Answer:
The correct answer is "1668". A further solution is provided below.
Step-by-step explanation:
According to the question,
Estimated proportion,
[tex]\hat{p} = \frac{574}{1007}[/tex]
[tex]=0.57[/tex]
Margin of error,
E = 0.02
Level of confidence,
= 90%
= 0.90
Critical value,
[tex]Z_{0.10}=1.65[/tex]
Now,
⇒ [tex]0.02=1.65\times \sqrt{\frac{0.57\times 0.43}{n} }[/tex]
[tex]0.0004=2.7225\times \frac{0.2451}{n}[/tex]
[tex]n=\frac{2.7225\times 0.2451}{0.0004}[/tex]
[tex]=1668.21[/tex]
or,
[tex]n \simeq 1668[/tex]
9 friends are lining up. Joe, Susan, John, and Meredith must be beside each other. How many ways can they line up?
This is one single number slightly over 17 thousand.
You may need to erase the comma when typing the answer in.
=========================================================
Explanation:
Let's say that another person steps in for Joe, Susan, John, and Meredith. I'll refer to this person as the teacher (perhaps these 9 friends are students on a field trip).
The 9 friends drops to 9-4 = 5 people when those four named people leave the group temporarily. Then it bumps up to 5+1 = 6 people when the teacher steps in. Wherever the teacher is located, the four friends that left will replace the teacher. This guarantees that those four friends stick together.
There are 6! = 6*5*4*3*2*1 = 720 ways to arrange those 6 people. The exclamation mark is a factorial symbol.
Within any of those 720 permutations, we have 4! = 4*3*2*1 = 24 ways to arrange those group of named people when they come back to replace the teacher.
So overall the answer is 4!*6! = 24*720 = 17,280
You may need to erase the comma when typing the answer in.
-------------
Side note: There are 9! = 362,880 ways to arrange all nine friends regardless if those four mentioned people stick together or not. We see that they stick together roughly (17,280)/(362,880) = 0.0476 = 4.76% of the time.
You bought a car that was $25500 and the value depreciates by 4.5% each year.
How much will the car be worth after 5 years?
How much after 8 years?
Answer:
(a) 20256.15625
(b) 17642.78546
Step-by-step explanation:
(a) There's a formula for this problem y = A(d)^t where, A is the initial value you are given, d is the growth or decay rate and t is the time period. So, in this case, as the car cost is decreasing it is a decay problem and we can write the formula as such; y = A(1-R)^t
So, in 5 years the car will be worth, 25500(1-4.5%)^5 or 20256.15625 dollars
(b) And after 8 years the car will be worth 25500(1-4.5%)^8 or 17642.78546 dollars.
I really need help please
9514 1404 393
Answer:
60
Step-by-step explanation:
The minimum number required is the least common multiple (LCM) of 15 and 4. The numbers 15 and 4 have no common factors, so their LCM is their product.
15×4 = 60 strands are required
A classmate walks into class and states that he has an extra ticket to a chamber orchestra concert on Friday night. He asks everyone in the class to put their name on a piece of paper and put it in a basket. He plans to draw from the basket to choose the person who will attend the concert with him. If there are 38 other people in class that night, what is your chance of being chosen to attend the concert
Answer:
2.56% chance of being selected
Step-by-step explanation:
Given
[tex]n = 39[/tex] --- you and 38 others
Required
Chance of you being selected
To do this, we simply calculate the probability using:
[tex]Pr(x) = \frac{n(x)}{n}[/tex]
Where:
[tex]n(x)= 1[/tex] --- i.e you are just 1 person
So:
[tex]Pr(x) = \frac{1}{39}[/tex]
[tex]Pr(x) = 0.0256[/tex]
Express as percentage
[tex]Pr(x) = 2.56\%[/tex]
Hello
Kb here just need help finding out this question I love this app thanks for all the help !
Step-by-step explanation:well its basiclly 2-1!
2. About 40 millions of aluminum cans can be recycled each month in the US. A quarter of these aluminum cans are used to make one aluminum boat. How many aluminum boats can be made in one year in the US?
Answer:
48
Step-by-step explanation:
About 40 millions of aluminum cans can be recycled each month in the US. A quarter of these aluminum cans are used to make one aluminum boat. How many aluminum boats can be made in one year in the US?
