The fifth term of a geometric sequence is 781.25. Each term of the sequence is 1/5 of the value of the following term. Which recursive formula represents the situation?
Answer choices are in the image attached.
Answers
The recursive formula of the geometric sequence is [tex]a_{n} = 5a_{n-1}[/tex] and a1 = 1.25
How to determine the recursive formula?The given parameters are:
Fifth term = 781.25
Term = 1/5 * following term
The second parameter above means that:
[tex]a_n = \frac{1}{5} * a_{n+ 1}[/tex]
Multiply both sides by 5
[tex]a_{n+1} = 5a_n[/tex]
Remove 1 from the terms
[tex]a_{n} = 5a_{n-1}[/tex]
Using the formula [tex]a_n = \frac{1}{5} * a_{n+ 1}[/tex], we have the first term to be:
[tex]a_1 = \frac 15 * a_2[/tex]
[tex]a_2 = \frac 15 * a_3[/tex]
[tex]a_3 = \frac 15 * a_4[/tex]
[tex]a_4 = \frac 15 * a_5 = \frac 15 * 781.25 = 156.25[/tex]
So, we have:
[tex]a_3 = \frac 15 * 156.25 = 31.25[/tex]
[tex]a_2 = \frac 15 * 31.25 = 6.25[/tex]
[tex]a_1 = \frac 15 * 6.25 = 1.25[/tex]
Hence, the recursive formula is [tex]a_{n} = 5a_{n-1}[/tex] and a1 = 1.25
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Answer:
A
Step-by-step explanation:
Related Questions
Help with this application of surface area and volume problem? i will reward brainly, this is 10th grade geometry! Any help appreciated! I am really struggling
Answers
Answer: 20.4
Step-by-step explanation:
A motor boat traveled 18 miles down a river in 2 hours but took 4.5 hours to return upstream. Find the rate of the motor boat in still water and the rate of the current.
Answers
b = speed of the boat in still water
c = speed of the current
when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.
now, going either way the boat travelled the same 18 miles.
[tex]\begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&18&b-c&4.5\\ Downstream&18&b+c&2 \end{array}\hspace{5em} \begin{cases} 18=(b-c)4.5\\\\ 18=(b+c)2 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{18=(b-c)4.5}\implies \cfrac{18}{4.5}=b-c\implies 4=b-c\implies \boxed{4+c=b} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{18=[~(4+c)+c~]2}\implies \cfrac{18}{2}=4+2c\implies 9=4+2c \\\\\\ 5=2c\implies \blacksquare~~ \cfrac{5}{2}=c ~~\blacksquare\hspace{5em}4+\left( \cfrac{5}{2} \right)=b\implies \blacksquare~~ \cfrac{13}{2}=b ~~\blacksquare[/tex]
[tex]x \6 - 1 = x \4 + 1 \2[/tex]
answer. the question pls pls pls pls
Answers
Answer:
-18
Step-by-step explanation:
Hope it helps....................................................
please help me!! i'll give brainliest if it's answered w work !!!! thank u im failing this class
Answers
Answer:
the correct answer is C her puppy weighted 20 pounds
Simplify the following fraction WITHOUT USING A CALCULATOR tan 45°.sin 30-cot45°
Answers
Answer:
tan 45°.sin 30° - cot45° = −(1÷2) = −0.5Step-by-step explanation:
45° Corresponds to (π÷4) which is a remarkable measure
We are all supposed to learn by heart the values of it’s ‘sin’ , ‘cos’ , ‘tan’ and ‘cot’ .
the same apply to 30° (corresponds to (π÷6))
……………………………………………………………
So without a calculator:
tan 45° = 1
cot 45° = 1
sin 30° = 1/2
therefore ,
tan 45°.sin 30° - cot45° = 1 × (1÷2) − 1 = (1÷2) − 1 = −(1÷2) = −0.5
Answer for 20 points :)
Answers
Answer:
sorry this question is do not understand
The function[tex]f(x)=-11sin (\frac{7}{3}x+\frac{1}{6}) - 2[/tex] models the average rate of change in temperature of a substance monitored in an experiment. In the function, x represents the number of minutes since the commencement of the experiment and the temperature of the substance is measured in degrees Fahrenheit.
