The triple integration of ∭E xy dV and The Solid Tetrahedron With Vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3), is 8 / 5.
What is integration?
When infinitesimal data are combined, concepts like displacement, area, and volume can be described by assigning numerical values to the functions that make up an integral. Integration is the procedure for locating integrals.
Given:
∭E xy dV and The Solid Tetrahedron With Vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3),
Calculate the equation of plane passing through the vertices (0,0,0),(8,0,0),(0,1,0),(0,0,3) as shown below,
x / 8 + y / 1 + z / 3 = 1
z = 24 - 3x -24y / 8
Put z = 0
y = 1 - 1 / 8x
Put y = o
x = 8
Calculate the integral as shown below,
[tex]\int \int\int_E xydV = \int _0^8 \int _0^{1-x/8} \int _0^{{24-3x-24y}/8} xy\ dz\ dy\ dx[/tex]
∫∫∫E = [tex]1/8 \int _0^8 [24xy^2 / 2 - 3x^2y^2 / 2 - 24xy^3 / 3]^{1-x /8}dx[/tex]
∫∫∫E = 1 / 8 × 64 / 5
∫∫∫E = 8 / 5
Thus, the triple integral is 8 / 5.
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In what ratio is the line segment joining (- 1/3 and 4 7 divided at the point?
The ratio in which line segment joining (-1, 3) and (4, -7) is is 3: 2 and at a point (2,-3).
What is line segment?A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
What is segment?a piece of a geometric figure that has been removed by one or more points, lines, or planes is known as segment.
The formula that we used is:
[tex]P(x,y)=\frac{mx2+nx1}{m+n},\frac{my2+ny1}{m+n}[/tex]
x = m(x₂) + n(x₁)/(m + n)
⇒ 2 = m(-1) + n(3)/(m + n)
⇒ 2(m + n) = 3n - m
⇒ 2m + 2n = 3n - m
⇒ m/n = 3/2
Therefore, The ratio in which line segment joining (-1, 3) and (4, -7) is is 3: 2 and at a point (2,-3).
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How do you prove closed under addition?
A closed under addition can be proved if the sum of any two members of the set also belongs to the set.
We can take any two even integers and add them together. The result is an even integer. A set is closed under scalar multiplication if the product of any member and a scalar is also in the set. In other words, if x is in S and a is any scalar then ax will be in the set if the set is closed under scalar multiplication. For example, the set of 2 x 2 diagonal matrices is closed under scalar multiplication.
For example,
A = {( x, y) , y = 0 }
B= { (x, y) , x+ y = 1 }
Typical elements of A are (1,0), (2,0). The element (1,1) is an element not in A. Typical elements of B are (1,0), (1/2,1/2). The element (1,1) is an element not in B. Now A and B carry an addition that is (x, y)+(x', y')=(x + y, x' + y')). Saying that A is closed under addition just means that whenever you take two elements in A, the sum of those elements is again in A. Let's check if this is the case: two elements in A have the form (x, 0) and (x', 0). The sum of those elements is (x + x', 0), and this is again in A. Thus A is closed under addition.
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Damian plans to repaint some classroom bookcases. All of the bookcases are the same size and each requires \
5
3
gallon of paint. If he's going to paint 19 bookcases, how many gallons of paint does he need? Express your answer in simplest form.
Answer: 95/3 gallon of paint
Step-by-step explanation:
I guess you mean each requires 5/3 gallon of paint
If so, we take 5/3 times 19 = 95/3 gallon of paint
95/3 = 31 2/3
What will be the mean deviation of the scores 12/15 18?
The mean deviation of the scores is 2 when the mean value is 15.
What is mean deviation?In the statistics, mean deviation indicates the average deviation relative to the mean value of a given statistical data. While calculating mean deviation mean value is subtracted from each data value. After that all these values are added and divided by the total amount of data.
How to calculate mean deviation?We are given three score 12, 15 and 18
Number of scores, N = 3
mean of the scores = (12+15+18)/ 3
=15
Let, mean score is denoted by X
List of scores X1 12
X2 15
X3 18
Now, we calculate X1 -X= 12- 15 = -3
X2-X = 15-15 = 0
X3-X = 18- 15 = 3
Absolute value of X1-X = |X1-X| = |-3| = 3
Absolute value of X2-X =|X2-X|= |0| = 0
Absolute value of X3-X = |X3-X| = |3| = 3
Sum of absolute value= ∑|Xi-X| = 6
Hence, mean deviation = ∑|Xi-X|/N = 6/3
mean deviation =2
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At a local sandwich shop, 45% of customers preferred white bread over whole wheat bread. Of those who chose whole wheat bread, 52% preferred ham for the protein, and 43% of those who chose white bread preferred turkey.
