Enter a recursive rule for the geometric sequence. 4, −16, 64, −256, ...
Answers
Answer:
The recursive rule is an = (-4) · an-1
Step-by-step explanation:
* Lets explain recursive formula for a geometric sequence:
1. Determine if the sequence is geometric (Do you multiply, or divide, the same amount from one term to the next?)
2. Find the common ratio. (The number you multiply or divide.)
3. Create a recursive formula by stating the first term, and then stating the formula to be the common ratio times the previous term.
# a1 = first term;
# an= r • an-1
- Where:
a1 = the first term in the sequence
an = the nth term in the sequence
an-1 = the term before the nth term
n = the term number
r = the common ratio
Ex: {3, 6, 12, 24, 48, 96, ...}
first term = 3, common ratio = 2
The recursive formula an = 2 · an-1
* In our problem:
- a1 = 4
- r = -16/4 = -4
- The recursive rule is
# an = (-4) · an-1
Answer:
here is the correct answer.
Step-by-step explanation:
Related Questions
Help ASAP PLEASE!!! match the term with the appropriate definition.
Answers
2) 5x+1>=11→5x+1-1>=11-1→5x>=10→5x/5>=10/5→x>=2: Option J. x>=2, closed dot at 2 and shaded to the right
3) x-7>-4→x-7+7>-4+7→x>3: Option H. x>3, open dot at 3 and shaded to the right
4) -2x<6→(-1/2)(-2x<6)→(-1/2)(-2x)>(-1/2)(6)→x>-3: Option G. x>-3, open dot at -3 and shaded to the right
5) 4<-4x→(-1/4)(4<-4x)→(-1/4)(4)>(-1/4)(-4x)→-1>x→x<-1: Option B. x<-1, open dot at -1 and shaded to the left
6) -2x+3<-7→-2x+3-3<-7-3→-2x<-10→(-1/2)(-2x<-10)→
(-1/2)(-2x)>(-1/2)(-10)→x>5: Option A. x>5, open dot at 5 and shaded to the right
7) 2x<=6→2x/2<=6/2→x<=3: Option I. x<=3, closed dot at 3 and shaded to the left
8) 3(x+4)>8x-6→3x+12>8x-6→3x+12-3x+6>8x-6-3x+6→18>5x→
18/5>5x/5→18/5>x→x<18/5: Option E. x<18/5, open dot at 18/5 and shaded to the left
9) -3x+4<-x+2→-3x+4+3x-2<-x+2+3x-2→2<2x→2x>2→2x/2>2/2→x>1: Option C. x>1, open dot at 1 and shaded to the right
10) -2(x-4)>5-(x+2)→-2x+8>5-x-2→-2x+8>3-x→-2x+8+2x-3>3-x+2x-3→
5>x→x<5: Option D. x<5, open dot at 5 and shaded to the left
The table shows the number of boys and girls that have black, blonde, brown, or red hair color. What is the probability that a student is a boy with red hair? (round to nearest hundredth)
Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
Answers
the probability that the student is a boy with red hair is 2/40 = 0.05.
Answer:
0.05
Step-by-step explanation:
Given :
Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
Solution :
Since ware required to find the probability that a student is a boy with red hair.
Total no. of boys with red hair = 2
Total no. of students = 4+4+10+2+5+6+8+1=40
Thus the probability that a student is a boy with red hair = [tex]\frac{\text{No. of boys with red hair }}{\text{total no. of students }}[/tex]
⇒[tex]\frac{2}{40}[/tex]
⇒[tex]\frac{1}{20}[/tex]
⇒[tex]0.05[/tex]
Hence the probability that a student is a boy with red hair is 0.05
Unsaved If you are studying the effects of UV rays on eyesight and you group 10 people together and make them wear sunglasses for 10 weeks and see if their eyesight is affected and then take another group and do not give them sunglasses and test their vision after 10 weeks, what is the treatment ? note this is not an ethical study.
sunglasses.
10 weeks.
eyesight.
vision test.
Answers
In the given example, the experimenter make 10 people wear sunglasses and check their eyesight after 10 weeks. To another group he does not give sunglasses and check their eyesight after 10 weeks.
So, sunglasses are such a factor which are under the control of experimenter. So the treatment in this case is sunglasses.
Hence 1st option is the correct answer.
Answer:
Sunglasses
Step-by-step explanation:
What is the area of sector GPH?
