Answer:
i. The amount made in interest is $65,000.
ii. Yes, because her expenses is lesser that her interest.
Step-by-step explanation:
i. The woman puts $1,000,000 in a savings account with an interest rate of 6[tex]\frac{1}{2}[/tex]%.
Interest rate = 6[tex]\frac{1}{2}[/tex]% = [tex]\frac{13}{200}[/tex]
The amount she would make in interest = [tex]\frac{13}{200}[/tex] × 1,000,000
= 65,000
The amount made in interest is $65,000.
ii. The total of her expenses last year is $47,0000 which is lesser than the amount made in inerest.
After her total expenses, should would have a remainder of;
= $65,000 - $47,0000
= $18,000
Therefore, she would be able to live off the interest.
1. Prove that quadrilateral DOGS is
a parallelogram. The coordinates
of DOGS are D(1, 1), (2, 4),
G(5, 6), and S(4,3).
-108
-6
-4
4
6
8
10
S doo
Page
1
1
2
-
+
Answer:
DOGS is a parallelogram.
Step-by-step explanation:
Given the quadrilateral DOGS with coordinates D(1, 1), O(2, 4), G(5, 6), and S(4,3).
To prove that it is a parallelogram, we need to show that the opposite lengths are equal. That is:
|DO|=|GS||OG|=|SD|Using the Distance Formula
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For D(1, 1) and O(2, 4)
[tex]|DO|=\sqrt{(2-1)^2+(4-1)^2}=\sqrt{1^2+3^2}=\sqrt{10} \:Units[/tex]
For G(5, 6), and S(4,3).
[tex]|GS|=\sqrt{(4-5)^2+(3-6)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{10}\:Units[/tex]
For O(2, 4) and G(5, 6)
[tex]|OG|=\sqrt{(5-2)^2+(6-4)^2}=\sqrt{(3)^2+(2)^2}=\sqrt{13}\:Units[/tex]
For S(4,3) and D(1, 1)
[tex]|SD|=\sqrt{(1-4)^2+(1-3)^2}=\sqrt{(-3)^2+(-2)^2}=\sqrt{13}\:Units[/tex]
Since:
|DO|=|GS||OG|=|SD|Then, quadrilateral DOGS is a parallelogram.
How many elements are in an m x n matrix?
Answer:
D. mn
Step-by-step explanation:
The amount of elements that are in an m x n matrix is mn.
An m x n matrix has m*n elements since the elements are the product of the number of rows (m) and the number of columns (n).
Explanation:An m x n matrix is a rectangular grid containing elements that are arranged in m rows and n columns.
So, the elements in a matrix are represented by the multiplication of the number of rows (m) and the number of columns (n). If, for instance, you have a matrix that is 3 x 4, this matrix contains 3 (rows) multiplied by 4 (columns) which equals to 12 elements total in the matrix.
Learn more about matrix here:https://brainly.com/question/33840317
#SPJ3
mariam measured the distance for 8 wavelengths of visible light as 5,600 nanometers. what is the distance for 1 wavelength
Answer:
700 nanometers
Step-by-step explanation:
8 wavelengths had a combined length of 5,600 nanometers.
We want to find the wavelength (in nm) of 1 of those wavelengths.
We will assume all of them are same wavelength. So, we can basically divide the total of 8 wavelengths by 8 to get 1 wavelength. Thus:
5600/8 = 700
Hence,
1 wavelength distance is 700 nanometers (or 700 nm)
Which expressions are equivalent to the one below? Check all that apply. log 2-log 6 A.log(2)+log(1/6) B.log 2 C.log 3 D.log(1/3)
The equivalent expression to log(2) - log(6) is D. log(1/3), since subtraction in logarithms indicates division, making the expression log(2/6) which simplifies to log(1/3).
Explanation:The question asks which expressions are equivalent to log(2) - log(6). According to the properties of logarithms, the logarithm of a number resulting from the division of two numbers is the difference between the logarithms of the two numbers (log a - log b = log(a/b)). Therefore, log(2) - log(6) = log(2/6) = log(1/3).
Hence, the only equivalent expression from the given options is D. log(1/3). Option A is incorrect because log(2) + log(1/6) would imply multiplication, not division. Option B is just log(2) without subtraction. Option C, log(3), does not represent the given difference.
