Answer:
False.Step-by-step explanation:
f(g(x)) = f of g of x
f(x) · g(x) = f at x times g at x, which is not the same thing.
what is the value of h in the equation 8h = 60
Answer:
h= 7.5
Step-by-step explanation:
8h=60
One solution was found :
h = 15/2 = 7.500
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
8*h-(60)=0
Step by step solution :
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
8h - 60 = 4 • (2h - 15)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 4 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : 2h-15 = 0
Add 15 to both sides of the equation :
2h = 15
Divide both sides of the equation by 2:
h = 15/2 = 7.500
One solution was found :
h = 15/2 = 7.500
Processing ends successfully
Answer: h = 7.5
Step-by-step explanation: To solve for h in this equation, we want to to get h by itself on the left side of the equation.
Since h is being multiplied by 8, to get h by itself, we need to divide by 8 on the left side of the equation.
If we divide by 8 on the left side,
we must also divide by 8 on the right side.
On the left, the 8's cancel out so we are simply left with h.
On the right we have 60/8 which is 7.5.
So we have h = 7.5.
who runs the fastest ? (ONLY ANSWER IF YOU KNOW IT BECAUSE CORRECT ONE GETS BRAINLIEST)
stephanie runs 14 feet per second
brooke runs 589 feet in 44 seconds
will runs 1 mile in 454 seconds
rob runs 548 feet in 1 minute
Answer:
Stephanie runs the fastest per second: 14 feet per second
Step-by-step explanation:
To find the fastest speed, you need to see which person runs the most per second:
Stephanie runs 14 feet per second
Brooke runs 589 feet in 44 seconds.
Find the amount of feet per second by dividing:
[tex]\frac{589}{44} =13.4[/tex]
Brooke runs about 13.4 feet per second
Will runs 1 mile in 454 seconds.
Convert the miles to feet:
There are 5,280 feet in a mile. If Will runs 5,280 feet in 454 seconds, divide to find how much he runs per second:
[tex]\frac{5280}{454}= 11.6[/tex]
Will runs about 11.6 feet per second.
Rob runs 548 feet in a minute.
Convert the minute into seconds. There are 60 seconds in a minute. Divide the feet by the seconds to find how fast he runs per second:
[tex]\frac{548}{60}= 9.1[/tex]
Rob runs about 9.1 feet per second.
Stephanie runs 14 feet per second, the fastest time:
| 14 |, 13.4, 11.6, 9.1
Finito.
what is 1/6 more than 2/6
3/6 or 1/2
could please check out my questions? thx!
During a chemical reaction, the function y=f(t) models the amount of a substance present, in grams, at time t seconds. At the start of the reaction (t=0) , there are 10 grams of the substance present. The function y=f(t) satisfies the differential equation dydt=−0.02y^2
The solution of the differential equation is:
[tex]y = \frac{1}{-0.1 + 0.02*t}[/tex]
How to solve the differential equation?
Here we need to solve:
[tex]\frac{dy}{dt} = -0.02*y^2[/tex]
This is a separable differential equation, we can rewrite this as:
[tex]\frac{dy}{y^2} = -0.02dt[/tex]
Now we integrate in both sides to get:
[tex]\int\limits\frac{dy}{y^2} = \int\limits-0.02dt\\\\-\frac{1}{y} = -0.02*t + C[/tex]
Where C is a constant of integration.
Solving for y, we get:
[tex]y = \frac{1}{-C + 0.02*t}[/tex]
And we know that for t = 0, there are 10 grams of substance, then:
[tex]10 = \frac{1}{-C + 0.02*0} = -\frac{1}{C} \\\\C = -1/10 = -0.1[/tex]
So the equation is:
[tex]y = \frac{1}{-0.1 + 0.02*t}[/tex]
If you want to learn more about differential equations, you can read:
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An environmentalist would like to compare air pollution levels in cities A and B. From each city 10 measurements are taken. For city A, the average of all measurements (where measurements are percentage of pollutants in the air) is 5 percent with sample standard deviation 1.5 percent. For city B the average of all 10 measurements is 5.4 percent with sample standard deviation 2 percent. Assume that for each city air pollution level at a random time and location follows a normal distribution, and nd a 90% confidence interval for difference between the true average air pollution levels of city A and city B.
