Find the constant of variation k for the direct variation
A) k=2.5
B) k=-2
C) k=2
D) k=0.5
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Related Questions
If u is a square matrix such that u^tu = i what can we say about det(u)
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[tex]\det(\mathbf{AB})=\det\mathbf A\det\mathbf B[/tex]
[tex]\det\mathbf A=\det\mathbf A^\top[/tex]
for any square matrices [tex]\mathbf A,\mathbf B[/tex]. So if
[tex]\mathbf U^\top\mathbf U=\mathbf I[/tex], and [tex]\det\mathbf I=1[/tex], we have
[tex]\det(\mathbf U^\top\mathbf U)=(\det\mathbf U)^2=1\implies\det\mathbf U=\pm1[/tex]
Group a contains 157 students. of these, 51 students in group a have taken math 2a, 80 have taken math 2b, and 70 have taken math 2c. 15 have taken both math 2a and 2b, 20 have taken both math 2a and 2c, and 13 have taken both math 2b and 2c. how many students in group a have taken all three classes?
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and this is the answer to you question
Answer:
86
Step-by-step explanation:
Please Help....Which statements include two quantities in the real world that are additive inverses? Select each correct answer. A plane ascends 500 yards and descends 100 yards. Twenty gallons of water leak from a pool and 20 gallons are put back into the pool. A driver drives 40 miles north and 30 miles south. A person deposits $100 in to her bank account and then withdraws $100 from the same account.
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Answer: Second and Fourth options are correct.
Step-by-step explanation:
Since we know that
Additive inverse means
[tex]a+(-a)=0[/tex]
so, -a is the additive inverse of a.
So, according to options, we get that
A plane ascends 500 yards and descends 100 yards.
Ascends = (+)500 yards
Descends = (-) 100 yards
So, -100 is not an additive inverse of +500.
Twenty gallons of water leak from a pool and 20 gallons are put back into the pool.
Number of gallons are leaked out = (-)20
Number of gallons are put back = (+)20
So, we can write
+20-20=0
So, -20 is the additive inverse of +20.
A driver drives 40 miles north and 30 miles south.
Number of miles towards north = +40
Number of miles towards south = -30
So, -30 is not additive inverse of +40.
A person deposits $100 in to her bank account and then withdraws $100 from the same account.
Amount he deposited into her bank = $100
Amount he withdraws from bank = -100
So, we can write as
+100-100=0
So, -100 is an additive inverse of 100.
Hence, Second and Fourth options are correct.
A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. if the geologist instructs a laboratory assistant to randomly select 15 of the specimens for analysis, what is the pmf of the number of basalt specimens selected for analysis? what is the probability that all specimens of one of the two types of rock are selected for analysis?
Answers
The PMF of the number of selecting basalt specimen is [tex]\boxed{\bf P=^{10}C_{x}(0.5)^{x}(0.5)^{10-x}}[/tex] and the probability of selecting all specimen of one of two type of rocks is [tex]\boxed{\bf 0.0325}[/tex].
Further explanation:
Concept used:
The probability of an event [tex]E[/tex] can be calculated as follpws:
[tex]\boxed{P(E)=\dfrac{n(E)}{n(S)}}[/tex]
Here, [tex]n(E)[/tex] is the number of favorable outcomes in an event [tex]E[/tex] and [tex]n(S)[/tex] is the number of element in sample space [tex]S[/tex].
The probability mass function of getting exactly [tex]r[/tex] success in [tex]n[/tex] independent trial in an experiment can be expresses as follows:
[tex]\boxed{P=^nC_{r}p^{r}q^{n-r}}[/tex]
Here, [tex]p[/tex] is the success probability and [tex]q[/tex] is the failure probability of an event.
Calculation:
A geologist has collected [tex]10[/tex] specimens of ballistic rock and geologist collected [tex]10[/tex] specimens of granite.
The total number of specimens is [tex]20[/tex].
The sample space is the collection of all possible outcomes in an experiment.
Therefore, the total possible outcomes are [tex]20[/tex].
The probability of selecting ballistic rock can be calculated as follows:
[tex]\begin{aligned}P_{b}&=\dfrac{10}{20}\\&=\dfrac{1}{2}\\&=0.5\end{aligned}[/tex]
The probability of selecting granite can be calculated as follows:
[tex]\begin{aligned}P_{g}&=\dfrac{10}{20}\\&=\dfrac{1}{2}\\&=0.5\end{aligned}[/tex]
The PMF of selecting exactly [tex]x[/tex] basalt specimen for analysis can be calculated as follows:
[tex]\boxed{P=^{10}C_{x}(0.5)^{x}(0.5)^{10-x}}[/tex]
Consider [tex]A[/tex] as an event that all rocks are selecting from one rock and [tex]n(A)[/tex] as the number of favorable outcomes in an event [tex]A[/tex].
The number of favorable outcomes in an event [tex]A[/tex] can be calculated as follows:
[tex]\begin{aligned}n(A)&=\left(^{10}C_{10}\cdot ^{10}C_{5}\right)+\left(^{10}C_{10}\cdot ^{10}C_{5}\right)\\&=\left(\dfrac{10!}{10!\cdot (10-10)!}\cdot \dfrac{10!}{5!\cdot (10-5)!}\right)+\left(\dfrac{10!}{10!\cdot (10-10)!}\cdot \dfrac{10!}{5!\cdot (10-5)!}\right)\\&=\dfrac{10\cdot 9\cdot 8\cdot 7\cdot 6}{5\cdot 4\cdot 3\cdot 2\cdot 1}+\dfrac{10\cdot 9\cdot 8\cdot 7\cdot 6}{5\cdot 4\cdot 3\cdot 2\cdot 1}\\&=252+252\\&=504\end{aligned}[/tex]
The total possible outcomes of selecting [tex]15[/tex] rocks in [tex]20[/tex] rocks can be calculated as follows:
[tex]\begin{aligned}n(S)&=^{20}C_{15}\\&=\dfrac{20!}{15!\cdot (20-15)!}\\&=\dfrac{20\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15!}{15!\cdot 5!}\\&=\dfrac{20\cdot 19\cdot 18\cdot 17\cdot 16}{5\cdot 4\cdot 3\cdot 2\cdot 1}\\&=19\cdot 3\cdot 17\cdot 16\\&=15504\end{aligned}[/tex]
The probability [tex]P(A)[/tex] of selecting all specimen of one of two type of rocks can be calculated as follows:
[tex]\begin{aligned}P(A)&=\dfrac{504}{15504}\\&=0.0325\end{aligned}[/tex]
Thus, the probability that all specimens of one of the two types of rock are selected for analysis is [tex]\boxed{\bf 0.0325}[/tex].
Learn more:
1. Learn more about functions https://brainly.com/question/2142762
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Answer details:
Grade: College school
Subject: Mathematics
Chapter: Probability
Keywords: Basalt specimen, geologist, rock, granite, PMF, probability mass function, exactly, probability, possible outcomes, favorable, failure success, , event, experiment, trial, P=n(E)/n(S).
The PMF of the number of basalt specimens selected for analysis ranges from P(X = 0) to P(X = 10), and the probability of selecting all specimens of one type of rock (either basalt or granite) is 0.000061036.
To solve this problem, we need to find the probability mass function (PMF) of the number of basalt specimens selected for analysis and the probability of selecting all specimens of either basalt or granite.
Given information:
- There are 10 specimens of basaltic rock and 10 specimens of granite.
- The laboratory assistant will randomly select 15 specimens for analysis.
Step 1: Find the PMF of the number of basalt specimens selected for analysis.
Let X be the random variable representing the number of basalt specimens selected for analysis.
The possible values of X range from 0 to 10 (since there are 10 basalt specimens).
The PMF of X can be calculated using the binomial probability formula:
P(X = k) = (C(n, k) [tex]\times[/tex] ([tex]p^k[/tex]) [tex]\times[/tex] [tex](1-p)^{(n-k)}[/tex])
where:
n = total number of trials (selecting 15 specimens)
k = number of successes (number of basalt specimens selected)
p = probability of success (selecting a basalt specimen) = 10/20 = 1/2
q = probability of failure (selecting a granite specimen) = 1 - p = 1/2
The PMF of X for different values of k is as follows:
P(X = 0) = C(15, 0) [tex]\times[/tex] [tex](1/2)^0[/tex] [tex]\times[/tex] [tex](1/2)^15[/tex] = 0.000030518
P(X = 1) = C(15, 1) [tex]\times[/tex] [tex](1/2)^1[/tex] [tex]\times[/tex] [tex](1/2)^14[/tex] = 0.001525879
P(X = 2) = C(15, 2) [tex]\times[/tex] [tex](1/2)^2[/tex] [tex]\times[/tex] [tex](1/2)^13[/tex] = 0.030517578
Step 2: Find the probability of selecting all specimens of one type of rock.
The probability of selecting all 10 basalt specimens = P(X = 10) = C(15, 10) [tex]\times[/tex] (1/2)^10 [tex]\times[/tex] (1/2)^5 = 0.000030518
The probability of selecting all 10 granite specimens = P(X = 0) = 0.000030518
Therefore, the probability of selecting all specimens of one type of rock (either basalt or granite) is:
P(X = 10) + P(X = 0) = 0.000030518 + 0.000030518 = 0.000061036
In summary, the PMF of the number of basalt specimens selected for analysis ranges from P(X = 0) to P(X = 10), and the probability of selecting all specimens of one type of rock (either basalt or granite) is 0.000061036.
An unknown number x is at most 30. Which graph best represents all the values of x?
Number line graph with closed circle on 30 and shading to the right.
Number line graph with closed circle on 30 and shading to the left.
Number line graph with open circle on 30 and shading to the left.
Number line graph with open circle on 30 and shading to the right
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Answer:
b
Step-by-step explanation:
PLEASE ANSWER THIS QUICKLY! THANK YOU!
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= 1/2 x 4/3
= 4/6
= 2/3
a = 2
b = 4
c = 3
d = 2
e = 3
The table shows the annual profits (in thousands of dollars) of a county fair from 2008 to 2012.what must the 2012 profit be ( in hundreds of dollars ) to brake even over the five year period?
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44 tens is the same as
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A rectangular flower box holds 1232 in3 of soil. Find the height of the box if it is 22 in. long and 7 in. wide
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Suppose that a person rolls two balanced dice three times in succession. determine the probability that on each of the three rolls, the sum of the two numbers that appear will be 7.
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The number of combinations that will result in a sum of 7 is:
1 + 6
6 + 1
2 + 5
5 + 2
3 + 4
4 + 3
For a total of 6 combinations per roll. While the total number of combinations per roll are:
6 * 6 = 36
Hence the probability that the sum is 7 would be:
Probability = 6 / 36 = 1 / 6
For a succession of three times, the overall probability that each three rolls will be a sum of 7 is:
Overall probability = (1/6) * (1/6) * (1/6)
Overall probability = 1/216 = 4.63 x 10^-3 = 0.463%
Final answer:
The probability of rolling a sum of 7 three times in succession using two balanced dice is 1/216.
Explanation:
To determine the probability that on each of the three rolls of two balanced dice, the sum of the two numbers that appear will be 7, we first need to identify the probability of rolling a sum of 7 with a single roll of two dice. There are six ways to roll a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The total number of possible outcomes when rolling two dice is 6*6 = 36. Therefore, the probability of rolling a sum of 7 on one roll is P(sum=7) = 6/36 = 1/6.
Since each roll is independent of the others, the probability of this event occurring three times in succession is the product of the individual probabilities. Thus:
P(First roll is 7) = 1/6P(Second roll is 7) = 1/6P(Third roll is 7) = 1/6Therefore, the probability of all three rolls resulting in a sum of 7 is:
P(Three 7's in a row) = P(First roll is 7) * P(Second roll is 7) * P(Third roll is 7) = (1/6) * (1/6) * (1/6) = 1/216.
The stock market decreased by 135 points during a 5 day week.
What was the average daily change in the market for that week?
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I need help please ❓❓
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(its too little characters so im putting this at the bottom disregard haha)
-18.4*0.45=-8.28
3.5 times (5.8 - 7.09)
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We can use PEMDAS to solve this.
3.5(5.8-7.09)
Parentheses
3.5 x -1.29
Multiplication
-4.51500
The answer is -4.51500
Hope this helps! :)
The value of the expression simplified using PEMDAS rule is -4.515.
What is PEMDAS?"The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)".
For the given question,
The expression is 3.5 times (5.8 - 7.09).
PEMDAS rule is used to simplify this expression.
The expression is simplified as [tex]3.5[/tex] × [tex](5.8 - 7.09)[/tex]
⇒[tex]3.5[/tex] × [tex](-1.29)[/tex]
⇒[tex]-4.515[/tex]
Hence we can conclude that the value of the expression simplified using PEMDAS rule is -4.515.
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If l is a line whose equation is y=5x-3, find the equation of the image of l under each of the following translations a. (x,y) --> (x, y-6) b. (x,y) --> (x+2,y)
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For example, let x=0, then y=-3. So (0, -3) is a point on the line.
If x=1, then y=5*1-3=5-3=2, so (1, 2) is a point on the line.
a)
Consider the transformations of these two points under (x,y) --> (x, y-6):
(0,-3) --> (0, -3-6)=(0, -9),
(1, 2) --> (1, 2-6)=(1, -4).
So (0, -3) and (1, 2) are translated to respectively (0, -9) and (1, -4).
The whole line is translated to the line containing (0, -9) and (1, -4).
The slope of the new line is [tex]m= \frac{-9-(-4)}{0-1}= \frac{-5}{-1}=5 [/tex]. The equation of the line is:
[tex]y-(-9)=5(x-0)[/tex],
that is, y=5x-9.
b)
Consider the transformations of these two points under (x,y) --> (x+2, y):
(0,-3) --> (0+2, -3)=(2, -3),
(1, 2) --> (1+2, 2)=(3, 2).
The slope of the new line is [tex]m= \frac{-3-2}{2-3}= \frac{-5}{-1}=5 [/tex].
The equation of the line is
[tex]y-2=5(x-3)[/tex],
which can be written as
y=5x-13.
Answer:
a) y=5x-9
b) y=5x-13
Find the slope of the line that passes through (90, 93) and (-4, 49).
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Train “A” leaves Westtown and travels at 50 mph toward Smithville, 330 miles away. At the same time, Train “B” leaves Smithville and travels at 60 mph. After how many hours do the two trains meet?
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train A travels at 50 mph
train B travels at 60 mph
60 +50 = 110
330/110 = 3
they will meet in 3 hours
Middle school has 450 students vanlue school has 600 students which school has a greater percent of girls explain
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(b) if the length, width, and height are increasing at a rate of 0.1 ft/sec, 0.2 ft/sec, and 0.5 ft/sec respectively, find the rate at which the surface area of the box is changing when x = 20 ft, y = 15 ft, and z = 25 ft.
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Final answer:
By applying the derivative of the surface area of a rectangular prism formula with respect to time, it is found that the surface area of the box is increasing at a rate of 61 ft^2/sec when the dimensions are 20 ft by 15 ft by 25 ft.
Explanation:
The question involves calculating the rate of change of the surface area of a box with respect to time using derivatives, a concept from calculus. Given the rates at which the length (x), width (y), and height (z) are increasing, we can find the rate at which the surface area S is changing by using the surface area formula for a rectangular prism, S = 2(xy + xz + yz), and differentiating with respect to time.
At the given dimensions (x = 20 ft, y = 15 ft, z = 25 ft), and rate of increase (dx/dt = 0.1 ft/sec, dy/dt = 0.2 ft/sec, dz/dt = 0.5 ft/sec), the rate of change of surface area dS/dt is calculated by:
dS/dt = 2( (dy/dt)z + y(dz/dt) + (dx/dt)z + x(dz/dt) + (dx/dt)y + x(dy/dt) )
dS/dt = 2( (0.2)(25) + (15)(0.5) + (0.1)(25) + (20)(0.5) + (0.1)(15) + (20)(0.2) )
dS/dt = 2(5 + 7.5 + 2.5 + 10 + 1.5 + 4)
dS/dt = 2(30.5)
dS/dt = 61 ft2/sec
Therefore, the surface area of the box is increasing at a rate of 61 ft2/sec when the dimensions x, y, and z are 20 ft, 15 ft, and 25 ft respectively.
Tan (pi/5) - tan (pi/30) / 1+tan (pi/5)tan (pi/30)
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[tex]\bf tan({{ \alpha}} + {{ \beta}}) = \cfrac{tan({{ \alpha}})+ tan({{ \beta}})}{1- tan({{ \alpha}})tan({{ \beta}})}\qquad tan({{ \alpha}} - {{ \beta}}) = \cfrac{tan({{ \alpha}})- tan({{ \beta}})}{1+ tan({{ \alpha}})tan({{ \beta}})}\\\\ -------------------------------\\\\[/tex]
[tex]\bf \cfrac{tan\left( \frac{\pi }{5} \right)-tan\left( \frac{\pi }{30} \right)}{1+tan\left( \frac{\pi }{5} \right)tan\left( \frac{\pi }{30} \right)}\implies tan\left( \frac{\pi }{5} -\frac{\pi }{30} \right)\implies tan\left( \frac{6\pi -\pi }{30} \right)[/tex]
[tex]\bf tan\left( \frac{5\pi }{30} \right)\implies tan\left( \frac{\pi }{6} \right)\implies \cfrac{sin\left( \frac{\pi }{6} \right)}{cos\left( \frac{\pi }{6} \right)}\implies \cfrac{\quad \frac{1}{2}\quad }{\frac{\sqrt{3}}{2}} \\\\\\ \cfrac{1}{2}\cdot \cfrac{2}{\sqrt{3}}\implies \cfrac{1}{\sqrt{3}}\implies \cfrac{\sqrt{3}}{3}[/tex]
True or false: the population proportion and sample proportion always have the same value.
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The sample is a randomly selected representation of the population, therefore it cannot represent the true data with 100% accuracy.
As the sample size increases, the sample proportion approaches the population proportion.
- Flase
The image shows a portion of a bridge supported by two vertical pillars built from the points B and C on the slope below. The length of the bridge between pillar B and pillar C is BLANK feet.
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The cosin of Angle A is Adjacent / Hypotenuse, or 40 / 50. Using this Info:
cos (A) = 40/50
cos (A) = .8
With this crucial piece of info, we can find the Total length of A-D (Point D being the point above C), by finding its relation to side AC (length of 50 + 70 =120 ft)
Cos (A) = adjacent / hypotenuse
Cos (A) = AD / (120) We know that cos (A) = .8
.8 = AD / (120) Multiply both sides by 120
96 = AD
We're almost there! Remember that we're trying the find x (?? in the diagram).
x + 40 = 96
x = 56 ft
Answer:
The length of the bridge between pillar B and pillar C is 56 feet.
Here's the answer from the plato.
A linear function has a slope of -7/9 and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y+11=-7/9(x-18)
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Answer:
A
Step-by-step explanation:
it has the same slope and the same y-intercept
In a scale diagram, 0.125 inch represents 125 feet. How many inches represents 1 foot?
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Its pretty obvious:
0.125=125 feet
So 0.001=1 feet
Your answer is 0.001 feet
0.001=1 feet
answer is: 0.001 feet
i hoped this helped and have a wonderful day!! :)
0.006 is greater than 0.1
Is this true?
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The length of the hypotenuse of a right triangle is 157 units. The length of one leg of the triangle is 132. Lara wrote the following step to find the length of the unknown leg: Length of the unknown leg = 1572 – 1322 = 24,649 – 17,424 = 7,225 units Which statement best explains whether Lara's step is correct or incorrect? It is correct because the length of the unknown side is the difference of the lengths of the sides. It is correct because the length of the unknown side is the difference of the squares of the sides. It is incorrect because the length of the unknown side is the square root of 42,073. It is incorrect because the length of the unknown side is the square root of 7,225.
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the correct answer for this is the last choice:
It is incorrect because the length of the unknown side is the square root of 7,225.
Answer:
It is incorrect because the length of the unknown side is the square root of 7,225.
Step-by-step explanation:
what is the slope of the line represented by the equation 2x+ 3y= -12
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Answer:
Slope: -2/3
Step-by-step explanation:
In order to solve this we first have to clear the equation for Y:
[tex]2x+ 3y= -12\\3y=-12-2x\\y=\frac{-12-2x}{3}\\ y=-4-\frac{2}{3} x[/tex]
Remember that the equation in the form of Y is represented in this way:
y=mx+c
Where M is the slope and C is the constant, so the slope is the number that is multiplying x, in the equation, in this case -2/3 is the number that is multiplying x, sot eh slope of the equation is -2/3
Which equation is an identity?
7m – 5 = 8m + 7 – m
3w + 8 – w = 4w – 2(w – 4)
9 – (2v + 3) = –2v – 6
–3y + 3 = –3y – 6
Please explain your answer.
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Norfolk va has a population of 242,628 people. Baltimore, Md has 376,865 more people than Norfolk. Charleston,SC has 496,804 less than Baltimore. What is the total population of all 3 cities?
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The total population of Norfolk, VA, Baltimore, MD, and Charleston, SC is 984,810 people. This is calculated by adding the respective populations of the three cities together.
Explanation:The total population of the three cities can be found by adding their respective populations together. Given that Norfolk, VA has a population of 242,628 people, and Baltimore, MD has 376,865 more people than Norfolk, we calculate the population of Baltimore by adding these two figures together to get 619,493 people. Charleston, SC has 496,804 less than Baltimore, so its population is found by subtracting 496,804 from 619,493 to get 122,689 people. To find the total population of all 3 cities, we add the populations of Norfolk, Baltimore and Charleston together, giving us 984,810 people in total.
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Use the distributive property to simplify the following expression 4x(2x-6)
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8x - 24x
= -16x
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
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[tex]\textsf{Using the distributive property, \textbf{a(b+c)=ab+ac}, expand the given expression:}[/tex]
[tex].\qquad\bullet\sf{4x(2x-6)=4x*2x-4x*6=8x^2-24x}[/tex]
[tex]\sf{\bf{$Answer: 8x^2-24x}}[/tex]
[tex]\Large\underbrace{\overbrace{\boldsymbol{Reflection - RoSe}}}^\star_\star[/tex]
What is the slope of the line that passes through th epoints (26, 7) and (-39, 12)?
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Use the slope formula: m = ------------ = -------- = -1/13
-39 - 26 -65