Find the 87th term of the arithmetic sequence 1,14,27,….
Answer:
[tex]a_{87}=1119[/tex]
Step-by-step explanation:
Arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
where d is the common difference between terms and n is the index of any given term.
Find the difference between the terms in the given sequence here:
[tex]14-1=13\\27-14=13[/tex]
Each term has a common difference of 13. Using that, you can write the equation for this sequence:
[tex]a_n=1+(n-1)13[/tex]
Finally, you can use this equation to find the 87th term by plugging in 87 for n:
[tex]a_{87}=1+(87-1)13\\a_{87}=1+(86)13\\a_{87}=1+1118\\a_{87}=1119[/tex]
3.Original DNA sequence: 3' TACCGCTTACGTCTGATCGCT 5'
Mutated DNA sequence: 3' TACCGCTTATTATTACGTGCTGCTATCGCT 5'
Type of mutation (3pts):
Amino acid ( 3pts):
Type of mutation ( 3pts):
4. Original DNA sequence: 3' TACCGCTTACGTCTGATCGCT 5'
Mutated DNA sequence: 3' TACCGCTAATTATTACGTGCTGCTATCGCT 5'
Type of mutation ( 3pts) :
Amino acid ( 3pts):
Type of mutation ( 3pts):
3. The original sequence
TAC - CGC - TTA - CGT - CTG - ATC - GCT
codes for
tyr - arg - leu - arg - leu - ile - ala
while the mutated sequence codes for
TAC - CGC - TTA - TTA - TTA - CGT - GCT - GCT - ATC - GCT
tyr - arg - leu - leu - leu - arg - ala - ala - ile - ala
There are several frameshift mutations involved here:
• the first inserts 6 bases (TTA - TTA)
• the second inserts 1 base (G) before the CTG triplet (underlined)
• the third inserts 2 bases (CT) after the CTG triplet
4. The original sequence is the same as before. The mutated sequence
TAC - CGC - TAA - TTA - TTA - CGT - GCT - GCT - ATC - GCT
codes for
tyr - arg - STOP - leu - leu - arg - ala - ala - ile - ala
Then
• there is a (nonsense) point mutation that swaps T for A in the original TTA triplet (nonsense since it produces a stop codon that would halt replication/expression)
• there is a frameshift mutation that inserts 3 bases (TTA)
as well as two other frameshift mutations that also occurred in the previous part.
Population grows.
The population of Boston, MA in 2019 was
692,600 people with an annual rate of increase
1.4%. In what year the population of Boston
will reach 1,000,000 people, if the grows rate
stays the same? The function describing
population grows is P(x)=692,600 - 1.014,
where x is number of years.
Population are often modelled by exponential functions
The population will reach 1000000 people after 26.5 years
The population function is given as:
[tex]P(x) = 692600 \times 1.014^x[/tex]
When the population reaches 1000000 people, we have:
P(x) = 1000000
So, the equation becomes
[tex]1000000 = 692600 \times 1.014^x[/tex]
Divide both sides by 692600
[tex]1.444=1.014^x[/tex]
Take logarithm of both sides
[tex]log(1.444)=log(1.014)^x[/tex]
Apply logarithm to both sides
[tex]log(1.444)=xlog(1.014)[/tex]
Make x the subject
[tex]x = \frac{log(1.444)}{log(1.014)}[/tex]
Solve the logarithms of 1.444 and 1.014
[tex]x = \frac{0.15957}{0.00603}[/tex]
Divide
[tex]x = 26.5[/tex]
The value of x, is the number of years the population reaches 1000000 people.
Hence, the population will reach 1000000 people after 26.5 years
Read more about population at:
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What is the value of x + 2x when x=2/3?
Answer:
2
Step-by-step explanation:
2/3+2(2/3)
2/3+2×2/3
2/3+4/3
2+4/3
6/3
=2
Ashley completes 3 homework assignments in 50 minutes. At this rate, how many minutes will it take her to complete 9 homework assignments?