Answerhshxbx
Ste-by-step explanation:
Hwsjbb
Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of automobiles years old showed a sample standard deviation for annual repair costs of and a sample of automobiles years old showed a sample standard deviation for annual repair costs of . Let year old automobiles be represented by population . a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles. b. Conduct the hypothesis test at a level of significance. Calculate the value of the test statistic (to 2 decimals).
Answer:
Step-by-step explanation:
Hello!
The researcher's objective is to test if the variance of the annual repair costs increases with the age of the automobile, i.e. the older the car, the more the repairs costs. The parameters of the study are the population variances of the annual repair costs of 4 years old cars and 2 years old cars.
X₁: Costs of annual repair of a 4 years old car.
Assuming X₁~N(μ₁;δ₁²)
A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $170
n₁= 26 and S₁= $170
X₂: Costs of annual repair of a 2 years old car.
Assuming X₂~N(μ₂;σ₂²)
A sample of 25 automobiles 2 years old showed a sample standard deviation for the annual repair cost of $100.
n₂= 25 and S₂= $100
a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for older automobiles.
H₀: δ₁² ≤ σ₂²
H₁: δ₁² > σ₂²
b. At a .01 level of significance, what is your conclusion? What is the p-value? Discuss the reasonableness of your findings.
This is a variance ratio test and you have to use a Snedecor's F-statistic:
[tex]F= \frac{S^2_1}{S_2^2} * \frac{Sigma_1^2}{Sigma_2^2}~~F_{n_1-1;n_2-1}[/tex]
[tex]F_{H_0}= \frac{28900}{10000}*1= 2.89[/tex]
This test is one-tailed to the right and so is the p-value, you have to calculate it under a F₂₅;₂₄
P(F₂₅;₂₄≥2.89)= 1 - P(F₂₅;₂₄<2.89)= 1 - 0.994= 0.006
Using the p-value approach the decision rule is:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
α: 0.01
The p-value is less than the level of significance, the decision is to reject the null hypothesis.
Then using a 1% level, you can conclude that the population variance of the cost of annual repairs for 4 years old cars is greater than the population variance of the cost of annual repairs for 2 years old cars.
I hope this helps!
During a fundraiser, Ms. Dawson’s class raised $560, which is 25% more than Mr. Casey’s class raised. How much money did Mr. Casey's class raise?
Answer:
$420
Step-by-step explanation:
To work this out you would need to find the 25% decrease of 560. To do this you would first divide 25 by 100, which gives you 0.25. Then you would minus 0.25 from 1, which gives you 0.75. This is because when finding percentage decreases you would first have to convert it into a decimal. Then you would have to minus it from 1 , to make sure that it will be a 25% decrease not a 75% decrease. Then you would multiply 560 by 0.75, which gives you 420.
1) Divide 25 by 100.
[tex]25/100=0.25[/tex]
2) Minus 0.25 from 1.
[tex]1-0.25=0.75[/tex]
3) Multiply 560 by 0.75.
[tex]560*0.75=$420[/tex]
A survey of high school girls classified them by two attributes: whether or not they participated in sports and whether or not they had one or more older brothers. Use the following data to test the null hypothesis that these two attributes of classification are independent:
Answer:
From hypothesis, there is sufficient evidence to conclude that there is significant difference in two proportions.
Step-by-step explanation:
sample proportion for 1=12/20=0.6
sample proportion for 2=13/40=0.325
pooled proportion=25/60=0.4167
Test statistic:
z=(0.6-0.325)/sqrt(0.4167*(1-0.4167)*((1/20)+(1/40)))
z=2.037
p-value=2*P(z>2.037)=0.0417
As,p-value<0.05,we reject the null hypothesis.
