Find sinθ, tanθ, and secθ, where θ is the angle shown in the figure. Give exact values, not decimal approximations.sinθ=tanθ=secθ=
Answers
1) We have here a right triangle, so we can use the Pythagorean Theorem to find the adjacent leg. Note that the hypotenuse is leg opposite to the right angle. In this case, a=4.
a²=b²+c²
4²=b²+3²
16=b²+9
16-9=b²
b=√7
2) Let's find the trigonometric functions. The first one is the sine (θ), which relates the opposite side and the hypotenuse:
[tex]\sin (\theta)\text{ =}\frac{3}{4}[/tex]2.2)Moving on, we can deal with the tangent of theta, relating the opposite side over the adjacent, for this one we have to rationalize it:
[tex]\begin{gathered} \tan (\theta)\text{ =}\frac{3}{\sqrt[]{7}} \\ \tan (\theta)=\frac{3\sqrt[]{7}}{7} \end{gathered}[/tex]Finally, let's find the reciprocal function of the cosine function by setting this as the reciprocal of the cosine, and then calculating it:
[tex]\begin{gathered} \sec \text{ (}\theta)=\frac{1}{\cos(\theta)}\Rightarrow\sec (\theta)=\frac{1}{\frac{\sqrt[]{7}}{4}}\Rightarrow\sec (\theta)\text{ =}\frac{4}{\sqrt[]{7}} \\ \sec (\theta)\text{ =}\frac{4\sqrt[]{7}}{7} \end{gathered}[/tex]Related Questions
Jacqueline took out a personal line of credit in her senior year of college with an annual simple interest rate of 4%.she takes 51 months to pay off the loan in full and pays 1530 in interest. A. How much was the original line of credit amount.B. How much did Jacqueline pay in total.
Answers
Given data:
The given annual interest is r=4%.
The given time is t=51 months= 4 year+3 months=4.25 years.
The interest ammount is i=1530.
A)
The expression for the simple innterest is,
i=(Prt)/100
Substitute the given values in the above expression.
1530=P(4)(4.25)/100
P=9000.
Thus, the original amount credit is 9000.
B)
The expression for the total amount is,
A=P+i
Substitute the above calculated values.
A=9000+1530
=10530
Thus, the total amount is 10530.
Find the distance between (2, 5) and (-5, 8).
Answers
Given:
The two points are,
[tex]\begin{gathered} (2,5) \\ (-5,8) \end{gathered}[/tex]Required:
To find the distance between the given points.
Explanation:
The distance between the two points (x1,y1) and (x2,y2) can be calculated by using the formula,
[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]Now the distance between the points (2,5) and (-5,8) is,
[tex]\begin{gathered} \sqrt{(-5-2)^2+(8-5)^2} \\ =\sqrt{(-7)^2+3^2} \\ =\sqrt{49+9} \\ =\sqrt{58} \end{gathered}[/tex]Final Answer:
The distance between two given points is
[tex]\sqrt{58}units[/tex]Evaluate the expression when c=4 and x=-4.-C+2x
Answers
ok
c = 4 x = 4
-c + 2x
Substitution
-4 + 2(4)
-4 + 8
Result
4
The answer for the second question is 2v + 15
Graph the line that has an z-intercept at (1,0) and a y-intercept at (0, - 4). What is the slope of this line? And what is m=
Answers
Answer: m= -5
Step-by-step explanation:
Answer:
m = 4
Step-by-step explanation:
Change in y over change in x
[tex]\frac{-4-0}{0-1}[/tex] = [tex]\frac{-4}{-1}[/tex] = 4
From the ordered pairs are in the form (x,y)
so your y's are -4 and 0
your x's are 0 and 1
Find a quadratic equation in standard form given its roots are 2+/- i square root of 3/2
Answers
We want to find a quadratic equation with the following roots:
[tex]\begin{gathered} x_+=2+i\sqrt{\frac{3}{2}} \\ x_-=2-i\sqrt{\frac{3}{2}} \end{gathered}[/tex]Then we have:
[tex]\begin{gathered} y=(x-x_+)\cdot(x-x_-) \\ y=(x-2-i\sqrt{\frac{3}{2}})\cdot(x-2+i\sqrt{\frac{3}{2}}) \\ y=x^2-2x+i\sqrt{\frac{3}{2}}x-2x+4-i2\sqrt{\frac{3}{2}}-i\sqrt{\frac{3}{2}}x+i2\sqrt{\frac{3}{2}}+\frac{3}{2} \\ y=x^2-4x+\frac{11}{2} \end{gathered}[/tex](Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
The slope of the wooden beam is 39.8 ft
STEP - BY -STEP EXPLANATION
What to find?
