Answers
The recursive formula for a geometric sequence is a₁=-4 and [tex]a_n}=6.a_{n-1}[/tex]. Therefore, option D is the correct answer.
What is a geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.
The given geometric sequence is -4, -24, -144, -864.
A recursive formula for a geometric sequence with common ratio r is given by [tex]a_n}=ra_{n-1}[/tex] for n≥2.
Here, a=-4 and r=-24/(-4) =6
So, recursive formula is [tex]a_n}=6.a_{n-1}[/tex]
Therefore, option D is the correct answer.
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Related Questions
A machine packs at a constant rate of 2/3 of a box every 1/2 minuet. What’s is the number of boxes per minute that’s the machine packs?
Answers
2/3 of a box ------> 1/2 minutes
x of a box ---------> 1 minute
Clearing x we have:
x = (1 / (1/2)) * (2/3)
Rewriting:
x = 2 * (2/3)
x = 4/3
Answer:
the number of boxes per minute that the machine packs is:
x = 4/3
Jax solved an equation and justified his steps as shown below. What reason would justify step 2?
3x + 5 > 2 Step 1: Given
3x > -3 Step 2: ?
x> -1 Step 3: Division Property of Equality
a. Combine Like Terms
b. Division Property of Equality
c. Subtraction Property of Equality
d. Multiplication Property of Equality
Answers
In the problem that Jax solved he subtract 5 from both sides of the equation. This is an example of the subtraction property of equality.
The property states that if you subtract the same amount from both sides of an equation the equation remains the same.
Step 2 can be justified using the Multiplication Property of Equality. This property states that if we multiply or divide both sides of an inequality by the same number, the inequality will still hold true.
Explanation:Step 2 can be justified using the Multiplication Property of Equality. This property states that if we multiply or divide both sides of an inequality by the same number, the inequality will still hold true.
In this case, Jax divided both sides of the inequality by 3. This is a valid step because dividing both sides of the inequality by a positive number does not change the inequality. So, by dividing both sides by 3, Jax found that x > -1.
The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width. recall that the formula for the volume of a rectangular prism is v = l · w · h, where l is the length, w is the width, and h is the height. write the equation that represents the volume of the storage container in terms of its width.
Answers
l ------------------> is the length
w -----------------> is the width
h ----------------- > is the height
we know that
h=6 ft
l=2+w
[the volume of the storage ]=[l]*[w]*[h]------> [2+w]*[w]*[6]
[the volume of the storage ]=[l]*[w]*[h]------> 6*[2w+w²]-----> 6w²+12w
the answer is
V=[6w²+12w] ft²
Answer:
V = 6w² + 12w
Step-by-step explanation:
Voluntary sampling is one type of sampling method that is not probability based. This means that
a)each member of a population is equally likely to be chosen for the survey.
b)the results of the survey cannot reliably be extended and generalized.
c)the likelihood of a member of the population volunteering to be surveyed is not probable.
d)the results of the survey are not mathematically probable.
Answers
Answer:
b)the results of the survey cannot reliably be extended and generalized.
Step-by-step explanation:
Voluntary sampling is a type of convenience sample; it is convenient for the researcher to perform.
However, voluntary sampling can lead to bias; usually only people who feel strongly one way or the other about the survey will volunteer to be members of a sample.
Since there is a possibility of bias, the results of the survey cannot reliably be extended and generalized.
The correct statement is,
b) the results of the survey cannot reliably be extended and generalized.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Since, We know that;
Voluntary sampling is a type of convenience sample and it is convenient for the researcher to perform.
However, voluntary sampling can lead to bias; usually only people who feel strongly one way or the other about the survey will volunteer to be members of a sample.
Now, Since there is a possibility of bias,
Hence, the results of the survey cannot reliably be extended and generalized.
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find the solution of this system of equations shown on the graph.
Answers
hope it helps
Two or more lines on a graph together is known as a
Answers
5. (10.01 MC) If sin θ = 1 over 4 and tan θ > 0, what is the value of cos θ? (1 point)
Answers
To find the value of cos θ when sin θ = 1/4 and tan θ > 0, use the Pythagorean identity. As the angle is in the first quadrant, cos θ is positive and equals the square root of 15/16 or √15/4.