Answers
The area of the shaded area = (40/360) * pi r^2
r = 9 cm
Area of the shaded area = 1/9 * 3.14 * 9^2
Area of the shaded area = 3.14 * 9
Area of the shaded area = 28.26
Notice one of the 9s disappeared. Where did it go?
You could begin the problem by writing out 9^2
Area = 1/9 * 3.14 * 9 * 9 Notice that 1/9 will cancel out 1 of the nines.
28.26 yds = Shaded area.
The area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\).[/tex]
To find the area of sector GPH, we use the formula for the area of a sector of a circle, which is given by [tex]\(\frac{\theta}{360^\circ} \times \pi r^2\)[/tex], where [tex]\(\theta\)[/tex] is the central angle of the sector in degrees, and [tex]\(r\)[/tex] is the radius of the circle.
Given that the central angle of sector GPH is [tex]\(90^\circ\) (or \(\frac{\pi}{2}\)[/tex] radians, since[tex]\(180^\circ\) is \(\pi\) radians)[/tex], and the radius [tex]\(r\)[/tex] is unspecified, we can express the area of the sector in terms of [tex]\(r\).[/tex]
Using the formula for the area of a sector:
[tex]\[ \text{Area of sector GPH} = \frac{\theta}{360^\circ} \times \pi r^2 \][/tex]
Substituting [tex]\(\theta = 90^\circ\):[/tex]
[tex]\[ \text{Area of sector GPH} = \frac{90^\circ}{360^\circ} \times \pi r^2 \][/tex]
Simplifying the fraction:
[tex]\[ \text{Area of sector GPH} = \frac{1}{4} \times \pi r^2 \][/tex]
So, the area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\)[/tex], which is one-fourth of the area of the entire circle. This makes sense because the sector represents a quarter of the circle's area due to its [tex]\(90^\circ\)[/tex] central angle.
BRAINLIEST!!!
Which statement about a dilation with a scale factor of 3 is true?
Answers
3/2 = 6/4
_____
The others are just plain false.
The statement which is true about the dilation is:
[tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]
Step-by-step explanation:We know that the dilation transformation changes the size of the original figure but the shape is preserved.
The dilation transformation either reduces the size of the original figure i.e. the scale factor is less than 1 or enlarges the size of the original figure i.e. the scale factor is greater than 1.
The ratio of the corresponding sides of the two figure are equal.
i.e.
[tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]
kaelyn has 14 coins that have a vaule of $ 1.20. she only has dimes and nickles. how many nickles does kaely have
Answers
Kaelyn has 14 coins made of dimes and nickels valued at $1.20. By setting up a system of equations and solving for the number of nickels, we determine that she has 4 nickels.
The student is asking a mathematical question involving coin values and combinations. When working with combinations of coins, we typically use a system of equations or algebraic expressions. Kaelyn has 14 coins consisting of dimes and nickels with a total value of $1.20. To systematize, let's let D be the number of dimes and N be the number of nickels. The following equations represent the relationships between the coins:
D + N = 14 (since there are 14 coins in total)0.10D + 0.05N = 1.20 (representing the total value of the coins in dollars)Multiply the second equation by 100 to deal with whole numbers:
10D + 5N = 120From the first equation, we can express D as:
D = 14 - NSubstitute this into the second equation:
10(14 - N) + 5N = 120140 - 10N + 5N = 120-5N = -20N = 4So, Kaelyn has 4 nickels and the rest are dimes.
Amy has 5 yards of border to put around a garden. She uses all the border to make four sections that are the same length. Which expession does not equal the length of one these sections in yards?
Answers
Answer:
F. 4 ÷ 5
Explanation:
We know that Amy has 5 yards of boarders and that she will use them to make 4 equal borders.
This means that:
she will divide 5 yards by 4 to know the length of each border
Among the given choices, choices G, H and J show the division of 5 by 4 which is correct representation of the length
On the other hand. choice F shows the division of 4 by 5 which is an incorrect representation of the length.
Hope this helps :)
Answer:
4 ÷ 5
Step-by-step explanation: becuz i said so
what is The desired outcomes of a specified event.
Answers
Answer:
Favorable Outcomes
Step-by-step explanation:
What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?
Answers
Answer:
The zeros to the quadratic equation are:
[tex]x= -4+\sqrt{\frac{41}{2}}\\\\x= -4-\sqrt{\frac{41}{2}}[/tex]
Step-by-step explanation:
A quadratic function is one of the form [tex]f(x) = ax^2 + bx + c[/tex], where a, b, and c are numbers with a not equal to zero.