The slope of the wooden beam.
Let y be the slope length.
To determine the slope length of the wooden beam we will follow the steps below.
Step 1
Write down the formula in calculating the sloping beam.
rise² + run² = slope length²
Step 2
Observe from the given diagram;
The value of the rise =12
The value of the run =76/2 = 38
Step 3
Substitute the values into the formula.
12²+ 38² = y²
Step 4
Simplify the above.
144 + 1444 = y²
1588 = y²
Step 5
Take the square root of both-side of the equation.
y = 39.8 ft
Therefore, the length of the sloping beam is 39.8 ft
Use a graphing calculator to find an equation of the line of best fit for the data. Round the slope to the nearest tenth and the y-intercept to the nearest integer.
X: 0 1 2 3 4 5 6 7
Y:-8 -5 -2 -1 -1 2 5 8
Answers
The Equation of line is 3x - y + 24 =0.
Given:
The table is given by:
X: 0 1 2 3 4 5 6 7
Y:-8 -5 -2 -1 -1 2 5 8
To find the equation of line by using the above data.
Now, According to the question:
From the table, We have
We know that,
Slope (m) = [tex]\frac{y_{2}-y_{1} }{x_{2} - x_{1} }[/tex]
and, slope (m) = [tex]\frac{-5-(-8)}{1-0}[/tex]
m = (-5 + 8)/ 1 = 3
So, [tex]y - y_{1} = m (x - x_{1} )[/tex]
y - 0 = 3 (x - (-8))
y = 3(x + 8)
y = 3x + 24
Hence, The Equation of line is 3x - y + 24 =0.
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(1) In the 1970’s the popular advice columnist Ann Landers published a letter from a young couple about to be married. The letter said, “so many of our friends seem to resent their children. They envy us and our freedom to go and come as we please. Then there’s the matter of money. They say their kids keep them broke. Will you please ask your readers the question: 'If you had it to do over again – would you have children?' ” Nearly 10,000 of her readers responded. 70% said “no.” (2) The Good Housekeeping magazine published the results of the poll with a sidebar that said, “All of us at Good Housekeeping know that no mother will be able to read Ann Landers’ report without passionately agreeing or disagreeing. We would like to know what your reaction is. Won’t you therefore, take a minute or two to let us know how you would answer the question: 'If you had it to do over again, would you have children?' ” The results for the Good Housekeeping poll were 95% “yes.” These two polls gave opposite results! What i
Answers
Now that the poll has been published in magazines and newspapers, it is up to the readers to decide whether they want to participate. Consequently, the findings are biased by D. volunteer responses.
How to illustrate the information?Option A is incorrect since the estimate need not be underrepresented.
Option B is incorrect since it omits mentioning the good housekeeping magazine.
Option C is incorrect since the discrepancy isn't the result of sampling variance. Both resources' audiences are distinct and do not accurately reflect the general population.
Therefore, this is a voluntary answer, Option D is accurate.
Note that the complete question is attached.
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I need to know the answer quick because I have to go somewhere
Answers
First, we need to remember to rules when working with exponents:
[tex]\begin{gathered} \frac{1}{b^a}=b^{-a} \\ \text{and} \\ b^a\cdot b^c=b^{a+c} \end{gathered}[/tex]So, going back to our problem
[tex]\begin{gathered} \frac{2^{\frac{3}{4}}}{2^{\frac{1}{2}}} \\ =2^{\frac{3}{4}}\cdot2^{-\frac{1}{2}}=2^{\frac{3}{4}-\frac{1}{2}}=2^{\frac{1}{4}} \end{gathered}[/tex]And this last result is equal to
[tex]\begin{gathered} 2^{\frac{1}{4}}=\sqrt[4]{2} \\ \Rightarrow\frac{2^{\frac{3}{4}}}{2^{\frac{1}{2}}}=\sqrt[4]{2} \end{gathered}[/tex]what is y = -5/2 - 4 in standard form?
