Answer:
Step-by-step explanation:
(a)
From the given information:
Let An denote the amount in the account at the end of n month
Thus,
[tex]A_o[/tex] =1000
After the first month ends, interest = [tex]=A_o \times \dfrac{3}{100} \times \dfrac{1}{12}[/tex]
= [tex]0.0025A_o[/tex]
Additional deposit = $200
Now,
[tex]A_1 = A_o + 0.0025A_o + 200[/tex]
[tex]=1.0025A_o + 200 --- eqn(1)[/tex]
Interest after 2nd month, = [tex]A_1 \times \dfrac{3}{100} \times \dfrac{1}{2}[/tex]
Additional deposit = $200
[tex]A_2 = A_1 + 0.0025A_1 + 200[/tex]
[tex]=1.0025A_1 + 200 --- eqn(2)[/tex]
Thus:
[tex]A_n = 1.0025A_{n-1} +200[/tex]
(b)
From above;
[tex]A_1 = 1.0025A_ 0+ 200[/tex]
Thus;
[tex]A _2 = 1.0025A_ 1+ 200[/tex]
[tex]A_2 = 1.0025( 1.0025A_ 0+ 200)+ 200[/tex]
[tex]A_2 = 1.0025^2A_o +200 ( 1+1.0025)[/tex]
[tex]A _3 = 1.0025A_ 2+ 200[/tex]
[tex]A _3 = 1.0025( 1.0025^2A_o +200 ( 1+1.0025))+ 200[/tex]
[tex]A _3 = 11.0025^3A_o +200 ( 1+1.0025 + 1.0025^2)[/tex]
To continuity...
[tex]A_n = 1.0025^n A_o + 200 (1+1.0025 +1.0025^2 +...+ 1.0025^{n-1} ) ---- (3)[/tex]
Thus, we have a geometric term [tex]1 + 1.0025 +1.0025^2 +...+ 1.0025^{n-1}[/tex]
where:
a = 1 (first term)
r = 1.0025>1 (common ratio)
Thus;
[tex]1 + 1.0025 +1.0025^2 +...+ 1.0025^{n-1} = \dfrac{a(r^n -1)}{r-1}[/tex]
[tex]= \dfrac{1(1.0025^n -1)}{1.0025-1}[/tex]
[tex]= 400(1.0025^n -1)[/tex]
From equation(3)
[tex]A_n = (1.0025^n \times 1000) + 80000(1.0025^n -1)[/tex]
[tex]A_n = 1.0025^n \times 81000-80000[/tex]
Using the table below, evaluate whether a monkey's age in years is a function of its height in inches.
Answer:
There is no function since there is no association between all the numbers
Step-by-step explanation:
If you were to put them in a graph they would be every where and make there be no function.
Given the side lengths 9.5 cm, 7.5 cm, and 10 cm, can they form a triangle and if so, what type of triangle?
Answer:
this number 6
Step-by-step explanation:
yes self 4
Answer:
yes
Step-by-step explanation:
because if you add correctly you will get the answer
A taxi agency collected data from a random sample of 600 people in their city asking whether or not they own a car. Based on the results, they report that 44% of the people in the state own a car. Why is this statistic misleading
Answer:
first of all 44% of 600 people is equal to 264 .
the statistics is misleading because 264 people can't unless the taxi angecy included themselves
Best answer gets brainiest. On Wednesday at camp, Diana went for a hike at 5:35 A.M. The hike took 1 hour and 30 minutes. As soon as she got back from the hike, Diana played volleyball for 55 minutes. What time did Diana finish playing volleyball?
Include A.M. or P.M. in your answer.
Answer:
Diana finshed playing volleyball at 8am
Step-by-step explanation:
So we know she started at 5:35 AM
And she hiked for an hour and 30 minutes
so 5:35+1 hour is 6:35
and 6:35+35 is 7:05
So before playing volley ball, the time is 7:05 am
Now volley ball was 55 minutes
so 7:05+55 is 8
So 8am
Answer:
She finish playing valleyball at 8:00 am
Step-by-step explanation:
Hike at 5:30 => 1h 30 min => 7:05
valleyball at 7:05 => 55 min => 8:00
choose all of the points that are solutions to y = 3x + 2 / 2x - 1.