The zeros of a quadratic function are the two values of x when [tex]f(x) = 0[/tex] or [tex]ax^2 + bx +c = 0[/tex].
To find the zeros of the quadratic function [tex]f(x)= 2x^2 + 16x -9[/tex] , we set [tex]f(x) = 0[/tex], and solve the equation.
[tex]2x^2+16x\:-9=0[/tex]
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=2,\:b=16,\:c=-9:\quad x_{1,\:2}=\frac{-16\pm \sqrt{16^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2}\\\\x=\frac{-16+\sqrt{16^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2}= -4+\sqrt{\frac{41}{2}}\\\\x=\frac{-16-\sqrt{16^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2}= -4-\sqrt{\frac{41}{2}}[/tex]
Experts/ace/geniuses helppp asapp
Answers
A cirlce with a radius of 8 cm rotates 30 degrees in one second. Determine the angle of rotation in radians.
Angle:___ w:___ v:___
Answers
[tex]\bf \begin{array}{ccll} de grees&radians\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 180&\pi \\\\ 30&x \end{array}\implies \cfrac{180}{30}=\cfrac{\pi }{x}\implies x=\cfrac{30\pi }{180}\implies x=\cfrac{\pi }{6}\\\\ -------------------------------\\\\ \stackrel{angular~velocity}{w}=\cfrac{\stackrel{central~angle}{\frac{\pi }{6}}}{\stackrel{time}{1~s}}\implies w=\cfrac{\pi }{6}~\frac{radians}{seconds}[/tex]
[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=8\\ \theta =\frac{\pi }{6} \end{cases}\implies s=8\cdot \cfrac{\pi }{6}\implies s=\cfrac{4\pi }{3} \\\\\\ \stackrel{linear~velocity}{v}=\cfrac{\stackrel{arc's~length}{\frac{4\pi }{3}}}{\stackrel{time}{1~s}}\implies v=\cfrac{4\pi }{3}~\frac{cm}{seconds}[/tex]
Mr. Morris left work at 5:53 P.M. and drove 47 minutes to his home. What time did he arrive?
Answers
First, we know that the remaining time until 6 PM is 7 minutes. So, we can subtract 7 minutes from 47 and now we have 40 minutes left to add and it is 6 PM. Next, since 40 is not more than 60 minutes, we'll add 40 minutes to 6 PM. This leaves us with the time 6:40.
ANSWER:
He arrived at 6:40
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Answer:
6:40
Step-by-step explanation:
A drink contains 20% cranberry juice and the rest is apple juice. What is the ratio of cranberry juice to apple juice? A.1:20 B.1:4 C.4:1 D.20:1
Answers
80% of the juice is apple
Our ratio would be 20:80
We can simplify it and it will become
1:4
So your answer would be B. 1:4
I hope this helps :)
please help with this word problem
Answers
There is no exact answer to this. It will have to shown in terms of the width. Also we need to use the Pythagorean Formula
Givens
L = 10 * W
W = W
Formula
L^2 + W^2 = C^2
Solution
(10W)^2 + (W^2) = C^2
C^2 = 100W^2 +W^2
C^2 = 101W^2 Now take the square root.
C = sqrt(101W^2)
C= W*sqrt(101) <<<<< Answer. I think this is what they mean
A right triangle has one side, s, and a hypotenuse of 12 meters. Find the area of the triangle as a function of s.
A) A(s) = 2s
144 - s2
B) A(s) = s
144 - s2
C) A(s) = 2s
12 - s2
D) A(s) = 12s
144 - s2
10)
The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)?
A) 12 ft
B) 13 ft
C) 14 ft
D) 15 ft
Answers
Answer: A(s) = [tex]\frac{s\sqrt{144-s^{2} } }{2}[/tex] ; 10) c) 14ft
Step-by-step explanation: Area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]
where:
b is base of a triangle
h is height of a triangle
For this right triangle, it is known one side, s, and hypotenuse, 12. To determine the other side, we use Pythagoras Theorem:
hypotenuse² = side² + side²
[tex]12^{2} = s^{2} + x^{2}[/tex]
[tex]x^{2} = 12^{2} - s^{2}[/tex]
[tex]x^{2} = 144 - s^{2}[/tex]
x = [tex]\sqrt{144 - s^{2} }[/tex]
To determine the Area of the right triangle as function of s:
A = [tex]\frac{b.h}{2}[/tex]
A = [tex]\frac{1}{2}[/tex](s.x)
A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])
Therefore, the area of the right triangle is:
A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])
The ladder and the wall form a right triangle. The height of it is 13 ft, the base is 5ft and the hypotenuse is the length of the ladder. So, to find the minimum length, use Pythagoras Theorem:
hypotenuse² = side² + side²
h² = 13² + 5²
h² = 169 + 25
h = [tex]\sqrt{194}[/tex]
h = 14
The minimum length the ladder has to have to reach the top is 14 ft.