Which question is a statistical question?
A. How many theaters are there in my city
B. How many students in my class like classical movies
C. How many movies do the students in my class watch in a month
D. How many students in my class watch movies on weekdays
Answer:
C. How many movies do the students in my class watch in a month
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Carpetland salespersons average $8000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson.
a. Develop the appropriate null and alternative hypotheses.b. In this situation, a Type I error would occur if it was concluded that the new compensation plan provides a population mean weekly sales greaterthan 8000 (correct) when in fact it does not.
c. In this situation, a Type II error would occur if it was concluded that the new compensation plan provides a
Answer:
Step-by-step explanation:
a) The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.
The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.
From the given situation,
Carpetland salespersons average $8000 per week in sales. This is the null hypothesis.
H0: µ = 8000
Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson. This is the alternative hypothesis.
Ha: µ > 8000
b) A type I error occurs when a true null hypothesis is rejected.
In this situation, a Type I error would occur if it was concluded that the new compensation plan provides a population mean weekly sales greater than 8000 (correct) when in fact it does not.
c) a Type II error would occur if it was concluded that the new compensation plan does not provide a population mean weekly sales greater than 8000 when in fact, it does.
To test Carpetland's new compensation plan, the null hypothesis is that weekly sales per salesperson is $8000, and the alternative is that it's greater than $8000. A Type I error means falsely concluding the new plan increases sales, while a Type II error refers to failing to detect an actual increase in sales.
In the case of Carpetland's new compensation plan, the appropriate null hypothesis (H0) and alternative hypothesis (H1) would be:
H0: The population mean weekly sales per salesperson is $8000. (μ = $8000)
H1: The population mean weekly sales per salesperson is greater than $8000. (μ > $8000)
A Type I error would occur if we reject the null hypothesis when it is actually true, meaning we conclude that the new compensation plan increases average sales when in reality, it does not. A Type II error would occur if we fail to reject the null hypothesis when the alternative hypothesis is true, meaning we conclude that the new compensation plan does not increase average sales when in fact, it does.
It is crucial to design a study properly to reduce the chances of these errors, weighing the consequences that each type of error may have on the business decisions.
Help fast it’s geometry
Answer:
a-area-22
a-perimeter-19
b-area-98
b-perimeter-42
Step-by-step explanation:
for the sides just add the numbers 2x
for the area multiply the numbers
hope this helps
The Reds and the Cubs are playing 3 games. In each game the probability that the Reds win is 0.54. The probability of the Reds winning is not affected by who has won any previous games.
(a) What is the expected value for the number of games the Reds will win? (Give your answer correct to two decimal places.) _______
(b) What is the expected value for the number of games the Cubs will win? (Give your answer correct to two decimal places.) _______
Answer:
(a) 1.6197
(b) 1.3803
Step-by-step explanation:
(a) Let X denote the number of games the Reds win. If Reds win exactly one it means that in the other two games Reds lost i.e Cubs won. Now, the probability of the Reds losing is determined by [tex] 1 -\text{probability of winning} = 1-0.54 = 0.46 [/tex]. So, if X wins exactly [tex]i[/tex] times, then we should multiply the probabilities associated with
[tex]P(X=0) = \binom{3}{0} \times 0.46 \times 0.46 \times 0.46 = 0.0973[/tex]
[tex] P(X=1) = \binom{3}{1} 0.54 \times 0.46 \times 0.46 = 0.3429[/tex]
[tex] P(X=2) = \binom{3}{2} 0.54 \times 0.54 \times 0.46 = 0.4023[/tex]
[tex] P(X=3) = \binom{3}{3} 0.54 \times 0.54 \times 0.54 = 0.1574[/tex]
Now,
[tex] E(X) = \sum_{i=0}^{3} i \times P(X=i) = 1.6197[/tex]
(b) Let Y denote the number of games won by Cubs. Then by the similar logic as above,
[tex] P(Y=3) = \binom{3}{0} 0.46 \times 0.46 \times 0.46 = 0.0973[/tex]
[tex] P(Y=2) = \binom{3}{1} 0.54 \times 0.46 \times 0.46 = 0.3429[/tex]
[tex] P(Y=1) = \binom{3}{2} 0.54 \times 0.54 \times 0.46 = 0.4023[/tex]
[tex] P(Y=0) = \binom{3}{3} 0.54 \times 0.54 \times 0.54 = 0.1574[/tex]
Now
[tex] E(Y) = \sum_{j=0}^{3} j \times P(Y=j) = 1.3803[/tex]
Eight children were in a ballet class. Three of them were wearing a pink leotard. What fraction of them did not have a pink leotard on?