There is sufficient evidence to conclude that there is significant difference in two proportions.
n monitoring lead in the air after the explosion at the battery factory, it is found that the amounts of lead over a 6 day period had a standard error of 1.91. Find the margin of error that corresponds to a 95% confidence interval. (Round to 2 decimal places)
Answer:
434.98
Step-by-step explanation:
Please help numbers 2-20 evens only
Answer: x=9,y=-1/3
Step-by-step explanation: This is for Q. 16
Rearrange terms to line up properly.
x-3y=10
x+3y=8
eliminate y terms
x=10
x=8 now add all like terms, remember it's a given that there's a one in
front of a variable.
2x=18 solve for x
x=9 now plug in the nine into one of the original eq.s and solve for y
9+3y=8
3y=-1
y=-1/3 always check solutions in both eq.s to vertify. they both work
Answer:
Q6: x= 10, y = -11
Q8: x= -3; y= 8
Q10: k= 7; j= -1
Step-by-step explanation:
Question6.
2x + y = 9..............1
-2x - 3y = 13...............2
Let's eliminate x by adding equation 1 and 2.
-2y = 22
y = 22/-2
y = -11
Substitute y = -11 in equation 1.
2x + y = 9
2x + (-11) = 9
2x - 11 = 9
2x = 9 + 11
2x = 20
x = 20/2
x = 10
x =10; y= -11
Question 8.
x + 2y = 13.............(I)
x + 6y = 45......…....(2)
By elimination method, let's take off x by subtracting equation 1 from 2.
6y - 2y = 45 - 13
4y = 32
y = 8.
Substitute y = 8 in equation 1.
x + 2y = 13
x + 2(8) = 13
x + 16 = 13
x = 13 - 16
x = -3
y= 8; x = -3
Question 10:
2j + 3k = 19 ..............1
2j + 7k = 47...............2
Let's eliminate j by subtracting equation 1 from equation 2.
4k = 28
k = 28/4
k= 7
Substitute k = 7 in equation 1.
2j + 3k = 19
2j + 3(7) = 19
2j + 21 = 19
2j = 19 - 21
2j = -2
j= -1
k= 7; j = -1
Victor has $40 in a savings account. The interest rate is 5%, compounded annually.
To the nearest cent, how much interest will he earn in 3 years?
Answer:
$6.31
Step-by-step explanation:
We are going to use the compound simple interest formula for this problem:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
Our first step is to change 5% into its decimal form:
5% -> [tex]\frac{5}{100}[/tex] -> 0.05
Next, plug in the values:
[tex]A=40(1+\frac{0.05}{1})^{1(3)}[/tex]
[tex]A=46.31[/tex]
Lastly, subtract 40 (our original value) from 46.31:
[tex]46.31-40=6.31[/tex]
Victor earned $6.31 in interest after 3 years.
For a sample of 27 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). He finds that SSE = 4,102,577 and SST = 7,622,089.
a. Calculate the standard error of the estimate.
Answer:
The standard error of the estimate is 413.4498
Step-by-step explanation:
According to the given data of ,in order to calculate the standard error of the estimate we would have to use the following formula:
Standard Error =sqrt(SSE/(n-p-1))
Standard Error =sqrt(4102577/(27-2-1))
Standard Error = 413.4498
The standard error of the estimate is 413.4498
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 94.5% of the people who have that disease. However, it erroneously gives a positive reaction in 1.5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease" to answer the following questions.
a. What is the probability of a Type I error?
b. What is the probability of a Type II error?
Answer:
a) Type 1 Error: 1.5%
b) Type 2 Error: 5.5%
Step-by-step explanation:
Probability of positive reaction when infact the person has disease = 94.5%
This means, the probability of negative reaction when infact the person has disease = 100- 94.5% = 5.5%
Probability of positive reaction when the person does not have the disease = 1.5%
This means,
Probability of negative reaction when the person does not have disease = 100% - 1.5% = 98.5%
Our Null Hypothesis is:
"The individuals does not have the disease"
Part a) Probability of Type 1 Error:
Type 1 error is defined as: Rejecting the null hypothesis when infact it is true. Therefore, in this case the Type 1 error will be:
Saying that the individual have the disease(positive reaction) when infact the individual does not have the disease. This means giving a positive reaction when the person does not have the disease.