Over what range of temperatures does the average rate of change in temperature fall?
Answers
Range of temperatures does the average rate of change in temperature fall -13F and 9 F
What is formula for Fahrenheit?The Fahrenheit temperature scale is used in the United States; the Celsius, or centigrade, scale is employed in most other countries and for scientific purposes worldwide. The conversion formula for a temperature that is expressed on the Celsius (°C) scale to its Fahrenheit (°F) representation is: °F = (9/5 × °C) + 32.
Given function:
f(x)= -11 sin(7/3 x+ 1/6) -2
The function will be maximum at
7/3 x +1/6= 3π/2
So, the maximum temperature will be
= -11 sin (3π/2) -2
= 11 -2
=9 F
The function will be minimum at
7/3 x +1/6= π/2
So, the maximum temperature will be
= -11 sin (π/2) -2
= -11 -2
= -13 F
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one lap around a dirt track is 1 /3 of a mile. It takes Bryce 1/9 of an hour to ride one lap.
Answers
Answer:
3 miles/hour.
Step-by-step explanation:
If the question is what is Bryce's average speed over the lap it is:
Distance / time
1/3 / 1/9
= 1/3 * 9
= 9/3
= 3 miles/hour.
The probability of spinning am even number is 40%. What is the probability of not spinning an even number, written as a decimal
Answers
Answer:
That would be 0.6 that means 60 percent.
Answer:
Probability of not spinning an even number is 0.6
Step-by-step explanation:
Total probability is 100 since it represented by %.
Therefore if 40% is the probability of spinning an even number then that of not spinning an even number is simply
100% - 40% = 60%
Expressing 60% as a decimal gives us 0.6
If the first number is increased by 7 and the second number is reduced by 6 times, the sum of these numbers is 29.
If the first number is reduced by 5 and the second number is increased 2 times, the difference between the second and first number is 9.
Find these numbers.
Answers
Answer:
First number = 20
Second number = 12
Explanation:
Let the 1st number be x
Let the 2nd number be y
=====================
Condition 1
[tex]\sf \rightarrow x + 7 + \dfrac{y}{6} = 29[/tex]
[tex]\rightarrow \sf x=-\dfrac{y}{6}+22[/tex]
=====================
Condition 2
[tex]\rightarrow \sf 2y - (x - 5) = 9[/tex]
[tex]\rightarrow \sf x = 2y -4[/tex]
=====================
Substitute equations
[tex]\rightarrow \sf -\dfrac{y}{6}+22 = 2y-4[/tex]
[tex]\rightarrow \sf y=12[/tex]
=====================
Find value of 1st number
[tex]\rightarrow \sf x = 2y - 4[/tex]
[tex]\sf \rightarrow x = 2(12) - 4[/tex]
[tex]\rightarrow \sf x = 20[/tex]
96x 3+(9*8) ÷ 126,980 =?
Answers
Answer:
288.000567018 or [tex]3(32x^{3} +\frac{3.8}{126980})[/tex]
Step-by-step explanation:
hope this helps
pls mark brainliest
2. f(x)=4x+1 and g(x)=x2−4x−5, find (g◦f)(4).
Answers
Answer:
(g · f)(4) = 45
Step-by-step explanation:
f(x)=4x+1
g(x)=x² - 4x- 5
(g · f)(x) = 4(x² - 5) + 1
(g · f)(4) = 4(4² - 5) + 1
Following pemdas
(g · f)(4) = 4(16 - 5) + 1
(g · f)(4) = 4(11) + 1
(g · f)(4) = 44 + 1
(g · f)(4) = 45
Which expression is equivalent to -15-(-8)
Answers
Answer:
the answer is 15-8
I hope this helps you
Answer:
-15+8
Step-by-step explanation:
How do negative exponents impact the value of a number?
Answers
Answer:
A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ. For example, 2⁻⁴ = 1 / (2⁴) = 1/16.
You collect a random sample of size n from a population and calculate a 95% confidence
with an increased margin of error?
O Use a 98% confidence level.
O Use a 90% confidence level.
O increase the sample size.
