Answers
Answer:
1) (Un) is a geometric sequence.
2) Un+1 - Un ≤ 0.
3) (Un) is decreasing.
4) (Un) is convergent.
5) sum = 155
Step-by-step explanation:
Un+1 = 0.5Un
U₀ = 80
1) U is a geometric sequence (reason : Un+1 = 0.5Un).
2) Un+1 - Un = 0.5Un - Un = Un×(0.5 - 1) = -0.5Un ≤ 0 (because Un ≥ 0).
Remark: use Mathematical induction to prove that Un ≥ 0
3) Un+1 - Un ≤ 0
then
Un+1 ≤ Un
then
the sequence U is decreasing.
4) U is decreasing and Un ≥ 0
Then U is convergent.
5) Since U is geometric sequence with first term U0 = 80 and common ratio = 0.5 .
Important: review the sum of consecutive terms of a geometric sequence.
Then
[tex]U_0+ U_1+ U_2+ U_3+ U_4=U_{0}\times \frac{1-\left( 0.5\right)^{5} }{1-0.5}=160\times(1-\left( 0.5\right)^{5} )=155[/tex]
Related Questions
Max is creating a playlist and can have at most 180 minutes of music. He currently has 45 minutes. How many more minutes of music could Max include in the playlist?
Answers
Answer:
max could still add 135 minutes of music into his playlist
Step-by-step explanation:
180 - 45 = 135
Answer:
So we know that Max's playlist can have at most 180 minutes of music meaning that our amount of music cannot exceed that number. We are also given that Max already has 45 minutes of music on there so we need to subtract that from 180 minutes to see how much we have left.
[tex]180\ minutes - 45\ minutes[/tex]
[tex]135\ minutes[/tex]
Max still has 135 minutes left on his playlist that he can fill up.
Hope this helps! Let me know if you have any questions
Can anyone help me with this please?
Answers
Step-by-step explanation:
since there are answer options we don't need to formally solve the system of equations, we only need to try the first point of every option, and see, where the equations are true.
if we cannot find it for the first point, then we would need to try the same thing for the serving points.
let's put (0, 6) into the first equation :
-2×0² + 6 = 6
6 = 6 true
let's put it into the second equation ;
4×0² + 3×6 = 28
18 = 28 false
that eliminates the first 2 answers.
let's put (-1, 4) into the first equation :
-2×(-1)² + 4 = 6
-2×1 + 4 = 6
-2 + 4 = 6
2 = 6 false
that eliminates the third answer.
let's put (-1, 8) into the first equation :
-2×(-1)² + 8 = 6
-2 + 8 = 6
6 = 6 true
let's put it into the second equation :
4×(-1)² + 3×8 = 28
4 + 24 = 28
28 = 28 true
and because the square function delivers the same result for -1 and +1, it is also true for the second point.
and the 4th answer is therefore correct.
can someone please help me this this??
Answers
Answers:
bio = 258
sociology = 169
============================================================
Work Shown:
x = number of bio textbooks
y = number of sociology textbooks
x+y = 427 books sold total
y = x-89 since 89 less sociology textbooks were sold compared to bio
Apply substitution to get the following
x+y = 427
x+x-89 = 427 ... replace y with x-89
2x-89 = 427
2x = 427+89
2x = 516
x = 516/2
x = 258 bio textbooks were sold
y = x-89
y = 258-89
y = 169 sociology textbooks were sold
Identify the type of segments as 2 CHORDS, 2 SECANTS, OR SECANT AND TANGENT. Then, find the variable.
Answers
Step-by-step explanation:
1)
SOLUTION
5(x+5) = 6. (6 +9)
90 = 5x + 25
13 = x
2)
SOLUTION
x (3) = (4) (6)
3x = 24
x= 8
3)
SOLUTION
3 (3 + x + 2) = (x+1)(x + 1 + x – 1) Use Theorem
3x + 15=2x²+2x
0 = 2x² – x – 15
0 = (x – 3) (2x + 5) Solve for x
3 = x Use positivesolution
Which is not a reason an athlete uses technology to assess performance?
A. To monitor development.
B. To tailor to their training program.
C. To send to college recruiters.
D. To analyze technique.
Answers
it’s C. To send to college recruiters
Reason:
You use technology to asses performance so you can better your technique, change up your training program to focus on the things you’re doing wrong and you can also see if you’ve made improvement.
Select the correct answer. Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14? A. 68% of the data points lie between 10 and 14. B. 68% of the data points lie between 8 and 12. C. 68% of the data points lie between 10 and 18. D. 68% of the data points lie between 10 and 16.
Answers
Answer: Option (c) is correct.
68% of the data points lie between 10 and 18.
Step-by-step explanation: Given : a normal distribution with a standard deviation of 4 and a mean of 14
We have to choose the sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.
Since, given 68% data.
We know mean of data lies in middle.
And standard deviation is distribute equally about the mean that is 50% of values less than the mean and 50% greater than the mean.
So, 68% of data lies
mean - standard deviation = 14 - 4 = 10
mean + standard deviation = 14 + 4 = 18
So, 68% of the data points lie between 10 and 18.
what is the negation of x is greater than
39
Answers
Step-by-step explanation:
that means the opposite ...
the opposite of
x > 39
is
x <= 39
Daniel's goal is to walk 100 miles.• He walks 5 miles every day.• He has
walked for 7 days. Daniel still needs to walk k more miles for his goal.
Which equation could be used to find how many more miles, k, Daniel
will have to walk to meet his goal
Answers
Answer:
65 miles
Step-by-step explanation:
Given:
k = how many more miles Daniel has to walkGoal = 100 milesDaily miles = 5 milesNumber of days already walked = 7 daysEquation:
5 × 7 + k = 100
Solving:
⇒ 5 × 7 + k = 100
⇒ 35 + k = 100
⇒ k = 100 - 35
⇒ k = 65
Which ratio represents the number of vowels to total letters in the word JACKSONVILLE?
Answers
Step-by-step explanation:
4:12 there are four vowels and 12 letters?
help will mark Brainliest
Answers
Answer:
The third box model
Step-by-step explanation:
Since she earns 162 from babysitting and got a total of $810, it would eman that (x represents the amount of money she got from mowing lawns) 810-162=x
x=648 so the third box model is correct
plssssss helppppp i give 98 points
Answers
To write 28 + 24 as a product of two factors, we need to determine the HCF of the addends (28 and 24). This can be done by listing the factors of the addends. The greatest factor that is common in 28 and 24 is the HCF.
If the number is in bolded text, the number is a common factor.
Factors of 28: 1, 2, 4, 7, 14, 28Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24Since 4 > 2 > 1, the HCF is 4.
2) Writing 28 and 24 as a product of two factorsNow, let us put the provided expression between parentheses.
⇒ (28 + 24)Finally, factor four out of the expression, as it is the GCF of 28 and 24.
⇒ (28 + 24)⇒ [(4 × 7) + (4 × 6)]⇒ 4(7 + 6)Therefore, 28 + 24 as a product of two factors is 4(7 + 6).
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Yellow Bird launches from point (10,0). His flight path reaches a maximum height of 22 yards and lands at point (42, 0).
Answers
The Equation for the launch of the yellow bird is y = -0.1( x - 26 )² + 20
what will be the equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values
Given:
Starting position of the bird = ( 10 , 0 )
Final position of the bird = ( 42 , 0 )
Maximum Height of the bird = 20 yards
To find: Equation that represent this condition.
Clearly, Birds flight path is not a straight line. It has a curved path.
So, the path bird follow is a PARABOLA.
Standard Equation of the parabola in vertex form, y = a( x - h )² + k
where ( h , k ) is the vertex of the parabola.
In our Question , vertex is the point at the highest position.
Vertex will be 20 yard above the mid point of the starting and final position.
Using Mid-Point Formula,
Mid-Point of ( 10 , 0 ) & ( 42 , 0 ) =
Now, the vertex = ( 26 , 0 + 20 ) = ( 26 , 20 )
⇒ Equation, y = a( x - 26 )² + 20
Now, we find value of by substituting value of (10 , 0) in the equation,
⇒ 0 = a( 10 - 26 )² + 20
a( -16 )² = -20
a(256) = -20
a = -20/256
a = −0.078125
a ≈ -0.1
Therefore, The Equation is y = -0.1( x - 26 )² + 20
To know more about Equations follow
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Write an equation in slope-intercept form for the line with -intercept -2 and slope2
.
Answers
hope this helps
2xy - 3x2y2 + 2xy +5x2y2
Answers
is this right? pls be fast
Answers
Answer:
first 2 I'm not sure about. for the first one I think its 0.5 if that's an option
Can someone answer theese questions
Answers
Question 1 ) A ray has one endpoint and continues forever in the opposite direction
Question 2)
⇒
IG
Question3)
⇒
DC
Hope this helps!
__[???]___, is the capacity to do work.
A: Energy
B: Velocity
C: Heat
D: Momentum
Answers
Hope this helps!!
help please !!!!!!!!!!
Answers
Answer:
it is -3
Step-by-step explanation:
go to x=-4 and see what the y value of the line is
Answer:
1
Step-by-step explanation:
Find the equation of the line. Start with the y-intercept, which is -1. Next find the slope by doing rise/run. To get from (0, -1) to (2, 0) you rise 1 and run 2, so the slope is 1/2.
The equation is y= 1/2x -1.
Plugin 4 for x and solve for y.
y = 1/2(4) -1
y = 2 - 1
y = 1
PLEASE HELP?! IM SO CONFUSED!!