What percentage of customers chose whole wheat bread with turkey? Round your answer to the nearest whole percentage.
52%
37%
29%
26%
If at a local sandwich shop, 45% of customers preferred white bread over whole wheat bread. The percentage of customers chose whole wheat bread with turkey is: D. 26%.
How to find the percentage?First step is to find the percentage of customers who preferred ham with whole wheat bread
Percentage = ( 1- .45)
Percentage = .55
Second step is to find the percentage of customers who preferred whole wheat bread
Percentage = (1- .52)
Percentage = .48
Now let find the percentage of customers chose whole wheat bread with turkey
Percentage = .48 × .55
Percentage = .26 ×100
Percentage =26%
Therefore the correct option is D.
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A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking for volunteers to participate in the study. One hundred subjects replied and were informed that one group would receive the new cream and the other group would receive a cream with no active ingredient. All 100 subjects were exposed to poison ivy. Fifty were then randomly assigned to the group with the new cream, and 50 were randomly assigned to the group with the cream with no active ingredient. After three days, the subjects’ level of irritation was measured.
Which of the following accurately describes the benefit of comparison in the experiment?
The overall level of irritation can be compared to see if the new cream had a significant effect.
The level of irritation for both groups can be compared to see if the new cream had a significant effect.
The level of irritation in the treatment group only can be compared to see if the new cream had a significant effect
Since one group received a cream with no active ingredient, the researchers will not be able to determine of the new cream is effective.
Answer:
The level of irritation for both groups can be compared to see if the new cream had a significant effect.
Step-by-step explanation:
In this experiment, the purpose of having two groups is one being the control group, and one being the group being experimented on. The control group is needed in order to know for sure that it is the cream that is beneficial, instead of an outside factor such as the poison ivy being bad.
By comparing the level of irritation for both groups, it will become apparent if the new cream has a side effect.
Answer:
The level of irritation for both groups can be compared to see if the new cream had a significant effect.
Step-by-step explanation:
the phrasing is a bit strange.
but I think the first one means "overall" in the sense of outside and inside the 2 test groups.
the third one would object compare results only inside the group that got the active ingredient.
the 4th one is just nonsense.
so, only the second answer option makes sense. these 2 groups are created so that their results can be compared. that is the whole point.
which is true? i. random scatter in the residuals indicates a model with high predictive power. ii. if two variables are very strongly associated, then the correlation between them will be near 1.0 or -1.0. iii. the higher the correlation between two variables the more likely the association is based in cause and effect.
Of the given options the one that is true is if two variables are very strongly associated then the correlation between them will be near 1.0 or -1.0. Hence, option A is correct.
Correlation of 1.0 indicates that the variables are directly related while a correlation of -1.0 indicates that the variables are inversely related.
The degree to which two variables are linearly connected is expressed by the statistical concept of correlation (meaning they change together at a constant rate). It's a typical technique for explaining direct connections without explicitly stating cause and consequence.
However, we utilise correlation to indicate a link between two quantitative variables in statistical terms.
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672,342 = 6.72342 × 10n
what is the value of n?
5
3
4
6
Answer: 5
Step-by-step explanation: If n is the exponent and the base is 10, 6.72342 is to be multiplied by 10 power 5 to give the answer as 672342.
6.72342 * 10^5 = 6.72342 * 100000
= 672342
which expressions represent the length of side \overline{hi} hi start overline, h, i, end overline? choose 2 answers: choose 2 answers:
The expressions represent the length of side, HI are sqrt(161) and 15 sin(90°- 75°) . So, option (a) and (c) are right answers.
What is Pythagoras theorem?A geometry theorem : the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides ( i.e base and prependicular) .
Mathematically, (GH)² + (HI)² = (GI)²
We have , provide a triangle GHI , since measure of angle H is 90° so it is a right angled triangle.
We have to calculate the length of side HI , for this we can use either triangular formulae or Pythagoras theorem. Here, we are using Pythagoras theorem,
As we have, GH (prependicular) = 8 unit , GI (hypotenuse) = 15 unit , HI ( base) = ?
