Answers
Given that the initial point of vector "u" is:
[tex](4,8)[/tex]And the terminal point:
[tex](-12,14)[/tex]You need to find the Component Form of the vector with this formula:
[tex]u=\langle x_2-x_2,y_2-y_1\rangle[/tex]In this case:
[tex]\begin{gathered} x_2=-12 \\ x_1=4 \\ y_2=14 \\ y_1=8 \end{gathered}[/tex]Then, you get:
[tex]u=\langle-12-4,14-8\rangle=\langle-16,6\rangle[/tex]Find the Magnitude using this formula:
[tex]||u||=\sqrt{x^2+y^2}[/tex]In this case:
[tex]\begin{gathered} x=-16 \\ y=6 \end{gathered}[/tex]Therefore, by substituting values and evaluating, you get:
[tex]||u||=\sqrt{(-16)^2+(6)^2}\approx17.088[/tex]In order to find the direction of the vector "u", you need to use this formula:
[tex]\theta=tan^{-1}(\frac{y}{x})[/tex]Then, when you substitute the values of "x" and "y" into the formula and evaluate, you get:
[tex]\theta=tan^{-1}(\frac{6}{16})\approx20.556°[/tex]Hence, the answer is:
Related Questions
There is a 0.99967 probability that a randomly selected 30-year-old female lives through the year. An insurance company wants to offer her a one-year policy with a death benefit of $900,000. How much should the company charge for this policy if it wants an expected return of $400 from all similar policies?
Answers
Using probability we can calculate that the company must charge $697 for an expected return of 400 .
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
The probability that a 30 year old female lives throughout the year
= 0.99967
Death benefit = $900,000
Expected amount the company would pay = probability that a person dies × insurance amount.
Expected amount = (1 - 0.99967) × 900000 = $297
Now Company wants a profit of $400
Cost charged by company =$( 297 + 400 ) = $ 697
Therefore using probability we can calculate that the company must charge $697 for an expected return of $400 .
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1. Use complete sentences to explain how the special angles created by the Intersection of A and B by D can beused to solve for x.2. Solve for x, showing all of your work.3. Find the measure of <6.
Answers
According to the graph we have:
1. If the lines A and B cut by the secant D are parallel, then the collateral angles are supplementary, i.e. add up to 180°. In this case:
[tex](3x+7)+(4x+5)=180[/tex]2. Solve for x:
[tex]\begin{gathered} 3x+7+4x+5=180 \\ 7x+12=180 \\ 7x+12-12=180-12 \\ 7x=168 \\ \frac{7x}{7}=\frac{168}{7} \\ x=24 \end{gathered}[/tex]Answer: x = 24
3. Angle 6 corresponds to angle 3x + 7 so they are equal. So:
[tex]\angle6=3x+7[/tex]Where: x = 24
Substitute the value:
[tex]\angle6=3(24)+7=72+7=79[/tex]Answer: <6 = 79°
please help me out with this
Answers
Answer:
c
Step-by-step explanation:
Solve the inequality.
C - 12 > -1
Answers
Answer:
c>11
Step-by-step explanation:
you +12 on both sides then u now have 11 rather than -1 which leaves u with c>11
a pound in lukes neighborhood has a depth of 81.6 inches. during the dry season the pond losses an average of 0.02 inches of water each day. luke wrote the function below to represent the depth of the pond in inches x days after the dry season begins. explain lukes error and rewrite the function correctly? f(x) = -0.02(x+81.6)
Answers
The correct function to represent the depth of the pond in inches x days after the dry season begins is f(x) = 81.6 - 0.02x
It is a question of functions.
Given that:-
Depth of pond in Luke's neighborhood = 81.6 inches.
Depth that pond loses everyday = 0.02 inches
Function written by Luke to represent the depth of the pond in inches x days after the dry season begins = f(x) = -0.02(x+81.6)
We have to find the error in Luke's function and then rewrite then correct function.
Let x be the number of days after the dry season begins.
We know that,
Depth of pond after x days = Initial depth of pond - (Depth that pond loses everyday)* (number of days after the dry season begins)
Hence, we can write,
f(x) = 81.6 - 0.02x
Luke has wrongly multiplied -0.02 with (x + 81.6) instead of only multiplying with x.
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Last year, Singer A performed two more than five times as many shows during concert tours than Team B. The number of Singer A concert tour shows exceeded the number of shows by Team B by 74. How many concert shows did each perform?