O Use the same confidence level, but compute the interval n times. Approximately 5% 0
© Nothing can guarantee that you will obtain a larger margin of error. You can only say
In a recent telephone survey, 5,000 randomly selected teenagers were asked to cite their primary social network site. Six of 10 teenagers said they use Mybook as
their primary social network site. A 95% confidence interval to estimate the true proportion of teenagers who use Mybook as their primary social network site is found to
be (0.2964, 0.9036). Which of the following is a correct interpretation of the confidence level?
O Ninety-five percent of all samples of this size would yield a confidence interval of (0.2964, 0.9036).
O There is a 95% chance that the true proportion of teenagers who use Mybook as their primary social network site is in the interval (0.2964, 0.9036).
O Ninety-five percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who use Mybook as their primary
social network site
O Ninety-five percent of all the samples of size 5,000 lie in the confidence interval (0.2964, 0.9036).
O There is a 95% chance that randomly selected teenagers will be part of the 60% who use Mybook as their primary social network site.
(05.04 MC)
Leon wants to estimate the proportion of the seniors at his high school who like to watch football. He interviews a simple random sample of 50 of the 200 seniors on
campus. He finds that 32 like to watch football. Is the random condition for finding confidence intervals met? Explain.
O Yes, the random condition for finding confidence intervals is met because np = 32 and n(1 - P) = 18, both of which are greater than 10
O Yes, the random condition for finding confidence intervals is met because the sample size is greater than 30.
O No, the random condition for finding confidence intervals is not met because np = 32 and n(1 - p) = 18, both of which are less than 100
O No, the random condition for finding confidence intervals is not met because the sample is not at least 50% of the population
O Yes, the random condition for finding confidence intervals is met because the sample is a simple random sample.
Cilantro tastes like soap to some people. This soap taste is inherited through the olfactory receptor gene OR6A2. About 14% of the population has this gene. You wa
to estimate the proportion of Americans who have this gene. How large a sample must you test, with a 3% margin of error and 95% confidence, to estimate the
proportion of people who carry the OR6A2 gene?
O 514 people
O 134 people
O 17.689 people
O 35 people
01.028 people
The faculty members at McAdenville High School want to determine whether there are enough students to have a Winter Formal. Sixty-three of the 150 students
surveyed said they would attend the Winter Formal. Construct and interpret a 99% confidence interval for p.
O The 99% confidence interval is (0.3162, 0.5238). We are 99% confident the true proportion of students attending the Winter Formal is between 31 62% and
52.38%.
© The 99% confidence interval is (0.3162, 0.5238). There is a 99% chance that a randomly selected student who will attend the Winter Formal lies between
31.62% and 52.38%
O The 99% confidence interval is (0.3162, 0.5238). Ninety-nine percent of all samples of this size will yield a confidence interval of (0.3162, 0.5238).
O The 99% confidence interval is (0.4762, 0.6838). We are 99% confident that the true proportion of students attending the Winter Formal is between 47 62%
and 68.38%
O The 99% confidence interval is (0. 4762, 0.6838). Ninety-nine percent of all samples of this size will yield a confidence interval of (0.4762, 0.6838)
PLEASE HELP ASAP, please don’t waste my time if you don’t know what your talking about THANK YOU GUYSSS
Answers
A strategy which would produce a new confidence interval with an increased margin of error is to: A. use a 98% confidence level.
What is a confidence interval?A confidence interval simply refers to a range of estimated values which defines the probability that a population parameter will lie within it.
How to calculate the margin of error?Mathematically, a margin of error is calculated by using this formula:
[tex]MOE_{\gamma}=Z_{\gamma} \times \sqrt{\frac{\sigma^2}{n} }[/tex]
From the above formula, we can deduce that the margin of error is directly proportional to the critical value and inversely proportional to the square root of sample size.
This ultimately implies that, increasing the confidence level from 95% to 98% would increase the critical value and by extension the margin of error and vice-versa.
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Cube Root Values
What two whole numbers does 81 lie between
Answers
Answer:
between 4 and 5
Step-by-step explanation:
consider perfect cubes either side of 81 , that is
64 < 81 < 125 , then
[tex]\sqrt[3]{64}[/tex] < [tex]\sqrt[3]{81}[/tex] < [tex]\sqrt[3]{125}[/tex] , that is
4 < [tex]\sqrt[3]{81}[/tex] < 5
Trigonometric ratio
adjacent= 12 cm
angle= 22°
find the opposite side by using tan.
