Retest: ProbabilityFor problems 1-3: Johnny Awesome has three red marbles, two blue marbles, five green marbles, and 7 yellowmarbles in a bag. What is the probability that'Johnny.....3) draws a blue marble, does not replace it, and then draws a green marble?
Answers
Answer
5/136
Step-by-step explanation
Events
• A: a blue marble is drawn
,• B: without replacing the first marble, a green marble is drawn
There are 17 (= 3 + 2 + 5 + 7) marbles in total in the bag. Two of them are blue, then the probability of drawing a blue marble is:
[tex]P(A)=\frac{2}{17}[/tex]After a blue marble is drawn, 16 marbles are left in the bag. Five of them are green, then the probability of drawing a green marble is:
[tex]P(B)=\frac{5}{16}[/tex]Finally, the probability of drawing a blue marble and then a green marble without replacement is:
[tex]\begin{gathered} P(A\text{ and }B)=P(A)\cdot P(B) \\ P(A\text{ and }B)=\frac{2}{17}\cdot\frac{5}{16} \\ P(A\text{ and }B)=\frac{5}{136} \end{gathered}[/tex]Related Questions
Help 20 points (show ur work)
There are 2 questions
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The length of the trail is equal to 3mi and the selling price of the item is equal to $120.
RatioIn mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.
In this question, we have to use the ratio given to determine the length of the trail.
Given that the ratio is 5in : 2mi, we have to convert the values to uniform units.
[tex]1mi = 63360in\\2mi = x\\x = 126720[/tex]
The ratio is now 5in : 126720in
Given that on the map, the length is 7.5in
[tex]5 = 126720\\7.5 = x\\x = 190080in[/tex]
Let's convert this into mi.
[tex]190080in = 3mi[/tex]
The actual length of the trail is 3in.
b)
To find the selling price of the item, let's use the percentage given to do that.
discount = 40%actual price = $200We can find 40% of 200 and then subtract the value from 200.
[tex]40\% of 200 = 0.4 * 200 = 80[/tex]
The discount price is $80 and we can find the selling price here.
[tex]selling price = actual price - discount price\\selling price = 200 - 80\\selling price = 120[/tex]
The selling price of the item is $120
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Given the parametric equations x = 7cos θ and y = 5sin θ, which of the following represents the curve and its orientation?
Answers
We have the following parameters
[tex]\begin{gathered} x=7cos\theta \\ y=5sin\theta \end{gathered}[/tex]the general equation of a circle with center (0,0) is the following,
[tex]x^2+y^2=r^2[/tex]Let's use the following tigonometric identity,
[tex]sin^2\theta+cos^2\theta=1[/tex]solving for cos and sin in the equations we are given,
[tex]cos\theta=\frac{x}{7},sin\theta=\frac{y}{5}[/tex]replace,
[tex](\frac{y}{5})^2+(\frac{x}{7})^2=1[/tex]Since we have two different numbers in the denominator, this is not a circle equation but an elipse, of the form,
[tex]\frac{y^2}{a^2}+\frac{x^2}{b^2}=1[/tex]where,
a is the vertex and,
b is the covertex
thus, in the x axis, the vertex is 7 and the y-axis the covertex is 5
Now, let's determine the direction by replacing
when Θ = 0 , then x = 7*cos0 = 7*1 = 7 , and y = 5*sin0 = 5*0 = 0
when Θ = 90° or π/2 , then x = 7*cos90° = 7*0 = 0 , and y = 5sin90° = 5*1 = 5
If we draw this, we can see that the direction is counterclockwise as in the bottom right image.
How many times in the parabola does a line intersect?
Answers
The line can intersect the parabola at one or two points.
See the example below.
The black line intersects the parabola at (1, -1)
The blue line intersects the parabola at two points: (0, 0) and (4, 8).
suppose s is between r and t use the segment addition postulate to solve for each variable RS equals 2z plus 6 St equals 4z - 3 RT = 5z + 12
Answers
If s is between r and t, then:
RS + ST = RT
Where RS = 2z + 6
ST = 4z - 3
RT = 5z + 12
So, we get:
(2z + 6) + (4z - 3) = 5z + 12
Solving for z, we get:
2z + 6 + 4z - 3 = 5z + 12
6z + 3 = 5z + 12
6z + 3 - 5z = 12
z + 3 = 12
z = 12 - 3
z = 9
Answer: z = 9
I need help question
Answers
Solution
- The first integral is bounded by the x-values of [6, 22]
- The second integral is bounded by the x-values of [6, 14]
- When we are asked to find the difference between the two integrals, since, they both begin at 6, it implies that, when the second integral is taken away from the first integral, there must be some extra x-values.
