Answer:
a) CI = ( 148,69 ; 243,31 )
b) n = 189
Step-by-step explanation:
a) If the Confidence Interval is 95 %
α = 5 % or α = 0,05 and α/2 = 0,025
citical value for α/2 = 0,025 is z(c) = 1,96
the MOE ( margin of error is )
1,96* s/√n
1,96* 163,7/ √46
MOE = 47,31
Then CI = 196 ± 47,31
CI = ( 148,69 ; 243,31 )
CI look very wide ( it sems that if sample size was too low )
b) Now if s (sample standard deviation) is 175, and we would like to have only 50 ppm width with Confidence level 95 %, we need to make
MOE = 25 = z(c) * s/√n
25*√n = z(c)* 175
√n = 1,96*175/25
√n = 13,72
n = 188,23
as n is an integer number we make n = 189
10=12-x what would match this equation
Answer:
x=2
Step-by-step explanation:
12-10=2
Answer:
x=2
Step-by-step explanation:
10=12-x
Subtract 12 from each side
10-12 = 12-12-x
-2 =-x
Multiply by -1
2 = x
Find the smallest positive integer that is greater than $1$ and relatively prime to the product of the first 20 positive integers. Reminder: two numbers are relatively prime if their greatest common divisor is 1.
Answer:
23
Step-by-step explanation:
since the number is relatively prime to the product of the first 20 positive numbers
It number must not have factor of (1-20)
Therefore the smallest possible number is the next prime after 20
Answer is 23
The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,
⇒ 23
What is Greatest common factors?The highest number that divides exactly into two more numbers, is called Greatest common factors.
Since, The number is relatively prime to the product of the first 20 positive numbers means a number which must not have factor of (1 - 20).
Hence, The smallest possible number is the next prime after 20 is, 23
Therefore, The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,
⇒ 23
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Which linear inequality is represented by the graph?
y > 2x + 2
y ≥ One-halfx + 1
y > 2x + 1
y ≥ One-halfx + 2
Answer: y > 2x + 1
Step-by-step explanation:
In the graph first, we can see two things:
The line is not solid (so the values in the line are not included), and the shaded part is above, so we will be using the symbol:
y > f(x)
Now, in the line we can see that when x = 0, y = 1.
So the linear equation must be something like:
f(x) = a*x + 1
The only one that has an y-intercept equal to 1 is y > 2x + 1
Answer:
C or y>2x +1
Step-by-step explanation:
edge
A truck averages 23 mpg. Gas costs $2.28 per gallon. How much would it cost to pay for the gas if this truck made a trip of 2,093 miles?
Answer:$207.48
Step-by-step explanation:You need to find how much gallons he would need so you divide 2,093 by 23 and you get 91. After that you multiply it by $2.28, The price per gallon and you get 207.48.
Two jokers are added to a $52$ card deck and the entire stack of $54$ cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?
Answer:
52/3.
Step-by-step explanation:
There are (54·53)/2 = 1431 ways the 2 jokers can be placed in the 54-card deck. We can consider those to see how the number of cards between them might work out.
Suppose we let J represent a joker, and - represent any other card. The numbers of interest can be found as follows:
For jokers: JJ---... there are 0 cards between. This will be the case also for ...
-JJ---...
--JJ---...
and so on, down to ...
...---JJ
The first of these adjacent jokers can be in any of 53 positions. So, the probability of 0 cards between is 53/1431.
__
For jokers: J-J---..., there is 1 card between. The first of these jokers can be in any of 52 positions, so the probability of 1 card between is 52/1431.
__
Continuing in like fashion, we find the probability of n cards between is (53-n)/1431. So, the expected number of cards between is ...
