A consumer magazine wants to compare lifetimes of ballpoint pens of three different types. The magazine takes a random sample of pens of each time and records the lifetimes (in minutes) in the table below. Do the data indicate that there is a difference in the mean lifetime for the three brands of ballpoint pens?
Answers
Answer:
The first step would be to look at the average for each brand.
The average can be calculated as:
A = (a1 + a2 + .... + an)/N
where a1 is the first lifetime, a2 is the second one, etc. And N is the total number of data points.
So, for Brand 1 we have:
A1 = (260 + 218 + 184 + 219)/4 = 220.25
Brand 2:
A2 = (181 + 240 + 162 + 218)/4 = 200.25
Brand 3:
A3 = (238 + 257 + 241 + 213)/4 = 237.25
So only from this, we can see that Brand 3 has the larger lifetime, then comes Brand 1 and last comes Brand 2.
Related Questions
Use a calculator to determine the pattern of attractors for the equation y =kx(1-x) for the given value of k and the given initial value of x
K=3.26, x=0.8
Guys, I need help quickly?
Answers
Answer:
0.5216
Step-by-step explanation:
Given the function y =kx(1-x), the pattern of attractors are the value(s) of y at the initial value of k and x. Given the value of k = 3.26 and x = 0.8, to get the pattern of attractors, we will substitute the given initial value into the function as shown;
[tex]y =kx(1-x)\\\\y = 3.26(0.8)(1-0.8)\\\\y = 3.26*0.8*0.2\\\\y = 0.5216\\\\[/tex]
Hence, the pattern of attractor for the equation y is 0.5216
What is the best first step in solving -4x + 5/3 > 5/10
Answers
Answer:
Step-by-step explanation:
The best first step to solve this is to just subtract 5/3 from both sides so it is easier to simplify.
Answer:
Subtract 5/3 to the other side
Step-by-step explanation:
Hey there!
Well the best first step is to -5/3 to both sides and move it to the right side.
-4x + 5/3 > 5/10
-5/3 to both sides
-4x > -7/6
Hope this helps :)
What is the prime factorization of 18?
Answers
Answer:
18 is a composite number. 18 = 1 x 18, 2 x 9, or 3 x 6. Factors of 18: 1, 2, 3, 6, 9, 18. Prime factorization: 18 = 2 x 3 x 3, which can also be written 18 = 2 x 3².
All the prime factorization of 18 are,
⇒ 2, 3, 3
Because 2×3×3 = 18
We have to given that,
To find all the prime factorization of number 18.
Now, We need to find all the factors of 18.
Hence,
18 = 2 x 9
= 2 x 3 x 3
Therefore, All the prime factorization of 18 are,
⇒ 2, 3, 3
Because 2×3×3 = 18
Learn more about the Greatest common factors visit:
https://brainly.com/question/219464
#SPJ6
Determine the t critical value for a lower or an upper confidence bound in each of the following situations. (Round your answers to three decimal places.)
a. Confidence level = 95%, df = 10
b. Confidence level = 95%, df = 15
c. Confidence level = 99%, df = 15
d. Confidence level = 99%, n = 5
e. Confidence level = 98%, df = 23
f. Confidence level = 99%, n = 32
Answers
Answer:
A. 1.812
B. 1.753
C. 2.602
D. 3.747
E. 2.069
F. 2.453
Step-by-step explanation:
A. 95% confidence level, the level of significance = 5% or 0.05
Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 10 degrees of freedom = 1.182
B. 95% confidence interval = 0.05 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 15 degrees of freedom = 1.753
C. 99% confidence interval = 0.01 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 15 degrees of freedom = 2.602
D. 99% confidence interval = 0.01 level of significance; DF (n - 1) = 5- 1 = 4
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 4 degrees of freedom = 3.747
E. 98% confidence interval = 0.02 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.02 significance level with 23 degrees of freedom = 2.069
F. 99% confidence interval = 0.01 level of significance; df (n - 1) = 32 - 1 = 31
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 31 degrees of freedom = 2.453
Plz help answer a - d 1. Miguel is playing a game in which a box contains four chips with numbers written on them two of the chips have the number one one chip has the number three and the other chip has the number 5 Miguel must choose to chips if both chips have the same number he wants to dollars if the two chipsy chooses have different numbers he loses $1 (-$1) Look at pictures for the questions
Answers
Answer:
Step-by-step explanation:
Hello!
