Answer:
Amara
Step-by-step explanation:
You can find mean by adding the total number of texts sent by each person and dividing it by the number of days.
In this case, the mean of Amara's texts sent is 6.714...
The mean of Marquis' texts sent is 9.428...
Therefore, Amara has the smaller mean.
in how many ways can four people sit in six chairs so that the leftmost chair is occupied and the right most is not
There are 96 ways for four people to sit in six chairs so that the leftmost chair is occupied and the rightmost is empty.
There are 4 guests and the leftmost seat is to be occupied, so there are 4 such ways to choose the occupant of that seat.
Then, for each of those 4 ways, there are 4 ways to decide the occupant for the second seat -- the remaining three people plus the possibility of that seat being empty, that makes a total of 16 ways to decide the configuration of the first two seats.
Then, for each of those 16 ways, there are 3 ways to choose the occupant for the third seat (either 3 remaining guests if the second seat was left empty, or the two remaining guests plus the possibility of leaving the 3rd seat empty). Hence, 16 times 3 is 48. For each of those ways, there are two choices for the next seat, i.e. 48 times 2 = 96, and finally one choice for the fifth seat. So in all, there are 96 ways.
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juan ran 3 miles in 45 minutes. at this rate how long will it take juan to run 7 miles
Answer:105
Step-by-step explanation:
The breaking strength of a rivet has a mean value of 10,100 psi and a standard deviation of 499 psi. (a) What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 10,000 and 10,300? (Round your answer to four decimal places.) (b) If the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given information? Explain your reasoning O Yes, the probability in part (a) can still be calculated from the given information O No, n should be greater than 30 in order to apply the Central Limit Theorem. O No, n should be greater than 20 in order to apply the Central Limit Theorem. O No, n should be greater than 50 in order to apply the Central Limit Theorem. You may need to use the appropriate table in the Appendix of Tables to answer this question.
the probability that the sample mean breaking strength for a random sample of 40 rivets is between 10,000 and 10,300 P(10000 ≤ x ≤ 10300) = 0.54
We would assume a normal distribution for the breaking strength of a rivet. We would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ/√n
Where
n = number of samples
x = Breaking strengths of rivet.
µ = mean breaking strength
σ = standard deviation
From the information given,
µ = 10,100 psi
σ = 499 psi
n = 40
The probability that the sample mean breaking strength for a random sample of 40 rivets is between 10000 and 10,300 is expressed as
P(10000 ≤ x ≤ 10300)
For x = 10000,
z = (10000 - 10100)/499/√40 = - 0.13
Looking at the normal distribution table, the probability corresponding to the z score is 0.45
For x = 10300,
z = (10300 - 10100)/499/√40 = 2.54
Looking at the normal distribution table, the probability corresponding to the z score is 0.99
Therefore,
P(10000 ≤ x ≤ 10300) = 0.99 - 0.45 = 0.54
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A chemical equation contains 4 hydrogen atoms and 2 oxygen atoms in the reactants. How many hydrogen and oxygen atoms should be in the products according to the law of conservation of matter? Responses 2 hydrogen atoms and 4 oxygen atoms 2 hydrogen atoms and 4 oxygen atoms 1 hydrogen atom and 1 oxygen atom 1 hydrogen atom and 1 oxygen atom, 4 hydrogen atoms and 2 oxygen atoms 4 hydrogen atoms and 2 oxygen atoms 5 hydrogen atoms and 1 oxygen atom 5 hydrogen atoms and 1 oxygen atom
The number of hydrogen and oxygen atoms that should be in the products according to the law of conservation of matter, is given as follows:
4 hydrogen atoms and 2 oxygen atoms.
What is stated by the law of conservation of matter?
The law of conservation of matter states that the amount of matter in the solution remains constant, even when the substance has a change in the format.
The amounts on the equation are given as follows:
4 hydrogen atoms.2 oxygen atoms in the reactants.The law of conservation of matter states that the amounts remain constant, hence the amounts of the solution are given as follows:
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The number of hydrogen and oxygen atoms that should be in the products according to the law of conservation of matter, is given as follows:
4 hydrogen atoms and 2 oxygen atoms.
What is stated by the law of conservation of matter?