[tex]E(n)=\sum\limits_{n=0}^{53}{\dfrac{n(53-n)}{1431}}=\dfrac{53}{1431}\sum\limits_{n=0}^{53}{n}-\dfrac{1}{1431}\sum\limits_{n=0}^{53}{n^2}\\\\=\dfrac{53(53\cdot 54)}{1431(2)}-\dfrac{1(53)(54)(107)}{1431(6)}=53-\dfrac{107}{3}\\\\\boxed{E(n)=\dfrac{52}{3}}[/tex]
Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
The answer is below
Step-by-step explanation:
Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
Given:
Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645
The margin of error (E) is given by:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]
The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)
The 90% confidence interval is from 7.3442 to 9.9278
ANSWER NEEDED ASAP!According to the table below, what is the probability that the age of a student chosen at random will be 15 or younger?
A) 0.74
B) 0.59
C) 0.56
D) 0.54
The correct answer is C) 0.56
Explanation:
In general terms, the probability of two or more events can be calculated by adding the probability of each event. This rule applies when an event is considered as mutually exclusive. Age is considered as a mutually exclusive event because if a random individual is selected he/she will be only one age. In this context, if you need to know the probability that a student is 15 or younger it is necessary to add the probability that a student is 15, the probability that the student is 14, and the probability that the student is 13. The process is shown below:
P (A or B or C) = P(A) + P(B) + P(C)
P = P(13) + P(14) + P(15)
P= 0.001 + 0.25 + 0.30
P= 0.56
Answer:
0.59
Step-by-step explanation:
add the probabilities of 13, 14, and 15
0.01 + 0.28 + 0.3 = 0.59
A type of probability distribution that shows the probability of x successes in n trials, where the probability of success remains the same from trial to trial, is referred to as a(n) ______.
Answer: Binomial distribution
Step-by-step explanation:
The binomial appropriation is a likelihood circulation that sums up the probability that a worth will take one of two free qualities under a given arrangement of boundaries or suspicions. The hidden suspicions of the binomial dispersion are that there is just a single result for every preliminary, that every preliminary has a similar likelihood of achievement, and that every preliminary is totally unrelated, or autonomous of one another.
Simplify.
Remove all perfect squares from inside the square roots.
Assume a and b are positive.
Answer:
9a^2sqrt(ab)
Step-by-step explanation:
The first noticable thing is that 81 has a perfect square of 9.
So it is now 9sqrt(a^5b)
you can split the a^5, to a^4 × a.
you can now take the sqrt of a^4, which is a^2, and pull it out from the sqrt
You are now left with 9a^2sqrt(ab)
Answer:
9a^2sqrt(ab)
Step-by-step explanation:
The formula to convert Fahrenheit to Celsius is C=5/9(F-32). Convert 30c to Fahrenheit. Round to the nearest degree
Answer:
86 degrees farenheit
Step-by-step explanation:
First, we plug 30 in for C.
Next, solve for F
Multiplying both sides by 9/5 gives us 54=F-32
Add 32 to both sides 86=F
Find the measure of the indicated angle to the nearest degree. Thanks.
Answer:
θ ≈ 40°
Step-by-step explanation:
Since, sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
In the picture attached,
Measures of adjacent side and opposite side of the triangle have been given. Therefore, tangent rule will be applied in the given triangle.
tanθ = [tex]\frac{19}{23}[/tex]
θ = [tex]\text{tan}^{-1}(\frac{19}{23})[/tex]
θ = 39.56
θ ≈ 40°
The container that hold the water for the football team is 1/5 full after pouring in 13 gallons of water, it is 7/10 full how many gallons can the container hold
Answer:
100% = 65 Gallons; 70% = 45.5 Gallons
Step-by-step explanation:
The important piece of information here is that 13 gallons of water makes the container 1/5 of the way full, aka 20%. If the question is simply, how many gallons will it hold, then we multiply 13 by 5 to get 100% at 65 gallons. To get the amount held at 7/10, or 70%, we simply multiply 65 with 7/10 to get 45.5 gallons.
