$3.90
29.20-13.60=15.6
15.6/4= 3.90
N Heracio's Computer Time Shopping Research 10% Videos 15% Homework 20% Games 20% Social dia 25% Heracio used the computer a total of 40 hours last week. How many more hours did Heracio use the computer to do homework than shop online?
Heracio used the computer 2 more hours to do homework than to shop online.
To solve the problem, we need to first calculate the number of hours Heracio spent on each activity:
Videos: 10% of 40 hours = 4 hours
Homework: 20% of 40 hours = 8 hours
Games: 20% of 40 hours = 8 hours
Social media: 25% of 40 hours = 10 hours
Shopping: 15% of 40 hours = 6 hours
To find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:
8 hours (homework) - 6 hours (shopping) = 2 hours
Therefore, Heracio used the computer 2 more hours to do homework than to shop online.
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Suppose that the function g is defined, for all real numbers, as follows.
The graph of the piecewise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
All the three definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.
The definitions are given as follows:
y = 2 to the left of x = 0.y = -1 at x = 0.y = -3 to the right of x = 0.More can be learned about piece-wise functions at brainly.com/question/19358926
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Select the correct answer from each drop-down menu. A system of linear equations is given by the tables. x y -1 1 0 3 1 5 2 7 x y -2 -7 0 -1 2 5 4 11 The first equation of this system is y = x + 3. The second equation of this system is y = 3x − . The solution of the system is ( , ).
The first equation of this system is y = 2x + 3, the second equation is y = 3x - 1, and the solution of the system is (4, 11).
a) The first equation of this system can be found by using the points given in the first table. We can use the two points (-1, 1) and (0, 3) to find the equation of the line passing through them using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
The slope of the line passing through (-1, 1) and (0, 3) is (3-1)/(0-(-1)) = 2/1 = 2.
Substituting one of the points in the slope-intercept form, we get 1 = 2(-1) + b, which gives us b = 3. Therefore, the equation of the line is y = 2x + 3.
b) Similarly, we can use the points given in the second table to find the equation of the second line. Using the points (0, -1) and (2, 5), we get the slope as
(5-(-1))/(2-0)
= 6/2
= 3.
Substituting one of the points in the slope-intercept form, we get
-1 = 3(0) + b, which gives us b = -1.
Therefore, the equation of the second line is y = 3x - 1.
c) To find the solution of the system, we need to find the point of intersection of the two lines. We can do this by solving the two equations simultaneously.
Substituting the second equation in the first, we get:
2x + 3 = 3x - 1
Simplifying, we get x = 4.
Substituting x = 4 in either of the equations, we get y = 11. Therefore, the solution of the system is (4, 11).
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The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
The correct option regarding which bus has the least spread among the travel times is given as follows: Bus 14, with an IQR of 6.
How to solveThe interquartile range is a better measure of spread compared to the range of a data-set, as it does not consider outliers.
For groups of 15 students, we have that:
The first half is composed by the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.
The second half is composed by the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.
The quartiles for Bus 14 are given as follows:
Q1 = 12.
Q3 = 18.'
Hence the IQR is of:
IQR = Q3 - Q1 = 18 - 12 = 6.
The quartiles for Bus 18 are given as follows:
Q1 = 9.
Q3 = 16.
Hence the IQR is of:
IQR = Q3 - Q1 = 16 - 9 = 7.
Hence Bus 14 is the more consistent bus, due to the lower IQR.
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Out of 400 people sampled, 160 preferred
Candidate A. Based on this, estimate what proportion of the voting population (p) prefers Candidate A.
Use a 90% confidence level, and give your answers as decimals, to three places. Use GeoGebra to calculate!