Given that:
Approximate Number of cans that can be recycled per month in the US = 40 million
Fraction of recycled cans that can be used to make an aluminum boat = 1/4
The number of aluminum boats that can be made in the US in one year :
If about 40 million cans are recycle per month :
The number of boat that can be made from each monthly recycled aluminum cans will be :
Number of monthly recycled can needed to make one boat:
1/4 * 40 million = 10 million cans
Hence, 40,000,000 / 10,000,000 = 4
4 aluminum boats can be made in one month :
Number of months in a year = 12
Number of aluminum boats that can be made in a year :
4 per month * 12 = 48 aluminum boats
The club will use the majority criterion method to determine the final winner. However, while finalizing the votes, a member of the club discovers that Mason did not meet the original criteria to be considered for the vacation package, because he is a county deputy, not a city police person, so Mason is eliminated from the votes. Who actually will win the tickets? Is the irrelevant alternative criterion supported in this case?
Answer and Explanation:
The irrelevant alternative criterion states that if two candidates A and B contest for an election and candidate B is preferred to candidate A then any other candidate X should not cause candidate A to win the election.
In this case if Mason was candidate A, then candidate B should still win by the majority criterion method and the irrelevant alternative criterion would still be supported. However if he is candidate B then the irrelevant alternative criterion is not supported.
Measurement error that is normally distributed with a mean of 0 and a standard deviation of 0.5 gram is added to the true weight of a sample. Then the measurement is rounded to the nearest gram. Suppose that the true weight of a sample is 166.0 grams.
(a) What is the probability that the rounded result is 167 grams?
(b) What is the probability that the rounded result is 167 grams or more?
Answer:
(a)[tex]0.15731[/tex]
(b)0.02275
Step-by-step explanation:
We are given that
Mean=0
Standard deviation=0.5 g
True weight of a sample=166 g
Let X denote the normal random variable with mean =166+0=166
(a)
P(166.5<X<167.5)
=[tex]P(\frac{166.5-166}{0.5}<\frac{X-\mu}{\sigma}<\frac{167.5-166}{0.5})[/tex]
=[tex]P(1<Z<3)[/tex]
=[tex]P(Z<3)-P(Z<1)[/tex]
[tex]=0.99865-0.84134[/tex]
[tex]=0.15731[/tex]
(b)
[tex]P(X>167)=P(Z>\frac{167-166}{0.5})[/tex]
[tex]=P(Z>2)[/tex]
[tex]=1-P(Z<2)[/tex]
[tex]=1-0.97725[/tex]
[tex]=0.02275[/tex]
Which law would you use to simplify the expression?
Answer:
A. quotient of Powers
Step-by-step explanation:
hope it helps
Answer:
A. Quotient of powers
Step-by-step explanation:
Hope it helps
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Solve the equations for x and match the solutions.
1
r
6
4 = 1
+ 5
-ar
20 = -14
7 + 2ar = 13
Answer:
..
Step-by-step explanation:
[tex]x = - \frac{a}{6} [/tex]
[tex]x = - \frac{6}{a} [/tex]
[tex]x = \frac{3}{a} [/tex]
SCALCET8 3.9.015. A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 35 ft from the pole
Answer:
[tex]X=6.67ft/s[/tex]
Step-by-step explanation:
From the question we are told that:
Height of pole [tex]H_p=15[/tex]
Height of man [tex]h_m=6ft[/tex]
Speed of Man [tex]\triangle a =4ft/s[/tex]
Distance from pole [tex]d=35ft[/tex]
Let
Distance from pole to man=a
Distance from man to shadow =b
Therefore
[tex]\frac{a+b}{15}=\frac{b}{6}[/tex]
[tex]6a+6b=15y[/tex]
[tex]2a=3b[/tex]
Generally the equation for change in velocity is mathematically given by
[tex]2(\triangle a)=3(\triangle b )[/tex]
[tex]2*4=3(\triangle b)[/tex]
[tex]\triangle a=\frac{8}{3}[/tex]
Since
The speed of the shadow is given as
[tex]X=\triangle b+\triangle a[/tex]
[tex]X=4+8/3[/tex]
[tex]X=6.67ft/s[/tex]
ASAP!!!!!!!!! Please show process!!! Using law of sines!!!!!!!! Thank you so much
Answer:
the answers are on the picture but the numbers may be rounded
2 - (-8) + (-3) =
O A) 12
OB) 7
O C
C) 14
OD 1
Answer:
B)7
Step-by-step explanation:
2-(-8)=10
10+(-3)=7
As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and
hair color among students. The table below contains the results of the survey.
Hair Color
Blue
Eye Color
Gray Green Brown Marginal Totals
5 21 10
78
Blond
42
Red
12
22
19
12
65
Brown
22
5
12
34
73
Black
9
3
11
64
87
Marginal Totals
85
35
63
120
303
From the sample population of students with blond hair, what is the approximate value of the relative frequency of students with green eyes?
Answer:
27%
Step-by-step explanation:
The approximate value of the relative frequency of students with green eyes from the given sample population is; 27%
What is the Relative Frequency?From the given table, the number of students with Blonde hair = 78
Number of students with blonde hair and green eyes = 21
Now, relative frequency is defined as the ratio of the number of outcomes in which a specified event occurs to the total number of trials, in an actual experiment.
Thus, in this question;
Relative frequency of students with green eyes = 21/78 = 2.7 = 27%
Read more about Relative Frequency at; https://brainly.com/question/27004507
#SPJ5
Find the solution set.
The solution set for 5v2 – 125 = 0
Answer:
5v2 – 125 = 0
5(v2−25)=0
v2−25=0
a couple more steps and the answer is...
v=-5
The x intercepts of the function f(x) = 2x(x-5)^2(x+4)^3
are…
Answer:
[tex]\boxed{\sf x- intercepts = 0 , 5 \ and \ -4}[/tex]
Step-by-step explanation:
A function is given to us and we need to find the x Intercepts of the graph of the given function . The function is ,
[tex]\sf \implies f(x) = 2x( x - 5 ) ^2(x+4)^3 [/tex]
For finding the x intercept , equate the given function with 0, we have ;
[tex]\sf \implies 2x ( x - 5 )^2(x+4)^3= 0 [/tex]
Equate each factor with 0 ,
[tex]\sf \implies 2x = 0[/tex]
Divide both sides by 2 ,
[tex]\sf \implies\bf x = 0[/tex]
Again ,
[tex]\sf \implies ( x - 5)^2=0 [/tex]
Taking squareroot on both sides,
[tex]\sf \implies x - 5 = 0 [/tex]
Add 5 to both sides,
[tex]\sf \implies \bf x = 5[/tex]
Similarly ,
[tex]\sf \implies \bf x = -4 [/tex]
Hence the x Intercepts are -4 , 0 and 5 .
{ See attachment also for graph } .
What is the value of M
Answer:....... no clue ut pls mark me brainiest
Step-by-step explanation:
The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 12 requests per hour. What is the probability that no requests for assistance are in the system
Answer:
0.1667
Step-by-step explanation:
We are given;
Arrival rate, λ = 10 requests per hour
Service rate, μ = 12 requests per hour
From queuing theory, we know that;
ρ = λ/μ
Where ρ is the average proportion of time which the server is occupied.
Thus;
ρ = 10/12
ρ = 0.8333
Now, the probability that no requests for assistance are in the system is same as the probability that the system is idle.
This is given by the Formula;
1 - ρ
probability that no requests for assistance are in the system = 1 - 0.8333 = 0.1667
You have $1000 to invest in two different accounts. To save the money you need for college, you need to average 5.7 percent interest. If the two accounts pay 4 percent and 6 percent interest, how much should you invest in each account?
$550 in 4%, $450 in 6%
$300 in 4%, $700 in 6%
$700 in 4%, $300 in 6%
$150 in 4%, $850 in 6%
9514 1404 393
Answer:
$150 in 4%, $850 in 6%
Step-by-step explanation:
The fraction that must earn the highest rate is ...
(5.7 -4.0)/(6.0 -4.0) = 1.7/2 = 0.85
That is 0.85 × $1000 = $850 must be invested at 6%. Matches the last choice.
_____
If you let x represent the amount that must earn 6%, then the total interest earned must be ...
x·6% +(1000 -x)·4% = 1000·5.7%
x(6 -4) = 1000(5.7 -4) . . . . . . multiply by 100, subtract 4·1000
x = 1000·(5.7 -4)/(6 -4) = 850 . . . . as above
The time to complete an exam in a statistics class is a normal random variable with a mean of 50 minutes and a standard deviation of 10 minutes. What is the probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes
Answer:
0.2061 = 20.61% probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 50 minutes and a standard deviation of 10 minutes.
This means that [tex]\mu = 50, \sigma = 10[/tex]
Class size of 30 students
This means that [tex]n = 30, s = \frac{10}{\sqrt{30}}[/tex]
What is the probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes.
This is the p-value of Z when X = 48.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{48.5 - 50}{\frac{10}{\sqrt{30}}}[/tex]
[tex]Z = -0.82[/tex]
[tex]Z = -0.82[/tex] has a p-value of 0.2061
0.2061 = 20.61% probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes
Amic and Bernie built a maze for their hamsters. Annic's hamster completed the maze 7 seconds less than twice the time it took Bernie's hamster to complete the maze. If Bernie's hamster completed the maze in b seconds, which expression represents the time, in seconds, it took Annie's hamster to complete the maze?
A. 7-2b
B. 2b-7
c. 2b+7
D. 2b/7
Answer:
2b-7
Step-by-step explanation:
Given that,
Bernie's hamster completed the maze in b seconds.