Answer:
144
Step-by-step explanation:
divide 50 by 3 and then multiply by 9
For every 50 emails that Nick sent in a month, he received 30 emails. What is the ratio in simplest form of the number of emails sent to the number of emails received by Nick that month? (5 points)
Question 2 options:
1)
5:2
2)
3:5
3)
2:5
4)
5:3
Answer:
50:30 or 50/30
Every 50 you get 30
Step-by-step explanation:
Solve two eighths times four fifths
Answer:
8/40 or 1/5
Step-by-step explanation:
2x4=8
8x5=40
That gives us the answer of 8/40 but if you need simplifying just divide 8/40 by 8/8 and you will get the final answer of 1/5
Solve the following system: 5x + 4y = 6 -2x – 3y = -1
Answer:
[tex]\left \{ {{y=-1} \atop {x=2}} \right.[/tex]
Step-by-step explanation:
[tex]\left \{ {{5x+4y=6} \atop {-2x-3y=-1}} \right. <=> \left \{ {{10x+8y=12} \atop {-10x-15y=-5}} \right.<=> \left \{ {{-7y=7} \atop {-10x-15y=-5}} \right. <=> \left \{ {{y=-1} \atop {-10x-15y=-5}} \right. <=> \left \{ {{y=-1} \atop {-10x+15=-5}} \right. <=>\left \{ {{y=-1} \atop {-10x=-20}} \right. => \left \{ {{y=-1} \atop {x=2}} \right.[/tex]
Mary has some chocolates. If she shares them equally among 4 friends or 5 friends, there are always 2 extra chocolates left. What is the possible number of chocolates Mary could have?
Answer:
22 chocolates
Step-by-step explanation:
First, let x represent the number of chocolates Mary has. Since she always has 2 extra chocolates, the number of chocolates distributed to her friends would be x - 2. And x - 2 is the least common multiple of 4 and 5 because x - 2 chocolates are evenly distributed among 4 and 5 friends. The LCM of 4 and 5 is 20, so x - 2 is 20. Mary has 22 chocolates.
PLS HELPPPPP!!!!!!!!
Answer:
not even bill nye could solve this
Help pls, will give brainliest
Simplify 2^3 x 2^18
Answer:
it is 2^21
Step-by-step explanation:
Answer:
2^21
Step-by-step explanation:
add 3 and 18 together
dont change 2
What system the system that is made up of the heart,blood, and blood vessels is called the ____ this is for sceince but i cant find sceince
Answer:
Cardiovascular system
Step-by-step explanation:
Find the value of x need help
Answer:
x = -8
Step-by-step explanation:
Angle 2 would be the same as 139
thus if angle 2 = x+147
then
139 = x + 147
x = -8
5. 4
Which input value produces the same output value for
the two functions on the graph?
(
*)
3
NO
O x= -1
O x = 0
O x= 1
O x= 2
-5 -3 -2 -
4
х
91x)
Answer:
x=1......................
Katerina is a real estate agent. Katerina works on a 4% commission. She earns a $4200
commission. What was the value of the house that she sold?
Answer:
105,000
Step-by-step explanation:
Question 9
The probability that a vehicle will change lanes while making a turn is 55%.
Suppose a random sample of 7 vehicles are observed making turns at a
busy intersection.
Calculate the expected value.
Answer:
3.85 (rounded to 4 cars)
Step-by-step explanation:
Let X be the discrete random variable the number of vehicles changing lanes
X~B(7, 0.55)
The expected value is found by:
E(X) = 7 × 0.55
E(X) = 3.85
y
is directly proportional to
x
2
.
If
y
=
8
when
x
=
2
find
y
when
x
=
3
Answer:
y = 18 when x = 3
Step-by-step explanation:
y is directly proportional to x^2, meaning:
[tex]y=ax^2[/tex]
where a is the proportion between them. We're given the values for both x and y, so plug those in and solve for a:
[tex]8=a(2)^2\\8=a4\\2=a\\a=2[/tex]
Now you can use a to solve for y when x is 3:
[tex]y=ax^2\\y=(2)(3)^2\\y=2(9)\\y=18[/tex]
Which of the following is a correct interpretation of the expression 5−8
Answer:
start at 5 on the number line and move 8 to the left.
