Answer:
125.6 square inches of plastic is needed
Step-by-step explanation:
To make 10 plastic beach balls each with a radius of 2 inches, the company would need approximately 502.4 square inches of plastic.
To determine the amount of plastic needed to make 10 beach balls, we first calculate the surface area of one beach ball. The formula for the surface area of a sphere is 4πr². Given the radius of 2 inches, we plug this into the formula:
A = 4πr² = 4 × 3.14 × (2 inches)² = 4 × 3.14 × 4 square inches = 50.24 square inches.
Since this is for one beach ball, we need to multiply this amount by 10, to account for the total plastic needed for 10 beach balls:
Total surface area for 10 beach balls = 50.24 square inches × 10 = 502.4 square inches.
Therefore, the company would need approximately 502.4 square inches of plastic to make 10 beach balls, rounding to the nearest tenth.
Juan ordered 4 CDs for $48.96, which includes a $5.00 shipping charge. If each CD was the same price, what was the cost of each CD? Worth 20 pls answer ASAP
Answer:
Each CD would be $10.99
Step-by-step explanation:
$48.96-5.00=43.96
43.96/4= 10.99
Answer:
The answer is $12.24 each CD. I just did this for my assessment. Looks like we are in the same online school program :D
Step-by-step explanation:
$48.96/4 = $12.24
you can check your answer by doing
$12.24 x 4
a circle with center (4 -3) contain the point (9,-3). what is an equation of the circle
Answer:
[tex]\large\boxed{(x-4)^2+(y+3)^2=25}[/tex]
Step-by-step explanation:
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (4, -3) and the point on the circle (9, -3).
The length of radius is equal to the distance between a center and an any point on a circle.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Susbtitute:
[tex]r=\sqrt{(9-4)^2+(-3-(-3))^2}=\sqrt{5^2+0^2}=\sqrt{5^2}=5[/tex]
The center (4, -3) → h = 4, k = -3.
Finally we have:
[tex](x-4)^2+(y-(-3))^2=5^2\\\\(x-4)^2+(y+3)^2=25[/tex]
Select the system of linear equations that has the solution (-6, 0).
A. X+ Y=0
X+y=-6
B.X+2y=-6
X-2y=-6
C. x-6y=1
-6x+y=4
D.4x+3y=-18
x-2y=12
Answer:
B.
• x+2y=-6
• x-2y=-6
Step-by-step explanation:
Try the solution in the equations and choose the set of equations that is true.
___
A. -6+0 ≠ 0 . . . not this system
__
B. -6 +2·0 = -6 . . . true
-6 -2·0 = -6 . . . true . . . . . this system has solution (-6, 0)
__
C. -6 -6·0 ≠ 1 . . . not this system
__
D. 4(-6)+3·0 ≠ -18 . . . not this system
A pet store owner wants to know what type of pet foods her customers prefer. At the bottom of each receipt, she provides a phone number for her customers to call in and answer survey questions. of the 94 responses, she found that 9 prefer orgianic pet food. She concludes that about 10% of her customers would prefer to feed organic food to their pets. Is this conclushion valid? Justify your answer.
yes, if you do 94/9 you get about 10%. this determines that out of all 94 responses, by dividing it by the 9 people who prefer organic food, you get 10.444 percent which is approximately 10%
The pet store owner's conclusion about her customers' preference for organic pet food is not entirely valid due to the small sample size and potential bias in her survey results. For more accurate conclusions, she should get responses from a larger, more diverse group of customers.
Explanation:The pet store owner's conclusion is not entirely valid because it is based on the assumption that the 94 responses she received are representative of her entire customer base. While 9 out of 94 responses did indicate a preference for organic pet food, this is a small sample size and may not accurately reflect the preferences of all customers. For a more accurate estimate, she would need to collect responses from a larger and more diverse group of customers, to allow the results to be more statistically significant.
A small sample size can lead to inaccuracies or bias in survey results. In addition, because these customers self-selected to respond tot he survey, they may not represent the full spectrum of her customers. This type of bias is known as a self-selection bias.
So, while it's a starting point, further sampling and more robust survey methods would help strengthen the validity of her conclusions about her customers' pet food preferences.
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Which equation could you use to solve for x in the proportion 4/5=9/x
20 points!!!!!!