Answer:
5/8
Step-by-step explanation:
8 children in class
3 have pink on
8-3 = 5
That means 5 do not have pink
Fraction that do not have pink
those that do not have pink/total
5/8
A jar contains 6 marbles numbered 1 through 6. An experiment consists of randomly selecting a marble from the jar, observing the number drawn, and then randomly selecting a card from a standard deck and observing the suit of the card (hearts, diamonds, clubs, or spades).
How many outcomes are in the sample space for this experiment?
Answer:
24 Outcomes
Step-by-step explanation:
The sample space of an event is the set of all possible outcomes.
A jar contains 6 marbles numbered 1 through 6
Sample Space of Selecting a Marble from the Jar =6
A standard deck contains 4 Suits
Sample Space of Selecting a Card and Observing the Suit = 4
Theorem(The Fundamental Counting Principle)
If there are “x” ways for one event to happen, and “y” ways for a second event to happen, then there are “x * y” ways for both events to happen.
Therefore the Sample Space of randomly selecting a marble from the jar, observing the number drawn, and then randomly selecting a card from a standard deck and observing the suit of the card is given as:
Sample Space of Selecting a Marble X Sample Space of Selecting a Card and observing the Suits
= 6 X 4
=24
There are 24 Outcomes in this experiment.
given that a triangle LMN has side inches of 18.5 inches, 10, inches, and 15.5 inches, prove triangle LMN is aright triangle.
Answer:
LMN is not a right triangle.
Step-by-step explanation:
To verify that the lengths of a triangle for a right triangle, all we need to do is to check it they satisfy the Pythagoras Theorem.
Pythagoras Theorem:[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]
The Hypotenuse is always the longest side.
Since no angle is given, the two other sides can be alternated.
Given lengths of triangle LMN: 18.5 inches, 10, inches, and 15.5 inches
[tex]LHS=18.5^2=342.25\\RHS=10^2+15.5^2=100+240.25=340.25\\Since \: LHS\neq RHS,\\$The triangle is not a right triangle.[/tex]
A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1000 bacteria present after 20 minutes. Write the exponential equation representing this scenario modeled as a continuous growth model.
The exponential equation that represents the growth of the bacteria over time, considering the given initial and future population sizes and the time that has passed, is P(t) = 360 × e^[(ln(1000/360)/15)t]. This formula adjusts the rate of growth to match the change from 360 bacteria to 1000 bacteria over a 15-minute period.
Explanation:In this situation, we are dealing with a phenomenon commonly seen in biology called exponential growth which can be modeled mathematically. For this case, we can use the exponential growth formula, P(t) = P_0 × e^(rt), where P(t) is the future population size, P_0 is the initial population size, r is the growth rate, and t is the time that has passed.
Firstly, we know the initial population size (P_0) is 360 bacteria. The population size after 15 minutes (from 5 minutes to 20 minutes is 15 minutes) is 1000 bacteria. Therefore, if we plug in these values, we have 1000 = 360 × e^(15r).
To solve for r, we start by dividing both sides by 360 which results in 1000/360 = e^(15r). Taking the natural logarithm (ln) of both sides to isolate the exponential part, we get ln(1000/360) = 15r. Finally, divide by 15 yielding r = ln(1000/360)/15.
Therefore, the exponential equation representing this scenario is P(t) = 360 × e^[(ln(1000/360)/15)t], showing the population P(t) of the bacteria at any time t.
Learn more about Exponential Growth Model here:https://brainly.com/question/33502063
#SPJ11
The number of miles y in a measure varies directly as the number of kilometers x. Write a direct variation equation that can be used to convert kilometers to miles, if 5 kilometers is about 3.1075 miles.