Step-by-step explanation:
AWNSER DOES ANYONE KNOW the wander PLEASE I WILL GIVE BRIANLIEST
Answer:
C - qd
Step-by-step explanation:
qid means four times a day
tid means three times a day
qd means every other day (answer)
qod also means every other day (but since it's not recommended to use this notation, the answer should be qd)
Answer:
C. qd
Step-by-step explanation:
qd stands for quaque die in latin. translated to english it means every day.
A triangle has two angles with measures of 50 degrees and 70 degrees joined by a side with a length of 20 centimeters.
Which figure represents this triangle?
709
50
O
20
50
2009
70
o
500
709
20
20
70°
50°
Answer:
Step-by-step explanation:
Given :-
Two angles in a triangle have measurements of 20° and 50 °.
To Find :-
Measurement of third angles of triangle
Solution :-
We know that the sum of all angles of triangle is 180°.
Measurement of third angles = x
20° + 50° + x = 180°
combine like terms
70° + x = 180°
subtract both sides from 70°.
70° - 70° + x = 180° - 70°
x = 110 °
Hence, the measurement of the third angie of a triangle is 110°.
Answer:
The third option is the correct answer.
A music streaming service conducted a survey asking subscribers where they most often listen to music. Of the 2,500 responses, 1,468 users stated that they most often listen to music while in vehicles.
Use this information to complete the statement. Round all answers to the nearest hundredth.
The approximate sample proportion is ___, which means that ___% of the subscribers surveyed most often listen to music somewhere other than in a vehicle.
Answer:
0.59 and 41%
Step-by-step explanation:
Plato/Edmentum
The approximate sample proportion is o.59, which means that 41% of the subscribers surveyed most often listen to music somewhere other than in a vehicle.
For this situation, the number of positive responses is 1486 out of a total sample size of 2500.
Substitute these values into the formula for sample proportion, where x is the number of positive responses and n is the sample size.
[tex]\hat p = \frac{x}{n}[/tex]
= [tex]\frac{1468}{2500}[/tex]
= 0.59
So, the approximate sample proportion is 0.59.
Since 0.59 represents the proportion who responded favorably, 1-0.59=0.41, represents the proportion which responded unfavorably.
This value of the same as 41%.
So, 41% of the subscribers surveyed most often listen to music somewhere other than in a vehicle.
Therefore, the approximate sample proportion is o.59, which means that 41% of the subscribers surveyed most often listen to music somewhere other than in a vehicle.
Learn more about the sample proportion here:
https://brainly.com/question/33593792.
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Linda deposits $90,000 into an account that pays 6% interest per year, compounded annually.
Bob deposits $90,000 into an account that also pays 6% per year. But it is simple interest.
Find the interest Linda and Bob earn during each of the first three years.
Then decide who earns more interest for each year.
Assume there are no withdrawals and no additional deposits.
Answer: Linda earns more interest
Step-by-step explanation:
Linda: 90000 x 1.06^3 -90000 = 17191.44
Bob: (90000 x 1.06 - 90000) x 3 = 16200
17191.44 > 16200
The sum of three terms in AP is 15. If the first two terms are each decreased by 1 and the last is increased by 1 then the resulting terms are in GP. find the numbers.
Answer:
3, 5, ,7 or 9, 5, 1
Step-by-step explanation:
Let the three terms in AP be a - d, a & a + d
where a = First term and d = Common difference.
Condition 1: sum of three terms in AP is 15.
a - d + a + a + d = 15
3a = 15
a = 15/3
a = 5
Condition 2: When first two terms are each decreased by 1 and the last is increased by 1 then new terms so obtained will be as follows:
a - d - 1, a - 1, a + d + 1
These terms are in G.P.
