Answer:
Stacey wanted to build a model airplane to display in her room. The scale ratio she planned to use was for every 4 feet the airplane was, the model airplane would be 1 inch. If the plane was 250 feet long, how long would the model airplane be?
Here, I used the ratio 4 : 1 as a scale in the problem.
Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c. What is the distance between the origin and the plane?
Answer:
The equation is:
(1/a)x + (1/b)y + (1/c)z = 1
Step-by-step explanation:
The direction vector between the points (a, 0, 0) and (0, b, 0) is given as:
<0 - a, b - 0, 0 - 0>
<-a, b, 0> .....................(1)
The direction vector between (0, 0, c) and (0, b, 0) is given as:
<0 - 0, b - 0, 0 - c>
= <0, b, -c> .....................(2)
To obtain the direction vector that is normal to the surface of the plane, we take the cross product of (1) and (2).
Doing this, we have:
<-a, b, 0> × <0, b, -c> = <-bc, -ac, -ab>
To find the scalar equation of the plane we can use any of the points that we know. Using (0, b, 0), we have:
(-bc)x + (-ac)y + (-ab)z = (-bc)0 + (-ac)b + (-ab)0
(bc)x + (ac)y + (ab)z = (ac)b
Dividing both sides by abc, we have:
(1/a)x + (1/b)y + (1/c)z = 1
We will call π, the plane with points P, Q, R ( the intercepts )
The solution is:
π : -bc×x + ac×y -ab×z - bac = 0
c) d = | bac|/√ ( -bc)² + (-ac)² + ( -ab)²
The intercepts P Q R are three points of the plane, according to that
P ( 0, b, 0 ) intercept with y-axis
Q ( a, 0, 0 ) intercept with x-axis
R ( 0, 0, c ) intercept with z-axis
We will find the vectors PQ and PR both are on the plane
PQ = [ a, 0, 0 ] - [ 0, b, 0 ] ⇒ PQ = ( a , -b, 0 )
PR = [ 0, 0, c ] - [ 0, b, 0 ] ⇒ PR = ( 0, -b c )
The vectorial product of these two vector will give us, one normal vector to the plane.
i j k
PQ * PR = a -b 0 = i (-bc) - j ( ac - 0 ) + k ( -ab - 0)
0 -b c
PQ * PR = [ -bc, -ac, -ab ]
we call this vector n = [ -bc, -ac, -ab ]
Let´s now find a vector between P, and a general point T ( x , y , z ) on the plane.
PT = [ x, y, z ] - [ 0, b, 0 ] ⇒ PT = [ x-0 , y - b , z - 0 ]
PT = [ x, y-b, z ]
Vector PT is perpendicular to vector n, then their dot product must be 0
Then:
PT × n = 0
[ x, y-b, z ] × [ -bc, -ac, -ab ] = 0
x × (-bc) + ( y - b )× (ac) + z × (- ab) = 0
-bc×x + ac×y -bac - ab×z = 0
-bc×x + ac×y -ab×z = bac (1)
Finally, we got the implicit equation for plane π as:
π : -bc×x + ac×y -ab×z - bac
c) The distance (d) between the plane and the origin is:
d = | D | / | n |
| n | = √ ( -bc)² + (-ac)² + ( -ab)²
|D| = | bac| the right side of the equation (1)
Then
d = | bac|/√ ( -bc)² + (-ac)² + ( -ab)²
Related Link :https://brainly.com/question/3914382
Ava bought some pens for $ 2 each and some pencils for $ 1 each. She bought 3 more pens than pencils and spent a total of $ 12. How many pencils did Ava buy?
Answer:
Step-by-step explanation:
price of 1 pen= $ 2
price of 1 pencil= $1
total money spent= $12
Let the number of pen be a and number of pencil be b.
2 a + b = 12 ----------------Equation 1
We have, she bought 3 more pens than pencils
a - b = 3 ------------------ Equation 2
Equation 1 +Equation 2,
2 a + b + a - b = 12 + 3
3a = 15
a = 5
Substituting in equation
5 - b = 3
b = 2
Number pencils Ava bought = 2
Let X1, X2 and X3 be three independent random variables that are uniformly distributed between 50 and 100.
A) Find the probability that the minimum of the three is between 75 and 90.