Answer:
[tex]y = 0.6215x[/tex]
Step-by-step explanation:
I am going to model an equation in the following format:
[tex]y = ax[/tex]
In which y is the number of miles, given the distance in kilometers x.
a is the slope, that is, how many miles each kilometer has.
5 kilometers is about 3.1075 miles.
So
5 km - 3.1075 miles
1 km - a miles
5a = 3.1075
a = 3.1075/5
a = 0.6215
So
[tex]y = 0.6215x[/tex]
According to the Mortgage Bankers Association, 8% of U.S. mortgages were delinquent in 2011. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of eight mortgages was selected. What is the probability that exactly one of these mortgages is delinquent?
Answer:
The probability that exactly one of these mortgages is delinquent is 0.357.
Step-by-step explanation:
We are given that according to the Mortgage Bankers Association, 8% of U.S. mortgages were delinquent in 2011. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure.
A random sample of eight mortgages was selected.
The above situation can be represented through Binomial distribution;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 8 mortgages
r = number of success = exactly one
p = probability of success which in our question is % of U.S.
mortgages those were delinquent in 2011, i.e; 8%
LET X = Number of U.S. mortgages those were delinquent in 2011
So, it means X ~ [tex]Binom(n=8, p=0.08)[/tex]
Now, Probability that exactly one of these mortgages is delinquent is given by = P(X = 1)
P(X = 1) = [tex]\binom{8}{1}\times 0.08^{1} \times (1-0.08)^{8-1}[/tex]
= [tex]8 \times 0.08 \times 0.92^{7}[/tex]
= 0.357
Hence, the probability that exactly one of these mortgages is delinquent is 0.357.
Find the sum of the first 10 terms.
8,20,32,44...
Answer:
8,20,32,44,56,68,80,92,104,116,128
Step-by-step explanation
Just keep adding 12
Answer: 620
Step-by-step explanation:
This is a progression but we need to find out whether it is Arithmetic Progression or an exponential or geometric progression.
From the quest, 8, 20, 32, 44, this is not an exponential function but an arithmetic progression because, when you subtract the first time from the second term , the common difference is 12.
20 - 8 = 12, so this is an arithmetic progression as said earlier. Now to find the sum of the first ten terms of the series, we apply the formula which is
S10 = n/2{(2a + ( n - 1 )d}, where n = 10, and a = 8 the first term and d the common difference = 12.. Now substitute for the values
S10 = 10/2{(2 x 8 + ( 10 - 1 )12}
= 5( 16 + 9 x 12)
= 5( 16 + 108 )
= 5( 124 )
= 620.
Therefore, the sum of the 10 terms of the series is 620.
But we can also solve it using other means . To solve this we first find the last term which is the 10th term using this formula
T10 = a + ( n - 1 )d
= 8 + (10 -1)12
= 8 + 9 x 12
= 8 + 108
= 116.
Now with this we could put this in the equation below.
S10 = n/2( a + L ) where L is the last term calculated above. Now we substitute to get the sum.
S10 = 10/2( 8 + 116)
= 5( 8 + 116 )
= 5( 124)
= 620.
I could have explained how we arrived at the formula above but the time could not permit, I will discuss that in the next lecture if I come across such question.
Whats the answer of (X+9)^2=25?
Answer:
x=-4,x= -14
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x2+18x+81=25
Step 2: Subtract 25 from both sides.
x2+18x+81−25=25−25
x2+18x+56=0
Step 3: Factor left side of equation.
(x+4)(x+14)=0
Step 4: Set factors equal to 0.
x+4=0 or x+14=0
x=−4 or x=−14
========================================================
Explanation:
Apply the square root to both sides
(x+9)^2 = 25 leads to x+9 = 5 or x+9 = -5
This is because (-5)^2 = 25 and (5)^2 = 25. This is the plus/minus you often see with quadratics.
Solve x+9 = 5 to get x = -4. We subtract 9 from both sides to get this.
Solve x+9 = -5 to get x = -14
That's why the two answers are x = -4 and x = -14.
------
To check our answers, we plug those x values into the original equation and simplify. We should get the same thing on both sides
(x+9)^2 = 25
(-4+9)^2 = 25 ... replace x with -4
(5)^2 = 25
25 = 25 ... So x = -4 has been confirmed
and,
(x+9)^2 = 25
(-14+9)^2 = 25 ... replace x with -14
(-5)^2 = 25
25 = 25 ... and x = -14 has been confirmed
Eitan sells a mean of $8000 worth of merchandise with a standard deviation of $1500 each month.
