Hi! I believe your answer is 0.42, (simplified form of 0.42424242424) which is 14/33 (or [tex]\frac{14}{33}[/tex] ) as a decimal. I hope this helps you! Good luck and have a great day. ❤️✨
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2.25
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3
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X =
13,84,85 are the last ones please help
Answer:
49,36,85
Step-by-step explanation:
c in step 4 comes from step 3... 49+36
a and b in step 3 come from step 2... in the same (you've got a - b and then 7 squared - 6 squared, so a is 49 and b is 36
1. If 15% of adults in a certain country work from home, what is the probability that fewer than 42 out of a random sample of 350 adults will work from home? (Round your answer to 3 decimal places)
2. Suppose we want to estimate the proportion of teenagers (aged 13-18) who are lactose intolerant. If we want to estimate this proportion to within 4% at the 95% confidence level, how many randomly selected teenagers must we survey?
Answer:
(1) 0.058
(2) 601
Step-by-step explanation:
(1)
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}=p\\[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
As the sample size is large, i.e. n = 350 > 30, the Central limit theorem can be used to approximate the sampling distribution of sample proportion of adults in a certain country work from home.
Compute the probability that fewer than 42 out of a random sample of 350 adults will work from home:
Sample proportion: [tex]\hat p=\frac{42}{350}=0.12[/tex]
[tex]P(\hat p < 0.12)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.12-0.15}{\sqrt{\frac{0.15(1-0.15)}{350}}})\\\\=P(Z<-1.57)\\\\=0.05821\\\\\approx 0.058[/tex]
Thus, the probability that fewer than 42 out of a random sample of 350 adults will work from home is 0.058.
(2)
The (1 - α)% confidence interval for population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
Given:
MOE = 0.04
Confidence level = 95%
Assume that the sample proportion is 50%.
The critical z-value for 95% confidence level is 1.96.
Compute the required sample size as follows:
[tex]MOE= z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\cdot\sqrt{\hat p(1-\hat p)}}{MOE}]^{2}\\\\=[\frac{1.96\times \sqrt{0.50(1-0.50)}}{0.04}]^{2}\\\\=600.25\\\\\approx 601[/tex]
Thus, the required sample size is 601.
1. Using the normal approximation to the binomial, it is found that there is a 0.05 = 5% probability that fewer than 42 out of a random sample of 350 adults will work from home.
2. Solving the equation for the margin of error of a confidence interval of proportions, it is found that we must survey 601 randomly selected teenagers.
Question 1:
Normal Probability Distribution
In a normal distribution 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]
It 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, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem:
15% work from home, thus [tex]p = 0.15[/tex].Sample of 350 adults, thus [tex]n = 350[/tex]Then, for the approximation:
[tex]\mu = np = 350(0.15) = 52.5[/tex]
[tex]\sigma = \sqrt{np(1-p)} = \sqrt{350(0.15)(0.85)} = 6.68[/tex]
Using continuity correction, the probability is [tex]P(X < 42 - 0.5) = P(X < 41.5)[/tex], which is the p-value of Z when X = 41.5. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41.5 - 52.5}{6.68}[/tex]
[tex]Z = -1.65[/tex]
[tex]Z = -1.65[/tex] has a p-value of 0.05.
0.05 = 5% probability that fewer than 42 out of a random sample of 350 adults will work from home.
Question 2:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
Within 4%, thus [tex]M = 0.04[/tex].We do not have an estimate for the true proportion, thus [tex]\pi = 0.5[/tex].95% confidence level, thus z has a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], thus z = 1.96.We have to solve for n, then:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96(0.5)[/tex]
[tex]\sqrt{n} = \frac{1.96(0.5)}{0.04}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96(0.5)}{0.04})^2[/tex]
[tex]n = 600.25[/tex]
Rounding up:
We must survey 601 randomly selected teenagers.
A similar problem is given at https://brainly.com/question/24261244
Eighteen cups are equally packed into 6 boxes. Two boxes of cups break. How many cups are unbroken?
Answer:12
Step-by-step explanation:
18/6=3 cups in each box
3*2=6 cups broke=2 boxes
18-6=12 cups are unbroken
5
Subtract 27 from 43
14
21
Answer:
-0.4522
Step-by-step explanation:
Please answer this correctly without making mistakes
Answer:
First figure out how many cups are in a gallon. 16 .
Next multiply 16×3= 48
Finally you divide price per cup or 20.16/ 48.
The cost is .42 cents per cup.
Which of these points is closest to the point (7,1)?
Answer:
6,7
Step-by-step explanation:
For the expression: 12 - 7k + 9 - k
What are the terms?
What are the like terms?
What are the coefficients?
What are the constants?