Annic's hamster completed the maze 7 seconds less than twice the time it took Bernie's hamster to complete the maze.
Twice the time it took Bernie's hamster to complete the maze is 2b.
7 seconds less than twice the time it took Bernie's hamster = 2b-7
So, the correct option is (b) "2b-7".
When studying radioactive material, a nuclear engineer found that over 365 days,
1,000,000 radioactive atoms decayed to 970,258 radioactive atoms, so 29,742 atoms
decayed during 365 days.
a. Find the mean number of radioactive atoms that decayed in a day.
b. Find the probability that on a given day, 50 radioactive atoms decayed.
a. The mean number of radioactive atoms that decay per day is
(Round to three decimal places as needed.)
Answer:
a) The mean number of radioactive atoms that decay per day is 81.485.
b) 0% probability that on a given day, 50 radioactive atoms decayed.
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval.
a. Find the mean number of radioactive atoms that decayed in a day.
29,742 atoms decayed during 365 days, which means that:
[tex]\lambda = \frac{29742}{365} = 81.485[/tex]
The mean number of radioactive atoms that decay per day is 81.485.
b. Find the probability that on a given day, 50 radioactive atoms decayed.
This is P(X = 50). So
[tex]P(X = 50) = \frac{e^{-81.485}*(81.485)^{50}}{(50)!} = 0[/tex]
0% probability that on a given day, 50 radioactive atoms decayed.
Simplify
b. 3a + 4b-2a-b
4 나
V
216 x
Х
18
Answer:
a+3b
Step-by-step explanation:
3a+4b-2a-b
=3a-2a+4b-b
=a+3b
Henry bought a coat with a regular price of $75 and used a coupon for o off. Janna bought a
coat with a regular price of $82 and did not use a coupon. How much more did Janna's coat cost
than Henry's coat?
A. $7.00
B. $15.50
C. $22.50
D. $29.50
Answer:
A. $7.00
Step-by-step explanation:
$82-$75=$7.00
Jose bought 217 shares of Darien Electric for $21.96 apiece. His broker charged him a commission of $106.12 for the
purchase. If the yearly dividend on Darien Electric is 77 cents per share, what is the annual yield on Jose's stock? Show
work.
Answer:
what is photosynthic ..
p.l.e.a.s.e join eti-fgdd-xjs
why do plant need it
XYZ has side lengths that measure 20 centimeters each. Which of the
following best describes this type of triangle?
A. Obtuse triangle
B. Right triangle
C. Scalene triangle
D. Equilateral triangle
Answer:
it's and equilateral triangle because
all sides are equal
Answer:
equilateral triangle i have a math proffesor helping me
Step-by-step explanation:
I have a math proffesor helping me
What is the area of this composite figure?
Answer:
Well, divide the shape into rectangles,
triangles or other shapes after that, you can find the area of and then add the areas back together.
Step-by-step explanation:
The area of composite shapes is defined as the area covered by any composite shape. A composite shape is made up of basic shapes put together. Thus, the area of the composite shape is found by individually adding all the basic shapes.
To calculate the area of a composite shape you must divide the shape into rectangles, triangles or other shapes you can find the area of and then add the areas back together.es
a total of 678 tickets were sold for the school play. They were either adult tickets or student tickets. there were 72 fewer student tickets sold than adult tickets. how many adult tickets were sold
Step-by-step explanation:
678-72=606/2=303+72=375
Which linear inequality is represented by the graph?
Answer:
y=2x-4
Step-by-step explanation:
If you are asking for point slope form, that would be it
Help me find the domain and range please!
Answer:
Domain: (-∞, 1]
Range: (-∞, 3]
Step-by-step explanation:
The function starts at point (1, 3) and goes to the left and down forever.
Domain: (-∞, 1]
Range: (-∞, 3]
Answer:
Domain: [tex](-\infty, 1][/tex]
Range: [tex](-\infty, 3][/tex]
Step-by-step explanation:
The domain of a function represents the range of x-values that are part of the function, read left to right. We can see that the function goes forever to the left and stops at [tex]x=1[/tex] when we read left to right. Therefore, the domain of this function is [tex]\boxed{(-\infty, 1]}[/tex].
The point at [tex]x=1[/tex] is a filled-in solid dot so it is included as part of the function. Use square brackets to denote inclusive.
The range of a function represents all y-values that are part of the function, read bottom to top. The function continues down forever and stops at [tex]y=3[/tex] when read bottom to top. Therefore, the range of this function is [tex]\boxed{(-\infty, 3]}[/tex]. Similar to the domain, we use a square bracket on the right to indicate that [tex]y=3[/tex] is included in the function. If the dot was not filled-in, then we would use a parenthesis to indicate that [tex]y=3[/tex] would not be part of the function.