From the above data, we can see that the probability of this event is 1.5%. Therefore, the probability of Type 1 error is 1.5%
Part b) Probability of Type 2 Error:
Type 2 error is defined as: Accepting the null hypothesis when infact it is false. Therefore, in this case the Type 2 error will be:
Saying that the individual does not have the disease(negative reaction) when infact the individual have the disease.
From the above data we can see that the probability of this event is 5.5%. Therefore, the probability of Type 2 error is 5.5%
Sam’s dry cleaning store has 3 employees who fold the clothes. Each employee can fold 45 shirts every hour. Assuming a level aggregate program how many more employees will Sam has to hire or fire to meet a demand of 1600 shirts per day if everyone works an 8 hour shift? Hire 5 more employees Hire 2 more employees Fire 1 employee Hire 17 more employees Fire 2 employee
Answer:
Hire 2 more employees.
Step-by-step explanation:
Multiply 45 by 8 to find out how many shirts 1 employee can fold for one day, one employee can fold 360 shirts in one day, then multiply that by 3 to see how many shirts they can fold a day with only the three employees. They can fold 1080 shirts in one day.
1600-1080= 520. Subtracting the demand by how many his store already can fold shows how many more he needs.
1 employee isn't enough because they can only fold 360 shirts a day so he would need to hire 2 employees because they can fold 720 shirts which meets the demand of shirts that need to be folded.
Which graph represents the function f(x) = 2/(x - 1) + 4x
HELP ASAP PLEASE!!!
What is the range for the set of data?
a. 4
b. 6
c. 3.5
d. 0
Answer:
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
because i said so
what’s the sum of interior angles of a 45-gon?
Answer:
Step-by-step explanation:
As each exterior angle is 45o , number of angles or sides of the polygon is 360o45o=8 . Further as each exterior angle is 45o , each interior angle is 180o−45o=135o .
The sum of the interior angles of a 45-gon is 7740 degrees.
To calculate the sum of interior angles of a 45-gon, or any polygon, we can use the formula (n - 2) *180 degrees, where n is the number of sides in the polygon. For a 45-gon, we substitute n with 45:
(45 - 2) * 180 = 43 * 180 = 7740
Therefore, the sum of the interior angles of a 45-gon is 7740 degrees.
Lisandro is using this diagram to find the equation of a circle. He notices that the radius, the blue line, and the red line form a right triangle. Which shows his correct reasoning and equation
a) The length of the red line is |x + h|.
The length of the blue line is |y + k|.
The equation of a circle is (x + h)2 + (y + k)2 = r2.
b) The length of the radius is r.
The area of a circle is πr2.
The equation of the circle is y = πr2x.
c) The length of the red line is |x – h|.
The length of the blue line is |y – k|.
The equation of a circle is (x – h)2 + (y – k)2 = r2.
d) The length of the red line is |x – h|.
The length of the blue line is |y – k|.
The equation of a circle is (x – h)2 + (y – k)2 = r.
Answer:
The correct answer to the question is C.
Step-by-step explanation:
The length of the red line is |x – h|. The length of the blue line is |y – k|. The equation of the circle will be (x-h)²+(y-k)²=r².
What is the equation of a circle?The equation of a circle is given by the general equation,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h,k) are the coordinates of the centre of the circle, and r is the radius of the circle.
As it is given that the blue line and the red line are the radii of the circle, therefore, they will be joining any point on the circle to the centre of the circle.
Given that the blue line is represented by |y+k| while the red line is represented by |x+h|, therefore, the coordinate of the centre of the circle will be (h,k). And the radius of the circle will be r. Thus, the equation of the circle will be (x-h)²+(y-k)²=r².
Learn more about Equation of a circle:
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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.
(20-(-16))=20+16=36 I need the answer to this question please!
Answer:
3.75
Step-by-step explanation:
Hope this helps
0.5 of what number is 15
Answer:
30
Step-by-step explanation:
0.5 * unknown number = 15
but
we see unknown number = 15 / 0.5 = 30
When the driver applies the brakes of a small-size truck traveling 10 mph, it skids 5 ft before stopping. How far will the truck skid if it is traveling 55 mph when the brakes are applied
Answer:
The truck will skid for 151 ft before stopping when the brakes are applied
Step-by-step explanation:
From the equations of motion, we will use
[tex]v^{2} = u^{2}-2aS[/tex]
We have to make sure that the parameters we are working with are in the same unit of length. Here, we will be converting from ft to miles
When the truck is travelling at 10 mph.
