Determine whether the lines given by the vector equations r1=2i + 2j + 3k + s(i + 3j + k) and r2=2i + 3j + 4k + t(i + 4j + 2k) intersect. If they intersect, give the coordinates of their point of intersection.
Answer:
i -j +2k . . . at s=t=-1
Step-by-step explanation:
For the lines to intersect, there must be values of s and t that make the coordinates of r1 equal to those of r2.
Equating i coefficients, we have ...
2 +s = 2 +t
Equating j coefficients, we have ...
2 +3s = 3 +4t
Equating k coefficients, we have ...
3 +s = 4 +2t
The first equation tells us s = t. Using t = s in each of the other two equations, they become ...
2 +3s = 3 +4s ⇒ s = -1
3 +s = 4 +2s ⇒ s = -1
Then the point of intersection is where s = t = -1. That point is ...
(2 +s)i +(2 +3s)j +(3 +s)k = (2 -1)i +(2 -3)j +(3 -1)k
= i -j +2k . . . . the point of intersection
PLEASE HELP ASAP
No explanation needed
The Kellen school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table, where Low represents the fewest days attended and High represents the most days attended for a single student. School Low High Range Mean Median IQR σ High School W 108 180 72 169 150 47.5 29.5 High School X 112 180 68 160 124 49.5 32.4 High School Z 130 180 50 162 151 39.5 27.5 Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically.
Answer:
(A) It should choose High school Z for the most consistent attendance among its students.
(B) It should choose High school W with the highest average attendance.
Step-by-step explanation:
We are given the data for attendance in the table below, where Low represents the fewest days attended and High represents the most days attended for a single student.
School Hight School W High School X High School Z
Low 108 112 130
High 180 180 180
Range 72 68 50
Mean 169 160 162
Median 150 124 151
IQR 47.5 49.5 39.5
S.D. (σ) 29.5 32.4 27.5
(A) It is stated that the school district wants to award the school that has the most consistent attendance among its students.
Now, to check which high school should it choose; we will look for the standard deviation (σ) of each of the three schools because consistency is measured through standard deviation and the school with the lowest standard deviation means that it has the most consistent attendance among its students.
So, after looking at the standard deviation of all the three schools; the High School Z has the lowest standard deviation of 27.5.
This means that it should choose High school Z.
(B) It is stated that the school district wants to award the school with the highest average attendance.
Now, to check which high school should it choose; we will look for the Mean of each of the three schools because average is measured through mean of the data, and the school with the highest mean means that it has the highest average attendance.
So, after looking at the Mean of all the three schools; the High School W has the highest average of 169.
This means that it should choose High school W with the highest average attendance.
14. You bought shoes for $60. They were on sale for 40% off their original price.
a. Write a proportion to solve for the original price of the shoes.
b. Solve the proportion in part (a).
PLSSS HELP PLSSSSSSSS MARKING BRAINLIST QUESTION BELOW
Answer:
Hey there!
CarMart's rate of sales is 11 cars per day.
Winston's rate of sales is 10 cars per day.
Compared with CarMart, Winston is selling fewer cars per day.
Compared with CarMart, Winston started with 2 fewer cars.
Let me know if this helps :)
Answer:
CarMart's rate of sales is 11 cars in a day.
Winston's rate of sales is 10 cars in a day.
Compared with CarMart, Winston is selling less cars in a day.
Compared with CarMart, Winston started with two fewer cars.
Step-by-step explanation:
Please Help ;-;" :Mr. Gordon’s science class is studying blood types. The table below shows the probability that a person living in the US has a particular blood type. ( Type 0=9/20) (Type A=41/100) (Type B=1/10) (Type AB=1/25) What is the probability that three students selected randomly from the class will have A, B, and AB blood, respectively? Explain how you would solve this problem.
Answer:
A = 6.9%
B = 0.1%
AB = 1.6%
Step-by-step explanation:
A=0.41=41/100
B=0.1=1/10
AB=0.25=1/25
41/100³ = 0.41³ = 0.069 = 6.9%
1/10³ = 0.1³ = 0.001 = 0.1%
1/25³= 0.25³ =0.016 = 1.6%
I did to the power of 3 because the equation just looks like this
41/100 x 41/100 x 4/100
this is because you are multiplying each number by the amount of students selected.
Vince and 11 of his friends went out for pizza on Saturday night to celebrate Vince’s birthday. The cost of the pizza and soft drinks before sales tax and tip was $47.96. What is the amount of sales tax for the bill if the rate is 7%? Show your work.
