Draw the triangle and label all parts.
Triangle ABC is a right triangle.
Angle A = 18 degrees
Angle B = 90 degrees
AC = 25 cm
Find AB. Do not label. Round your final answer to the nearest tenth.
Answers
The Length of side AB is approximately 72.4 cm.
To draw triangle ABC, we can start by drawing a straight line AB and then drawing a perpendicular line segment BC that meets AB at a 90-degree angle. This gives us a right triangle where angle B is 90 degrees. Finally, we can draw a line segment AC to connect points A and C, making sure that the length of AC is 25 cm since that is given in the problem.
To label the parts of the triangle, we can use the following conventions:
- Side AB is the hypotenuse of the right triangle and is opposite the right angle B.
- Angle A is opposite side AC, and angle C is opposite side BC.
Using this labeling convention, we can write:
- AB is the hypotenuse.
- AC is the side opposite angle A.
- BC is the side opposite angle C.
To find the length of AB, we can use the trigonometric ratio for the sine of angle A:
sin A = opposite / hypotenuse
sin 18 = AC / AB
Multiplying both sides by AB, we get:
AB * sin 18 = AC
Substituting the value of AC as 25 cm, we get:
AB * sin 18 = 25
Dividing both sides by sin 18, we get:
AB = 25 / sin 18
Using a calculator, we can evaluate this to get:
AB ≈ 72.4 cm (rounded to the nearest tenth)
Therefore, the length of side AB is approximately 72.4 cm.
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Related Questions
The midpoint of a segment is (4, 3) and one endpoint is (10, 8). Find the coordinates of the other endpoint
Answers
The coordinates of the other endpoint of the segment, given the midpoint (4, 3) and one endpoint (10, 8), are (-2, -2).
To find the coordinates of the other endpoint of a segment given its midpoint and one endpoint, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, we are given the midpoint as (4, 3) and one endpoint as (10, 8). Let's assume the coordinates of the other endpoint are (x, y).
Using the midpoint formula, we can set up the following equations:
((10 + x)/2, (8 + y)/2) = (4, 3)
From the first equation, we can solve for x:
(10 + x)/2 = 4
10 + x = 8
x = 8 - 10
x = -2
From the second equation, we can solve for y:
(8 + y)/2 = 3
8 + y = 6
y = 6 - 8
y = -2
Therefore, the coordinates of the other endpoint are (-2, -2).
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20. Graph the absolute value function f(x) = |x – 2| on the coordinate plane someone please answer showing work on how to do this problem
Answers
The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.
The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.
We have,
The absolute value function f(x) = |x – 2| is a piecewise function that returns the positive distance between the input value x and the number 2.
Geometrically,
It represents the distance of a point on the number line from point 2.
On the coordinate plane,
The graph of the absolute value function is V-shaped, with its vertex at the point (2, 0).
The two arms of the V extend indefinitely in opposite directions, passing through the points (-∞, 2) and (2, +∞) on the positive and negative sides of the x-axis, respectively.
Thus,
The absolute value function f(x) = |x – 2| takes a non-negative value for all real numbers x, and it returns 0 only when x = 2.
The graph of f(x) is symmetric about the vertical line x = 2 and has a vertical asymptote at x = 2.
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when we draw small and large samples from the same population, small samples group of answer choices produce a more peaked and narrower distribution. vary more from the population mean result in more degrees of freedom
Answers
When we draw small and large samples from the same population, small samples produce a more peaked and narrower distribution.
This phenomenon is due to the presence of fewer degrees of freedom associated with the small samples. Variations between sample and population mean result in fewer degrees of freedom, which results in a greater variation between samples and the population mean.
Degrees of freedom (df) is a statistical measure that quantifies the number of values in the final calculation of a statistic that are free to vary. When we sample data from a population, we calculate the sample mean, standard deviation, and other statistics
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A bank manager wishes to provide prompt service for customers at the bank's drive-up window. The bank currently can serve up to 10 customers per 15-minute period without significant delay. The mean arrival rate is 7 customers per 15-minute period. Let X denote the number of customers arriving per 15-minute period. Assume X has a Poisson distribution.
a. Find the probability that 10 customers will arrive in a particular 15-minute period.
b. Find the probability that 10 or fewer customers will arrive in a particular 15-minute period.
c. Find the probability that there will be a significant delay at the drive-up window. That is, find the likelihood that more than 10 customers will arrive during a particular 15-minute period.
Answers
To find the probability that 10 customers will arrive in a particular 15-minute period, we can use the Poisson distribution formula:
P(X = k) = (e^(-λ) * λ^k) / k!
Where λ is the mean arrival rate, which is 7 in this case, and k is the number of customers we're interested in, which is 10.
P(X = 10) = (e^(-7) * 7^10) / 10!
Calculating this expression will give us the probability that exactly 10 customers will arrive in a particular 15-minute period.
b. To find the probability that 10 or fewer customers will arrive in a particular 15-minute period, we need to sum up the probabilities of different arrival counts from 0 to 10.
P(X ≤ 10) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 10)
We can use the Poisson distribution formula for each value of k and sum them up to find the cumulative probability.
c. To find the probability of more than 10 customers arriving during a particular 15-minute period, we can calculate the complement of the probability of 10 or fewer customers.
P(X > 10) = 1 - P(X ≤ 10)
This will give us the probability of there being a significant delay at the drive-up window due to more than 10 customers arriving.
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Of the 95children in 6th grade 3/5 went to holiday parties how many students went to holiday parties in all?
Answers
Answer:
57
Step-by-step explanation:
95/5 x 3 = 57
Select all of the equations below in which q is inversely proportional to r.
q=r+4
q=4/r
q=r/4
q=4r
q=r-4
Answers
The equation that represents q being inversely proportional to r is:
q = 4/r
This is because when we say that q is inversely proportional to r, it means that as one variable increases, the other variable decreases in such a way that their product remains constant.
In this case, we can see that if we multiply q and r, we get a constant value of 4.
This is not true for the other equations, so they do not represent q being inversely proportional to r.
Therefore, the equation q = 4/r is the only one in the given options that represents q being inversely proportional to r.
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i need this now in 5 mins please
Answers
Answer:
6x + 9 + 13x - 95 = 180
19x - 86 = 180
19x = 266
x = 14
z = 6(14) + 9 = 84 + 9 = 93
to numerically summarize the center of the distribution of a quantitative variable we can use the
Answers
To numerically summarize the center of the distribution of a quantitative variable, we can use the measures of central tendency, which include the mean, median, and mode.
The mean is the sum of all the values divided by the number of values, and it is influenced by extreme values or outliers. The median is the middle value in a set of data when they are arranged in order, and it is not affected by outliers. The mode is the most frequent value in a set of data, and it is not always unique or well-defined. Each measure of central tendency has its advantages and disadvantages and should be chosen based on the characteristics of the data and the research question.
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Please answer as soon as possible!
The triangle ABC has its coordinates as shown below.
A:(3,3)
, B:(−2,−2)
, and C:(4,−4)
Triangle ABC is translated 2 units up, 3 units left and then dilated by a scale factor of 4 about the origin to form triangle A' B' C'. What are the coordinates of the vertex B' ? Enter your answer in the box below.
Answers
The coordinates of the vertex B' are (-20, 0).
What is a translation?In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image;
g(x) = f(x + N)
Based on the information provided about triangle ABC, we have the following translation:
(x, y) → (x - 3, y + 2)
Point B (-2, -2) → (-2 - 3, -2 + 2) = point B (-5, 0)
Next, we would dilate point B by a scale factor of 4 about the origin:
point B (-5, 0) → (-5 × 4, 0 × 4) = point B' (-20, 0).
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HELP WITH THIS QUESTION!!!
Answers
Given 6 email addresses and 6 distinct passwords. Each password is entered once and can give access to only one email address. In how many ways can the passwords be entered to that no password matches its email address?
Please show steps!
Answers
The formula for the number of derangements of n elements is:
D(n) = n!(1/0! - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!)
Using this formula, we can find the number of derangements of a set of 6 elements:
D(6) = 6!(1/0! - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6!)
D(6) = 6!(0.36787944)
D(6) = 265
Therefore, there are 265 ways to enter the passwords so that no password matches its email address.
Annie has $9,000 in an account that earns 5% interest compounded annually.
To the nearest cent, how much interest will she earn in 2 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
$
Answers
Answer:
B=$18900.00
Step-by-step explanation:
B=?
P=9000
r=5%=0.05
t=2
B=p(1+r)t
B=9000×(1+0.05)×2
B=9000×(1.05)×2
B=9000×2.1
B=18900
Which technique is most appropriate to use to solve each equation?
Drag the name of the technique into the box to match each equation.
Answers
The most appropriate technique to use to solve each equation is as follows:
x ² + 4 x = 15: Completing the square2x ( x - 3) = 0: Zero product propertyHow to solve the equations ?When engaging in the process of completing the square, it is advisable to relocate the constant variable to the opposite side of the equation. Calculate the square of half of the coefficient of the term containing x. You can balance the equation by adding this numerical value to each side of it. Compute the square root for each end of the equation.
x ² + 4x = 15
x ² + 4x - 15 = 0
( x + 2) ² = 16
x + 2 = 4 or x + 2 = -4
x = 2 or x = -6
For the zero product property, Factor the left side of the equation. Set each factor equal to 0 and solve for x.
2x ( x - 3) = 0
2x = 0 or x - 3 = 0
x = 0 or x = 3
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912 is what percent of 1900
Answers
48%
912 of 1900 can be written as:
912
1900
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
912
1900
×
100
100
= (
912 × 100
1900
) ×
1
100
=
48
100
Therefore, the answer is 48%
If you are using a calculator, simply enter 912÷1900×100 which will give you 48 as the answer.
Answer: 912 is what percent of 1900, the percent is 48%
Write a recursive formula for the sequence an = (5)(3)n-1
Answers
This formula says that the nth term in the sequence is equal to three times the (n-1)th term in the sequence. By starting with a1 = 5 and applying the recursive formula repeatedly
A recursive formula is a mathematical expression that defines a sequence in terms of previous values in the sequence. For the given sequence an = (5)(3)n-1, we can create a recursive formula using the following steps:
First, we define the base case for the sequence. In this case, the base case is a1 = 5.
Next, we define the recursive formula for the sequence. This formula uses the previous term in the sequence to calculate the next term. For this sequence, we can use the formula an = (5)(3)n-1 = 3an-1.
Using these steps, we can write the recursive formula for the sequence as follows:
a1 = 5
an = 3an-1 for n > 1
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ANSWER BY THE CHOICE IN THE BOTTOM NOT BY WHAT YOU WANT
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 2, 5
3 1, 3, 4
4 1, 1, 5
5 0, 6
6 7
Key: 3|1 means 3.1
What is the mean, and what does it tell you in terms of the problem?
3.1 feet; The value means the furthest the ball went.
3.875 feet; The value means that a typical throw of the ball results in 3.875 feet.
4.1 feet; The value means this measurement had the most occurrences.
4.65 feet; The value means that a typical throw of the ball results in 4.65 feet.
Answers
The mean distance that the heavy ball was thrown in feet is 4.65 feet. This value tells us that on average, a typical throw of the ball results in a distance of 4.65 feet.
To find the mean, we need to first list all the distances and then find the sum of the distances. Finally, we will divide the sum by the number of distances.
Distances: 2.0, 2.2, 2.5, 3.1, 3.3, 3.4, 4.1, 4.1, 4.5, 5.0, 5.6, 6.7
Sum of distances: 2.0 + 2.2 + 2.5 + 3.1 + 3.3 + 3.4 + 4.1 + 4.1 + 4.5 + 5.0 + 5.6 + 6.7 = 51.5
Number of distances: 12
Mean = Sum of distances / Number of distances
Mean = 51.5 / 12 = 4.29 (rounded to two decimal places)
The closest answer to our calculated mean is:
4.65 feet; The value means that a typical throw of the ball results in 4.65 feet.
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Answer Immeditely Please
Answers
Answer:
9
Step-by-step explanation:
This situation creates 3 similar triangles, so the lengths of corresponding sides are proportional.
1/3 = 3/x
x = 3 × 3
x = 9
A 0.2 pound packet of candies cost $4. If each candy's
weight is 0.001 pound, the average cost of each candy is
Answers
The calculated average cost of each candy is $0.02
Calculating the average cost of each candyFrom the question, we have the following parameters that can be used in our computation:
A 0.2 pound packet of candies cost $4.Each candy's weight is 0.001 pound,using the above as a guide, we have the following:
Average cost = Unit rate * Each candy's weight
Substitute the known values in the above equation, so, we have the following representation
Average cost = 4/0.2 * 0.001
Evaluate
Average cost = 0.02
Hence, the average cost of each candy is $0.02
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What is the y-intercept the equation y=(x+4)2? The equation you wrote to answer the last question should help you. (Only enter the y-coordinate.)
