Answer:
The angle between them is 60 degrees
Step-by-step explanation:
Given
[tex]a = 2i + j -3k[/tex]
[tex]b = 3i - 2j -k[/tex]
Required
The angle between them
The cosine of the angle between them is:
[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]
First, calculate a.b
[tex]a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)[/tex]
Multiply the coefficients of like terms
[tex]a \cdot b =2 * 3 - 1 * 2 - 3 * -1[/tex]
[tex]a \cdot b =7[/tex]
Next, calculate |a| and |b|
[tex]|a| = \sqrt{2^2 + 1^2 + (-3)^2[/tex]
[tex]|a| = \sqrt{14[/tex]
[tex]|b| = \sqrt{3^2 + (-2)^2 + (-1)^2}[/tex]
[tex]|b| = \sqrt{14}[/tex]
Recall that:
[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]
This gives:
[tex]\cos(\theta) = \frac{7}{\sqrt{14} * \sqrt{14}}[/tex]
[tex]\cos(\theta) = \frac{7}{14}[/tex]
[tex]\cos(\theta) = 0.5[/tex]
Take arccos of both sides
[tex]\theta =\cos^{-1}(0.5)[/tex]
[tex]\theta =60^o[/tex]
Mackenzie earns 4% commission as a salesperson. She sold a digital camera that cost $767. How much commission did Mackenzie earn?
Answer:
like about $500 and because of the ca!erlsn
A 19 in. monitor has a length of 16 in. What is its width?
10.25 in.
14.64 in.
16.51 in.
18.91 in.
In how many ways could nine people be divided into two groups of two people and one group of five people?
Nine people could be divided into two groups of two people and one group of five people ways.
(Type a whole number.)
Answer:
your can only divide then up in that specific sequence one time
if cars A and B are traveling at the speed of 55km/hr and 75km/hr respectively. What is their average speed?
Answer:
130 km/hr
Step-by-step explanation:
Average Speed = Total Distance / Total Time.
Let us just make up 2 distances from a time
A: 55 km/hour for 2 hours = 110 km
B: 75 km/hour for 2 hours = 150 km
Total Distance = 260 km
Total Time = 2 hours.
Average Speed = 260 / 2 = 130 km/hr
Now let's try it again. If we get a different answer, then the problem is unanswerable.
A: 55 km/hr for 3 hours = 165 km
B: 75 km/hr for 3 hours = 225 km
Total distance = 390 km
Total time = 3 hours
Average speed = 390 / 3 = 130 which is the same answer we got before.
A differential equation is an equation involving an unknown function and its derivatives. Consider the differential equation 0. a. Show that satisfies the equation for any constant A. b. Show that satisfies the equation for any constant B. c. Show that satisfies the equation for any constants A and B.
Answer: hi your question is poorly written below is the correct question
answer :
a) y1 = Asint, y'1 = Acost , y"1 = -Asint
b) y2 = Bcost, y'2 = Bsint , y"2 = - Bcost
c) y = Asint + B cost satisfies the differential equation for any constant A and B
Step-by-step explanation:
y" + y = 0
Proves
a) y1 = Asint, y'1 = Acost , y"1 = -Asint
b) y2 = Bcost, y'2 = Bsint , y"2 = - Bcost
c) y3 = y1 + y2 , y'3 = y'1 + y'2, y"3 = y"1 + y"2
∴ y"1 + y1 = -Asint + Asint
y"2 + y2 = -Bcost + Bcost
y"3 - y3 = y"1 + y"2 - ( y1 + y2 )
= y"1 - y1 + y"2 - y2
= -Asint - Asint + ( - Bcost - Bcost ) = 0
Hence we can conclude that y = Asint + B cost satisfies the equation for any constant A and B
NEED ANSWER QUICK!!
Camillo needs 2,400 oz of jelly for the food challenge. If 48 oz of jelly cost $3.84, how much will Camillo spend on jelly? Explain how you can find your answer.
Answer:
$192
Step-by-step explanation:
2400/48=50
50x3.84=192
Answer:Sample Response: First, find the unit price of the jelly. The unit cost of jelly is $0.08 per ounce. Next, find the total price of 2,400 oz by multiplying the unit price by the quantity. The total price is $192.
Step-by-step explanation:Pls mrk me as brainliest need award
11 George will cover part of a floor with tiles.
The part of the floor is in the shape of a triangle as shown.
305 cm
371.5 cm
George buys tiles in packs.