Singer A had
Correct shows and Team B had
Correct
Answers
ANSWER. B = 18, A = B + 23 = 18+23 = 41.
Step-by-step explanation:
Which equation shows direct variation?O y = 2xO y = x+2O y = 2x+2
Answers
In order to determine which equation shows direct variation, you take into account that a direct variation is a linear equation that can be written in the following form:
y= kx
here k is a constant fdifferent of zero. By comparing the given options you can notice that only the equation y = 2x
Hence, y = 2x shows a direct variation.
(-4,-1) that is perpendicular to the line with the equation 4x+5y=5 how do I do this
Answers
To find the line that is perpendicular to the one we have, the first step is to rewrite the expression in the slope-intercept form.
[tex]\begin{gathered} 4x+5y=5 \\ 5y=5-4x \\ y=\frac{5-4x}{5} \\ y=-\frac{4}{5}x+1 \end{gathered}[/tex]The slope of this line is -4/5. The one that is perpendicular to it has a slope that is negative reciprocal to this one, which means that we need to invert the fraction and the signal.
[tex]\begin{gathered} m=-(\frac{1}{\frac{-4}{5}}) \\ m=-(\frac{-5}{4})_{} \\ m=\frac{5}{4} \end{gathered}[/tex]The equation for the perpendicular line so far is:
[tex]y=\frac{5}{4}x+b[/tex]To find "b" we need to replace the coordinates of (-4,-1) and solve for b.
[tex]\begin{gathered} -1=\frac{5}{4}\cdot(-4)+b \\ -1=-5+b \\ b=-1+5 \\ b=4 \end{gathered}[/tex]The full expression is:
[tex]y=\frac{5}{4}x+4[/tex]Given the system of equation 3x - 2y-9=0 X + 8y-3 = 0 Is (3, 0) a solution to the given system?
Answers
Yes (3,0) is the solution of the given equation.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given Data
Equation
3x - 2y-9=0
X + 8y-3 = 0
Solution(3, 0)
Finding the values of x,
x + 8y - 3=0
x = 3 + 8y...(1)
Substituting x in the equation
3x - 2y = 9
3(3+ 8y) -2y = 9
9 + 24y - 2y = 9
22y = 0
y = 0
Substituting the value in (1)
x = 3 + 8(0)
x = 3
Yes (3,0) is the solution of the given equation.
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Identify which is a function and which are not
Answers
Answer:(5,4) , (4,-2) , (-1,0) , (-2,-4)
Step-by-step explanation: Each input can only have one output
9 ft19 ftPlease refer to the rounding rules in the instructions.Circumference of the base = 59.5feetArea of the base = 254.3square feetSlant height = 19feetHeight = 16.7feetLateral area =536.9square feetSurface area = 791.2square feetVolume =cubic feetBlank 1: 59.5Blank 2: 254.3Blank 3: 19Blank 4: 16.7Blank 5: 536.9Blank 6: 791.2Blank 7:
Answers
The volume of a right cone is one-third of the product of the area of the base B and the
[tex]V=\frac{1}{3}Bh[/tex]Since the area of the base and the height is already given, substitute the values in to the equation and then simplify.
[tex]\begin{gathered} V=\frac{1}{3}(254.3)(16.7) \\ =\frac{1}{3}(4246.81) \\ \approx1415.603 \end{gathered}[/tex]We may also find the exact value by substituting the given values into the equation below.
[tex]V=\frac{\pi r^2h}{3}[/tex]where V is the volume, r is the radius, and h is the height.
To obtain the exact value of the height, we use the Pythagorean theorem.
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2=c^2-b^2 \\ a=\sqrt[]{c^2-b^2} \end{gathered}[/tex]where a and b are the legs of the formed right triangle while c is its hypothenuse.
From the figure, the slant height is the hypothenuse while the radius, 9 ft, serve as one of the legs. Thus, the other leg, which is the height of the cone can be solved as follows.
[tex]\begin{gathered} a=\sqrt[]{19^2-9^2} \\ =\sqrt[]{361-81} \\ =\sqrt[]{280} \end{gathered}[/tex]Therefore, the height of the cone is as stated above.
Substitute the obtained height and the radius into the second formula that was stated.
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{\pi(9^2)(\sqrt[]{280})}{3} \end{gathered}[/tex]Simplify the right side of the equation. Evaluate the exponential expression.
[tex]V=\frac{\pi(81)(\sqrt[]{280})}{3}[/tex]Multiply the numerator and then divide it by 3.
[tex]\begin{gathered} V=\frac{\pi(81)(\sqrt[]{280})}{3} \\ \approx\frac{(3.1416)(81)(16.7332)}{3} \\ \approx\frac{4258.0907}{3} \\ \approx1419.36 \end{gathered}[/tex]Note that the value that we obtain at first, 1415,603, is slightly different from the one that we obtained, which is 1419.36, since there are values that we already rounded off before substituting the values in the equation.
Therefore, to be more exact, it is best to indicate that the volume of the given cone is approximately 1419.36 ft³.
HELPPPP PLEASEEE!!!
(MATH AND CHEMISTRY RELATED)
Answers
b) 0.72 m^3
c) 1728 kg
Divide the steps into three manageable parts. Calculate the volume of each part and add them together. Convert units into m^3. Finally, multiply by the given density to find the steps’ weight.
See details:
The sample space S= [E1, E2, E3, E4, E5, E6, E7, E8, E9, E10]
Given A = [E1, E3, E6, E9], define Ȃ
Given A = [E1, E3, E7, E9] and B = [E2. E3, E, E9]
a) What is A intersection B?
b) What is the union of A & B?
c) Is the union of A & B collectively exhaustive?
Answers
A is defined as a subset of the sample space, that is, the universal set
a. A∩B = { E3, E9}
b. A∪B = {E, E1, E2, E3,E7, E9}
c. Yes, the union of A and B is collectively exhaustible
What are sets?Sets are defined as in mathematical and logical collection of elements or objects, numbers or functions.
The members of a set are listed in enclosed braces.
The elements and objects of a set are well-defined and fixed.
Given the sets as;
S= [E1, E2, E3, E4, E5, E6, E7, E8, E9, E10]
A = [E1, E3, E6, E9]
A is defined as a subset of the sample space, S
a. It is important to note that the intersection of two sets involves the elements or objects that are common between them.
Given that;
A = [E1, E3, E7, E9]
B = [E2. E3, E, E9]
A∩B = { E3, E9}
b. Note that the union of sets involves the collection of the elements of both sets without repetition.
A∪B = {E, E1, E2, E3,E7, E9}
c. The union of the sets A and B are together exhaustive as it contains all the elements in both sets.
Hence, A is defined as a subset of the universal set.
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What is Prime factorization ?
Answers
the prime factors of a positive integer are the prime numbers that divide that integer exactly.
(-35) x 6 =? i need help!
Answers
Answer: -210 is your answer
Step-by-step explanation:
I took the test and worked it out
Answer: -210
Step-by-step explanation: remembered answering this question once and -210 was the right answer
The cost in dollars of making x items is given by ()=10+500. The fixed cost is
determined when zero items are produced. Find the fixed cost for this item. What
is the cost of making 25 items? Suppose the maximum cost allowed is $1500.
What are the domain and range of the cost function, C(x) ?
Answers
The answer is
(a) the fixed cost when zero items are produced is $500 .
(b) cost for making 25 items is $750 .
(c) the domain and range of cost function is [0,100] and [500,1500] respectively .
It the question ,
it is given that
the cost function is C(x)=10x+500
Part(a)
to determine the fixed cost when 0 items are produced
Since 0 items are produced , we substitute the value x=0 in the cost function , we get
C(0)=10(0)+500
= 500
the fixed cost is $500.
Part(b)
to find the cost of making 25 items , we substitute x=25
On substituting the x=25 , we get
C(25)=10(25)+500
= 250+500
=750
the cost for 25 items is $750.
Part(c)
to find the domain of the cost function C(x)
Given that the maximum cost allowed is 1500
So, 1500=10x+500
10x=1500-500
10x=1000
x=100
So minimum 0 items and maximum 100 items can be produced ,
hence the Domain is [0,100]
to find the range
substituting x=0, the cost = $500
on substituting x=100 , the cost = $1500
the Range is [500,1500]
Therefore , (a) the fixed cost when zero items are produced is $500 .
(b) cost for making 25 items is $750 .
(c) the domain and range of cost function is [0,100] and [500,1500] respectively .
The given question is incomplete , the complete question is
The cost in dollars of making x items is given by C(x)=10x+500. The fixed cost is determined when zero items are produced.
(a) Find the fixed cost for this item.
(b) What is the cost of making 25 items?
(c) Suppose the maximum cost allowed is $1500. What are the domain and range of the cost function, C(x) ?
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Over the last three evenings, James received a total of 90 phone calls at the call center. The second evening, he received 2 times as many calls as the third evening. The first evening, he received 6 more calls than the third evening. How many phone calls did she receive each evening?
Answers
Answer:
first evening = 27 calls
second evening = 42 calls
third evening = 21 calls
Step-by-step explanation:
Total of 90 calls
f = first evening
s = second evening
t = third evening
Solve:
f=t+6
s = 2t
t=t
f+s+t=90
t+6 + 2t + t
(2t+t+t)+6 = 90
4t+6 = 90
4t=84
t=21
ANSWER:f=t+6=21+6
= 27
s = 2t
= 42
t = t
= 21
1. A survey of 36 students was conducted to find out how many students enjoy playing volleyball, and 17 said they did. If 648 students were surveyed, how many would say they enjoy playing volleyball?
Answers
The total number of students calculated with the method called simplification and who are playing volleyball is 206.
How simplification method work?
In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.
According to the question, the given survey data for the playing volleyball is written below and it is solved by the simplification method:
survey of students: 36
play volleyball: 17
As per question, the simplification expression for the given statement which state that, if the survey of 648 students how many students play volleyball?
Therefore, the required simplified expression can be written as:
Required expression: 648÷36= 18
Now, playing volleyball =18×17=206 students play volleyball
Hence, the total number of students calculated with the method called simplification who are playing volleyball is 206.
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Mr. House wrote 8 tenths minus 5 hundredths on the board. Maggie said the answer is 3 hundredths
because 8 minus 5 is 3. 5 Is she correct? Explain.
Answers
0.8 is 8 tenths minus
0.05
Which would basically be
0.80-
0.05 which is
0.75
5. Evaluate using a calculator (or desmos). Round to 2 decimal places: log 23.6
Answers
We get 1.37 when we evaluate log 23.6
Given,
log 23.6
We have to evaluate this using a calculator or desmos.
Desmos:
Desmos is a free math teaching and graphing application that is accessible on the web, iOS, and Android. There are classroom activities available to assist students in learning about a number of arithmetic concepts in addition to graphing equations.
Evaluation of logarithms:
You can use a calculator to assess logarithms by utilising the change of base formula, M = log a, M log a, and selecting either the common log or the natural log.
Lets evaluate log 23.6
log 23.6 = 1.372912003
Lets round to 2 decimal places:
log 23.6 = 1.37
That is,
We get 1.37 when we evaluate log 23.6
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--- nerweter de 2 mm. em. 4 em 12 manam 2) Find the perimeter. Use 3.14 for it when needed. 20 m semicircle -2n trola To 31.1 10 m 2 2 P. = 314 = 77.4 D 31.141/2 + 2+2 P - Find area of figure. Round to the nearest hundredth if neces 41 in. 136 in. 45.5 in. 1 area of figure. Round to the nearest hundredth if ne 17 m 9 m n
Answers
The perimeter of the semicircle with different r values is:
(When r = 2) = 10.28 mm(When r = 4) = 20.56 mm(When r = 12) = 61.68 mmWhat is a semicircle?A circle is divided into exactly two parts in geometry to create a semicircle, a plane figure. Therefore, using the area and perimeter of a circle, we can calculate the area and perimeter of a semicircle. A semicircle is a one-dimensional locus of points in mathematics (and more specifically geometry) that makes up one-half of a circle. A semicircle's full arc (equivalent to π radians or a half-turn) is always 180° in length. It only has one symmetry line (reflection symmetry).So, the formula for the perimeter of the semicircle:
πr + 2rNow, insert values as follows:
(A) (When r = 2)
πr + 2r3.14 × 2 + 2 × 26.28 + 410.28 mm(B) (When r = 4)
πr + 2r3.14 × 4 + 2 × 412.56 + 820.56 mm(C) (When r = 12)
πr + 2r3.14 × 12 + 2 × 1237.68 + 2461.68 mmTherefore, the perimeter of the semicircle with different r values is:
(When r = 2) = 10.28 mm(When r = 4) = 20.56 mm(When r = 12) = 61.68 mmKnow more about semicircles here:
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The correct question is given below:
2 mm. em. 4 em 12 Manam. Find the perimeter of the semicircle. Use 3.14 for it when needed.
Zach and Ginny are building model cars. Ginny's car is 2 more than 3 times the length of Zach's car. The sum of the lengths of both cars is 30 inches. Write an equation to determine the lengths of Zach's and Ginny's cars.
3x + 2 = 30
x + 2 + 3x = 30
2x + 3 = 30
x + 2x + 3 = 30
Answers
3x=30+2
3x=32
3/3x=32
X=32/3
X=1.6666....
Triangle ABC has its vertices at the following coordinates:
A(5,-10) B(-8, 4) C(2, 0)
Give the coordinates of the image triangle A'B'C' after a 90 rotation counterclockwise about the origin.
]
A'(-10, 5) B'(4,-8) C'(0, 2)
A (10, 5) B (-4,-8) C (0, 2)
A'(10, 5) B'(-4,-8) C'(0, 2)
A'(5, 10) B'(-8,-4) C'(2, 0)
A (5, 10) B (-8,-4) C (2, 0)
Answers
The coordinates of the vertices of the image triangle A'B'C' after a rotation 90° counterclockwise about the origin are: A' (10, 5), B' (-4, -8), C'(0, 2)
What is a rotation?A rotation simply refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
In Geometry, rotating a point 90° about the origin in a counterclockwise (anticlockwise) would produce a point that has the coordinates (-y, x).
By applying a rotation of 90° counterclockwise to triangle ABC, the coordinates of the vertices of the image triangle A'B'C' include the following:
(x, y) → (-y, x)
Point A = (5, -10) → Point A' = (-(-10), 5) = (10, 5)
Point B = (-8, 4) → Point B' = (-4, -8)
Point C = (2, 0) → Point C' = (0, 2)
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A company uses two factories to manufacture three different sizes of boats. Each boat takes a different amount of time to perform each task. For example, the small boat requires 1 hour of cutting, 0.5 hours of assembly, and 0.2 hours of packaging. The medium boat requires 1.6 hours of cutting, 1 hour of assembly, and 0.2 hours of packaging. Finally, the large boat requires 2.5 hours of cutting, 2 hours of assembly, and 1.4 hours of packaging time. The factory pays each department at each factory differently, according to this pay scale: Factory A pays out $15 per hour for cutting, $12 for packaging, and $11 for assembly. Factory B pays out $13 for cutting, $11 for assembly, and $10 for packaging. How much will each factory have to pay in wages to construct each type of boat?
Answers
Using proportions, the costs for the boats are given as follows:
Factory A:
Small: $22.9.Medium: $37.4.Large: $76.3.Factory B:
Small: $20.5.Medium: $33.8.Large: $68.5.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using the standard operations such as addition, subtraction, multiplication and division with the unit rates to find the equivalent amounts.
Considering the costs per hour and the number of hours needed, the cost of a small boat at Factory A is given by:
15 x 1 + 11 x 0.5 + 12 x 0.2 = $22.9.
For example, 15 x 1 is because it requires one hour of cutting, and each hour of cutting pays of $15.
The cost of a medium boat at Factory A is given by:
15 x 1.6 + 11 x 1 + 12 x 0.2 = $37.4.
The cost of a large boat at Factory A is given by:
15 x 2.5 + 11 x 2 + 12 x 1.4 = $76.3.
The cost of a small boat at Factory B is given by:
13 x 1 + 11 x 0.5 + 10 x 0.2 = $20.5.
The cost of a medium boat at Factory B is given by:
13 x 1.6 + 11 x 1 + 10 x 0.2 = $33.8.
The cost of a large boat at Factory B is given by:
13 x 2.5 + 11 x 2 + 10 x 1.4 = $68.5.
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Can someone please help me with this? I can’t understand it
Answers
Let us prepare an inequality statement to answer the question.
There is a one-time fee of $85 and a fee of $23 per guest. If x represents the number of guests, the amount spent will be:
[tex]85+23x[/tex]If the amount spent cannot exceed $1750, we have the inequality statement to be:
[tex]85+23x\leq1750[/tex]We can solve as follows:
[tex]\begin{gathered} 23x\leq1750-85 \\ 23x\leq1665 \\ x\leq\frac{1665}{23} \\ x\leq72.39 \end{gathered}[/tex]Since we cannot have a fraction of a person, the answer will be 72.
her maximum number of guests is 72.
A math class consists of 21 female students and 16 male students. Two students are selected at random to participate in a probability experiment. Compute the following probabilities. Write your answers in decimal form. Round to the nearest thousandth as needed.a. A male is selected, then a female. b. A female is selected, then a male. c. Two males are selected. d. Two females are selected. e. No males are selected.
Answers
To solve this problem, we will use the conditional probability definition: Given events A,B such that P(B)>0 we have that
[tex]P(A|B)=\frac{P(\text{A}\cap B)}{P(B)}[/tex]Where P(A|B) means the probability of A given B occurred. This also leads to the following
[tex]P(A|B)\cdot P(B)=P(A\cap B)[/tex]Now, let us define two events. Let M1 be the event that we select a male first and let F2 be the event that we select a female second. We want to calculate the following probabilty
[tex]P(M_1\cap F_2)_{}[/tex]Using the definition of conditional probability, this is the same as
[tex]P(M_1\cap F_2)=P(F_2|M_1)\cdot P(M_1)[/tex]Now, we will calculate P(M1). At the beginning, when we have not picked anyone yet, we have 37 people (21 Female and 16 Male). So the probability of picking a male first is simply
[tex]P(M_1)=\frac{16}{37}[/tex]Now, we will calculate the second probability. Since we already picked one male, we have now 36 people (21 female and 15 male). Then the probability of picking a female is
[tex]P(F_2|M_1)=\frac{21}{36}[/tex]So,
[tex]P(M_1\cap F_2)=\frac{16}{37}\cdot\frac{21}{36}=\frac{28}{111}=0.252[/tex]Nga buys three sports books. Each book costs £12, correct to the nearest pound. What is the maximum possible total price that Nga pays for the three books?
Answers
Answer:
The answer would be £36
Step-by-step explanation:
12+12+12=36
Enter a range of values for x.85°5x - 1025Sk[ ? ]
Answers
°
the two triangles have a bisetor that makes the adjacent side equal, so based on this 25 = 5x- 10
25+ 10 = 5x
meaning your x = 7
but on the equation 5x-10 =0
we get that x = 10/5
x >2
so the range would be 2
There are 9 candidates for three positions at a restaraunt. One position is for a cook. The second position is for a food server. The third position is for a cashier. If all 9 candidates are equally qualified for the three positions, in how many different ways can the three positions be filled?
Answers
The number of different ways that the three positions can be filled is 504 ways.
How to calculate the value?From the information, there are 9 candidates for three positions at a restaraunt. Based on the data, one position is for a cook, the second position is for a food server and the third position is for a cashier.
Therefore, the number of ways will be:
= 9P3
= 9! / (9 - 3)!
= 9! / 6!
= 9 × 8 × 7
= 504
The number of ways is 504 ways.
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the information given. When applicable, eraph the equations.2m =4y=2x-16aŭ= 28 b=_-16Equation of Line: 4y - 2x = 16Rewritten: ya2x-16Im =2x + m = -2I lineI line
Answers
From the given equation :
[tex]4y-2x=16[/tex]This can be written in the slope-intercept form :
[tex]y=mx+b[/tex]where m is the slope
and b is the y-intercept
Rewriting the equation :
[tex]\begin{gathered} 4y-2x=16 \\ 4y=2x+16 \\ y=\frac{2}{4}x+\frac{16}{4} \\ y=\frac{1}{2}x+4 \end{gathered}[/tex]The equation will be y = 1/2 x + 4
the slope is m = 1/2
nd the y-intercept is b = 4
Note that parallel lines have the same slope.
So the slope of parallel line is m = 1/2
Perpendicular lines have a slope of negative reciprocal with each other.
So the slope of perpendicular line to this line is m = -2
Equation of parallel line :
we have :
[tex]y=\frac{1}{2}x+b[/tex]Let's say the line passes at the origin (0, 0)
If a line passes thru the origin, the y-intercept is always b = 0
Therefore, the equation of parallel line is y = 1/2 x
quation of perpendicular line :
we have :
[tex]y=-2x+b[/tex]Let's also say that the line passes at the origin (0, 0)
and the y-intercept is also b = 0
he equation of the perpendicular line is yy = -2x
raphing these equations will be :
Original line (Blue)
Parallel line (Orange)
Perpendicular line (Pink)
y-intercepts :
(0, 0) and (0, 4)