Answer:
4x=45
Step-by-step explanation:
Cross multiply to get a simplified equation.
4/5=9/x
4x=45
x=11.25
Answer:
Step-by-step explanation:
4/5=9/x
cross multiphication
x=9*5/4
x=45/4
[tex] {7}^{2} - 3 + 9 \times 8 \div 2 \\ w = [/tex]
Answer:
82
Step-by-step explanation:
49 - 3 + 72/2
= 46 + 36
= 82
For this case we must find the value of the following expression:
[tex]7 ^ 2[/tex]-3 + 9 * 8÷2 =
According to the PEMDAS algebraic order of operations:
P: Perform any calculation within parentheses
E: Simplify any exponential expressions.
MD: Do all the multiplications and divisions, from left to right, as they appear.
AS: Do all the addition and subtraction, from left to right, as they appear.
So:
49-3 + 9 * 8÷2 =
49-3 + 72÷2 =
49-3 + 36 =
46 + 36 =
82
ANswer:
82
(15 points ) PLEASE HELP ASAP! Also please show your work! Solve.
Use the quadratic formula. Write solutions in simplist radical form. 2x^2+2x-1=0
Answer:
Step-by-step explanation:
ax^2+bx+c
-b +- sqaure root of b^2 -4ac/2a
-2 +- square root (2)^2-4(2)(-1)/2(2)
-2 +- square root 4+8 /4
-2 +- 2 square root 3 /4
reduce
-1 +- square root 3/2
Answer:
[tex]\large\boxed{x=\dfrac{-1-\sqrt3}{2}\ or\ x=\dfrac{-1+\sqrt3}{2}}[/tex]
Step-by-step explanation:
The quadratic formula of a quadratic equation:
[tex]ax^2+bx+c=0[/tex]
Discriminant of a Quadratic is [tex]\Delta=b^2-4ac[/tex]
If Δ < 0, then an equation has no real solution (has two complex solutions)
If Δ = 0, then an equation has one real solution [tex]x=\dfrac{-b}{2a}[/tex]
If Δ >0, then an equation has two real solutions [tex]x=\dfrac{-b\pm\sqrt{\Delta}}{2a}[/tex]
==========================================
We have the equation:
[tex]2x^2+2x-1=0\\\\a=2,\ b=2,\ c=-1[/tex]
Substitute:
[tex]\Delta=2^2-4(2)(-1)=4+8=12>0\\\\\sqrt\Delta=\sqrt{12}=\sqrt{4\cdot3}=\sqrt4\cdot\sqrt3=2\sqrt3[/tex]
[tex]x=\dfrac{-2\pm2\sqrt3}{(2)(2)}=\dfrac{-2\pm2\sqrt3}{4}[/tex] simplify by 2
[tex]x=\dfrac{-1\pm\sqrt3}{2}[/tex]
Two different antibiotics can be used to treat an infection. Treatment with antibiotic 1 is known to be successful 80% of the time. This treatment costs $80. Antibiotic 2 is successful 90% of the time and costs $100. The two treatment plans are: Plan A: Treat with antibiotic 1. If not effective, treat with antibiotic 2. Plan B: Treat with antibiotic 2. If not effective, treat with antibiotic 1. Based on the data provided, what is the probability that a patient treated under plan A will be successfully treated?
A. 0.98
B. 0.72
C. 0.80
D. 0.90
Answer: Option A
A. 0.98
Step-by-step explanation:
Plan A consists of:
Plan A: treat with antibiotics 1. If not effective, treat with antibiotics 2
Antibiotic 1 has a probability P (1) of 0.8 to be effective
Antibiotic 2 has a probability P (2) of 0.9 to be effective.
For a patient to be treated successfully with plan A it can happen that:
The antibiotic 1 works, or that the antibiotic 1 does not work but the 2 antibiotic if it works.
So the probability that plan A works is:
[tex]P = P (1) + P (not\ 1) P (2)\\\\P = 0.8 + (1-0.8) (0.9)\\\\P = 0.8 + 0.2 * 0.9\\\\P = 0.98[/tex]
The probability of a patient being successfully treated under plan A, which involves treatment with antibiotic 1 and then antibiotic 2 if the first fails, is 0.98, or 98%.