Each month, Eitan earns a base salary of $2000 plus a commission of 30% of his sales. He calculates his total
salary according to this formula:
[total salary) = commission + base salary]
What will be the mean and standard deviation of the distribution of Eitan's total monthly salary?
Answer:
t = $4400 +/- $450
mean = $4400
standard deviation = $450
Step-by-step explanation:
Given;
Base salary b = $2000
Sales s = $8000 +/- $1500
Commission c = 30% sales = 0.3 × s
Total Salary t = base salary + commission = b + c
Commission c = 0.3×s = 0.3×($8000 +/-$1500)
c = $2400 +/- $450
Total salary t = b + c
Substituting the values;
t = $2000 + ($2400 +/- $450)
t = $4400 +/- $450
mean = $4400
standard deviation = $450
In one region of the Caribbean Sea, daily water temperatures are normally distributed with a mean of 77.9 degrees Fahrenheit and a standard deviation of 2.4 degrees Fahrenheit. What temperature separates the lowest 59.5% of temperatures from the rest?
Answer:
The temperature that separates the lowest 59.5% of temperatures from the rest is 83.66 degrees Fahrenheit.
Step-by-step explanation:
Mean temperature = u = 77.9
Standard Deviation = [tex]\sigma[/tex] = 2.4
Since the distribution is normal and we have the value of population standard deviation, we will use the concept of z-score to find the desired value.
We have to find the value that separates lowest 59.5% of the temperature from the rest. This means our desired value is above 59.5% of the data values.
From the z-table we can find a z-score which is above 59.5% of the values and then convert it to its equivalent temperature using the formula.
From the z-table, the z-score which is above 59.5% of the value is:
z = 0.24
The formula for z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the values we have:
[tex]0.24=\frac{x-77.9}{2.4}\\\\ 5.76=x-77.9\\\\ x=83.66[/tex]
This is our data value equivalent to a z-score of 0.24. Just like 59.5% of z values were below 0.24, in the same manner, 59.5% of temperatures are below 83.66 degrees Fahrenheit.
Therefore, the temperature that separates the lowest 59.5% of temperatures from the rest is 83.66 degrees Fahrenheit.
The ABX Company is interested in conducting a study of the factors that affect absenteeism among its≈α= 0.05
production employees. Data on 77 employees of the ABX Company have been collected. These data areavailable in the worksheet entitled "ABSENT7R". The variable ABSENT is the number of distinct occasionsthat the worker was absent during 2003. (Each occasion consists of one or more consecutive days ofabsence.) The following possible explanatory variables are:In this exercise, use which is the reciprocal of the seniority variable, and COMPLXas two of the explanatory variables. The variable SATIS should be transformed into indicator variables asfollows:HOWEVER, recall that five indicator variables couldbe created to represent all five supervisorsatisfaction categories, but only four need to be used in the regression.Therefore, fit thisregression model for absenteeism:ABSENT = β0+ β1COMPLX + β2SENINV + β3FS1 + β4FS2 + β5FS3 + β6FS4Run the regression with the explanatory variables described here. Answer the following questions.(a) Is there a difference in average absenteeism for employees in different supervisorsatisfaction groups? Perform a hypothesis test to answer this question. Use a 5% level ofsignificance. State the hypotheses to be tested
Answer:
import pandas as pd
import import statsmodels.api as sm
dataframe = pd.read_csv(Your model)
mod = sm.OLS(formula = ABSENT ~ COMPLX + SENING+FS1+FS2+FS3+FS4)
res = mod.fit()
print(res.summary())
Step-by-step explanation:
Using python you can load the dataframe using pandas library. Once you have your pandas library imported to the system you can also import the statsmodels.api module. What you do is this. You fit the model using the variables mentioned "COMPLX" ,"SENINV","FS1","FS2","FS3", once you fit the model you use .summary() and that will give you a summary of each coefficient and the level of significance, the level of significance must be less than 5% in order to be significant. The code would look like this.
import pandas as pd
import import statsmodels.api as sm
dataframe = pd.read_csv(Your model)
mod = sm.OLS(formula = ABSENT ~ COMPLX + SENING+FS1+FS2+FS3+FS4)
res = mod.fit()
print(res.summary())
The question involves performing a regression analysis on absenteeism data from the ABX Company, with a particular focus on the variable of supervisor satisfaction. Hypotheses are formulated to test if there is a significant difference in absenteeism among different supervisor satisfaction groups. The result of the F-test in the regression analysis will provide the answer.