Miguel has four chips, two have the number "1", one has the number "3" and the other has the number "5"
If the experiment is "choosing two chips and looking at their numbers" there are the following possible outcomes:
S= {(1,1)(1,3)(1,5)(3,1)(5,1)(3,5)(5,3)}
The sample space for the experiment has 7 possible combinations.
a)
Be X: the amount of money Miguel will receive or owe.
If two chips with the same number are chosen he will receive $2
If the chips have different number he will owe $1
Looking at the possible outcomes listed above, out of the 7, in only one he will select the same number (1,1)
So the probability of him receiving $2 will be 1/7
Now out of the 7 possible outcomes, 6 will make Miguel owe $1, so you can calculate its probability as: 6/7
xi | $2 | -$1
P(xi) | 1/7 | 6/7
b)
To calculate the expected value or mean you have to use the following formula:
[tex]\frac{}{X}[/tex]= ∑[xi*P(xi)]= (2*1/7)(-1*6/7)= -4/7= $-0.57
c)
The expected value is $-0.57, meaning that Miguel can expect to owe $0.57 at the end of the game.
d)
To make the game fair you have to increase the probability of obtaining two chips with the same number. Any probability close to 50% will make the game easier. For example if you change the experiment so that for earning $2 the probability is 4/7 and for owing $1 the probability is 3/7, the expected earnings will be:
(2*4/7)+(-1*3/7)= $0.71
I hope this helps!
A normal population has a mean of 61 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is: (
Answers
This question is incomplete
Complete Question
A normal population has a mean of 61 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is: (Round z values to 2 decimal places and final answers to 4 decimal places.)
(a) Greater than 64
(b) Less than 57
Answer:
(a) Greater than 64 = 0.1788
(b) Less than 57 = 0.1094
Step-by-step explanation:
To solve the above questions we would be using the z score formula
The formula for calculating a z-score :
z = (x - μ)/σ,
where x is the raw score
μ is the population mean = 61
σ is the population standard deviation = 13
(a) Greater than 64
z = (x - μ)/σ,
where x is 64
μ is the 61
σ is the 13
In the above question, we are given the number of samples = 16
Sample standard deviation = popular standard deviation/ √16
= 13/√16
z = 64 - 61 ÷ 13/√16
z = 3/3.25
z = 0.92308
Approximately, z values to 2 decimal places ≈ 0.92
Using the z score table of normal distribution to find the Probability (P) value of z score of 0.92
P(z = 0.92) = 0.82121
P(x>64) = 1 - P(z = 0.92)
= 1 - 0.82121
= 0.17879
Approximately , Probability value to 4 decimal places = 0.1788
(b) Less than 57
z = (x - μ)/σ,
where x is 57
μ is the 61
σ is the 13
In the above question, we are given the number of samples = 16
Sample standard deviation = popular standard deviation/ √16
= 13/√16
z = 57 - 61 ÷ 13/√16
z = -4/3.25
z = -1.23077
Approximately, z values to 2 decimal places ≈ -1.23
Using the z score table of normal distribution to find the Probability (P) value of z score of -1.23
P(z = -1.23) = P(x<Z) = 0.10935
Approximately , Probability value to 4 decimal places = 0.1094
how to simplify this expression ?
Answers
Answer:
[tex]\large \boxed{\sf \ \ \dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{2x+1}{x^2(x+1)} \ \ }[/tex]
Step-by-step explanation:
Hello,
This is the same method as computing for instance:
[tex]\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{3+2}{2*3}=\dfrac{5}{6}[/tex]
We need to find the same denominator.
Let's do it !
For any x real different from 0, we can write:
[tex]\dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{1}{x^2}+\dfrac{1}{x(x+1)}\\\\=\dfrac{x+1+x}{x^2(x+1)}=\dfrac{2x+1}{x^2(x+1)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A police office claims that the proportion of people wearing seat belts is less than 65%. To test this claim, a random sample of 200 drivers is taken and its determined that 126 people are wearing seat belts. The following is the setup for this hypothesis test:
H0:p=0.65
Ha:p<0.65
In this example, the p-value was determined to be 0.277. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)
Select the correct answer below:
A. There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%.
B. There is NOT sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%.
C. There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 35%.
D. There is NOT sufficient evidence to conclude that the pronortion of people wearing seat belts is less than 35%
Answers
Answer:
Option A - There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%
Step-by-step explanation:
The police officers claim is that the proportion of people wearing seat belts is less than 65%.