Answers
The slope-intercept form of the equation of a line is:
y = mx + c
where m is the slope
and c is the y-intercept
The given equation is:
[tex]y\text{ = -}\frac{5}{2}x\text{ - 4}[/tex]Comparing the given equation with y = mx + c:
The slope, m = -5/2
The equation perpendicular to y = mx + c and passing through the point (x₁, y₁) is given by the equation:
[tex]\text{y - y}_1=\frac{-1}{m}(x-x_1)[/tex]Since m = -5/2
-1/m = 2/5
The line passes through the point (5, 4)
x₁ = 5, y₁ = 4
The equation becomes:
[tex]\begin{gathered} y\text{ - 4 = }\frac{2}{5}(x\text{ - 5)} \\ y\text{ - 4 = }\frac{2}{5}x\text{ - 2} \\ \text{y = }\frac{2}{5}x\text{ - 2 + 4} \\ y=\frac{2}{5}x\text{ + 2} \end{gathered}[/tex]Alondra bought a $1,700 television on an installment plan. The installment agreement included a
$170 down payment and 18 monthly payments of $105 each. What is the total finance charge?
Answers
The total finance charge is $360.
Given:
Alondra bought a $1,700 television on an installment plan.
The installment agreement included a $170 down payment and 18 monthly payments of $105 each.
Total amount paid = down payment + payment of each month * number of months.
= 170 + 105 * 18
= 170 + 1890
Total amount paid = $2060
Total finance charge = total amount paid - $1700
= $2060 - $1700
= $360.
Therefore the total finance charge is $360.
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part (a) Solve for x: 1 /x − 1 /x + 1 = 3.
part (b) Solve for t: 2 = Square root √ (1 + t) power of 2 + (1 − 2t) power of 2
part (c) Solve for t: 3/√5 = Square root √(1 + t) power of 2 + (1 − 2t)power of 2
part (d) Solve for t: 0 = Square root √ (1 + t)power of 2 + (1 − 2t)power of 2
Answers
The value of x in part (a) is [-3+√21]/6 and [-3-√21]/6, the value of t in part (b) is (1/5+√11/5) and (1/5-√11/10), the value of t in part (c) is 1/5 and the value of t in part (d) is 1/5-3/5i and 1/5+3/5i.
Part a. Solving for x,
1/x - 1/(x+1) = 3
(1-x+x)/x(x+1) = 3
1/(x²+x) = 3
1 = 3x²+3x
3x²+3x-1=0
Solving the quadratic by using quadratic formula,
x = [-b±√(b²-4ac)]/2a
Here,
a = 3
b = 3
c = -1
Putting all the values,
x= [-3±√(3²-4(3)(-1)]/6
x = [-3±√21]/6
We get,
x = [-3+√21]/6 and
x = [-3-√21]/6
Part b. Solving for t;
2 =√[(1+t)²+(1-2t)²]
Squaring both sides,
4 = (1+t)²+(1-2t)²
4 = 1+t²+2t+1+4t²-4t
2 = 5t²-2t
5t²-2t-2=0
Solving the equation by using quadratic formula,
t= [-b±√(b²-4ac)]/2a
Here,
a = 5
b = -2
c = -2
Putting all the values,
t = [2±√(4-4(5)(-2))]/10
t = [2±√44]/10
We get
t = (1/5+√11/5) and (1/5-√11/10)
Part c. Solving for t;
3/√5 = √[(1 + t)² + (1 − 2t)²]
Squaring both sides,
9/5 = (1+t)²+(1-2t)²
9/5 = 1+t²+2t+1+4t²-4t
9 = 5+5t²+10t+5+20t²-20t
25t²-10t+1=0
t = [-b±√(b²-4ac)]/2a
Here,
a = 25
b = -10
c = 1
Putting all the values,
t = [10±√(100-4(25))]/50
t= [10±0]/50
t= 1/5
Part d. Solving for t;
0 = √[(1 + t)²+(1 − 2t)²]
Squaring both sides,
(1+t)² =-(1-2t)²
1+t²+2t = -(1+4t²-4t)
1+t²+2t = -1-4t²+4t
5t²-2t+2=0
Solving the equation by using quadratic formula,
t = [-b±√(b²-4ac)]/2a
Here,
a = 5
b = -2
c = 2
Putting all the values,
t = [2±√(4-4(5)(-2)]/10
t = [2±√(-36)]/10
t = [2±6√(-1)]/10
√-1 is 'iota' or i.
t = (2±6i)/10
We get,
t = 1/5-3/5i and 1/5+3/5i
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You deposit $3000 each year into an account earning 8% interest compounded annually. How much will youhave in the account in 20 years?
