The legitimate probability distribution for the discrete random variable X whose possible values are 0, 3, 4, 5 and 6 is: P(X=0) = 0.2, P(X=3) = 0.2, P(X=4) = 0.3, P(X=5) = 0.2, and P(X=6) = 0.1.
For a probability distribution to be legitimate, the probabilities of all the possible values of a random variable need to add up to 1. So, in this case, the sum of all the probabilities must be equal to 1.
For the given values, we can assign the probability of 0.2 to the values 0 and 3, 0.3 to the value 4 and 0.1 to the value 6, so that the sum of all the probabilities is 1.
Therefore, the legitimate probability distribution for the given discrete random variable X is as follows:
| Value (x) | P(X=x) |
|---|---|
| 0 | 0.2 |
| 3 | 0.2 |
| 4 | 0.3 |
| 5 | 0.2 |
| 6 | 0.1 |
The legitimate probability distribution for the discrete random variable X whose possible values are 0, 3, 4, 5 and 6 is: P(X=0) = 0.2, P(X=3) = 0.2, P(X=4) = 0.3, P(X=5) = 0.2, and P(X=6) = 0.1.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
The distance on the map from Chicago to NY is 1.5 inches. In reality, the distance from
Chicago to NY is 816 miles. On the map, the distance from Chicago to STL is 0.5 inches. How far in reality is the distance from Chicago to STL?
inches Inches
miles = miles
Answer: 272 miles
Step-by-step explanation:
The scale factor is [tex]\frac{816}{1.5}=544[/tex] inches per mile.
So, the distance from Chicago to STL is [tex]544(0.5)=272[/tex] miles.
In the given circle, the diameter EB is parallel to DC, and AB is parallel to ED. The angles AEB and ABE are in the ratio 4 : 5. What is the degree measure of angle BCD?
The degree measure of angle BCD is 130.
What is the measure of angle?
An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Here, we have
Given: the diameter EB is parallel to DC, and AB is parallel to ED. The angles AEB and ABE are in the ratio 4: 5.
We can let ∠AEB be 4x and ∠ABE be 5x because they are in the ratio 4: 5.
When an inscribed angle contains the diameter, the inscribed angle is a right angle. Therefore by the triangle sum theorem,
= 4x+5x+90 = 180
x = 10 and
∠ABE = 50.
∠ABE =∠BED because they are alternate interior angles and AB||ED.
Opposite angles in a cyclic quadrilateral are supplementary,
so ∠BED + ∠BCD = 180
Use substitution to get ∠ABE + ∠BCD = 180
50 + ∠BCD = 180
∠BCD = 130
Hence, the degree measure of angle BCD is 130.
To learn more about the measure of angle from the given link
https://brainly.com/question/25770607
#SPJ4
Each of the 39 students in the eighth grade at Lincoln Middle School has one dog or one cat or both a dog and a cat. Twenty students have a dog and 26 students have a cat. How many students have both a dog and a cat?
Number of 7 students have both a dog and a cat, out of the 39 eighth grade students at Lincoln Middle School.
Total number of 8th grade students: 39
Number of students with a dog: 20
Number of students with a cat: 26
Number of students with both a dog and a cat: 20 + 26 - 39 = 7. Therefore, 7 have both a dog and a cat.
There are 39 students in the 8th grade at Lincoln Middle School. Of those students, 20 have a dog, 26 have a cat, and 7 have both a dog and a cat. To calculate this number, we added the number of students with a dog (20) and the number of students with a cat (26) and then subtracted the total number of students (39). The result of this calculation, 7, is the number of students who have both a dog and a cat. This means that 7 out of 39 8th grade students at Lincoln Middle School have a dog and a cat.
Learn more about number here
https://brainly.com/question/17429689
#SPJ4
Repost but with a photo
Show your work
Simplify the equation below:
Answer:
With work shown...
Answer: 2^23 + 12 / 2
Step-by-step explanation:
WORK:
(1) -A negative base raised to an odd power equals a negative.
4^7 x (-8^3) + 12 / 2
(2) -Multiplying two negatives equals a positive: (-) x (-) = (+)
2^14 x 2^9 + 12 / 2
(3) -Calculate the product
2^23 + 12 / 2
The solution is located at the top.
Hope this helped <3
last month, the liberty township fire department responded to 8 home fires and 6 brush fires give the rations in lowest terms
The ratio between home fires to bush fires is 4:3.
What is the ratio?We can determine how much of one quantity is in the other by comparing two amounts of the same units and finding the ratio. Ratios can be divided into two groups. One is the part-to-whole ratio, and the other is the part-to-part ratio. The link between two distinct entities or groupings is depicted by the part-to-part ratio.
Given the number of home fires = 8
number of bushfires = 6
ratio of home fires to bush fires = 8:6
the common factor of 8 and 6 is 2
divide both terms by 2
(8/2) : (6/2)
= 4:3
Hence the rations in the lowest terms is 4:3.
Learn more about ratios;
https://brainly.com/question/13419413
#SPJ1
the frequency of breakdown of a machine that issues lottery tickets is given in the following table. repairs cost an average of $235. a service firm is willing to provide preventive maintenance under either of two options:
Option 1 is the more cost-effective option for preventive maintenance.
Option 1: Flat fee of $400 per month
Option 2: Pay a fee of $25 per breakdown
Option 1 is the more cost-effective option since the cost is fixed. This option would provide a guaranteed cost of $400 per month, regardless of the frequency of breakdowns.
On the other hand, Option 2 would cost more in the long run if the frequency of breakdowns is high. The cost would be calculated as follows:
Frequency of Breakdowns x Cost per Breakdown = Total Cost
For example, if the frequency of breakdowns is three times per month, the total cost would be 3 x $25 = $75 per month.
In comparison, the cost of Option 1 would remain at $400 per month, regardless of the frequency of breakdowns. Therefore, Option 1 is the more cost-effective option for preventive maintenance.
Learn more about total cost here:
https://brainly.com/question/28652728
#SPJ4
What is the lower bound of the polynomial function?
f(x)=x^4−4x^3−9x^2+x−16
Answer:
f(x) has a global minimum at x = 4.08628
Step-by-step explanation:
Find and classify the global extrema of the following function:
f(x) = x^4 - 4 x^3 - 9 x^2 + x - 16
Find the critical points of f(x):
Compute the critical points of x^4 - 4 x^3 - 9 x^2 + x - 16
To find all critical points, first compute f'(x):
d/(dx) (x^4 - 4 x^3 - 9 x^2 + x - 16) = 4 x^3 - 12 x^2 - 18 x + 1:
f'(x) = 4 x^3 - 12 x^2 - 18 x + 1
Solving 4 x^3 - 12 x^2 - 18 x + 1 = 0 yields x≈-1.13994 or x≈0.0536696 or x≈4.08628:
x = -1.13994, x = 0.0536696, x = 4.08628
f'(x) exists everywhere:
4 x^3 - 12 x^2 - 18 x + 1 exists everywhere
The critical points of x^4 - 4 x^3 - 9 x^2 + x - 16 occur at x = -1.13994, x = 0.0536696 and x = 4.08628:
x = -1.13994, x = 0.0536696, x = 4.08628
The domain of x^4 - 4 x^3 - 9 x^2 + x - 16 is R:
The endpoints of R are x = -∞ and ∞
Evaluate x^4 - 4 x^3 - 9 x^2 + x - 16 at x = -∞, -1.13994, 0.0536696, 4.08628 and ∞:
The open endpoints of the domain are marked in gray
x | f(x)
-∞ | ∞
-1.13994 | -21.2213
0.0536696 | -15.9729
4.08628 | -156.306
∞ | ∞
The largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:
The open endpoints of the domain are marked in gray
x | f(x) | extrema type
-∞ | ∞ | global max
-1.13994 | -21.2213 | neither
0.0536696 | -15.9729 | neither
4.08628 | -156.306 | global min
∞ | ∞ | global max
Remove the points x = -∞ and ∞ from the table
These cannot be global extrema, as the value of f(x) here is never achieved:
x | f(x) | extrema type
-1.13994 | -21.2213 | neither
0.0536696 | -15.9729 | neither
4.08628 | -156.306 | global min
f(x) = x^4 - 4 x^3 - 9 x^2 + x - 16 has one global minimum:
Answer: f(x) has a global minimum at x = 4.08628
plot each point and form the triangle abc. verify that the triangle abc is a right triangle. find its area.
The triangle ABC is shown in the figure below. All 3 sides of the triangle are labeled a, b, and c, and the right angle is located at the vertex C.
To verify that the triangle ABC is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that the sum of the squares of the two shorter sides of the right triangle is equal to the square of the longest side (hypotenuse). Therefore, in the case of triangle ABC, we can calculate a^2 + b^2 = c^2. When we calculate, we can see that the equation is true, meaning that the triangle ABC is indeed a right triangle.
To find the area of triangle ABC, we can use Heron's formula. Heron's formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c), where s is the semiperimeter (the sum of the three sides divided by 2). Therefore, in the case of triangle ABC, the area is equal to the square root of s(s-a)(s-b)(s-c), which is equal to 6.
Therefore, triangle ABC is a right triangle with an area of 6.
Learn more about triangle here:
https://brainly.com/question/2773823
#SPJ4
42+8/9r, r=-1/2
pls helppppppp
Answer:
Step-by-step explanation:
=42+\frac{8}{9}\left(-\frac{1}{2}\right)
=42+\frac{8}{9}\left(-\frac{1}{2}\right)=42+\frac{8}{9}\left(-\frac{1}{2}\right)
Answer:
Step-by-step explanation:
Which function is the inverse of
f(x)= sq x-2
6
The inverse function of the function f(x) will be f⁻¹(x) = 36x² + 2. Then the correct option is A.
What is the inverse function?Let the function f is given as
y = m(x + a) + c
Then the inverse function of the function f will be given by swapping x with y and y with x.
The function is given below.
f(x) = √(x - 2) / 6
Replace x with y and f(x) with x. Then the inverse function is given as,
x = √(y - 2) / 6
6x = √(y - 2)
36x² = y - 2
y = 36x² + 2
f⁻¹(x) = 36x² + 2
The inverse function of the function f(x) will be f⁻¹(x) = 36x² + 2. Then the correct option is A.
More about the inverse function is given below.
https://brainly.com/question/2541698
#SPJ1
The complete question is given below.
given: - > 10. choose the solution set. {x | x < -40/7} {x | x > -35/2} {x | x < -35/2} {x | x > -40/7}
The solution set is {x | x < -35/2} and {x | x > -40/7}.
To find the solution set of these two inequalities, first we need to solve them.
The first inequality is x < -40/7. To solve this inequality, we need to divide both sides of the inequality by -7. This gives us x > -40/7.
The second inequality is x > -35/2. To solve this inequality, we need to divide both sides of the inequality by 2. This gives us x < -35/2.
Therefore, the solution set is {x | x < -35/2} and {x | x > -40/7}.
learn more about solution here
https://brainly.com/question/30109489
#SPJ4
[References]
a. When 36.714 and 98.77 are multiplied, the answer should have
Enter the answer, using the correct number of significant figures:
36.714 x 98.77 =
=
[Review Topics]
b. When 36.714 and 98.77 are summed, the answer should have
point.
Enter the answer, using the correct number of decimal places:
36.714+98.77=
significant figure(s).
digit(s) after the decimal
36.714 x 98.77 = 3627.7198
36.714 + 98.77 = 135.484 (4 decimal places)
2. Solve-11 + 3(b + 5) = 7
0 1
0:
-1
O 3
O-3
On solving -11 + 3(b + 5) = 7, we get the value of b = 1.
Solving Linear Equations:Solving an equation indicates finding the value of variables in a given expression that can satisfy the given condition in the equation.
To solve an equation we can add or subtract the same integer which cannot change the condition of the equation. Similarly, we can multiply or divide by the same integers on both sides.
Here we have
Solve -11 + 3(b + 5) = 7
The given expression can be solved as follows
=> -11 + 3(b + 5) = 7
Multiply 3 and (b + 5)
=> - 11 + 3b + 15 = 7
=> 3b + 4 = 7
Subtract 4 from both sides
=> 3b + 4 - 4 = 7 - 4
=> 3b = 3
Divide by 3 into both sides
=> 3b/3 = 3/3
=> b = 1
Therefore,
On solving -11 + 3(b + 5) = 7, we get the value of b = 1.
Learn more about Linear Equations at
https://brainly.com/question/11897796
#SPJ1
the cup on the 9th hole of a golf course is located dead center in the middle of a circular green which is 30 feet in radius. your ball is located as in the picture below. the ball follows a straight line path and exits the green at the right-most edge. assume the ball travels 8 ft/sec. introduce coordinates so that the cup is the origin of an xy-coordinate system. provide numerical answers below with two decimal places of accuracy. (a) the x-coordinate of the position where the ball enters the green will be . (b) the ball will exit the green exactly 9.014 incorrect: your answer is incorrect. seconds after it is hit. (c) suppose that l is a line tangent to the boundary of the golf green and parallel to the path of the ball. let q be the point where the line is tangent to the circle. notice that there are two possible positions for q. find the possible x-coordinates of q: smallest x-coordinate
A circle is formed by all points on a plane equidistant from a given point
The possible x-coordinates of Q are -134.71 and +134.71
Known parameters are;
The radius of the golf course, r = 30 feet
Point the ball exits the green = The right-most edge
Speed of the ball = 8 ft./sec
Location of the cup = The origin (0, 0)
Location the ball starts = (-40. -50)
Required:
To find the possible x-coordinates of Q, the point where the line L parallel to the path of the ball is tangent to the circle
The coordinates of the rightmost edge of the golf course = (30, 0)
[tex]slope,m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
the slope of the path: [tex]m=\frac{-50-0}{-40-30}[/tex]
m=-50/-70
m=5/7
The equation of a circle is (x - h)² + (y - k)² = r²
The center of the circular green, (h, k) = (0, 0)
The equation of the given circle is (x - 0)² + (y - 0)² = x² + y² = 30²
the slope of the radius at the tangent Point [tex]m_{r} =-\frac{1}{m}[/tex]
The equation of the radius at a tangent point is therefore;
[tex]y=-\frac{7}{5} .x[/tex]
Which gives the equation of the circle as follows;
[tex]x^{2} +(-\frac{7}{5} .x)^2=30^2\\\\\frac{31.x^2}{25} =30^2\\\\x=\frac{\sqrt{30^2*25} }{31} \\\\x=\frac{750}{31}*\sqrt{31}[/tex]
x=±134.70
The possible x-coordinates of point Q are -134.70 and +134.70
Learn more about the equation of a circle:
https://brainly.com/question/14456881
#SPJ4
the sum of a number with the square of its following algebraic language
[tex]\bold{n + (n+1)^{2}}[/tex]
Step by step explanation:An unknown number can be interpreted with any letter of the alphabet, they will be our unknowns to be able to form an algebraic expression.
Well, in this case, I will use the variable n, to name the unknown number.
Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.
(grouping the data the following algebraic expression is obtained):
[tex]\bold{n + (n+1)^{2}}[/tex]
Answer:
(n + 1 )
Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.
Classify these events. Some businesses have large stores and some businesses have large parking lots. These events would be considered:SubjectiveIndependentDependentClassical
These events would be considered as: Subjective, Independent, Dependent, Classical
Subjective event: An event that is based on individual opinion or belief. This event would not be represented by a formula or calculation.
Independent event: An event that is not influenced by other events. This event can be represented by a formula such as P(A) = P(A) which calculates the probability of an event occurring on its own.
Dependent event: An event that is influenced by other events. This event can be represented by a formula such as P(A|B) = P(A ∩ B) / P(B) which calculates the probability of an event occurring given that another event has already occurred.
Classical event: An event that is determined by predetermined probabilities or odds. This event can be represented by a formula such as P(A) = n(A) / n(S) which calculates the probability of an event occurring based on the number of favorable outcomes divided by the total number of outcomes.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ4
question content area top part 1 find all x in that are mapped into the zero vector by the transformation for the given matrix a.
The equation to find all x in the given matrix that are mapped into the zero vector by the transformation is ax = 0, where a is the matrix. Solving this equation yields the solutions for the x values that map to the zero vector.
In order to find all x in the given matrix that are mapped into the zero vector by the transformation, we have to solve the equation ax = 0. Here, a is the matrix we are given. This equation is a system of linear equations, and can be solved using various methods, such as Gaussian elimination, matrix inversion, or Cramer's rule. Once the equation is solved, we can obtain the solutions for the x values that map to the zero vector. For example, if we are given the matrix A = [[1, 2], [3, 4]], then the equation to solve is 1x + 2y = 0, 3x + 4y = 0. Solving this equation yields the solutions x = 2, y = -1. Therefore, the x values that are mapped into the zero vector by the transformation are (2, -1).
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
Find the volume of the rectangular prism.
Answer:
Q9:
[tex]\boxed{V = \dfrac{7}{96}\;cubic\;feet}}[/tex]
Q10
[tex]\boxed{V = \dfrac{64}{125}\;cubic\;yards}[/tex]
Step-by-step explanation:
For a rectangular prism, the volume = length x width x height
Given these 3 dimensions simply multiply them to get the volume
Q9
[tex]V = \dfrac{7}{8} \cdot \dfrac{2}{3} \cdot \dfrac{1}{8}\\\\[/tex]
[tex]V = \dfrac{7\cdot 2\cdot 1}{8\cdot 3 \cdot 8}\\\\V = \dfrac{14}{192}\\\\[/tex]
Divide numerator and denominator to reduce to lowest fraction
[tex]V = \dfrac{14 \div 2}{192\div 2}\\\\\boxed{V = \dfrac{7}{96}\;cubic\;feet}}[/tex]
Q10
This is a cube since each side is the same length
For a cube of side a, the volume = a³
So for this particular cube
[tex]V = \left(\dfrac{4}{5}\right)^3\\\\\\\boxed{V = \dfrac{64}{125}\;cubic\;yards}[/tex]
Suppose that $5,800 is invested at 4.6% annual interest rate, compounded monthly. How much money will be in the account in (A) 6 months? (B) 4 years?
Answer:
Step-by-step explanation:
5800 divided by 100=58x4.6=126 something like that
HELP ME BRO PLEASE this due tonight ion even know what to do frfr
Answer: (-1, 5)
Step-by-step explanation: I wrote down all the explanations refer to the image please
determine the set of all real x satisfying (x^2 3x-1)^2<9. enter your answer in interval notation.
The required sets of all real and satisfying numbers are:
(-∞ , -4) , (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)
What are sets?Sets are groups of clearly defined objects or elements in mathematics.
A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
The empty set, finite set, singleton set, equivalent set, subset, power set, universal set, superset, and infinite set are the various types of sets.
Now, solve for (x^2 + 3x - 1)^2 = 9:
To make this true, either
x^2 + 3x - 1 = 3 or x^2 + 3x - 1 = -3
x^2 + 3x - 4 = 0, x^2 + 3x + 2 = 0
(x + 4) ( x - 1) = 0, (x + 1) ( x + 2) = 0
x = -4, x= 1, x = -1, x = -2
Therefore, we have five potential intervals to test.
(-∞ , -4) , (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)
Therefore, the required sets of all real and satisfying numbers are:
(-∞ , -4) , (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)
Know more about sets here:
https://brainly.com/question/13458417
#SPJ4
Suppose A and B are two events. Write expressions involving unions, intersections, and complements that describe the following
a) Both events occur
b) At least one event occurs
c) Neither event occurs
d) Exactly one event occur
a) Both events occur: A ∩ B
b) At least one event occurs: A ∪ B
c) Neither event occurs: A' ∩ B'
d) Exactly one event occurs: (A ∩ B') ∪ (A' ∩ B)
In Event A and B, the intersection A ∩ B tells us the outcome where both events occur. The Union of A and B tells us the outcome where at least one event occurs. The intersection of the complements of A and B (A' ∩ B') tells us the outcome where neither event occurs.
Finally, the union of the intersection of A and the complement of B and the intersection of the complement of A and B ( (A ∩ B') ∪ (A' ∩ B) ) tells us the outcome where exactly one event occurs.
Read more about Set theory:
https://brainly.com/question/2166579
#SPJ4
Four equally qualified people apply for two identical positions in a company. One and only one applicant is a member of a minority group. The positions are filled by choosing two of the applicants at random.
a List the possible outcomes for this experiment.
b Assign reasonable probabilities to the sample points.
c Find the probability that the applicant from the minority group is selected for a position.
Due to the fact that the two candidates were chosen at random, we may assume that all options are equally likely, hence each sample point has a chance of 1/6.
What is probability?Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true.The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.(a) The four candidates are marked as [tex]$A_1, A_2, A_3$[/tex], and M. The sample space is as follows because order doesn't matter (we just need two persons and it doesn't matter what order we choose):
[tex]$\mathcal{S}=\left\{A_1 A_2, A_1 A_3, A_1 M, A_2 A_3, A_2 M, A_3 M\right\}$[/tex]
(b) We may assume equally likely possibilities because the two candidates were selected at random, hence each sample point has a probability of 1 / 6
(c) Let C = {minority hired} Then P(C) =
[tex]P\left(A_1 M\right)+P\left(A_2 M\right)+P\left(A_3 M\right)=3 / 6=1 / 2$[/tex]
To learn more about probability, refer to:
https://brainly.com/question/24756209
#SPJ4
compare the values of the method of moments estimate and the maximum likelihood estimate if a random sample of size 5 consists of the numbers 17, 92, 46, 39, and 56
The method of moments estimate and the maximum likelihood estimate are the same.
The method of moments estimate is the sample mean, which can be calculated by adding the numbers together and dividing by 5. In this example, the mean is 52. The maximum likelihood estimate is the mean of the population distribution, which can be estimated by maximizing the likelihood function. This involves taking the partial derivatives with respect to the parameters and solving for the values that make the derivative equal to zero. In this example, the maximum likelihood estimate will also be 52. Thus, the method of moments estimate and the maximum likelihood estimate are the same.
Learn more about distribution here:
https://brainly.com/question/1539005
#SPJ4
first we translate b and place its tail at the tip of a, being careful to draw a copy of b that has the same length and direction. then we draw the vector a b (see the middle figure) starting at the ---select--- point of a and ending at the terminal point of the copy of
First, we translate b and place the tail at the tip of a, being careful to draw a copy of b that has the same length and direction. then we draw the vector a+b (see the middle figure) starting at the initial point of a and ending at the terminal point of the copy of b.
Alternatively, we could place b so it starts where a start and construct a+b by the parallelogram law as in the bottom figure.
The parallelogram law says that if we place two vectors so they have the same initial point, and then complete the vectors into a parallelogram, then the sum of the vectors is the directed diagonal that initiates at the same point as the vectors.
Read more about vectors:
https://brainly.com/question/25811261
#SPJ4
10 points
Find the product of (x + 5)(x - 5). (1 point)
x² - 10x + 25
x² + 10x + 25
Ox²-25
Ox²+25
Find the product of (2x + 5y)(2x - 5y). (2 points)
4x² - 20xy + 25y²
4x²+20xy + 25y²
4x²+25y²
4x²-25y²
Answer:
Solution in attached photo.
Step-by-step explanation:
SolutionTo expand the brackets, we will use the rainbow expansion method.
A kitchen sink has a volume of 65.9dm3 . Find how many milliliters of water it would take to completely fill the kitchen sink. Use the table of conversion facts, as needed.
Answer:
65,900 mL
Step-by-step explanation:
You want to know the volume in mL of a sink with a volume of 65.9 dm³.
ConversionThe relation between dm³ and mL is ...
1 dm³ = 1000 mL . . . . . . . . . . also, 1 L (liter)
ApplicationMultiplying the above relation by 65.9, we have ...
65.9 dm³ = 65,900 mL
__
Additional comment
For many problems involving volumes in liters and dimensions in centimeters or meters, it can be convenient to convert the dimensions to decimeters (dm). Since 1 dm³ = 1 L, that can make the desired volume easily calculated.
Solve each cubic equation all radicandsare perfect cubes.
X^3 = 512
The solution of the equation are x = 8 , x = -4 + 4i√3 and x = -4 - 4i√3.
What is a equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
An equation of the form ax³+bx²+cx+d=0 with a nonzero an is referred to as a cubic equation in one variable. The roots of the cubic function defined by this equation's left side are the answers to this equation.
The equation is given as
x³ = 512
⇒ x³ - 512 = 0
⇒x³ - 8³ = 0
⇒(x-8)(x² + 8x + 64) = 0
So, the solutions are
x = 8 and
x² + 8x + 64 = 0 .....(A)
Solving equation A we get,
x = [tex]\frac{-8 + \sqrt{8\x^{2} - 4*1*64} }{2} = \frac{-8 + \sqrt{64 - 256} }{2}[/tex] = -4 ± 4i√3
The solution of the equation are x = 8 , x = -4 + 4i√3 and x = -4 - 4i√3.
To learn more about Equation refer to :
https://brainly.com/question/29209591
#SPJ1
find a basis for the nullspace of the matrix. (if there is no basis, enter none in any single cell.) a
The basis for the nullspace of A is {(-1, -1, 1)}.
Let A be the given matrix. The nullspace of A is the set of all vectors x such that Ax = 0. To find a basis for the nullspace of A, we need to solve the following system of equations:
Ax = 0
Since A is a 2x3 matrix, we must have 3 variables and 2 equations. We can solve this system of equations by using Gaussian elimination. We start by subtracting the first equation from the second equation and then eliminating the middle variable by subtracting the first equation from the third equation. This gives us the following:
x1 + x3 = 0
x2 + x3 = 0
We solve this system of equations by setting x1 = -x3 and x2 = -x3. This gives us the basis for the nullspace of A as {(-1, -1, 1)}. Thus, the basis for the nullspace of A is {(-1, -1, 1)}.
Learn more about nullspace here:
https://brainly.com/question/13254423
#SPJ4
draw the dot plot of the distribution of possible data values that has the largest possible standard deviation (there were ten people at the talk, so there should be ten dots on your dot plot)
The dot plot consists of ten dots, each representing the data value of a single person at the talk. The data values are spread out as far as possible, resulting in the largest possible standard deviation.
A dot plot is a graph that is used to represent the distribution of data. It consists of dots, each of which represents a single data value. In this case, the dot plot represents the distribution of possible data values from a talk with ten people. To achieve the largest possible standard deviation, the data points should be spread out as far as possible. Each dot should be placed on the graph in such a way that the difference between any two adjacent data points is maximized. This is done by placing the highest and lowest values at opposite ends of the graph, and then evenly spacing out the remaining data points in between. All of this should result in the largest possible standard deviation of the data set.
Learn more about standard deviation here
https://brainly.com/question/13905583
#SPJ4