Write an equation of the line with the given slope, m, and y-intercept (0,b) m=-3/5 b=7/10
Answers
The equation of the line with a slope of -3/5 and a y-intercept of 7/10 is y = (-3/5)x + (7/10).
Explanation:To write an equation of a line with a given slope (m) and y-intercept (0,b), we use the slope-intercept form of a linear equation which is y = mx + b. In this case, the slope is -3/5 and the y-intercept is 7/10.
Substituting these values into the slope-intercept formula, the equation of the line is y = (-3/5)x + (7/10).
Learn more about Equation of a line here:
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Yanis fires pottery in a kiln. He decides to measure the rate of change of temperature of the pottery over time. What would be an appropriate unit for Yanis's purpose?
Answers
Answer with explanation:
Pottery is on a Kiln.
Unit of temperature can be Kelvin(°K) or Degree Celsius(°C) or Fahrenheit(°F).
Unit of time is second, minute and hour.
Rate of change of temperature of the pottery over time can be written as
[tex]1.=\frac{\text{Degree Celsius}}{\text{Second}}\\\\2.=\frac{\text{Degree Celsius}}{\text{Minute}}[/tex]
Internationally , Kelvin is used as S.I unit of Temperature.
So,Yanin can use
[tex]1.=\frac{\text{Kelvin}}{\text{Second}}\\\\2.=\frac{\text{Kelvin}}{\text{Minute}}[/tex]
as Rate of change of temperature of the pottery over time.
The exponential function y = 2(3)x grows by a factor of 9 between x = 1 and x = 3. What factor does it grow by between x = 5 and x = 7?
Answers
the growth factor between x=1 and x=3 is given by:
[2(3)^3]/[2(3)^1]
=54/6
=9
thus the growth factor between x=5 and x=7 will be as follows:
[2(3)^7]/[2(3)^5]
simplifying the above we get:
=[3^7]/[3^5]
=3^(7-5)
=3^2
=9
Answer:
9
Step-by-step explanation:
What is the null hypothesis if we want to test the hypothesis that the mean score on campus 1 is higher than on campus 2? h0: µ1 = 0?
Answers
____________
No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.
Therefore, the null hypothesis would be:
H₀: µ₁ - µ₂ = 0
where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Now, We test this null hypothesis against the alternative hypothesis that the mean score on campus 1 is higher than on campus 2:
Hₐ: µ₁ > µ₂
Hence, if there is sufficient evidence to reject the null hypothesis and conclude that there is a significant difference between the mean scores of campus 1 and campus 2.
Thus, No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.
Therefore, the null hypothesis would be:
H₀: µ₁ - µ₂ = 0
where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.
Learn more about the subtraction visit:
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Which of the following functions are their own inverses? Select all that apply.
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y
d. d(p) = 1/x^2
Answers
The appropriate choices are ...
a. t(p) = p
b. y(j) = -1/j
c. w(y) = -2/y
Answer:
a,b and c.
Step-by-step explanation:
We have to find the the functions that are their own inverses.
a.t(p)=p
Then the inverse function of given function is
[tex]p=t^{-1}(p)[/tex]
Therefore, the given function is inverse function of itself.
Hence, option a is true.
b.y(j)=[tex]-\frac{1}{j}
Let y(j)=y then we get
[tex]y=-\frac{1}{j}[/tex]
[tex]j=-\frac{1}{y}[/tex]
[tex]j=-\frac{1}{y(j)}[/tex]
[tex]j=-\frac{1}{\frac{-1}{j}}[/tex]
[tex]j=j[/tex]
Hence, the function is inverse of itself.Therefore, option b is true.
c.[tex]w(y)=-\frac{2}{y}[/tex]
Suppose that w(y)=w
Then [tex]w=-\frac{2}{y}[/tex]
[tex]y=-\frac{2}{w}[/tex]
[tex]w(y)=-\frac{2}{-\frac{2}{w}}[/tex]
[tex]w(y)=w[/tex]
[tex]w(y)=-\frac{2}{y}[/tex]
Hence, the function is inverse function of itself.Therefore, option c is true.
d.[tex]d(p)=\frac{1}{x^2}[/tex]
Let d(p)=d
If we replace [tex]\frac{1}{x^2}by p then we get
[tex]d=\frac{1}{x^2}[/tex]
[tex]x^2=\frac{1}{d}[/tex]
[tex]x=\sqrt{\frac{1}{d}}[/tex]
[tex]x=\sqrt{\frac{1}{d(p)}[/tex]
Hence, the function is not self inverse function.Therefore, option d is false.