Now, we are told that the p - value is 0.277.
In hypothesis, for a significance value of 0.05, if the P value is less than 0.05, we reject the null hypothesis and if P value is greater than or equal to 0.05, we fail to reject the null hypothesis.
Now, since the significance level is 5% = 0.05,we can see that the P-value is greater than the significance value of 0.05. Thus, we fail to reject the police claim that the proportion of people wearing seat belts is less than 65%.
So the correct option is A.
If jimmy has 15 apples and give 7 to gohn how many does jimmy have?
Answers
Answer:
Hey there!
Jimmy has 15-7, or 8 apples left.
Hope this helps :)
Enter your answer in the box
____
Answers
Answer:
[tex]\boxed{2144}[/tex]
Step-by-step explanation:
The sum can be found by adding the parts:
[tex]\sum\limits_{n=1}^{32}{(4n+1)}=4\sum\limits_{n=1}^{32}{n}+\sum\limits_{n=1}^{32}{1}=4\cdot\dfrac{32\cdot 33}{2}+32\\\\= 2112+32=\boxed{2144}[/tex]
__
The sum of numbers 1 to n is n(n+1)/2.
How large a sample must be drawn to estimate population proportion confidence interval width to within .04, with 95% confidence, if we believe the true percentage is 80%
Answers
Answer:
Sample size 'n' = 384
Step-by-step explanation:
Explanation:-
Given margin of error = 0.04
The sample proportion 'p'= 0.80
The margin of error is determined by
[tex]M.E = \frac{Z_{\alpha } \sqrt{p(1-p)} }{\sqrt{n} }[/tex]
[tex]0.04 = \frac{1.96 \sqrt{0.80(1-0.80)} }{\sqrt{n} }[/tex]
Cross multiplication, we get
[tex]\sqrt{n} = \frac{1.96 \sqrt{0.80(1-0.80)} }{0.04 }[/tex]
√n = 19.6
Squaring on both sides , we get
n = 384.16≅384
A cash register has $10 and $50 dollars bills with total of $1080.there are 28 bills in total how many of each bills.
Answers
Hey there! I'm happy to help!
Let's set this up as a system of equations, where x is equal to the number of 10 dollar bills and y is equal to the number of 50 dollar bills.
10x+50y=1080
x+y=28
We want to solve for x or y. We can rearrange the second equation to find the value of one of the variables.
x+y=28
Subtract x from both sides.
y=28-x
Now, we have a value for y. So, we could replace the y in the first equation with 28-x and the solve for x.
10x+50(28-x)=1080
We use distributive property to undo the parentheses.
10x+1400-50x=1080
We combine like terms.
-40x+1400=1080
We subtract 1400 from both sides.
-40x=-320
We divide both sides by -40.
x=8
Since there are 28 total bills, this means that there must be 20 50 dollar ones because there are 8 10 dollar bills.
Have a wonderful day! :D
A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is$31 . The total cost to rent 6 chairs and 5 tables is $59 . What is the cost to rent each chair and each table?
Answers
Answer:
The cost to rent each chair is $2.75 and the cost to rent each table is $8.50
Step-by-step explanation:
Let the:
Cost to rent a chair = x
Cost to rent a table = y
We would form an algebraic equation.
The total cost to rent 2 chairs and 3 tables is $31
2x + 3y = 31 ...... Equation 1
The total cost to rent 6 chairs and 5 tables is $59
6x + 5y = 59 ......... Equation 2
We solve the above equation above using elimination method
Multiply Equation 1 all through by the coefficient of x = 6 in Equation 2
Multiply Equation 2 all through by the coefficient of x = 2 in Equation 1
Hence, we have:
2x + 3y = 31 ...... Equation 1 × 6
6x + 5y = 59 ......... Equation 2 × 2
12x + 18y = 186........ Equation 3
12x + 10y = 118 .…...... Equation 4
Subtracting Equation 4 from Equation 3
= 8y = 68
y = 68/8
y = 8.5
Therefore, the cost to rent a table = $8.50
Substituting 8.5 for y in Equation 1 to get the value of x
2x + 3y = 31 ...... Equation 1
2x + 3(8.5) = 31
2x = 31 - 3(8.5)
2x = 31 - 25.5
2x = 5.5
x = 5.5/2
x = 2.75
The cost to rent a chair = $2.75
Therefore, the cost to rent each chair is $2.75 and the cost to rent each table is $8.50
Use the functions m(x) = 4x + 5 and n(x) = 8x − 5 to complete the function operations listed below. Part A: Find (m + n)(x). Show your work. (3 points) Part B: Find (m ⋅ n)(x). Show your work. (3 points) Part C: Find m[n(x)]. Show your work. (4 points)
Answers
Answer:
Step-by-step explanation:
Part A
(m + n)x = 4x + 5 + 8x - 5
(m + n)x = 12x The fives cancel
Part B
(m - n)x = 4x + 5 - 8x + 5
(m - n)x = -4x + 10
Part C
The trick here is to put n(x) into m(x) wherever m(x) has an x.
m[n(x)] = 5(n(x)) + 5
m[n(x)] = 5(8x - 5) + 5
m[n(x)] = 40x - 20 + 5
m[n(x)] = 40x - 15
A que hora después de las 3 las agujas de un reloj determinan un ángulo que mide 54 por primera vez
Answers
Answer:
3:06
Step-by-step explanation:
primero debemos calcular a cuántos minutos equivale un ángulo de 54°. Para hacer esto utilizamos una regla de 3 simple donde 60 minutos equivale a 360° grados, entonces:
60 minutos ----- 360°
x minutos -------- 54°
Resolviendo para x, tenemos:
[tex]x=\frac{54*60}{360}=9[/tex]
Entonces si las manecillas están a 9 minutos de diferencia, el ángulo será 54°. Si la hora es después de las 3, significa que la manecilla de la hora estará en el minuto 15 y la otra debe estar 9 minutos antes, es decir en el minuto 6.
Por lo tanto, la hora después de las 3 en la cual se forma un ángulo de 54° por primera vez es a las 3:06
Express the equation in the slope y-intercept form: y = mx + b. 2x−3y+1 = 0
Answers
Answer:
y = 2/3x+1/3
Step-by-step explanation:
2x−3y+1 = 0
Solve for y
Add 3y to each side
2x−3y+1 +3y= 0+3y
2x +1 = 3y
Divide by 3
2/3 x + 1/3 =3y/3
2/3x +1/3 = y
The slope is 2/3 and the y intercept is 1/3
y = 2/3x+1/3
That guy this question is evil help
Answers
Answer:
450 mins/night
Step-by-step explanation:
The average of a data set is the sum of all of the data divided by the number of data elements in the set. In this case, that would be:
(8 + 6.5 + 7 + 8.5) / 4
= 30 / 4
= 7.5 hours
7.5 hours is 7.5 * 60 = 450 mins/night
Answer:
450 mins per night
Step-by-step explanation:
average = [tex]\frac{sum \: of \: terms}{number \: of \: terms}[/tex]
average = (8 + 6.5 + 7 + 8.5)/4
average = 30/4
average = 7.5
The average is 7.5 hrs.
Convert hrs to mins.
7.5 × 60 = 450
G(x) = 5x + 3
Find g(b2)
Answers
Answer:
g(2) =10x+6
Step-by-step explanation:
g(x) =5x+3
g(2)=5x+3
g(2)=10x+6
have a great day
If you sleep an average of 7.5 hours each night, how many hours do you sleep in a year?
Answers
Answer:
[tex]\boxed{\sf 2737.5 \ hours}[/tex]
Step-by-step explanation:
The average is 7.5 hours of sleep each night.
There are 365 nights in 1 year.
[tex]\sf Multiply \ the \ value \ by \ 365.[/tex]
[tex]7.5 \times 365[/tex]
[tex]2737.5[/tex]
Answer:
2,737 hours for a normal year, 2,745 if it is a leap year.