The law of conservation of matter states that the amount of matter in the solution remains constant, even when the substance has a change in the format.
The amounts on the equation are given as follows:
4 hydrogen atoms.
2 oxygen atoms in the reactants.
The law of conservation of matter states that the amounts remain constant, hence the amounts of the solution are given as follows:
4 hydrogen atoms.
2 oxygen atoms in the reactants.
there are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, how many have sprinkles or filling?
There are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, 10 have sprinkles or filling
What is Venn Diagram ?Circles that overlap or do not overlap each other are used in a Venn diagram to illustrate similarities and distinctions between objects or groups of objects.Objects that share characteristics are represented as overlapping circles, whereas objects that are unique stand alone.Venn diagrams are currently utilized in many academic and business settings as demonstrations.Let S represent the set for donut with Sprinklers.
Let F represent the set for donut with Filling.
To find :- How many have sprinkles or filling?
i.e. n ( S ∪ F )
Formula,
n ( S ∪ F ) = n ( S ) + n ( F ) + n ( S ∩ F )
Given,
n ( S ) = 6
n ( F ) = 7
n ( S ∩ F ) = 3
Putting in formula
n ( S ∪ F ) = n ( S ) + n ( F ) - n ( S ∩ F )
= 6 + 7 - 3
= 10
Donuts with Sprinklers or Filling = 10
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10c - cd + d^3 (if c = -6 and d= 2)
Answer:
-40
Step-by-step explanation:
Given that,
c = -6
d = 2
To find the value of the given expression, replace c & d with 6 & 2 respectively.
Let us solve it now.
10c - cd + d³
( 10 × -6 ) - ( -6 × 2 ) + 2³
- 60 - ( -12 ) + 8
- 60 + 12 + 8
- 40
On the venn diagram shade the set P' ∩ ( Q ∪ R)
The desired set is shaded on the Venn Diagram given by the image at the end of the answer.
How to shade the Venn Diagram?The first step towards shading the Venn Diagram is finding the meaning of each symbol, as follows:
Symbol U: represents the union of the two sets, and the shaded elements are the elements that belong to at least one of the two sets.Inverted Symbol U: represents the intersection of two sets, and the shaded elements are the elements that belong to both sets.The negation symbol of the elements of P is given as follows:
P'.
The union is applied between the sets:
R and Q.
The intersection is then applied between:
The negative of P and the union of R and Q.
Then the shaded region is given by the elements that belong to at least one of the sets Q or R, without belonging to set P, as shown by the image presented at the end of the answer.
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Ezra applied the distributive property to the expression 8(y+2). He then used the commutative property.
Drag and drop expressions to the boxes to correctly complete the statements. Need help fast!!!!!!!!!!!
Put responses in the correct input to answer the question. Select a reply, navigate to the desired information and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button, or touchpad. Responses can also be moved by dragging with a mouse.
After applying the distributive property, Ezra's expression was the Response area.
After he used the commutative property, his expression was the Response area.
The results of the expressions after the properties are applied in this problem are given as follows:
Distributive property: 8y + 16Commutative property: 16 + 8y.What are the properties?The expression in the context of this problem is defined as follows:
8(y + 2).
The distributive property states that the outside term multiplies each of the inside terms, hence it is applied as follows:
8(y + 2) = 8 x y + 8 x 2 = 8y + 16.
The commutative property states that two terms of an addition can have the order exchanged.
The terms of the addition, after the distributive property, are 8y and 16, hence after the application of the commutative property, the expression is given as follows:
16 + 8y.
As the terms were exchanged.
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the subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x, y}, {w, x, y}, and { } (the empty subset). how many subsets of the set {w, x, y, z} contain w ?
Answer:
4
Four subsets of {w, x, y} contain w.
Step-by-step explanation:
There are four subsets that have w in it:
{w} has w in it.
{w, x} has w in it.
{w, y} has w in it.
{w, x, y} has w in it.
The answer is 4.
A quadrilateral has 4 sides. one angle of a regular quadrilateral measures (6w 13)°. determine the value of w. round to the nearest whole number. w = 13 w = 23 w = 59 w = 90
A regular quadrilateral is one in which the lengths of all the sides and the measures of all the angles are equal. A regular quadrilateral must have all of its angles measured (6w 13°) if one of its angles does.
A quadrilateral's angles measure a total of 360 degrees. The total measure of the angles of a regular quadrilateral is 4 (6w 13)°, which equals 24w + 52°. A regular quadrilateral contains four angles, of which each measure (6w 13)°. Thus, we obtain the equation shown below:
24w + 52° = 360°
Solving for w, we get:
24w = 308°
w = 13
Consequently, w has a value of 13, and w = 13 is the right response.
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what quotients are equivalent to -48/-17
The quotient of the expression will be;
⇒ 2.823
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The equation is,
⇒ - 48 / - 17
Now,
Solve the equation as;
The equation is,
⇒ - 48 / - 17
After divide we get;
⇒ - 48 / - 17
⇒ 48 / 17
⇒ 2.823
Thus, The quotient of the expression will be;
⇒ 2.823
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f we start at the point (1,3,2), then in what direction should we move if we want to maximize the directional derivative?
To maximize, it has positive direction at x=1 in first quadrant
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).
Given function:
F=x³z - yz²
Find the following :
[tex]\partial F/\partial x+ \partial F/\partial y + \partial F/\partial z[/tex]
= 3x²z + (-z²) + (x³-2yz)
So, gradient = 3x²z -z² + x³-2yz
Find the gradient at (1,3,2):
x=1, y=3 and z=2
gradient = 3*1*2 - 9 +1 - 12 = -14
To maximize, it has positive direction at x=1 in first quadrant = 14
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30% of = 30 i need to find some thing 30% that is 30.
Answer:
9
Step-by-step explanation:
We can turn 30% into a decimal, then multiply 30% by 30.
30% = 0.3
0.3*30 = 9
Answer:
9
Step-by-step explanation:
1. Turn 30% into a decimal:
(Move the decimal place over twice to get:)
30% = 0.30
2. Multiply
0.30 x 30 = 9
Solution:
9
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 5 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
103.019 to the nearest tenth
The value of 103.019 rounded to the nearest tenth is 103.0.
What is Rounding Off?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For whole numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done. The significant figures are preserved when numbers are rounded off.
Round the number up if 5, 6, 7, 8, or 9 follow the number you are rounding. For instance, 40 when rounded to the nearest ten is 38. Round the number down if the rounded number is followed by a 0, 1, 2, 3, or 4.
Therefore, the number is 103.0.
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Answer:
103.0
Step-by-step explanation:
suppose x is a normal random variable with and find p(x > 105.0). a) 0.9993 b) 0.9994 c) 0.9995 d) 0.0007 e) 0.0006 f) none of the above.
The value of the probability p(x > 105.0) for the given normal random variable is found as 0.6915.
Explain the term normal random variable?A randomly distributed variable with a mean of 0 and a standard deviation of 1 is referred to as a standard random variable. The letter Z will always stand in for it. regularly distributed random variable, also known as a with standard deviation, is a continuous random variable which probabilities are defined by the normal distribution of mean and standard deviation.For the stated question -
The formula for the z score -
z = (x - μ)/σ
In which,
μ = 140 and σ = 20
Put the values-
z = (150 - 140)/20
z = 0.5
p(x > 105.0) = p(z > 0.5)
p(x > 105.0) = 0.6915
Thus, the value of the probability p(x > 105.0) for the given normal random variable is found as 0.6915.
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The complete question is-
suppose x is a normal random variable with μ = 140 and σ = 20 and find p(x > 105.0).
for question 44 is f(2pi/4) a positive or a negative number
Please help
Answer:
Amplitude = 3
Period = π
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.7cm}\underline{Standard form of a cosecant function}\\\\$y=A\csc(Bx)$\\\\where:\\\\\phantom{ww}$\bullet$ $|A|$ is the stretch factor. \\ \\\phantom{ww}$\bullet$ $\dfrac{2\pi}{|B|}$ is the period.\\\\\phantom{ww}$\bullet$ $x=\dfrac{\pi}{|B|}$ is the interval of vertical asymptotes.\\\end{minipage}}[/tex]
Given function:
[tex]f(x)=3 \csc 2x[/tex]
Therefore:
A = 3B = 2Period
[tex]\textsf{Period} = \dfrac{2 \pi}{|B|}=\dfrac{2 \pi}{|2|}=\pi[/tex]
Amplitude
The amplitude of the given function is 3, so:
minimum points are when y = 3.maximum points are when y = -3.x-values of minimum points
[tex]\begin{aligned}3\csc(2x)=3 \implies \csc(2x)&=1\\\dfrac{1}{\sin(2x)}&=1\\\sin(2x)&=1\\2x&=\dfrac{\pi}{2}+2\pi n\\x&=\dfrac{\pi}{4}+\pi n \end{aligned}[/tex]
[tex]\implies \textsf{Minimum points}: \left(\dfrac{\pi}{4}\pm \pi n,3 \right)[/tex]
x-values of maximum points
[tex]\begin{aligned}3\csc(2x)=-3 \implies \csc(2x)&=-1\\\dfrac{1}{\sin(2x)}&=-1\\\sin(2x)&=-1\\2x&=-\dfrac{\pi}{2}+2\pi n\\x&=-\dfrac{\pi}{4}+\pi n \end{aligned}[/tex]
[tex]\implies \textsf{Maximum points}: \left(-\dfrac{\pi}{4}\pm \pi n,-3 \right)[/tex]
Asymptotes:
[tex]\implies x=\dfrac{\pi}{|B|}=\dfrac{\pi}{|2|}=\dfrac{1}{2} \pi[/tex]
Therefore, there are vertical asymptotes every ¹/₂π.
To graph the given function:
[tex]\textsf{Draw vertical asymptotes at} \;\;x = 0 + \dfrac{\pi}{2} n[/tex][tex]\textsf{Plot minimum points at}\; \left(\dfrac{\pi}{4}\pm \pi n,3 \right)[/tex][tex]\textsf{Plot maximum points at}\; \left(-\dfrac{\pi}{4}\pm \pi n,-3 \right)[/tex]Draw curves between the asymptotes with the given min/max points.What is the sequence of transformations that maps △ABC to △A′B′C′?
Select from the drop-down menus to correctly identify each step.
The transformation taking place in triangles are 90° rotation counterclockwise about origin and translation 3 units up.
What is transformation?A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Given that, △ ABC is transformed in to △ A′B′C′
Firstly, △ ABC is being rotated 90° counterclockwise about the origin, and then it translated 3 units up.
Hence, The transformation taking place in triangles are 90° rotation counterclockwise about origin and translation 3 units up.
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a kite 75ft above the ground moves horizontally at a speed of 8ft/s. at what rate is the angle between the string and the horizontal decreasing when 200ft of string has been let out?
When 200ft of string has been let out, the angle is decreasing at a rate of 0.015 radians per second.
In this question, we have been given the height of the kite from the ground is y = 75 ft.
The kite moves horizontally at a speed of 8 ft/s
So, dx/dt = 8 ft/s
The length of the string is 200 ft
so, L = 200 ft
Consider the following figure for this situation.
Now consider the sine of angle theta.
sin(θ) = 75/200
sin(θ) = 3/8
Now consider the tangent of angle theta.
tan(θ) = 75/x
1 / tanθ = x/75
cot(θ) = x/75
Differentiating the above equation with respect to t.
-csc²(θ) * dθ/dt = 1/75 * dx/dt
- csc²(θ) * dθ/dt = 1/75 * 8
- csc²(θ) * dθ/dt = 8/75
We know that, csc(θ) = 1/sin(θ)
csc(θ) = 8/3
So above equation becomes,
-(8/3)² × dθ/dt = 8/75
dθ/dt = - (8/75 * 9/64)
dθ/dt = 0.015
Therefore, the angle is decreasing at a rate of 0.015 radians per second.
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HELP ME I DONT UNDERSTAND THIS!!!!!!!!!!!!!!
Answer:
x=4
Step-by-step explanation:
4(3x+3)=5(x+8) ------- Given
12x + 12 = 5x + 40
12x-5x= 40-12
7x = 28
x = 4
8x+8
Step-by-step explanation:
from the first you can see that there is a 3 in front of the x and if equal then 8 has to be in front of x as well
A meteor crashed onto a planet and caused crater that was 16,495.92 in deep.
Use the table of facts to find the depth of the crater In yards.
Conversion facts for length
Round your answer to the nearest tenth.
12 Inches (in) = 1 foot (ft)
3 feet (ft) = 1 yard (yd)
36 Inches (in) =
yard (yd)
5280 feet (ft) = 1 mile (mi)
1760 yards (yd) = 1 mile (mi)
yd
x5
Answer:
Step-by-step explanation:
The depth of the crater in yards is 387.2 yards
Converting Inches to yards
Since the crater is 13,937.63 in deep, we convert this to yards.
Since 36 in = 1 yard, we use this conversion factor to convert to yards
13,937.63 in × 1 yard/36 in = 387.16 yards
≅ 387.2 yards to the nearest tenth
So, the depth of the crater in yards is 387.2 yards
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The depth created by the meteor in different units will be 1,374.66 feet, 458.22 yards, and 0.26 miles.
What is conversion?Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
A meteor crashed onto a planet and caused a crater that was 16,495.92 inches deep.
The conversion ratio is given below.
12 Inches (in) = 1 foot (ft)3 feet (ft) = 1 yard (yd)36 Inches (in) = 1 yard (yd)5280 feet (ft) = 1 mile (mi)1760 yards (yd) = 1 mile (mi)⇒ 16,495.92 / 12 = 1,374.66 feet
⇒ 16,495.92 / 36 = 458.22 yards
⇒ 1,374.66 feet = 0.26 miles
The depth created by the meteor in different units will be 1,374.66 feet, 458.22 yards, and 0.26 miles.
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An airplane is preparing to land at an airport. It is 44,100 feet above the ground and is descending at the rate of 3,500 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,800 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be? Use pencil and paper. Use two other methods to solve the problem. Explain which methods are easier to use and which are more difficult to use for the situation.
Answer:
Step-by-step explanation:you add the nmer than you divid them so when you divd them you answer is right there
Suppose that you have data recording the body weight and the running speed for each of several different jackrabbits. To summarize this data, it suffices to note the mean and SD for each of these two variables. a. True b. False
Answer:
True.
Step-by-step explanation:
I think that it is true because it is asking for a summary of the data and finding the mean of the speeds and weight would give you the summary of all the data.
How to Graph y=1/2x-3/2
Answer:
See below
Step-by-step explanation:
There is a great free graphing program called Desmos.
y = 1/2 x - 3/2
I highlighted 3 points for you.
The y-intercept is (0, -1.5) This is where the graph crosses the x axis. Another name for -1.5 is -3/2. That is the number that you see at the end of the equation.
The slope is 1/2. Look at the other two points on the line (-1,-2) and (1,-1) If you start at the first point and go up 1 and then 2 right you will end up at the second point. That is the slope.
wisconsin: 5.82\times 10^{6}5.82×10 6 vermont: 6.24\times 10^{5}6.24×10 5 how many times greater was the population of wisconsin than the population of vermont? write your answer in standard notation, rounding to the nearest tenth.
Population of Wisconsin is 9.3 × 10⁰ times greater than the population of Vermont.
As given in the question,
Population of Wisconsin is equal to 5.82 × 10⁶
Population of Vermont is equal to 6.24 × 10⁵
Let 'x' represents the number of times population of Wisconsin is greater than the Vermont
⇒ x = ( population of Wisconsin ) / (Population of Vermont)
⇒ x = ( 5.82 × 10⁶ ) / ( 6.24 × 10⁵ )
⇒ x = 0.933 × 10⁶⁻⁵
⇒ x = 0.933 × 10¹
⇒ x = 9.3 × 10⁰ ( Standard notation , rounding to nearest tenth)
Therefore, population of Wisconsin is 9.3 × 10⁰ times greater than the population of Vermont as per given data.
The complete question is:
The approximate populations of Wisconsin and Vermont (as of 2019) are listed below: Wisconsin: 5.82 × 10⁶ Vermont: 6.24 × 10⁵. How many times greater was the population of Wisconsin than the population of Vermont? Write your answer in standard notation, rounding to the nearest tenth.
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if you have an unfair coin with probability p heads, what is the expected number of flips before you end up with a head?
The scenario assumed to be the number of flips until you land on a head is P(x) = 1 + (1 - p)/p.
Given info,
If you have an unfair coin with probability p heads, what is the expected number of flips before you end up with a head,
To solve the above condition, have a formula;
P(x) = 1 + ( 1 - p )/p
Hence, P(x) = 1 + ( 1 - p )/p is the case expected to number of flips before you end up with a head.
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If May is 15 and John is five years older than may and Jay is 15 years older than John. How old is Jay?
Answer:
Jay is 35
Step-by-step explanation:
Creating an equationLet:
x = age of mayy = age of john z = age of jayHere, we are given that
May is 15 so x = 15John is 5 years older than may or y = x + 5 Jay is 15 years older than john or z = y + 15Solving for the agesGiven that x = 15 , y = x + 5 and z = y = 15
We can firstly find the age of john or "y" as we are given the value of x
y = x + 5
==> plug in x = 15
y = 15 + 5
==> add 15 and 5
y = 20
So John is 20
Now that we have the value of y we can easily find Jay's age or the value of z
z = y + 15
==> y = 20
z = 20 + 15
==> add 20 and 15
z = 35
Hence, Jay is 35
Answer:
35
Step-by-step explanation:
i did the math and also try adding them together?
From 2006-2018 Jeff Bezo's net worth increased by 127 billion dollars. During that time Mr. Bezos paid 1.4 million in federal taxes. What percentage of that increase in worth was paid to the federal government in form of taxes? ALL WORK MUST BE SHOWN IN SCIENTIFIC NOTATION.
He paid 0.0012% of his total wealth increase as federal tax.
What is a expression? What is a mathematical equation? What is Equation Modelling? What is differentiation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. We can write -
y = f(x)
y' = dy/dx = (d/dx)[f(x)]
We have Mr. Bezos, who paid 1.4 million in federal taxes between 2006 -2018. His net worth increased by 127 billion dollars during this time span.
Assume that he paid [x]% of money to federal taxes. Then, we can write -
1.4 x 1,000,000 = (x/100) x 127 x 1000,000,000
1.4 = (x/100) x 127000
x = (1.4 x 100)/(127000)
x = 1.4/1270
x = 14/12700
x = 0.0012%
Therefore, he paid 0.0012% of his total wealth increase as federal tax.
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find three vectors with which you can demonstrate that the vector cross product need not be associative, i.e., that a x (b x c) need not be the same as (a x b) x c. g
The cross product of three vectors is not associative in nature.
Considering three vectors such as : A=(2,1,3), B=(1,0,2) and C=(1,1,0)
we know that the associative law depicts that :
A x (B x C) = (A x B) x C ,while doing the operation for the considered vectors :
A x (B x C) =(2,1,3)x ((1,0,2)x (1,1,0))
=(2,1,3)x (-2,2,1)
=(-5,-8,6)
(A x B) x C= ((2,1,3)x (1,0,2))x (1,1,0)
= (2,-1,1) x (1,1,0)
=(-1,1,3)
So for this vector operation, A x (B x C) is not equal to (A x B) x C, so you can sum up that cross product of three vectors can't be associative every possible time.
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for what value of x is line a parallel to line b?
Two lines are parallel : Two lines (in the same plane) are said to be parallel to each other if they never intersect no matter how far they extend to either side.
The value of x is 15° for the given lines i.e a and b are parallel to each other.
As you can see in the picture above, there are two lines , i.e. a and b are parallel to each other.
Properties of parallel lines:
If you have a horizontal line that intersects two parallel lines at two different points, it makes four angles at each point.Corresponding angles formed by two parallel lines and a transverse line are equal. The pairs of interior angles on the same side of the intersection are supplementary angles.Upper and lower diagonals and vertical angles are equal.Alternate interior/interior angles are equal.i.e. angle b° = angle f° and angle a° = angle e°
Now, we conclude that
angle (6x+3)° = angle 93°
=> 6x + 3 = 93
=> 6x = 93 - 3 = 90
=> x = 15°
Hence, the value of x is 15°.
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In a survey of six year olds at a party, 0.83 liked the cake at the party, 0.52 liked the pizza and 0.40 liked the cake and pizza. What is the probability of choosing a six year old who liked the pizza or cake? Round to four decimals, as needed.
Answer:
Step-by-step explanation:
1+1
2/555