S = distance the truck skids = [tex]\frac{5ft}{5286ft/mile}= 0.00094697miles[/tex]
Final velocity of truck, v = 0 m/s (this is because the truck decelerates to a halt)
Initial velocity of truck u = 10 mph
Hence, we have
[tex]0^{2}=10^{2}-2a\times 0.00094697[/tex]
[tex]a= 52799.9miles/hr^{2}[/tex]
This is the deceleration of the truck
We will work based on the assumption that the car decelerates at the same rate each time the brakes are fully applied.
When the truck is travelling at u= 55 mph.
We will need to use the deceleration of the car to find the distance traveled when it skids.
[tex]0^{2}=55^{2}-2\times52799.98\times S[/tex]
[tex]S= 0.0286 miles\approx 151 ft[/tex]
∴The car skids for about 151 ft when it is travelling at 55 mph and the brakes are applied.
What is the best estimate of the difference between 48 and 21
Answer: 27?
Step-by-step explanation:
Answer
The best estimate for 48 and 21 is 50 and 20. 50-20= 30 so 30 is ur answer
Step-by-step explanation:
Which sentence can represent the inequality One-half x + three-fourths greater-than-or-equal-to 5 and one-fourth?
The sum of half of a number and three-fourths is at least five and one quarter.
Half the sum of a number and three-fourths is not more than five and one quarter.
The sum of half of a number and three-fourths is at most five and one quarter.
Half the sum of a number and three-fourths is not less than five and one quarter.
Answer:
The sum of half of a number and three-fourths is at least five and one quarter
Step-by-step explanation:
It's all about making sense of an English sentence.
"half the sum ..." is different from "the sum of half ..."
And ...
"at least" and "not less than" mean the same (≥)
"not more than" and "at most" mean the same (≤)
_____
Since all of the expressions are written out in words, it is a matter of matching the ideas expressed. That's a problem in reading comprehension, not math.
__
"One-half x + three-fourths [is] greater-than-or-equal-to 5 and one-fourth"
means the same as ...
"The sum of half of a number and three-fourths is at least five and one quarter"
Final answer:
The correct sentence for the inequality one-half x + three-fourths ≥ 5 and one-fourth is 'The sum of half of a number and three-fourths is at least five and one quarter'.
Explanation:
The correct representation of the inequality one-half x + three-fourths ≥ 5 and one-fourth (0.5x + 0.75 ≥ 5.25) in a sentence is The sum of half of a number and three-fourths is at least five and one quarter. This means that when you take half of a certain number (which we call x), add three-fourths to it, the result should be no less than five and one quarter. The other options either incorrectly suggest that the inequality is an equation, or misrepresent the inequality by suggesting the sum is 'at most' or not more or less than the given value, which changes the meaning of the original inequality.
what is the ratio of 3 circles to 4 triangles
The ratio of 3 circles to 4 triangles is 3:4, meaning there are 3 circles for every 4 triangles.
To find the ratio of 3 circles to 4 triangles, we compare the number of circles to the number of triangles.
Given:
Circles = 3
Triangles = 4
The ratio of circles to triangles is expressed as 3:4. This means for every 3 circles, there are 4 triangles.
If we want to express it as a fraction, we can write it as 3/4. This implies that for every set of 3 circles, there are 4 triangles.
To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 1 in this case. Therefore, the simplified ratio is still 3:4.
In conclusion, the ratio of 3 circles to 4 triangles is 3:4, meaning there are 3 circles for every 4 triangles.
The complete question is here:
What is the ratio of 3 circles to 4 triangles?
A watch cost $48 more than a clock. The cost for the clock is 4/7 the cost of the watch. You'll find the total cost of the two items
Final answer:
To find the total cost of the watch and the clock, set up equations based on the given relationships, solve for the individual costs, and then add them together. The total cost amounts to $176.
Explanation:
The student is asking to find the total cost of two items - a watch and a clock. The clock costs 4/7 of what the watch costs, and the watch costs $48 more than the clock. Let's denote the cost of the clock as c and the cost of the watch as w. The problem gives us two equations: w = c + $48 and c = (4/7)w. Now, we can solve these equations to find the individual costs of the clock and the watch, then sum them to find the total cost.
Step-by-step Solution
Substitute the value of c from the second equation into the first equation: w = (4/7)w + $48.
Multiply both sides of the equation by 7 to eliminate the fraction: 7w = 4w + $336.
Subtract 4w from both sides: 3w = $336.
Divide both sides by 3 to find the cost of the watch: w = $112.
Now that we have the cost of the watch, we can substitute it back into the equation c = (4/7)w to find the cost of the clock: c = (4/7) x $112 = $64.
The total cost of both items is the sum of the cost of the clock and the cost of the watch: w + c = $112 + $64 = $176.
Therefore, the total cost of the watch and the clock together is $176.
GPA and study time. A survey was conducted on 218 undergraduates from Duke University who took an introductory statistics course in Spring 2012. Among many other questions, this survey asked them about their GPA and the number of hours they spent studying per week. The scatterplot below displays the relationship between these two variables. a) The explanatory variable is and the response variable is ? b) The relationship between the variables is and . c) Is this experiment or an observational study? A. Experiment B. Observational study d) Can we conclude that studying longer hours leads to higher GPAs? A. No. We cannot conclude that studying longer hours leads to higher GPA since this study is observational. B. Yes, we can conclude that studying longer hours leads to higher GPA since this study is an experiment. C. Yes, we can conclude that studying longer hours leads to higher GPA since this study this is an observational study. D. No. We cannot conclude that studying longer hours leads to higher GPA since this study is an experiment. E. We cannot draw any conclusion because the scatterplot has no distinct form.
Answer: a) The explanatory variable is hours of study per week and the response variable is GPA.
b) The relantioship between the variables seems to be positive.
c) B. Observational Study.
d) A. NO. We cannot conclude that studying loger hours leads to higher GPA since this study is observational.
Step-by-step explanation: a) Explanatory Variable is a type of independent variable, which means it is a variable that doesn't depend on the other variables. However, in explanatory variable, there is a subtle relation between variables. For that reason, Hours of Study per week is an explanatory variable. Response Variable is the dependent variable, it is the result when you change the other variable. For that reason, GPA is the response variable.
b) Observing the graphic, which is in the attachment, it can be observed that students who study more hours per week, tend to have higher GPA. For example, people who studied 60 hours per week have a GPA closer to 4.
c) Observational Studies are those experiment where the researches only observe their object of interest without changing or interfering in the outcome. Experimental Studies are the ones where the researchers introduce an interference and study their effect on the randomized groups.
Since this experiment is based on observation only, the study is an Observational Study.
d) Because it's an observational study, we can't correlate or associate the variables, since the researchers only obtain their results through observation of the behaviour of the students, without changing it.
Suppose you owe â$700 on your credit card and you decide to make no new purchases and to make the minimum monthly payment on the account. Assuming that the interest rate on your card is 2â% per month on the unpaid balance and that the minimum payment is 3â% of the totalâ (balance plusâ interest), your balance after t months is given by âB(t) = 700â(.9894tâ).
1. Find your balance at each of the given times in partsâ (a) throughâ (c) below.
(a) five months
(b) one year (remember that t is in months)
(c) is the balance paid off in two years?
The credit card balance at 5 months, 1 year, and 2 years to see the progression of debt repayment is $695, $669.67 and $669.70 respectively.
Calculate B(5) by substituting t = 5 into the formula B(t) = 700(.9894t), giving B(5) = 700(.9894*5) = $695.58.
Find B(12) by substituting t = 12 into the formula, giving B(12) = 700(.9894*12) = $669.67.
To check if the balance is paid off after 2 years, find B(24) = 700(.9894*24) = $632.70.
which indicates the balance is not paid off in 2 years.
Provided below are summary statistics for independent simple random samples from two populations. Use the nonpooled t-test and the nonpooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.
X1 = 11, S1 = 5, n1 = 25, x2 = 10, S2 = 4, n2 = 20
A) What are the correct hypotheses for aright-tailed test? α = 0.05
i. Compute the test statistic.
ii. Determine the P-value.
B) The 90% confidence interval is from _______ to ________
Using the t-distribution, we have that:
a)
The null hypothesis is [tex]H_0: x_1 - x_2 \leq 0[/tex].The alternative hypothesis is [tex]H_1: x_1 - x_2 > 0[/tex]i) The test statistic is t = 0.746.
ii) The p-value is of 0.2299.
b) The 90% confidence interval is from -1.25 to 3.25.
Item a:
For a right-tailed test, we test if [tex]x_1[/tex] is greater than [tex]x_2[/tex], hence:
The null hypothesis is [tex]H_0: x_1 - x_2 \leq 0[/tex].The alternative hypothesis is [tex]H_1: x_1 - x_2 > 0[/tex]The standard errors are:
[tex]S_{e1} = \frac{5}{\sqrt{25}} = 1[/tex]
[tex]S_{e2} = \frac{4}{\sqrt{20}} = 0.8944[/tex]
The distribution of the difference has mean and standard error given by:
[tex]\overline{x} = x_1 - x_2 = 11 - 10 = 1[/tex]
[tex]s = \sqrt{S_{e1}^2 + S_{e2}^2} = \sqrt{1^2 + 0.8944^2} = 1.34[/tex]
We have the standard deviation for the samples, hence, the t-distribution is used.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{1 - 0}{1.34}[/tex]
[tex]t = 0.746[/tex]
The test statistic is t = 0.746.
The p-value is found using a t-distribution calculator, with t = 0.746, 25 + 20 - 2 = 43 df and 0.05 significance level.
Using the calculator, it is of 0.2299.Item b:
The critical value for a 90% confidence interval with 43 df is [tex]t = 1.6811[/tex].
The interval is:
[tex]\overline{x} \pm ts[/tex]
Hence:
[tex]\overline{x} - ts = 1 - 1.6811(1.34) = -1.25[/tex]
[tex]\overline{x} + ts = 1 + 1.6811(1.34) = 3.25[/tex]
The 90% confidence interval is from -1.25 to 3.25.
A similar problem is given at https://brainly.com/question/25840856
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = 6x − 6y subject to x 5 ≤ y y ≤ 2x 7 x + y ≥ 9 x + 2y ≤ 22 x ≥ 0, y ≥ 0.
Answer:
no optimal solution as feasible region is empty
Step-by-step explanation:
The complete question is:
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = 6x − 6y subject to 5x ≤ y y ≤ 2x 7 x + y ≥ 9 x + 2y ≤ 22 x ≥ 0, y ≥ 0.
See the attachment to understand the following explanation.
The shaded regions shown in attachment obeys all constraints except for 5x ≤ y and y ≤ 2x. The shaded region 1 obeys all constraints except y ≤ 2x and shaded region 2 obeys all constraints except 5x ≤ y. So there is no feasbile region. Hence no optimal solution exists
To solve the linear programming problem, the constraints must be graphed to identify the bounded feasible region, if any exists. The objective function is then minimized by evaluating it at each vertex of this region. The solution is either one of these vertices or the problem may indicate no solution if the region is empty or the function is unbounded.
Explanation:The given linear programming (LP) problem requires us to minimize the objective function c = 6x - 6y subject to a set of given constraints. To solve this problem, we graph the constraints and identify the feasible region. The constraints are:
x + 5 ≤ yy ≤ 2x + 7x + y ≥ 9x + 2y ≤ 22x ≥ 0, y ≥ 0Given that the inequalities form a bounded region, we then inspect the vertices of this feasible region to find the point that minimizes the objective function. The solution is either one of these vertices or it is non-existent if the feasible region is empty or the objective function is unbounded. In this problem, given the constraints and the positive coefficients of the objective function, the feasible region is bounded, and thus we should be able to find a minimum point by evaluating the objective function at each vertex of the feasible region.
Learn more about Linear Programming here:https://brainly.com/question/34674455
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