Answer:
a) The sample mean is of 49 and the sample standard deviation is of 11.7.
b) The range of the true mean at 90% confidence level is of 9.62 hours.
c) The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.
Step-by-step explanation:
Question a:
Sample mean:
[tex]\overline{x} = \frac{34+40+46+49+61+64}{6} = 49[/tex]
Sample standard deviation:
[tex]s = sqrt{\frac{(34-49)^2+(40-49)^2+(46-49)^2+(49-49)^2+(61-49)^2+(64-49)^2}{5}} = 11.7[/tex]
The sample mean is of 49 and the sample standard deviation is of 11.7.
b)Determine the range of the true mean at 90% confidence level.
We have to find the margin of error of the confidence interval. Since we have the standard deviation for the sample, the t-distribution is used.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0.150
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample. So
[tex]M = 2.0150\frac{11.7}{\sqrt{6}} = 9.62[/tex]
The range of the true mean at 90% confidence level is of 9.62 hours.
(c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time.
This is the confidence interval, so:
The lower end of the interval is the sample mean subtracted by M. So it is 49 - 9.62 = 39.38 hours.
The upper end of the interval is the sample mean added to M. So it is 49 + 9.62 = 58.62 hours.
The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.
What procedure might one use to solve percent problems using proportions ?
Answer:
Proportions and percent
BRAINLIESTT A spinner is divided into 8 equal-sized sections, and each section is labeled with a number 1 through 8.
if Kathryn spins the arrow on the spinner twice, what is the probability that the arrow will land on a section with an odd number the first time
and a number greater than 6 on the second spln?
Answer:
The probability would be 1/8.
Step-by-step explanation:
The probability of the spinner landing on an odd number is 1/2, and the probability of the spinner landing on a number greater than 8 is 1/4. So we multiply those two probabilites to get our answer 1/8.
A BYU-Idaho professor took a survey of his classes and found that 82 out of 90 people who had served a mission had personally met a member of the quorum of the twelve apostles. Of the non-returned missionaries that were surveyed 86 of 110 had personally met a member of the quorum of the twelve apostles. Calculate a 99% confidence interval for the difference in the two proportions.
Answer:
The 99% confidence interval for the difference in the two proportions is (-0.0247, 0.2833).
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A BYU-Idaho professor took a survey of his classes and found that 82 out of 90 people who had served a mission had personally met a member of the quorum of the twelve apostles.
This means that:
[tex]p_S = \frac{82}{90} = 0.9111[/tex]
[tex]s_S = \sqrt{\frac{0.9111*0.0888}{90}} = 0.045[/tex]
Of the non-returned missionaries that were surveyed 86 of 110 had personally met a member of the quorum of the twelve apostles.
This means that:
[tex]p_N = \frac{86}{110} = 0.7818[/tex]
[tex]s_N = \sqrt{\frac{0.7818*0.2182}{110}} = 0.0394[/tex]
Distribution of the difference:
[tex]p = p_S - p_N = 0.9111 - 0.7818 = 0.1293[/tex]
[tex]s = \sqrt{s_S^2+s_N^2} = \sqrt{0.045^2+0.0394^2} = 0.0598[/tex]
Calculate a 99% confidence interval for the difference in the two proportions.
The confidence interval is:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.1293 - 2.575*0.0598 = -0.0247[/tex]
[tex]p + zs = 0.1293 + 2.575*0.0598 = 0.2833[/tex]
The 99% confidence interval for the difference in the two proportions is (-0.0247, 0.2833).
how many models does the following set have? 5,5,5,7,8,12,12,12,150,150,150
The three modes are 5, 12, and 150 since they occur the most times and they tie one another in being the most frequent (each occurring 3 times).
Only the 7 and 8 occur once each, and aren't modes. Everything else is a mode. It's possible to have more than one mode and often we represent this as a set. So we'd say the mode is {5, 12, 150} where the order doesn't matter.
A five-year prospective cohort study has just been completed. The study was designed to assess the association between supplemental vitamin A exposure and mortality and morbidity for measles. The relative risk for incidence of measles was 0.75 and the relative risk for measles mortality was 0.5. Regarding the relative risk, which statement is correct?
a. Exposure to vitamin A appears to protect against morbidity and mortality for measles.
b. Exposure to vitamin A appears to be a risk factor for morbidity and mortality for measles.
c. Exposure to vitamin A is not associated with morbidity and mortality for measles.
d. Exposure to vitamin A is a risk factor for morbidity and a protective factor for mortality for measles.
Answer:
Assessing the association between supplemental vitamin A exposure and mortality and morbidity for measles:
Regarding the relative risk, the correct statement is:
a. Exposure to vitamin A appears to protect against morbidity and mortality for measles.