Explanation:The problem involves the analysis of absenteeism data collected from the employees of the ABX Company with the goal of determining the effects of various variables on absenteeism. These variables include supervisor satisfaction (SATIS), which is transformed into indicator variables (FS1, FS2, FS3, FS4), as well as the reciprocal of the seniority variable (SENINV), and COMPLX.
The regression equation to be fitted is: ABSENT = β0 + β1COMPLX + β2SENINV + β3FS1 + β4FS2 + β5FS3 + β6FS4.
To test the hypothesis that there is a difference in average absenteeism for employees in different supervisor satisfaction groups, the null and alternative hypotheses are defined as follows:
H0: There is no difference in average absenteeism among different supervisor satisfaction groups (β3 = β4 = β5 = β6 = 0). H1: There is a difference in average absenteeism among different supervisor satisfaction groups (at least one βi ≠ 0).
These hypotheses are tested using the F-test in the regression analysis. The F-statistic will tell you if the variations in the SATIS groups are significantly different. If the p-value associated with this F-statistic is less than your significance level (0.05 in this case), you would reject the null hypothesis and conclude that there is a difference in average absenteeism among the different satisfaction groups.
Learn more about Regression Analysis here:https://brainly.com/question/32707297
#SPJ11
Lo que tú y yo ganamos suman $400. Si tu ganaras $80 más y yo $80
menos, tendríamos la misma cantidad de dinero. ¿Cuánto tenemos cada
uno?
Answer:
$280 y $120
Step-by-step explanation:
Primero haces una ecuación. Entonces puedes adivinar y verificar o usar la ecuación. Solía adivinar y comprobar.
¡Espero que esto haya ayudado!
The exercise involving data in this and subsequent sections were designed to be solved using Excel.
The following estimated regression equation was developed for a model involving two independent variables.
y=40.7+ 8.63x1+ 2.71x2
After x2 was dropped from the model, the least-squares method was used to obtain an estimated regression equation involving only x1 as an independent variable. y=42.0+9.01x1
a. In the two independent variable cases, the coefficient x1 represents the expected change in (Select your answer: y, x1, x2) corresponding to a one-unit increase in (Select your answer: y, x1, x2) when (Select your answer: y, x1, x2) is held constant.
In the single independent variable case, the coefficient x1 represents the expected change in (Select your answer: y, x1, x2) corresponding to a one-unit increase in (Select your answer: y, x1, x2).
b. Could multicollinearity explain why the coefficient of x1 differs in the two models? Assume that x1 and x2 are correlated.
Answer:
Step-by-step explanation:
Hello!
You have two regression models:
The multiple regression model that was estimated is y=40.7+ 8.63x1+ 2.71x2
The Simple regression model that was estimated is y=42.0+9.01x1
a.
MRmodel the 8.63 represents the modification in the estimated mean of Y when X₁ increases one unit and X₂ remains constant.
SRmodel the 9.01 represents the modification in the estimated average of Y when X₁ increases one unit.
b.
Yes, since both variables X₁ and X₂ are correlated, the effect that X₁ has over Y is directly affected by the precence of X₂
I hope you have a nice day!
Using polynomial regression fit a cubic equation to the following data: x 3 4 5 7 8 9 11 12 y 1.6 3.6 4.4 3.4 2.2 2.8 3.8 4.6 Plot the data and the cubic equation. Along with the coefficients, determine r2 and sy/x.
Final answer:
Fitting a polynomial regression model involves determining coefficients that minimize the sum of squared differences between observed and predicted values. After plotting the data, the cubic model is fitted using statistical software. The coefficients, r-squared, and standard error of the estimate are then calculated to assess the model's accuracy.