(prependicular)²+( base)² = (hypotenuse)²
=> (GH)² + (HI)² = (GI)²
=> (8)² + (HI)² = (15)²
=> (HI)² = (15)² - (8)²
=> (HI)² = 225 - 64 = 161
=> HI = sqrt(161) = 12.68
Using Trigonometric functions,
measure of angle G = 180° - 90° - 75° = 15°
In right triangle GHI, sin 15° = HI /15
=> HI = 15 sin 15° = 15 sin(90°- 75°)
So, the length of side HI is sqrt(161) or 15 sin 15° .
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Complete question:
Consider right triangle ∆GHI present above. Which expressions represent the length of side HI? Choose 2 answers:
a)15 sin(90° - 75°)
b)15 cos(90° - 75°)
c) sqrt(161)
d)tan(90° -
Quadrilateral ABCD with vertices A(-4, 1), B(-2, 3), C(0, -2) and D(-5, -2): k=3
The vertices of the image of quadrilateral ABCD, after a dilation with a scale factor of 3, are given as follows:
A'(-12,3).B'(-6,9).C'(0,-6).D'(-15,-6).What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure, thus a dilation is classified as a non-rigid transformation.
The vertices of the quadrilateral ABCD in this problem are given as follows:
A(-4, 1), B(-2, 3), C(0, -2) and D(-5, -2).
The scale factor of the dilation is given as follows:
k = 3.
Then the coordinates of the image, given by the answer at the beginning of the answer, were obtained multiplying the coordinates of each of the vertices by 3.
Missing InformationThe problem asks for the coordinates of the image of quadrilateral ABCD after the dilation with the given scale factor.
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a researcher is interested comparing quality of sleep between people who work overnight shifts and people who work day shifts. a sample of 50 day shift workers and 50 night shift workers are asked to complete a quality of sleep measure, which the researcher will treat as an interval scale measure. the researcher will compare the mean levels of each group to see if there is a statistically significant difference between the groups. which analysis would be acceptable to use?
The correct analysis would be 3 option
Describe statistics using an example.
A statistic is a numerical expression of a sample characteristic. The average amount of points obtained by students in one math class at the conclusion of the term, for instance, is an example of a statistic if we see that class as a sample of the population of all math classes.
The right response is selection 3. To compare the means of two independent groups, use the independent samples t test. to determine whether there is a substantial difference between the means of the two groups. In this instance, we are comparing two different groups of people: those who work the night shift and those who work the day shift. By definition, these two groups of persons would differ, therefore neither a matched sample test nor a one-sample test would be appropriate. Furthermore, we are not interested in person's r, which is a measure of linear correlation between two variables.
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What is the range of real numbers?
The optimal response is The ranges below encompass all real numbers: From 0 through all actual numbers. The domain of this function is all real numbers since x can be entered with any value.
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
answer to the question is that all real numbers or (−∞,∞)
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How do you find a 30 degree angle?
We can construct a 30-degree angle by bisecting a 60-degree constructed angle.
By following the given steps we can create a 30-degree angle,
Use a straightedge to create a segment of a line. Label the ends of it. We will refer to them as points A and B in our design.The drawing compass needle should be positioned on point A and adjusted to meet point B. Draw an arc high above the line segment, starting at point B. Move the needle to point B without changing the compass.Make an arc that crosses the first arc swing upward.Create a line segment from point A all the way up to the junction of the two arcs using the straightedge.Mark the new terminus of that line segment as Point D. The angle ∠ABD constructed is a 60-degree angle.Move the needle arm toward one of the rays' points without altering the compass. On the inside of the angle, swing an arc.The needle arm should be moved to the opposite ray's point without adjusting the compass. Draw an arc inside the angle.Use a straight line to connect the intersection of the two arcs with Point B of the 60° angle. That line segment is an angle bisector of the angle ABD, yielding two 30° angles.Read more questions about Triangles and angles from:
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Tim ha 13 pickle to put in 5 lunch bag. He put the ame number of pickle in each bag? how many pickle are left? and he put in a many pickle a he can. How many pickle doe tim put in each bag? How many pickle are left
Tim puts two pickles in each of the five lunch bags, leaving him with three pickles.