Step-by-step explanation:
Relative risk for incidence of measles = 0.75
Relative risk for measles mortality = 0.5
Relative risk for mortality and morbidity for measles = 0.375 (0.75 * 0.5)
The combined relative risk is less than 50%
The association is weak because RR is less than 1.
Therefore, there is no association between supplemental vitamin A exposure and mortality and morbidity for measles.
which choice are equivalent to the expression below? Check all that apply
I could not get the expressions to type correctly because I am new so I am sending a picture. I am having trouble working backwards to figure out which once to choose.
Answer:
A, B, and E apply
Step-by-step explanation:
One thing we can do is to make everything in the same format, under one square root, with no non-square roots.
First, we can say that 6 is equal to √36 as 6² =36, and 6 ≥ 0. Therefore, 6√3 = √36 * √3 = √108
For A, √3 * √36 = √108, so this applies
For B, √18 * √6 = √108, so this applies
For C, 108² = √something bigger than 108 = √11664, so this does not apply
For D, √54 ≠ √108, so this does not apply
For E, √108 = √108, so this applies
For F, √3 * √6 = √18, so this does not apply
If x and y are positive integers such that 5x+3y=100, what is the greatest possible value of xy? please include steps. Thank you!
Answer:
The greatest possible value of xy is 165.
Step-by-step explanation:
Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
\begin{cases} y=-2x+7 \\\\ y=5x-7 \end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
y=−2x+7
y=5x−7
x=x=x, equals
y=y=y, equals
Answer:
x=2
y=3
Step-by-step explanation:
y=−2x+7
y=5x−7
Set the two equations equal since they are both equal to y
−2x+7 =5x−7
Add 2x to each side
-2x+7+2x = 5x-7+2x
7 = 7x-7
Add 7 to each side
7+7 = 7x-7+7
14 =7x
Divide by 7
14/7 = 7x/7
2 =x
Now find 7
y = 5x-7
y = 5(2) -7
y = 10-7
y = 3
Given that y=y=y,
→ -2x+7 = 5x-7
Let's find the value,
→ -2x+7 = 5x-7
→ 7 = 5x+2x-7
→ 7 = 7x-7
→ 7+7=7x
→ 14 = 7x
→ x = 14/7
→ [x = 2]
Then we can find 7,
→ y = 5x-7
→ y = 5(2) -7 y = 10-7
→ [y = 3]
This is required answer.
Which table shows a proportional relationship between x and y?
OA.
X
у
N
4
3
.6
4
9
ОВ.
X
y
3
4
9
16
15
20
C.
x
у
12
4. 5
15
6
18
D.
х
y
1
4
N
00
3
15
CAN SOMEONE PLEASE ANSWER MY QUESTION?!
Answer:
0.02 m/sec
Step-by-step explanation:
26/30=0.89 —> 0.89 min —> 53.4 sec
42/50=0.84 meters
speed=0.84 / 53.4 = 0.015 m/sec = 0.02 m/sec
PLEASE HELP!!!!!! (answer in decimal!!!!)
Answer:
0.706....
Step-by-step explanation:
Which of the following best describes the expression 4(y + 6)?
The product of a constant factor of four and a factor with the sum of two terms
The sum of a constant factor of six and a factor with the product of two terms
The product of two constant factors four and six plus a variable
The sum of two constant factors four and six plus a variable
Answer:
The product of a constant factor of four and a factor with the sum of two terms
Step-by-step explanation:
4(y + 6)
This is two terms, a constant 4 and a term with y+6
We a multiplying so we have a product
Answer:
A
Step-by-step explanation:
I believe A is the best answer because 4 is the constant factor with the sum of y + 6. I just think it best rrepresents the equation! :)
(07.05A)
Which statement best explains whether y = 4x + 8 is a linear function or a nonlinear function?
Answer:
Step-by-step explanation:
There are no statements provided, but since it is modeled after the linear function y = mx + b, it is a line. m is the slope or rate of change (which is constant; that's what makes this a line!), and b is the y-intercept (the value of y when x is equal to 0). Its slope is 4 (the function raises 4 units for every 1 unit it moves to the right). Its y-intercept is 8, having the coordinate (0, 8).
Answer:
y = 4x + 8 is a linear function.
Step-by-step explanation:
No statements are given, but here's why:
- It's in slope-intercept form, y = mx + b.
- It has a constant slope.
- A non-linear function does not have a constant slope, and this one does.
What are the zeros of f(x) = (x - 2)(x + 7)? Select all that apply.
A. X= -7
B. X = -2
C. X = 2
D. X = 7
Answer:
2 = x -7 = x
Step-by-step explanation:
f(x) = (x - 2)(x + 7)
y = (x - 2)(x + 7)
Set y = 0
0 = (x - 2)(x + 7)
Using the zero product property
0 = x-2 0 = x+7
2 = x -7 = x
Answer:
Zeros happen when f(x) = 0. There are two zeros in the given function:
when (x - 2) = 0when (x + 7) = 0Therefore solve both equations above and you'll get:
Zero #1 = 2Zero #2 = -7can someone please help me?
