Answer:
0.3902
Step-by-step explanation:
The question meets the criteria for the calculation of the confidence interval of a one sample proportion ;
Sample size, n = 27
Number of students with faster reaction time = 14
Phat = x / n = 14 / 27 = 0.6296
The confidence interval is calculated thus :
C. I = Phat ± Zcritical * √[p(1 - p)/n]
Zcritical at 99% = 2.576
C. I = 0.6296 ± 2.576 * √[0.6296(0.3704)/27]
C.I = 0.6296 ± 0.2394042
The lower boundary of C.I = 0.6296 - 0.2394042
Lower boundary = 0.3902
define ascending and descending order by your and give one example
Answer:
ascending order} an order of numbers from least to greatest like 1 2 3 4
descending order} an order of numbers from greatest to least like 4 3 2 1
SI unit of areaWhat is the SI unit of area
square meter is the SI unit of area.
Which phrase describes the linear relationship between the x and y values shown in the table?
x l y
8 l 2
9 l 3
10 l 4
A. y is 6 times x
B. x is 6 times y
C. y is 6 less than x
D. y is 6 more than x
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Answer:
C. y is 6 less than x
Step-by-step explanation:
It is not hard to check.
A. 6 times x is 6×8 = 48, not 2
B. 6 times y is 6×2 = 12, not 8
C. 6 less than 8 is 2; 6 less than 9 is 3
D. 6 more than 8 is 14, not 2
__
The relation described in C matches the table.
Differentiate 4x^2+y^2=36 with respect to x. Hence find the turning points of the curve.
If y = y(x), then the derivative with respect to x is dy/dx. Differentiating both sides of the given equation gives
d/dx [4x ² + y ²] = d/dx [36]
8x + 2y dy/dx = 0
2y dy/dx = -8x
dy/dx = -4x/y
The turning points of the curve, taken as a function of x, are those points where the derivative vanishes.
-4x/y = 0 ===> x = 0
This value of x corresponds to two points on the curve,
4×0² + y ² = 36 ===> y ² = 36 ===> y = ±6
So there are two turning points, (0, -6) and (0, 6).
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 127 brakes using Compound 1 yields an average brake life of 42,814 miles. A sample of 163 brakes using Compound 2 yields an average brake life of 37,197 miles. Assume that the population standard deviation for Compound 1 is 1819 miles, while the population standard deviation for Compound 2 is 1401 miles. Determine the 98% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
Step 1 of 3 is Point estimate so 42,814 - 37,197 = 5,617
Step 2 of 3 :
Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.
Step 3 of 3:
Construct the 98% confidence interval. Round your answers to the nearest whole number. (lower and upper endpoint)
Answer:
The point estimate is 5,617.
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
The 98% confidence interval for the difference between the two population means is (5163, 6071).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
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.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Compound 1:
127 brakes, average brake life of 42,814 miles, population standard deviation of 1819 miles. This means that:
[tex]\mu_1 = 42814[/tex]
[tex]s_1 = \frac{1819}{\sqrt{127}} = 161.41[/tex]
Compound 2:
163 brakes, average brake life of 37,197 miles, population standard deviation of 1401 miles. This means that:
[tex]\mu_2 = 37197[/tex]
[tex]s_2 = \frac{1401}{\sqrt{163}} = 109.73[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 42814 - 37197 = 5617[/tex]
The point estimate is 5,617.
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{161.41^2 + 109.73^2} = 195.18[/tex]
Confidence interval
The confidence interval is:
[tex]\mu \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = zs[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
Margin of error:
[tex]M = zs = 195.18*2.327 = 454.18386 [/tex]
The margin of error of a confidence interval for the difference between the two population means is 454.18386 .
For the confidence interval, as we round to the nearest whole number, we round it 454. So
The lower bound of the interval is:
[tex]\mu - zs = \mu - M = 5617 - 454 = 5163[/tex]
The upper bound of the interval is:
[tex]\mu + zs = \mu + M = 5617 + 454 = 6071[/tex]
The 98% confidence interval for the difference between the two population means is (5163, 6071).