Answers
The rule of the compounded interest is
[tex]A=P\frac{\lbrack(1+\frac{r}{n})^{nt}-1\rbrack}{\frac{r}{n}}[/tex]A is the final amount
P is the amount each year
r is the interest rate in decimal
t is the time
n is the number of periods per year
Since you deposit $3000 each year, then
P = 3000
Since the annual rate is 8%, then
r = 8/100 = 0.08
n = 1
Since the time is 20 years, then
t = 20
Substitute them in the rule above to find A
[tex]\begin{gathered} A=\frac{3000\lbrack(1+\frac{0.08}{1})^{1(20)}-1\rbrack}{\frac{0.08}{1}} \\ A=\frac{3000\lbrack(1.08)^{20}-1\rbrack}{0.08} \\ A=137285.8929 \end{gathered}[/tex]You will earn $137 285.8929 after 20 years
F(x)=x+2 g(x)=x-4 (f g)(x)=
Answers
Given functions are:
[tex]\begin{gathered} f(x)=x+2 \\ g(x)=x-4 \end{gathered}[/tex]So:
[tex]\begin{gathered} f(x)\times g(x)=(x+2)(x-4) \\ f(x)\times g(x)=x^2-4x+2x-8 \\ f(x)\times g(x)=x^2-2x-8 \end{gathered}[/tex]grgrgrgrggrdfb rgedg ee
Answers
The history museum charges a $10 fee plus $15 per student for a field trip.
The aquarium charges a $20 fee plus $10 per student. The lines in the graph
represent the cost of each field trip,
For what number of students will the total cost of each field trip be the same,
and what will that cost be?
O A. 120 students: $10
O B. 2 students: $40
O G. 40 students: $2
OD. 10 students: $120
Need help fast
Answers
Method 1
Write an equation for the total cost for each trip.
The history museum
Let the number of students = n
Total cost = 10 + 15n
The aquarium
Let the number of students = n
Total cost = 20 + 10n
Next, equate the two equations to find what number of students will the total cost of each field trip be the same.
[tex]\begin{gathered} 10\text{ + 15n = 20 + 10n} \\ 15n\text{ - 10n = 20 - 10} \\ 5n\text{ = 10} \\ n\text{ = }\frac{10}{5} \\ n\text{ = 2} \end{gathered}[/tex]The number of students = 2
The cost = 20 + 10(2) = 20 + 20 = $40
Answer
2 studnets; $40
Method 2:
To find number of students will the total cost of each field trip be the same.
From the graph, look for the point where the two graphs intercept.
Read the number of students as 2 and the cost as $40
Final answer
2 studnets; $40 Option B
What matrix results from B+ A?
Enter your answer by filling in the boxes.
Answers
Answer:
[tex]\begin{bmatrix}6 & -5\\-5 & 1\\13 & 6\\-15 & -9\\\end{bmatrix}[/tex]
======================================================
Explanation:
In the top left corner of matrix B is the value 7
For matrix A, the top left corner is -1
The values add to 7+(-1) = 6 which is the result in the top left corner box of the answer matrix.
Add the other corresponding values the same way.
As you can see, the two matrices must be the same size in order to add them. They must have the same number of rows, and the same number of columns.
Matrix addition is commutative allowing us to write B+A = A+B
This probability distribution shows thetypical grade distribution for a Geometrycourse with 35 students.GradeАBсDFFrequency 5101532Using the frequencies given, find theprobability that a student earns a grade of A.p = [?]
Answers
Probability is expressed as
number of favourable outcomes/total number of possible outcomes
Looking at the given scenario, the number os students that earned a grade of A is 5. Since we are concerned with these students, then, the number of favourable outcomes is 5.
The total number of students for all grades is 35. This means that the total number of possible outcomes is 35
Thus, the probability that a student earns a grade of A is
5/35
= 0.14
The solution of a quadratic equation are called it’s ____1- x-intercepts2- zeros 3- roots4- all of the above
Answers
ANSWER
All of the above.
EXPLANATION
The solutions to a quadratic equation are the points where the graph of the equation touches the x-axis of the coordinate grid. This is why the solutions are called x-intercepts.
When solving for the solutions of a quadratic equation, the equation is equated to 0. This is why the solutions to a quadratic equation are called zeros of the equation or roots of the equation.
Hence, the correct option is All of the above.
Chloe makes flapjacks.
A pack of flapjacks costs Chloe 60p to make.
She sells the flapjacks for a profit of 30%.
For how much does Chloe sell a pack of flapjacks?
Answers
Answer: 78p
Step-by-step explanation:
If she sells them with a profit of 30%, this means she is getting 30% more than they cost to make. They cost 60p, so we will set up an equation. Don't forget that a percent divided by 100 becomes a decimal.
60p * 130% = 60p * 1.3 = 78p
(30/100)*60 = (30*60)/100 = 18
Susana is enrolled in a photography class and has been Complete each statement.
pricing entry-level DSLR cameras. The prices are
Normally distributed.
Use the z-table to answer the question.
w
88%
-2 -1
Z-score
1 2 3
The Z-score of about
tells us that 88% of
the observations in the distribution are at or below
standard deviations above the mean.
The Z-score of about
tells us that 12%
of the observations in the distribution are at or below
standard deviations below the mean.
Answers
Answer:
Step-by-step explanation:
1.175
1.175
-1.175
1.175
First find the closest values possible to 0.88 (88%) on the z-score table. Once found we can see that it is located at positive 1.1 and directly in-between .07 and .08. Therefore we take the half of the two, .075, and get the answer of 1.175. The positive z-score, 1.175, tells us that we are 1.175 standard deviations above the mean.
Second find the closest values possible to 0.12 (12%) on the z-score table. We find it at -1.1 and perfectly in-between .07 and .08. We repeat the same steps as before and get -1.175. The negative z-score, -1.175, tells us the we are 1.175 standard deviations below the mean.
Answer:
The z-score of about
✔ 1.175
tells us that 88% of the observations in the distribution are at or below
✔ 1.175
standard deviations above the mean.
The z-score of about
✔ –1.175
tells us that 12% of the observations in the distribution are at or below
✔ 1.175
standard deviations below the mean.
Step-by-step explanation:
edge 2023
4. How many integers are in the solution set of the inequality x² - 10 ≤ 0?
(a)1
(b) 2
(c) 3
(d) 6
(e) 7
Answers
Answer: 7
Step-by-step explanation: There are an infinite number of integers that satisfy the inequality. There are only seven integers that don't satisfy the inequality which are -3, -2, -1, 0, 1, 2 and 3.
Out of Retries Correct Answer Show Enter an estimate. Round each mixed number to the nearest whole in your estimate. 1 WIN Estimate: 0 Find the difference and enter it in simplest form. 3
Answers
The mixed fraction are simplify as :
[tex]a\frac{b}{c}=\frac{(a\times c)+b}{c}[/tex]The given expression is :
[tex]5\frac{1}{4}-3\frac{8}{9}[/tex]Simplify the mixed fraction:
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9} \\ 5\frac{1}{4}-3\frac{8}{9}=\frac{(5\times4)+1}{4}-\frac{(3\times9)+8}{9} \\ 5\frac{1}{4}-3\frac{8}{9}=\frac{21}{4}-\frac{35}{3} \end{gathered}[/tex]LCM of ( 4 & 3 ) is 12 So,
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9}=\frac{21}{4}-\frac{35}{3} \\ 5\frac{1}{4}-3\frac{8}{9}=5.25-11.6667 \\ 5\frac{1}{4}-3\frac{8}{9}=5-11 \\ 5\frac{1}{4}-3\frac{8}{9}=-6 \end{gathered}[/tex]Answer :
a)
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9}\text{ can be express as :} \\ \text{Estimate : 5 - 11 =- 6} \end{gathered}[/tex]b)
Diffreence is :
[tex]\text{ 5}\frac{1}{4}\text{ - 3}\frac{8}{9}\text{ = }-6[/tex]
Work out a)4/5-1/5 b)9/11+5/11 c)3/4+1/8
Answers
The solutions are:
a) 3/5
b) 14/11
c) 7/8
What are the steps of adding and subtracting fractions?The steps for adding and subtracting fractions are as follows:
Step 1: Match the denominators.
Step 2: Add and subtract the numerators.
Step 3: Make the fraction simpler.