B) Find the probability that the second smallest of the three is between 75 and 90.
Answer:
a) the probability that the minimum of the three is between 75 and 90 is 0.00072
b) the probability that the second smallest of the three is between 75 and 90 is 0.396
Step-by-step explanation:
Given that;
fx(x) = { 1/5 ; 50 < x < 100
0, otherwise}
Fx(x) = { x-50 / 50 ; 50 < x < 100
1 ; x > 100
a)
n = 3
F(1) (x) = nf(x) ( 1-F(x)^n-1
= 3 × 1/50 ( 1 - ((x-50)/50)²
= 3/50 (( 100 - x)/50)²
=3/50³ ( 100 - x)²
Therefore P ( 75 < (x) < 90) = ⁹⁰∫₇₅ 3/50³ ( 100 - x)² dx
= 3/50³ [ -2 (100 - x ]₇₅⁹⁰
= (3 ( -20 + 50)) / 50₃
= 9 / 12500 = 0.00072
b)
f(k) (x) = nf(x) ( ⁿ⁻¹_k₋ ₁) ( F(x) )^k-1 ; ( 1 - F(x) )^n-k
Now for n = 3, k = 2
f(2) (x) = 3f(x) × 2 × (x-50 / 50) ( 1 - (x-50 / 50))
= 6 × 1/50 × ( x-50 / 50) ( 100-x / 50)
= 6/50³ ( 150x - x² - 5000 )
therefore
P( 75 < x2 < 90 ) = 6/50³ ⁹⁰∫₇₅ ( 150x - x² - 5000 ) dx
= 99 / 250 = 0.396
Achemistry student atrwered 81 questions correctly on a 90-question test. What
percent did the INCORRECT (WRONG)?
Answer:
The student got 90% correct and 10% incorrect.
Step-by-step explanation:
Find the product and write the result in standard form 6i(7-6i)
6i(7-6i)
42i-36i^2
hope it helps
Answer:
36+42i
Step-by-step explanation:
6i(7-6i)
=42i-[tex]36i^2[/tex]
=42i-(36x -1)
=42i+36
=36+42i
Given f(x) = x^2 - 2x - 15 find the average rate of change over the interval [0, 5].
Answer:
Average Rate of Change : 3
Step-by-step explanation:
" Remember that the average rate of change of function f say, on interval [a,b] would be f(b) - f(a) / b - a. Similarly we can solve for the average rate of this function. "
f(5) = x² - 2x - 15 = 5² - 2(5) - 15 = 25 - 10 - 15 = 0,
f(0) = 0² - 2(0) - 15 = 0 - 0 - 15 = - 15
And the average rate of change will be,
f(5) - f(0) / 5 - 0 = 0 - ( - 15 ) / 5 - 0
= 0 + 15 / 5 = 15 / 5 = 3
The average rate of change over the interval [0, 5] is hence 3.
a softball league has 13 teams, if every team must play every other team in the first round of league play, how many games must be scheduled
Answer:
78 games
Step-by-step explanation:
Think of it this way. Let's name the teams Team 1 through Team 13. Team 1 needs to have 12 games to play each other team. Once those are scheduled, Team 2 needs to have 11 games scheduled to play all the other teams (remember their game against Team 1 was already scheduled). Team 3 needs to have 10 games scheduled to play all the other teams (remember their games against Team 1 and Team 2 have already been scheduled). This patten continues until you schedule a single game between Team 12 and Team 13. So the total number of games that need to be scheduled are:
12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 78
I don't know if the concept of triangular numbers has been touched on in your class, but if so, there is a much simpler way to calculate this using the triangular number formula with n = 12. The formula is:
T = (n * (n + 1)) / 2
So in this case:
(12 * (12 + 1)) / 2 = (12 * 13) / 2 = 6 * 13 = 78
The three bulls practically destroyed the china shop. Bull 1 broke the fewest number of plates. Bull 2 broke 6 more than bull 1. Bull 3 was the worst of all. He broke 4 more plates than bull 2. If all 3 broke a total of 58 plates, how many did bull 1 break?