Step-by-step explanation:
Since the original price is $47.96 and bill rate is 7%, $47.96 × 1.07 ≈ $51.32
Answer:
$51.32
The amount of sales tax for the bill if the rate is 7% will be $3.36.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
Vince and 11 of his friends went out for pizza on Saturday night to celebrate Vince’s birthday.
The cost of the pizza and soft drinks before sales tax and tip was $47.96.
Then the amount of sales tax for the bill if the rate is 7% will be
⇒ $47.96 x 0.07
⇒ $3.36
More about the percentage link is given below.
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PLEASE HELP!!!! WILL GIVE BRAINLIEST!!
Find the output, h, when the input, x, is -18.
h = 17 + x/6
Answer:
14
Step-by-step explanation:
The expression is h = 17 + x/6
Replace x by -18
● h = 17 + x/6
● h = 17 + (-18/6)
● h = 17 +(-3)
● h = 17 -3
● h = 14
So the output when x = -18 is 14
h=14
h=17+18/6
h=17+-3
h=17-3
h=14
-15 POINTS- A company makes wax candles shaped like rectangular prisms. Each candle is 5cm long, 4cm wide, and 12cm tall. If the company used 3840 cm³ of wax, how many candles did they make?
Answer:
16 candles
Step-by-step explanation:
first you must know what the volume of the rec prism is so multiply the b*h*w and you will have 240. divide 3840 by 240 and you will have 16
Answer:
16
Step-by-step explanation:
We need to find out the area of each candle. We can do this by multiplying all the lengths out and getting 240 [tex]cm^3[/tex] per candle. Now we divide 3840, the total amount of wax used, by 240 the amound needed for one candle, and we get 16. This means 16 candles were made.
Solve for x. Just give the equations.
15.
[tex]FH=2\cdot UH\\\\5x-7=2\cdot19\\\\5x=38+7\\\\5x=45\quad|:5\\\\\boxed{x=9}[/tex]
16.
[tex]KU=UM\\\\3x+3=4x-4\\\\4x-3x=3+4\\\\\boxed{x=7}[/tex]
Answer:
15) x=9 16) x=7
Step-by-step explanation:
19(2)=5x-7
38=5x-7
5x=38+7
5x=45
x=45/5
x=9
-----------------
3x+3=4x-4
3=4x-3x-4
3=x-4
x=3+4
x=7
Interpret the average rate of change of –14/3 that you found previously. What does this mean in terms of the waterslide, from x = 0 to x = 15?
Answer:
Solution: The average rate of change of represents that the second variable is decrease by 14 if the first variable increase by 3. In terms of water slide the vertical height of slide is decreased at the rate of 4.66 per unit. The vertical height of the slide decrease 70 units from x = 0 to x = 15.
Explanation:
The rate of change shows the change in first variable with respect to change in second variable.
If the rate of chang is given by it means second variable is decrease by 14 if the first variable increase by 3.
In the context of water slide it shows that the vertical height of slide is decreased by 14 units as we cover the distance of 3 units.
If we cover the distance from x = 0 to x = 15, it means we cover the distance of 15 units.
Let the vertical height of the slide covered from x = 0 to x =15 be y.
It means when distance increased by 15 units the height of slide decreased by y units.
So rate of change = .
It is given that the rate of change is .
Equate both equations.
Therefore, the average rate of change of represents that the second variable is decrease by 14 if the first variable increase by 3. In terms of water slide the vertical height of slide is decreased at the rate of 4.66 per unit. The vertical height of the slide decrease 70 units from x = 0 to x = 15.
A park is mapped on a coordinate plane, where C1, C2, C3, and C4 represent chairs and SW1, SW2, and SW3 represent swings. How far is C2 from SW1? A. 89−−√ units B. 145−−−√ units C. 97−−√ units D. 41−−√ units
Answer:
Option (B)
Step-by-step explanation:
To calculate the distance between C2 and SW1 we will use the formula of distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
d = [tex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^2 }[/tex]
Coordinates representing positions of C2 and SW1 are (2, 2) and (-6, -7) respectively.
By substituting these coordinates in the formula,
Distance between these points = [tex]\sqrt{(-6-2)^2+(-7-2)^2}[/tex]
= [tex]\sqrt{(64)+(81)}[/tex]
= [tex]\sqrt{145}[/tex] units
Therefore, Option (B) will be the correct option.
Kara has twenty-four thousand, five hundred sixty stickers in her album.
Raul has 20,000 + 4,000 + 500 + 60 stickers in his collection.
Answer:
they are both the same thing the first one with kara is in numbers and with raul it is in words
Step-by-step explanation:
hope i helped and have a great day :)
Plzzz help I’ll give brainlest
Answer:
cos y = r/q
Step-by-step explanation:
If we know sin y = 7/q, then we know that the base is 7 and the hypotenuse is q due to sine = opposite/hypotenuse.
If we know tan y = 7/r, then we know that the base is 7 and the right side is r due to tan = opposite/adjacent.
Cos = adjacent / hypotenuse
So cos y = r/q, because the right side is r and the hypotenuse is q.
Answer:
ignore sorry
Step-by-step explanation:
A package of 8-count AA batteries costs $6.32. A package of 20-count AA batteries costs $16.00. Which statement about the unit prices is true?
Answer:
A
Step-by-step explanation:
The first option is correct.
The 8 count pack of AA batteries has a lower unit price of $0.79 per battery.
What is unitary method?The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.
According to the given question.
Cost of a package with 8 AA batteries = $6.32
⇒ Cost of 1 AA battery of this package = [tex]\frac{6.32}{8}[/tex] = $0.79
And, cost of another package with 20 AA batteries = $16.00
⇒ Cost of 1 AA battery of another package = [tex]\frac{16}{20}[/tex] = $0.8
Hence, the 8 count pack of AA batteries has a lower unit price of $0.79 per battery.
Find out more information about unitary method here:
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Which of the following statements is true for a function with equation f(x) = 5(3)*?
The graph has y-intercept (0,5) and increases with a constant ratio of 3.
The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.
The graph has y-intercept (0, 3) and increases with a constant ratio of 5.
The graph has y-intercept (0,5) and decreases with a constant ratio of 3.
Answer:
The graph has y-intercept (0,5) and increases with a constant ratio of 3
Step-by-step explanation:
The value of the function when x=0 is 5·3^0 = 5, so the y-intercept is (0, 5).
Each increase of 1 in x causes the function value to increase by a factor of 3, so the 'constant ratio' is 3. (That is the base of the exponential term.)
Kim is building a triangular dog pen. She will use an existing 10 m wall as one side. She will then build a fence going out at a 45°
angle on one side of the wall and a 65° angle on the other side. How much chain-link fence is needed to complete the fence?
es )
Answer:
17.2 ft
Step-by-step explanation:
The angle that the fence makes opposite the wall is ...
180° -45° -65° = 70°
The law of cosines can be used to find the lengths of fence needed.
The fence opposite the 45° angle will have a length of ...
short side = (10 ft)·sin(45°)/sin(70°) = 7.525 . . . feet
The fence opposite the 65° angle will have a length of ...
long side = (10 ft)·sin(65°)/sin(70°) = 9.645 . . . feet
Then the total length of fence required is ...
7.525 ft +9.645 ft = 17.170 ft
About 17.2 feet of chain-link fence is required to complete the enclosure.
_____
We have assumed there is no chain-link fence along the 10 ft wall.
_____
The Law of Sines tells you that for sides a, b, c and opposite angles A, B, C, you have ...
a/sin(A) = b/sin(B) = c/sin(C)
For some given side 'a' and opposite angle A, the other two sides can be found from their opposite angles as ...
b = sin(B)·a/sin(A)
c = sin(C)·a/sin(A)
asap please x÷7=11÷15help
Answer:
x = 77/15 or 5 2/15
Step-by-step explanation:
x/7 = 11/15
Multiply each side by 7
x/7 *7 = 11/15 *7
x = 77/15
We can leave as an improper fraction or change to a mixed number
15 goes into 77 5 times with 2 left over
5 2/15
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 77/15, 5 2/15, or 5.13
▹ Step-by-Step Explanation
x ÷ 7 = 11 ÷ 15
15x = 77
Divide both sides by 15:
x = 77/15, 5 2/15, or 5.13
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Find the length of MK¯¯¯¯¯¯ A. 7 B. 47 C. 19 D. 34
Answer:
19
Step-by-step explanation:
JH = 47 (70 - 23)
HM = 23
MK = 19 (42 - 23)
KU = 34 (81 - 47)
UC = 7 (47 - 40)
CN = 40
Answer:
19
Step-by-step explanation:
HM + MK = HK
23 + MK = 42
Subtract 23
MK = 42-23
MK =19
Which mean the same as 60%? Check all that apply
a.3/5
b. 0.06
c. 0.60
d. 6/10
e. 6/100
Find the average rate of change of g(x)= – x2 over the interval [ – 8, – 2]. Write your answer as an integer, fraction, or decimal rounded to the nearest tenth. Simplify any fractions.
Answer:
[tex]Average\ Rate = 10[/tex]
Step-by-step explanation:
Given
[tex]g(x) = -x^2[/tex]
[tex](-8,-2)[/tex]
Required
Determine the average rate of change;
Average rate of change is calculated as thus;
[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex]
Where
[tex](a,b) = (-8,-2)[/tex]
i.e. a = -8 and b = -2
[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex] becomes
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 - (-8)}[/tex]
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 + 8}[/tex]
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]
Calculating g(-2)
Substitute -2 for x in [tex]g(x) = -x^2[/tex]
[tex]g(-2) = -(-2)^2[/tex]
[tex]g(-2) = -4[/tex]
Calculating g(-8)
Substitute -8 for x in [tex]g(x) = -x^2[/tex]
[tex]g(-8) = -(-8)^2[/tex]
[tex]g(-8) = -64[/tex]
Substitute values for g(-2) and g(-8)
[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]
[tex]Average\ Rate = \frac{-4 - (-64)}{6}[/tex]
[tex]Average\ Rate = \frac{-4 + 64}{6}[/tex]
[tex]Average\ Rate = \frac{60}{6}[/tex]
[tex]Average\ Rate = 10[/tex]
Hence, the average rate of change is 10
write the fraction for each of the following do number 3 and 4 thanks
Answer:
7
Step-by-step explanation:
Drag each value to the correct location on the equation. Each value can be used more than once.
Answer:
[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}[/tex]
Step-by-step explanation:
If a quadratic equation is in the form of ax²+ bx + c = 0
Then the roots of this quadratic equation can be obtained by,
1). Factoring the expression.
2). By quadratic formula.
If we use the method to get the value of x or roots of the equation,
x = [tex]\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}[/tex]
where a, b and c are the coefficients used in the quadratic equation.
Which constants could each equation be multiplied by to eliminate the x-variable using addition in this system of equations? 2x+3y=25 -3x+=22 first equation can be multiplied by –3 and the second equation by 2. The first equation can be multiplied by –4 and the second equation by 2. The first equation can be multiplied by 3 and the second equation by 2. The first equation can be multiplied by 4 and the second equation by –3.
Answer:
The first equation can be multiplied by 3 and the second equation by 2.
Step-by-step explanation:
Given
[tex]2x+3y=25[/tex]
[tex]-3x + y=22[/tex]
Required
How to eliminate x
To eliminate x using addition, we have to do the following;
1. Take the coefficient of x in equation 1; Coefficient = 2
2. Take the coefficient of x in equation 2; Coefficient = -3
3. Multiply equation 1 by 3
[tex]3(2x + 3y = 25)[/tex]
[tex]6x +9y = 75[/tex]
4. Multiply equation 2 by 2
[tex]2(-3x + y = 22)[/tex]
[tex]-6x + 2y = 44[/tex]
5. Add both resulting equations
[tex]6x +9y = 75[/tex] + [tex]-6x + 2y = 44[/tex]
[tex]6x - 6x + 9y + 2y = 75 + 44[/tex]
[tex]11y = 75 + 44[/tex]
Notice that x has been eliminated;
6(y + 5) = 15y + 12
What value of y makes the equation true
Answer:
[tex]\boxed{y=2}[/tex]
Step-by-step explanation:
[tex]6(y + 5) = 15y + 12[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]6y+30=15y+12[/tex]
[tex]\sf Subtract \ 12 \ and \ 6y \ from \ both \ sides.[/tex]
[tex]6y+30-12-6y=15y+12-12-6y[/tex]
[tex]30-12=15y-6y[/tex]
[tex]18=9y[/tex]
[tex]\sf Divide \ both \ sides \ by \ 9.[/tex]
[tex]\displaystyle \frac{18}{9} =\frac{9y}{9}[/tex]
[tex]2=y[/tex]
(k) 1 + tan 4A . tan 2A = sec 4A.
Please help me.... question from multiple angle of trigonometry!!!!!
it was a long proof...
follow the caption and steps and you'll understand it
proved...
Step-by-step explanation:
this is too easy method to solve this problem
What is the determinant of k= 6 8 0 3
Answer:
18
Step-by-step explanation:
Evaluate the following expression: 2 + 1 x 2 *Please help i don't have that much time*
Answer:
The answer to your question is 4.
Step-by-step explanation:
Evaluating and simplifying the expression comes to a result of four using the order of operations. Hope this helps you!
Which point below is not on the graph of h(x) ^3√x+64 = ? (65, 5) (-37, 3) (-72, -2) (-64, 0)
Answer:
(-37, 3)
Step-by-step explanation:
The frequency table above is presented as a pie chart
The sectorial angle of score"3" is ....
Answer:
[tex]Angle = 96[/tex]
Step-by-step explanation:
Given
The frequency table
Required:
Determine the sectorial angle of "3"
First we need to determine the total frequency;
[tex]Total = 3 + 4 + 6 +8 + 5 + 4[/tex]
[tex]Total = 30[/tex]
The sectorial angle is calculated as thus;
[tex]Angle = \frac{Frequency}{Total\ Frequency} * 360[/tex]
Where Frequency of "3" = 8
So;
[tex]Angle = \frac{8}{30} * 360[/tex]
[tex]Angle = \frac{8* 360}{30}[/tex]
[tex]Angle = \frac{2880}{30}[/tex]
[tex]Angle = 96[/tex]
Hence; the sectorial angle of "3" is 96
You are making the kite shown at the right from
five pairs of congruent panels. In parts (a)-(d)
below, use the given information to find the side
lengths of the kite's panels.
Answer:
a. Side lengths of ΔBEX are;
BE = 15 ft.
EX = 12 ft.
BX = 9 ft.
b. Side lengths of XEFY are;
XY = 6 ft.
EX = 12 ft.
FY = 7.5 ft.
EF = 7.5 ft.
c. Side lengths of YFGZ are;
GZ = 6 ft.
FY = 7.5 ft.
YZ = 2 ft.
FG = 2.5 ft.
d. Side length of triangle ZGC
GZ = 6 ft.
GC = 10 ft.
ZC = 8 ft.
Step-by-step explanation:
The given parameters are;
XY : YZ : ZC is 3 : 1 : 4
The length of BC = 25 in.
The length of EB = 15 in.
Therefore, EC = √(BC² - EB²) = √(25² - 15²) = √400 = 20 in.
Given that EX║ YF║GZ, we have;
EF : FG : GC is 3 : 1 : 4 (Parallel lines cut segments in equal proportions)
Therefore;
EF = 20 × 3/(3 + 1 + 4) = 7.5 ft.
FG = 20×1/8 = 2.5 ft.
GC = 20×4/8 = 10 ft.
EC/EX = BC/EB
20/EX = 25/15
EX = 15×20/25 = 12 ft.
XC = √(EC² - EX²) = √(20² - 12²) = 16
XY : YZ : ZC is 3 : 1 : 4
Therefore;
XY = 16 × 3/8 = 6 ft.
YZ = 16 × 1/8 = 2 ft.
ZC = 16 × 4/8 = 8 ft.
GZ = √(GC² - ZC²) = √(10² - 8²) = 6
Area of triangle ΔZGC = 1/2×6×8 = 24 ft²
XB = BC - XC = 25 - 16 = 9 ft.
Area of ΔBEX = 1/2×9×12 = 54 ft²
a. Side lengths of ΔBEX are;
BE = 15 ft.
EX = 12 ft.
BX = 9 ft.
FY = √(FC² - YC²) = √((10 + 2.5)² - (8 + 2)²) = 7.5 ft.
Area of YFGZ = (GZ + FY)/2 × YZ = (6 + 7.5)/2 × 2 = 13.5 ft²
Area of YFGZ = 13.5 ft²
Area of XEFY = XY × (EX + FY)/2 = 6 × (12 + 7.5)/2 = 58.5 ft.²
b. Side lengths of XEFY are;
XY = 6 ft.
EX = 12 ft.
FY = 7.5 ft.
EF = 7.5 ft.
c. Side lengths of YFGZ are;
GZ = 6 ft.
FY = 7.5 ft.
YZ = 2 ft.
FG = 2.5 ft.
d. Side length of triangle ZGC
GZ = 6 ft.
GC = 10 ft.
ZC = 8 ft.