Fractions with different denominators can be added or subtracted by using Least Common Multiple(LCM) to convert them to like fractions.
a) 4/5 - 1/5
The denominators of the fractions are the same so we have to just subtract the numerators.
= (4 - 1)/5
= 3/5
b) 9/11 + 5/11
Similarly, the denominators of these fractions are also equal so we have to just add the numerators.
= (9 + 5)/11
= 14/11
c) 3/4 + 1/8
First, we find the Least Common Multiple (LCM) of the denominators to convert them into like denominators and then add the respective numerators.
LCM of 4 and 8 = 8
= [tex]\frac{6+1}{8}[/tex] = 7/8
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This is the problem I am having.
Answers
Answer:
Can you send a better picture please thanks.
Step-by-step explanation:
The graph shown below expresses a radical function that can be written in the form f(x) = a(x+k)lin+c. What does the graph tell you about the value of k in this function? 1 1 15 1 1 1 1 1 1 1 1 1 1 1: 18 4 A kis greater than zero. B. It is not possible to tell whether kis greater than or less than zero. c. kis less than zero. D. kequals zero.
Answers
Given,
The function of the graph is,
[tex]undefined[/tex]For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.
Answers
Given the function (f + g) (x) as
[tex]4x^2+x-7[/tex]The domain of the function above is the set of x values except the for x- values that will make the function undefined
For the function above, the domain is defined at all set of real numbers and the interval notation is given as
[tex]-\inftyHence, the correct option is B06 WS Solving Systems of Equations and Inequalities Word Problems
Systems of Equations: Use two equations with two variables to solve each of the following problems.
(1) The sum of two numbers is 51 and their difference is 13. Find the two numbers.
som of
One Saturday the theat
Answers
The two numbers are 19 and 32 respectively.
What is equation?
Equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
According to question, let x and y be two numbers
x + y = 51 and
x- y = 13
from equation two,
x = 13+y
put this in equation one,
y+13+y = 51
2y = 51 - 13
2y = 38
y = 38/2 = 19
x = 13+y
x = 13+19
x = 32
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An insurance agent estimates that it takes 2/3 of an hour to
process a customer's claim. If the agent spends 22 hours per
week processing claims, about how many claims does he
process in a week?
Answers
DATA ANALYSES AND STATISTICSUnderstanding likelihoodThere are two boxes containing only blue and purple pens.Box A has 6 purple pens and 2 blue pens.Box B has 12 purple pens and 8 blue pens,A pen is randomly chosen from each box,List these events from least likely to most likelyEvent 1: choosing a purple or blue pen from Box B.Event 2: choosing a blue pen from Box B.Event 3: choosing a red pen from Box A.Event 4: choosing a purple pen from Box A.Least likelyMost likelyEvent ). Event | Event | .Event
Answers
Answer
Event 3, Event 2, Event 4, Event 1.
Explanation
Given data:
Box A has 6 purple pens and 2 blue pens.
Box B has 12 purple pens and 8 blue pens.
Let X represents purple, Y represents blue, and Z represents red.
Box A: n(X) = 6, n(Y) = 2, and n(Z) = 0. Hence, n(S) = 6 + 2 + 0 = 8
Box B: n(X) = 12, n(Y) = 8, and n(Z) = 0. Hence, n(S) = 12 + 8 + 0 = 20
So if a pen is randomly chosen from each box, the probability of:
Event 1: choosing a purple or blue pen from Box B. will be:
[tex]\begin{gathered} p(X\text{ or Y})=p(X)+p(Y)=\frac{n(X)}{n(S)}+\frac{n(Y)}{n(S)}=\frac{12}{20}+\frac{8}{20}=\frac{12+8}{20}=\frac{20}{20}=1 \\ \end{gathered}[/tex]Event 2: choosing a blue pen from Box B will be:
[tex]p(Y)=\frac{8}{20}=\frac{1}{5}=0.4[/tex]Event 3: choosing a red pen from Box A will be:
[tex]p(Z)=\frac{n(Z)}{n(S)}=\frac{0}{8}=0[/tex]Event 4: choosing a purple pen from Box A wil be:
[tex]p(X)=\frac{n(X)}{n(S)}=\frac{6}{8}=\frac{3}{4}=0.75[/tex]If a pen is randomly chosen from each box, the list of the events from least likely to most likely are:
Event 3, Event 2, Event 4, Event 1.