If sin θ = 1/4 and tan θ > 0, we need to determine the value of cos θ. When the sine of an angle is positive and the tangent is positive, we know the angle must be in the first quadrant, where all trigonometric functions are positive. To find cos θ, we utilize the Pythagorean identity sin2 θ + cos2 θ = 1. Rewriting this identity for cos θ, we get cos2 θ = 1 - sin2 θ.
Substituting the given value of sin θ, we have:
cos2 θ = 1 - (1/4)2
cos2 θ = 1 - 1/16
cos2 θ = 15/16
Since θ is in the first quadrant, and cos θ is positive, the value of cos θ is the positive square root of 15/16:
cos θ = √(15/16)
cos θ = √15/4 or approximately 0.9682
Solve the system of equations
1.8x-0.5y=-6.4
0.6x+2.1y=2.4
_______________________
x= ??
y= ??
Answers
{1.8 x - 0.5 y = -6.4
{0.6 x + 2.1 y = 2.4
In the first equation, look to solve for x:
{1.8 x - 0.5 y = -6.4
{0.6 x + 2.1 y = 2.4
1.8 x - 0.5 y = (9 x)/5 - y/2 and -6.4 = -32/5:
{(9 x)/5 - y/2 = -32/5
Add y/2 to both sides:
{(9 x)/5 = 1/10 (5 y - 64)
{0.6 x + 2.1 y = 2.4
Multiply both sides by 5/9:
{x = 1/18 (5 y - 64)
{0.6 x + 2.1 y = 2.4
Substitute x = 1/18 (5 y - 64) into the second equation:
{x = 1/18 (5 y - 64)
{2.1 y + 0.0333333 (5 y - 64) = 2.4
2.1 y + 0.0333333 (5 y - 64) = 2.1 y + (0.166667 y - 2.13333) = 2.26667 y - 2.13333:
{x = 1/18 (5 y - 64)
2.26667 y - 2.13333 = 2.4
In the second equation, look to solve for y:
{x = 1/18 (5 y - 64)
{2.26667 y - 2.13333 = 2.4
2.26667 y - 2.13333 = (34 y)/15 - 32/15 and 2.4 = 12/5:
(34 y)/15 - 32/15 = 12/5
Add 32/15 to both sides:
{x = 1/18 (5 y - 64)
{(34 y)/15 = 68/15
Multiply both sides by 15/34:
{x = 1/18 (5 y - 64)
y = 2
Substitute y = 2 into the first equation:
Answer: {x = -3, y = 2
What are two solutions of 3 + 4 |x/2 + 3| = 11?
Answers
4 abs(x/2 + 3) = 11 - 3
4 abs(x/2 + 3) = 8 Divide by 4
abs(x/2 + 3) = 8/4
abs(x/2 + 3) = 2
Solution 1
x/2 + 3 = 2 Subtract 3
x/2 = 2 - 3
x/2 = - 1 Multiply by 2
x/2 *2 = - 2
x = - 2
Solution 2
x/2 + 3 = - 2
x/2 = - 2 - 3
x/2 = - 5 Multiply by 2
x = -5 * 2
x = -10
Solutions
x = - 2 <<<< answer 1
x = -10 <<<< answer 2
20 POINTS!! EASY QUESTION! WILL MARK BRAINLIEST!! READ THE INFO! THEN FILL IN THE BLANKS!
The cost for a single class session for each dance class is below.
Clodagh’s Dance = $6.00
New Steps = $7.50
Stepping High = $6.50
The class hours are below.
Clodagh’s Dance = 3:00pm - 4:00pm
New Steps = 4:00pm - 5:30pm
Stepping High = 9:00am - 10:15am
How would these answers change if you were to write the unit rate in cost per hour?
Fill in the blanks!
Dance Classes | Total Hours for Each Payment | Cost Per Hour
| |
Clodagh’s Dance | $6.00 | $6.00
New Steps | $7.50 | _____
Stepping High | $6.50 | _____
Answers
To find the unit rate in cost per hour, you will write the amount of money over the total time for each class. Then divide the cost by the time to find the unit rate.
