the denominator how many times has he wore that.
\(\frac{250}{2}=125\)3) So the cost per wear, was $125 per wear so far.
what is relative intrest
Answers
Relative interest refers to the comparison of interest rates between different financial instruments or investment opportunities. It allows individuals or investors to assess and evaluate the attractiveness of various options based on their potential returns.
1. Understand the basic concept: Interest is the cost of borrowing money or the return earned on invested funds. Relative interest involves comparing the interest rates of different financial instruments or investments to determine which one offers a more favorable return.
2. Identify the investment options: Start by identifying the different investment opportunities or financial instruments available. These can include savings accounts, certificates of deposit (CDs), bonds, stocks, or other investment vehicles.
3. Research interest rates: Research and gather information about the current interest rates offered by each investment option. This information can usually be found on financial websites, through financial institutions, or by consulting with a financial advisor.
4. Compare interest rates: Once you have the interest rates for each investment option, compare them side by side. Look for the differences in rates and identify which options offer higher or lower returns.
5. Assess risk and return: Consider the level of risk associated with each investment option. Higher returns often come with higher risk, so it's essential to evaluate the risk-reward tradeoff.
6. Make an informed decision: Based on the comparison of interest rates and the risk-reward assessment, make an informed decision on which investment option aligns with your financial goals and risk tolerance.
Always remember to consider your financial goals, risk tolerance, and consult with a financial advisor if needed.
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