Step-by-step explanation:
Because there 365 days in a year, you should multiply the amount you sleep every day (7.5) by the number of days in a year (365)
[tex]7.5*365[/tex]
Multiply 7.5 by 365 to get
[tex]2,737.5[/tex]
Every year you will sleep 2,737 hours if you sleep 7.5 hours each day.
(If it is a leap year, just change 365 to 366 which will give you 2,745 hours)
I hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
Select all angle measures for which cos0= 1/2
Answers
Answer:
cos -60° = [tex]\frac{1}{2}[/tex] ,
cos 660° = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
hope it helps
Answer:
-60 and 660
Step-by-step explanation:
Edge 2020
2 questions
1) how to make 1, 2, 3, 4, 5 = 1
2) how to make 1, 2, 3, 4, 5 = 3
Answers
Answer:
5+2+1 - 4 -3 = 1
5+4 - 3-2-1 =
Step-by-step explanation:
we have to ad and subtract number in such a way that result is 1.
1, 2, 3, 4, 5
5+2+1 - 4 -3 = 1
8-7 = 1
___________________________________________
In this problem we have use mathematical signs to get 3.
we add 5 and 4 which gives 9
and subtract 3,2 and 1 from it.
5+4 - 3-2-1 = 9 - 6 = 3
2) A basketball player scores 70% of his shots on average. What is the probability that he scores at least 18 successful shots tonight if he gets 20 shots?
Answers
Answer:
3.54%
Step-by-step explanation:
This question represents a binomial distribution. A binomial distribution is given by:
[tex]P(x)=\frac{n!}{(n-x)!x!} p^xq^{n-x}[/tex]
Where n is the total number of trials, p is the probability of success, q is the probability of failure and x is the number of success.
Given that:
A basketball player scores 70% of his shots on average, therefore p = 70% = 0.7. Also q = 1 - p = 1 - 0.7 = 0.3.
The total number of trials (n) = 20 shots
The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20)
P(x = 18) = [tex]\frac{20!}{(20-18)!18!}*0.7^{18}*0.3^{20-18}=0.0278[/tex]
P(x = 19) = [tex]\frac{20!}{(20-19)!19!}*0.7^{19}*0.3^{20-19}=0.0068[/tex]
P(x = 20) = [tex]\frac{20!}{(20-20)!20!}*0.7^{20}*0.3^{20-20}=0.0008[/tex]
The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20) = 0.0278 + 0.0068 + 0.0008 = 0.0354 = 3.54%
Which fraction is equal to 60%?
2 of
100
600
60
100
100
60
6.0
100
Answers
Answer:
Step-by-step explanation:
[tex]60\% =\\\\\frac{60}{100} \\=0.6[/tex]
Answer:
3/5
Step-by-step explanation:
60% as a fraction is 3/5 :)
find the value of a, b, c, and d,
type exact answers and use radicals as needed
Answers
Step-by-step explanation:
Using trigonometrical functions we can obtain the required side lengths.
[tex] \sin 45\degree = \frac{a}{16\sqrt 2}\\\\
\therefore \frac{1}{\sqrt 2}= \frac{a}{16\sqrt 2}\\\\
\therefore a = \frac{16\sqrt 2}{\sqrt 2}\\\\
\huge\red {\boxed {\therefore a = 16}} \\\\
\cos 45\degree = \frac{c}{16\sqrt 2}\\\\
\therefore \frac{1}{\sqrt 2}= \frac{c}{16\sqrt 2}\\\\
\therefore c = \frac{16\sqrt 2}{\sqrt 2}\\\\
\huge\purple {\boxed {\therefore c = 16}} \\\\
\sin 30\degree = \frac{a}{b}\\\\
\therefore \frac{1}{2}= \frac{16}{b}\\\\
\therefore b = {16\times2}\\\\
\huge\orange{\boxed {\therefore b = 32}} \\\\
\tan 30\degree = \frac{a}{d}\\\\
\therefore \frac{1}{\sqrt 3}= \frac{16}{d}\\\\
\therefore d = {16\times\sqrt 3}\\\\
\huge\pink {\boxed {\therefore d = 16\sqrt 3}} \\\\
[/tex]
I need an answer for the attachment below:
Answers
Answer:
[tex] - \frac{ 1}{4} [/tex]Step-by-step explanation:
The line passes through points ( - 1 , 2 ) and ( 3 , 1 )
Let there points be A and B
A ( -1 , 2 ) -----> ( x1 , y1 )
B ( 3 , 1 ) -------> ( x2 , y2 )
Now, Let's find the gradient ( slope)
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
plug the values
[tex] = \frac{1 - 2}{3 - ( - 1)} [/tex]
Calculate the difference
[tex] = \frac{ - 1}{3 - ( - 1)} [/tex]
When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression
[tex] = \frac{ - 1}{3 + 1} [/tex]
Add the numbers
[tex] = \frac{ - 1}{4} [/tex]
Use [tex] \frac{ - a}{b} = \frac{a}{ - b} = - \frac{a}{b} [/tex] , to rewrite the fraction
[tex] = - \frac{1}{4} [/tex]
Hope this helps...