Each pack covers 1 m2 and costs £39.95
The tiles can be cut and joined.
George gets off the cost of the packs of tiles.
Work out the lowest cost of the tiles for George.
Answer:
484ed+36_67'ten 355+(36)8wwhThe lowest cost of the tiles for George, for coring the considered triangular floor with the tiles of rate £39.95 per meter sq. is £226.3 approximately.
How can we interpret measurement of something?Remember that volume, area, length etc all are measured relatively.
If you are 1.7 meters tall, then you're height is measured relative to meters. This is called unit of the measurement. It means that if we collect 1 meter and 0.7 meters too,they together will be equally tall as you.
Similarly, if we say that a triangle has area of 40 square inches, then it means that its area is equal to 40 squares of 1 inch sides.
In the same way, volume is measured usually relative to unit cubes. Like how many unit cubes (cubes with 1 unit length of their sides) can be fitted (without any overlap or gap, but can be sliced to make them fit inside) inside the considered shape.
For this case, the tiles we will use will have the same area as the area of the triangular floor.
The triangular floor is of height and base of size 305 cm and 371.5 cm
Since the price rate of tiles is in meter sq, so it would be better if we convert the legths specified in meters.
100 cm = 1 m
1 cm = 1/100 m
305 cm = 305/100 = 3.05 m
371.5 cm = 3.715 m
The area of a triangle is half of the product of its base and height.
Thus, we get:
Area of tiles that will be used = area of the considered triangular floor =
[tex]\dfrac{3.05 \times 3.715}{2} \approx 5.665 \: \rm m^2[/tex]
Since 1 sq. m cost £39.95, therefore, 5.665 sq. meters will cost [tex]5.665 \times 39.95 \approx 226.3 \: \rm euros[/tex]
Thus, the lowest cost of the tiles for George, for coring the considered triangular floor with the tiles of rate £39.95 per meter sq. is £226.3 approximately.
Learn more about interpretation of measurement here: https://brainly.com/question/3424879
Simultaneous equations 5x-4y=19
x+2y=8
Answer:
x = 5 and y = 1.5
Step-by-step explanation:
hope this helps please like and mark as brainliest
The angle of elevation of the top of the tower from a point on the ground is 30 degree, If the height of the tower is 40 space m e t e r s, then the distance between the tower and the point is
Answer:
[tex]40\sqrt3\ m[/tex]
Step-by-step explanation:
Given that,
The height of the tower, h = 40 m
The angle of elevation is 30°
We need to find the distance between the tower and the point. Let the distance is x. Using trigonometry,
[tex]\tan(30)=\dfrac{h}{x}\\\\\dfrac{1}{\sqrt3}=\dfrac{40}{x}\\\\x=40\sqrt3\ m[/tex]
So, the distance between the tower and the point is equal to [tex]40\sqrt3\ m[/tex].
What conclusion can be determined from the dot plot below?
A dot plot showing five dots above 9, six dots above 10, three dots above 11, and one dot above 12.
The number of observations is 10.
The median of the data set is 10.
The mean of the data set is 15.
The range of the data set is 12.
solve the system of equations using substitution or graphing.
Step-by-step explanation:
I think substitution would be the easiest since you already have one of the variables solved for.
[tex]y=-x^2+4x+5\\y=x+1\\x+1=-x^2+4x+5\\x^2-3x-4=0\\(x-4)(x+1)=0\\x-4=0\\x=4\\x+1=0\\x=-1[/tex]
(You can just set the equations equal to each other since they both equal y).
Now, to get the points, plug in x = 4 and x = -1 into one of the equations (I'm going to plug them into y = x+1 because that one is much simpler)
[tex]y(4)=4+1\\y(4)=5\\y(-1)=-1+1\\y(-1)=0[/tex]
So, your final points are:
(4,5) and (-1,0)
Answer: A
Step-by-step explanation:
We can use substitution to solve this problem. Since we are given y=-x²+4x+5 and y=x+1, we can set them equal to each other.
-x²+4x+5=x+1 [subtract both sides by x]
-x²+3x+5=1 [subtract both sides by 1]
-x²+3x+4=0
Now that we have the equation above, we can factor it to find the roots.
-x²+3x+4=0 [factor out -1]
-1(x²-3x-4)=0 [factor x²-3x-4]
-1(x+1)(x-4)=0
This tells us that x=-1 and x=4.
We can narrow down our answer to A, but let's plug in those values to be sure it is correct.
-(-1)²+4(-1)+5=(-1)+1 [exponent]
-1+4(-1)+5=-1+1 [multiply]
-1-4+5=-1+1 [add and subtract from left to right]
0=0
-------------------------------------------------------------------------------------------
-(4)²+4(4)+5=(4)+1 [exponent]
-16+4(4)+5=4+1 [multiply]
-16+16+5=4+1 [add and subtract from left to right]
5=5
Therefore, we can conclude that A is the correct answer.
Which of these figures has rotational symmetry?
Hello!
The answer is a.
Good luck! :)
11. Which point is not on the graph of 2x + 3y - Z - 12 = 0?
(6, 0, 0)
(3,3,3)
(0, 4,0)
(1, 1, 7)
jenny has 3 cherry candies and 3 orange candies. She takes out 2 candies without looking.What is the probability in fractions that both are cherry?
The function y=5(1/2)^x Models the number of grams of radioactive material, y, left in a container after x days. Sketch the graph of this function below
Answer:
see graph
Step-by-step explanation:
what are the following proof triangle LMN equals triangle OPQ
Answer:
D. SSS
Step-by-step explanation:
Was given to us that the corresponding sides are congruent so is SSS.
Side Side Side Theorem tells us that if am the sides of a triangle are having the same measurement with the corresponding sides of another triangle then the two triangles are congruent.
HELP PLEASE QUICK
use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
f(x)=2x+3
g(x)=f(x)-2
Answer:
2x - 1
Step-by-step explanation:
that is the procedure above
which ordered pairs are in the solution set of the system of linear inequalities?
y > -1/3x+2
-
y <2x+3
A. (2,2), (3,1) (4,2)
B. (2,2) (3,-1) (4,1)
C. (2,2) (1,-2) (0,2)
D. (2,2) (1,2) (2,0)
==========================================================
Explanation:
The graph of [tex]y \ge -\frac{1}{3}x+2[/tex] has the boundary y = (-1/3)x+2 which is a solid line. This line goes through (0,2) and (3,1). We shade above the boundary because of the "greater than" sign.
The graph of y < 2x+3 has a dashed boundary line of y = 2x+3, and we shade below the boundary because of the "less than" sign.
The two regions overlap in the upper right corner where it's shaded in the darkest color. The points (2,2), (3,1) and (4,2) are in this upper right corner region. If we plug the coordinates of each point into each inequality, then we'll get true statements.
For instance, let's try (x,y) = (2,2) into the first inequality
[tex]y \ge -\frac{1}{3}x+2\\\\2 \ge -\frac{1}{3}(2)+2\\\\2 \ge -\frac{2}{3}+2\\\\2 \ge -\frac{2}{3}+\frac{6}{3}\\\\2 \ge \frac{-2+6}{3}\\\\2 \ge \frac{4}{3}\\\\2 \ge 1.33\\\\[/tex]
Which is true since 2 is indeed larger than 1.33, so that confirms (2,2) is in the shaded region for [tex]y \ge -\frac{1}{3}x+2\\\\[/tex]
Let's check the other inequality as well
[tex]y < 2x+3\\\\2 < 2(2)+3\\\\2 < 4+3\\\\2 < 7\\\\[/tex]
That works too. So (2,2) is in BOTH shaded regions at the same time; hence, it's a solution to the system. You should find that (3,1) and (4,2) work for both inequalities also. This will confirm choice A is the answer.
--------------------------------
Extra info (optional section)
A point like (3,-1) does not work for the first inequality as shown below
[tex]y \ge -\frac{1}{3}x+2\\\\-1 \ge -\frac{1}{3}(3)+2\\\\-1 \ge -1+2\\\\-1 \ge 1\\\\[/tex]
Since -1 is neither equal to 1, nor is -1 larger than 1 either. The false statement at the end indicates (3,-1) is not a solution to that inequality.
Based on the graph, the point (3,-1) is not above the blue solid boundary line. All of this means we can rule out choice B.
You should find that (1,-2) is a similar story, so we can rule out choice C. Choice D can be ruled out because (2,0) is not a solution to the first inequality.
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 12 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 11.5.
Answer:
we conclude that population mean is not 11.5
Step-by-step explanation:
The hypothesis :
H0 : μ = 11.5
H1 : μ ≠ 11.5
The test statistic :
(xbar - μ) ÷ (s/√(n))
Test statistic = (12 - 11.5) ÷ (2/√(16))
Test statistic = (0.5) ÷ (2 ÷ 4)
Test statistic = 0.5 / 0.5
Test statistic = 1
The Pvalue from test statistic value, df = n - 1 = 16 - 1 = 15
Pvalue = 0.333
Pvalue > α ; we fail to reject the null ; Hence, we conclude that population mean is not 11.5
Two different types of injection-molding machines are used to form plastic parts. Two random samples, each of size 300, are selected. 15 defective parts are found in the sample from machine 1 and 8 defective parts are found in the sample from machine 2. Is it reasonable to assume that both machines have the same defective rate
Answer:
No it is not since there is 15 defectice parts in 2machines and there is 8 broken parts in the one machine
Hope This Helps!!!
its
A bag contains 5 green candies and 7 blue candies.
A piece of candy is selected at random, put back into the bag, and then
another piece of candy is chosen.
What is the probability that both pieces are green?
Answer:
[tex]P(Green\ and\ Green) = \frac{25}{144}[/tex]
Step-by-step explanation:
Given
[tex]Green=5[/tex]
[tex]Blue = 7[/tex]
Required
[tex]P(Green\ and\ Green)[/tex]
This is calculated as:
[tex]P(Green\ and\ Green) = P(Green) * P(Green)[/tex]
Since, it is a probability with replacement, we have:
[tex]P(Green\ and\ Green) = \frac{Green}{Total} * \frac{Green}{Total}[/tex]
So, we have:
[tex]P(Green\ and\ Green) = \frac{5}{12} * \frac{5}{12}[/tex]
[tex]P(Green\ and\ Green) = \frac{25}{144}[/tex]
9 friends are lining up. Joe, Susan, John, and Meredith must be beside each other. How many ways can they line up?
This is one single number slightly over 17 thousand.
You may need to erase the comma when typing the answer in.
=========================================================
Explanation:
Let's say that another person steps in for Joe, Susan, John, and Meredith. I'll refer to this person as the teacher (perhaps these 9 friends are students on a field trip).
The 9 friends drops to 9-4 = 5 people when those four named people leave the group temporarily. Then it bumps up to 5+1 = 6 people when the teacher steps in. Wherever the teacher is located, the four friends that left will replace the teacher. This guarantees that those four friends stick together.
There are 6! = 6*5*4*3*2*1 = 720 ways to arrange those 6 people. The exclamation mark is a factorial symbol.
Within any of those 720 permutations, we have 4! = 4*3*2*1 = 24 ways to arrange those group of named people when they come back to replace the teacher.
So overall the answer is 4!*6! = 24*720 = 17,280
You may need to erase the comma when typing the answer in.
-------------
Side note: There are 9! = 362,880 ways to arrange all nine friends regardless if those four mentioned people stick together or not. We see that they stick together roughly (17,280)/(362,880) = 0.0476 = 4.76% of the time.
6v^2x^3y^7 and 20v^8x^5
Answer:
LCD????
[tex]2v^2x^3[/tex]
Step-by-step explanation:
Mary is 3 years older than Sarah. Winifred is twice as old as Mary. Altogether their ages total 89. How old is Sarah?
24 years old
22 years old
18 years old
None of these choices are correct.
Answer:
Step-by-step explanation:
M = S+3
W = 2M = 2(S+3) = 2S+6
M+S+W = 89
(S+3)+S+(2S+6) = 89
S = 20
Answer:
20
Step-by-step explanation:
Sarah: 21
Mary: 24
Winifred: 48
No
Sarah: 20
Mary: 23
Winifred: 46
Yes
help pls, i need help pls
9514 1404 393
Answer:
no
Step-by-step explanation:
For lines to be parallel, any obtuse angle where a transversal crosses must be supplementary to any acute angle at that transversal. Here the sum of the obtuse and acute angles is 105° +65° = 170°, so it is not possible for this geometry to include parallel lines.
Solve by using matrices. 2x – y +2 + w = -3 x + 2y – 3z + w = 12 3x - y - + 2w = 3 -2x + 3y + 2 – 3w = -3
Some symbols and numbers are missing. I assume the system is supposed to read
2x - y + 2z + w = -3
x + 2y - 3z + w = 12
3x - y - z + 2w = 3
-2x + 3y + 2z - 3w = -3
In matrix form, this is
[tex]\begin{bmatrix}2&-1&2&1\\1&2&-3&1\\3&-1&-1&2\\-2&3&2&-3\end{bmatrix}\begin{bmatrix}x\\y\\z\\w\end{bmatrix}=\begin{bmatrix}-3\\12\\3\-3\end{bmatrix}[/tex]
which we can strip down to the augmented matrix,
[tex]\left[\begin{array}{cccc|c}2&-1&2&1&-3\\1&2&-3&1&12\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]
Now for the row operations:
• swap rows 1 and 2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\2&-1&2&1&-3\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]
• add -2 (row 1) to row 2, -3 (row 1) to row 3, and 2 (row 1) to row 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&-7&8&-1&-33\\0&7&-4&-1&21\end{array}\right][/tex]
• add 7 (row 2) to -5 (row 3), and row 3 to row 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&16&-2&-24\\0&0&4&-2&-12\end{array}\right][/tex]
• multiply through rows 3 and 4 by 1/2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&8&-1&-12\\0&0&2&-1&-6\end{array}\right][/tex]
• add -4 (row 4) to row 3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&0&3&12\\0&0&2&-1&-6\end{array}\right][/tex]
• swap rows 3 and 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&3&12\end{array}\right][/tex]
• multiply through row 4 by 1/3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&1&4\end{array}\right][/tex]
• add row 4 to row 3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&0&-2\\0&0&0&1&4\end{array}\right][/tex]
• multiply through row 3 by 1/2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• add -8 (row 3) and row 4 to row 2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&0&0&-15\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• multiply through row 2 by -1/5
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• add -2 (row 2) and 3 (row 3) and -1 (row 4) to row 1
[tex]\left[\begin{array}{cccc|c}1&0&0&0&-1\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
Then the solution to the system is (x, y, z, w) = (-1, 3, -1, 4).
When you buy the latest iPad for $799, they offer you an extended warranty for $90; they will replace the iPad if it breaks in the next 2 years. The probability that it will break is 0.1. Assume there is no chance the ipad can break more than one time in the next two years. Calculate the total expected cost of the ipad if you take the warranty (i.e. include cost of ipad and warranty). Enter this value below in dollars (calculated to nearest cent, i.e. $10.90, etc).
Answer:
889 dollars
Step-by-step explanation:
There are 4 contestants in a beauty pageant. How many results are possible for the first, second, and third place?
Explanation:
There are 4 choices for first place, 3 choices for second place, and 2 choices for third place. Overall, there are 4*3*2 = 24 permutations.
Given: CD is an altitude of triangle ABC.
Prove: a^2 = b^2 +c^2 = 2bccos A
Answer:
Step-by-step explanation:
Statements Reasons
1). CD is an altitude of ΔABC 1). Given
2). ΔACD and ΔBCD are right 2). Definition of right triangles.
triangles.
3). a² = (c - x)² + h² 3). Pythagoras theorem
4). a² = c² + x² - 2cx + h² 4). Square the binomial.
5). b² = x² + h² 5). Pythagoras theorem.
6). cos(x) = [tex]\frac{x}{a}[/tex] 6). definition of cosine ratio for an angle
7). bcos(A) = x 7). Multiplication property of equality.
8). a² = c² - 2c(bcosA) + b² 8). Substitution property
9). a² = b² + c² - 2bc(cosA) 9). Commutative properties of
addition and multiplication.
SOMEONE PLS HELP ME I WILL MAKE U BRAINLIST ! In a survey sample of 83 respondents, about 30.1 percent of the samplework less than 40 hours per week. What is the estimated standard error for the group of respondents who work 40 hours or more per week?
(*round to two decimal places)
Answer:
Answer = √(0.301 × 0.699 / 83) ≈ 0.050
A 68 percent confidence interval for the proportion of persons who work less than 40 hours per week is (0.251, 0.351), or equivalently (25.1%, 35.1%)
Step-by-step explanation:
√(0.301 × 0.699 / 83) ≈ 0.050
We have a large sample size of n = 83 respondents. Let p be the true proportion of persons who work less than 40 hours per week. A point estimate of p is because about 30.1 percent of the sample work less than 40 hours per week. We can estimate the standard deviation of as . A confidence interval is given by , then, a 68% confidence interval is , i.e., , i.e., (0.251, 0.351). is the value that satisfies that there is an area of 0.16 above this and under the standard normal curve.The standard error for a proportion is √(pq/n), where q=1−p.
Hope this answer helps you :)
Have a great day
Mark brainliest