For a normal distribution with mean 47 and standard deviation 6, find the probability of obtaining a value less than 45 or greater than 49.
Answer:
0.7392 = 73.92% probability of obtaining a value less than 45 or greater than 49.
Step-by-step explanation:
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.
Mean 47 and standard deviation 6
This means that [tex]\mu = 47, \sigma = 6[/tex]
Less than 45:
p-value of Z when X = 45, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{45 - 47}{6}[/tex]
[tex]Z = -0.3333[/tex]
[tex]Z = -0.3333[/tex] has a p-value of 0.3696.
More than 49:
1 subtracted by the p-value of Z when X = 49. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 47}{6}[/tex]
[tex]Z = 0.3333[/tex]
[tex]Z = 0.3333[/tex] has a p-value of 0.6304.
1 - 0.6304 = 0.3996
Less than 45 or greater than 49:
2*0.3696 = 0.7392
0.7392 = 73.92% probability of obtaining a value less than 45 or greater than 49.
95% confident that the true mean difference in mean crying time after being given a vitamin K shot between infants using conventional methods and infants held by their mothers is between ____________and ___________________. In other words, the mean crying time of infants given vitamin K shot using conventional methods is anywhere from ______________ less than to _______________more than the mean crying time of infants given vitamin K shot using new methods.
Solution :
Two sample T-test and CI : Conventional methods, New methods
Two sample T for conventional method Vs new method
N Mean StDev Se Mean
Conventional mean 30 35.3 20.8 3.8
New methods 30 35.1 22.3 4.1
Difference = μ (conventional method) - μ (new method)
Estimate for difference : 0.17
95% CI for difference : (-10.976, 11.309)
T-Test of difference = 0(vs <): T-value = 0.03 P-value =0.5119 DF = 57
95% confident that the true mean difference in mean crying time after being given a vitamin K shot between infants using conventional methods and infants held by their mothers is between -10.976 and 11.309. In other words, the mean crying time of infants given vitamin K shot using conventional methods is anywhere from -10.976 less than to 11.309 more than the mean crying time of infants given vitamin K shot using new methods.
Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. let x represent the length of each of the equal pieces of yarn that julie decides to cut. what is the equation that can be used to determine the total length of all the yarn that she ends up cutting, y? is the graph of the equation continuous or discrete?
Answer:
The answer is below
Step-by-step explanation:
Let x represent the length of each of the equal piece of yarn. Since they are 4 equal pieces of yarn, then the total length of the equal pieces of yarn = 4x.
Also, besides cutting the 4 equal pieces of yarn Julie further cuts a yarn 7.75 inches long, therefore if y represent the total length of all the yarn that she ends up cutting, hence:
y = 4x + 7.75
Since the graph produced by this equation have all points connected to each other, hence this is a continuous graph.
Solve for x.
5x - 3 = 12
A) X = 3
B) X = -3
C) X = -9/5
D) X = 9/5
Answer:
A. x = 3
Step-by-step explanation:
5x - 3 = 12
5x = 12 + 3
5x = 15
x = 15/5
= 3
The area between z=.34 and z=1.93
Answer:
34.013%
0.36693 - 0.0268 = 0.34013
Step-by-step explanation:
z=.34 and z=1.93
0.34 0.36693
1.93 0.0268
solve the inequality y-6>/2y-4
Answer:
Step-by-step explanation:
Let's solve your inequality step-by-step.
y - 6 > 2y - 4
y - 2y > -4 + 6
-y > 2
now divide by -1 and inequality sign changes
-y/-1 < 2/-1
y < -2
There are 3 red marbles and 8 blue marbles in a bag. (a) What is the ratio of all marbles in the bag to blue marbles? (b) What is the ratio of red marbles to all marbles in the bag?