New Steps: $7.50/1.5 hours = $5 per hour
Stepping High: $6.50/1.25 hours = $5.20 per hour
Answer:
To find the unit rate in cost per hour, you will write the amount of money over the total time for each class. Then divide the cost by the time to find the unit rate.
New Steps: $7.50/1.5 hours = $5 per hour
Stepping High: $6.50/1.25 hours = $5.20 per hour
The population P(t) of a species satisfies the logistic differential equation dP/dt= P(2-(P/5000)) where the initial population 3,000 and t is the time in years. What is the lim t>infinity P(t)?
Answers
[tex] \frac{dP}{dt} = rP[1- \frac{P}{K}] [/tex]
where r = growth parameter and K = carrying parameter.
In order to write you equation in this form, you have to regroup 2:
[tex] \frac{dP}{dt} = 2P[1- \frac{P}{10000}] [/tex]
Therefore, in you case r = 2 and K = 10000
To solve the logistic differential equation you need to solve:
[tex] \int { \frac{1}{[P(1- \frac{P}{K})] } } \, dP = \int {r} \, dt [/tex]
The soution will be:
P(t) = [tex] \frac{P(0)K}{P(0)+(K-P(0)) e^{-rt} } [/tex]
where P(0) is the initial population.
In your case, you'll have:
P(t) = [tex] \frac{3E7}{3E3+7E3 e^{-2t} } [/tex]
Now you have to calculate the limit of P(t).
We know that
[tex] \lim_{t \to \infty} e^{-2t} -\ \textgreater \ 0 [/tex]
hence,
[tex] \lim_{t \to \infty} P(t) = \lim_{t \to \infty} \frac{3E7}{3E3+0} = 10^{4} [/tex]
The lim t>infinity P(t) is 5,000, which is the carrying capacity of the species.
Explanation:The logistic differential equation dP/dt = P(2-(P/5000)) models the population growth of a species. To find the lim t>infinity P(t), we need to find the stable population when t becomes very large. In this equation, the population growth rate is initially exponential, but as the population approaches its carrying capacity (Q), the growth rate slows down and levels off to zero.
Solving the differential equation, we find that the equation represents logistic growth. The solution to the equation is P(t) = Q / (1 + (Q/Po)e^(-rt)), where Po is the initial population, Q is the carrying capacity, and r is the growth rate.
In this case, the initial population is given as 3,000. To find the carrying capacity (Q), we set dP/dt = 0 and solve for P. Substituting the values into the equation, we find Q = 5,000.
As t becomes very large, e^(-rt) approaches 0, and the equation simplifies to P(t) = Q. Therefore, the lim t>infinity P(t) is 5,000, which is the carrying capacity of the species.
Which group of measurements could be the side lengths of a right triangle?
A.
57 in, 86 in, 95 in
B.
47 in, 76 in, 95 in
C.
57 in, 76 in, 95 in
D.
57 in, 76 in, 105 in
Answers
if the hypotenuse is H and other 2 sides are A and B, then equation is as follows;
H² = A² + B²
1. A - 57 in. B - 86 in.
H² = A² + B²
H² = 57² + 86²
H² = 3249 + 7396
H = √10645
= 103.17 in.
third side given is not 103 in therefore this is not a right angled triangle
2. A - 47 in. B - 76 in.
H² = A² + B²
H² = 47² + 76²
= 2209 + 5776
H = √7985
H = 89.3 in.
third side given is 95 in. therefore this is not a right angled triangle.
3. A- 57 in. + B - 76 in.
H² = A² + B²
H² = 57² + 76²
= 3249 + 5776
H = √9025
H = 95 in.
third side given is 95 in. therefore this is a right angled triangle.
4. A - 57 in. B - 76 in.
As calculated in the third equation with the same side lengths of A and B, hypotenuse should be 95 in. however the third side length given is 105 in. so this is not a right angle triangle
write an equation of the line that is parallel to the line y = -x + 4 and passes through the points 0, 10.
Please help me!
Answers
Gradient = -1
Equation of line: y = -x + c
Point : (0,10) replace in the above equation
y = -x + c
10 = -0 + c
c = 10
Equation is: y = -x + 10
Hope it helped!
WILL MARK AS BRAINLIEST
Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of [tex]\frac{ \pi }{2} [/tex], and a vertical shift up 3 units.
y=__________
Answers
The amplitude is given by a, so a = 1.
The period is given by 2*pi/b, so 2*pi/b = pi/2, and b = 4.
The variable c gives the horizontal shift, of which there is none, so c = 0.
Finally, the vertical shift of 3 units means that d = 3.
So the equation is:
y = sin(4x) + 3
Answer:
y = sin(4x) + 3
Step-by-step explanation:
PLEASE HELP QUICK!!!!
11PTS AND BRAINLIEST AVAILABLE TO CORRECT ANSWER
Answers
What is the reciprocal of 4 3/7? Please help!
Answers
I hope this helped! :-)
The reciprocal of number 4 3/7 is 7/31.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
Given the mixed number
4 3/7 = (7×4 + 3)/7
⇒ 31/7
Now reciprocal is nothing but an interchange of numerator and denominator.
So
Reciprocal of 31/7 → 7/31
Hence "The reciprocal of number 4 3/7 is 7/31".
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10 POINTS + BRAINLIEST ANSWER
A box contains 30 pieces of chocolate, distributed as shown in the table below. Each piece is made of either white chocolate or dark chocolate, and each piece contains either cream filling or no filling. If one piece is selected at random, what is the probability that the piece is either white chocolate with cream filling or dark chocolate with no filling? (10 POINTS + BRAINLIEST ANSWER)
A. 8/30
B. 12/30
C. 20/30
D. 22/30
Answers
8/30
I need 20 characters
The probability of selecting a chocolate at random that is either white chocolate with cream filling or dark chocolate with no filling is [tex]\frac{8}{30}[/tex].
What is probability?Probability is the chance of happening an event or incident.
Given, the box contains 30 chocolates.
The number of chocolates that are white chocolate with cream filling is 5.
Therefore, the probability of selecting a chocolate at random that is white chocolate with cream filling is [tex]= \frac{5}{30}[/tex].
The number of chocolates that are dark chocolate with no filling is 3.
Therefore, the probability of selecting a chocolate at random that is dark chocolate with no filling is [tex]= \frac{3}{30}[/tex].
Now, the probability of selecting a chocolate at random that is either white chocolate with cream filling or dark chocolate with no filling is
[tex]= \frac{5}{30} + \frac{3}{30} \\= \frac{8}{30}[/tex]
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Find the slope of the line that passes through the points (2 , 0) and (2 , 4).
Answers
[tex]\text {Slope = } \dfrac{4-0}{2-2} = \dfrac{4}{0} = \infty[/tex]
The graph is a vertical line , x = 2
The slope of the line passing through the given points (2, 0) and (2, 4) is ∞ (undefined).
Given the following data:
Points on the x-axis = (2, 2)Points on the y-axis = (0, 4)To find the slope of the line passing through the given points (2, 0) and (2, 4):
The slope of a straight line.Mathematically, the slope of a line is given by the following formula;
[tex]Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Substituting the points into the formula, we have;
[tex]Slope, \;m = \frac{4 - 0}{2 - 2}\\\\Slope, \;m = \frac{4}{0}[/tex]
Slope, m = ∞ (undefined).
Note: A mathematical expression is considered to be undefined when its denominator is zero (0).
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how do graphs of y=1/x and y=5/(x+6) compare? I know the second graph shifts to left by 6 units but does it move down and how many units?
Answers
Answer:
y = 5/x +6 makes your raises your graph 6 units higher.
Step-by-step explanation:
Lena runs 2/3 mile each day she wants to know how many miles she has to run before she has has run a whole number
Answers
For a machine, the output force is 20 N, and the output distance is 4 m. Which must be true about the work input? A. It equals 80 J. B. It must be greater than 80 J. C. It must be less than 80 J.
Answers
Work = (20 N)*(4 m)
Work = (20*4) Nm
Work = 80 J
So 80 joules of work is the output. Ideally we'd expect 80 J to be the input but that's not the case. There will always be things like heat loss, leading to some level of inefficiency. So if we input some amount of work, say 100 J, then it might drop to 80 J of actual output work after the wasted energy is accounted for.
In short, you have to put more work in than the work you want out. This is why the answer is choice B) It must be greater than 80 J
Simplify these 12 radicals:
1) √80 2) √64
3) √45 4) √54
5) √32 6) √36
7) √150 8) √20
9) √180 10) √72
11) √8 12) √50
Answers
[tex]4 \sqrt{5} [/tex]
2)
[tex]8[/tex]
3)
[tex]3 \sqrt{5} [/tex]
4)
[tex]3 \sqrt{6} [/tex]
5)
[tex]4 \sqrt{2} [/tex]
6)
[tex]6[/tex]
7)
[tex]5 \sqrt{6} [/tex]
8)
[tex]2 \sqrt{5} [/tex]
9)
[tex]6 \sqrt{5} [/tex]
10)
[tex]6 \sqrt{2} [/tex]
11)
[tex]2 \sqrt{2} [/tex]
12)
[tex]5 \sqrt{2} [/tex]
People who reach retirement age will have accidents and health issues. True False
Answers
Answer:
Its FALSE on odyssey
Please help ASAP!!!! 52 points and will give brainliest for RIGHT answer!
Answers
5x - 20 = 2x + 10 How do you solve this problem?
Answers
3x = 30
x is 10
x=10
add 20 to both sides
5x= 2x + 30
subtract 2x from both sides
3x= 30
divide both sides by 3
x= 10
Hope this helps! :)
A bag of marbles contains 5 red, 10 blue, 3 yellow and 7 green marbles. lisa chooses one marble at random from the bag. what is the probability of not choosing a red marble?
Answers
There are 20 non-red marbles and there are 25 total marbles
A job applicant estimates that his chance of passing a qualifying examination is 2/3, and his chance of being appointed if he does pass is 1/4. What is the probability that he will receive the job?
Answers
2 * 1
- -
3 * 4
so 2 /12
1/6 when simplified
Hence, the probability that he will receive job is:
1/6
Step-by-step explanation:It is given that:
chance of passing a qualifying examination is 2/3=P
and chance of being appointed if he does pass is 1/4=P'
Now, we are asked to find the probability that he will receive the job.
We are asked to find the probability that he will receive the job.
The probability is calculated as:
Probability that he qualify exam×Probability that he is being appointed.
=P×P'
=(2/3)×(1/4)
=1/6
check my work please will give medals if you tell if this is right or not!!!
Let f(x)=x+5 and g(x)=x^2. find (g o f) (4)
A. 9 <--- my answer
B. 81
C. 20
D. 1
2. police can estimate the speed of a vehicle before the brakes are applied using the formula 0.75d=s^2/30.25, where s is the speed in miles per hour and d is the length of the vehicle's skid marks. what was the approximate speed of a vehicle that left skid marks measuring 140 feet?
A. about 10 miles per hour <-- my answer
B. about 75 miles per hour
C. about 15 miles per hour
D. about 56 miles per hour,
Answers
Since f(x)=(x+5) and g(x)=x^2,
First substitute 4 into f which is
f(4)=4+5=9.
then g(f(4))=g(9).
9^2=81
2.The answer is D. about 56 miles per hour
75d=s^2/30.25
given: d= 140
so 0.75*140=s^2/30.25
s^2=105*30.25=3176.25
= +/- sqrt 3176.25
s=56.358
=56 miles per hour.
Find the slope of the line that contains the points named. C(3, 8), D(-2, 5) -3/5 3/5 5/3
Answers
Answer: [tex]\dfrac{3}{5}[/tex]
Step-by-step explanation:
The slope of a line passing through two points X(a,b) and Y(c,d) is given by :-
[tex]m=\dfrac{d-b}{c-a}[/tex]
Given points : C(3, 8) and D(-2, 5)
Then , the slope of a line passing through two points C(3, 8) and D(-2, 5) is given by :-
[tex]m=\dfrac{5-8}{-2-3}=\dfrac{-3}{-5}=\dfrac{3}{5}[/tex]
Hence, the slope of the line that contains the points C(3, 8) and D(-2, 5) is [tex]\dfrac{3}{5}[/tex]
.
darren has 3/4 of a gallon of soil.he needs to plant 5 small plants.if he splits the soil evenly between the plants.how much soil will each plant get?
Answers
3/4 x 1/5 = 3/20 of a gallon