- The extra values are from 14 to 22.
- Thus, we have:
[tex]\int_6^{22}f(x)-\int_6^{14}f(x)=\int_{14}^{22}f(x)[/tex]Final Answer
[tex]\begin{gathered} b=22 \\ a=14 \end{gathered}[/tex]Tell whether the sequence is arithmetic. If it is what is the common difference? Explain.
{1, 5, 9, 13, …}
Answers
The sequence is arithmetic because the common difference is 4.
Answer:
the sequence is arithmetic. the cd is 4
Step-by-step explanation:
1 + 4 = 5
5 + 4 = 9
9 + 4 = 13
In ACDE, m/C= (5x+18), m/D= (3x+2), and m/B= (2+16)°.
Answers
Angle (D) = m(D) = 50°, CDE provides the following: 3. angles
m=C=(5x+18), m=D=(3x+2), and m=E=(x+16)°.The total of the angles in a triangle is 180°What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.CDE provides the following: 3. angles
m<C=(5x+18),m<D=(3x+2), andm<E=(x+16)degree.The total of the angles in a triangle is 180 degrees, so:
"mC + mD + mE = 180°"(5x+18)° + (3x+2)° + (x+16)° = 180°5x + 18 + 3x + 2 + x + 16 = 180°5x + 3x + x + 18 + 2 + 16 = 180°9x +36= 180°From both sides, deduct 36 as follows:
9x + 36 - 36 = 180° - 36°9x = 144°x = 144°/9x = 16From the aforementioned query, we are requested to determine:
angular D (m<D)Hence:
m∠D=(3x+2)°m∠D=( 3 × 16 + 2)°m∠D=(48 + 2)°m∠D= 50°Therefore, angle (D) = m(D) = 50°, CDE provides the following: 3. angles
m=C=(5x+18), m=D=(3x+2), and m=E=(x+16)°.The total of the angles in a triangle is 180°To learn more about angles, refer to:
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Solve each equation for the variable. h/2 + 3.5 = 7.1
Answers
To answer this question, we can proceed as follows:
[tex]\frac{h}{2}+3.5=7.1[/tex]1. Subtract 3.5 to both sides of the equation:
[tex]\frac{h}{2}+3.5-3.5=7.1-3.5\Rightarrow\frac{h}{2}+0=3.6[/tex]2. Multiply by 2 to both sides of the equation:
[tex]2\cdot\frac{h}{2}=2\cdot3.6\Rightarrow h=7.2[/tex]We can check this result as follows:
[tex]\frac{7.2}{2}+3.5=3.6+3.5=7.1\Rightarrow7.1=7.1[/tex]This result is TRUE. Then, the value for h = 7.2.
4. A bookstore owner ordered 4032 books. The books were sent in 9 boxes. Each box hadthe same number of books. How many books were in each box?
Answers
448 books in each box
Number of books: 4032
Number of boxes: 9
Since each box had the same number of books, divide the number of books by the number of boxes.
4032/9 = 448
Solve each system of equations algebraically.[tex]y = {x}^{2} + 4 \\ y = 2x + 7[/tex]
Answers
From the problem, we two equations :
[tex]\begin{gathered} y=x^2+4 \\ y=2x+7 \end{gathered}[/tex]Since both equation are defined as y in terms of x, we can equate both equations.
