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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what is the difference between a convex set and a convex function with respect to linear programming?
A real-valued function defined on an interval with the property that its epigraph—the collection of points on or above the function's graph—is a convex set—is said to be convex. The challenge of minimizing convex functions over convex sets is the subject of the optimization discipline known as convex minimization.
What is linear programming?A mathematical model whose needs are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming. When a linear function is subjected to various constraints, it is maximized or minimized using the mathematical modeling technique known as linear programming. In business planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
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Refer to the previous question, the physics student used the regression model to predict that a force of 377.28N would be required to stretch the spring by 15cm. Remarkably, his prediction was horribly wrong. Can you explain why? (Check all that apply)
A. Correlation does not imply causation.
B. He made a prediction outside of the range of forces observed.
C. He made a prediction outside of the range of stretched distances measured.
D. He had outliers or influential points in his data.
E. None of the above
The physics student predicted that a force of 377.28N would be needed to stretch the spring by 15 cm using the regression model.
The relevant points from the regression model are
B. He predicted something that was outside the range of forces seen.
C. He predicted something that was outside the range of stretched distances that were observed.
D. His data contained outliers or significant points.
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- Clare removed marbles from a container of
water. When she removed 2 marbles, the
water level was 80 ml. When she removed
4 more marbles, the water level was 40 ml.
Write an equation for the water level y after
x marbles are removed.
Answer:
y = 100 - 10x
Step-by-step explanation:
Let y₀ be the original water level before any marbles were removed
Let y = water level after x marbles are removed.
Let d be the water level drop for every marble removed
Then we have the general equation:
y = y₀ - x.d
We have to find d and y₀
So we get one equation for the water level after removal of 2 marbles
80 = y₀ - 2d [1]
After 4 more marbles were removed, the water level drops to 40ml. That means for 4 marbles removed, the water level drops from 80 to 40. So drop in water level for 4 marbles = 80-40 = 40ml
For each marble then, water level drop = 40/4 = 10ml. This is the value of d
Plug this value of d into [1] to get the original water level y₀
80 = y₀ - 2( 10)
80 = y₀ - 20
100 = y₀
or,
y₀ = 100
So original water level is 100ml and the equation for water level after x marbles are removed is
y = 100 - 10x
complete the table of values y=x² - 4x - 2
show that differentiation reverses parity: if f is even, then f' is odd, and if f is odd, then f' is even. hint: differentiate f (-x ).
Differentiation reverses the parity of a function, means if f(x), is an even function, then its derivative f'( x ) is odd which is true i.e f(x) is even function implies f'(x) is odd and if f(x) is odd function implies f'(x) is even .
First, let's we start with the definition of even and odd functions.
f is even if and only if f(x) = f(-x) --(1)
f is odd iff f(x) = -f(-x) ---(2)
If f is even and differentiating equation (1) we get,
f'(x) = f'(-x)× (-1) = -f'(-x).
f'(x) = - f'(-x).
Since, f'(x) is some function, then let
g(x) = f'(x) So, we see g(x) = -g(-x) which shows that the derivative of an even function is an odd function.
If f is odd then: f(x) = -f(-x)
differentiating above function with respect to x we get ,
f'(x) = -f'(-x)× (-1 ) = f'(-x).
Let g(x) = f'(x), then g(x) = g(-x) which shows that the derivative of an odd function is an even function.
Hence, Differentiation reverses the parity is hold.
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values for the random variables or uncertain variable inputs to a simulation are a. randomly generated from the specified probability distributions b. equal to the most likely value c. selected by the decision maker d. calculated by fixed mathematical formulas e. controlled by the decision maker
The correct option is:
a. randomly generated from the specified probability distributions
Given,
In the question:
Values for the random variables or uncertain variable inputs to a simulation are:-
a. randomly generated from the specified probability distributions
b. equal to the most likely value
c. selected by the decision maker
d. calculated by fixed mathematical formulas
e. controlled by the decision maker
Choose the correct one.
Now, According to the question:
Let's Know:
How do you generate a random number from a probability distribution?
In general, generating a random number from a probability distribution means transforming random numbers so that the numbers fit the distribution. Perhaps the most generic way to do so is called inverse transform sampling: Generate a uniform random number in [0, 1].
The correct option is:
a. randomly generated from the specified probability distributions
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an item is regulary priced at $40. Brian bought it at 40% off the regular price. HOw much did brian pay
Answer: Brian payed $24.00
How u do it:
Discount= original price x discount%/100
Discount = 40 × 40%/100
Discount = 40 x 0.4
You save = $16.00
Final Price = Original Price - Discount
Final Price = 40 - 16
Final Price = $24.00
Question is below! Mark brainliest!
Answer: (-84, 272)
x = -84
y = 272
Hope this helps!
Answer:
Below
Step-by-step explanation:
-6x - 2y = - 40 <====multiply this entire equation by -1 to get:
6x + 2y = 40 <===== then add it to the second equation
-7x -2y = -44 to get:
-x = -4
so x = 4 use this value in one of the equations to compute y
-6(4) - 2y = -40
-2y = -16
y = 8 (4,8)
72 +1-5 x 3; value: 135
Answer:
58
Step-by-step explanation:
72 + 1 - 5 x 3
= 72 + 1 - 15
= 73 - 15
= 58
Multiply the following polynomials. Write the simplified answer in descending order. Use the ^ (shift + 6) to indicate exponents.
DO NOT add spaces between any numbers or characters. For example: (x+2)(x+3) = x^2+5x+6.
(2x - 3y)(4x - y)
Answer:
8x^2-14xy+3y^2 (I think)
Step-by-step explanation:
You probably don't need it now but like here
Question
What is another way to write the expression t⋅(14−5)?
helpp meee
14t-5t is another way to write the expression t⋅(14−5)
What is Number system?A number system is defined as a system of writing to express numbers.
The given expression is t(14-5)
An expression is combination of variables, numbers and operators.
t times of fourteen minus five
Here t is the variable
We need to find other way to write this expression
t(14-5)
Apply distributive property
14t-5t
9t
Hence, 14t-5t is another way to write the expression t⋅(14−5)
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Find the slope of the line that passes through each pair of points.
(5, 7), (1, -3)
Answer:
5/2 or 2.5
Step-by-step explanation:
Slope is rise/run. We take the difference of the y-coordinates and divide it by the difference of the x-coordinates.
From this, we get [tex](7--3)/(5-1)[/tex], or [tex]10/4[/tex], which can be simplified to 5/2, or 2.5.
Jasmine checks rental car rates. She discovers that a midsize car costs $50.00 plus $19.99 per day to rent. Which recursive formula shows the sequence of costs to rent the car for 1 day, 2 days, 3 days, and so on? Responses an=19.99+50.00an−1 where n>1 a n = 19.99 + 50.00 a n − 1 where n > 1 an=50.00+19.99an−1 where n>1 a n = 50.00 + 19.99 a n − 1 where n > 1 a1=69.99an=an−1+19.99 where n>1 a 1 = 69.99 a n = a n − 1 + 19.99 where n > 1 a1=50.00an=an−1+19.99 where n>1 a 1 = 50.00 a n = a n − 1 + 19.99 where n > 1
Recursive relation is [tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex] where n>1
What do you mean by recursive realtion?
A recursive sequence is one in which terms are defined by reference to one or more previously defined terms.
The recursive formula [tex]a_{n+1}=a_{n}[/tex] + d can be used to find the (n+1)th term of an arithmetic series if you know the nth term and the common difference, d.
It is given that cost of midisze car is $50.00
Rent per day = $19.99
We need to find the sequence of costs to rent the car for 1 day, 2 days, 3 days, and so on.
According to the question:
Cost become = 50.00 + 19.99n where n represents the number of days
Recursive formula become:
[tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex] where n>1
Therefore, recursive relation is [tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex] where n>1
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what is the probability of first drawing a red card, then a jack, and then a black card? do not round your intermediate computations. round your final answer to four decimal places.
The probability of first drawing a red card, then a jack, and then a black card is 0.0612
First we will describe the standard deck of 52 cards in terms of black, red and face cards found in a standard deck
Following is a table of distribution of colored and face card found in a standard deck:
Type Number of cards
1 - 10 40
Black 26
Red 26
Face 12
The numerical cards from digit ( 1 to 10 ) are found in all 4 suits ( Clubs, Diamonds, Spades, and Hearts ). Hence, 10 x 4 = 40
- The entire deck is split in two colors ( Red and Black ) equally. So, the number of Black and Red cards are = 52 / 2 = 26 cards.
- The face cards are of three types ( King, Queen and Jack ). These three face cards are found in each of the 4 suits. Hence, Total number of face cards are = 4 * 3 = 12
- We will now consider the probabilities associated with each type. We will define 3 events and write down their probability as expressed:
Event ( A ): First draw is a red card.
- The probability of this event can be determined with the help of the table given above. There are a total of 26 red card in a standard deck of 52 cards. Hence,
p ( A ) = [ Number of red cards ] / [ Total cards in a deck ]
p ( A ) = [ 26 ] / [ 52 ]
p ( A ) = 1 / 2
- After we make the first draw of a red card. Our deck distribution is changed to Number of Red cards remaining = 25 and total deck now has 51 cards remaining.
- We will define the next event as:
Event ( B ): The second draw is a face card.
- The probability of this event can be determined with the help of the table given above. There are a total of 12 face cards in a standard deck of 52 cards which is now down to 51 cards. Hence,
p ( B ) = [ Number of face cards ] / [ Total cards in a deck ]
p ( B ) = [ 12 ] / [ 51 ]
p ( B ) = 4 / 17
- After we make the first draw of a face card. Our deck distribution is changed to Number of Face cards remaining = 11 and total deck now has 50 cards remaining.
- We will define the next event as:
Event ( C ): The third draw is a black card.
- The probability of this event can be determined with the help of the table given above. There are a total of 26 black cards in the deck. The total number of cards are down to 50 cards only. Therefore,
p ( C ) = [ Number of black cards ] / [ Total cards in a deck ]
p ( C ) = [ 26 ] / [ 50 ]
p ( C ) = 13 / 25
- The entire drawing process consists of 3 events which are dependent on each draw. However, for the overall event to occur i.e drawing a red card , then a face card, and then a black card. We will multiply all three outcomes as follows:
p ( T ) = p ( A ) * p ( B ) * p ( C )
p ( T ) = [ 1 / 2 ] * [ 4 / 17 ] * [ 13 / 25 ]
p ( T ) = [ 26 / 425 ] ≈ 0.0612
Hence we get the required answer.
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Diego states that diagonal WY bisects angles ZWX
and ZYX. Is he correct? Explain your reasoning.
The given statement that Diagonal WY bisects angles ZWX and ZYX has been proven below to be true.
How to prove bisection of angles?Bisection of an angle is simply defined as dividing an angle into two equal parts.
We are given that Diagonal WY bisects angles ZWX and ZYX.
Now, from the image attached, we can see that side XY is congruent to side ZY and so; XY ≅ ZY.
Similarly, XW is congruent to ZW and as such; XW ≅ ZW
Since XY is congruent to ZY and XW is congruent to ZW, then the statement that diagonal WY bisects angles ZWX and ZYX is true
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trey walks 12 miles in 3 hours which graph has the slope that best represents this rate?
The graph of the proportional relationship d = 4t is given by:
Graph B.
What is the proportional relationship?The general model of a proportional relationship is given as follows:
y = kx.
Meaning that it's graph is that of a linear function, in which:
The slope is the constant of proportionality k.The intercept is of zero.The relation between velocity, distance and time is given as follows:
v = d/t.
Then the equation for the distance as a function of time is given as follows:
d = vt.
Meaning that the slope is the velocity.
Trey walks 12 miles in 3 hours, hence the slope of the graph is of:
v = 12/3 = 4 miles per hour.
Among the options given by the image shown at the end of the answer, the correct option is:
Graph B.
As it goes through point (4,16).
Missing InformationThe options are given by the image shown at the end of the answer.
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The value of y varies exponentially with respect to x and the 1-unit growth factor is 1.7. Which of the following is the best explanation for the meaning of this growth factor?Whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.Whenever x changes by 1, the value of y becomes 11.7 times as large as its previous value.Whenever x changes by 1.7, the value of y doubles its previous value.Whenever x changes by 1.7, the value of y becomes 1 unit larger than its previous value.Whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value
We concluded that whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.
What is the growth factor?
The rate at which a quantity multiplies itself over time is known as its growth factor. A quantity's growth rate is the factor by which it grows (or shrinks) over time.
Here, we have
The required expression for y with respect to x is:
y = (1.7)ˣ.......(1)
Where, 1.7 = 1-unit growth factor
Now we check,
Whenever x changes by 1
x →x +1 .....(2)
Now we put Equation (2) in (1) and we get
y' = (1.7)ˣ⁺¹
y' = (1.7)ˣ (1.7).....(3)
Taking the ratio of equations 3 & 1, we get
y'/y = (1.7)ˣ (1.7)/(1.7)ˣ
y' = 1.7y
Hence, we observe that whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.
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The density of some steel is 7.92/cm³
What is the mass of 60cm³ of this steel?
Give your answer to 1 d.p.
Answer:
below
Step-by-step explanation:
density * volume = mass
7.92 g / cm^3 * 60 cm^3 = 475.2 g
Which graph shows the solution of the inequality ? x+5_> 2
The graph of the solution of the inequality is shown in figure.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ x + 5 ≥ 2
Now,
Since, The inequality is,
⇒ x + 5 ≥ 2
Hence, Simplify the inequality as;
⇒ x + 5 ≥ 2
Subtract 5, we get;
⇒ x + 5 - 5 ≥ 2 - 5
⇒ x ≥ - 3
Thus, The graph of the solution of the inequality is shown in figure.
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Help please!
-8+2(3 + 8) = -4(g + 1)
Answer: -9/2
Let's solve this equation step-by-step.
−8+2(3+8)=−4(g+1)
Step 1: Simplify both sides of the equation.
−8+2(3+8)=−4(g+1)
−8+2(3+8)=(−4)(g)+(−4)(1) (Distribute)
−8+22=−4g+−4
(−8+22)=−4g−4 (Combine Like Terms)
14=−4g−4
Step 2: Flip the equation.
−4g−4=14
Step 3: Add 4 to both sides.
−4g−4+4=14+4
−4g=18
Step 4: Divide both sides by -4.
−4g/−4 = 18/−4
g = −9/2
Please help me with this!
answer:
I believe it's D
tickets to movie cost $5 for adults and $3 for students. A group of friends purchased 18 tickets for $82.00. How many adults ticket did they buy
Answer: 14 Adult tickets
Step-by-step explanation:
The equation for the total number of tickets would be
x+y=18
5x+3y=82
y=18-x
5x+3(18-x)=82
2x=28
x=14
x= Number of adult tickets
How much sales taxes will cody have in his pay of purchase
Answer:
Where is the equation? It's ok but still.
Step-by-step explanation:
Mihir has 14,203 beads. He uses 36 beads to
make one necklace. How many necklaces can
he make?
And I also need the remainder
Answer:
394.527
Step-by-step explanation:
Divide the total number of beads by the number he needs to make each necklace and you will have your answer.
bailey has 5 skirts, 9 blouses, and 8 pairs of shoes. how many different skirt-blouse-shoe outfits can she wear? (assume that each item matches all the others, so she is willing to wear any combination.)
There are 360 different skirt-blouse-shoe outfits can she wear.
What is outfits?
A group of clothes that have been specifically chosen or designed to be worn together is known as an outfit. The term "outfit" can also refer to a business, an association, or a team of people who collaborate frequently. It can be used as a verb to mean "provide with the necessary gear."
A dress is different from a blouse and a skirt! So I'll rephrase this as how many ways can she dress, to wear one blouse, one skirt and one pair of matching shoes.
You just multiply the number of blouses, the number of skirts, and the number of pairs of shoes;
= 5*9*8 = 360
Hence, there are 360 different skirt-blouse-shoe outfits can she wear.
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Luke climbed from an elevation of 23,201 ft up to the summit of k2 which is at 28,251 ft. How many ft did Luke climb?
I need to explain the variable
write an equation
and solve it
The number of ft that Luke climbed, given the elevation he started from, and the summit, is 5, 050 ft
How to find the feet climbed?The number of feet that Luke climbed, can be found by the formula:
Number of feet climbed = Summit of K2 - Luke's starting elevation
Summit of K 2 = 28, 251 ft
Luke's starting elevations = 23, 201 ft
Elevation climbed by Luke was therefore:
= 28, 251 - 23, 201
= 5, 050 ft
In conclusion, the total elevation that Luke climbed from his starting point to the summit of K2 is 5, 050 ft.
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(I NEED HELP URGENTLY, THIS IS DUE TOMORROW!)
The table represents a proportional relationship.
A. Find the constant of proportionality:
B: Write a equation to represent the relationship. Equation: y=
The constant of proportionality is 1/3, and the equation is y = (1/3)x represents the relationship.
What is the constant of proportionality?The value of the proportionality constant is determined by the type of proportion between the two specified values.
Proportional relationships are written in the form y = kx
where k is the constant of proportionality.
As per the given table, the constant of proportionality will be
k = (1 - 2/3)/(3-2)
k = (1/3)/1
k = 1/3
So, the equation is y = (1/3)x.
Thus, the constant of proportionality is 1/3, and the equation is y = (1/3)x represents the relationship.
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A bag contains 3 red, 6 blue, 5 purple, and 2 orange marbles. One marble is selected at random. What is the probability that the marble chosen is blue?.
Given that there are six blue marbles in the bag out of a total of 16, there is a 3/8 chance that the marble selected will be blue.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
Total number of marbles in bag,
=3+6+5+2
=16 marbles
Number of blue marbles=6
Probability of selecting blue marbles,
=6/16
=3/8
The probability that the marble chosen is blue will be 3/8 as the bag contains 6 blue marbles when total number of marbles is 16.
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8. An organization published an article stating that in any one-year period, approximately 8.3 percent of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country.
Part (a)
Is this a test of one mean or proportion?
State the null and alternative hypotheses.
Is this a right-tailed, left-tailed, or two-tailed test?
What symbol represents the random variable for this test?
In words, define the random variable for this test.
Calculate the following.
(i) Enter your answer as a whole number.
x =
(ii) Enter your answer as a whole number.
n =
(iii) Enter your answer to two decimal places.
p' =
Part (g)
Calculate σx. (Round your answer to three decimal places.)
Show the formula set-up.
State the distribution to use for the hypothesis test.
Find the p-value. (Round your answer to four decimal places.)
[tex]z = \frac{0.08 - 0.083}{\sqrt{0.083 * 0.917/100} }[/tex]
= 0.108
pₐ = P( z < -0.108 ) = 0.4562
So the p-value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%)
Data given and notation
n = 100 represent the random sample taken
X=8 represent the people with depression or a depressive illness
p = 8/100 = 0.08 estimated proportion of people with depression or a depressive illness
p₀ = 0.083 is the value that we want to test
α = 0.05 represent the significance level assumed
Confidence = 83% or 0.83 assumed
z would represent the statistic (variable of interest)
pₐ represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportions of people with depression or a depressive illness is lower than the general adult population value of 8.3% or 0.083:
Null hypothesis:
p ≥ 0.083
Alternative hypothesis:
p < 0.083
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z = \frac{p- p_{0} }{\sqrt{p_{0} ( 1 - p_{0} )/ n } }[/tex] --------------------- (1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z = \frac{0.08- 0.083 }{\sqrt{0.083 ( 1 - 0.083 )/ 100 } }[/tex]
= - 0.083 / √ 0.0076
= -0.083 / 0.028
= -0.108
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level assumed is α = 0.05 . The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
pₐ = P( z < -0.108 ) = 0.4562
So the p value obtained was a very high value and using the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%).
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a cookie store sells 6 varieties of cookies. it has a large supply of each kind. (a) how many ways are there to select 15 cookies? (b) how many ways are there to select 15 cookies if at least three must be chocolate chip? (c) how many ways are there to select 15 cookies if at most 2 can be sugar cookies? (d) how many ways are there to select 15 cookies if at most 2 can be sugar cookies and at least 3 must be chocolate chip?
The tottal number of ways to selct 15 cookies is 15504 and the ways are there to select 15 cookies if at least three is 6188.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
we have to select 15 Cookies from 6 varieties so we can think an n₁+n2+n3+n4 + N5 +N6=15 with each o≤ni ≤15
C([tex]\frac{20}{12}[/tex]) = 15504
NOW we have One category is fixed let K Chocolate chips are Selected in I way The A we have to (15-K) Cookies from the varieties
C([tex]\frac{19-k}{15-5}[/tex])
So for k=0, C1=3876
k=1, C2 =3060
k=2, C3=2380
So C =C1+C2+C3=9316.
So the number of ways 15504-9316= 6188.
Hence, The tottal number of ways to selct 15 cookies is 15504 and ways are there to select 15 cookies if at least three is 6188.
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