If Tim puts the same number of pickles in each of the lunch bags and as many as possible, only a maximum of two can be put in each of the bags:
Dividing 13 pickles by 5 lunch bags, the answer is 2 pickles with a reminder of 3 pickles
13 ÷ 5 = 13/5
Therefore, Tim puts two pickles in each of the five lunch bags and is left with three pickles.
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Find the coordinates of point P along the directed line segment AB so that
AP to PB is in the ratio 3 to 7] Round your answer to the nearest tenth.
B(4, 5)
A(-2, 1)
-4
-2
Ay
61
-4-
Coordinates: P
N.
2
4 x
(1+x)
2-3
x) = 8 bris E= SVIÐ
V/22
Answer:
P(-0.2, 2.2)
Step-by-step explanation:
You want the coordinates of point P that divides AB into segments with the ratio AP/PB = 3/7. The end points are A(-2, 1) and B(4, 5).
Dividing pointThe point that divides AB in the ratio m/n is ...
P = (mB +nA)/(m+n)
P = (3(4, 5) +7(-2, 1))/(3+7) = (12 -14, 15 +7)/10
P = (-0.2, 2.2)
1) {(9,-8), (8,-9), (-9, 5), (3, 8), (7, 8) }
Domain:
Range:
Function?: function or not?
The domain is {9, 8, -9, 3, 7}, the range is {-8,-9, 5, 8} and the relation is a function
How to determine the domain and the range?From the question, we have the following parameters that can be used in our computation:
{(9,-8), (8,-9), (-9, 5), (3, 8), (7, 8) }
The domain is the set of the x values
So, we have the following representation
x = {9, 8, -9, 3, 7}
Remove repeated entries
x = {9, 8, -9, 3, 7}
So, the domain is {9, 8, -9, 3, 7}
Similarly, we have
Range = {-8,-9, 5, 8}
Also, the relation is a function
This is because the no x value has several y values
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What will be the roots of the equation 3x² 7x 5 0?
The roots of the Given quadratic equation are 0.57 and -2.9 solved using the algebraic method.
The given equation is a quadratic equation because the degree of the given equation is 2.
How can one tell whether or not a given equation is a quadratic equation?
A quadratic equation is a two-variable polynomial equation of degree two of the form [tex]f(x) = ax^2+bx+c = 0[/tex] with the variables a, b, and c being real numbers and a not equal to 0. With "a" denoting the leading coefficient and "c" denoting the absolute term of f, it is a quadratic equation in its general form (x). The values of x that fulfil the quadratic equation are known as the roots.
The given equation is 3x²+7x - 5 = 0 a =3,b=7, c =-5
lets roots of the given equation is (α, β).
roots can be found using Shreedhara Acharya's formula.
[tex](\alpha, \beta) = [-b \± \sqrt(b^2 - 4ac) ]/2a[/tex]
α = [-b + √(b^2 – 4ac)]/2a
β = [-b - √(b^2 – 4ac)]/2a
b^2 – 4ac = 49-4*3*(-5) = 49+60 = 109
α = (-7+[tex]\sqrt{109}[/tex])/2*3
α = (-7+10.44)/6
α = 0.57
β = (-7 - 10.44)/6
β = -2.9
So the roots of the Given quadratic equation are 0.57 and -2.9.
-- The given question is incomplete, the complete question is
"What will be the roots of the equation 3x^2+7x-5=0" --
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Which theorem has two sides and a non-included angle?
Angle-Angle-Side (AAS) Theorem has two sides and a non-included angle.
What is Angle-Angle-Side (AAS) Theorem?The triangles are congruent if two angles and a non-included side in one triangle are congruent with two angles and the corresponding non-included side in another triangle, according to the Angle-Angle-Side (AAS) Congruence Theorem.The side-angle-side (SAS) theorem is the first such theorem. The triangles are congruent if two sides and the included angle of one triangle are equivalent to two sides and the included angle of another triangle.When two angles and an unincluded side of one triangle are equal to two angles and the corresponding unincluded side of the other triangle, two triangles are said to be congruent (AAS=AAS).To learn more about Angle-Angle-Side (AAS) Theorem refer to:
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A number of plums were shared among 3 friends. George received 3/8, Terry received 1/4,Samuel 3/16 And jude received the remaining 36 plums. from the number of plums george received,he gave 22 to jude.how many plums did george remain with?
The plums that remain with George after sharing 22 with Jude will be equal to 50.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.
Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data mentioned in the question,
We first need to determine how many plums Jude received. Decide to round everything to the sixteenth.
George is having 3/8 = 6/16
Terry is having 1/4 = 4/16
Samuel is having 3/16
So, remaining will go to Jude = (16 - (6 + 4 + 3))/16 = 3/16
Consequently, if Jude received 3/16 of the plums, and she received 36 plums, 1/16 of the total plums is,
= 36/3 = 12 plums (As a side note, there were 192 plums in total).
George has got 6/16 plums = 6 × 12 = 72
Then, he gave 22 plums to Jude, so he has left with,
72–22 = 50 left.
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pleaseee help :15x+32=200
Answer:
11.2
Step-by-step explanation:
15x + 32 = 200 Subtract 32 from both sides
15x + 32 - 32 = 200 - 32
15x = 168 Divide both sides by 15
[tex]\frac{15x}{15}[/tex] = [tex]\frac{168}{15}[/tex]
x = 11.2
Answer:
i think the answer is x= 11.2
Step-by-step explanation:
15x= 200-32
15x=168
x=168/15
x=11.2
The graph of which function has an axis of symmetry at x = 3?
The graph of which the function has an axis of symmetry at x = 3 is the graph of
y = x² - 6x - 1How to find the graph with axis of symmetry x = 3The axis of symmetry of a quadratic function is the line that bisects the curve into two.
The formula for the axis of symmetry is of the form
x = -b / 2a
for the function y = x² - 6x - 1
b = -6
a = 1
the axis of symmetry, x = -(-6/(2 * 1))
= - (-3)
= 3
hence the axis of symmetry is x = 3
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When the equation y 4x 10 is written in the standard form the value of C Square will be?
The value of c square when the given equation y = 4x - 10 is written in standard form is equal to 100.
As given in the question,
Given equation is equal to :
y = 4x - 10
Standard form of the equation in the slope intercept form is written as:
y = mx + c
Here value of m represent slope is equal to 4
And value of c represents the y-intercept form is equal to -10.
Value of c square is given by :
c = -10
Squaring both the sides we get,
⇒c² = ( -10 )²
⇒c² = 100
Therefore, the value of c square in the given equation is equal to 100.
The given question is incomplete , the complete question is :
When the equation y = 4x - 10 is written in the standard form the value of C Square will be?
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100 POINTS HELP PLEASE ILL GIVE BRAINLIEST
Answer:
A. It is a decrease in assets.
Step-by-step explanation:
The business paid $700,000 to the Loans Payable via cash, reducing their assets by 700,000 dollars AND increasing the credits. The business increased its credit score since it paid the exact amount it got a loan for back to the Loan Company.
That money was the payable loan depicted in the Debit section.
Answer:
OptionA) Decrease in assets
Step-by-step explanation:
The business paid $700,000 to the Loans Payable via cash, reducing their assets by 700,000 dollars AND increasing the credits.
How do you find the asymptotes and holes of a rational function?
To find the asymptotes and holes of a rational function, factor the denominator of the function and set it to zero. This will give you the x-values of the holes. To find the asymptotes, take the degree of the numerator and subtract it from the degree of the denominator. This will give you the degree of the asymptote.
To find the asymptotes and holes of a rational function, you must first factor the denominator of the function and set it to zero. This will give you the x-values of the holes, or the values where the function is undefined. To find the asymptotes, take the degree of the numerator and subtract it from the degree of the denominator. This will give you the degree of the asymptote. For example, if the numerator is a second degree polynomial and the denominator is a third degree polynomial, the asymptote will be a first degree polynomial. To find the equation of the asymptote, divide the numerator and denominator by the highest degree term of the denominator. The resulting quotient will be the equation of the asymptote. The asymptotes will be straight lines, so the equation will be in the form of y = mx + b. The holes will be the x-values of the points where the denominator equals zero. The asymptotes and holes will divide the graph of the rational function into distinct regions, and can be used to analyze the behavior of the function.
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In AOPQ, m/O = (2x − 5)°, mZP = (3x − 8)°, and mZQ = (10x – 17)º.
-
What is the value of x?
Answer:
x = 14
Step-by-step explanation:
You want the value of x in ∆OPQ, where ∠O = (2x − 5)°, ∠P = (3x − 8)°, and ∠Q = (10x – 17)º.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°. This means ...
