Find the tangent vector T to the given line (t) = 〈 x(t), y(t), z(t) 〉, with parametric equations,
x(t) = -1 + 3t
y(t) = 6 - 3t
z(t) = 3 + 7t
by differentiating (t) component-wise:
T = '(t) = 〈 dx(t)/dt, dy(t)/dt, dz(t)/dt 〉
T = 〈3, -3, 7〉
Scale T by any real number t to get the line through the origin (when t = 0) and the point (3, -3, 7) (when t = 1), which of course runs parallel to '(t). This gives the vector tT. Translate this by any vector v = 〈a, b, c〉 to force this line to pass through the point (a, b, c) instead of the origin, while still remaining parallel. You want the new line to pass through (0, 11, -9), so take v = 〈0, 11, -9〉.
Then the vector equation of the new line is
tT + v = t 〈3, -3, 7〉 + 〈0, 11, -9〉 = 〈3t, 11 - 3t, -9 + 7t〉
with parametric equations
x(t) = 3t
y(t) = 11 - 3t
z(t) = -9 + 7t
The question is:
Which calculation and answer show how to convert 13/16 into a decimal
Answer:
I think the answer is D
Step-by-step explanation:
Answer is D, because if you divide 13 and 15 it gives you 0.8125
. A cell phone company has three different production sites. Five percent of the cars from Site 1, 7% from Site 2, and 9% from Site 3 have been recalled due to unexpected shutdown issue. Suppose that 60% of the phones are produced at Site 1, 30% at Site 2, and 10% at Site 3. If a randomly selected cell phone has been recalled, what is the probability that it came from Site 3 (write it up to second decimal place)
Answer:
0.15 = 15% probability that it came from Site 3
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Being recalled
Event B: Recalled from site 3.
Probability of being recalled:
5% of 60%(from site 1)
7% of 30%(from site 2)
9% of 10%(from site 3).
So
[tex]P(A) = 0.05*0.6 + 0.07*0.3 + 0.09*0.1 = 0.06[/tex]
Probability of being recalled, being from site 3.
9% of 10%.
[tex]P(A \cap B) = 0.09*0.1 = 0.009[/tex]
If a randomly selected cell phone has been recalled, what is the probability that it came from Site 3?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.009}{0.06} = 0.15[/tex]
0.15 = 15% probability that it came from Site 3
I NEED HELP!
The area of a rectangle is 12a^2 - a - 6 square inches. The width is 4a - 3inches. What is the length. Show your work.
Answer:
The length of rectangle is (3a+2).
What is the mean of 8,7,6,9,8.5,7.5,10,5.5,7,9,8.5,7,9.5,8,8.5
Answer:
the mean is 7.93
Step-by-step explanation:
min5.5
median8
max10
What is the slope of the line
(Picture below)
Lydia is buying a ring.
The ring costs £60
She pays a deposit of 40%.
Work out how much she pays as the deposit.
Answer: I believe it's £24
Step-by-step explanation: I suck at math so sorry if it's wrong.
the average motorcycle weighs 32,000 grams. How many kilograms does the average motorcycle weigh?
Answer:
The average motorcycle would weigh 32 kilograms.
Step-by-step explanation:
1 kilogram = 1000 grams
so, to find how many kilograms a motorcycle is, we just need to divide the amount of grams by 1000
32,000 / 1000 = 32 kg
Fractions closer to 1 than to 0
Answer:
Fractions that are above 1/2 or 0.5
Step-by-step explanation:
-7 + 5
Explain Thank you
Answer:
-7 + 5 = -2
Step-by-step explanation:
Basically, this equation can be thought of as 5 - 7, which would equal -2.
13
5
ө
12
What is the length of the side opposite to angle θ
Answer: Sin θ =
Step-by-step explanation:
In the figure attached, ABC is a right angle triangle.
Sides of this triangle are AB = 12 BC = 5 and CA = 13
Angle opposite to the side having length = 12 is θ.
Now we have to calculate sin θ.
Since Sinθ =
=
Therefore, ratio which represents sinθ will be
Step-by-step explanation:
-4x+y=3 plzz answerrr simplify itt
Answer:
x= -3/4 + y/4
Step-by-step explanation:
Move all terms that don't contain
x to the right side and solve.