Explanation:
The probability that a patient treated under plan A will be successfully treated is calculated by summing the probabilities of success in each step. Initially, the patient is treated with antibiotic 1 which has an 80% success rate. If this fails (which will happen 20% of the time), then the patient is treated with antibiotic 2 which has a 90% success rate. This 90% will only occur, though, for the remaining 20% of patients who failed the initial treatment. Thus, we calculate this like so: Probability(successful treatment under plan A) = (successful treatment with antibiotic 1) + ((failed treatment with antibiotic 1)*(successful treatment with antibiotic 2)) = 0.8 + (0.2*0.9) = 0.98. Therefore, the probability of successful treatment under plan A equals 98% or 0.98, which corresponds to Choice A.
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Which decimal is equivalent to 8/11?
Answer:
.72 or .73 which ever one is on your sheet
Step-by-step explanation:
Answer:
0.72 or 0.73
Step-by-step explanation:
8/11 expressed as a decimal is 0.72 or 0.73
I NEED HELP!
You pick a card at random. Without putting the first card back, you pick a second card at random. There're 3 cards. One is 7, one is 8, and the other is a nine. What is the probability of picking a 7 and then picking a number greater than 7? (Write the probability as a fraction or whole number.)
The probability of picking a 7 and then picking a number greater than 7 is [tex]\dfrac{1}{3}[/tex] or [tex]0.\overline{3}[/tex].
ProbabilityProbability shows us the chances of an event occurring.
[tex]\bold{Probability =\dfrac{Desired\ Outcome}{Total\ number\ of\ outcomes\ possible}}[/tex]
Now, given that we have already picked three cards. therefore, 7, 8, and 9.
The number of possible outcomes is 3.
the probability of card 7,[tex]\bold{Probability(7) =\dfrac{Number\ 7(1)}{Total\ number\ of\ outcomes\ possible (3)}= \dfrac{1}{3}}[/tex]
Now, as card seven is already picked up cards 8 and 9 are the only card left.
therefore, the sample size(possible outcomes) was reduced to 2 only.
Also, cards 8 and 9 both are greater than 7, thus the desired outcome is also 2.
Further the probability of the number greater than 7 occurring,
[tex]\bold{Probability(n>7) =\dfrac{cards\ 8\ and\ 9(2)}{Total\ number\ of\ outcomes\ possible (2)}= \dfrac{2}{2} = 1}[/tex]
Probability picking a number greater than 7The probability of picking a 7 and then picking a number greater than 7
= Probability of card 7 occuring x probability of card 8 and 9 occurring
[tex]=\dfrac{1}{3}\times 1[/tex]
[tex]=\dfrac{1}{3}[/tex]
Hence, the probability of picking a 7 and then picking a number greater than 7 is [tex]\dfrac{1}{3}[/tex] or [tex]0.\overline{3}[/tex].
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20 POINTS
Which property or postulate justified the statement below?
"If WX=YZ, then WX+RS=YZ+RS"
A. Transitive Property of Equality
B. Addition Property of Equality
C. Segment Addition Postulate
D. Substitution Property of Equality
Answer:
A because they are opposites.
Step-by-step explanation:
They equal the same they are just swapped the 2 set of numbers are the same but the first set of numbers are different when you add them they become the same number in the end :) hope this helps
B. Addition Property of Equality justified the statement,
"If WX=YZ, then WX+RS=YZ+RS".
What are the properties of equality?Facts regarding any two or more quantities connected by the equal sign are known as properties of equality.
There are four types of properties of equality.
Addition property, when two equal quantities are increased by a common value, the equality is preserved.
Transitive property of equality, entities that are equivalent to one another are also equivalent to one another.
Subtraction property, equality is maintained when a common term is subtracted from two equal terms.
Multiplying by a common term do not alter the equality, according to the multiplication property of equality.
Given, An equation WX = YZ, Now, In this expression WX + RS = YZ + RS
We have added RS to both side of the equation to maintain the equality sign.
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What is the length of YA ?
AYZ is a right triangle (we're given that YA is perpendicular to XZ). So, we can use the pythagorean theorem to find the missing side:
[tex]YA^2+AZ^2=YZ^2[/tex]
But we're also given [tex]YZ = 2AZ[/tex], so we have
[tex]YA^2+AZ^2=(2AZ)^2=4AZ^2[/tex]
Since AZ is half of YZ, which is 10, we deduce AZ=5.