A.(-2, 4/5)
B.(-1, -5)
C.(0, -2)
D.(0, -2/3)
E.(1, 3/2)
F.(1, 5)
G.(4, 14)
Answer:
a d f g
Step-by-step explanation:
Answer:
its abfg
Step-by-step explanation:
The pencils produced by the machine are unsharpened, so two employees in the factory need to sharpen each pencil by hand. Employee A can sharpen 8 pencils per minute and Employee B can sharpen 5 pencils per minute. Employee A breaks 10% of the pencils they sharpen and Employee B breaks 15% of the pencils they sharpen. What is the probability that a broken pencil was broken by Employee A
Answer:
0.4156
Step-by-step explanation:
Given that:
Employer A:
8 pencils per minute
Probability of breaking a pencil = p(A) = 10%
Employer B:
5 pencils per minute
Probability of breaking a pencil = p(B) = 15%
Hence,
Probability of breaking a pencil:
P(breaking a pencil) = (P(A breaks pencil) * P(A)) + (p(B breaks pencil) * p(B))
P(A breaks pencil) = 0.1 * 8 = 0.8
P(B breaks pencil) = 0.15 * 5 = 0.75
P(breaking a pencil) = (0.8 * 0.1) + (0.75 * 0.15) = 0.1925
Hence, probability that a broken pencil was broken by employer A will be :
(P(A breaks pencil) * P(A)) / probability of breaking a pencil
= (0.8 * 0.1) / 0.1925
= 0.08 / 0.1925
= 0.4155844
= 0.4156
The inter quartile range of a distribution is 7. If the 25th percentile is 16. Find the upper quartile
Given:
Inter quartile range(IQR) of a distribution = 7
25th percentile = 16
To find:
The upper quartile.
Solution:
We have,
IQR = 7
25th percentile = lower quartile = 16
We know that,
IQR = Upper quartile - Lower quartile
Let the upper quartile be [tex]Q_3[/tex].
Using the above formula, we get
[tex]7=Q_3-16[/tex]
Adding 16 on both sides, we get
[tex]7+16=Q_3-16+16[/tex]
[tex]23=Q_3[/tex]
Therefore, the upper quartile of the distribution is 23.
16 out of 25 tables are wooden. What percent of the tables are wooden?
This is a question on homework i have
Answer:
64%
Step-by-step explanation:
16/25 will give you 64%
please give thanks by clicking heart button!
Answer:
64%
Step-by-step explanation:
Page 2 I need help with this whole page! And be careful, my teacher said “think about what part of the equation deals with price “
Answer:
a) Already correct
b) If x represents each one dollar increase in price, than prices that are increased by $16 and $28
c) $6
d) Maximum Revenue would be $2,420
e) x = -5 but it's extraneous
(if we were using imaginary numbers then it would be 5i)
Step-by-step explanation:
8n^2-17
I NEED AN ANSWER
Answer: 37
Step-by-step explanation:
27/9 = 18/ x
Please select the best answer from the choices provided.
A: x = 9
B: x = 8
C: x = 6
D: x = 3
Answer:
x= 6 answer is correct answer
Answer:
C. x=6
Step-by-step explanation:
Hope this helped have an amazing day!
Alexandra has 4 bags of beads. Some of the bags contain 3 purple beads and the rest contain 6 indigo beads. If Alexandra has 21 beads in all, how many bags of each color bead does Alexandra have?
Please help me fast!!
Answer:
4 bags of purple beads and 3 bags of indigo beads.
Step-by-step explanation:
Total number of beads = 21 beads'
Total bags of beads = 4 bags
Purple beads = 3 purple beads
Indigo beads = 6
Let x be each bags of purple beads
Let y be each bags of indigo beads
Since there are 4 bags of bead then;
x + y = 4 ....1
If some of the bags contain 3 purple beads and the rest contain 6 indigo beads, then;
3x + 6y = 21
x + 2y = 7.....2
Subtract 1 from 2
y - 2y = 4 - 7
-y = -3
y = 3
Sunce x + y =7
x = 7-y
x = 7-3
x = 4
Hence there are 4 bags of purple beads and 3 bags of indigo beads.
Solve the following equation for x: -3(x-2)=12
I need help!!