[tex] {(a - 1)}^{2} = (a - d - 1)(a + d + 1) \\ \\ {(5 - 1)}^{2} = (5 - d - 1)(5 + d + 1) \\ \\ {(4)}^{2} = (4 - d)(6 + d) \\ \\ 16 = 24 + 4d - 6d - {d}^{2} \\ \\ 0 = 8 - 2d - {d}^{2} \\ \\ {d}^{2} + 2d - 8 = 0 \\ \\ {d}^{2} + 4d - 2d - 8 = 0 \\ \\ d(d + 4) - 2(d + 4) = 0 \\ \\ (d + 4)(d - 2) = 0 \\ \\ d + 4 = 0 \: \: or \: \: d - 2 = 0 \\ \\ d = - 4 \: \: or \: \: d = 2 \\ \\ when \: d = - 4 \\ \\ a - d = 5 - ( - 4) = 9 \\ a = 5 \\ a + d = 5 - 4 = 1 \\ \\ when \: d = 2 \\ a - d = 5 - 2 = 3 \\ a = 5 \\ a + d = 5 + 2 = 7 \\ \\ thus \: three \: terms \: in \: AP \: are: \\9, \: 5, \: 1 \: \: or \: \: 3, \: 5, \: 7[/tex]
Find the area of the figure.
7cm
8cm
11cm
Area is ___ square cm?
Answer:
616cm³
Step-by-step explanation:
you just need to multiply those numbers
7 x 8 x 11= 616
[tex]\text{Perimeter of the triangle,}\\\\ 2s = 7 + 8 +11 =26}\\\\\\\implies s = \dfrac{26}2 = 13\\\\\\\text{Apply Heron's formula to find the area of the triangle,}\\\\A = \sqrt{s(s-8)(s-7)(s-11)}\\\\\implies A = \sqrt{13(13-8)(13-7)(13-11)}\\\\\implies A = \sqrt{780} \\\\\implies A = 27.93~~ \text{cm}^2[/tex]
ivan earns $8 each time he walks his neighbors dog.He already walked the dog 5 times
Answer:
8 x 5..
Step-by-step explanation:
45$
Answer:
SO if you were to find how much Ivan make
So 8 dollars each time he walks his neighbors dog.
ANd already 5 times.
So we can do 8*5=40
$40 earned
3. Solve the formula A = 1/2 (b1+ b2))h for h. Show your work.
[tex]A = \dfrac 12 (b_1 + b_2)h\\\\\implies 2A = (b_1+b_2) h\\\\\implies h =\dfrac{2A}{b_1+b_2}[/tex]
3,311L how many millilters
Answer:
3311 mililiters
Step-by-step explanation:
1 L = 1 liter = 1000 mililiters
3.311L = 3.311 liters = 3.311*1000 = 3311 mililiters
Can someone help me? Will mark brainiest :)
According to his running log, Baldwin averaged 4 miles per week last month and 25% more this month. How much did he average this month?
Answer:
4(1.25) = if it’s only one month then it’s 5 miles
Step-by-step explanation:
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Question 7
Charlie asked a random sample of both boys and girls how much time they had spent on math homework that week. Charlie displayed his data in the box plots below
Minutes Spent on Homework
Boys
Girls
10 20 30
50 60 70
Which statement is a correct inference based on this data?
А
The amount of time spent on homework is less variable for the boys than for the girls
B
The amount of time spent on homework is generally greater for the boys than for the girls
С
The percentage of boys who spent less than the median amount of time on homework is less than the percentage of girls who spent less than the median
D
The data for the boys has a greater range of values than does the data for the girls
62021 Iluminate Education, Inc
The percentage of boys who spent less than the median amount of time is less than the number of girls who spent less than the median amount of time in doing the homework.
The median is a measure of central tendency. The median of a given data set shows the middle number in a given set of scores when they arranged in ascending or descending order.
The box plots in the question shows the random sample of both boys and girls how much time they had spent on math homework in a week. We can see from the box plot that the percentage of boys who spent less than the median amount of time is less than the number of girls who spent less than the median amount of time in doing the homework.
Learn more about median; https://brainly.com/question/300591