[tex]\begin{gathered} y=y \\ x^2+4=2x+7^{} \end{gathered}[/tex]Simplify and solve for x :
[tex]\begin{gathered} x^2+4=2x+7 \\ x^2-2x+4-7=0 \\ x^2-2x-3=0 \end{gathered}[/tex]Factor completely :
[tex]\begin{gathered} x^2-2x-3=0 \\ (x-3)(x+1)=0 \end{gathered}[/tex]Equate both factors to 0 then solve for x :
x - 3 = 0
x = 3
x + 1 = 0
x = -1
We have two values of x, x = 3 and -1
Substitute x = 3 and -1 to any of the equation, let's say equation 2 :
For x = 3
y = 2x + 7
y = 2(3) + 7
y = 6 + 7
y = 13
One solution is (3, 13)
For x = -1
y = 2x + 7
y = 2(-1) + 7
y = -2 + 7
y = 5
The other solution is (-1, 5)
The answers are (3, 13) and (-1, 5)
A line passes through the point −6, 3 and has a slope of 32 .Write an equation in slope-intercept form for this line.
Answers
The equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195.
What is the slope - intercept form of the equation of a straight line?
The slope - intercept form of the equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line that passes through the point (−6, 3) and has a slope of 32.
We know that the slope - intercept form can be written as -
y = mx + c
Now, the slope of the line = [m] = 32
Since, the line passes through the point (-6, 3), we can write -
3 = 32 x -6 + c
3 = -192 + c
c = 3 + 192
c = 195
So, the equation of the straight line that passes through the point (-6, 3) will be -
y = 32x + 195
Therefore, the equation of the straight line that passes through the point (-6, 3) will be y = 32x + 195
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find the measures of GH and CH.
Answers
The length of the lines GH and CH are 16 units and 12 units.
What is a line?A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. The term "line" can also be used to describe a line segment in daily life that has two points that serve as its ends. In geometry, lines are drawn with arrows at either end to indicate that they extend indefinitely. Two line points can be used to name a line (for example, AB) or just a letter, usually in lowercase (for example, line m ). The ends of a line segment are two.So, the measure of lines GH and CH:
We know that AC ⊥ GH hence cuts GH in two equal lines.
GB = BH GB is 8 units then BH is also 8 units.GB = BH = 8 units.But,
GH = GB + BHGH = 8 + 8GH = 16 unitsWe can observe that △GCH is an isosceles triangle.
GC = CHGC = CH = 12 unitsTherefore, the length of the lines GH and CH is 16 units and 12 units.
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Miscavage Corporation has two divisions: the Beta Division and the Alpha Division.
The Beta Division has:
sales of $320,000,
variable expenses of $158,100,
and traceable fixed expenses of $72,300.
The Alpha Division has:
sales of $630,000,
variable expenses of $343,800,
and traceable fixed expenses of $135,100.
The total amount of common fixed expenses not traceable to the individual divisions is $137,200.
What is the total company's net operating income?
Answers
The total net operating income (NOI) of both divisions is $1,03,500.
What is net operating income?Real estate professionals use the formula known as Net Operating Income, or NOI, to quickly determine the profitability of a specific investment. After deducting required operating costs, NOI calculates the revenue and profitability of investment real estate property. Let's say, for illustration purposes, that you own a duplex with a gross monthly income of $2,000 and monthly operating expenses of $400. You would start with your annual gross income ($24,000) and deduct your operating expenses ($4,800) to arrive at your net operating income.So, the total net operating income:
The formula for net operating income: NOI = Gross Income - Operating ExpensesNow, substitute the values and get the NOI as follows:
NOI = Gross Income - Operating ExpensesNOI = (Sales+Sales) - [(variable expenses + variable expenses) + (fixed expenses + fixed expenses) + 137,200] NOI = (320,000+630,000) - [(158,100 + 343,800) + (72,300 + 135,100) + 137,200]NOI = 9,50,000 - (5,01,900 + 2,07,400 + 137,200)NOI = 9,50,000 - 8,46,500NOI = 1,03,500Therefore, the total net operating income (NOI) of both divisions is $1,03,500.
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polynomials - diving polynomialssimplify the following expression with divisionbare minimum of steps
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HELP PLEASEEEEE!!!!!!
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The rational number is -91/100 or -0.91.
What is Rational number?Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.
The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
Given:
We have to find the rational number between -1/3 and -1/2
Tale LCM for 3 and 2 = 6
-1/3 x 2/2 and -1/2 x 3/3
-2/6 and -3/6
Now, multiply 10
-2/6 x 10/10 and -3/6 x 10/10
-20/60 and -30/60.
Hence, the rational number is -21/60.
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write the following basic forms in their single form
2√3
Answers
The expression which represents the written form of the basic form expression; 2√3 as a single form is; √12.
What is the single form expression which is equivalent to the basic form expression; 2√3?It follows from the task content that the basic form expression be written as it's equivalent single form expression.
Since the given radical expression is; 2√3; it follows that the expression can be written as a single form expression as follows;
First, the square of 2, 2² is equal to 4;
Hence, by the converse;
2 = √4.
The given expression can therefore be written as; √4 • √3.
The expression above can therefore be written in its single form as; √(4 × 3) = √12.
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Write an equation and solve to find the value of your variable. 7.3 less than -2 times a number is the same as 16 1/2. n=?
Answers
The equation is -2n - 7.3 = 16 1/2
The value of the variable n = -11.9
STEP - BY - STEP EXPLANATION
What to find?
• Write the equation of the given statement.
,• The value of n.
Given:
find the value of your variable. 7.3 less than -2 times a number is the same as 16 1/2. n=?
To solve follow the steps below:
Step 1
Translate the given statement into equation.
Let n be the number.
-2n - 7.3 = 16 1/2
Step 2
Convert 16 1/2 to decimal.
-2n - 7.3 = 16.5
Step 3
Add 7.3 to both-side of the equation.
-2n = 16.5 + 7.3
Step 4
Simplify the right-hand side of the equation.
-2n =23.8
Step 5
Divide both-side of the equation by -2.
[tex]\frac{\cancel{-2}n}{\cancel{-2}}=\frac{23.8}{-2}[/tex]n = -11.9
Therefore, the value of the variable n = -11.9
solve using the quadratic formulax^2+2x-17=0
Answers
A boutique in Lanberry specializes in leather goods for men. Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This month, they sold 94 wallets and 22 belts, for a total of $3,230. How much does the boutique charge for each item?
Answers
Let w represent the cost of each wallet.
Let b represent the cost of each belt.
Last month, the company sold 56 wallets and 63 belts, for a total of $3,920. This means that
56w + 63b = 3920
This month, they sold 94 wallets and 22 belts, for a total of $3,230. This means that
94w + 22b = 3230
We would solve the equations by applying the method of elimination. To eliminate w, we would multiply the first equation by 94 and the second equation by 56. The new equations would be
5264w + 5922b = 368480
5264w + 1232b = 180880
Subtracting the second equation from the first, we have
5264w - 5264w + 5922b - 1232b = 368480 - 180880
4690b = 187600
b = 187600/4690
b = 40
Substituting b = 40 into 56w + 63b = 3920, we have
56w + 63(40) = 3920
56w + 2520 = 3920
56w = 3920 - 2520 = 1400
w = 1400/56
w = 25
Thus, the boutique charges $25 for each wallet and $40 for each belt
Lesson 6.07: In a random sample of 74 homeowners in a city, 22 homeowners said they wouldsupport a ban on nonnatural lawn fertilizers to protect fish in the local waterways. The samplingmethod had a margin of error of +3.1%. SHOW ALL WORK!A) Find the point estimate.B) Find the lower and upper limits and state the interval.
Answers
Confidence interval is written in the form,
(point estimate +/- margin of error)
The given scenario involves population proportion
The formula for the point estimate is
p' = x/n
where
p' = estimated proportion of success. p' is a point estimate for p which is the true proportion
x represents the number of success
n represents the number of samples
From the information given,
n = 74
x = 22
p' = 22/74 = 0.297
The formula for finding margin of error is expressed as
[tex]\begin{gathered} \text{margin of error = z}_{\frac{\alpha}{2}}(\sqrt[]{\frac{p^{\prime}q^{\prime}}{n}} \\ q^{\prime}\text{ = 1 - p'} \\ q^{\prime}\text{ = 1 - 0.297 = 0.703} \end{gathered}[/tex]A) The point estimate is 0.297
B) margin of error = +/-3.1% = 3.1/100 = +/- 0.031
Thus,
the lower limit would be 0.297 - 0.031 = 0.266
Expressing in percentage, it is 0.266 x 100 = 26.6%
the upper limit would be 0.297 + 0.031 = 0.328
Expressing in percentage, it is 0.328 x 100 = 32.8%
Thus, the confidence interval is between 26.6% and 32.8%
Monica did an experiment to compare two methods of warming an object. The results are shown in thetable below. Which statement best describes her results?