Answer:
x = -2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
-3(x - 2) = 12
Step 2: Solve for x
Divide -3 on both sides: x - 2 = -4Add 2 on both sides: x = -2Help quick please algebra one
Answer:
b. (5,-2)
Step-by-step explanation:
When we substitute the x and y values into the equation and simplify the equation we end up with these equations:
-2 ≤ 0
-2 ≥ -9
Once simplified, the equations are proven to be correct.
(I hope this helps)
Answer:
The answer is B, (5,-2)
Step-by-step explanation:
If you input the x and y values from (5,-2) into the system on inequalities both the equations end up being true, while all the other make one or more solution set incorrect when you input the x and y values.
What is the area of the trapezoid?
Answer:
a+b/2×h=56
Step-by-step explanation:
thanks needed.......
In the accompanying diagram, lines AB and CD
intersect at point E. If m
m
The required value of x is 40 which is determined by the substitute that equals the vertical angles.
What are the vertical angles?When two lines intersect at a location, vertical angles are generated. They are always equal to each other.
As per the given accompanying diagram, lines AB and CD intersect at point E.
Since ∠AED and ∠BEC are vertical angles then they are congruent, thus
⇒ ∠AED = ∠BEC
⇒ (x + 10) = 50
Subtract 10 from both sides of the above equation,
⇒ x + 10 - 10 = 50 - 10
⇒ x = 40
Thus, the required value of x is 40.
Learn more about the Angles here:
brainly.com/question/2125016
#SPJ2
A store pays $675.58 for a rowboat. The store marks up the price by 10%. What is the amount of the mark-up? Round your answer to the nearest cent: $
Answer:
743.1
Step-by-step explanation:
675.58 • 1.10 = 743.138
743.138 rounded to the nearest tenth is 743.1.
Two fair dice, one yellow and one blue, are rolled. The value of the blue die is subtracted from the value of the yellow die. Which of the following best describes the theoretical probability distribution?
Answer:
symmetric
Step-by-step explanation:
its correct.
Answer:
B symmetric
Step-by-step explanation:
write an expression to represent f(20)
Answer:
Tommy has f amount of marbles. His wife has 20 times Tommy's amount.
Step-by-step explanation:
f×20
Dominic is deciding between two different movie streaming sites to subscribe to. Plan A costs $27 per month plus $3 per movie watched. Plan B costs $35 per month plus $1 per movie watched. Let
A
A represent the monthly cost of Plan A if Dominic watches
x
x per month, and let
B
B represent the monthly cost of Plan B if Dominic watches
x
x movies per month. Write an equation for each situation, in terms of
x
,
x, and determine the interval of movies watched,
x
,
x, for which Plan A is cheaper than Plan B
what is the area of this figure
enter your answer in the box
__ units2
Answer:
44
Step-by-step explanation:
Well if you see the picture
triangle 1 has an area of
[tex]\frac{3*4}{2}=6[/tex]
triangle 2 has an area of
[tex]\frac{3*4}{2}=6[/tex]
rectangle 3 has an area of
[tex]8*3=24[/tex]
and triangle 4 has an area of
[tex]\frac{2*8}{2}=8[/tex]
if we add then up
[tex]6+6+24+8=44[/tex]
one - step adding/ subtraction equation / multiplication/ division problems
The height of the water in an above ground pool is 36 inches. The pool needs to be drained. As the water drains, the height of the water changes at a rate of -1/2 inch per minute. Write and solve and equation to find out how many minutes it will take to drain the pool.
Answer:
It would take x = 72 minutes to drain the pool.
Step-by-step explanation:
We know that the slope-intercept form of the line equation is
[tex]y = mx+b[/tex]
where m is the rate of change or slope and b is the y-intercept
Let 'y' be the height of the water poolLet 'x' be the time in the minute of the water poolAs the height of the water of the pool is 36 inches, meaning the basic condition of the pool states that the ground pool is 36 inches.
Thus,
y-intercept = b = 36As the water drains, the height of the water changes at a rate of -1/2 inch per minute.
Thus, the rate of change or slope = m = -1/2Thus, using the equation
[tex]y = mx+b[/tex]
substituting m = -1/2 and b = 36
[tex]y\:=\:-\frac{1}{2}x+36[/tex]
We know that when the pool drains, the height of water reduces to zero.
Thus, substituting y = 0 in the equation
[tex]0=-\frac{1}{2}x+36[/tex]
switching sides
[tex]-\frac{1}{2}x+36=0[/tex]
subtract 36 from both sides
[tex]-\frac{1}{2}x+36-36=0-36[/tex]
[tex]-\frac{1}{2}x=-36[/tex]
Multiplying both sides by -2
[tex]\left(-\frac{1}{2}x\right)\left(-2\right)=\left(-36\right)\left(-2\right)[/tex]
[tex]x=72[/tex]
Therefore, it would take x = 72 minutes to drain the pool.
The probability of waiting 2 minutes or longer for checkout at a particular supermarket counter is 0.3. On a given day, a man and his wife decide to shop individually at the market, each checking out at different counters. They both reach the counters at the same time. What is the probability that one or the other or both will wait 2 minutes or longer?
Answer:
The probability answer is 69/100
Step-by-step explanation:
The probability of waiting 2 minutes or longer = 0.3= (3/10)
The probability of not waiting longer = 1 - (3/10) = (7/10)
For the man,
P(waiting 2 mins or longer) = 3/10
For the woman,
P(waiting 2 mins or longer) = 3/10
Therefore,
The probability that one or the other or both will wait 2 minutes or longer
= P(man waits 2 mins or longer) or P(woman waits 2 mins or longer) or P(both waits 2 mins or longer)
= (3/10) or (3/10) or ( (3/10) and (3/10) )
= (3/10) + (3/10) + ( (3/10) X (3/10) )
= (6/10) + (9/100)
= (69/100)
how many number of permutations are in the word : entree
Answer:
120
Step-by-step explanation:
entree has 6 letters so 6! in numerator and e repeated 3 times so 3! in denominator.
(x-2)^2(x-3)(x+1)<0
Answer:
−1<x<2 or 2<x<3
Step-by-step explanation:
You need to find the critical points of the inequality first. Factor must be at left side of equation. Then set factors to 0. Be sure to check intervals in between critical points (test the intervals to see if they work/fit).
Hope this helps!
What is the missing length for this one?
Answer:
The missing length is 8
Step-by-step explanation:
Represent the missing length with x
The non-parallel sides of the given shape are directly proportional.
Mathematically:
3 to 6 and 4 to x
Represent as a ratio:
[tex]3 : 6 = 4 : x[/tex]
Convert to fraction
[tex]\frac{3}{6} = \frac{4}{x}[/tex]
Cross Multiply:
[tex]3 * x = 6 * 4[/tex]
[tex]3x = 24[/tex]
Divide through by 3
[tex]x = \frac{24}{3}[/tex]
[tex]x = 8[/tex]
The length of the missing side is 8
what is 9/4-2(4x+4/3)+5/2x?
9514 1404 393
Answer:
-11/2x -5/12
Step-by-step explanation:
Eliminate parentheses and collect terms.
9/4 -2(4x +4/3) +5/2x . . . . given
= 9/4 -8x -8/3 +5/2x
= (-16/2 +5/2)x +27/12 -32/12 . . . . use common denominators
= -11/2x -5/12
An insurance company receives nine claims per week, on average. Use this information to answer the next two questions. What is the probability that exactly 7 claims will be received in one week
Answer:
P(X = 7) = 0.11712
Step-by-step explanation:
From the information given:
Average no. of claims received per week λ = 9
The required probability that exactly 7 claims will be received is determined by applying the Poisson distribution formula:
[tex]P(X=x) = \dfrac{\lambda ^x e^{-\lambda}}{x!}[/tex]
[tex]P(X=7) = \dfrac{9 ^7 e^{-9}}{7!}[/tex]
[tex]P(X=7) = \dfrac{4782969 \times1.23409804 \times 10^{-4}}{5040}[/tex]
[tex]P(X=7) = \dfrac{590.2652672}{5040}[/tex]
P(X = 7) = 0.11712
Does anyone know the answers to the Geometry test? I need help with the answers on transformation and congruence
Answer:
We can surely help you on your geometry test. Please post the questions and our experts will gladly help you!Which is greater 3/8 or 6/16
Answer:
they are the same
Step-by-step explanation:
They are the same
[tex]\frac{3}{8}\\\\=\frac{3}{8}\times\frac{2}{2}\\\\=\frac{3*2}{8*2}\\\\=\frac{6}{16}[/tex]