Four data sets are shown below. Set 1: {10, 19, 38, 50, 51} Set 2: {5, 21, 26, 39, 51} Set 3: {9, 38, 50, 50, 51} Set 4: {5, 28, 28, 28, 51} Which data set has the largest standard deviation? * Set 1 Set 2 Set 3 Set 4
Answer:
Set 1: {10, 19, 38, 50, 51}
Step-by-step explanation:
To calculate the standard deviation of a data set, we first find the mean of the data set. The mean is simply the sum of all the values in the data set divided by the number of values. For example, the mean of Set 1 is:
(10+19+38+50+51)/5=33.6
Next, we find the variance of the data set. The variance is the average of the squared differences between each value in the data set and the mean. For example, the variance of Set 1 is:
((10−33.6)^2+(19−33.6)^2+(38−33.6)^2+(50−33.6)^2+(51−33.6)^2)/5=323.84
Finally, we take the square root of the variance to get the standard deviation. For example, the standard deviation of Set 1 is:
[tex]\sqrt{323.84}[/tex]=17.99
We can repeat this process for each of the four data sets and find that Set 1 has the largest standard deviation.
Please help me with this
Answer:
a) y = 5.2727x + 32.5276
b) y = 5.2727(6) + 32.5276
= 64.1638 inches
c) y = 5.2727(7.153) + 32.5276
= 70.2432 inches
PLEASE ANSWER FAST!!!! NEED TO UNDERSTAND!!!
Step-by-step explanation:
X component = 4.5 - 2.1 = 2.4
Y component = 7.8 - 2.1 = 5.7
Find magnitude using Pythagorean theorem
m^2 = 2.4^2 + 5.7^2
magnitude = 6.18 units
Remember for a right triangle tangent Φ = opposite leg / adjacent leg
angle = arctan ( 5.7 / 2.4 ) = 67.2 degrees
what is the solution to
-15x=90
Answer:
option c) x=-6
Step-by-step explanation:
-15x = 90
= x = 90/-15
= x = (-6)
Can anyone help me on this
hi I need help on questions 10-17 on this paper. if you are a expert (know what to do) of vertical angles and angle relationships in a triangle then please help me.
Answer:
10) 73
11) 107
12) 107
13) x = 23
14) 135
15) 45
16) 123, 28 29
17) 180 - 72 - 28 = 80
Angle K is 80
Step-by-step explanation:
10:
Vertical angels are congruent. The same measurement.
11:
Supplements angles add to 180
180 - 73 = 107
12:
Same as 11
13:
135
Vertical angles are congruent
5x + 20 = 3x + 66 Subtract 3x from both sides
2x + 20 = 66 Subtract 20 from both sides
2x = 46 Divide both sides by 2
x = 23
14:
5x + 20 Substitute 23 for x
5(23) + 20
115 + 20
135
15:
This angle is supplemental to ABC
180 - 135 = 45
16:
The sum of the interior angles of a triangle is 180
123 + x-2 + x -3 = 180 Combine like terms
118 +2x = 180 Subtract 118 from both sides
2x = 62 Divide both sides by 2
x = 31
x- 2
31 - 2 = 29
x - 3
31 - 3 = 28
Three angles 123, 29, 28
17:
The sum of the interior angles is 180
180 - 72 - 28 = 80
Helping in the name of Jesus.
A salesman earns $60,000 in commission in his first year and then has his commission reduced by 20% the second year. What percent increase in commission over the second year will give him $57,600 in the third year?
first off, let's find out how much he's making on the 2nd year, so since he's getting slashed by 20%, that means his new commission is 100% - 20% = 80%, so 80% of 60000, how much is that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of 60000}}{\left( \cfrac{80}{100} \right)60000}\implies 48000[/tex]
now, if we want to go up to 57600, that means we need to increase his commission by 57600 - 48000 = 9600.
So, if we take 48000(origin amount) to be the 100%, what's 9600 off of it in percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 48000 & 100\\ 9600& x \end{array} \implies \cfrac{48000}{9600}~~=~~\cfrac{100}{x} \\\\\\ 5 ~~=~~ \cfrac{ 100 }{ x }\implies 5x=100\implies x=\cfrac{100}{5}\implies \boxed{x=20}[/tex]
Baristas at Hot Cocoa Coffee Shop tested their new hot chocolate machine. The following table shows the number of seconds the machine was turned on and the amount of hot chocolate that filled up the cup. Time (seconds) 4 8 12 16 20 24 Hot Chocolate Amount (fluid ounces) 5 7.5 9 11 13 16 Which representation is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time? scatter plot titled New Machine with the x axis labeled hot chocolate amount in fluid ounces going from 0 to 18 and the y axis labeled time in seconds going from 0 to 26, with points at 5 comma 4, 7 and a half comma 8, 9 comma 12, 11 comma 16, 13 comma 20, and 16 comma 24 line graph titled New Machine with the x axis labeled hot chocolate amount in fluid ounces going from 0 to 18 and the y axis labeled time in seconds going from 0 to 26, with points at 5 comma 4, 7 and a half comma 8, 9 comma 12, 11 comma 16, 13 comma 20, and 16 comma 24, with line segments connecting each point to the next scatter plot titled New Machine with the x axis labeled time in seconds going from 0 to 28 and the y axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16 line graph titled New Machine with the x axis labeled time in seconds going from 0 to 28 and the y axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16, with line segments connecting each point to the next
The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine.
Which representation is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time?
The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine with the x-axis labeled time in seconds going from 0 to 28 and the y-axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16.
A scatter plot is a useful way to show the relationship between two variables, in this case, the amount of hot chocolate and time. Each point on the scatter plot represents a pair of values for time and hot chocolate amount. A line graph with line segments connecting each point to the next would not be appropriate because the data is not continuous, and there is no reason to assume that the relationship between time and hot chocolate amount is linear.
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1. Bill scored the following number of points in a basketball games: 22, 18, 19, 16, 32, 24, 19, 20, 22 and 22
a. Box and Whisker plot:
b. What is the range:
c. Are there any outliers?
IQR:
b. The range is 32 - 16 = 16. and IQR 4
c. 32
how to find range?a. Here is a box and whisker plot to represent the given data:
The horizontal axis shows the range of the data, and the vertical axis represents the frequency. The box represents the middle 50% of the data, with the bottom of the box being the 25th percentile and the top of the box being the 75th percentile. The whiskers represent the lowest and highest values within 1.5 times the interquartile range (IQR) of the box, and any points outside the whiskers are considered outliers.
b. The range is the difference between the highest and lowest values in the data set. In this case, the range is 32 - 16 = 16.
c. There is one outlier in the data set, which is the value of 32. It is outside the whiskers of the box and is considered to be an outlier.
The interquartile range (IQR) is the difference between the 75th and 25th percentiles of the data set. In this case, the IQR is:
IQR = Q3 - Q1
= 22 - 18
= 4
where Q1 is the first quartile (the value below which 25% of the data falls), and Q3 is the third quartile (the value below which 75% of the data falls).
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To reach escape velocity, a rocket must travel at the rate of 2.2×106 feet per minute. Express this number in standard notation.
The rocket must travel at a rate of 2,200,000 feet per minute to reach escape velocity.
Expressing this number in standard notation.2.2×10^6 feet per minute is in its scientific notation.
In scientific notation, a number is written as the product of a coefficient and a power of 10.
So, 2.2×10^6 is already in scientific notation, where the coefficient is 2.2 and the power of 10 is 6.
If you want to convert it to standard notation, you can multiply the coefficient by the power of 10:
2.2×10^6 = 2.2 x 1,000,000 = 2,200,000
Therefore, the rocket must travel at a rate of 2,200,000 feet per minute to reach escape velocity.
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50 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
A. The 51st note on a piano keyboard corresponds to a pitch of 440 cycles per second.
B. The pitch that is 73 notes higher on the keyboard has a frequency of about 1760 cycles per second.
How to determine frequency?A. Use the formula to find how many notes up the piano keyboard the pitch of 440 cycles per second corresponds to:
440 = 27.5 × 2⁽ⁿ⁻¹⁾/12
Dividing both sides by 27.5 and taking the logarithm with base 2 gives:
log₂(440/27.5) = (n-1)/12
n-1 = 12 × log₂(440/27.5)
n-1 = 12 × 4.1702 ≈ 50.042
n ≈ 51.042
Therefore, the pitch of 440 cycles per second is the 51st note up the piano keyboard.
B. Use the same formula to find the frequency of the pitch that is 73 notes up the keyboard:
73 = 1 + 12 log₂(f/27.5)
72 = 12 log₂(f/27.5)
6 = log₂(f/27.5)
f/27.5 = 2⁶
f = 27.5 × 2⁶
f ≈ 1760
Therefore, the frequency of the pitch that is 73 notes up the keyboard is approximately 1760 cycles per second.
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Do you use integration by parts to solve this problem? If so, how? I can't seem to figure out the right answer
The integral of [tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] is (2/3)[tex]e^{3/2}[/tex] - (4/9).
To find the integral of [tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] , we can use integration by parts. Let u = ln x and dv = [tex]x^{1/2}[/tex] dx. Then du/dx = 1/x and v = (2/3) [tex]x^{3/2}[/tex] .
Using the formula for integration by parts, we have:
∫[tex]x^{1/2}[/tex]lnx dx = uv - ∫v du/dx dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - ∫(2/3) [tex]x^{3/2}[/tex] * (1/x) dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - (2/3) ∫ [tex]x^{1/2}[/tex] dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - (4/9) [tex]x^{3/2}[/tex] + C
where C is the constant of integration.
To evaluate the definite integral from 1 to e, we substitute e for x in the expression above and subtract the result when x = 1:
[tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] = [(2/3) [tex]e^{3/2}[/tex] ln e - (4/9) [tex]e^{3/2}[/tex] ] - [(2/3)[tex]1^{3/2}[/tex]ln 1 - (4/9)[tex]1^{3/2}[/tex]]
= (2/3) [tex]e^{3/2}[/tex] - (4/9)
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Evaluate each expression using the graphs of y=f(x) and y=g(x) shown below.
The composition of functions is solved and the expressions are
a) ( g o f ) ( -1 ) = 1
b) ( g o f ) ( 0 ) = 4
c) ( f o g ) ( -1 ) = -2
d) ( f o g ) ( 4 ) = -1
Given data ,
Let the composition of function be represented as A
Now , the value of A is
a)
( g o f ) ( -1 ) = g ( f ( -1 ) )
On simplifying the function , we get
when x = -1 , f ( -1 ) = 2
g ( 2 ) = 1
So , ( g o f ) ( -1 ) = 1
b)
( g o f ) ( 0 ) = g ( f ( 0 ) )
On simplifying the function , we get
when x = 0 , f ( 0 ) = 0
g ( 0 ) = 4
So , ( g o f ) ( 0 ) = 4
c)
( f o g ) ( -1 ) = f ( g ( -1 ) )
On simplifying the function , we get
when x = -1 , g ( -1 ) = 2
f ( 2 ) = -2
So , ( f o g ) ( -1 ) = -2
d)
( f o g ) ( 4 ) = f ( g ( 4 ) )
On simplifying the function , we get
when x = 4 , g ( 4 ) = 1
f ( 1 ) = -1
So , ( f o g ) ( 4 ) = -1
Hence , the composition of function is solved
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Help me out please y’all
The piecewise function is
f(x) = { x -3 , x≤3
8, -3 < x ≤ 5
x+10, x>6
For values less than or equal to -3, we have a line with a positive slope. We have two lines, y = x - 2, and y = x - 3.
1. For y = x - 2
-5 = -3 - 2= -5
2. For y = x - 3
-5 = -3-3 = -6
The fact that the domain is specified for x less than -3 further demonstrates that the first choice is not an option.
Additionally, we know that the function's value is equal to 8 for the range from x greater than -3 to less than or equal to 5.
Additionally, the equation is given as y = -x + 10 and the line has a negative slope for values greater than 6.
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I need help finding the answer to this question
Answer: I believe it would be 2/5.
Step-by-step explanation:
Reduction means the fraction is reduced to it's simplest form.
7/7=1
2/5=2/5
15/13=1 2/13
See as the '2/5' does not change in reduction.
So, '2/5' would be your answer.
Hope this helps! :)
Someone help i really need help with this
Step-by-step explanation:
step A is incorrect.
-40/5 does not equal to -40/-5.
-40/-5 is equal to 40/5 as we can simplify the negative 1 out.