Solving for YA, we have
[tex]YA^2+AZ^2=4AZ^2 \iff YA^2 = 3AZ^2 \iff YA = AZ\sqrt{3} = 5\sqrt{3}[/tex]
subtract: (2x^2-7x+5)-(-6x^2-4x-2)
A. -4x^2-11x+3
B. -4x^2-5x+3
C. 8x^2-13x+7
D. 8x^2-3x+7
Answer:
[tex]\large\boxed{D.\ 8x^2-3x+7}[/tex]
Step-by-step explanation:
[tex](2x^2-7x+5)-(-6x^2-4x-2)\\\\=2x^2-7x+5-(-6x^2)-(-4x)-(-2)\\\\=2x^2-7x+5+6x^2+4x+2\qquad\text{combine like terms}\\\\=(2x^2+6x^2)+(-7x+4x)+(5+2)\\\\=8x^2-3x+7[/tex]
Answer:
8x^2-3x+7
Step-by-step explanation:
By simplifying the expression.
A survey was done to determine how many people between the ages of 6 and 25 have downloaded a new song. The results are displayed in the histogram below.
Which statements is correct?
The mode is people aged 11 - 15
The mode is people aged 16 - 20
The mode is people aged 21 - 25
Answer:
16-20
Step-by-step explanation:
Mode is the one that happens the most and 16-20 has the highest bar
The mode is in people of age between 16- 20 , Therefore Option B is the answer.
What is Mode ?Mode is the measure of central tendency of data , It is the value that is occurring continuously in a data set.
A histogram is given in the question ,
As from the definition mode is the value which is occurring repeatedly in the data , The mode is in people of age between 16- 20 , Therefore Option B is the answer.
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What is the 100th term of a sequence with a1=222 and d=-5
Answer:
- 273
Step-by-step explanation:
The n th term of an arithmetic sequence is
• [tex]a_{n}[/tex] = a₁ + (n - 1)d ← substitute in values
[tex]a_{100}[/tex] = 222 + (99 × - 5 ) = 222 - 495 = - 273
The midpoint of the line segment with end points (-3,1) and (1,-4) is (-1,-1.5)
Yes or no?
Answer:
Answer: yes.
Step-by-step explanation:
x: (x1 + x2)/2 = (-3 + 1)/2 = -2/2 = - 1 So far so good.
y: (y1 + y2)/2 = (1 - 4 )/2 = (-3/2) = -1.5
The midpoint is (-1 , - 1.5)
True
you are miguel cervantes de navas y colin, captain in the royal spanish army in sevilla in the year 1842. Outside your barracks window is a stack of cannonballs. on an idle afternoon you decide to calculate the number on cannonballs. what is the number of the cannonballs?
Answer: it’s 506
Step-by-step explanation:
The number of cannonballs in the stack exists at 650. Since the stack is in the formation of the square pyramid the total number of balls can be acquired by utilizing the formula for discovering the total number of spheres in the square pyramid.
How to calculate the total number of cannon balls?Find the number of cannonballs in the stack:
Given that the pyramid stands a square pyramid and the numeral of balls that form the side of the square exists 12.
By utilizing the formula of a square pyramid,
n(n+1)(2n+1)/6
12(12+1)(2(12)+1)/6
12(13)(25)/6
2*13*25
=650
Therefore the number of cannonballs in the stack exists at 650.
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4n − 3 = −2 n + 9n = 2 Is 2 the solution? yes or no, how do you know?
[tex]
4n-3=-2n+9n \\
6n-3=9n \\
3n=-3 \\
n=\boxed{-1}
[/tex]
2 is not a solution but -1.
ANSWER
No, n=2 is not a solution.
EXPLANATION
The given equation is
[tex]4n - 3 = - 2n + 9n[/tex]
If n=2 is a solution, then it must satisfy this equation.
We substitite n=2 into the equation to get:
[tex]4(2)- 3 = - 2(2)+ 9(2)[/tex]
[tex]8- 3 = - 4+ 18[/tex]
[tex]5 = 14[/tex]
This statement is false
Therefore n=2 us not a solution.