Answer:
[tex]x = - \frac{3}{4} + \frac{1}{4} y[/tex]
Step-by-step explanation:
[tex] - 4x + y = 3[/tex]
[tex] - 4x = 3 - y[/tex]
[tex]x = - \frac{3}{4} + \frac{1}{4} y[/tex]
[tex]x = - \frac{3}{4} + \frac{1}{4} y[/tex]
The stock market dropped 220 points on Monday. It lost another 48 points on Tuesday, and on Wednesday, it gained 96 points. What was the amount of change over those three days.
48 points gained in those 3 days.
Subtract 220 with 48, then add 96. Last step would be subtracting 220 with the amount they have now in those 3 days to find how much points the stock market gained in those 3 days.
Subtract 220-48.It‘ll be 172.
Add 172 with 96. 172+96=268.
Subtract 268 with how much points the stock market had 3 days ago. 268-220 would be 48.
The amount of change over those three days is 268 points.
Here,
The stock market dropped 220 points on Monday.
It lost another 48 points on Tuesday, and on Wednesday, it gained 96 points.
We have to find, the amount of change over those three days.
What is amount?
The sum total of two or more quantities or sums, is called amount.
Now,
The stock market dropped 220 points on Monday.
It lost another 48 points on Tuesday.
Hence, the points after loss = 220 - 48 = 172
And, when it gained 96 points.
Then, the points after gain = 172 + 96 = 268
Hence, The amount of change over those three days is 268 points.
Learn more about the amount visit:
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Find the value of each variable in the parallelogram.
Answer:
u = 4; v = 18
because this is a parallelogram
=> 2u + 2 = 5u - 10
6 = v/3
<=> 3u = 12
v = 6.3
<=> u = 4
v = 18
write the algebraic expression for: The length of a rectangle is 3 feet less than 4 times its width.
Answer:
Perimeter (P) is: 48
Problem to solve:
48=2(2x+3)+2(x)
48=4x+6+2x
48=6x+6
48-6=6x+6-6
42=6x
42/6=6x/6
7=x
Step-by-step explanation:
The length of a rectangle is 3 more than twice its width. The perimeter is 48 feet. Find the width. Hint: You did this in Module 3 Assignment 5. Now you have to write the equation and solve it.
a. 16
highlight%28b%29. 7
c. 8
d. 21
e. 24
:
Formula for the perimeter of a rectangle is: highlight%28P=2L%2B2W%29, P is perimeter, L is length, W is width.
Let Width (W) be:x
Then length (L)is: 2x+3
Write the following number in scientific notation:
4, 332
4.332 x 10³
Step-by-step explanation:
hope it helps!
Latoya can plant 1/3of her garden in 2/5 hour. If she continues working at this rate, what fraction of Latoya’s garden can she plant in one hour?
Answer:
Latoya can plant 5/6 of her garden in one hour.
Step-by-step explanation:
☆We can solve using proportion!
[tex] \frac{ \frac{1}{3 } \: of \: garden }{ \frac{2}{5} \: of \: hour } = \frac{x}{1 \: hour} \\ \\ \frac{ \: \frac { 2}{5}x }{ \frac{2}{5} } = \frac{ \frac{1}{3} }{ \frac{2}{5} } \\ \\ x = \frac{5}{6} [/tex]
PLS I HAVE 10 min TO FINISH I NEED HELP WITH MATH
Answer:
B is the answer
Step-by-step explanation:
I worked it out
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Place the indicated product in the proper location on the grid.
(2x - 3y )(4x - y )
xy - -4x²
Step-by-step explanation:
(2x - 3y)(4x -y)
2x( 4x -y) -3x( 4x - y)
8x² - 2xy - 12x² + 3xy
8x²- 12x²- 2xy + 3xy
-4x² + xy
xy - -4x²
The diameter of a circle is 8 cm. Find its circumference in terms of pi
Answer:
25.13 or 8 × pi
Step-by-step explanation:
diameter × pi = circumference
Answer:
8π
Step-by-step explanation:
formula for circumference of a circle=
C=2πr, r= radius
the radius is the diameter divided by 2
radius= 8/2=4
plug into formula
C=2π4
multiply 2 and 4
C=8π
Please help. I dont understand how to do this. Enter the coordinates of the vertices of (Ry-axis ∘ r(90°, O))(QRST).