Answers
Answer:
C.
Step-by-step explanation:
-3 7/8 rounds down to -4
4.63 rounds up to 5
-4 x 6 + 5
-24 + 5
-19
her answer (-19.14) also rounds to -19
So yes, it is reasonable and the correct response is C.
URGENT!!!! What is the number of solutions in this system?
A None
B one
C Infinite
Answers
Answer:
C? Not 100% sure
Step-by-step explanation:
# The size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles. If the greater of the opposite interior angles exceeds smaller by 30°, find the measure of the interior angles of the triangle.
please help me
Answers
Answer:
30° and 60°
Step-by-step explanation:
Let the interior angles be ∠x₁ (smaller) and ∠x₂ (larger), and the exterior angle ∠X.
Making the statements into equations :
Size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles ⇒ ∠X + ∠x₁ + ∠x₂ = 180° [Equation 1]
Greater of the opposite interior angles exceeds smaller by 30° :
⇒ ∠x₂ = ∠x₁ + 30° [Equation 2]
By exterior angle property :
⇒ ∠x₁ + ∠x₂ = ∠X [Equation 3]
Substituting Equation 3 in Equation 1 :
⇒ ∠x₁ + ∠x₂ + ∠x₁ + ∠x₂ = 180°
⇒ 2 (∠x₁ + ∠x₂) = 180°
⇒ ∠x₁ + ∠x₂ = 90°
⇒ ∠x₂ = 90° - ∠x₁ [Equation 4]
Substituting Equation 4 in Equation 2 :
⇒ 90° - ∠x₁ = ∠x₁ + 30°
⇒ 2∠x₁ = 60°
⇒ ∠x₁ = 30°
Substituting the value of ∠x₁ in Equation 2 :
⇒ ∠x₂ = 30° + 30°
⇒ ∠x₂ = 60°
The measures of the interior angles are 30° and 60°
Help Me, I only have 2 minutes
Answers
Answer:
[tex]6 \frac{2}{13} [/tex]
How many students were surveyed?
Answers
Answer:
20
Step-by-step explanation:
count the dots
Answer:
20 students
Step-by-step explanation:
You just need to count the number of dots.
hope this helps
have a good day
Two buildings are 96 ft apart . The first building is 164ft tall. The second building is 92ft tall. If a string is stretched between the top of the two buildings so that it forms a straight line from the top of one to the top of the other, how long would the string be
Answers
Answer:
120ft
Step-by-step explanation:
Help please
worth 14 points
Answers
Answer:
Ok I can walk you through if you comment the questions ok?
Step-by-step explanation:
Trust me :-)
Answer:
1. obtuse
2.straight
3.right
4. acute
5. <EAF
6. <DAF
7. <BAF
8. They are perpendicular to each other
Use the information in the table to find the indicated probability.
Number of Degree Recipients at a Local College
Degree Male Female
Associate's 224 387
Bachelor's 547 776
Advanced 245 322
Find P(the recipient is male).
Answers
Using it's concept, it is found that the desired probability is given as follows:
P(the recipient is male) = 0.4242 = 42.42%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there was a total of 224 + 387 + 547 + 776 + 245 + 322 = 2501 recipients, out of which 224 + 547 + 245 = 1016 are males, hence the probability is given by:
P(the recipient is male) = 1016/2501 = 0.4242 = 42.42%.
More can be learned about probabilities at https://brainly.com/question/14398287
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what is he inverse of the function f(x) = 1/2x+10?
Answers
Hope it helps!!!
(-2) +[(-13) +4]=[(-2) +(13) ]+4
Answers
A 3-yard roll of waxed paper costs $9.81. What is the price per foot?
Answers
Answer:
1.09
Step-by-step explanation:
9.81÷3=3.27 This shows the cost of 1 yard
3.27÷3= 1.09 since theres 3 feet in a yard, when you divide by 3 it shows how much 1 foot costs
. If you sampled 2000 people, how many would you expect to have BP> 160? Give your answer to the nearest person. Note: I had a bit of an issue encoding rounded answers, so try rounding both up and down if there's an issue!
Answers
Using the normal distribution, it is found that 84 people would be expected to have BP > 160.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Researching the problem on the internet, the mean and the standard deviation for the BPs are given, respectively, by:
[tex]\mu = 122, \sigma = 22[/tex].
The proportion of adults with BP > 160 is given by one subtracted by the p-value of Z when X = 160, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{160 - 122}{22}[/tex]
Z = 1.73
Z = 1.73 has a p-value of 0.9582.
1 - 0.9582 = 0.0418.
Out of 2000 people:
0.0418 x 2000 = 83.6.
Rounding to the nearest integer, 84 people would be expected to have BP > 160.
More can be learned about the normal distribution at https://brainly.com/question/24663213
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