Answer:
The correct answer is step A
Select the statement that is true a.16.7-8=2.9×3 b. 4×3.2=17.8-5 c.10.5÷5+1=8.8÷4 d.
Answer:
b
4 x 3.2 = 12.8
17.8 - 5 =12.8
so,
4 x 3.2 = 17.8-5
12.8=12.8
Sally is putting her dominions back into their storage tin. She wants to know how many dominoes can fit in the tin. While placing the dominoes in the tin, she counts how many dominos can be stacked on top of each other and she finds that to be 3 dominoes. She counts how many can be set side-by-side and she finds that to be 9 dominoes. Finally she counts how many can be placed end-to-end in the tin and she finds that to be 4 dominoes. Sally knows she can use addition to figure out how many total dominoes fit in the tin. She also knows that 27 dominoes fit in one row in the tin when she stacks up as many as she can in that row. Write an expression using only addition to show how Sally can determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked
The expression that Sally can use to determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked is (Number of rows stacked ÷ 0.75) x (9 x 4)
Sally can use the fact that she can fit 3 dominoes stacked on top of each other, 9 dominoes side-by-side, and 4 dominoes end-to-end in the tin to figure out how many dominoes can fit in the tin. Since she knows that 27 dominoes fit in one row stacked, she can use addition to determine the total number of dominoes that can fit in the tin.
First, she can find the number of dominoes that can fit in one layer of the tin by multiplying the number of dominoes that fit side-by-side and the number that fit end-to-end: 9 x 4 = 36.
Then, she can divide the total number of dominoes that fit in one row (27) by the number of dominoes that can fit in one layer (36): 27 ÷ 36 = 0.75.
This means that each layer of the tin can hold 0.75 rows of dominoes.
To find the total number of dominoes that can fit in the tin, Sally can multiply the number of layers by the number of dominoes in each layer: Number of layers x Number of dominoes in each layer = Total number of dominoes that can fit in the tin.
Therefore, the expression that Sally can use to determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked is:
Total number of dominoes = Number of layers x Number of dominoes in each layer
Total number of dominoes = (Number of rows stacked ÷ 0.75) x (9 x 4)
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A pair of standard dice are rolled. Find the
probability of rolling a sum of 3 with these dice.
scheduled payment of $1010 due five months ago and $1280 due today are to be repaid by a payment of $615 in four month and the balance in seven months. If money is worth 7.75% p.a , and the focal date is in seven months, what is the amount of the final payment?
The amount of the final payment is $1,004.99.
To solve the given problem, we will use the concept of present value. We need to find the present value of the two payments due in the past, and then find the future value of the remaining payments due in the future.
Let's first find the present value of the two past payments:
PV1 = $1010 / (1 + 0.0775/12)⁵ = $868.15
PV2 = $1280 / (1 + 0.0775/12)⁰ = $1280
Next, we can find the future value of the remaining payments due in the future
FV1 = $615 x (1 + 0.0775/12)⁴ = $664.69
FV2 = X
Now we can set up an equation to solve for X, the final payment:
PV1 + PV2 = FV1 + FV2 / (1 + 0.0775/12)⁷
Substituting the values we have calculated:
$868.15 + $1280 = $664.69 + X / (1 + 0.0775/12)⁷
Simplifying and solving for X
X = ($868.15 + $1280 - $664.69) x (1 + 0.0775/12)⁷ = $1,004.99
Therefore, the amount of the final payment is $1,004.99.
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Carson is organizing textbooks on his bookshelf. He has a Spanish textbook, a math textbook, a history textbook, and a health textbook. How many different ways can he line the textbooks up on his bookshelf?
Carson can line up his textbooks on his bookshelf in 24 different ways
What is Permutation?
Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.
What is Combination?
The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.
According to the given information:
Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:
n! / (n - r)!
where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).
On substituting the values in the formula,
4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.
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Two points on the path of a planet are A and B. The points A and B have coordinates (1, 4, 2) and (2, –1, 3) respectively.
The line l has equation r= (2i-j+3k)+µ(i-j+k)
(a) Calculate the distance between the points A and B .
(b) The line AB makes an acute angle θ with l. Calculate θ.
(c) The point P on the line l is where λ = p.
(i) for the vector AP how that :
AP. (i-j+k)=7+3p
(ii) Hence find the coordinates of the foot of the perpendicular from the point
A to the line l.
(c) Determine the cartesian equation of line l.
(d) Determine the cartesian equation of line A
Answer:
Step-by-step explanation:
(a) The distance between two points A(x1, y1, z1) and B(x2, y2, z2) is given by the formula: AB = √((x2-x1)² + (y2-y1)² + (z2-z1)²). Substituting the coordinates of points A and B into this formula gives: AB = √((2-1)² + (-1-4)² + (3-2)²) = √(14).
(b) The direction vector of line l is given by the vector (i-j+k). The direction vector of line AB is given by the vector AB = (2-1)i + (-1-4)j + (3-2)k = i - 5j + k. The cosine of the angle between two vectors is given by the dot product of the vectors divided by the product of their magnitudes. Therefore, cos(θ) = (AB.(i-j+k)) / (|AB|.|i-j+k|) = ((i - 5j + k).(i-j+k)) / (√14.√3) = -3/√42. Hence θ = cos⁻¹(-3/√42).
©(i) Let P be the point on line l where λ = p. Then P has position vector r = (2i-j+3k)+p(i-j+k) = (2+p)i + (-1-p)j + (3+p)k. The vector AP is given by AP = r - a = ((2+p)i + (-1-p)j + (3+p)k) - (i+4j+2k) = pi - (5+p)j + pk. Taking the dot product of AP with (i-j+k), we get AP.(i-j+k)=7+3p.
©(ii) The foot of the perpendicular from point A to line l is the point on line l that is closest to point A. This point is obtained when AP is perpendicular to the direction vector of line l, which is (i-j+k). Therefore, AP.(i-j+k)=0. Substituting the expression for AP.(i-j+k), we get 7+3p=0, so p=-7/3. Substituting this value of p into the expression for r, we get r = (2-7/3)i - 8/3j + 2k. Hence, the coordinates of the foot of the perpendicular from point A to line l are (1/3,-8/3,2).
(d) The cartesian equation of a line with direction vector d and passing through a point with position vector a is given by r=a+λd. For line l, d=(i-j+k), a=(2i-j+3k), so its cartesian equation is r=(2i-j+3k)+λ(i-j+k).
Write the equation of the line in slope-intercept form.
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-5}{0 +4} \implies \cfrac{ -5 }{ 4 } \implies - \cfrac{ 5 }{ 4 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{ 5 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y -4 = - \cfrac{ 5 }{ 4 } ( x +4) \\\\\\ y-4=- \cfrac{ 5 }{ 4 }x-5\implies {\Large \begin{array}{llll} y=- \cfrac{ 5 }{ 4 }x-1 \end{array}}[/tex]
Alejandro is learning how to play guitar. One day out of the week, he attends a 45-minute lesson. The remaining days of the week, he practices guitar for 25 minutes per day. What total number of minutes does Alejandro spend at his lesson and practicing in 3 weeks?
Answer:
3 x 195 = 585 minutes
Step-by-step explanation:
In one week, Alejandro attends a 45-minute lesson and practices for (6 x 25) = 150 minutes (assuming a 7-day week). So, the total number of minutes that Alejandro spends on his guitar in one week is:
45 + 150 = 195 minutes
In 3 weeks, the total number of minutes that Alejandro spends on his guitar is:
3 x 195 = 585 minutes
Therefore, Alejandro spends 585 minutes on his guitar in 3 weeks, including attending a 45-minute lesson once a week and practicing for 25 minutes on the remaining days of the week.
Answer: The mean absolute deviation is approximately is 11.43.
can someone please helppp
Answer:
6 presents / minute
Step-by-step explanation:
We can represent the given information in a ratio:
amount of present wrapped : minutes it took to wrap
2/3 : 1/9
Then, we can multiply both sides by 9 (the reciprocal of 1/9) so that the right side of the ratio is 1 minute.
presents : minutes
2/3 : 1/9
× 9 × 9
6 : 1
So, Patricia can wrap 6 presents in 1 minute.