Best regards!!
Barry spent 1/5 of his monthly salary for rent and 1/7 of his monthly salary for his school loans. If $851 was left, what was his monthly salary?
Answers
Answer:
1295$
Step-by-step explanation:
Let's denote the monthly salary of Barry A.
Then we have:
A - (1/5)A - (1/7)A = 851
or
(35A - 7A - 5A)/35 = 851
or
23A = 851 x 35
or
23A = 19785
or
A = 1295$
Find: ∠x ∠a ∠b Please help
Answers
Answer:
a=90 degrees
b=90 degrees
x=22 degrees
Step-by-step explanation:
3x+22+(5x-18)=180
8x=176
x=22
Answer:
x = 22°, ∠a = 88°, ∠b = 92°.
Step-by-step explanation:
Angle b has the same measurement as the angle of 5x - 18, since the two angles are corresponding angles.
Angle a has the same measurement as the angle of 3x + 22, since the two angles are alternate interior angles.
Since angle a and the angle of 5x - 18 form a straight line, the two angles add up to be 180 degrees. Since angle a is the same as the angle of 3x + 22, we can substitute the angle for angle a.
(5x - 18) + (3x + 22) = 180
5x + 3x - 18 + 22 = 180
8x + 4 = 180
8x = 176
x = 22°.
3(22) + 22 = 66 + 22 = 88 degrees.
That means that ∠a = 88°.
5(22) - 18 = 110 - 18 = 92 degrees.
That means that ∠b = 92°.
Hope this helps!
m−4+m−5 how do I solve this ?
Answers
Answer:
2m - 9
Step-by-step explanation:
To simplify this, we need to combine like terms. m + m = 2m and -4 - 5 = -9 so the simplified version would be 2m - 9.
Let f(x) = −x^2 and g(x) = 1/√x. Find formulas for f ◦g and g◦f and state the domain of each composition. I only need the domains if possible.
Answers
Answer: see below
Step-by-step explanation:
[tex]f(x)=-x^2\qquad g(x)=\dfrac{1}{\sqrt x}[/tex]
[tex]f og(x)=f\bigg(\dfrac{1}{\sqrt x}\bigg)\\\\.\qquad =-\bigg(\dfrac{1}{\sqrt x}\bigg)^2\quad \\\\.\qquad =-\dfrac{1}{x}\\\\\text{Domain:}\ x>0[/tex]
[tex]gof(x)=g(-x^2)\\\\.\qquad =\dfrac{1}{\sqrt{-x^2}}\\\\.\qquad =\dfrac{1}{xi}\\\\\text{Domain: Does Not Exist since result is an imaginary number}[/tex]
What is the area of this triangle on a Coordinate Grid?
Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2), is drawn inside a rectangle
Answers
Answer: 8.5 sq. units.
Step-by-step explanation:
Formula:
Area of triangle : [tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Given: Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2)
Then, Area of triangle IJK = [tex]\dfrac{1}{2}|3(-4-(-2))+7(-2-(-7))+4(-7-(-4))|[/tex]
[tex]\dfrac{1}{2}|3(-2)+7(5)+4(-3)|\\\\=\dfrac{1}{2}|-6+35-12|\\\\=\dfrac{1}{2}(17)\\\\=8.5\text{ sq. units}[/tex]
Hence, the area of this triangle IJK on a Coordinate Grid = 8.5 sq. units.