Explanation:
The process of fitting a polynomial regression model involves finding the coefficients that minimize the sum of the squares of the differences between the observed values and the values predicted by the model. For a cubic equation, we will be fitting a model in the form y = a + bx + cx2 + dx3, where a, b, c, and d are the coefficients that need to be determined from the data.
To fit a cubic equation to the data and assess the goodness-of-fit, we usually perform the following steps:
Scatter plot: Draw a scatter plot of the given data points to visualize the trend and the relationship between x and y.Polynomial regression: Use a statistical software or a calculator with polynomial regression capability to fit the cubic model to the data.Plot the cubic equation: Alongside the scatter plot, plot the regression curve represented by the cubic equation.Calculate the coefficients and r-squared (r2): Obtain the values of the coefficients and the coefficient of determination, which shows the proportion of the variance in the dependent variable explained by the regression model.Calculate standard error of the estimate (sy/x): Compute the standard error to get an idea of the typical distance between the actual data points and the estimated regression curve.The calculation of r2 (r-squared) is important because it tells us the strength of the relationship between the independent and dependent variables. An r2 value of 0.72, for instance, would indicate that 72% of the variability in the dependent variable can be explained by the model. The r2 value cannot be negative because it represents the proportion of variance explained, which is inherently non-negative.
Coefficient of determination is the square of the correlation coefficient (r), and since the correlation coefficient ranges between -1 and +1, its square will always be non-negative as well.
The area of a figure is 13 square inches. If all the dimensions of the figure are multiplied by 4, the area of the figure will be multiplied by _____. 2 4 8 16
Answer:
option D.
Step-by-step explanation:
Given,
Area of a figure = 13 in²
All dimension is multiplied by 4.
Area of the figure will be multiplied by = ?
We know that,
[tex]Area\ \alpha \ (Length)^2[/tex]
If length is multiplied by 4.
[tex]Area\ \alpha \ 4^2 (L)^2[/tex]
Where L is the dimension of the figure.
[tex]Area\ \alpha \ 16 (L)^2[/tex]
Area of the figure will be multiplied by 16.
Hence, correct answer is option D.
Morgan throws a ball up into the air. The height of the ball above the ground, in feet, is modeled by the function h(t)=-16t+24t, where t represents the time, in seconds, since the ball was thrown. What is the appropriate domain for this situation?
The appropriate domain for this situation is all non-negative real numbers or the interval [0, ∞).
Explanation:The appropriate domain for this situation can be determined by considering the values that the independent variable, t, can take in the given function. In this case, the function is h(t) = -16t^2 + 24t, where t represents the time since the ball was thrown.
Since time cannot be negative in this context, the domain of the function is t ≥ 0. This means that the appropriate domain for this situation is all non-negative real numbers or the interval [0, ∞).
Suppose that the random variable X represents the amount of electrical energy used (in kwH) in a month for residents in Virginia. The historical amount of electrical energy used in a month for residents is 102 kwH. The following data (in kwH per month) were recorded from a random sample of 8 residents: 111 113 145 105 90 100 150 88(a) Calculate the mean and sample variance of X. (b) What is t statistic with this problem?
Answer:
a)[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]\bar X = 112.75[/tex]
[tex]s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]
[tex] s^2 = 540.5[/tex]
b) [tex] t = \frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}[/tex]
And if we replace we got:
[tex] t = \frac{112.75-112}{\frac{23.249}{\sqrt{8}}}= 0.0912[/tex]
Step-by-step explanation:
Part a
For this case we have the following data: 111 113 145 105 90 100 150 88
We can calculate the mean with the following formula:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X = 112.75[/tex]
And the sample variance can be calculated with this formula:
[tex]s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]
And replacing we got:
[tex] s^2 = 540.5[/tex]
Part b
For this case we want to check is the true mean is equal to 102 or no, the t statistic is given by:
[tex] t = \frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}[/tex]
And if we replace we got:
[tex] t = \frac{112.75-112}{\frac{23.249}{\sqrt{8}}}= 0.0912[/tex]
To answer the student's question, the sample mean of electrical energy usage is calculated to be 112.75 kwH. The sample variance requires computing the squared differences of each data point from the mean, summing them up and dividing by n-1. The t-statistic can then be calculated using the historical mean, the sample mean, and the sample standard deviation.