Step-by-step explanation:
D. RAMONA SAVED THE MOST IN 2006
D. Ramona saved the most in 2006
Hi, hiw do we do this question?
[tex]\displaystyle \int\sec x\:dx = \ln |\sec x + \tan x| + C[/tex]
Step-by-step explanation:
[tex]\displaystyle \int\sec x\:dx=\int\sec x\left(\frac{\sec x+ \tan x}{\sec x + \tan x}\right)dx[/tex]
[tex]\displaystyle = \int \left(\dfrac{\sec x\tan x + \sec^2x}{\sec x + \tan x} \right)dx[/tex]
Let [tex]u = \sec x + \tan x[/tex]
[tex]\:\:\:\:\:\:du = (\sec x\tan x + \sec^2x)dx[/tex]
where
[tex]d(\sec x) = \sec x\tan x\:dx[/tex]
[tex]d(\tan x) = \sec^2x\:dx[/tex]
[tex]\displaystyle \Rightarrow \int \left(\frac{\sec x\tan x + \sec^2x}{\sec x + \tan x}\right)\:dx = \int \dfrac{du}{u}[/tex]
[tex]= \ln |u| + C = \ln |\sec x + \tan x| + C[/tex]
answer plz no explanation needed
Answer:
x is 1. i looked it up so that's all you need
Suppose that the length of a side of a cube X is uniformly distributed in the interval 9
Answer:
[tex]f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.[/tex]
Step-by-step explanation:
Given
[tex]9 < x < 10[/tex] --- interval
Required
The probability density of the volume of the cube
The volume of a cube is:
[tex]v = x^3[/tex]
For a uniform distribution, we have:
[tex]x \to U(a,b)[/tex]
and
[tex]f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.[/tex]
[tex]9 < x < 10[/tex] implies that:
[tex](a,b) = (9,10)[/tex]
So, we have:
[tex]f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]
Solve
[tex]f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]
[tex]f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]
Recall that:
[tex]v = x^3[/tex]
Make x the subject
[tex]x = v^\frac{1}{3}[/tex]
So, the cumulative density is:
[tex]F(x) = P(x < v^\frac{1}{3})[/tex]
[tex]f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex] becomes
[tex]f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.[/tex]
The CDF is:
[tex]F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx[/tex]
Integrate
[tex]F(x) = [v]\limits^{v^\frac{1}{3}}_9[/tex]
Expand
[tex]F(x) = v^\frac{1}{3} - 9[/tex]
The density function of the volume F(v) is:
[tex]F(v) = F'(x)[/tex]
Differentiate F(x) to give:
[tex]F(x) = v^\frac{1}{3} - 9[/tex]
[tex]F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}[/tex]
[tex]F'(x) = \frac{1}{3}v^{-\frac{2}{3}}[/tex]
[tex]F(v) = \frac{1}{3}v^{-\frac{2}{3}}[/tex]
So:
[tex]f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.[/tex]
Help! Given that tanθ=-1, what is the value of secθ, for 3π/2<θ<2π?
Answer: Choice B) [tex]\sqrt{2}[/tex]
Work Shown:
[tex]\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}\\\\[/tex]
Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.
Find the product :
1) 6/10 × 10/6 × 5/9
2) 6/10 × 4/3 × 10/20
Hello!
1) 6/10 × 10/6 × 5/9 = 1/10 × 10 × 5/9 = 1 × 5/9 = 5/9 or 0,5
2) 6/10 × 4/3 × 10/20 = 6 × 4/3 × 1/20 = 2 × 4 × 1/20 = 2 × 1/5 = 2/5 or 0,4
Good luck! :)
Answer:
1) 5/9
2) 2/5
Explanation:
1) 6/10 × 10/6 × 5/9=
Multiply all the denominators and all the numerators then simplify= 300/540 = 5/9
2) 6/10 × 4/3 × 10/20=
Multiply all the denominators and all the numerators then simplify= 240/600 = 2/5
answers please formula
Answer:
-5
2
-125
-3
Step-by-step explanation:
5 + A = 0
Subtract 5 from both sides.
A = -5
-8/4 - B = -4
-2 - B = -4
B + 2 = 4
B = 2
C ÷ 25 = -5
C = -125
D × 13 = -39
D × 13/13 = -39/13
D = -3
Lakisha wants to buy some bitcoins. The exchange rate is $1 USD to 0.004 bitcoin. How many bitcoins can she buy with $400?
Answer:
1.6 Bitcoins
Step-by-step explanation:
Given data
We have the rate as
$1 USD to 0.004
Hence $400 will buy x bitcoins
Cross multiply to find the value of x
1*x= 400*0.004
x=1.6
Hence $400 will get you 1.6 Bitcoins
th of
cm.
4 Mrs. Ayer is painting the outside of her son's toy
box, including the top and bottom. The toy box
measures 3 feet long, 1.5 feet wi de, and 2 feet high.
What is the total surface area she will paint?
1) 9.0 ft
2) 13.5 ft?
3) 22.5 ft?
4) 27.0 ft
Chau Took 5 3/8 hours to clean the bedroom. Then he took a 1/2 to clean the den. How much total time did he take to clean two rooms.
Answer:
It took Chau 5 hours, 52 minutes, and 30 seconds to clean both rooms.
Step-by-step explanation:
Given that Chau took 5 3/8 hours to clean the bedroom, and then he took a 1/2 to clean the den, to determine how much total time did he take to clean two rooms the following calculation must be performed:
5 + 3/8 + 1/2 = X
5 + 0.375 + 0.5 = X
5.875 = X
0.875 = 7/8
60/8 x 7 = 52.5
Therefore, it took Chau 5 hours, 52 minutes, and 30 seconds to clean both rooms.
Substituting the equation y = 4x + 1 into the equation 2y = -x – 1 will produce the equation ________.
Answer:
Step-by-step explanation:
Substituting y = 4x+1 into 2y = -x-1 gives the equation
2(4x+1) = -x-1
Solve the equation:
8x+2 = -x-1
9x = -3
x = -⅓
Substituting y = 4x+1 into 2y = -x-1 will produce the equation 2(4x+1) = -x-1
What are the equations?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. Based on the degree, there are four different main types of equations. Equations that are linear, quadratic, cubic, and polynomial
Given, the equation y = 4x + 1 and another equation 2y = -x – 1.
Substituting equation 1 into equation 2 we will get
2(4x+1) = -x-1
Solve the equation:
8x+2 = -x-1
9x = -3
x = -⅓
Therefore, The equation 2(4x+1) = -x-1 is created when y = 4x+1 is substituted into 2y = -x-1.
Learn more about equations here:
https://brainly.com/question/16255566
#SPJ2
Please look at the file below. (No links will give brainiest)
Answer:
3.564 m^2
Step-by-step explanation:
The area of the original garden is
A = 5.4 * 1.5 = 8.1
The new garden is
5.4*1.2 = 6.48 by 1.5*1.2 =1.8
The area is
A = 6.48*1.8=11.664
The increase in area is
11.664-8.1=3.564
The given information is,
To find the increase in area of the garden.
Formula we use,
→ Area = Length × Width
Area of the real garden is,
→ 5.4 × 1.5
→ 8.1 m
The new garden will be,
→ 5.4 × 1.2 = 6.48 m
→ 1.5 × 1.2 = 1.8 m
The area of the new garden is,
→ 6.48 × 1.8
→ 11.664
Then the increase in area of the garden,
→ 11.664 - 8.1
→ 3.564 m²
Hence, 3.564 m² is the increase in area.
Suppose you are conducting a study to determine if women are better drivers than men. You send your survey to over 1000 students on your campus and 5 students respond that women are better drivers and 4 students respond that women are not better drivers. What is the sample proportion for women as the better drivers using the large-sample method?
Answer:
555.56
Step-by-step explanation:
Purpose of the study: To determine if women are better drivers than men.
Survey or Opinion population: 1,000
You are experimenting on 9 out of a thousand opinions.
5 of these opinions are that women are better drivers
4 of these opinions are that women are not better drivers
You want to know the sample (full sample size is 9) proportion for women as better drivers; using the large sample method. This method is also called the asymptotic method.
This involves approximating the desired statistic, with just a small fraction of the population; in this case, 9/1000.
This approximation will get more and more accurate as sample size increases and you know that a larger sample size gives a better representation and interpretation of the population preference!
So using ratio, the sample proportion for women as the better drivers is given by:
5/9 x 1000 = 555.56 opinions
If a + b = s and a - b = t, then which of the following expresses the value of ab in terms of s and t?
Please help me out
Answer:
=(s^2 - t^2)/4
Step-by-step explanation:
a + b = s and a - b = t,
Add the two equations together
a + b = s
a - b = t
----------------
2a = s+t
a = (s+t)/2
Subtract the two equations
a + b = s
- a + b = -t
-------------------
2b =(s-t)
b = (s-t)/2
We want to find ab
ab = (s+t)/2 * (s-t)/2
FOIL
=(s^2 - t^2)/4
Last year Diana sold 800 necklaces. This year she sold 1080 necklaces. what is the percentage increase of necklaces she sold?
Answer:
the percentage increase is 35%
Create a sample of 10 numbers that has a mean of 8.6.
Answer:
10 + 8 + 10 + 10 + 10 + 10 + 8 + 8 + 6 + 6