What is the expression simplified?
Answer:
like terms is -7k-k and 12+8
21947÷205 divide and check the result
Answer (3dp):
107.058
Step-by-step explanation:
(image is explanation)
Find the height of a triangle whose
Area=64dm
Base=1.6m
Answer:
102.4?
Step-by-step explanation:
Answer:
h=2A/b
2 (64dm)/1.6m
128dm/1.6m
=80d
Solve the following
Answer:
Q1
|a-b| = b-a when a<b
Q2
104159/33000
Step-by-step explanation:
Q1
If a<b then a-b will always be negative. To get the absolute value, we can take -(a-b) = -a+b = b-a.
Q2
Let x = 3.12789789789...
We isolate the repeating decimal to start after the decimal, so we multiply by 100.
100x = 312.789789789...
We want to multiply by 10 for each digit that repeats (in this case 3), to get the repeating part to the left of the decimal.
100000x = 312789.789789
Subtracting the two...
x(100000-100) = 312789.789789 - 312.789789
99900x = 312477
x = 312477/99000 = 104159/33000
PLEASSSEEE HELPPP ASAPPPPP
Answer:
first one is 32
the second one is 53
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let RS = x , then PS = x²
2x² + 2x = 84
x² + x - 42 = 0
(x + 7)(x - 6) = 0
x = 6
PQ and RS are 6
QR and SP are 36
Factor 15x-10x^3
PLEASE ASNWER ASAP
Answer:
[tex]\huge\boxed{\sf 5x(3-2x^2)}[/tex]
Step-by-step explanation:
[tex]\sf 15x-10x^3\\\\Greatest Common Factor = 5x\\\\So, We'll \ take \ 5x \ common\\\\= 5x ( 3-2x^2)\\\\Thus, this \ is \ the \ factorized\ form\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807Plzz Due today!
The table below represents a linear function f(x) and the equation represents a function g(x): (See pic)
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
Answer: The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 -12 0 -6 1 0 g(x) g(x) = 2x + 6 Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
PART B: y=mx +b is slope intercept form of linear equation where m=slope and b =y intercept
slope for line for function f(x) =-5-(-1) / -1-0 =-5+1/-1=-4/-1=4
y = 4x+b
3=4(1)+b
3=4+b
-1 =b
y=4x-1
f(x)=4x-1 slope = 4
g(x)=2x -7 slope = 2
b) y intercept for f(x) is -1
and g(x) is -7
so f(x) is having greater y intercept
Which line has a slope of 0?
Answer:
y= -5
Step-by-step explanation:
Answer:
y= -5
Step-by-step explanation:
In this graph the y-intercept of the line is (Blank). The equation of the line is y=(Blank) x (Blank) .
Answer:
In the graph, the y-intercept is -2. The equation of the line is [tex] y = x - 2 [/tex]
Step-by-step explanation:
The equation of the line can be written in the slope-intercept form, y = mx + b.
First we need to find:
The slope = m
the y-intercept = b
Using two points on the line, (0, -2) and (2, 0) the slope can be calculated as follows:
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 -(-2)}{2 - 0} = \frac{2}{2} = 1 [/tex]
The y-intercept is simply the point at which the line intercepts the y-axis. It is the value of y when x = 0.
Therefore, the y-intercept, b, = -2.
Substitute m = 1 and b = -2 into [tex] y = mx + b [/tex].
Thus, the equation if the line would be:
[tex] y = (1)(x) + (-2) [/tex]
[tex] y = x - 2 [/tex]
1+3 pls help me nowwwww
Answer:
4
Step-by-step explanation:
3=1+1+1,
1+1+1+1=4 :p
The manufacturer of a certain brand of lightbulbs claims that the variance of the lives of these bulbs is 4100 square hours. A consumer agency took a random sample of 26 such bulbs and tested them. The variance of the lives of these bulbs was found to be 5900 square hours. Assume that the lives of all such bulbs are (approximately) normally distributed. Test at the 20% significance level whether the variance of such bulbs is different from 4100 square hours. a)The value of the test statistic x is 15.743; we fail to reject the null hypothesis. b)The value of the test statistic x is 32.859; we fail to reject the null hypothesis. c)The value of the test statistic y is 32.859; we reject the null hypothesis. d)The value of the test statistic is 35.976; we fail to reject the null hypothesis. e)The value of the test statistic is 15.743; we reject the null hypothesis. f)The value of the test statistic x is 35.976; we reject the null hypothesis.