Cheers.
simplify (3+3 / x(x+1) )(x-3 / x(x-1) )
Answer:
I think it is [tex]\frac{6x-18}{x^{4} }[/tex]
Step-by-step explanation:
5/12 +( 5/12 + 3/4 ) =
Answer:
Proper: 15/4
Improper: 3 3/4
Step-by-step explanation:
Well to solve the following question,
5/12 + (5/12 + 3/4)
We solve the part in the parenthesis first,
5/12 + 3/4 = 14/4
Simplified -> 7/2
5/12 + 7/2
= 45/12
Simplified -> 15/4
Thus,
the answer is 15/4 or 3 3/4.
Hope this helps :)
Answer:
19/12= [tex]1 \frac{7}{12}[/tex]Step-by-step explanation:
[tex]\frac{5}{12}+\left(\frac{5}{12}+\frac{3}{4}\right)\\\\=\frac{5}{12}+\frac{5}{12}+\frac{3}{4}\\\\\mathrm{Add\:similar\:elements:}\:\frac{5}{12}+\frac{5}{12}=2\times \frac{5}{12}\\=2\times \frac{5}{12}+\frac{3}{4}\\\\=\frac{5\times \:2}{12}\\\\=\frac{10}{12}\\\\=\frac{10}{12}\\\\=\frac{5}{6}+\frac{3}{4}\\L.C.M =12\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\\frac{5}{6}=\frac{5\cdot \:2}{6\times \:2}=\frac{10}{12}\\\\\frac{3}{4}=\frac{3\times \:3}{4\times \:3}=\frac{9}{12}\\[/tex]
[tex]\\=\frac{10}{12}+\frac{9}{12}\\\mathrm{Since\:the\:denominators\:are\:equal\\\:combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{10+9}{12}\\\\=\frac{19}{12}[/tex]
6th grade math , help me please :)
Answer:
A. Eric rode 2 more miles per week than Kim rode
Step-by-step explanation:
Number of miles Kim rode bicycle in 9 weeks = 135 miles
Let x be the number of miles per week.
135miles => 9 weeks
x miles => 1 week
[tex] x = \frac{135}{9} [/tex]
[tex] x = 15 [/tex]
Kim rode the bicycle 15 miles per week
Number of miles Eric rode bicycle in 6 weeks = 102 miles
Let x be the number of miles per week Eric rides the bicycle.
102 miles => 6 weeks
x miles => 1 week
[tex] x = \frac{102}{6} [/tex]
[tex] x = 17 [/tex]
Kim rode the bicycle 17 miles per week
Comparing the number of miles per week they rode, we would conclude that: "Eric rode 2 more miles per week than Kim rode".
I need the co-ordinates to answer this can anyone give them to me? If not it's fine! :)
Hi there!
Answer:
Find points for the equation y = 2x + 1 by plugging in x values:
For example, when x = 1, substitute in the value of 'x' into the equation:
y = 2(1) + 1
y = 2 + 1
Solve for the y-value:
y = 3
Repeat this process for multiple points:
X Y
-2 -3
-1 -1
0 1
1 3
2 5
To get the graph of y = 2x + 1, simply graph these points. :)
24=3(n-5) solve for n
Answer:
n = 13
Step-by-step explanation:
24 = 3 (n-5)
3n - 15 = 24
3n = 24 +15
3n = 39
n = 39/3
n = 13
Answer:
[tex]\boxed{\sf n=13}[/tex]
Step-by-step explanation:
[tex]\sf 24=3(n-5)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]\sf 24=3n-15[/tex]
[tex]\sf Add \ 15 \ to \ both \ sides.[/tex]
[tex]\sf 24+15=3n-15+15[/tex]
[tex]\sf 39=3n[/tex]
[tex]\sf Divide \ both \ sides \ by \ 3.[/tex]
[tex]\sf \frac{39}{3} =\frac{3n}{3}[/tex]
[tex]\sf 13=n[/tex]
Which inequality has a dashed boundary line when graphed? A y>=3/5x+1 B y>= -1/3x+1 C y>3x+1
Answer: C y>3x+1
Step-by-step explanation:
When we graph an inequality with strictly greater of less than sign ('<' or '>'), then the graph has a dashed boundary line .Further it indicates that it does not include the points on the line.From all the given options , only C contains inequality with '>' sign .
Hence, y>3x+1 is the inequality has a dashed boundary line when graphed.
hence, the correct option is C.
PLEASE HELP WILL GIVE BRAINLIEST PRECALC
Answer:
[tex]270^o[/tex] and [tex]450^o[/tex]
Step-by-step explanation:
Recall that [tex]\frac{\sqrt{2} }{2}[/tex] is a value of the function cosine for the special angles: [tex]135^o[/tex] and [tex]225^o[/tex], then:
[tex]\frac{x}{2} =135^o\\x=270^o\\or\\ \frac{x}{2} =225^o\\x=450^o\\[/tex]
Which of the following is the solution to 4|x+2|≥16
Answer:
x ≥ 2 or x ≤ -6
Step-by-step explanation:
4|x + 2| ≥ 16
|x + 2| ≥ 4
x + 2 ≥ 4 or -(x + 2) ≥ 4
x ≥ 2 or x + 2 ≤ -4 → x ≤ -6
[tex]\text{Solve the absolute value}\\\\4|x+2|\geq 16\\\\\text{We can make this equation a lot simpler by dividing both sides by 4}\\\\|x+2|\geq4\\\\\text{According to the absolute value, there can be two outcomes. In this case,}\\\text{it would be either:}\\\\x+2\geq4\,\,or\,\,x+2\leq-4\\\\\text{Solve first outcome:}\\\\x+2\geq4\\\\\text{Subtract both sides by 2}\\\\x\geq2\\\\\text{Solve second outcome:}\\\\x+2\leq-4\\\\\text{Subtract 2 from both sides}\\\\x\leq-6\\\\[/tex]
[tex]\boxed{x\geq2\,\,or\,\,x\leq-6}[/tex]
Hong buys a bag of 11 tangerines for $2.86.
Find the unit price in dollars per tangerine.
If necessary, round your answer to the nearest cent.
Answer:
$0.26
Step-by-step explanation:
To find the unit price, divide the cost by the amount you have.
$2.86/11 = $0.26
The unit price is $0.26.
what is the value of A when we rewrite 4^31x as A^x
Answer:
.
Step-by-step explanation:
The value of A is A = 4³¹
What are Exponents?Exponents are the base raised by power, it is written in the superscript of a number.
The expression is
[tex]\rm 4^{31x}\\[/tex]
To write in form Aˣ
A will be obtained by comparing the expressions
Aˣ = [tex]\rm 4^{31x}\\[/tex]
A = 4³¹
Therefore, the value of A is A = 4³¹.
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Given p(x) = x4 + x3 - 13x2 - 25x - 12
1. What is the remainder when p(x) is divided by X - 4?
2. Describe the relationship between the linear expression and the polynomial?
How do we describe the relationship?
A train goes past you in 10 seconds and goes past a 100 meter long bridge in 30 seconds. What is the length (in meters) and the speed (inm/s) of the train?
Answer:
Bridge = 300 m
Speed = 10 m/s
Step-by-step explanation:
If a goes past you in 10 seconds, it means the train has speed of
100 m/ 10 seconds as it is 100 m long
The speed in m/s is:
100 m/ 10 s = 10 m/sThen it take 3 times of 10 seconds to cross the bridge, so
The length of the bridge is:
3*100 m= 300 mAnswer:
Length : 50m
Speed : 5 m / s
Rachel's waist circumference is 37 inches and her hip circumference is 39 inches. Based on this information, what does her waist-to-hip ratio tell you?
Answer:
[tex]n = 0.949[/tex]. The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.
Step-by-step explanation:
The waist-to-hip ratio of Rachel is:
[tex]n = \frac{37\,in}{39\,in}[/tex]
[tex]n = \frac{37}{39}[/tex]
[tex]n = 0.949[/tex]
The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.
The length of her waist circumference is 94.9% the length of her hip circumference.
From the information given, Rachel's waist circumference is 37 inches and her hip circumference is 39 inches.
Therefore, her waist to hip ratio will be calculated thus:
n = 37/39
n = 0.949
This implies that the length of her waist circumference is 94.9% the length of her hip circumference.
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a parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the equation of the parabola.
Answer:
The standard equation of the parabola is:
[tex]y=-\frac{3}{2}x^2+12x-18[/tex]
Step-by-step explanation:
An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.
We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.
[tex]y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2[/tex]
Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:
[tex]y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}[/tex]
Then the equation of the parabola becomes:
[tex]y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18[/tex]
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)
Answer:
b. [tex]g(x)=f(x)-5[/tex]
Step-by-step explanation:
You have that the function f(x) has its y-intercept for y=3.
Furthermore, you have that g(x) is a transformation of f(x) with y-intercept for y=-2.
In this case you have that f(x) has been translated vertically downward.
The general way to translate a function vertically in the coordinate system is:
[tex]g(x)=f(x)+a[/tex] (1)
being a positive or negative.
if g(x) has its y-intercept for y=-2, and the y-intercept of f(x) is for y=3, then the value of a in the equation (1) must be a = -5, which is the difference between both y-intercepts, in fact:
a = -2 -3 = -5
Then, the answer is:
b. [tex]g(x)=f(x)-5[/tex]
Answer: g(x) = f(x) - 5
Step-by-step explanation:
just took this
What is the simplified value of $\frac{10! + 11! + 12!}{10! + 11!}$?
Answer:
12
Step-by-step explanation:
We can factor out 10! on the numerator and the denominator,.
This gives: 10! (1 + 11 + (11 * 12)) / 10! (1 + 11)
This is because 10! * 11 is equal to 11! meaning we can factor out 10!.
10! * 11 * 12 also equals 12! which is why we can factor 10! out of that too.
Seeing as 10! is at the top and bottom we can cancel those out.
This leaves us with: 144 / 12 which is equal to 12.
Farmer Hanson is putting together fruit baskets. He has 240 apples and 150 pears. What is the largest number of baskets he can put together so that he can have the same number of apples and same number of pears in each basket considering no fruit is left out?HELP NOWWWWW
Answer: The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.
Step-by-step explanation:
Given, Farmer has 240 apples and 150 pears.
The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out = GCF(240,150)
Prime factorization of 240 and 150 :
[tex]240=2\times2\times2\times2\times3\times5\\150=2\times3\times5\times5[/tex]
Greatest common factor of 240 and 150 = [tex]2\times3\times5=30[/tex]
Hence, the largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.
Pat is taking an economics course. Pat's exam strategy is to rely on luck for the next exam. The exam consists of 100 true-false questions. Pat plans to guess the answer to each question without reading it. If a grade on the exam is 60% or more, Pat will pass the exam. Find the probability that Pat will pass the exam.
Answer:
The probability that Pat will pass the exam is 0.02775.
Step-by-step explanation:
We are given that exam consists of 100 true-false questions. Pat plans to guess the answer to each question without reading it.
If a grade on the exam is 60% or more, Pat will pass the exam.
Let X = grade on the exam by Pat
The above situation can be represented through binomial distribution such that X ~ Binom(n = 100, p = 0.50).
Here the probability of success is 50% because there is a true-false question and there is a 50-50 chance of both being the correct answer.
Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).
So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]100 \times 0.50[/tex] = 50
and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{100 \times 0.50 \times (1-0.50)}[/tex]
= 5
So, X ~ Normal([tex]\mu=50, \sigma^{2} = 5^{2}[/tex])
Now, the probability that Pat will pass the exam is given by = P(X [tex]\geq[/tex] 60)
P(X [tex]\geq[/tex] 60) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{60-50}{5}[/tex] ) = P(Z [tex]\geq[/tex] 2) = 1 - P(Z < 2)
= 1 - 0.97725 = 0.02275
Hence, the probability that Pat will pass the exam is 0.02775.