==========================================================
Work Shown:
x = number of plates Bull 1 broke
y = number of plates Bull 2 broke
z = number of plates Bull 3 broke
y = x+6 because the second bull broke 6 more plates compared to the first
z = y+4 since the third bull broke 4 more plates compared to the second
They all broke a combined 58 plates, meaning,
x+y+z = 58
Replace z with y+4 to get
x+y+z = 58
x+y+y+4 = 58
x+2y+4 = 58
Then replace y with x+6
x+2y+4 = 58
x+2(x+6)+4 = 58
From here solve for x
x+2(x+6)+4 = 58
x+2x+12+4 = 58
3x+16 = 58
3x = 58-16
3x = 42
x = 42/3
x = 14
Bull 1 broke 14 plates
---------------------------
If you want to find out how many plates the other bulls broke, then use that x value to find y and z
y = x+6 = 14+6 = 20
Bull 2 broke 20 plates
z = y+4 = 20+4 = 24
Bull 3 broke 24 plates
Overall, they broke 14+20+24 = 58 plates in total, which matches the total given in the instructions. The answer has been confirmed.
Answer:
B1 = 14 plates broken
Step-by-step explanation:
Method 1
We start with (58 - 6- 4) = (58 - 10) = 48
= 48 : We prove 6+4 = 10
To find who has the fewest plates we can now try again
with 48-6 = 42 or 48-4 = 44
42/3 = 14
We add 6 = 20
We add 4 = 24
We get 14+ 20 +24 = 58 broken plates.
So we know starting with -6 gets us our answer and our order correct.
Method 2 ; We deduct the difference from the total to find B1 distribution
B1 = 14 so 58-6 is 52 (-10)
We divide 42/3
To get 14
Conclusion;
We find method 1 shows us
B1 = 48 B2 = 48 (+6) =54 B3 = 54(+4) = 58
And try now for (14 + 14 + 6 ) + ( 22 + 4)
= 14 + 20 + 24 = 58 broken plates.
Find the product 3 − 9 × 3
Answer:
24
Step-by-step explanation:
The answer is 24 because you have to use PEMDAS which is parenthesis, exponents, multiply and divide left to right (which means whichever one is first), lastly add and subtract left to right.
Match each expression to its exponential form.
Exponent. | Solution
(3+2) x 5. 125
5^3. 5^2
10^2/2. 50
Step-by-step explanation:
5³ = 5×5×5 =125
10²/2 =100/2 =50
(3+2) ×5 = 5×5 = 25
Evaluate the expression (21 + 3) · 6 - 9
Answer:
135.
Step-by-step explanation:
(21 + 3) · 6 - 9
*21 + 3 = 24
24 · 6 - 9
**24 · 6 = 144
144 - 9
***144 - 9 = 135
Use compatable numbers, then divide. 448 ÷ 8 a. 450 ÷ 10 = 45 b. 500 ÷ 10 = 50
Answer: B
Step-by-step explanation: I think thats right
What is the correct equation for a line that has a slope of 1/3, and a y intercept of 4
Answer:
y=1/3x+4
Step-by-step explanation:
It should be correct as the gradient = 1/3
and the y-intercept = C
= +4
what is the definition of addition
Answer:
the difinition of addition is adding two things together
Step-by-step explanation:
Answer: Hi!
The definition of addition is when you add two or more more numbers (positive or negative.)
Hope this helps!
Which of the following statements are true for images formed by spherical mirrors?
A. A concave mirror always produces a real image of an object placed in front of it.
B. A convex mirror always produces a virtual image of an object placed in front of it.
C. A concave mirror always produces an image that is the same size as the object.
D. A convex mirror always produces an upright image of an object placed in front of it.
E. A convex mirror always produces an image that is the same size as the object.
F. A concave mirror always produces an inverted image on an object placed in front of it.
Answer:
B and D
Step-by-step explanation:
A convex mirror ALWAYS produces a virtual and upright image.
The true statements are:
B. A convex mirror always produces a virtual image of an object placed in front of it. D. A convex mirror always produces an upright image of an object placed in front of itF. A concave mirror always produces an inverted image on an object placed in front of it.A spherical mirror is a mirror with curved surface; it can either be convex or concave.
Convex mirrors
The image of a convex mirror is a virtual and an upright/erect image
Concave mirrors
The image of a concave mirror can be real or virtual, but the image is always inverted.