Answer:
124345
Step-by-step explanation:
True of False:the following polynomial is written in standard form
2x^4-x^3+5x^2+x-7
9. The expression x(x-7)+4(x-7) is equivalent to each of the following except which choice?
(1) (x+4)(x-7)
(3) x2-28
(2) x2 – 3x – 28
(4) (x-7)(x+4)
Answer:
I the answer is number 3
x(x-7)+4(x-7)
x²-7x + 4x-28
=x²-3x-28
(x+4)(x-7)
x²-7x+4x-28
=x²-3x-28
(x-7)(x+4)
x²+4x-7x-28
=x²-3x-28
x2 – 3x – 28
the factored form is
=(x+4)(x-7)
Is [tex]\sqrt{103}[/tex] irrational or rational? What is your reasoning?
Answer: irrational
Step-by-step explanation:
[tex]\sqrt{103}[/tex] is an irrational number because it is not a perfect square. Irrational numbers keep on terminating, so the answer to the question is irrational.
Hope this helps you!
The graph displays the distance a CO2 car traveled in a race.
Help!!!
Answer:
5 seconds per foot
Step-by-step explanation:
Answer:A
Step-by-step explanation:
{ vowels in the word ALGEBRA}
Answer:
3 counting ALL VOWELS, or, 2 counting no double ups
Step-by-step explanation:
vowels - a, e, i, o, u
What fraction is larger 3/8 or 10/24?
Answer:
10/24
Step-by-step explanation:
hope this helps :)
Answer:
5/8
Step-by-step explanation:
Have a good day! :)
A length of chain is to be constructed by placing 36 component links end to end. The length of a link produced by a production process is known to be a random variable with a mean of 2.5 cm with a standard deviation 0.2 cm. The 36 links are chosen at random from this process to produce the chain. The mean and standard deviation of the length of chain are, respectively _________.
a. 90 cm, 7.2 cm
b. 36 cm, 1.2 cm
c. 90 cm, 2.7 cm
d. 90 cm, 1.2 cm
e. 36 cm, 7.2 cm
Answer:
d. 90 cm, 1.2 cm
Step-by-step explanation:
Given that:
The sample size n = 36
For the length of the link:
The mean [tex]\overline x[/tex] = 2.5
The standard deviation s = 0.2 cm
In a chosen 36 links, The mean and standard deviation for the length chain is as follows:
Mean = n[tex]\overline x[/tex]
Mean = 36×2.5
Mean = 90 cm
The Standard deviation = s×√n
The Standard deviation = 0.2×√36
The Standard deviation = 0.2×6
The Standard deviation = 1.2 cm
jose trabaja 4 3/4 horas el lunes, 3 1/2 horas el martes, 6 3/4 horas el miercoles, 4 1/2 horas el jueves y 6 horas viernes, y 5 horas el sabado en promedio cuantas horas diarias trabaja
Answer:
5 horas
Step-by-step explanation:
Answer:
Step-by-step explanation:
( [tex]4\frac{3}{4}[/tex] + [tex]3\frac{1}{2}[/tex] + [tex]6\frac{3}{4}[/tex] + [tex]4\frac{1}{2}[/tex] + 6 + 5 ) ÷ 6 =
( 4 + 3 + 6 + 4 + 6 + 5 + [tex]\frac{6}{4}[/tex] + 1 ) ÷ 6 = 30.5 ÷ 6 = [tex]\frac{61}{2}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{61}{12}[/tex] = [tex]5\frac{1}{12}[/tex] horas al dia
Race to get brainliest, need help!
The sum of digits in a two-digit number is 14. If you double the reversed number and add the result to the original number, the sum would be 222. Find the original number
Answer:
Original number is 86
Step-by-step explanation:
Original: 10x + y
Double reversed: 2(10y + x)
Constraints:
x + y = 14 ===> x = 14 - y
2(10y + x) + 10x + y = 222 ===> 21y + 12x = 222
Substitution to find y:
21y + 12x = 222
21y + 12(14 - y) = 222
21y + 168 - 12y = 222
9y + 168 = 222
9y = 54
y = 6
Substitution to find x:
x = 14 - y
x = 14 - 6
x = 8
Original: 10x + y
10(8) + (6)
80 + 6
86
Slope for (20,8)(9,16)?
Answer:
m=-8/11
Step-by-step explanation:
[tex]\frac{Y2-Y1}{X2-X1} =\frac{y}{x}[/tex]
[tex]\frac{16-8}{9-20} =\frac{-8}{11}[/tex]
what is the slope of an equation of the line that passes through the point (3,-5) and has a slope of 0
Answer:
y=0x-5
Step-by-step explanation:
hope this helps :3
if it did pls mark brainliest
what is y=(-2/3)x+400 as a function?
Answer:
y= −2x/3 + 400
Step-by-step explanation:
Hope this helps :)
Answer: what the other dude said
Step-by-step explanation: