Missing part of the question
b)What is the value of R?
Answer:
a. X = 155.2
b. R = 4.4
Step-by-step explanation:
a. Calculating the value of x.
The value of x is the mean of the mean observation; i.e. the mean column
Mean is calculated as: the summation of all observation divided by the number of observations.
Summation of Observation = 158.9 + 151.2 + 155.6 + 155.5 + 154.6
Summation of Observation = 775.8
Number of Observations = 5
X = Mean = 775.8/5
X = 155.16
X = 155.2 ----- Approximated to 1 decimal place
b. Calculating the value of R.
The value of R is the mean/average of the Range
Mean is calculated as: the summation of all observation divided by the number of observations.
Summation of Observation = 4.0 + 4.6 + 4.3 + 5.0 + 4.3
Summation of Observation = 22.2
Number of Observations = 5
R = Mean = 22.2/5
R = 4.44
R = 4.4 ----- Approximated to 1 decimal place
The average diameter [tex](\( \overline{x} \))[/tex] of the pistons from the provided data is 155.16 mm, calculated by summing the daily means and dividing by the number of days.
In the context provided, [tex]\( \overline{x} \)[/tex] refers to the average of the piston diameters measured across different days at Wemming Chung's plant.
To find this value, we need to calculate the mean of the daily means [tex](\( \overline{x} \))[/tex] which are 158.9, 151.2, 155.6, 155.5, and 154.6 mm. This is done by summing these values and dividing by the number of days (5 in this case).
[tex]\[ \overline{x} = \frac{158.9 + 151.2 + 155.6 + 155.5 + 154.6}{5} \][/tex]
[tex]\[ \overline{x} = \frac{775.8}{5} \][/tex]
[tex]\[ \overline{x} = 155.16 \text{ mm} \][/tex]
Hence, the value of [tex]\( \overline{x} \)[/tex] is 155.16 mm.
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An obtuse triangle is sometimes an example of a/an:
I.
scalene triangle
II.
isosceles triangle
III.
equilateral triangle
IV.
right triangle
Answer:
I.
Scalene triangle
Step-by-step explanation:
A certain flight arrives on time 8484 percent of the time. Suppose 143143 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that (a) exactly 108108 flights are on time. (b) at least 108108 flights are on time. (c) fewer than 124124 flights are on time. (d) between 124124 and 128128, inclusive are on time. (a) P(108108)equals=0.00200.0020 (Round to four decimal places as needed.) (b) P(Xgreater than or equals≥108108)equals=0.99800.9980 (Round to four decimal places as needed.) (c) P(Xless than<124124)equals=0.77960.7796 (Round to four decimal places as needed.) (d) P(124124less than or equals≤Xless than or equals≤128128)equals=0.19230.1923 (Round to four decimal places as needed.)
Answer:
a) P(x=108)=0.0020
b) P(x≥108)=0.9980
c) P(x<124)=0.7794
d) P(124≤x≤128)=0.1925
Step-by-step explanation:
We know the population proportion, that is p=0.84.
We take a sample of size n=143.
We will use the normal approximation to the binomial distribution to model this problem.
The mean and standard deviation of the normal approximation to the binomial distribution will be:
[tex]\mu=np=143*0.84=120.12\\\\\sigma=\sqrt{np(1-p)}=\sqrt{143*0.84*0.16}=\sqrt{19.22}=4.38[/tex]
a) We have to calculate the probability that exactly 108 flights are on time.
As the normal distribution considers the random variable to be continous, we have to apply the continuity correction factor.
In this case, the probability of 108 flights on time can be calculated as P(107.5<x<108.5):
[tex]P(x=108)=P(107.5<x<108.5)=P(x<108.5)-P(x<107.5)\\\\\\ z_1=(x_1-\mu)/\sigma=(107.5-120.12)/4.38=-12.62/4.38=-2.88\\\\z_2=(x_2-\mu)/\sigma=(108.5-120.12)/4.38=-11.62/4.38=-2.65\\\\\\P(x<108.5)-P(x<107.5)=P(z<-2.65)-P(z<-2.88)\\\\P(x<108.5)-P(x<107.5)=0.0040-0.0020=0.0020[/tex]
b) Now we have to calculate that at least 108 flights are on time.
As the probability includes 108, the continuity factor will indicates that we calculate P(x>107.5). The z-value for x=107.5 has been already calculated in point a:
[tex]P(x\geq108)=P(x>107.5)=P(z>-2.88)=0.9980[/tex]
c) We have to calculate the probability that fewer than 124 flights are on time. According to the continuity factor, we have to calculate the probability P(x<123.5), as the flight number 124 is not included in the interval.
[tex]P(x<124)=P(x<123.5)=P(z<0.77)=0.7794\\\\\\z=(x-\mu)/\sigma=(123.5-120.12)/4.38=0.77[/tex]
d) We have to calculate the probability that between 124 and 128 flights, inclusive, are on time.
This interval corresponds to the probability P(123.5<x<128.5)
[tex]P(123.5<x<128.5)=P(x<128.5)-P(x<123.5)\\\\\\ z_1=(x_1-\mu)/\sigma=(128.5-120.12)/4.38=8.38/4.38=1.91\\\\z_2=(x_2-\mu)/\sigma=(123.5-120.12)/4.38=0.77\\\\\\P(x<128.5)-P(x<123.5)=P(z<1.91)-P(z<0.77)\\\\P(x<128.5)-P(x<123.5)=0.9719-0.7794=0.1925[/tex]
n=400 people under the age of 25 was asked whether they check social media sites right after they wake up. 42% check social media sites in the morning and 58% said that they don’t. Using a 5% significance level, test to see if there is evidence that less than 50% of people under the age of 25 check social media sites right after they wake up.
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
p = 0.5
For the alternative hypothesis,
p < 0.5
Considering the population proportion, probability of success, p = 0.5
q = probability of failure = 1 - p
q = 1 - 0.5 = 0.5
Considering the sample,
P = 42/100 = 0.42
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
n = 400
z = (0.42 - 0.5)/√(0.5 × 0.5)/400 = - 3.2
Recall, population proportion, p = 0.5
We want the area to the left of 0.5 since the alternative hypothesis is lesser than 0.5. Therefore, from the normal distribution table, the probability of getting a proportion < 0.5 is 0.00069
So p value = 0.00069
Since alpha, 0.05 > than the p value, 0.00069, then we would reject the null hypothesis.
Therefore, there is significant evidence to conclude that that less than 50% of people under the age of 25 check social media sites right after they wake up.
Bank of America's Consumer Spending Survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment. Using data from a sample of credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2). Using the difference data, the sample mean difference was , and the sample standard deviation was .
Answer:
a) Null hypothesis: [tex]\mu_d= 0[/tex]
Alternative hypothesis: [tex]\mu_d \neq 0[/tex]
b) [tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{850 -0}{\frac{1123}{\sqrt{42}}}=4.905[/tex]
The next step is calculate the degrees of freedom given by:
[tex]df=n-1=42-1=41[/tex]
Now we can calculate the p value, since we have a left tailed test the p value is given by:
[tex]p_v =2*P(t_{(41)}>4.905) =0.000015[/tex]
So the p value is lower than any significance level given, so then we can conclude that we can reject the null hypothesis that the difference between he two groups are equal.
Step-by-step explanation:
Assuming the following questions:
We assume the following data: [tex] n = 42 ,\bar d= 850 , s_d = 1123[/tex]
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
a. Formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_2- \mu_1 = 0[/tex]
Alternative hypothesis: [tex]\mu_2 -\mu_1 \neq 0[/tex]
Or equivalently
Null hypothesis: [tex]\mu_d= 0[/tex]
Alternative hypothesis: [tex]\mu_d \neq 0[/tex]
b. Use a .05 level of significance. Can you conclude that the population means differ? What is the p-value?
[tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{850 -0}{\frac{1123}{\sqrt{42}}}=4.905[/tex]
The next step is calculate the degrees of freedom given by:
[tex]df=n-1=42-1=41[/tex]
Now we can calculate the p value, since we have a left tailed test the p value is given by:
[tex]p_v =2*P(t_{(41)}>4.905) =0.000015[/tex]
So the p value is lower than any significance level given, so then we can conclude that we can reject the null hypothesis that the difference between he two groups are equal.
What is the vertex of the graph of the function f(x) = 2(x − 2)2 + 3? Enter your answer in the boxes.
Answer:
The vertex of the function is at (2,3).
Step-by-step explanation:
I graphed the equation on the graph below.
If this answer is correct, please make me Brainliest!
The vertex of the graph of the function [tex]f(x)=2(x-2)^2+3[/tex] is at (2, 3). This is obtained by comparing the given function of the graph with the vertex form function of a parabola.
What is the vertex of a parabola?The vertex of a parabola is the point of intersection of the parabola and its line of symmetry.For a parabola whose equation is given in the standard form [tex]y=ax^2+bx+c[/tex], then the vertex will be the minimum of the graph if a>o and the maximum of the graph if a<0.The vertex form of a parabola is [tex]y=a(x-h)^2+k[/tex]. Where (h, k) is said to be the vertex of the graph.Finding the vertex:Given that the function of the graph is [tex]f(x)=2(x-2)^2+3[/tex].
We have the vertex form as [tex]y=a(x-h)^2+k[/tex]
So, the graph shows a parabola for the given equation.
On comparing the given equation with the vertex form,
f(x)=y, a=2, h=2, and k=3.
Then, (h, k)=(2, 3)
It is shown in the graph below.
Therefore, the vertex of the graph is at the point (2, 3).
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Sandra deposited $2,500 into a simple interest account. She earned $75 in interest after 1 year. Ron deposited $8,000 into an account that has the same interest rate as Sandra's account. How much money did Ron earn in interest after 1 year? *
Answer:
the interest amount is $240
Step-by-step explanation:
I hope it helps.
A certain type of bacteria, given favorable growth medium, quadruples in population every 6 hours. Given that there were 150 bacteria to start with, how many bacteria will there be in two and a half days?
Answer:
157,286,400 bacteria.
Step-by-step explanation:
We have been given that a certain type of bacteria, given favorable growth medium, quadruples in population every 6 hours. Given that there were 150 bacteria to start with.
We will use exponential growth function to solve our given problem.
[tex]y=a\cdot b^x}[/tex], where
y = Final value,
a = Initial value,
b = Growth factor.
x = Time.
Quadruples meaning 4 at a time, so growth factor is 4.
We are also told that population becomes 4 times every 6 hours, so time would be [tex]\frac{1}{6}x[/tex].
Initial value is given as 150.
Upon substituting these values in above formula, we will get:
[tex]y=150(4)^{\frac{1}{6}x}[/tex]
Let us convert two and a half days into hours.
1 day = 24 hours.
2.5 days = 2.5*24 hours = 60 hours.
To find the bacteria population in two and half days, we will substitute [tex]x=60[/tex] in our formula as:
[tex]y=150(4)^{\frac{1}{6}(60)}[/tex]
[tex]y=150(4)^{10}[/tex]
[tex]y=150(1048576)[/tex]
[tex]y=157,286,400[/tex]
Therefore, there will be 157,286,400 bacteria in two and a half days.
According to the Bureau of Labor Statistics it takes an average of 22 weeks for someone over 55 to find a new job. Assume that the probability distribution is normal and that the standard deviation is two weeks. What is the probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job
Answer:
The probability that eight workers over the age of 55 will take an average of more than 20 weeks to find a job is 0.9977 or 99.77%
Step-by-step explanation:
Average time to find a new job for someone over 55 years = μ = 22 weeks
Standard deviation = σ = 2 weeks
We have to find the probability that if 8 workers are selected at random what will be the probability that it will take them more than 20 weeks to find a job. So, this means that the sample size is n = 8.
Since, the distribution is normal and we have the value of population standard deviation, we will use the z-distribution to find the desired probability. For this, first we need to convert the value (20 weeks) to its equivalent z-score. The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
x = 20, converted to z-score will be:
[tex]z=\frac{20-22}{\frac{2}{\sqrt{8}}}=-2.83[/tex]
Thus, probability of time being greater than 20 weeks is equivalent to probability of z score being greater than - 2.83.
i.e.
P( X > 20 ) = P( z > -2.83 )
Using the z-table we can find this probability:
P( z > -2.83 ) = 1 - P( z < -2.83)
= 1 - 0.0023
= 0.9977
Since, P( X > 20 ) = P( z > -2.83 ), we can conclude that:
The probability that eight workers over the age of 55 will take an average of more than 20 weeks to find a job is 0.9977 or 99.77%
The probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job is approximately 99.77%.
To solve this problem, we need to use the concepts of the sampling distribution of the sample mean and the properties of the normal distribution. Here are the steps to find the probability that the average time for eight workers over the age of 55 to find a job is more than 20 weeks:
Step 1: Understand the given data
- Mean time[tex](\(\mu\))[/tex] = 22 weeks
- Standard deviation [tex](\(\sigma\))[/tex] = 2 weeks
- Sample size [tex](\(n\))[/tex] = 8 workers
Step 2: Define the sampling distribution of the sample meanThe sample mean [tex]\(\bar{X}\)[/tex] for a sample of size (n) from a normal distribution with mean [tex]\(\mu\)[/tex] and standard deviation [tex]\(\sigma\)[/tex] is itself normally distributed with:
- Mean:[tex]\(\mu_{\bar{X}} = \mu\)[/tex]
- Standard deviation: [tex]\(\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}\)[/tex]
Calculate the standard deviation of the sample mean:
[tex]\[\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} = \frac{2}{\sqrt{8}} = \frac{2}{2.828} \approx 0.707\][/tex]
Step 3: Convert the problem to a standard normal distribution (Z)We want to find the probability that the sample mean [tex]\(\bar{X}\)[/tex] is greater than 20 weeks. First, we convert this to a Z-score:
[tex]\[Z = \frac{\bar{X} - \mu_{\bar{X}}}{\sigma_{\bar{X}}}\][/tex]
Calculate the Z-score for [tex]\(\bar{X} = 20\)[/tex] weeks:
[tex]\[Z = \frac{20 - 22}{0.707} = \frac{-2}{0.707} \approx -2.83\][/tex]
Step 4: Find the probability corresponding to the Z-scoreUsing standard normal distribution tables or a Z-score calculator, we find the probability that (Z) is less than -2.83.
The cumulative probability for (Z = -2.83) is approximately 0.0023. This represents the probability that the sample mean is less than 20 weeks. However, we want the probability that the sample mean is more than 20 weeks:
[tex]\[P(\bar{X} > 20) = 1 - P(\bar{X} \leq 20) = 1 - 0.0023 = 0.9977\][/tex]
Step 5: ConclusionThe probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job is approximately 0.9977, or 99.77%.
Therefore, we can conclude that there is a very high probability (99.77%) that the average time for these eight workers to find a job is more than 20 weeks.
Use the confidence level and sample data to find a confidence interval for estimating the population muμ. Round your answer to the same number of decimal places as the sample mean. A random sample of 9595 light bulbs had a mean life of x overbar equals 510x=510 hours with a standard deviation of sigma equals 37 hours.σ=37 hours. Construct a 90% confidence interval for the mean life, muμ, of all light bulbs of this type.
Answer:= (504, 516)
Therefore, the 90% confidence interval (a,b) = ( 504, 516)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean gain x = 510
Standard deviation r = 37
Number of samples n = 95
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
510+/-1.645(37/√95)
510+/-1.645(3.796)
510+/-6.24
510+/-6
= (504, 516)
Therefore at 90% confidence interval (a,b) = ( 504, 516)
An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 364364 watts with a standard deviation of 1212 watts. What is the probability that the mean amplifier output would be greater than 364.8364.8 watts in a sample of 5252 amplifiers if the claim is true? Round your answer to four decimal places.
Answer:
The probability that the mean amplifier output would be greater than 364.8 watts in a sample of 52 amplifiers is 0.3156
Step-by-step explanation:
Mean output of amplifiers = 364
Standard deviation = [tex]\sigma[/tex] = 12
We have to find the probability that the mean output for 52 randomly selected amplifiers will be greater than 364.8. Since the population is Normally Distributed and we know the value of population standard deviation, we will use the z-distribution to solve this problem.
We will convert 364.8 to its equivalent z-score and then finding the desired probability from the z-table. The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
x=364.8 converted to z score for a sample size of n= 52 will be:
[tex]z=\frac{364.8-364}{\frac{12}{\sqrt{52} } }=0.48[/tex]
This means, the probability that the output is greater than 364.8 is equivalent to probability of z score being greater than 0.48.
i.e.
P( X > 364.8 ) = P( z > 0.48 )
From the z-table:
P( z > 0.48) = 1 - P(z < 0.48)
= 1 - 0.6844
= 0.3156
Since, P( X > 364.8 ) = P( z > 0.48 ), we can conclude that:
The probability that the mean amplifier output would be greater than 364.8 watts in a sample of 52 amplifiers is 0.3156
A study was conducted to measure the effectiveness of a diet program that claims to help manage weight. Subjects were randomly selected to participate. Before beginning the program, each participant was given a score based on his or her fitness level. After six months of following the diet, each participant received another score. The study wanted to test whether there was a difference between before and after scores. What is the correct alternative hypothesis for this analysis?
a. μ≠0
b. μd≠0
c. p1≠p2
Answer:
x=test value before , y = test value after
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex]
If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:
Null hypothesis: [tex]\mu_d = 0[/tex]
Alternative hypothesis: [tex]\mu_d \neq 0[/tex]
Step-by-step explanation:
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=test value before , y = test value after
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex]
If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:
Null hypothesis: [tex]\mu_d = 0[/tex]
Alternative hypothesis: [tex]\mu_d \neq 0[/tex]
Triangle E F G. Side E F is 6 meters, F G is 5 meters, E G is 7 meters. Triangle K L J. Side K L is 28 meters, L J is 24 meters, J K is 20 meters. Given that these triangles are similar, which side corresponds to side GE? Given that these triangles are similar, which side corresponds to side JK?
The first one is KL and the second one is FG
Side GE corresponds to side EJ, which is 24 meters long and side JK corresponds to side LK, which is 60/7 meters (or approximately 8.57 meters) long.
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
To determine which side of triangle EFG corresponds to side GE
we need to find the ratio of the lengths of corresponding sides.
The sides that share vertex E are EF and EJ, so we can write:
EF / EJ = FG / FJ = EG / EK
Substituting the given values, we get:
6 / ? = 5 / ? = 7 / 20
To solve for the missing value, we can cross-multiply and simplify:
6 × 20 = 5 × x
x = 24
To determine which side of triangle KLJ corresponds to side JK, we can use the same approach.
The sides that share vertex J are JL and JF, so we can write:
JL / JF = LK / EF = LJ / FG
Substituting the given values, we get:
24 / ? = 20 / 6 = 28 / 5
Cross-multiplying and simplifying:
24 × 5 = x × 28
x = 60 / 7
Therefore, side GE corresponds to side EJ, which is 24 meters long and side JK corresponds to side LK, which is 60/7 meters (or approximately 8.57 meters) long.
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what is the 20th shape the pattern is triangle,circle,circle
Answer:
Circle
Step-by-step explanation:
I don't know if there is a more "professional" way to solve this, but I wrote out the pattern until I got to the twentieth shape and it ended up being a circle :)
The 20th shape in the pattern is a circle.
Explanation:To determine the 20th shape in the pattern of triangle, circle, circle, we need to analyze the pattern. The pattern starts with a triangle and is followed by two circles. This sequence repeats - triangle, circle, circle. To find the 20th shape, we need to determine how many times this sequence repeats within the first 20 shapes. Each complete sequence consists of 3 shapes (triangle, circle, circle), so we divide 20 by 3 to get 6 complete sequences. The 6th complete sequence ends with a circle, so the 20th shape in the pattern is also a circle.
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Evaluate the function
Given f(x) = x^2-3x+2, find f(-2)
Answer:
f( - 2) =12
Step-by-step explanation:
[tex]f(x) = x^2-3x+2 \\ plugging \: x = - 2 \\ f( - 2) = ( - 2)^2-3( - 2)+2 \\ f( - 2) =4 + 6+2 \\ f( - 2) =12 \\ [/tex]
The normal curve with a mean of 0 and standard deviation of 1 is called?
Answer:
A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. so its A
Step-by-step explanation:
i looked it up and i think this is right :)
Write an equation in slope intercept form for $750 and $600 and $1150
Answer:
y = 0.5x + 10
Step-by-step explanation:
Step 1 :
Identify the independent and dependent variables.
The independent variable (x) is the square footage of floor space.
The dependent variable (y) is the monthly rent.
Step 2 :
Write the information given in the problem as ordered pairs.
The rent for 600 square feet of floor space is $750 :
(600, 750)
The rent for 900 square feet of floor space is $1150 :
(900, 1150)
Step 3 :
Find the slope.
m = (y₂ - y₁) / (x₂ - x₁)
Substitute (600, 750) for (x₁, y₁) and (900, 1150) for (x₂, y₂).
m = (1150 - 750) / (900 - 600)
m = 400 / 300
m = 4/3
Step 4 :
Find the y-intercept.
Use the slope 4/3 and one of the ordered pairs (600, 750).
Slope-intercept form :
y = mx + b
Plug m = 4/3, x = 600 and y = 750.
750 = (4/3)(600) + b
750 = (4)(200) + b
750 = 800 + b
-50 = b
Step 5 :
Substitute the slope and y-intercept.
Slope-intercept form
y = mx + b
Plug m = 4/3 and b = -50
y = (4/3)x + (-50)
y = (4/3)x - 50
Problem 2 :
Hari’s weekly allowance varies depending on the number of chores he does. He received $16 in allowance the week he did 12 chores, and $14 in allowance the week he did 8 chores. Write an equation for his allowance in slope-intercept form.
Solution :
Step 1 :
Identify the independent and dependent variables.
The independent variable (x) is number of chores Hari does per week
The dependent variable (y) is the allowance he receives per week.
Step 2 :
Write the information given in the problem as ordered pairs.
For 12 chores, he receives $16 allowance :
(12, 16)
For 8 chores, he receives $14 allowance :
(8, 14)
Step 3 :
Find the slope.
m = (y₂ - y₁) / (x₂ - x₁)
Substitute (12, 16) for (x₁, y₁) and (8, 14) for (x₂, y₂).
m = (14 - 16) / (8 - 12)
m = (-2) / (-4)
m = 1/2
m = 0.5
Step 4 :
Find the y-intercept.
Use the slope 0.5 and one of the ordered pairs (8, 14).
Slope-intercept form :
y = mx + b
Plug m = 0.5, x = 8 and y = 14.
14 = (0.5)(8) + b
14 = 4 + b
10 = b
Step 5 :
Substitute the slope and y-intercept.
Slope-intercept form
y = mx + b
Plug m = 0.5 and b = 10
y = 0.5x + 10
A psychological study found that men who were distance runners lived, on average, five years longer than those who were not distance runners. The study was conducted using a random sample of 50 men who were distance runners and an independent random sample of 30 men who were not distance runners. The men who were distance runners lived to be 84.2 years old, on average, with a standard deviation of 10.2 years. The men who were not distance runners lived to be 79.2 years old, on average, with a standard deviation of 6.8 years.
What is the test statistic for the appropriate test to determine if men who are distance runners live significantly longer, on average, than men who are not distance runners?
Answer: C
Step-by-step explanation:
What can you tell about the mean of each distribution
The mean of a distribution indicates its central tendency, with more observations clustering around this central value in a normally distributed dataset.
When examining various distributions, the mean of each distribution is a critical value that gives information about the central tendency of the data. In a normally distributed dataset, the mean is at the peak of the bell curve, suggesting that more observations cluster around this central value.
As for different types of distributions, such as binomial or normal, knowing the mean helps us compare them effectively.
For instance, if both distributions are normal with the same mean, they will overlap, but varying standard deviations will affect the spread of the data around that mean. The larger the standard deviation, the wider the distribution.
Additionally, the concept of skewness also affects the mean. In a positively skewed distribution, the mean is higher than the median, while in a negatively skewed distribution, the mean is less than the median. Considering skewness helps gauge the data's asymmetry and the mean's position relative to other central tendency measures.
Understanding the characteristics of a probability distribution, especially the normal distribution, which is symmetrical about its mean, is fundamental in statistics. The probability density functions have properties that allow us to predict the likelihood of outcomes within a range, expressed through confidence intervals or the standard deviation.
Find the slope of the line that passes through the pair of points.
(5,-4) AND (9,-4)
USE THE SLOPE FORMULA
Answer:
0
Step-by-step explanation:
The slope formula is ...
m = (y2 -y1)/(x2 -x1)
Filling in the given point values, we find the slope to be ...
m = (-4 -(-4))/(9 -5) = 0/4 = 0
The slope is 0.
_____
The y-values are the same at -4, the equation of the line is y = -4. It is a horizontal line with zero slope.
The monthly incomes from a random sample of workers in a factory are given below in dollars. Assume the population has a normal distribution and has a standard deviation of $518. Compute a 95% confidence interval for the mean of the population. Round your answers to the nearest whole dollar and use ascending order. Monthly Income 12390 12296 11916 11713 11936 11553 12000 12428 12354 12291
Answer:
[tex]12087.7-1.96\frac{518}{\sqrt{10}}=11766.64[/tex]
[tex]12087.7+1.96\frac{518}{\sqrt{10}}=12408.76[/tex]
So on this case the 95% confidence interval would be given by (11767;12409)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
Data: 12390 12296 11916 11713 11936 11553 12000 12428 12354 12291
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
The mean calculated for this case is [tex]\bar X=12087.7[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that [tex]z_{\alpha/2}=1.96[/tex]
Now we have everything in order to replace into formula (1):
[tex]12087.7-1.96\frac{518}{\sqrt{10}}=11766.64[/tex]
[tex]12087.7+1.96\frac{518}{\sqrt{10}}=12408.76[/tex]
So on this case the 95% confidence interval would be given by (11767;12409)
To compute a 95% confidence interval for the mean of the population, use the formula (sample mean) +/- (critical value) * (standard deviation / sqrt(sample size)).
Explanation:To compute a 95% confidence interval for the mean of the population, we can use the formula:
(sample mean) +/- (critical value) * (standard deviation / sqrt(sample size))
Given the sample data and the standard deviation, we can find the sample mean by taking the average of the incomes. The critical value can be found using a z-table or calculator. With a sample size of 10, the standard deviation is divided by sqrt(10). Plugging in the values, we get a 95% confidence interval of ($11627, $12460).
(1 point) Let pp be the quartic (degree 4) polynomial that satisfies p(i)=2i,i=0,1,2,3,4. p(i)=2i,i=0,1,2,3,4. Then p(x)=p(x)= . Hint: You may have a better idea, but a brute force approach is to write p(x)=ax4+bx3+cx2+dx+e p(x)=ax4+bx3+cx2+dx+e where aa, bb, cc, dd, and ee, are the unknown coefficients, and then solve the linear system p(0)=1p(0)=1, p(1)=2p(1)=2, p(2)=4p(2)=4, p(3)=8p(3)=8, and p(4)=16p(4)=16 for aa, bb, cc, dd, and ee. Preview My AnswersSubmit Answers
Answer:
a = 1/3
b = -3
c = 26/3
d = -6
e = 0
Step-by-step explanation:
Given the quartic polynomial
p(x)=ax⁴+bx³+cx²+dx+e and
p(i) =2i when i=0,1,2,3,4
If i = 0:
p(0) = 2(0)
p(0) = 0
0 = 0+0+0+0+0++e
e = 0
When i = 1
p(1) = 2(1) = 2
2 = a(1)⁴+b(1)³+c(1)²+d(1)+e
2 = a+b+c+d+0
a+b+c+d = 0... (1)
When i = 2, p(2) = 2(2)
p(2) = 4
4 = a(2)⁴+b(2)³+c(2)²+d(2)+e
4 = 16a+8b+4c+2d+0
16a+8b+4c+2d = 4
8a+4b+2c+d = 2... (2)
When i = 3
p(3) = 8
8 = a(3)⁴+b(3)³+c(3)²+d(3)+0
8 = 81a+27b+9c+3d..(3)
When i = 4
p(4) =16
16 = a(4)⁴+b(4)³+c(4)²+d(4)+0
16 = 256a+64b+16c+4d
64a+16b+4c+d = 4...(4)
Solving equation 1 to 4 simultaneously.
Check the attachment for solution.
The problem here is to determine the coefficients of a quartic polynomial to match the given conditions. This results in a system of linear equations which can be solved to find the desired coefficients.
Explanation:This question is a
polynomial problem
and involves finding the coefficients of a
quartic polynomial
, and for that we form a system of linear equations. Using the given conditions, we get the following equations:
For p(0), we get e = 2*0 = 0 For p(1), we get a + b + c + d + e = 2 For p(2), we get 16a + 8b + 4c + 2d + e = 4 For p(3), we get 81a + 27b + 9c + 3d + e = 6 For p(4), we get 256a + 64b + 16c + 4d + e = 8By solving the above system of equations, we can find the values of a, b, c, d and e that satisfy those equations simultaneously.
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what two numbers have the sum of 2 and product of -48
Answer:
-6 and +8
Step-by-step explanation:
Hi there,
The best way to think about these is the fact that the sum is very small, but the product is big. So, these numbers must:
1. have a large absolute difference, since their sum is so small
2. the numbers are relatively close to each other in magnitude. Otherwise, you wouldn't get such a big product.
-6 * 8 = -48
-6 + 8 = +2
This makes sense, because they have a large absolute difference of 14 (8+6). Also, as absolute value +6 and +8 are pretty close to each other.
Keep practicing and have fun.
A very joyous band of cows reproduces at a rate of 30% per year. Curiously, however, 20% of the cow population per year spontaneously turn into rhinoceroses. The rhinoceroses also reproduce at 30% per year. 20% of the rhinoceroses per year run off to join the circus. Aliens with bad aim beam up 6 rhinoceroses per year. (a) Write down a system C and R, reflecting the facts above. Note the system is non-homogeneous. (b) Find and classify the equilibrium of the system.
Answer:
See explaination
Step-by-step explanation:
Kindly check attachment for the step by step solution of the given problem.
Given the following 3 vertices, F(-5,1), A(-2,5), C(6,-1), find the fourth vertex, E, to make the figure a rectangle. Prove that FACE is a rectangle.
Answer:
E(3, -5)
Step-by-step explanation:
In a rectangle, the diagonals are the same length and bisect each other. That means their midpoints are the same. Then ...
(F +C)/2 = (A +E)/2
E = F +C -A
E = (-5, 1) +(6, -1) -(-2, 5) = (-5+6+2, 1-1-5)
E = (3, -5) . . . . . . . E is chosen so that the midpoint of AE is that of FC
__
To prove the figure is a rectangle, we can show the lengths of the diagonals are the same. Using the distance formula, ...
FC = √((6-(-5))^2 +(-1-1)^2) = √(11^2 +2^2) = √125
AE = √((3-(-2))^2 +(-5-5)^2) = √(5^2 +10^2) = √125
The diagonals are the same length and have the same midpoint, so the figure is a rectangle.
Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets. From past experience, she knows that the number of people who will attend is a linear function of the price per ticket. If she charges 5 dollars, 1160 people will attend. If she charges 7 dollars, 930 people will attend. How much should she charge per ticket to make the most money
Answer:
$7.54
Step-by-step explanation:
Using the two-point form of the equation of a line, we can write the equation for the number tickets (t) as a function of price (p).
t = (t2 -t1)/(p2 -p1)(p -p1) +t1
t = (930 -1160)/(7 -5)(p -5) +1160
t = -230/2(p -5) +1160
t = -115p +1735 = -115(p -15 2/23)
The revenue from ticket sales will be the product of the price and the number of tickets sold:
r = pt = p(-115)(p -15 2/23)
This is the equation of a downward-opening parabola with zeros at p=0 and p=15 2/23. The vertex of the parabola (maximum revenue) will be found at a ticket price halfway between these values. The price for maximum revenue is ...
(0 +15 2/23)/2 = 7 25/46 ≈ 7.54
Rosalie should charge $7.54 per ticket to obtain the most revenue.
Jason is entering a weight
lifting contest. Currently, his
maximum bench press weight is
105 pounds. If he increases the
weight by 7 pounds each week,
What is the maximum weight
he be able to bench press
after 13 weeks?
Answer:
196
Step-by-step explanation:
7 x 13 = 91 + 105
How many 9s are there in 63?
.
Answer:
7
Step-by-step explanation:
63 ÷ 9 = 7
The bumper car ride at the state fair has 2 red cars, 4 green cars, an for the ride and is assigned a the probability that both events A and B occur. Express your answer your answer to the nearest tenth d 2 blue cars. Garth is first in line car at random. Patty is next in line and is randomly assigned a car. Find as a percent. If necessary, round
Event A: Garth will drive a red bumper car.
Event B: Patty will drive a red bumper car.
a. 6.3%
b. 25%
c. 96.4%
d. 3.6%.
Answer:
a) 3.6%
Step-by-step explanation:
The given question mixed up, below is the correct question:
The bumper car ride at the state fair has 2 red cars, 4 green cars, and 2 blue cars. Garth is first in line for the ride and is assigned a car at random. Patty is next in line and is randomly assigned a car. Find the probability that both events A and B occur. Express your answer as a percent. If necessary, round your answer to the nearest tenth.
Calculation:
Given that the state fair has 2 red cars, 4 green cars and 2 blue cars.
There are therefore 2+4+2 = 8 cars in total.
Probability that Events A occurs P(A) = [tex]\frac{2}{8}[/tex] = 4
Probability that Events B occurs P(B) = [tex]\frac{1}{7}[/tex]
Probability that Events A and B occur P(A ∩ B) = [tex]\frac{2}{8}[/tex] × [tex]\frac{1}{7}[/tex] = [tex]\frac{2}{56}[/tex] = 0.0357 = 3.57% ≈ 3.6%
Therefore, the probability that both events A and B occur is 3.6%
Final answer:
The probability that both Garth and Patty will drive a red bumper car is found by multiplying the probability of Garth picking a red car (1/4) by the probability of Patty picking a red car after Garth (1/7), resulting in 1/28 or approximately 3.6%.
Explanation:
To solve the problem, we need to calculate the probability that both events A and B happen, which involves Garth and Patty both getting a red bumper car. Initially, there are 2 red cars, 4 green cars, and 2 blue cars, totaling 8 cars.
Event A: Garth picks a red car. The probability of this happening is the number of red cars over the total number of cars. So P(A) = 2/8 = 1/4.
After Garth picks a red car, there is 1 red car, 4 green cars, and 2 blue cars left, totaling 7 cars.
Event B: Patty picks a red car after Garth has already picked one. The probability of this happening is the number of remaining red cars over the total number of remaining cars. So P(B after A) = 1/7.
The probability that both A and B occur is the product of the probability of A and the probability of B given A has occurred. So P(A and B) = P(A) × P(B after A) = (1/4) × (1/7).
P(A and B) = 1/28. To express this as a percent, we multiply by 100%: (1/28) × 100% ≈ 3.6%.
Therefore, the probability that both Garth and Patty will drive a red bumper car is approximately 3.6%, which corresponds to option d.
A bag contains eight yellow marbles nine Green marbles three purple marbles five red marbles to marbles are chosen from the bag what expression would give the probability that one marble is yellow and others read the expression that would best represent the solution
Answer:
P(Y and R) = P(Y)*P(R) + P(R)*P(Y)
P(Y and R) = 16/125 = 0.128 = 12.8%
Step-by-step explanation:
There are 8 Yellow marbles in the bag
There are 9 Green marbles in the bag
There are 3 Purple marbles in the bag
There are 5 Red marbles in the bag
The total number of marbles in the bag are
Total marbles = 8 + 9 + 3 + 5 = 25
We want to find the probability of selecting two marbles that is one Yellow marble and one Red marble from the bag.
The probability of selecting a Yellow marble is given by
P(Y) = number of Yellow marbles/total number of marbles
P(Y) = 8/25
The probability of selecting a Red marble is given by
P(Y) = number of Red marbles/total number of marbles
P(Y) = 5/25
P(Y) = 1/5
It is possible that the first marble selected is Yellow and the second is Red, and it is also possible that first marble selected is Red and the second is Yellow.
P(Y and R) = P(Y)*P(R) + P(R)*P(Y)
P(Y and R) = (8/25)*(1/5) + (1/5)*(8/25)
P(Y and R) = 16/125
P(Y and R) = 0.128
P(Y and R) = 12.8%
Answer:
probability of selecting one yellow and one red = 2/15
Step-by-step explanation:
We are told there are;
8 yellow marbles
9 green marbles
3 purple Marbles
5 red Marbles
Since two Marbles are selected,
Number of ways of selecting one yellow and one red is:
C(8,1) x C(5,1) = 8!/(1!(8 - 1)!) x 5!/(1!(5 - 1)!)
This gives 40
Now, the total number of Marbles in the question will be;
8 + 9 + 3 + 5 = 25 Marbles
Thus, number of ways to select any two Marbles from the total is;
C(25,2) = 25!/(2!(25 - 2)!) = 300
Thus; probability of selecting one yellow and one red = 40/300 = 2/15
Let X denote the voltage at the output of a microphone, and suppose that X has a uniform distribution on the interval from −1 to 1. The voltage is processed by a "hard limiter" with cutoff values −0.5 and 0.5, so the limiter output is a random variable Y related to X by Y = X if |X| ≤ 0.5, Y = 0.5 if X > 0.5, and Y = −0.5 if X < −0.5.
Answer:
Step-by-step explanation:
Please kindly go through the attached file for a step by step approach to the question.
The question discusses a scenario where the voltage output of a microphone, denoted by X, has a uniform distribution from -1 to 1. A hard limiter is applied which limits the output of X (denoted as Y) between -0.5 and 0.5, regardless of X's value.
Explanation:We have been given that X is a uniform distribution from -1 to 1. This essentially means that each value between -1 and 1 has an equal probability of occurring. A 'hard limiter' is applied with cutoff values of -0.5 and 0.5. Hence, the output Y is related to X as follows:
Y = X if |X| ≤ 0.5Y = 0.5 if X > 0.5Y = -0.5 if X < -0.5
This indicates that any voltage output greater than 0.5 or less than -0.5 will be limited, leading Y to fluctuate only between -0.5 and 0.5, irrespective of the value of X. Thus, the 'hard limiter' acts as a sort of boundary for the voltage output.
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