Answers
Answer:
x-intercepts: (-4,0)
y-intercepts: (0,16)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
have a great day and thx for your inquiry :)
out of 550000 given to a school, an amount of 325000 was used.what fraction of the total amount was used
Answers
Answer:
Step-by-step explanation:
[tex]\frac{325000}{550000} \\= \frac{325}{550} \\= \frac{65}{110}\\ = \frac{13}{22}[/tex]
Maricopa's Success scholarship fund receives a gift of $ 145000. The money is invested in stocks, bonds, and CDs. Stocks pay 6. 7 % interest, bonds pay 2. 5 % interest, and CDs pay 5. 75 % interest. Maricopa Success invests $ 10000 more in bonds than in CDs. If the annual income from the investments is $ 6977. 5 , how much was invested in each account?
Maricopa Success invested $ in stocks. Maricopa Success invested $ in bonds. Maricopa Success invested $ in CDs
Answers
Then, the amount invested in bonds is x + $10,000.
The amount invested in stocks is $145,000 - (x + x + $10,000) = $125,000 - 2x - $10,000 = $115,000 - 2x.
The annual income from the stocks is 6.7% of ($115,000 - 2x), which is 0.067($115,000 - 2x) = $7715 - 0.134x.
The annual income from the bonds is 2.5% of (x + $10,000), which is 0.025(x + $10,000) = $250 + 0.025x.
The annual income from the CDs is 5.75% of x, which is 0.0575x.
The total annual income is $7715 - 0.134x + $250 + 0.025x + 0.0575x = $6977.5.
Simplifying and solving for x, we get:
0.9485x + $7465 = $6977.5
0.9485x = $-487.5
x = $513.56 (rounded to the nearest penny)
Therefore, Maricopa Success invested $115,000 - 2x = $113,972.88 in stocks, $10,000 + x = $10,513.56 in bonds, and x = $513.56 in CDs.
Packs of 14 juice boxes are on sale for $11. 34. Packs of 16 juice boxes are on sale for $12. 64. Which is the better buy?
Answers
To determine which option is the better buy between packs of 14 juice boxes for $11.34 and packs of 16 juice boxes for $12.64, we need to compare the cost per juice box for each option. The better buy is the one that offers a lower cost per juice box.
To calculate the cost per juice box for each option, we divide the total cost of the pack by the number of juice boxes in the pack.
For the pack of 14 juice boxes priced at $11.34, the cost per juice box is:
$11.34 / 14 = $0.81 per juice box
For the pack of 16 juice boxes priced at $12.64, the cost per juice box is:
$12.64 / 16 = $0.79 per juice box
Comparing the two options, we find that the pack of 16 juice boxes offers a lower cost per juice box ($0.79) compared to the pack of 14 juice boxes ($0.81).
Therefore, the better buy is the pack of 16 juice boxes for $12.64, as it provides a lower cost per juice box.
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To determine which option is the better buy between packs of 14 juice boxes for $11.34 and packs of 16 juice boxes for $12.64, we need to compare the cost per juice box for each option. The better buy is the one that offers a lower cost per juice box.
To calculate the cost per juice box for each option, we divide the total cost of the pack by the number of juice boxes in the pack.
For the pack of 14 juice boxes priced at $11.34, the cost per juice box is:
$11.34 / 14 = $0.81 per juice box
For the pack of 16 juice boxes priced at $12.64, the cost per juice box is:
$12.64 / 16 = $0.79 per juice box
Comparing the two options, we find that the pack of 16 juice boxes offers a lower cost per juice box ($0.79) compared to the pack of 14 juice boxes ($0.81).
Therefore, the better buy is the pack of 16 juice boxes for $12.64, as it provides a lower cost per juice box.
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What is the freezing point in c of a 0.33 m aqueous solution of Na2so3
Answers
The freezing point of a 0.33 m aqueous solution of Na₂SO₃ is -0.077 °C.
To find the freezing point of a solution, we can use the formula:
ΔTf = Kf · m
where ΔTf is the change in freezing point, Kf is the freezing point depression constant (for water, Kf = 1.86 °C/m), and m is the molality of the solution (in moles of solute per kilogram of solvent).