Can someone help me with this problem
Answer:
C = 20.65 + 0.75M
Step-by-step explanation:
Given in the question that,
standard charge by the rental company = S = 16.95 + 0.60M
insurance charge by the rental company = I = 3.70 + 0.15M
Total charge C = S + I
16.95 + 0.60M + 3.70 + 0.15M = C
20.65 + 0.75M = C
So the equation which represent total charge that includes insurance in terms of M is
C = 20.65 + 0.75MConsider the function f(x)=x^2−6x−2 . Which equation shows function f written in vertex form? f(x)=(x−3)^2−5 f(x)=(x+3)^2−11 f(x)=(x+3)^2−5 f(x)=(x−3)^2−11
Answer:
f(x) = (x − 3)² − 11
Step-by-step explanation:
To convert to vertex form, complete the square.
f(x) = x² − 6x − 2
f(x) = x² − 6x + 9 − 9 − 2
f(x) = (x − 3)² − 11
We need to complete the square: if we add and subtract 11 from the expression, we have
[tex]f(x)=x^2-6x-2=x^2-6x-2+11-11=x^2-6x+9-11=(x-3)^2+11[/tex]
John ran the 100-m dash with a time of 9.87sec. If this pace could be maintained for an entire 26-mi marathon, what would his time be? (Notice that 1 m ≈ 3.281 ft and 1 mi = 5280 ft.)
Hr____
Minutes____
Seconds____
Answer:
1 hour
8 min
49 sec
Step-by-step explanation:
we know that
1 m=3.281 ft
1 mi=5,280 ft
Convert 26 mi to ft
26 mi=26*5,280=137,280 ft
Convert 137,280 ft to m
137,280 ft=137,280/3.281=41,840.90 m
using proportion
9.87/100=x/41,840.90
x=41,840.90*(9.87)/100
x=4,129.70 sec
Remember that
1 hour=3,600 sec
1 hour=60 min
1 min=60 sec
4,129.70 sec=4,129.70/3,600= 1.147 h
0.147*60=8.82 min
0.82*60=49 sec
therefore
1 hour
8 min
49 sec
John could maintain his 100-m dash pace for an entire 26-mi marathon, his time would be 1 hour, 8 minutes, and approximately 50 seconds.
First, we need to convert John's 100-meter dash time into a pace that can be extrapolated over the marathon distance. Given that John ran a 100-m dash in 9.87 seconds, we need to find out how many meters he runs per second. This would be 100 m / 9.87 s = 10.13 meters per second.
Next, we convert the marathon distance from miles to meters. As there are 5280 feet in a mile and 3.281 feet in a meter, there are 5280 / 3.281 = 1609.34 meters in a mile. The marathon distance is therefore 26 miles * 1609.34 meters/mile = 41842.84 meters.
Using John's pace, we can calculate the time it would take to run the marathon: 41842.84 meters / (10.13 meters/second) = 4129.64 seconds.
Finally, we convert the total seconds to hours, minutes, and seconds. There are 3600 seconds in an hour and 60 seconds in a minute:
Hours: 4129.64 sec / 3600 sec/hr = 1.147 hours (1 hour)Minutes: (4129.64 sec - 1 hour × 3600 sec) / 60 sec/min = 8.827 minutes (8 minutes)Seconds: 4129.64 sec - 1 hour × 3600 sec - 8 minutes × 60 sec = 49.64 seconds (approximately 50 seconds)Therefore, if John could maintain his 100-m dash pace for an entire 26-mi marathon, his time would be 1 hour, 8 minutes, and approximately 50 seconds.
The population of Oak Forest is increasing at a rate of 2% per year. If the population is 53,768 today, what will it be in three years?
Answer:
56,994
Step-by-step explanation: multiply the population by 0.02, round it to the nearest whole number, and then multiply that number by 3 and add it onto 53,768
The population of Oak Forest in three years will be approximately 57,091.
Explanation:To find the population of Oak Forest in three years, we can use the formula for exponential growth. The formula is: P = P0 * (1 + r)t, where P is the final population, P0 is the initial population, r is the growth rate, and t is the number of years. In this case, P0 is 53,768, r is 0.02 (2% as a decimal), and t is 3. Plugging these values into the formula, we get:
P = 53,768 * (1 + 0.02)3
Simplifying the expression inside the parentheses:
P = 53,768 * (1.02)3
Calculating (1.02)3:
P = 53,768 * 1.0604
Calculating the final population:
P ≈ 57,091
Therefore, the population of Oak Forest in three years will be approximately 57,091.