The above highlights mean that options (b), (d) and (f) are correct.
Read more about spherical mirrors at:
https://brainly.com/question/13068249
PLEASE I NEED ASAP, I WILL GIVE BRAINLYEST, 35 POINTS!!!
Evaluate this expression then round your answer to the two decimal places
7^4/7^6
Translate into a variable expression.
the square of the difference between a number n and fifty
Answer:
f(n)= (n-50)²
Step-by-step explanation:
The difference between a number n and fifty:
n - 50Square of this difference:
(n-50)²It would look like this as variable expression:
f(n)= (n-50)²Use and accessibility of internet on mobile phone
Answer:
Through a cellular service provider, the phone connects to the Internet through data transfer the same way a PC does, but with a wireless link. ... Cell phones have an in-built antenna which is used to send packets of digital information back and forth with cell-phone towers via radio waves. so the use of the internet it allows u to download apps,visit sites, (ect.)
Hope this helps_ /(TwT)\_
Please help! I’ll mark you as brainliest if correct!!!
Answer:
Brainleist!
Step-by-step explanation:
7 dollars
6+3 = 9 dollars spent
he will have -2 dollars
this is not possible but this is a fake made up problem so it is -2
Answer:
He'd have nothing because he can't afford it. So if he wants to eat at all he can have a sandwich, which will bring him down to a dollar
Step-by-step explanation:
-136=8(6x-5) can someone please help ?
Answer:
[tex]\Huge \boxed{x=-2}[/tex]
Step-by-step explanation:
[tex]-136=8(6x-5)[/tex]
Dividing both sides by 8.
[tex]-17=6x-5[/tex]
Adding 5 to both sides.
[tex]-12=6x[/tex]
Dividing both sides by 6.
[tex]-2=x[/tex]
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 2}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - 136 = 8(6x - 5)}[/tex]
Distribute 8 through the parentheses
⇒[tex] \sf{ - 136 = 48x - 40}[/tex]
Swap the sides of the equation
⇒[tex] \sf{48x - 40 = - 136}[/tex]
Move 40 to right hand side and change it's sign
⇒[tex] \sf{48x = - 136 + 40}[/tex]
Calculate
⇒[tex] \sf{48x = - 96}[/tex]
Divide both sides of the equation by 48
⇒[tex] \sf{ \frac{48x}{48} = \frac{ - 96}{48} }[/tex]
⇒Calculate
[tex] \sf{x = - 2}[/tex]
Hope I helped!
Best regards!!
24 13/1,000 as a decimal number
Answer:
24.013.
Step-by-step explanation:
Simplify: 24 13/1,000 = 24013/1000. Than just use a calculator to make it into a decimal.
desperate pls answer!!
Answer:
Step-by-step explanation:
a) Since the x's of the original equation are equal to the y's of the inverse equation, and vice versa, you can simply put the x-values of the table for the inverse equation into the y-values of the original equation. The same principle applies to the inverse equation. The table should look like the tables attached.
b) The x's and y's in the points of the inverse are switched. The points will be
(10, 27) --> (27, 10)
(3.5, 14) --> (14, 3.5)
(a, b) --> (b, a)
(x, y) --> (y, x)
How to solve 1/2(x-3)=9 linear equation
Answer:
[tex] \boxed{ \bold{ \sf{ \boxed{x = 21}}}}[/tex]Step-by-step explanation:
[tex] \sf{ \frac{1}{2} (x - 3) = 9}[/tex]
Distribute 1/2 through the parentheses
⇒[tex] \sf{ \frac{1}{2} x - \frac{1}{2} \times 3 = 9}[/tex]
Multiply the fractions
⇒[tex] \sf{ \frac{1}{2} x - \frac{1 \times 3}{2 \times 1} = 9}[/tex]
⇒[tex] \sf{ \frac{1}{2} x - \frac{3}{2} = 9}[/tex]
While performing the addition or subtraction of like fractions, you just have to add or subtract the numerator respectively in which the denominator is retained same.
⇒[tex] \sf{ \frac{x - 3}{2} = 9}[/tex]
Apply cross product property
⇒[tex] \sf{x - 3 = 9 \times 2}[/tex]
Multiply the numbers
⇒[tex] \sf{x - 3 = 18}[/tex]
Move 3 to right hand side and change it's sign
⇒[tex] \sf{x = 18 + 3}[/tex]
Add the numbers
⇒[tex] \sf{x = 21}[/tex]
Hope I helped!
Best regards!!
Isiah knows 1/4 is written .025 as a decimal how can you find a decimal for 5/4 without division
Answer:
0.25 x 5 = 1.25
This will not require any division. So, this is the answer. Hope this helps!
kara needs to fence her yard. How many feet of fencing is needed ?
Answer:
500 ft
Step-by-step explanation:
Perimeter: The total border of the outside of a given shape
Step 1: Find missing length
100 - 80 = 20 ft
Step 2: Add all together
100 + 150 + 80 + 85 + 65 + 20 = 500 ft
So we would need 500 ft of fence to border her yard completely.
Plz help fast
Thank you
Answer:
1.25 is largest, 1.1 is second, 0.924 third, 0.61 fourth, 0.5 fifth, 0.12 sixth.
Step-by-step explanation:
I will edit this post and explain later because you said you need the answer fast. :)
2) We are filling the storage room with packages of toilet paper. The packages measure 18
inches x 13 inches x 9 inches, the warehouse measures 12 feet by 20 feet by 8 feet. Inside
each box are 9 rolls of toilet paper. How many rolls are in this warehouse?
Answer:
14,175
Step-by-step explanation:
since measurement of packages are used in inches we will convert warehouse dimension in inches to keep the unit same.
1 foot = 12 inch
dimension of room
12 feet by 20 feet by 8 feet
dimension of room in inches
12 feet = 12*12 inches = 144 inches
20 feet = 12*20 inches = 240 inches
8 feet = 12*8 inches = 96 inches
volume of cube = length *width *height
dimension of room = 144 inches * 240 inches * 96 inches
= 3,317,760 cubic inches
volume of 1 package = 18 inches * 13 inches * 9 inches = 2,106 cubic inches.
let there be n packages in the room
volume of n package = n*volume of 1 package = 2,106*n cubic inches.
This volume of n packages should be equal to volume of warehouse
2,106*n= 3,317,760
=> n= 3,317,760/2,106 = 1,575.38
since package cannot be in fraction and value after decimal is less than 5 we will round the value to 1,575.
Thus, no of packages is 1,575
1 package has 9 rolls
1,575 package has 9*1575 rolls
thus, no of rolls in the warehouse = 14,175
The state of Mississippi only has 60% seatbelt use. Suppose you randomly select a resident from Mississippi and note their seatbelt use. Call this random variable Y. How does SD(X) compare with SD(Y)
Answer:
Population and Sample
Step-by-step explanation:
The state of Mississippi is the population
The randomly selected resident is the sample
Population Belt Use: 60%
Population No-belt Use: 40%
Sample (selected resident's) Seat-belt Use = Y
Note: the question doesn't state or ask whether Y is positive (use of seat belt) or negative (no use of seat belt).
How does the standard deviation of X compare with the standard deviation of Y?
X is the population standard deviation of seat belt use from the mean value of seat belt use WHILE Y is the sample standard deviation of seat belt use from the mean value (of all persons in the sample) of seat belt use.
Solve the equation for the specified variable.
U = Y(b + R), for b
Answer:
b= u/y -r
Step-by-step explanation:
What is the equation of the line given the two points
(-1,-6) and (-3, -8)
Answer:
y=x-5
Step-by-step explanation:
First we need to find the slope.
(-8+6)/(-3+1)
-2/-2
So the slope is 1
Using -1,-6 because we know the slope is 1, if we add 1 to x, we add 1 to y
So the y intercept is 0,-5
The equation is y=x-5
First find the gradient
[tex] \frac{y2 - y1}{x2 - x1} = \frac{( - 8) - ( - 6)}{( - 3) - ( - 1)} = \frac{5}{2} [/tex]
then using the formula y-y1 = m(x-x1)
y - (-6) = 5/2(x-(-1))
y + 6 = 5/2 (x+1)
2y + 12 = 5x + 5
2y - 5x = 5-12
2y - 5x = -7
5x - 2y = 7
so equation of the line is 5x -2y = 7
Sorry if im wrong