The vector [v] whose direction is same as that of vector [u] is given as -
[v] = -24i + 45j.
What is an expression? What is a expression? What is a mathematical equation? What is vector?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A vector quantity is a quantity that has both magnitude and direction.
We have the a vector [v] with the given magnitude and the same direction as u.
We can write vector [u] as -
[u] = - 8i + 15j
Unit vector {u} along vector [u] -
{u} = [u] / |u|
{u} = (- 8i + 15j)/17
We can write vector [v] as -
[v] = 51 x (- 8i + 15j)/17
[v] = 3(- 8i + 15j)
[v] = -24i + 45j
Therefore, the vector [v] is given by [v] = - 24i + 45j.
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The Excel Cable Company has a monthly fee of $32.00 and an additional charge of $8.00 for each premium channel. The Best Cable Company has a monthly fee of $26.00 and an additional charge of $10.00 for each premium channel. The Horton family is deciding which of these two cable companies to subscribe to. For which number of premium channels will be the total monthly subscription fee for the excel and best cable companies be the same
Answer:
We can set up the following equation:
Excel Cable Company fee = Best Cable Company fee
32 + 8x = 26 + 10x
Here, x represents the number of premium channels. We can solve for x by subtracting 26 from both sides and then dividing both sides by 2 to get:
6 + 6x = 10x
6 = 4x
x = 6/4
x = 1.5
Therefore, the total monthly subscription fee for the Excel and Best cable companies will be the same for 1.5 premium channels. Note that this is not a whole number, so it is not possible for the subscription fees to be the same for a whole number of premium channels
Answer: 3 channels
Step-by-step explanation:
The ECC has an initial fee of $32.00 with a $8.00 fee for each channel, so we can label that as Total = 8(x) + 32.00.
The BCC has an initial fee of $26.00 with a $10.00 fee for each channel, so we can label that as Total = 10(x) + 26.00.
Since we want to find how many premium channels each company needs till the monthly subscription rate will be equal, we can set those equal to eachother.
8x + 32.00 = 10x + 26.00
2x = 6
x = 3, so when each company has 3 premium channels used, the prices will be the same.
what is the correct answer (with the appropriate number of significant figures) for the calculation of 7.5 2.26 1.311 2?
The appropriate number of significant figures for the calculation of 7.5 + 2.26 + 1.311 + 2 is equivalent to 10.
Significant figures:
Any non-zero number is significant. The number 33.2 has 3 significant digits because all digits present are non-zero.
Zeros between two non-zero numbers are valid. 2051 has 4 significant digits. Zero is between 2 and 5.
For numbers in exponential notation:
N x 10x, all numbers spanning N are valid. "10" and "x" are not important. 5.02 x 10^4 has 3 significant digits.
"5.02." "10" and "4" are not important.
Provides the ability to change the precision of a value by manipulating its shape. For example, write 1100 with 3 significant digits. 1100 has 2 significant digits. The trailing two zeros are not significant. Adding a decimal at the end brings the number to the 1100th significant digit (according to rule 5).
We can create a 3-significant digit of 1.10 x 10^3.
In the question of adding all we get,
7.5 + 2.26 = 9.76
9.76 + 1.311 + 2
9.76 + 1.311 = 11.071
11.071 + 2
11.071 + 2 = 13.071
13.071
Round 13.071 → 13
This is because the total sum of the numbers gives a value of 13.071.
However, the number '2' has only one significant figure.
Therefore, we need to restrict our solution to one significant figure.
Therefore, on rounding off the solution becomes '10' with only one significant figure.
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How long does it take to travel 200 km at 40 km per hour?
Answer:
5 hours
Step-by-step explanation:
Time = 200÷40 = 5 hours.
Which trigonometric ratio should be used to find height (h) of the escalator? (MGSE9-12.G.SRT.7, MGSE9-12.G.SRT.8)
The trigonometric ratio is sin 10° = h/109
Which ratios in trigonometry are there?
Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). The branch of geometry known as trigonometry examines the sides and angles of a right-angled triangle.
What three types of trigonometry are there?
Three crucial trigonometric functions—sine, cosine, and tangent—are represented by the abbreviations sin, cos, and tan. tan
Given that :
Hypotenuse = 109 ft
Height = h
Hence sin = height / Hypotenuse
sin 10° = h/109
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brawdy plastics, inc., produces plastic seat belt retainers for general motors at their plant in buffalo, new york. after final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. how fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. to test this theory, brawdy plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. the following data were collected. excel file: data14-05.xlsx line speed number of defective parts found 20 23 20 21 30 19 30 16 40 15 40 17 50 14 50 11 if required, enter negative values as negative numbers. a. select a scatter diagram with the line speed as the independent variable. a. b. c. d. a b. what does the scatter diagram developed in part (a) indicate about the relationship between the two variables? negative relationship c. use the least squares method to develop the estimated regression equation (to 1 decimal). d. predict the number of defective parts found for a line speed of feet per minute.
a. The scatter diagram indicates that the Number of Defective Parts found increases with Line Speed
b. The regression model is Y = 27.5 - 0.3·X
c. When the line speed is 25 feet per minute, the number of expected defective parts is 20 defective parts.
According to the Question:
The give data is presented as follows'
Line Speed; 20, 20, 30, 30, 40, 40, 50, 50
Number of Defective; 23, 21, 19, 16, 15, 17, 14, 11
Now,
1. From the scatter diagram there is an apparent correlation between increase line speed and the number of defective parts found.
2. The equation for linear regression by the least squares method is presented as follows;
Y = a + b·X
Where;
b = N ∑XY - (∑X) (∑Y) / N ∑X² - (∑X)² -------------------- (1)
and
a = ∑Y - b ∑X / N ---------------------------- (2)
Now, after calculation, we have;
∑X = 280, ∑Y = 136, ∑X² = 10,800, ∑XY = 4,460, (∑X)² = 78,400, N = 8
Putting in equation (1) and (2), we get;
b = (8×4460 - 280×136) / (8×10,800 - 78,400) = -0.3
and,
a = (136 - (-0.3)×280)/8 = 27.5
Therefore, we have the linear regression as follows;
Y = 27.5 - 0.3·X
Therefore, when the line speed is 25 feet per minute, we have;
Y = 27.5 - 0.3 × 25 = 20
The number of defective parts expected to be found when the line speed is 25 feet per minute, Y = 20 defective parts.
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Problem
The sum of 3 consecutive even numbers is 132.
What is the third number in this sequence?
Answer:
46
Step-by-step explanation:
because it is ...... maybe
2.Select the number below that is irrational.
Answer:
Step-by-step explanation:
the second one
a cable company must provide service for 6 houses in a particular neighborhood. they would like to wire the neighborhood in a way to minimize the wiring costs (or distance). what is the minimal length of the network required to span the entire neighborhood?
The minimal Length of network to cover the entire neighborhood is 1200 yard , the correct option is (d) .
In the question ,
a table of of distance between the 6 cities is given ,
we have to find the minimal length in which all the neighbor hood can be connected .
From the table we can see that ;
the minimum distance to connect the house 1 to house 2 = 100 yards.
the minimum distance to connect the house 3 is from 2 to 3 = 300 yards.
the minimum distance to connect the house 4 is from 2 to 4 = 250 yards.
the minimum distance to connect the house 5 is from 4 to 5 = 300 yards.
the minimum distance to connect the house 6 is from 4 to 6 = 250 yards.
On adding all the distance ,
we get , the minimum distance = 100 + 300 + 250 + 300 + 250 = 1200 yards .
Therefore , the minimal length of the network is 1200 yards .
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now, assume that you have laid out the namecards for 14 people, and you want to hide 4 golden tickets, at most one under each namecard. in how many ways is this possible?
Assume that you have laid out the namecards for 14 people, and you want to hide 4 golden tickets, at most one under each namecard. The total number of ways = 784
From the question, we have
The total number of people in each party = 8
The total number of winners in each party = 2
The total number of ways of selecting two winners from 8 people = P(8,2) = 28
The total number of ways of selecting two winners from each political party = 28*28 = 784
The total number of ways = 784
Multiplication:
To determine the sum of two or more numbers, mathematicians multiply the numbers. It is a basic mathematical procedure that is widely used in daily life. Multiplication is used when we need to mix groups of like sizes. Multiplication is a representation of the underlying idea of adding the same number repeatedly.
The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.
Complete question:
In celebration of Chinese new year, you are arranging name cards for 16 people to sit around this table. Since the cards are placed on the rotating lazy Susan, the specific chair of a guest does not matter, only who is to their left and right. That is, two namecard arrangements are considered different iff there is a guest whose person on their right or left changes. Now when you hide four golden tickets under the placed name cards, you want to ensure that each party has two winners. In how many ways can you choose to do so?
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Please help!!! i need this done by tonight!! 30 points!!
The symbol ∠ is used to denote an angle. The symbol m ∠ is sometimes used to denote the measure of an angle.
What is angle for example?The two hands together make different sets of lines from a common point. These sets of lines from a common point is called angle. The two hands form different angles every minute of the time. A clock forms an example of angles in real life.When the angle between two lines is it is said to be zero angle. The angle between twAn angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle. The word angle comes from a Latin word named 'angelus,' meaning “corner or rays becomes when both the rays are in the same direction.Tape random straight lines across students' tables to create lots of angles where the tape overlaps. Then ask your students to sit around the table with a marker, and encourage them to classify as many angles as they could. After classifying angles, your pupils can then move on to measuring them.x = 15
∠H = 82
∠I = 49
∠G = 49
Note that side HG and side HI are congruent ( indicated by the little dashed line ) which means that their opposite angles are congruent ( ∠I and ∠G to be more specific. )
Angles in a triangle add up to equal 180°
Hence, 3x + 37 + 2 ( 4x - 11 ) = 180 ( note that the 2 in 2(4x - 11) came from angles I and G being congruent )
We now solve for x
3x + 37 + 2 ( 4x - 11 ) = 180
step 1 distribute the 2 to the 4x and -11
2 + 4x = 8x
-11 * 2 = -22
we now have 3x + 37 + 8x -22 = 180
step 2 combine like terms
3x + 8x = 11x
37 - 22 = 15
we now have 11x + 15 = 180
step 3 subtract 15 from each side
15 - 15 cancels out
180 - 15 = 165
we now have 11x = 165
step 4 divide each side by 11
11x / 11 = x
165 / 11 = 15
we're left with x = 15
Our final step is to find the measures of ∠G, ∠H and ∠I
We can do this by simply replacing x with 15 in their given expression
∠H = 3x + 37
* substitute 15 with x *
3 ( 15 ) + 37
3 * 15 = 45
45 + 37 = 82
Hence, ∠H = 82
∠I = 4x - 11
* substitute x with 15 *
4(15) - 11
4 * 15 = 60
60 - 11 = 49
Hence, ∠I = 49
Like stated previously ∠G and ∠I are congruent
Hence, ∠G = 49
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please help!!
Ray BX is an angle bisector of angle ABC. If m∠ABX = 2y+10, and m∠ABC = 10y-4, calculate the measure of angle XBC.
The measure of angle XBC is 18°.
Given that, ray BX is an angle bisector of angle ABC.
What is an angle bisector?The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.
Here,
m∠ABX = 2y+10, and m∠ABC = 10y-4
Now, m∠ABC = m∠ABX + m∠XBC
m∠ABX = m∠XBC
⇒ 10y-4 = m∠ABX+m∠ABX
⇒ 10y-4 = 2∠ABX
⇒ 10y-4 = 2(2y+10)
⇒ 10y-4 = 4y+20
⇒ 10y-4y = 20+4
⇒ 6y = 24
⇒ y=4
So, m∠XBC=2y+10
= 18°
Therefore, the measure of angle XBC is 18°.
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which of the following is the most appropriate interpretation of the y-intercept? group of answer choices for a car weighing 68.17 pounds we would expect a fuel efficiency rating of 0 mpg. for a car weighing 6,817 pounds we would expect a fuel efficiency rating of 0 mpg. for a car weighing 0 lbs we would expect a fuel efficiency rating of 6,817 mpg. for a car weighing 0 lbs we would expect a fuel efficiency rating of 68.17 mpg.
The correct interpretation regarding the y-intercept of the least squares regression line is given as follows:
For a car weighing 0 lbs we would expect a fuel efficiency rating of 68.17 mpg.
What is the y-intercept?For a function, the y-intercept represents the value assumed by the output of the function when the input of the function assumes a value of zero.
For the least squares regression line in this problem, the input variable and the output variable are defined as follows:
Input variable: weight of each car.Output variable: fuel efficiency of the car.The y-intercept in this problem has a value of:
68.17.
Meaning that when the weight is of 0 pounds, the fuel efficiency is of 68.17 mpg.
Missing InformationThe missing part of the problem is of:
"For this data set, X represents the weight of each car in hundreds of pounds, and Y represents the predicted fuel efficiency of each car in miles per gallon (mpg). Note that 68.17 is reasonable value for the y-intercept of the least squares regression line. Which of the following is the most appropriate interpretation of the y-intercept?"
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Lily measures the circumference of three pillars.
Complete the table to show Lily’s measurements, the actual measurements, the difference between the measurement and the actual, and the percent error.
By using the concept of percentage, the complete table has been shown below
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage. For example 13% means [tex]\frac{13}{100}[/tex]. Here 13 is expressed as a fraction of 100.
For marble
Lily's Measurement = 90 cm
Actual Measurement = 90 + 10 = 100 cm
Absolute difference = 10 cm
Percent error = [tex]\frac{10}{100} \times 100[/tex] = 10 %
For granite
Lily's Measurement = 65 cm
Actual Measurement = 50 cm
Absolute difference = 15 cm
Percent error = [tex]\frac{15}{50} \times 100[/tex] = 30 %
For concrete
Lily's Measurement = 30 + 6 = 36 cm
Actual Measurement = 30 cm
Absolute difference = 6 cm
Percent error = [tex]\frac{6}{30} \times 100[/tex] = 20 %
Marble Granite Concrete
Lily's
Measurement 90 cm 65 cm 36
Actual
Measurement 100 cm 50 cm 30
Absolute
Difference 10 cm 15 cm 6
Percentage
Error 10% 30% 20%
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Complete Question
The table has been attached
In the diagram below, quadrilateral STUV is inscribed in circle W. Find the
measure of U.
76⁰
3
W.
77°
104 degrees is the measure of angle U.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that a quadrilateral STUV is inscribed in circle W
We need to find the measure of U.
A quadrilateral is a four-sided polygon, having four edges and four corners.
In quadrilateral the sum of opposite angles should be equal to 180 degrees.
Let the measure of U is x.
∠S+∠U=180
76+x=180
Subtract 76 from both sides
x=180-76
x=104
Hence, the measure of U is 104 degrees.
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5 years ago Patricia put 1200 in a saving account with a 1.5% interest rate. how much does she have now in her savings account now
PLEASE HELP!!!!!
The amount of money in her account after five years will be $1,292.74.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
A long time back Patricia put 1200 in a saving record with a 1.5% financing cost. Then the amount of money in her account after five years will be given as,
A = $1,200 × (1 + 0.015)⁵
Simplify the expression, then we have
A = $1,200 × (1.015)⁵
A = $1,200 × 1.07728
A = $1,292.74
The amount of money in her account after five years will be $1,292.74.
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Question 7 (Essay Worth 6 points)
(04.03 MC)
On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.
Can drive Cannot drive Row Totals
0.60
Likes to fly
Do not like to fly
Column totals 0.55
0.18
0.45
1.00
Complete the relative frequency table, showing all necessary calculations.
×84 DID
Source C
BIUS x, x Tx
I
E E 99
=
Styles
▾
Format
▼
Font
(
Size
A- A
The completed relative frequency table is given by the image shown at the end of the answer.
How to complete the relative frequency table?First we look at the row total of people who like to fly, which is of 70%, hence:
It is stated in the table that the proportion of those who like to fly and can drive is of 0.32.Hence the relative frequency of those who like to fly and cannot drive is of: 0.7 - 0.32 = 0.38.Amount those who can drive, we have that:
The total is of 0.45.0.32 like to fly.Hence the relative frequency of those who do not like to fly is of: 0.45 - 0.32 = 0.13.Amount those who cannot drive, we have that:
The total is of 0.55.0.38 like to fly.Hence the relative frequency of those who do not like to fly is of: 0.55 - 0.38 = 0.17.Thus the total frequency of the second row is given as follows:
0.17 + 0.13 = 0.30.
Missing InformationThe table is given by the image shown at the end of the answer. I don't know if the values are the same but you will have to follow the same procedure to obtain the missing values.
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Answer:
I took the test
the answer is in the image below
Step-by-step explanation:
a group of nine people are attending the movies together. (a) two of the nine insist on sitting side-by-side. in how many ways can the nine be seated together in a row? 40320 (b) two of the people do not like each other and do not want to sit side-by-side. now how many ways can the nine be seated together in a row?
a group of nine people are attending the movies together . now 40320 ways can the nine be seated together in a row by combination.
(a) The two people who insist on sitting side-by-side can be seated in 1 way. The remaining 7 people can be seated in 7! ways. Therefore, the total number of ways in which the 9 people can be seated together in a row is 1 x 7! = 40320.
(b) In this case, the two people who do not like each other can be seated in (7-1)! ways. The remaining 7 people can be seated in 7! ways. Therefore, the total number of ways in which the 9 people can be seated together in a row by combination is (7-1)! x 7! = 40320.
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what is
11.49 - (-21 )
A five-card hand is dealt at random from a standard deck. What is the probability that the hand contains exactly two face cards?
By using the concept of probability, it can be calculated that
Probability that the hand contains exactly two face cards = [tex]\frac{209}{833}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
From the set of five cards, two cards can be chosen in [tex]{5 \choose 2}[/tex] ways = 10 ways
Number of face cards = 12
Number of non face cards = 52 - 12 = 40
Probability that the hand contains exactly two face cards = [tex]{5 \choose 2}\times \frac{12}{52} \times \frac {11}{51} \times \frac{40}{50} \times\frac{39}{49}\times \frac{38}{48}\\[/tex]
[tex]\frac{209}{833}[/tex]
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answered
Nakeisha's family took a road trip to Mount Rushmore. Nakeisha fell asleep 18% of the way through the trip. If the total length of the trip was 400 miles, how many miles had they travelled when Nakeisha fell asleep?
a. How did you identify and name the semicircles?
Answer:
___And Its Name Is Half Circle
Which transformation shows that △ ABC and △ DEF are similar?
C. A reflection across the x-axis followed by a translation of 1 unit right and 1 unit down
Preimage Points are:
A(-4,1) B(-6,5) C(-1,2)
Image points are:
D(-2, 3) E(-5, -6) F(0, -3).
What is reflection:
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected image should be the same size and shape as the original, but it faces the opposite way. Changes in position during reflection may also result in translation. Pre-image and image are terms used to refer to the same thing in this context.
So in our Questions reflection across the x axis will negate the y coordinate of each point this will map
A(-4, 1)→(-4, -1)
B(-6, 5)→(-6, -5)
C(-1, 2)→(-1, -2)
We can see that each x-coordinate is 1 lower and each y-coordinate is 1 higher than the image points by comparing these points to the points in DEF. This means that we should translate 1 unit to the right and 1 unit to the bottom to subtract 1 from each x-coordinate and 1 from each y-coordinate.
Given Question is incomplete complete question here?
What series of transformations from △ABC to △DEF shows that △ABC≅△DEF ?
A . a reflection across the y-axis followed by a translation of 1 unit right and 2 units up
B . a clockwise rotation of 90° about the origin followed by a translation of 4 units right and 4 units up
C. a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down
D . a reflection across the line y = x followed by a positive rotation of 270° about the center
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X-y=-6
6x-3y=-9
Can you show the steps please
Answer:
Step-by-step explanation:
x-y=-6 (1)..
6x-3y=9 (2)...
First, multiply (1) by 6:
6x-6y=-36
Now subtract the whole eqaution:
6x-6y=-36
- 6x-3y=9
----------------------
-3y = -45
y=15
Now substitute y into one of the equations:
x-15=-6
x=9
So the answer is x=9, and y=15.
-5x+8=y
I don’t know the answer to this
Answer:
Let x=1
-5*x+8=y
-5*1+8=y
-5+8=y
3=y
Another
Let x=-1
-5*(-1)+8=y
5+8=y
13=y
There are multiple endings I suppose this is a point of intersection question that needs to be done on graph
the problem with measurement is that researchers cannot account for errors statistically question 1 options: true false
It is partially true that the problem with measurement is that researchers cannot account for errors statistically.
Why do errors occur in measurement?During measurements, there is a huge possibility that an error will occur and even no result or measurement can be 100% accurate. This happens due to many factors like mistakes, approximations, and other physical factors.
Coming to the statement, definitely researchers cannot account for errors. This is true, but this is not a problem since it is something that will, for sure, occur. The major goal is towards minimizing it.
So, the given statement is partially true.
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which list orders the fractions from least to greatest 2/3, 7/12, 17/24, 3/4 ?
Answer:
The bigger the denominator the less the value will be.
Just for clarification of what he said.
What is the slope of AB?
m=
A (-6, -4)
B(-3,4)
Find the equation of the line with Slope = 2 and passing through (2,11). Write your equation in the form
y=mx+b
Answer:
y = 2x + 7
Step-by-step explanation:
Use the formula y - y1 = m(x - x1)
Step-by-step explanation:
formula =y-y1=m(x-x1)
A lap around the track is 1/4 of a mile. Josie completes a lap in 1.3 minutes. If she continues at the same pace, how long will it take her to complete
a mile? Express your answer as a decimal in simplified form..
minutes
Answer:
5.2 or 5:12
Step-by-step explanation:
1.3*4 = 5.2 or 5:12. That's a pretty fast mile.
I need help with this question
Answer:
not really sure but it could be a