Answers
The opposite side of the right angle triangle by using Tan.
Solution:[tex]tan \: 22 = \frac{x}{12} [/tex]
[tex]x = 12 \times tan \: 22[/tex]
[tex]x = 4.8 \: cm[/tex]
Therefore, the opposite side of the right angle triangle is 4.8 centimeters
x/12
x= 12*tan 22
x= 4.8 cm
hope this helps
Guests at a wedding have an appetizer
choice of soup or a salad, an entrée choice
of chicken, steak, or vegetarian, then a
dessert choice of vanilla or chocolate cake.
How many different meals are possible?
Answers
3421880 number of the different meals are possible.
What is the combination?The arrangement of the different things or numbers in the number of the ways is called as the combination.
It is given that:-
Number of appetizers is 7, the number of entres is 10, and that there's 4 choices of desserts.
So let's take each course by itself. You can choose 1 of 7 appetizers. So we have n = 7 After that, you chose an entre,
so the number of possible meals to this point is
n = 7 x 10 = 70
Finally, you finish off with a dessert, so the number of meals is:
n = 70 x 4 = 280
Therefore the number of possible meals you can have is 280. Note: If the values of 77, 1010 and 44 aren't errors, but are actually correct, then the number of meals is
n = 77 x 1010 x 44 = 3421880
Therefore 3421880 different meals are possible.
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2. What is the new correction equation using the Equal Values Method for the following system below?
y=2x+1
y = 6-3x
Answers
Answer:
new equation: 2x +1 = 6 -3x
solution: (x, y) = (1, 3)
Step-by-step explanation:
The Equal Values Method of solving a system of equations has you equate the two expressions that are equal to the same variable or expression. Here, we have two expressions that are equal to y.
equationThe next step is to set them equal to each other:
2x +1 = 6 -3x
__
solutionThis equation can be solved by adding 3x -1 to both sides to get ...
5x = 5
Then dividing both sides by 5 gives ...
x = 1
Substituting into either expression for y gives its value:
y = 2x +1 = 2(1) +1 = 3
The solution to the system is (x, y) = (1, 3).
Drag numbers to the table so it shows a proportional relationship between x and y.
PLEASE HELP
Answers
Answer:
4 box: 9
5 box:4.5
6 box: 27
Step-by-step explanation:
Do 3/.5= 6 so multiply the numbers by 6
1.5•6=9
4.5•6=27
Hope this helps! ;-)
Please awnser last question if correct we can do thisss
Answers
Answer:
B = (8,2)
C = (8,9)
D = (5,4)
Step-by-step explanation:
Hope this helps!
Answer:
Point B: (-8,2) Point C: (-8,9) Point D: (-5,4)
Step-by-step explanation:
Since you are reflecting over the y-axis, the numbers in the coordinates will be the same but they will all have a negative "x" value instead of both numbers in the coordinate being positive.
Point B: (8,2) --> (-8,2)
Point C: (8,9) --> (-8,9)
Point D: (5,4) --> (-5,4)
4. Which of the following is a true statement?
A. -4(2x - 3) = -8x - 12
B.-7(4x - 8) = -28x + 56
=
C. 5(3x + 6) = 15x + 6
D. 10-2(x + 5) = -2x + 20
Answers
Step-by-Step Explanation:
=> -7(4x - 8) = -28x + 56
On opening the brackets on L.H.S,
= -28x + 56 = -28x + 56
=> L.H.S = R.H.S
Therefore this is a True Statement
is 2.06532 rational or irrational?
Answers
Answer:
irrational
Step-by-step explanation:
irrational because it has decimals at the end.
Since we can write the given decimal number into fractional form therefore it is a rational number.
Use the concept of decimals defined as:
Every digit in a number has a place value in mathematics. The value a digit in a number represents based on where it is in the number is known as place value.
The given number is:
2.06532
The number 2.06532 is rational because it can be expressed as a fraction of two integers.
In this case,
It can be written as the fraction 206532/100000.
Hence,
The given number is a rational number.
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Which is the graph of f(x) = x^2- 2x + 3?