Answer:
a.) 11:8
b.) 3:11
Step-by-step explanation:
a)
Add all marbles
8 + 3 = 11
Blue marbles = 8
So, the ratio will be 11:8
b)
Red marbles = 3
All marbles = 11
So, the ratio will be 3:11
Hope this helps.
Answer:
Step-by-step explanation:
A square steel bar has a length of 5.1 ft and a 2.7 in by 2.7 in cross section and is subjected to axial tension. The final length is 5.10295 ft . The final side length is 2.69953 in . What is Poisson's ratio for the material
Answer:
The Poisson's ratio for the material is 0.0134.
Step-by-step explanation:
The Poisson's ratio ([tex]\nu[/tex]), no unit, is the ratio of transversal strain ([tex]\epsilon_{t}[/tex]), in inches, to axial strain ([tex]\epsilon_{a}[/tex]), in inches:
[tex]\nu = -\frac{\epsilon_{t}}{\epsilon_{a}}[/tex] (1)
[tex]\epsilon_{a} = l_{a,f}-l_{a,o}[/tex] (2)
[tex]\epsilon_{t} = l_{t,f}-l_{t,o}[/tex] (3)
Where:
[tex]l_{a,o}[/tex] - Initial axial length, in inches.
[tex]l_{a,f}[/tex] - Final axial length, in inches.
[tex]l_{t,o}[/tex] - Initial transversal length, in inches.
[tex]l_{t,f}[/tex] - Final transversal length, in inches.
If we know that [tex]l_{a,o} = 61.2\,in[/tex], [tex]l_{a,f} = 61.235\,in[/tex], [tex]l_{t,o} = 2.7\,in[/tex] and [tex]l_{t,f} = 2.69953\,in[/tex], then the Poisson's ratio is:
[tex]\epsilon_{a} = 61.235\,in - 61.2\,in[/tex]
[tex]\epsilon_{a} = 0.035\,in[/tex]
[tex]\epsilon_{t} = 2.69953\,in - 2.7\,in[/tex]
[tex]\epsilon_{t} = -4.7\times 10^{-4}\,in[/tex]
[tex]\nu = - \frac{(-4.7\times 10^{-4}\,in)}{0.035\,in}[/tex]
[tex]\nu = 0.0134[/tex]
The Poisson's ratio for the material is 0.0134.
The president of the student council wants to survey the student population about parking. She decides to take a random sample of 100 of the 1,020 students at the school. Which of the following correctly labels the population?
1–1020
01–1020
001–1020
0001–1020
I think its (B), 01-1020.
Answer:
Should be (B)
01-1020
ED2021
The correct label for the population is 1 - 1020,
Option A is the correct answer.
What is random sampling?It is the way of choosing a number of required items from a number of population given.
Each items has an equal probability of being chosen.
We have,
The population in this case refers to the entire group of interest, which is the entire student body of the school.
The total number of students is 1,020.
The population is usually labeled with a range or interval that includes all the possible values of the variable of interest.
In this case, the variable of interest is whether or not a student has an opinion on parking.
The correct label for the population is 1-1020, as this range includes all possible student identification numbers at the school.
The other options (01-1020, 001-1020, and 0001-1020) are not correct because they suggest that there are leading zeros in the student identification numbers, which is not usually the case.
Thus,
The correct label for the population is 1-1020,
Learn more about random sampling here:
https://brainly.com/question/12719656
#SPJ7
product of a positive and a negative integer is ___________
Answer:
negative
Step-by-step explanation:
because when positive and negative integers are multiplied it results to a negative answer
6. 5x = -25
a. X= 5
b. X=-5
c. x=2
Answer:
x = -5
Step-by-step explanation:
5x = -25
Divide each side by 5
5x/5 = -25/5
x = -5
Answer:
[tex]Option\ B,\ x = -5[/tex]
Step-by-step explanation:
Step 1: Divide both sides by 5
[tex]5x = -25[/tex]
[tex]5x / 5 = -25 / 5[/tex]
[tex]x = -25/5[/tex]
[tex]x = -5[/tex]
Answer: [tex]Option\ B,\ x = -5[/tex]
A cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used. Part 1. In January, the total cost for 150 minutes was $ 62 while in February, the total cost for 175 minutes was $ 64 . The constant charge for each minute used is:
a. 0.09
b. 0.1
c. 0.08
Part 2. The fixed montly fee charged by the carrier is;
fee = $__________________
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Answer:
c. $0.08
fee = $50
Step-by-step explanation:
We are given two ordered pairs:
(minutes, charges) = (150, 62) and (175, 64)
The slope of the graph of charges is ...
m = (y2 -y1)/(x2 -x1) = (64 -62)/(175 -150) = 2/25 = 0.08
The charge for each minute is $0.08.
__
The y-intercept of the graph can be found from ...
b = y -mx
b = 62 -150(0.08) = 62 -12 = 50
The fixed monthly fee is $50.
i will give brainliest help please
Answer:
SA = 52 square meters
Step-by-step explanation:
First, the equation I'll be using for this problem is SA=2(wl+hl+hw)! Our width is 4m, our length is 3m, and our height is 2m. To begin to solve this problem we are going to input these values in to the equation above.
SA = 2(4 × 3 + 2 × 3 + 2 × 4)
Next, we are going to multiply our values inside the parenthesis based on the PEMDAS strategy (if you have any questions about this, feel free to ask below :).
SA = 2(12 + 6 + 8)
Now, we can add our values inside the parenthesis.
SA = 2(26)
Finally, all we have to do is distribute the 2 outside of the parenthesis to inside the parenthesis.
SA = 52 square meters
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Rs 600 will gave Rs 90 simple interest at 5 % per annum.
Step-by-step explanation:
interest=90
principal=600
rate=5%
time = I × 100/p×r
= 90×100/600×5
= 3 years.
What lines are parallel?
find each measurement indicated round your answers to the nearest tenth. Part 1d. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Answer:
see explanation
Step-by-step explanation:
Using the Sine rule in all 3 questions
(1)
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values , firstly calculating ∠ B
[ ∠ B = 180° - (78 + 49)° = 180° - 127° = 53° ]
[tex]\frac{a}{sin78}[/tex] = [tex]\frac{18}{sin53}[/tex] ( cross- multiply )
a sin53° = 18 sin78° ( divide both sides by sin53° )
a = [tex]\frac{18sin78}{sin53}[/tex] ≈ 22.0 ( to the nearest tenth )
(3)
[tex]\frac{c}{sinC}[/tex] = [tex]\frac{a}{sinA}[/tex] , substitute values
[tex]\frac{35}{sinC}[/tex] = [tex]\frac{45}{sin134}[/tex] ( cross- multiply )
45 sinC = 35 sin134° ( divide both sides by 35 )
sinC = [tex]\frac{35sin134}{45}[/tex] , then
∠ C = [tex]sin^{-1}[/tex] ( [tex]\frac{35sin134}{45}[/tex] ) ≈ 34.0° ( to the nearest tenth )
(5)
Calculate the measure of ∠ B
∠ B = 180° - (38 + 92)° = 180° - 130° = 50°
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values
[tex]\frac{BC}{sin38}[/tex] = [tex]\frac{10}{sin50}[/tex] ( cross- multiply )
BC sin50° = 10 sin38° ( divide both sides by sin50° )
BC = [tex]\frac{10sin38}{sin50}[/tex] ≈ 8.0 ( to the nearest tenth )
What is the equation of a line that passes through the point (8,-2) and is parallel to the line whose equation is 3x+4y=15?
Answer:
y = -3x/4 + 4
Step-by-step explanation:
slope m = -3/4
-2=(-3/4)×8+b
or, b = 4
y = mx + b
y = -3x/4 + 4
Answered by GAUTHMATH
If p is true and ~ q is false, then p ~ q is _____ false.
a. sometimes
b. always
c. never
At what point on the curve x = 6t2 + 6, y = t3 − 2 does the tangent line have slope 1 /2 ?
Answer:
Hello,
P=(30,6)
Step-by-step explanation:
[tex]x=6t^2+6\\y=t^3-2\\\\\dfrac{dx}{dt}= 12t\\\dfrac{dy}{dt}= 3t^2\\\\\dfrac{dy}{dx} =\dfrac{\dfrac{dy}{dt} }{\dfrac{dx}{dt} } =\dfrac{3t^2}{12t} =\dfrac{t}{4} \\\\\dfrac{t}{4} =\dfrac{1}{2} \Longrightarrow t=2\\\\\\x=6t^2+6=6*2^2+6=30\\\\y=t^3-2=2^2-2=8-2=6\\\\\\Tangence\ point=(30,6)\\[/tex]
The point on the curve x = 6t² + 6, y = t³ - 2 where the tangent line have slope 1/2 is (30, 6).
How to depict the point on the curve?From the information given, x = 6t² + 6, y = t³ - 2. We'll find the first order derivative of x and y which will be:
dx/dt = 12t
dy/dt = 3t²
Therefore, 3t²/12t = t/4, t = 2.
We'll put the value of t back into the equations.
x = 6t² + 6,
x = 6(2)² + 6
x = 24 + 6 = 30
y = t³ - 2.
y = (2)³ - 2
y = 8 - 2 = 6
In conclusion, the correct options is (30, 6).
Learn more about slope on:
https://brainly.com/question/3494733
One number is eight less than a second number. Five times the first is 6 more than 6 times the second. Find the numbers.
The value of the first number is -
Answer:
-42/11
Step-by-step explanation:
x = y - 8
5x = 6 - 6y
So now solve the system of equations, divide everything in the second equation by 5 to get it to x = 6/5 - 6y/5
Now...
x = y - 8
x = 6/5 - 6y/5
Now substitute first equation into the second and x is gonna be -42/11 or the first number
ZA and ZB are complementary angles. If m A = (8x + 27)° and m
ZB = (6x – 21)°, then find the measure of ZB.
Answer:
15
Step-by-step explanation:
Complementary angles add to 90 degrees
8x+27 + 6x-21 = 90
Combine like terms
14x+6 = 90
Subtract 6 from each side
14x+6-6 = 90-6
14x = 84
Divide by 14
14x/14 = 84/14
x=6
We want angle B
B = 6x-21 = 6*6-21 =36-21 = 15
find the quadratic equations whose roots are 3 and -4
Answer:
Hello,
Step-by-step explanation:
(x-3)*(x+4)=0 or x²+x-12=0
Answer:
Step-by-step explanation:
[tex]\displyastyle \Large \boldsymbol{} (x-x_1)(x-x_2) \ \ x_1 \ ; \ x_2 -roots \\\\(x-3)(x-(-4))=(x-3)(x+4)=\boxed{x^2+x-12}[/tex]
Please help! Thank you!!!!!
9514 1404 393
Answer:
f(x) = x² -3g(x) = 6x +7h(x) = 3^xStep-by-step explanation:
f(x) is copied from the problem statement.
g(x) is a symbolic representation of the English wording, using x to represent "a number."
h(x) is the exponential function that corresponds to the geometric sequence in the table. It has a common ratio of 3, and a multiplier of 1 at x=0.
From -13°C to 15°C.
a. -28°C
b. -2°C
C. 28°C
d. 2°C
ccccccccccccccccccccccc
Answer:
Option B
-13°c-2°c= 15°c
hope it helps
Describe what is contained in a credit report
Answer:
Your credit report contains personal information, credit account history, credit inquiries and public records. This information is reported by your lenders and creditors to the credit bureaus. Much of it is used to calculate your FICO® Scores to inform future lenders about your creditworthiness.