Explanation:To calculate the mean of the sample data, we sum all the sample values and divide by the number of observations. The sample data for electrical energy usage in kwH per month are: 111, 113, 145, 105, 90, 100, 150, and 88. The sum of these values is 902 kwH, and with 8 residents in the sample, the mean (μ) is 902 kwH / 8 = 112.75 kwH.
The sample variance (s²) is calculated by taking the sum of squared differences from the mean and dividing by the sample size minus one. First, we find the squared differences for each data point: (111-112.75)², (113-112.75)², (145-112.75)², (105-112.75)², (90-112.75)², (100-112.75)², (150-112.75)², and (88-112.75)², which then summed up give us the total sum of squares. Dividing this total by 7 (n-1), we obtain the sample variance.
For the t statistic, we would need the hypothesized population mean to compare our sample mean against. However, we can calculate the t-value if we assume the historical mean provided (102 kwH) is the population mean we are testing against. The t-statistic is calculated using the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(n)). In this scenario, n=8 and we would need the sample standard deviation, which is the square root of the variance we calculated earlier. Once these values are obtained, the t-statistic can be computed.
What is the volume of this rectangular prism? The length is 5 1/2. The width is 1 3/8. The height is 1 2/3.
Answer:
12 29 /48 in mixed number form,
≈ 12.6 as a rounded decimal
Step-by-step explanation:
Multiply all three numbers together for the volume.
Complete the table for the given rule. Rule: y=3x
x y
? 15
10 ?
? 45
Answer:
x = 5, 15 y = 30
Step-by-step explanation:
y=3x is the rule, thus you can use it to find all values.
15 = 3x Divide 15 by 3 in order to isolate the variable
5 = x
y = 3(10) Multiply 3 by 10 in order to find y
y = 30
45 = 3x Divide 45 by 3 in order to isolate the variable
15 = x
Jose rides his bicycle for 5 minutes to travel 8 blocks .He rides for 10 minutes to travel 16 blocks
Answer:
Step-by-step explanation:
A: 8
B: 15
C: 40
(A) The rides in 5 minutes are 8, (B) the time to cover 24 blocks is 15 minutes, and (C) in 25 minutes Jose rides 40 blocks.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Jose rides his bicycle for 5 minutes to travel 8 blocks
Speed = distance cover / time taken
Speed = 8/5
Now, at the same speed
A) Distance covered in 5 minutes
8/5 = Distance/5 ⇒ Distance = 8 blocks.
B) Time taken in 24 blocks
8/5 = 24/Time ⇒ Time = 15 minutes.
C) Distance covered in 25 minutes
8/5 = Distance/25 ⇒ Distance = 40 blocks.
Hence "The rides in 5 minutes are 8, the time to cover 24 blocks is 15 minutes and in 25 minutes Jose rides 40 blocks".
Options are missing in the given question
Correct options are in the table and ask the same question as answered.
For more information about ratio and proportion,
brainly.com/question/26974513
#SPJ2
What is 5 4/9 take away 1 7/9
Answer:
4 13/9 - 1 7/9
3 6/9
3 2/3
Step-by-step explanation:
The answer would be 3.6 because I simplified my answer into decimal. Hope this helps! If you have any other questions, please ask me. Stay safe! And have a good day!
Earlier, we considered data from the GSS on numbers of close friends people reported having. The mean for this variable is 7.44, with a standard deviation of 10.98. Let's say that you decide to use the GSS data to test whether people who live in rural areas have a different mean number of friends than does the overall GSS sample. Again, treat the overall GSS sample as the entire population of interest. Let's say that you select 40 people living in rural areas and find that they have an average of 3.9 friends. What is the z statistic for this sample
Answer:
The z statistic for this sample is -2.04.
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 7.44[/tex]
The alternate hypotesis is:
[tex]H_{1} \neq 7.44[/tex]
The z-statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the population mean(the hypothesis tested), [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
In this problem:
[tex]X = 3.9, \mu = 7.44, \sigma = 10.98, n = 40[/tex]. So
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.9 - 7.44}{\frac{10.98}{\sqrt{40}}}[/tex]
[tex]z = -2.04[/tex]
The z statistic for this sample is -2.04.