Answers
Answer:
you didn't give a picture bestie but it'll be kind of money U and it should be up 3 on the graph
How do I look at the recently posted questions? i'm lost and I want to answer some questions but I forgot how to go to the section. Send help please.
Answers
Tap it and all the recently posted questions appear.
There should be q icon that says give answer, to find new questions in that section refresh the page
A rice field in the shape of a parallelogram is 300 m long. The perpendicular distance between the base and its opposite side is 7. What is asked for in the problem? 120 m. What is its area? 8. What facts are given? 9. What is the formula to solve the problem? 10. What is the complete answer?
Answers
Question : A rice field in the shape of a parallelogram is 300 m long. The perpendicular distance between the base and its opposite side is 120m . Find area .
Answer36000 sq. m
SolutionGiven :
parallelogram is 300 m long and distance between base and its opposite side is 120m* .
Length = 300 m
Perpendicular height = 120 m
Formula used :Area of parallelogram = Length × Perpendicular height.
=> 300 × 120
=> 36000 sq. m
_____________Parallelogram is a type of quadrilateral whose opposite sides are equal .A point is plotted on the number line at 4 3/5 . A second point is plotted at −3 3/4 .
What is the length of a line segment joining these points?
Enter your answer as a simplified mixed number in the box.
Answers
Answer:
8 7/20
Step-by-step explanation:
Converting both numbers to improper fractions :
4 3/5
⇒ (4 x 5/5) + 3/5
⇒ 20/5 + 3/5
⇒ 23/5
-3 3/4
⇒ - (3 x 4/4 + 3/4)
⇒ - (12/4 + 3/4)
⇒ -15/4
Take the LCM as 20 and convert :
23/5
⇒ 23/5 x 4/4
⇒ 92/20
-15/4
⇒ -15/4 x 5/5
⇒ -75/20
Now find the difference :
⇒ 92/20 - (-75/20)
⇒ 92/20 + 75/20
⇒ 92 + 75 / 20
⇒ 167/20
Now convert into a mixed number :
⇒ 167/20
⇒ 8 7/20
Find the difference
4-3/5-(-3-3/4)23/5+15/44(23)+5(15)/2092+75/20167/208-7/201
Select the correct answer.
Which function defines (f + g)(),
f(t) = ln(2x) – 15
g(x) = 3 sin(I) – 7
=
OA. (f + 9) () = ln(2x) + 3 sin(x) + 22
3a )
OB
B. (f + g)() = ln(2x) + sin(o) – 66
OC. (f + 3)(0) = ln(2x) + 3 sin(a) – 22
(
In
D. ( + g)(x) = ln(2x) – 3 sin(x) = 8
Reset
Next
Answers
The addition of the functions f(x) and g(x) will be ln (2x) + 3 sin(x) – 22. Then the correct option is C.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The functions are given below.
f(x) = ln (2x) – 15
g(x) = 3 sin(x) – 7
Then the addition of the function will be
(f + g)(x) = f(x) + g(x)
(f + g)(x) = ln (2x) – 15 + 3 sin(x) – 7
(f + g)(x) = ln (2x) + 3 sin(x) – 22
Then the correct option is C.
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Answer:
See photo
Step-by-step explanation:
Plato/Edmentum
A cone has a volume of 37.68cm3. If the height of the cone is 9cm what is the radius of the cone's
base?
cm
Radius:
(Use 3.14)
Answers
Answer:
[tex]2cm[/tex]
Step-by-step explanation:
Volume of a cone= [tex]\pi r^2\frac{h}{3}[/tex]
Substitute: [tex]37.68cm^3=\pi r^2(\frac{9}{3})[/tex]
[tex]37.68cm^3=\pi r^2(3)[/tex]
[tex]37.68cm^3=\pi r^2(3)[/tex] Divide by 3
[tex]12.56cm=\pi r^2[/tex] Divide by pi
[tex]4cm=r^2[/tex]
[tex]r=\sqrt{4}[/tex]
[tex]r=2[/tex]
PLEASE HELP ME IF YOU DO you will get the most loyal friend and honest and nicest
Answers
Answer:
Below:
Step-by-step explanation:
1. 2 15/28
2. 2 7/10
3. 5/6
4. 1 5/12
5. 2 1/12