First, we need to calculate the molality of the solution:
m = moles of solute / mass of solvent (in kg)
We are given that the solution is 0.33 m, which means there are 0.33 moles of Na₂SO₃ per kilogram of water. The molar mass of Na₂SO is:
2 Na + 1 S + 3 O = 2(23.0 g/mol) + 32.1 g/mol + 3(16.0 g/mol) = 126.0 g/mol
So, 0.33 moles of Na₂SO₃ is equal to:
0.33 mol × 126.0 g/mol = 41.6 g
Since we have 1 kg of water, the mass of the solvent is 1000 g. Therefore, the molality of the solution is:
m = 41.6 g / 1000 g = 0.0416 mol/kg
Now, ΔTf = Kf · m = (1.86 °C/m) · (0.0416 mol/kg) = 0.077 °C
freezing point = 0 °C - ΔTf = 0 °C - 0.077 °C = -0.077 °C
Therefore, the freezing point of a 0.33 m aqueous solution of Na₂SO₃ is -0.077 °C.
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Answer: -1.84
Step-by-step explanation:
3x1.86x0.33=1.84
0.00-1.84= -1.84
late answer but hope it helps someone!
let f be the function defined by f(x)=2x^2 + 7x -2. Find the following
a. f(-3)
b. f(a+3)
c. f(3a)
d. f(a+h)
Answers
The values are a. f(-3) = 7, b. f(a+3) = 2a² + 19a + 37, c. f(3a) = 18a² + 21a - 2, d. f(a+h) = 2a² + 4ah + 2h² + 7a + 7h - 2
What is a function?
A function is a mathematical relationship or rule that assigns a unique output value to each input value. It is a fundamental concept in mathematics and plays a central role in various branches, including calculus, algebra, and analysis.
To evaluate the given function at various values, we substitute the given values into the function and simplify the expression.
a. To find f(-3), we substitute -3 into the function: f(-3) = 2(-3)² + 7(-3) - 2 = 18 - 21 - 2 = 7.
b. To find f(a+3), we substitute a+3 into the function: f(a+3) = 2(a+3)² + 7(a+3) - 2. Expanding and simplifying the expression yields 2a² + 12a + 18 + 7a + 21 - 2 = 2a² + 19a + 37.
c. To find f(3a), we substitute 3a into the function: f(3a) = 2(3a)² + 7(3a) - 2. Simplifying the expression gives 18a² + 21a - 2.
d. To find f(a+h), we substitute a+h into the function: f(a+h) = 2(a+h)² + 7(a+h) - 2. Expanding and simplifying the expression yields 2a² + 4ah + 2h² + 7a + 7h - 2.
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what is the probavility of rolling an eveen number on a 6-sided die first, or rolling a 1 on the second roll
Answers
The probability of rolling an even number on the first roll or rolling a 1 on the second roll is 2/3.
To calculate the probability of rolling an even number on the first roll or rolling a 1 on the second roll of a 6-sided die, we can use the principle of addition.
The probability of rolling an even number on the first roll is 3 out of 6 since there are three even numbers (2, 4, and 6) out of six possible outcomes. Therefore, the probability is 3/6 or 1/2.
The probability of rolling a 1 on the second roll is 1 out of 6 since there is only one outcome that results in rolling a 1.
To calculate the combined probability, we add the individual probabilities:
P(rolling an even number on the first roll) + P(rolling a 1 on the second roll) = 1/2 + 1/6 = 4/6 = 2/3
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Solve using substitution method. 9x -y +7=0 13x - 4y +5 = 0.
Answers
The value of x = -1 and y = -2 by solving the system of equation by using the substitution are 9x - y + 7 = 0 and 13x - 4y + 5 = 0
Given that,
The system of equation are 9x - y + 7 = 0 and 13x - 4y + 5 = 0
We have to solve the system of equation by using the substitution method.
We know that,
Take the system of equation
9x - y + 7 = 0 --------->equation(1)
13x - 4y + 5 = 0 ---------> equation(2)
From the equation (1)
9x - y + 7 = 0
y = 9x + 7
Substitute y = 9x + 7 in equation(2)
13x - 4y + 5 = 0
13x - 4(9x + 7) + 5 = 0
13x - 36x - 28 + 5 = 0
- 23x - 23 = 0
-23x = 23
x = -1
Now, Substitute x = -1 in equation(1)
y = 9(-1) + 7
y = -9 + 7
y = -2
Therefore, The value of x=-1 and y=-2
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Given that information, which figures are reflections of ABCD? Check all that apply.
ABCD
KLMN
WXYZ
WZYX
PQRS
Answers
It is based on the given information, the only figure that is definitely a reflection of ABCD is ABCD itself.To determine which figures are reflections of ABCD, we need to understand the concept of reflection. In a reflection, the image is created by flipping the original figure over a line of reflection.
From the given options, we need to analyze each figure and check if it can be obtained by reflecting ABCD.
ABCD: This is the original figure itself.
KLMN: Without more information about the figure KLMN and the line of reflection, we cannot determine if it is a reflection of ABCD.
WXYZ: Without more information about the figure WXYZ and the line of reflection, we cannot determine if it is a reflection of ABCD.
PQRS: Without more information about the figure PQRS and the line of reflection, we cannot determine if it is a reflection of ABCD.
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All of the figures that are reflections of ABCD include the following:
B. KLMN
D. WZYX
What is a reflection?In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
Generally speaking, all congruent geometric figure are reflections of one another. This ultimately implies that, the geometric figures that are reflections of ABCD must be congruent to it and these include the following under a reflection over the y-axis and x-axis:
KLMN
WZYX
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Complete Question:
ABCD ≅ KLMN ≅ PQRS ≅ WXYZ
Given that information, which figures are reflections of ABCD? Check all that apply.
ABCD
KLMN
WXYZ
WZYX
PQRS
Fifteen words were randomly selected from a book. The line plot shows the number of letters in each of the 15 words.
What is the mean length of the words?
Just type the number No Units.
Answers
The mean length of the words that are given above in a line plot would be = 4
How to calculate the mean length of given words?The total number of words that where selected form the book = 15
The number of letters in each word is represented above in a line plot such as follows;
words with one letter = 3 ×1 = 3 letters
words with two letters = 2×2 = 4
Words with 3 letters = 1×3 = 3
words with four letters =4×4 = 16
words with six letters = 2 × 6 = 12
words with seven letters = 2×7 = 14
Words with eight letters = 1×8 = 8
Total word length = 3+4+3+16+12+14+8 = 60
But mean = total of given data/number of data
= 60/15
= 4
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10.8.5: assigning bedrooms to daughters. (a) a family has four daughters. their home has three bedrooms for the girls. two of the bedrooms are only big enough for one girl. the other bedroom will have two girls. how many ways are there to assign the girls to bedrooms?
Answers
Answer: 12 different ways.
Step-by-step explanation:
For a set of M elements, the number of combinations of N elements (N ≤ M) is given by:
In this case, we know that there is a room that can hold two of the girls, then the number of combinations of the two girls that can be in that room is:
So these are the different combinations for the larger room.
So we assume that two girls already have a room, then we have two girls left and two rooms left.
For the first room, there are two possible girls that can be in, let's choose one of them.
For the last room, we have only one girl left, so we have one option.
The total number of combinations will be equal to the product between the number of options for each event (where the events are assigning the girls to the rooms)
Then the number of different outcomes is:
C = 6*2*1 = 12
There are 12 different ways.
Which of the following is a unit vector perpendicular to the plane determined by the vectors A-2i+ 4j and B=i+j - k? o (-2i+ j - k) ot(+2) 0 1 (-2; - ; -1) -2i+j-k
Answers
The vector perpendicular to a plane determined by two vectors A and B can be found by taking their cross product. The unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.
A x B = (-2i+4j+0k) x (i+j-k)
= (-4k + 2i + 6j)
To find a unit vector perpendicular to the plane, we need to normalize this vector by dividing it by its magnitude:
|A x B| = sqrt((-4)^2 + 2^2 + 6^2) = sqrt(56)
So, a unit vector perpendicular to the plane determined by A and B is:
(-4k + 2i + 6j) / sqrt(56)
which simplifies to:
(-2i + 3j - k) / sqrt(14)
Therefore, the answer is (-2i + 3j - k).
To find a vector perpendicular to the plane determined by vectors A and B, you need to calculate the cross product of A and B.
A = -2i + 4j
B = i + j - k
Step 1: Calculate the cross product (C) of vectors A and B:
C = (A_y * B_z - A_z * B_y)i - (A_x * B_z - A_z * B_x)j + (A_x * B_y - A_y * B_x)k
Step 2: Plug in the values of A and B:
C = (4 * (-1) - 0 * 1)i - (-2 * (-1) - 0 * 1)j + (-2 * 1 - 4 * 1)k
Step 3: Simplify the expression:
C = -4i + 2j - 6k
Step 4: Find the magnitude of C:
|C| = √((-4)^2 + 2^2 + (-6)^2) = √(16 + 4 + 36) = √56
Step 5: Divide each component of C by its magnitude to find the unit vector:
Unit vector = (-4/√56)i + (2/√56)j + (-6/√56)k
So, the unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.
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