The second vector that's perpendicular to the line we want (call it L) is missing; I'll denote it by ⟨a, b, c⟩.
The cross product of ⟨1, 1, 0⟩ and ⟨a, b, c⟩ is perpendicular to both of these vectors. The direction vector of L will be parallel to this cross product.
Compute the cross product.
⟨1, 1, 0⟩ × ⟨a, b, c⟩ = ⟨1•c - 0•b, 0•a - 1•c, 1•b - 1•a⟩ = ⟨c, -c, b - a⟩
Then the vector equation of L is
L(t) = ⟨c, -c, b - a⟩ t + ⟨-3, 3, -1⟩
As parametric equations, we write
x(t) = ct - 3
y(t) = -ct + 3
z(t) = (b - a) t - 1
Eliminating the parameter above, we get
x + y = (ct - 3) + (-ct + 3) = 0 ⇒ x = -y
and substituting
x = ct - 3 ⇒ t = (x + 3)/c
into z(t), we get
z = (b - a) (x + 3)/c - 1 ⇒ x = c (z + 1)/(b - a) - 3
As symmetric equations, then, we write
x = -y = c (z + 1)/(b - a) - 3
(b) by how much could the smallest sample observation, currently 8.1, be increased without affecting the value of the sample median?
The smallest sample observation that can increase 8.1 without changing the sample median's value is 4.4.
By sample median, what do you mean?The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set. Simply expressed, the sample median is the middle value after sorting the observations in ascending order if the sample size is odd. The sample median is the average of the two middle values if the sample size is equal. The data set's median value is the value that falls in the middle, ordered by magnitude. The sample median is the average of the two middle terms when the number of samples in the data set is even. When the data set is symmetrically distributed, the sample mean serves as a reliable indicator of the central tendency.
The median can be calculated as (12.5+12.6)/2=12.55.
The incremented least observed value is 12.5-8.1=4.4, and the difference is that.
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What is 1/2+(-5/6)+1/4 as A fiction
Answer: A=-1/12
Step-by-step explanation:
[tex]\displaystyle\\\frac{1}{2}+(-\frac{5}{6} )+\frac{1}{4}=\\\\\frac{1*6-5*2+1*3}{12} =\\\\ \frac{6-10+3}{12}= \\\\\frac{-1}{12}= \\\\-\frac{1}{12}[/tex]
Which numbers are irrational?
√100 √21 √36 √47
Which numbers are irrational? Select all that apply.
A. √21
B. √ 100
C. √47
D. √36
A bug crawls up a pole 2in. in 2min., then slips down 1in. in 1min,, then crawls up 2in. in 2min., and so on. At this rate, how long will it take the bug to reach the height of 10in.
Answer: It would take the bug 26min to clime the pole
Step-by-step explanation: For me I drew a pole and labeled it like a number line.
1. use or make a number line and plot 0-10 on it.
2. jump 2 points from 0 on the number line
3. Jump backwards once to make the equation accurate
4. plot the times it takes along the way to find the answer until you get to 10
I hope
Mr. Johns is using a high-clearance sprayer with two 30-foot booms. It will spray a 60-foot-wide strip. He sprayed a
960-foot-wide wheat field for weeds.
a. How many feet from the edge should he start?
b. How many round trips are needed to cover the field?
a) He will start 900 feet from the edge
b) 16 Round trips are needed to cover the field.
Because Mr. Johns intends to check a wheat field 960 feet wide for weeds so he will distribute a 60-foot wide strip using a high clearance sprayer that has two 30-foot booms.
a) 960 foot - 60 foot = 900 foot
Therefore, he should start 900 feet from the edge.
b) 960 foot / 60 foot = 16 Trips.
Therefore, 16 round trips are needed to cover the field.
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işlemleriyle çözer misiniz?
The oldest zoo in the United
States is the Central Park Zoo
in New York City. The zoo
opened in 1864.
1. How many years had the
Central Park Zoo been open
in 19642
2. How many years had it been
open in the year 2000?
researchers studied the food‑obtaining behavior of the bird known as parus major. in the wild, the birds can obtain food by finding it themselves or by taking advantage of the efforts of other birds via scrounging (e.g., stealing the food of others, joining food patches found by others). to investigate this behavior, researchers set up a puzzle-box where the bird slides a door to the side to reveal food, and the door stays open long enough for a non-solving bird to also take some of the food. the researchers used radio-frequency identification (rfid) tags to individually track data for each bird. they also used cameras to distinguish when a bird employed the producing strategy of solving the puzzle from when a bird surrounded by taking food after a different bird solved the puzzle. the researchers examined if the birds tended to generalize across the producing and scrounging strategies, if they specialized in a strategy, or if they showed some other pattern of food‑obtaining behavior. the histogram shows the proportion of each bird's total visits to the puzzle box that were scrounges. the frequencies indicate the number of birds whose visits to the box have the specified proportion of scrounges. only birds with at least 50 visits are included.
It can be concluded that only 2 birds of species A make alarm calls and 10 do not. For species B, there are no alarm calls.
What are birds and species?A class of warm-blooded animals known as the Aves, birds are distinguished by their feathers, toothless beaked jaws, hard-shelled eggs, high metabolic rates, four chambered hearts, and robust yet light skeletons.A species is, in its most basic sense, a group of biological individuals capable of interbreeding. Birds are grouped according to how closely related they are using DNA, morphological investigations, and behavioral analysis.Now,
When food is distributed, there are only 2 birds of species A that make alarm cries, compared to 10 species that do not. In light of this, it may be said that the species does not exhibit misleading behavioral false alarm.However, when food is distributed in Species B, there are no species making alarm sounds, demonstrating that Species A is using deceit.When food is concentrated and Species B are present, there are species of A that produce alarm cries, but only 2 do not.Hence, It can be concluded that only 2 birds of species A make alarm calls and 10 do not. For species B, there are no alarm calls.
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Identify each as an expression, equation, or inequality
Answer:
Equations
expression
inequality
equation
expression
equation
Step-by-step explanation:
An expression does not have an equal sign.
An equation does have an equal sign
Inequality has a > or< symbols
use a scalar projection to show that the distance from a point p1sx1, y1d to the line ax 1 by 1 c − 0 is
The distance from the given point to the given line is d = 13/5 units.
Given:
Point P = (-2 , 3 )line : 3x - 4y + 5 = 0To find:
Use projection to demonstrate the given formula.Use the formula to calculate the distance between two points and lines.So,
Let us define line L as follows:
ax + by + c = 0Choose A as the fixed point on line L with the coordinates ( m, k ).
The line L now gives the coordinates of any point (x, y):
a*( x - m ) + b*( y - k ) + c = 0That was accomplished by subtracting the coordinates (x,y) from (m,k).
The dot product of constants (a, b) to vector coordinates between points (x,y) to (m,k):
( a, b ) . ( x - m, y - k) = 0For the above expression to be true, the dot product of two orthogonal vectors must be zero.
As a result, vector (a, b) is always perpendicular to every vector pointing in the direction of line L.
The vector is:
v = ( x-m , y-k)It could be the line connecting the points (x_1, y_1) and (m, k).
The magnitude of the scalar projection of v onto a gives the distance d from the point P 1: (x_1, y_1) to the line L because the latter is the duration of the side of a right triangle with two vertices being P_1 and (m, k), and the other vertex lying on L.
So:
d = | component v along x |d = | v . ( a , b ) | / | (a , b ) |d = | (x_1 - m , y_1 - k ) . ( a, b)| / sqrt(a² + b²)d = | ax_1 + by_1 - (a*m + b*k) | / sqrt(a² + b²)In which point A (m,k) is on the line;
am + bk + c = 0 c = - (am + bk)Then,
d = | ax_1 + by_1 + c | / sqrt(a² + b²)Given a point P (-2,3) and a line L, the equation is 3x - 4y + 5 = 0.
Where.
(x_1 , y_1) = (-2 , 3 )(a, b) = ( 3 , -4 )c = 5Now, calculate:
d = | 3×(-2) + -4×3 + 5 | / sqrt(3² + 4²)d = | - 13 | / 5d = 13 / 5 unitsTherefore, the distance from the given point to the given line is d = 13/5 units.
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The correct question is given below:
Use scalar projection to show that the distance from a point P1(x1,y1) to the line ax+by+c=0 is |ax1+by1+c|/underfoot(a^2 +b^2)
Use this formula to find the distance from the point (-2,3) to the line 3x-4y+5=0
Pls pls help whoever gets it right gets a crown
Answer:
8/45m² + 2/35m
Step-by-step explanation:
...........................
What are the steps for using a compass and straightedge to construct the bisector of A?
Drag the steps and drop them in order from start to finish.
The correct sequence of the steps required to construct the bisector of [tex] \angle{A}[/tex] is presented as follows;
Place the point of the compass at point A and draw an arc that intersects the sides of [tex] \angle{A}[/tex]. Label the points of intersection as points B and C.Place the point of the compass on point B and draw an arc in the interior of the angleWithout changing the opening of the compass, place the point of the compass at point C and draw another arc in the interior of the angleLabel the intersection of the arcs in the interior of the angle as point D.Use the straight edge to draw [tex] \overrightarrow{AD}[/tex]What is the correct order of steps required to construct the bisector of [tex] \angle{A}[/tex]?The game given steps and their number of appearance in the question photo are;
1. Label the intersection of the arcs in the interior of the angle as point D.
2. Without changing the opening of the compass, place the point of the compass at point C and draw another arc in the interior of the angle
3. Place the point of the compass on point B and draw an arc in the interior of the angle
4. Use the straight edge to draw [tex] \overrightarrow{AD}[/tex]
5. Place the point of the compass at point A and draw an arc that intersects the sides of [tex] \angle{A}[/tex]. Label the points of intersection as points B and C.
The correct order of the steps required to construct the bisector of [tex] \angle{A}[/tex] is as follows;
Step 5 → Step 3 → Step 2 → Step 1 → Step 4
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Question 11(multiple choice worth 2 points) (order of operations mc) joshua purchased a game card for the arcade for a total of $18. he played two basketball hoop games for $3.25 each and four rounds of air hockey for $1.75 each. how much did he have left on the game card? $4.50 $6.50 $13.00 $13.50
The total balance remaining on Joshua's game card is $4.5. So, the correct option is (A).
In the Question, It is given that Joshua purchase a game card for $18 which makes the Balance Bal = $18 on his card.
Now, He played 2 rounds of Basketball hoop and each costs $3.25 which makes total for Basketball B = 2*3.25 => B = $6.25
And, He played 4 rounds of Air Hockey each game cost $1.75 which makes the total for Air Hockey A = 4*1.75 => A = $7
To calculate the remaining balance on his card we need to subtract these games' costs from the balance on his card :
=> T = Bal - B - A, Where T = Total, Bal = Balance on card, B = Basketball, A = Air Hockey
=> T = 18 - 6.25 - 7 => T = $4.5
Hence, the Total balance remaining on his card T = $4.5
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A bag contains 3 blue balls and x yellow balls. Write down the total number of balls in the bag
The answer to the question is 3+x
and the probability of blue balls is 3/3+x
We are required to find out the total number of balls that is the sum of blue and yellow balls
so the total number of balls in the bag is 3+x
The concept here used is probability.
Probability is the quantitative relation of rangethe amount|the quantity} of outcomes in thorough set of equally possible outcomes that manufacture a given event to the whole number of doable outcomes
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
probability of blue balls=blue balls/total balls
=3/3+x
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Hey your question is incomplete, the complete question is
A bag contains 3 blue balls and x yellow balls.Write down the total number of balls in the bag.If a ball is drawn from the bag, write down the probability that it is blue.
One x-intercept for a parabola is at the point (-4,0) use the factor method to find the other x-intercept for the parabola defined by this equation y=X^2-2x+8
According to the statement if One x-intercept for a parabola is at the point (-4,0) of the equation the other x-intercept for the parabola is (2, 0).
What is parabola?A parabola is an U-shaped mirror-symmetrical planar curve. It matches a variety of seemingly dissimilar mathematical formulations, all of which identify the same curves. A point and a line are two ways to describe a parabola.
What is the significance of the term "parabola"?Apollonius, who discovered numerous features of conic sections, is credited with the name "parabola." It signifies "application," referring to the "application of regions" notion, which, as Apollonius demonstrated, has a connection with this curve. Pappus is responsible for the focus-directrix attribute of the parabola as well as other conic sections.
According to the given statement:given equation: y=X² -2x+8
on solving the equation:
y==X² -2x+8
X² + 4x -2x -8
x(x - 4) -2(x - 4)
-1(x-2)(x+4)
According to the statement if One x-intercept for a parabola is at the point (-4,0) of the equation the other x-intercept for the parabola is (2, 0).
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What’s the distance between (2,-3) and (4,-3)
What expressions are equivalent to 4d+6+2d4d+6+2d4, d, plus, 6, plus, 2, d ?
solve for a in terms of b and c
b = 3a + 5ac
The hexagon is made from a rectangle and two identical triangles
Answer:
108cm^2
Step-by-step explanation:
Find the areas of the rectangle and the two triangles. Then add all three areas together. See image.
I need help, please IT CAN NOT WAIT
Answer:
D and E
Step-by-step explanation:
In order for the equations to have infinite amount of solutions, they have to be equal to each other.
A: 3x-1 doesn't equal 3x+1
B: 2x-1 is not equal to 1-2x since they negate each other.
C: 3x-2 doesn't equal 2x-3
D: 3(x-1)=3x-1*3=3x-3 ==> D is an answer.
E: 2(x+1)=2x+1*2=2x+2 ==> E is an answer
F: 3(x-2)=3x-6. However, 2(x-3)=2x-6. 3x-6 doesn't equal 2x-6.
Hence, 3(x-2) doesn't equal 2(x-3).
There are three number a,b and c, where a>b and b>c. Describe the positions of numbers on a number line
Answer:
the numbers lie on the number line from left to right: c, b, a
Step-by-step explanation:
a > b > c
bigger numbers are to the right on the number line
1. Construction workers build 54 feet of a bridge each day for 9 days. To determine whether the bridge is at least 490 feet long, can you use an estimate, or is an exact answer required? Explain.
The total length of the bridge built is less than the total length of the bridge.
How to Estimate Lengths?
We are given;
Length of bridge to be built per day = 54 feet
Number of days they built the bridge = 9 days
Thus, to find the total length that the bridge will span, we multiply the length built each day by the number of days. Thus;
Total Length of bridge = (54 * 9)
Total Length of bridge = 486 ft
Since we want to find if the bridge is at least 490 feet long. Thus, the total length of the bridge built is less than the total length of the bridge.
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Team Dragon's kite is 4 feet long and 3 feet across. How much fabric does it take to make their kite?
The area of a Dragon's kite with the given dimensions is 6 square feet.
Given that, team Dragon's kite is 4 feet long and 3 feet across.
We need to find how much fabric it takes to make their kite.
What is the area of the kite?The area of a kite can be defined as the amount of space enclosed or encompassed by a kite in a two-dimensional plane. Like a square, and a rhombus, a kite does not have all four sides equal.
The area of a kite is half the product of the lengths of its diagonals. The formula to determine the area of a kite is Area = ½ × d1 × d2. Here d1 and d2 are long and short diagonals of a kite.
Now, the area of Dragon's kite = 1/2 × 4 × 3=6 square feet.
Therefore, the area of a Dragon's kite with the given dimensions is 6 square feet.
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A teacher has $230 in a bank account to spend on school supplies and wins an additional $50 to put toward the school supplies. The teacher spends $120 on binders for students and wants to buy the classroom a new $180 tablet.
Answer:
-20
Step-by-step explanation:
pharmaceutical company conducts an experiment in which a subject takes 75 mg of a substance orally. the researchers measure how many seconds it takes for one quarter of the substance to exit the bloodstream. what kind of variable is the company studying?
The pharmaceutical company uses the quantitative variable to conducts an experiment.
Variables:
A variable is a characteristic of an object. Their values may occur more than once for a set of data. We consider just two main types of variables in this course.
Quantitative Variables - Variables whose values result from counting or measuring something.
Qualitative Variables - Variables that are not measurement variables. Their values do not result from measuring or counting.
Given,
A pharmaceutical company conducts an experiment in which a subject takes 75 mg of a substance orally.
And the researchers measure how many seconds it takes for one quarter of the substance to exit the bloodstream.
Here we need to find the kind of variable is the company studying.
Here the company uses the Qualitative Variable because here they measure the effects of the medicine not the measurement.
So, the experiment uses the Qualitative Variable.
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Jack has 150 feet of barb wire and needs to put it on 35 3/4 feet of fencing. how much barb wire can he use for each foot
Jack can use 3 3/14 feet of Barb wire used for each foot when he has 150 feet of barb wire which needs to be put on 35 3/4 feet of fencing.
We are given that:
Jack has 150 feet of Barb wire.
The fencing is:
35 3/4 feet that is equal to
= 140 / 3 feet
For each foot the Barb wire will be calculated by dividing the total Barb wire by the wire required for fencing.
So, we get that:
Barb wire used for each foot = 150 ÷ 140 / 3
Barb wire used for each foot = 450 / 140
Barb wire used for each foot = = 45 / 14
Barb wire used for each foot = 3 3/14 feet.
So, Jack can use 3 3/14 feet of Barb wire used for each foot when he has 150 feet of barb wire which needs to be put on 35 3/4 feet of fencing.
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For each situation, write an equation that will model the situation.
where he kicked
Twinkle Toes Tony kicked a football, and it landed 100 feet from
also reached a maximum height of 125 feet. Write an equation that models the path of the
ball while it was in the air.
The equation that models the path of the ball is y = -0.05·x² + 5·x.
Given,
The distance where the football landed from where it was kicked = 100 feet
The maximum height that the football reached = 125 feet
We have to write an equation that models the path of the ball while it was in the air.
The path may be parabola.
So, equation is like:
y = a·(x - h)² + k
Where;
(h, k) = The coordinate of the vertex (which is the coordinates of the highest point reached by the ball)
Therefore, taking the x-coordinate of the highest point reached by the ball as midpoint of the horizontal distance moved by the ball, we have;
The x-coordinate of the midpoint of the horizontal distance moved by the ball = (50, 0)
We have;
The coordinate of the highest point reached by the ball = (50, 125)
Therefore;
(h, k) = (50, 125)
Substituting the above values in the equation of the parabola gives;
y = a·(x - 50)² + 125
At x = 100, y = 0, which gives;
0 = a·(100 - 50)² + 125 = a·2500 + 125
0 = a·2500 + 125
a = -125/2500 = -0.05
Therefore, we have;
y = a·(x - h)² + k = y = -0.05 × (x - 50)² + 125 = -0.05·x² + 5·x - 125 + 125
y = -0.05·x² + 5·x - 125 + 125 = -0.05·x² + 5·x
y = -0.05·x² + 5·x
The equation that models the path of the ball is y = -0.05·x² + 5·x.
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pls help me it’s due today!!
By checking the piecewise function and evaluating it at x = 1, the result of the piecewise function is equal to - 4.
How to evaluate a piecewise function at a given point of the real set
Piecewise functions are functions formed by several expressions constrained by intervals in the real set. In this case we find a piecewise functions consisting in two expressions constrained by two intervals in the real set. The piecewise function is defined by these expressions:
f(x) = (x + 2)² - 5 for x ≠ 1, that is x < 1 and x > 1.f(x) = - 4 for x = 1.Then, we need to evaluate the piecewise function at x = 1. By direct inspection, we conclude that the value according to the piecewise function evaluated at x = 1 is equal to - 4.
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to determine customer opinion on their service uisness depot randomly selects 130 stores during a certain week
As we first choose a cluster of the store before surveying all of the customers present in the store, they employed cluster sampling in this instance.
Describe cluster sampling and its variations?A population is divided into several clusters that are representative of homogeneous traits and have an equal chance of being included in the sample using the sampling technique known as cluster sampling.
Cluster sampling using a single stage: As the name implies, sampling only happens once.
Two-stage cluster sampling: In this case, a small number of individuals are chosen from each group by means of systematic or simple random sampling rather than the entire cluster.
Multiple stage cluster sampling: Compared to two stage sample, multiple stage cluster sampling goes one or more steps beyond. Complex clusters must be formed in order to conduct effective research across several geographies, and this can only be done by employing the multiple-stage sampling technique.
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nb 3 all parts pls pls very important pls and thank you!!
Step-by-step explanation:
(a)
First:
Get AE using Pythagoras
[tex] {ae}^{2} = {6}^{2} + {8}^{2} [/tex]
[tex] {ae}^{2} = 100[/tex]
AE =10
Connect OM to form Traingle AOM.
AM=5cm (AE is 10 and AM=ME meaning that they are divided into two equal parts)
AM^2=OM^2+AO^2
5^2=OM^2+4^2
OM^2=5^2-4^2
OM=3
(B) OM is parallel to BE because of midpoint theorem
The Theorem states that The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
(C) AOM is a right angled triangle at O because angle AOM is 90°. Because OM is a perpendicular Line that bisects the chord of AB