Answers
The correct answer is,
The temperature using method 2 changed exponentially.
A committee must be formed with 4 teachers and 4 students. If there are 7 teachers to choose from, and 9 students, how many different ways could the committee be made?
Answers
ANSWER
4,410
EXPLANATION
The number of ways we can choose 4 teachers from 7 teachers is,
[tex]_7C_4=\frac{7!}{(7-4)!\times4!}=\frac{7\times6\times5\times4!}{3!\times4!}=\frac{7\times6\times5}{3\times2}=\frac{7\times6\times5}{6}=7\times5=35[/tex]There are 35 ways of choosing 4 teachers out of 7.
And the number of ways we can choose 4 students from 9 students is,
[tex]\begin{gathered} _9C_4=\frac{9!}{(9-4)!\times4!}=\frac{9\times8\times7\times6\times5\times4!}{5!\times4!}=\frac{9\times8\times7\times6\times5}{5\times4\times3\times2} \\ _9C_4=\frac{9\times8\times7}{4}=\frac{9\times(2\times4)\times7}{4}=9\times7\times2=126 \end{gathered}[/tex]There are 126 ways of choosing 4 students out of 9.
The committee is formed by 4 teachers and 4 students. The number of ways it can be made is,
[tex]_7C_4\times_9C_4=35\times126=4,410[/tex]Hence, there are 4,410 ways to choose 4 students and 4 teachers out of 9 students and 7 teachers.
a construction company orders tile flooring for the kitchen in three bathrooms of a new home the kitchen floor measures 48 square feet 2 bathrooms have floor that each Measure 30 and 1/2 square feet the third bathroom floor measures 42 1/2 square feet if the tile cost 2.39 per square foot what is that the least amount of money to the nearest cent the company spends on tile for all three bathrooms
Answers
We are not concerned with the tiles needed for the kitchen.
From the given information, there are two bathroom floors with the same measurement in terms of area. The area of each floor is 30.5 square feet
Area of both bathroom floors = 30.5*2 = 61 square feet
Area of the third bathroom = 42.5 square feet
Area of the three bathroom floors = 61 + 42.5 = 103.5 square feet
Given that the tile costs 2.39 per sqare foot, the least amount of money that the company would spend for all three tiles is
103.5 * 2.39 = 247.365
Rounding up to the nearest cent means rounding up to the nearest hundredth or 2 decimal places
Rounding up to the nearest cent, it becomes 247.37
X 즈 - + 3 = 15 -4someone help me confused
Answers
First we have to transfer the number 3 the other side of equal sign as follows,
[tex]\begin{gathered} \frac{x}{-4}=15-3 \\ \frac{x}{-4}=12 \end{gathered}[/tex]Now, we need to transfer (-4) to the other side of the equal side by multiplying with the number 12.
[tex]\begin{gathered} \frac{x}{-4}=12 \\ x=12\ast(-4) \\ x=-48 \end{gathered}[/tex]Thus, the answer of the x is (-48).
solve the following d. be sure to take into account whether a letter is capitalized or not .3y^3 ×m=5Qd
Answers
Step 1: Write out the equation.
[tex]3g^3+m=5Qd[/tex]Step 2: Divide both sides of the equation by 5Q, we have
[tex]\frac{3g^3+m}{5Q}=\frac{5Qd}{5Q}[/tex]this implies that
[tex]d=\frac{3g^3+m}{5Q}[/tex]Red Tickets: 50 tickets for $37.50A sign at the fair advertises ticket prices for the carnival games,Blue Tickets: 20 tickets for $16.00Yellow Tickets: 5 tickets for $5.00Find the price per ticket for each:Red ticketBlue Ticket:Yellow Ticket:How much would 40 red tickets costs?123456 7 10
Answers
The price per ticket can be calculated as follows;
[tex]\begin{gathered} \operatorname{Re}d=\frac{\text{Price}}{No\text{ of tickets}} \\ \operatorname{Re}d=\frac{37.50}{50} \\ \operatorname{Re}d=0.75 \\ \text{Blue}=\frac{16}{20} \\ \text{Blue}=0.8 \\ \text{Yellow}=\frac{5}{5} \\ \text{Yellow}=1.00 \end{gathered}[/tex]The price per ticket for each is given as;
Red tickets = $0.75
Blue tickets = $0.80
Yellow tickets = $1.00
Therefore, 40 red tickets would cost
40 Red = 0.75 x 40
40 Red tickets = $30.00
Question 1-3
The distance traveled by car, for a duration of time, can be modeled with the equation s= 45t, where s is the distance, in miles, and it is
the time, in hours. Which graph represents this proportional relationship correctly?