If you have 2500 to invest at 6 interest compounded quarterly. For how many years will the money need to be invested for that amount to triple?
Answers
P (t) = P * (1 + r / n) ^ (n * t)
Where,
P: initial investment
r: interest rate
n: periods
Substituting values:
3 * 2500 = 2500 * (1 + 0.06 / 4) ^ (4 * t)
Rewriting:
3 = (1,015) ^ (4 * t)
Clearing t:
log1.015 (3) = log1.015 ((1.015) ^ (4 * t))
4 * t = log1.015 (3)
t = (1/4) * log1.015 (3)
t = 18.45 years
Answer:
the money will need to be invested 18.45 years for that amount to triple
HELP
______________________
Answers
x*50 = y
Answer:
The answer is the third option/choice.
The period if a function is 4pi
How many cycles of the function occur in a horizontal length of 12pi?
(answer was 3)
QUESTION: Which type of transformation of the parent function would be shown by the graph?
Answers
Answer:
She's right the answer is a horizontal stretch.
what is the product of r and t if R equals 5.33 and T equals 0.5
Answers
replace the letters with the numbers you have 5.33 x 0.5 = 2.665
Which ordered pair is the vertex of y = [x - 3]+ 2?
A.(2, –3)
B.(–3, 2)
C.(3, 2)
D.(2, 3)
Answers
A die is tossed. find the odds against rolling a number greater than 11.
Answers
On Sunday, 370 people bought tickets to the county fair. Tickets cost $7 for adults and $3 for children. The total revenue from ticket sales on Sunday was $1750. The system of equations below represents the number of people and total sales for the county fair on Sunday, where x represents the number of child tickets and y represents the number of adult tickets.
Answers
Number of adult tickets: y
1) x+y=370
2) 3x+7y=1750
Using the method of substitution
a) Isolating y in the first equation:
1) x+y=370→x+y-x=370-x→y=370-x
b) Replacing y=370-x in the second equation:
2) 3x+7y=1750→3x+7(370-x)=1750
c) Solving for x: Distributive property:
3x+7(370)-7x=1750
3x+2590-7x=1750
Adding similar terms:
-4x+2590=1750
-4x+2590-2590=1750-2590
-4x=-840
Dividing both sides of the equation by -4:
-4x/(-4)=-840/(-4)
x=210
Replacing x=210 in the first equation:
1) y=370-x→y=370-210→y=160
Answer:
The number of child tickets was 210 and
the number of adult tickets was 160
Evaluate: 18.4 ÷ 2.3 × 3.4 + 13.812 =
Answers
Two events are independent when the following is true:
a. the outcome of one event determines the outcome of the other event
b. there is no correlation between the two events
c. the outcome of one event does NOT determine the outcome of the other event
d. The outcome of the event is determined by the theoretical probability of the event
Answers
Solution:
Independent Events:
Consider an experiment of Rolling a die, then getting an even number and multiple of 3.
Total favorable outcome = {1,2,3,4,5,6}=6
A=Even number = {2,4,6}
B=Multiple of 3 = {3,6}
A ∩ B={6}
P(A)=[tex]\frac{3}{6}=\frac{1}{2}[/tex], P(B)= [tex]\frac{2}{6}=\frac{1}{3}[/tex]
P(A ∩ B)=[tex]\frac{1}{6}[/tex]
So, P(A)× P( B)=[tex]\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}[/tex]=P(A ∩ B)
Hence two events A and B are independent.
Option (c). the outcome of one event does NOT determine the outcome of the other event
Answer:
C on edge or the outcome of one event does NOT determine the outcome of the other event
Step-by-step explanation:
help me out with this
Answers
The sum is ...
(2+1-3)x³ +(-4+6+2)x² +(6-8-4)x +(-3+12-7)
= 0x³ +4x² -6x +2
The sum is 4x² -6x +2
_____
* The process is easier because there are no "carry" operations from one column to another as there may be when adding multi-digit numbers.