∠O +∠P +∠Q = 180°
(2x -5)° +(3x -8)° +(10x -17)° = 180° . . . . . use the given expressions
15x -30 = 180 . . . . . . divide by °, collect terms
x -2 = 12 . . . . . . . . . divide by 15
x = 14 . . . . . . . . . . add 2
The value of x is 14.
__
Additional comment
The measures of the angles are ...
O = 23°, P = 34°, Q = 123°
what is 5a+6b=c
and what is 5a+8=7b-6
whats the answer for as well for 6a+3=8b+10
The numeric value of the expression c = 5a + 6b is given as follows:
c = 759.5.
How to obtain the numeric value of the expression?The expression in this problem is defined as follows:
c = 5a + 6b.
To obtain the numeric value of the expression, the values of a and b have to be known, and they are discovered solving the system of equations presented as follows:
5a + 8 = 7b - 6.6a + 3 = 8b + 10.In standard format, the system is given as follows:
5a - 7b = -14.6a - 8b = 7.Multiplying the first equation by 6 and the second by -5, we have that:
30a - 42b = -84.-30a + 40b = -35.Adding the two equations, we have that the variable b is given as follows:
-2b = -119
b = 119/2
b = 59.5.
Then the variable a is obtained as follows:
5a + 8 = 7(59.5) - 6
a = (7(59.5) - 6 - 8)/5
a = 80.5.
Thus the numeric value of the expression is given as follows:
c = 5(80.5) + 6(59.5)
c = 759.5.
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2.3.4 In a game between two equal teams; the home team wins with probability p > 1/2_ In a best of three playoff series; a team with the home advantage has a game at home, followed by a game away, followed by a home game if necessary The series is over as soon as one team wins two games. What is P[H], the probability that the team with the home advantage wins the series? Is the home advantage increased by playing a three-game series rather than a one-game playoff? That is, is it true that P[H] > p for all p > 1/2?
The team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.
For the team with the homecourt advantage, let [tex]Wi[/tex] and [tex]Li[/tex] denote whether the game '[tex]i[/tex]' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.
The probability that the team with the home-court advantage wins is
P [H] = P [[tex]W1W2[/tex]] + P [[tex]W1L2W3[/tex]] + P [[tex]L1W2W3[/tex]]
= [tex]p(1-p)[/tex] + [tex]p3[/tex] + [tex]p(1-p){2}[/tex]
Note that P[H] ≤ pfor 1/2≤p≤1.
Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.
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For the team with the homecourt advantage, let and denote whether the game '' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.
The probability that the team with the home-court advantage wins is
P[H] ≤ pfor 1/2≤p≤1.
Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.
Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 1 − √6, 1+ √6, and 5-i
(Simplify your answer)
What is polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Since we know that complex solutions ALWAYS come in pairs, the minimal polynomial must include the root of 4-i as an acceptable root..
This leads to a polynomial of ...
p(x) = (x - 5)(x - (4+i))(x - (4-i))
Now we can simplify...
(x - (4+i))(x - (4-i)) --> x2 + [(4+i)+(4-i)]x + (4+i)(4-i) --> x2 + 8x + [ 16 -4i + 4i -i2 ] = x2 + 8x +17
Take this quadratic and multiply by (x-5) to get the final, minimal polynomial...
p(x) = (x-5)(x2 + 8x +17) = x3 + 8x2 + 17x -5x2 + 40x - 85 = x3 + 3x2 + 57x - 85
So p(x) = x3 + 3x2 + 57x - 85
p(x) has only real coefficients, the leading coefficient of 1, and is the smallest to allow for the two solutions requested
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How many solutions of the given simultaneous equations 2x 3y 8 4x 6y 7?
The simultaneous equations 2x + 3y = 8 and 4x + 6y = 7 supplied do not have a solution
What do simultaneous equations mean?A collection of two or more equations, each of which contains two or more variables, each of whose values can simultaneously fulfil one or more of the equations in the collection, with the total number of variables in the collection being equal to or fewer than the total number of equations.
Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. The equations are referred to as simultaneous equations since they are solved simultaneously.
Here are a few examples of simultaneous equations:
2x + 4y = 14
4x − 4y = 4.
Given,
2x + 3y = 8 and 4x + 6y = 7
We get,
2x + 3y = 8 ….. (i)
4x + 6y = 7 ….. (ii)
Then we have Multiply (i) by 4
4x + 6y = 16..... (iii)
Therefore, LHS of (ii) and (iii) are same but RHS is different. As a result, the answer is false.
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points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.
Points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.
True