120
105
90
Distance (mi)
Distance (mi)
75
60
45
120
30
105
90
15
75
60
45
30
0
15
2
Time (hr)
Time (hr)
100
lon
3
+X
X
120
105
90
Distance (mi)
75
60
45
30
15
0
1
2
Time (hr)
co
X
Answers
The equation s = 45t, where s is the distance in miles and it is the time in hours, can be used to simulate the distance driven by a car over a period of time then the car will travel 135 hours in 3 hours.
What is meant by the constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
Given: The distance traveled by car at a constant rate is proportional to the time spent driving.
In the equation d = 45 t, d denotes the distance (in miles) and t denotes the time (in hours).
d / t = 45 miles per hour
The constant of proportionality = 45 miles per hour.
Also, the distance traveled by car in 1 hour = 45 miles
The distance traveled by car in 3 hours = 3 × 45 = 135 miles
Therefore, a car will travel 135 hours in 3 hours.
The complete question is:
The distance traveled by car at a constant rate is proportional to the time spent driving. In equation d = 45t, d represents the distance (in miles) and t represents the time (in hours).
A. What is the constant of proportionality? _____ miles per hour
B. How far will the car travel in 3 hours? _______ miles
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Find the equation of the line parallel to the line y=-1, going through point (-5,4)
Answers
In this problem, want to find the equation of a line that will be parallel to a given function through a point.
Recall that parallel lines have the same slope.
We are given the line
[tex]y=-1[/tex]and the point
[tex](-5,4)[/tex]Notice that the equations is technically in slope-intercept form, by the value of the slope will be 0:
[tex]y=0x-1[/tex]Therefore, the slope of the line through (-5,4) will also be zero. We can use that information to find the equation.
Using the form
[tex]y=mx+b[/tex]we can substitute the point and the slope to solve for b:
[tex]\begin{gathered} 4=0(-5)+b \\ \\ 4=b \end{gathered}[/tex]So, the equation of our line is:
[tex]y=0x+4\text{ or }\boxed{y=4}[/tex]Find two unit vectors orthogonal to both j-k and i+j.
Answers
The two unit vectors orthogonal to both j-k and i+j are [tex]\frac{i}{\sqrt{3} }- \frac{j}{\sqrt{3} } -\frac{k}{\sqrt{3} }[/tex]
Let a bar = j- k = < 0,1,-1>
b bar = i+j = <1,1,0>
the cross product a x b bar is orthogonal to both a and b bar
= i ( 0-(-1) ) -j ( 0-(-1) ) + r (0-1)
= i-j-k
A unit vector is a vector whose length is 1 unit
There the unit vector is :
[tex]\frac{i-j-k}{\sqrt{1^2+(-1)^2+(-1)^2} } = \frac{i-j-k}{\sqrt{3} }[/tex]
= [tex]\frac{i}{\sqrt{3} }-\frac{j}{\sqrt{3} }-\frac{k}{\sqrt{3} }[/tex]
The second unit vector orthogonal to both a and b bar would be negative of the previous vector.
= [tex]-\frac{i}{\sqrt{3} }-\frac{j}{\sqrt{3} }-\frac{k}{\sqrt{3} }[/tex]
Hence the two unit vectors orthogonal to both j-k and i+j are [tex]\frac{i}{\sqrt{3} }- \frac{j}{\sqrt{3} } -\frac{k}{\sqrt{3} }[/tex]
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1: Are the two slopes parallel.
perpendicular or neither?
Answers
The slopes of two parallel lines are the same, while the slopes of two perpendicular lines are the opposite reciprocals of each other. Each line has infinitely many lines that are parallel to it and infinitely many lines that are perpendicular to it.
P.S hopes this helps