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I don't get how to do this ration help me I need this finished
answer part A and B
For part two using what we already know can you figure out the length of the segment?
answer D) 24
if the long tail is to the right, the distribution of the data is said to be:
A. a symmetric distribution
B. a negatively skewed distribution
C. a positively skewed distribution
D. none of the choices are correct
Answer:
Negatively skewed.
Step-by-step explanation:
In a negatively skewed distribution, the mode is greater then the median, and the median is greater then the mean. Overall, the majority of the data is to the right, which means that the distribution of data is skewed to the left, or negatively skewed.
Answer: Hence, Option 'C' is correct.
Step-by-step explanation:
As we know that if one tail is longer than the other, the distribution is said to be skewed.
And there are two types of skewed distribution :
1) Negatively skewed
2) Positively skewed
It depends on the direction of the long tail.
If the long tail is to the right , then it is said to be positively skewed distribution.
If the long tail is to the left , then it is said to be negatively skewed distribution.
According to question, the distribution here is a positively skewed distribution.
Hence, Option 'C' is correct.
Please help I will give BRAINLIEST
Pages Minutes
15 1
45 3
75 5
300 20
600 40
15 x 2= 39
45x 2= 90
75x2=150
30x20=60
600 x 2 = 1,200
Two lines intersecting at a right angle
form a line.
are parallel.
are perpendicular.
form a ray.
Answer: THIRD OPTION
Step-by-step explanation:
We need to remember that a right angle is an angle that measures 90 degrees.
By definition, when two or more lines intersect (or cross one another ) at a 90-degree angle, then these lines are called "Perpendicular".
Therefore, in this case, we know that these two lines intersects at a right angle (angle of 90 degrees), then, we can conclude that these lines are Perpendicular.
This matches with the third option.
Answer:
Perpendicular lines
Step-by-step explanation:
Two or more lines are called intersecting lines.That point would be on each of these lines.
Can I have a explaination of what the mathmatical term 'permutation' is.
15 points
Answer:
In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting. These differ from combinations, which are selections of some members of a set where order is disregarded.
Step-by-step explanation:
Find the surface area of the following rectangular prism.
surface area = ft2
There are 2 sides that are 2 x 1 = 2 ft^2 each
2 sides are 1 x 8 = 8 ft^2 each
And 2 sides 2 x 8 = 16 ft^2 each
Total surface area = 2 + 2 +8+ 8 +16 + 16 = 52 ft^2
Answer: [tex]\text{Surface area =}52\text{ ft.}^2[/tex]
Step-by-step explanation:
The surface area of a rectangular prism is given by :-
[tex]S.A.=2(lw+wh+lh)[/tex], where l is length, w is width and h is height of prism.
From the given picture, length =2ft
height = 8 ft.
width = 1 ft
Then , the surface area of prism will be :-
[tex]S.A.=2((2)(1)+(1)(8)+(8)(2))\\\\\Rightarrow\ S.A.=2(26)\\\\\Rightarrow\ S.A.=52\text{ ft.}^2[/tex]
Please help!
Express the series using sigma notation. 8 + 10 + 12 + ... + 24.
Answer:
C
Step-by-step explanation:
Number on top: largest value of k
On the right: the expression for k
Bottom: the first number for k
So,
1. 2³ = 8, but k can not be 3, so it can't be A or B.
2. 8 ÷ 2 = k, which means that the first k should be 4.
So, the answer is C.
Answer:
C
Step-by-step explanation:
Help with the 2 question .. 20 points
Answer:
see explanation
Step-by-step explanation:
c = a - 2b
= < 4, 5, 6 > - 2 < 1, 2, 3 > ← multiply each component by 2
= < 4, 5, 6 > - < 2, 4, 6 > ← subtract corresponding components
= < 4 - 2, 5 - 4, 6 - 6 > = < 2, 1, 0 >
| c | = [tex]\sqrt{2^2+1^2+0^2}[/tex] = [tex]\sqrt{4+1+0}[/tex] = [tex]\sqrt{5}[/tex]
-------------------------------------------------------------------------------------------------
sum the product of corresponding components
u.v = (3 × 2) + (- 2 × - 1) + (4 × - 6) = 6 + 2 - 24 = - 16