Answer:
I think it's
Q = ( 1 , 3 )
R = ( 3 , 3 )
S = ( 0 , 2 )
T = ( -2 , 1 )
Step-by-step explanation:
please tell me if this is wrong.
Hope this helps!
Find the value of x if A, B, and C are collinear points and B is between A and C. AB=6x,BC=x−5,AC=23
Answer:
The value of x = 4 if A, B, and C are collinear points and B is between A and C.
Step-by-step explanation:
We need to find the value of x if A, B, and C are collinear points and B is between A and C.
We have AB=6x,BC=x−5,AC=23
If points are collinear and B is between A and C we can write:
AC=AB+BC
Putting values and finding value of x
[tex]AC = AB+BC\\23=6x+x-5\\23=7x-5\\7x=23+5\\7x=28\\x=\frac{28}{7}\\x=4[/tex]
The value of x = 4 if A, B, and C are collinear points and B is between A and C.
A state Motor Vehicle Department requires learners to pass a written test on the motor vehicle laws of the state. The exam consists of twenty true-or-false questions, of which eighteen must be answered correctly to qualify for a permit. In how many different ways can a learner who answers all the questions on the exam qualify for a permit
Answer:
211 ways
Step-by-step explanation:
Given :
Number of questions = 20
Number of correct correct questions to be answered in other to qualify should be atleast 18
Hence,
Correct questions could be either 18, 19 or 20 ;
Using combination :
nCr = n! ÷ (n-r)!r!
20C18 = 20! / (20 - 18)!18!
20C18 = (20* 19) / (2 * 1) = 190 ways
20C19 = 20! / (20-19)!19!
20C19 = 20 / 1 = 20 ways
20C20 = 20! / 0! 20! = 1 ways
Hence, total number of possible ways = (190 + 20 + 1) = 211 ways
Steven earns extra money babysitting. He charges $37.00 for 4 hours and $55.50 for 6 hours. Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
Answer:
Step-by-step explanation:
3.2
if x is the first of two consecutive integers, express the sum of the two integers in terms of x
Answer:
2x+1
Step-by-step explanation:
x = 1st integer
x+1 = next consecutive integer
The sum is
x+ (x+1)
Combine like terms
2x+1
let the first integer be x and the second be x + 2
then the sum is x +x+2 = 2x +2
A new factory is growing fast and hiring a lot of new workers. Every week, the total number of workers doubles in size. If it takes 18 weeks for the factory to be at full capacity, how many weeks would it take for the factory to be at half capacity?
Answer:
9 weeks
Step-by-step explanation:
divide the full capacity by 2 to get 9 because 9 x 2 is 18 and half of the full capacity would be half capacity
One card is selected at random from a deck of cards. Determine the probability that the card selected is a card greater than 3 and less than 8.
Answer:
4/13
Step-by-step explanation:
Count all cards that are 4, 5, 6, and 7 (each of 4 different suits) so the number of cards that is greater than 3 and less than 8 = 4(4) = 16.
There are 52 cards in a standard deck of cards.
P(greater than 3 and less than 8)
= 16/52
= 4/13
The diameter of a circle is 9 feet. Find the radius.
Answer:
4.5
Step-by-step explanation:
Diameter is equal to 2r. In other words, to find radius from the diameter, you divide the diameter by two. In this case, its 9/2. That gives you 4.5
Answer:
4 1/2 feet
Step-by-step explanation:
The radius fo the circle is half of the diameter so 4 1/2 Feet.
PLease do all this i will give brainiest
Answer:
The cost of 10 pens is $2.25.
You would have 30 hard boiled eggs.
You will need 18 hard boil eggs for 54 scrambled.
Step-by-step explanation:
What is 2k2 – 13k – 24 factored
Answer:
(2k+3) (k−8)
Step-by-step explanation:
3x+1=6x-4 solve for x
Answer:
x = 5/3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityStep-by-step explanation:
Step 1: Define
3x + 1 = 6x - 4
Step 2: Solve for x
Subtract 3x on both sides: 1 = 3x - 4Add 4 to both sides: 5 = 3xDivide 3 on both sides: 5/3 = xRewrite: x = 5/3Answer:
Exact form
x=5/3
Decimal form
x=1.6
Mixed number form
x= 1 2/3
Step-by-step explanation: