Here is the set up:
Side 1 is 4x.
Side 2 is 5x + 3
Side 3 is 5x + 1
The perimeter is 102.
Perimeter = side 1 + side 2 + side 3
102 = 4x + 5x + 3 + 5x + 1
102 = 14x + 4
Take it from here.
Marianne is 15 years old and her brother is 5 years old; is the relationship between their ages proportional?
Answer:
The ratio is 15:5 or 3:1. If Marianne is 3 years old, her brother is 1. And it is proportional...
Step-by-step explanation:
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
what is the degree measure of f?
5
Subtract 27 from 43
14
21
Answer:
-0.4522
Step-by-step explanation:
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
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!
~AnonymousHelper1807Is 319,459 divisible by 2?
yes
no
Submit
Answer:
no
Step-by-step explanation:
319,459 is not an even number
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! :)
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
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
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
What is the answer for number 2
Answer:
Your answer would be x = 63
Step-by-step explanation:
What I would do first is to isolate the -1/9x, which means I would subtract 17 on each side, giving me -1/9x = -7
Next I would multiply -9 (which is the inverse of -1/9) on both sides, negating the negative sign and making 63 positive, and thus isolating x as well.
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
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:
Solve the following inequality using both the graphical and algebraic approach:
5-x<2(x - 3) + 5
A) x<2 Graph A
B) x>2 Graph A
C) x<2 Graph B
D) x>2 Graph B
Answer:
a
Step-by-step explanation:
a
The correct answer for the given inequality 5-x<2(x - 3) + 5 is x<2 Graph A
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that, an inequality 5-x<2(x - 3) + 5
On solving, we get,
5-x < 2x-6+5
5-x < 2x-1
5+1 < 3x
x < 2
Let y₁ = 5-x, and y₂ = 2(x - 3) + 5
Plotting the graph, we get the graph A
Hence, the correct answer for the given inequality 5-x<2(x - 3) + 5 is x<2 Graph A
For more references on inequality, click;
https://brainly.com/question/28823603
#SPJ2
What is an equation of the line that passes through the point (-8,0) and is perpendicular to the line x+2y=14
Step-by-step explanation:
let eqn be y = mx + b.
Since perpendicular, m = - 1/(-0.5) = 2
sub (-8, 0):
0 = 2(8) + b
b = - 16
therefore equation is y = 2x - 16
Topic: coordinate geometry
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
Can someone help plz helpppp!!!!!
Answer:
4N left
5N left
0N (balanced)
9N right
Step-by-step explanation:
The net force is the vector sum of all of the forces acting on an object. To find the net force when there are two opposite forces subtract the smaller number from the larger, for example, 7-2. Then take to total, 5N, and add the direction of the stronger force. If the equation equals zero that means you have a balanced force. To find the force of two actions in the same direction simply add them.
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
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
Which line has a slope of 0?
Answer:
y= -5
Step-by-step explanation:
Answer:
y= -5
Step-by-step explanation:
1) Find the interior angle sum of a 36-gon.
6120°
720°
900°
1800º
Sum of interior angles = ( number of sides -2) x 180 degrees.
Sum = (36-2) x 180
Sum = 34 x 180
Sum = 6,120 degrees.
Express x^2+y^2+4x-6y+1=0 in polar coordinates form
Answer:
Step-by-step explanation:
d over d x over y=-1 over 2 y plus 3 over 2
Help me with this pls
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:
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 unit price of a 2 1/2 pound turkey for $6.25
Answer:
$2.50
Step-by-step explanation:
6.25/2.5=2.5
Solve the system by substitution or elimination. {y=2x+8y=3x−1 A. (95,585) B. (7, 22) C. (9, 26) D. (75,545)
Answer:
C. (9, 26)
Step-by-step explanation:
By Substitution:
y = 2x + 8
y = 3x - 1
---------------------
2x + 8 = 3x - 1
-x + 8 = -1
-x = -9
x = 9
Now we can choose either of the two equations given to solve for y:
y = 2x + 8
y = 2(9) + 8
y = 18 + 8
y = 26
(9, 26)
By Elimination:
For this process, I am going to rewrite the equation in "x + y" for as it will make it easier to eliminate the variables
y = 2x + 8
2x - y = -8
y = 3x - 1
-3x + y = -1
-----------------
2x - y = -8
-3x + y = -1
-----------------
-x = -9
x = 9
2x - y = -8
2(9) - y = -8
18 - y = -8
-y = -26
y = 26
(9, 26)
{ 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 is -7 as a fraction and explain plss
Answer:
-7/1
Step-by-step explanation:
any number over 1 in a fraction is the number on the top of one for example
2/1 is 2 and 100/1 is 100 and even -7/1 is -7
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]