Answer:
a(t)= 2000(1+r)^T
*make sure to add the power to t
a(t)=2000(1+.10)^5
= 3221.02
Hope this helps!
The exponential decay function is given by y=2000×0.9ˣ and the stock will be worth $1180.98 after a period of 5 years.
What is exponential decay function?In mathematics, exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y=a(1-b)ˣ wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.
Given here: The value of the stock in 2012 was $2000 and the value decreases each year by 10%
We know the exponential decay is given by y=a(1-b)ˣ
where x is the number of years and 1-b is the decreasing factor
Thus based on the given information we can construct the exponential decay function as y=2000(1-10%)ˣ
or y=2000×0.9ˣ
Therefor in 5 years i.e in 2017 the stock will be worth
y=2000×0.9⁵
=$1180.98
Hence, The exponential decay function is given by y=2000×0.9ˣ and the stock will be worth $1180.98 after a period of 5 years.
Learn more about functions here:
https://brainly.com/question/28303908
#SPJ2
Suppose that a random sample of 20 items is selected from the machine. If the machine produces 5% defectives, find the probability that the sample will contain at least three defectives, by using the following methods. (a) the normal approximation to the binomial (Round your answer to four decimal places.) (b) the exact binomial tables (Round your answer to three decimal places.)
Answer:
a) 0.0618 = 6.18% probability that the sample will contain at least three defectives.
b) 0.076 = 7.6% probability that the sample will contain at least three defectives
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Sample of 20 items is selected from the machine.
This means that [tex]n = 20[/tex]
5% defectives
This means that [tex]p = 0.05[/tex]
(a) the normal approximation to the binomial
The mean is:
[tex]\mu = E(X) = np = 20*0.05 = 1[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.05*0.95} = 0.9747[/tex]
The probability is, using continuity correction, [tex]P(X \geq 3 - 2.5) = P(X \geq 2.5)[/tex] , which is 1 subtracted by the pvalue of Z when X = 2.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.5 - 1}{0.9747}[/tex]
[tex]Z = 1.54[/tex]
[tex]Z = 1.54[/tex] has a pvalue of 0.9382
1 - 0.9382 = 0.0618
0.0618 = 6.18% probability that the sample will contain at least three defectives.
(b) the exact binomial tables
This is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.358[/tex]
[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.377[/tex]
[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.189[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.358 + 0.377 + 0.189 = 0.924[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.924 = 0.076[/tex]
0.076 = 7.6% probability that the sample will contain at least three defectives
Please solve the following problem.
Express the complex number [tex]z = 8 \text{cis} \frac{2\pi}{3}[/tex] in rectangular form [tex]a+bi[/tex].
Answer:
- 4 + 4√3 i, where a = -4 & b = 4√3
Step-by-step explanation:
z = 8 cis(2π/3)
z = 8 [cos(2π/3) + i sin(2π/3) ]
z = 8 [cos(π - π/3) + i sin(π - π/3)]
z = 8 [ - cosπ/3 + i sin(π/3)]
z = 8[ - 1/2 + i √3/2 ]
z = - 4 + 4√3 i [in a + bi form]
Note that: cis x = cosx + i sinx
Answer:
[tex]a + bi = - 4 + 4 \sqrt{3} i[/tex]
Step-by-step explanation:
we are given [tex]\displaystyle cis(\dfrac{2\pi}{3})[/tex]
recall complex number trigonometric form:
[tex] \displaystyle \: r( \cos( \theta) + i \sin( \theta) )[/tex]
we are already given that [tex]\theta=\dfrac{2\pi}{3}[/tex]
recall complex number rectangular form
[tex] \displaystyle \: a + bi[/tex]
where [tex]\displaystyle a=r\cos(\theta)\: and\: b=r\sin(\theta)[/tex]
let's work with a:
substitute the value of [tex]\theta[/tex] and r
[tex] \displaystyle \: a = 8 \times \cos( \frac{2\pi}{ 3} ) [/tex]
recall unit circle
so [tex]\cos(\dfrac{2\pi}{3})[/tex] should be in Q:II
[tex] \displaystyle \: a = 8 \times - \frac{1}{2} [/tex]
simplify multiplication:
[tex] \displaystyle \: a = - 4[/tex]
let's work with b:
substitute the value of [tex]\theta[/tex] and r:
[tex] \displaystyle \: b = 8\sin( \frac{3\pi}{2} ) [/tex]
recall unit circle so [tex]\sin(\dfrac{3\pi}{2})[/tex] should be in Q:II
[tex] \displaystyle \: b = 8 \times \frac{ \sqrt{3} }{2} [/tex]
simplify:
[tex] \displaystyle \: b = 4 \sqrt{3} [/tex]
so
[tex] \displaystyle \: b i= 4 \sqrt{3} i[/tex]
hence,
[tex]a + bi = - 4 + 4 \sqrt{3} i[/tex]
In 2013 the most expensive cocktail (made with 1858 ‘Cuvee Leonie’ cognac) was sold in Australia for $12,000. What would have been the equivalent price just one year later, in 2014?
Answer:
$14,000
Step-by-step explanation:
What's the measure of angle B in degrees?
Answer:
angle B is 27 degrees.
Step-by-step explanation:
pentru triunghiurile congruente ijk si lmn sau scris cate trei congruente ale elementelor acestora scrie congruentele lipsa
i am just doing this so I can get more answers
Step-by-step explanation:
Branliest to correct answer explain how you solved it please
Answer:
0.03
Step-by-step explanation:
.25% for the tails times .5 for the odd number on the dice times 0.25 for the clubs because it is a 13/52 chance you will pull a clubs and put that all together and you get 0.03125 simplified and you get 0.03
Answer:
0.03
Step-by-step explanation:
The probability of landing on 1 tail is 1/2, since it is 1 out of 2 options, a tail or a head. If you want the probability of two tails, it would be 1/2 * 1/2 = 1/4.
Next we can take the probability of rolling an odd number on a fair die. A fair die has 3 even numbers: 2,4,6; and 3 odd numbers: 1,3,5. Since 3/6 or 1/2 of the numbers are odd, there is a 50% chance that it would roll an odd number.
Finally, drawing a club out of standard deck of cards is 1/4, since there are 4 choices: hearts, spades, clubs, or diamonds. You now get the idea, and you can figure out that the probability would be 1/4.
Our last step is to multiply all the answers we get, since to get all of them at once would lower your chances. 1/4 * 1/2 * 1/4 = 1/32 = 0.03125; rounded to 0.03.
Dawn bought 12 grams of chocolate. She ate half of the chocolate. How many grams of chocolate did she eat
What is the value of (52 - 10) = 5 x 23?
А
0
B
18
C
24
D 40
Answer:
I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer. I don't know the answer.The table shows a function. Is the function linear or non linear
Answer:
To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is, you're looking at a linear function!
HELP PLS MIGHT GIVE BRAINLIST BUT ONLY IF 2 PEOPLE ANSWER!
WILL MARK!
For parallelogram ABCD, find x.
Answer:
x = 16
Step-by-step explanation:
If the figure is a parallelogram, the opposite sides are the same length
3x+20 = 5x-12
Subtract 3x from each side
3x+20 -3x = 5x-12-3x
20 = 2x-12
Add 12 to each side
20+12 = 2x-12+12
32 = 2x
Divide each side by 2
32/2 = 2x/2
16 =x
PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
add 6 to both sides and dividing both sides by 5.
Answer:
add 6 to both sides then divide both sides by 5
Step-by-step explanation:
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
15
12
Answer:
x = 9
Step-by-step explanation:
[tex]a^{2} = c^{2} - b^{2}[/tex]
[tex]a^{2} = 15^{2} - 12^{2}[/tex]
[tex]a^{2} = 225 - 144[/tex]
[tex]a^{2} = 81[/tex]
[tex]\sqrt{a^2} = \sqrt{81}[/tex]
[tex]a = 9[/tex]
Noah has $5.
1.
a.
Elena has 40% as much as Noah. How much does Elena have?
b.
Compare Elena's and Noah's money using fractions. Draw a diagram to
illustrate.
Answer:
a. $4
b. Noah has 5/5. Elena has 4/5.
Step-by-step explanation:
Noah has $5.
a.
Elena has 80% of Noah's money.
80% of $5 = 0.80 * $5 = $4
b.
Noah has $5. We can consider $5 to be the full amount.
A full amount is 100% or 1 or 5/5.
Elena has 80% of Noah's money, so she has 80/100 of Noah's money.
80/100 reduces to 4/5.
Noah has 5/5, and Elena has 4/5.
The money that Elena has is $2.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
The given problem can be solved as follows,
(a) The amount of money Elena has is 40% of that of Noah.
It can be written as follows,
40% × 5
= 40/100 × 5
= 2
(b) Since the Elena has 40% of the Noah's money,
In the form of fraction it can be written as follows,
40% = 40/100
= 2/5
This can be represented in a diagram as follows,
In the diagram shown the circle has in total 5 sectors of which 2 yellow sectors represent Elena's money.
Hence, the amount of money Elena has is $2 which is shown in the diagram.
To know more about percentage click on,
brainly.com/question/29306119
#SPJ2
A man who is 2m tall stands on horizontal ground 30m from a tree . The Angel of elevation of the top of the tree from his eyes is 28 . Fine the distance between the man eyes to the top of the tree
Answer:
33.97 m
Step-by-step explanation:
Given that,
The height of a man = 2 m
He stands on a horizontal ground 30m from a tree.
The angle of elevation of the top of the tree from his eyes is 28°.
We need to find the distance between the man eyes to the top of the tree. Let the height of the tree be h
Using trigonometry to find such that,
[tex]\tan28=\dfrac{h}{30}\\\\h=\tan28\times 30\\\\h=15.95[/tex]
Now let us consider that the distance between the man eyes to the top of the tree is x. Using Pythagoras theorem,
[tex]x^2=30^2+15.95^2\\\\x=33.97\ m[/tex]
So, the distance between the man eyes to the top of the tree is 33.97 m.
PLZ HURRY, TIMED, WILL MARK BRAINLIEST********
K [Not drawn to scale] Which is true about the diagram? Select two options. MZIKH+MZIKL= 180° MZIKLU MZILK+mZKIL = 180° DmZJKH= MZJLK O MZIKLU MZILK= 90° OmZKIL= MZKLJ
Determine whether the given scenario meets the criteria of a binomial distribution. If not, identify the requirement that is not satisfied. If there is more than one requirement that is not satisfied, please indicate this by selecting the correct choice below. You ask ten randomly chosen college students to rate their experience at the dining hall on a scale of 1-5.
a. Yes, this scenario can be modeled using a binomial distribution.
b. No, there is no fixed number of trials and there are more than two possible outcomes for each trial.
c. No, there are more than two possible outcomes for each trial.
d. No, there is no fixed number of trials.
Answer:
c. No, there are more than two possible outcomes for each trial.
Step-by-step explanation:
Binomial probability distribution:
Only two possible outcomes, success or failure.
In each trial, the probability of a success must be the same.
The number of trials must be fixed.
You ask ten randomly chosen college students to rate their experience at the dining hall on a scale of 1-5.
There are 10 trials, which is a fixed number and respects the binomial distribution. However, there are five possible outcomes(numbered 1 to 5). Since there is more than two possible outcomes, the scenario cannot be modeled using a binomial distribution, and the correct answer is given by option c.
Tom surveyed a random sample of the junior of his school to determine whether the Fall Festival should be held in October or November. Of the 80 students surveyed, 24.8% said they preferred November. Based on this information, about how many students in the entire 230-person class would be expected to prefer having the Fall Festival in November. SHOW YOUR WORK PLEASE!!!
a. 50
b. 60
c. 75
d. 80
9514 1404 393
Answer:
b. 60
Step-by-step explanation:
We assume the percentage for the sample holds for the whole class, so the estimated number preferring November is ...
0.248 × 230 = 57.04 ≈ 60
About 60 students prefer November.
PLZ HELP DEW BY 5PM
This graph represents the relationship between x and y.What is an equation showing the relationship between x and y?Enter your answer in the box.
Answer:
Points I guess
Ran has 17 cameras to clean. He cleans 10 cameras.Then rah finds 8 more cameras to clean. How many cameras does ran has to clean now?
Answer:
total of 25 to clean.
did 10
has 15 left
Answer: 15
Step-by-step explanation:
Ran Needs to clean 17 cams... he already cleaned 10, so subtract 17-10... it would be 7
he finds 8 cams to clean... so we add 8+7... and it becomes 15...
brainliest appreciate
The following data will be used to construct a box plot. What will be the value of the median? 2, 5, 10, 11, 12, 15, 21, 32, 32, 46
a sector has a radius of 4 and a central angle of 40 degrees. Find the arc length and area of sector
Answer:
Step-by-step explanation:
θ = 2π/9 radians
arc length = rθ = 8π/9 units
area of sector = πr²/9 = 16π/9 square units
which of the following phrases describes the expression 2 - 2x
Answer:c
Step-by-step explanation:cccccc
Find b and c so that y =
2x^2 + bx+c has vertex (0,-2)
b=
C=
Answer:
Step-by-step explanation:
2x - 3
L
M
x + 4
X =
?
Answer: 7
Step-by-step explanation:
2x - 3 = x + 4
2x - x - 3 = 4 Mius x from the both side
x - 3 = 4
x = 7 Add the 3 from both side
HELP I WILL GIVE BRAINLEIST OR WHATEVER 50 POINTS
answer:
a. scarf costs today = $6
b. scarf costs 3 days from now = $3
step-by-step explanation:
1/2 off means you would multiply the amount by 1/2 then subtracta. original price of scarf: $12
12 X 1/2 = 6
12 - 6 = 6
— scarf costs today = $6
do the same thing but this time it is a different numberb. 12 X 3/4 = 9
12 - 9 = 3
— scarf costs 3 days from now = $3
Number 1 and solve please
ok.........................................
solve the inequality 0<5x-2<8
Answer:
×= 2 this is what I got as a result to my equations
I will mark as the brainlest if correct
Answer:
Answer A
Step-by-step explanation:
Please answer this :/
Answer:
-60
Step-by-step explanation:
-45+s=-105
s=-105+45
s=-60