We can expect 2 black horses out of a sample of 15 horses from the stable.
What is probability?To determine how likely something is gonna occur, use probability. The event is typically stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty.
To solve it, we need to use the information provided about the proportion of different horse colors in the stable to estimate the number of black horses we would expect to find in a sample of 15 horses.
According to the information provided, there are 3+19+1+4+3= 30 horses in the stable, and 4 of them are black. Therefore, the proportion of black horses in the stable is:
4/30 = 0.1333...
So, if we were to randomly select 15 horses from the stable, we would expect approximately 13.33% of them to be black. To find the expected number of black horses in a sample of 15 horses, we can multiply the proportion by the sample size:
0.1333... x 15 = 1.999...
Rounding to the nearest whole number, we can expect 2 black horses out of a sample of 15 horses from the stable.
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Leon asks his classmates how many mystery books and how many adventure books they own. He states that because the mean number of mystery books, 5, is less than the mean number of adventure books, 10, there is less variability in the number of mysstery books. Do you agree?
To make any conclusions about the variability of the two datasets.
What is variable?a variable is a symbol or letter that represents a value that can change or vary. Variables are used to express mathematical relationships and equations, and they can take on different values depending on the context.
by question.
No, we cannot conclude that there is less variability in the number of mystery books based solely on the mean number of mystery books being less than the mean number of adventure books. The variability of the data is captured by the standard deviation or variance, and we would need this information to make any conclusion about the variability of the two types of books. It's possible that there is less variability in the number of mystery books,
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Fluffy, Spot, and Shampy have a combined age in dog years of 82. Spot is 14 years younger than Fluffy. Shampy is 6 years older than Fluffy. What is Fluffy's age, f, in dog years?
The age of fluffy is 30 in dog years. The solution has been obtained by using linear equation.
What is a linear equation?One is the degree of the linear equation. The absence of variables in linear equations with exponents greater than one is obvious. The graph's equation results in a straight line.
We are given that combined age of 3 dogs in dog years is 82.
Let Fluffy's age be 'f'.
Age of Spot = (f - 14)
Age of Shampy = (f + 6)
From this, we get
f + (f - 14) + (f + 6) = 82
On solving this, we get
⇒f + f - 14 + f + 6 = 82
⇒3f - 8 = 82
⇒3f = 90
⇒f = 30
Hence, the age of fluffy is 30 in dog years.
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Graph the solution to the following system of inequalities.
2x +7vs - 14
-3x +5y> 5
Then give the coordinates of one point in the solution set.
Point in the solution set: (П.П)
A solution to the given system of linear inequalities is (-6, -1).
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;
2x + 7y ≤ -14 .....equation 1.
-3x + 5y > 5 .....equation 2.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region below the solid and dashed line, and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (-6, -1).
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College Algebua - „,1 Modellng with Quadratles Mahemet Koothall Thrun - Cine caact atswens, the and the fanctian ta ibcin your animen. - Show all necinary calnulations - Wrice par answis in ceptreste itriansich. reresest? 2. What a theytipenret' What dors it repericnt? Hha happris? ia at 10 irst be isurn wa fer be isle ta catis thin forchile College Algebra - 3.1 Modeling with QuadraticsMahomes Football Throw At a Kansas City Chiefs football practice, Patrick Mahomes is practicing his throws. He stands at one end of the football field and throws the ball. The ball's height, (in feet) as a function of horizontal distance,x(in feet), from Mahomes can be described by the following function:f(x)=−1201(x−88)2+151058- Give exact answers. Use only the function to obtain your answers. - Show all necessary calculations. - Write your answers in complete sentences. 1. What is the positivex-intercept? What does it represent? 2. What is they-intercept? What does it represent? 3. What is the maximum height that the foothall reaches?. What is the horizontal distance from Mahomes when this happens? 4. Travis Kelce is standing along the path of the football 160 feet from Patrick Mahomes. Travis can catch a ball that is at 10 feet or lower. Will he be able to catch this football? 5. What is the horizontal distance of the football from Patrick Mahomes when it first reaches a height of 40 feet?
1. The positive x-intercept of the function f(x)= -1201(x-88)^2 + 151058 is 88 feet.
2. The y-intercept of the function f(x) = -1201(x-88)^2 + 151058 is 151058 feet.
3. The maximum height that the football reaches is 151058 feet, and the horizontal distance from Patrick Mahomes when this happens is 88 feet.
4. Yes, Travis Kelce will be able to catch the football, since it reaches a height of 10 feet or lower at the horizontal distance of 160 feet from Patrick Mahomes.
5. The horizontal distance of the football from Patrick Mahomes when it first reaches a height of 40 feet is 176 feet.
1. The positive x-intercept represents the horizontal distance from Patrick Mahomes at which the football is initially released.
2. The y-intercept of the function represents the height of the football when it is released from Patrick Mahomes.
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Please refer to this output. Method DE H-Value P-value
Not adjusted for ties 2 0.01 0.994
Adjusted for ties 2 0.01 0.994 Ten cities are selected, and the number of daily passenger trips (in thousands) for subways and commuter rail service is obtained. At alpha equal to 0.05, the researcher wants to check the strength of relationship between the variables. Assume that data is normally distributed For the next questions, please refer to this problem.
What does the test for significant relationship tell you? 1 point a. There is a significant relationship between the number of daily passenger trips (in thousands) for subways and commuter rail service? b. The simple linear regression equation conforms to the strength of relationship defined. c. It is good to proceed with defining the simple linear regression equation, d. There is no significant relationship between the number of daily passenger trips (in thousands) for subways and commuter rail service?
There is a significant relationship between the variables (H-value = 2 and P-value = 0.994)
The test for significant relationship is used to determine whether there is a statistically significant relationship between two or more variables. In this case, the test can be used to determine whether there is a statistically significant relationship between the number of daily passenger trips (in thousands) for subways and commuter rail service. Based on the H-value and P-value, the result of this test indicates that there is a significant relationship between the variables (H-value = 2 and P-value = 0.994). Therefore, option (a) is correct and option (d) is incorrect.
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help :(( What should be reason 5 in the following proof?
Answer:
Reason 5 should be "Alternate Interior Angles Converse".
Step-by-step explanation:
QUESTION 4 A and B are events with P(A) = 0.5 , P(BA)=0.6, and P(BIA) = = 0.8. Find P(AB) (if rounding is necessary, give answers to within 1% of the exact value). QUESTION 5 A and B are events with P(A) = 0.2, P(B) = 0.6 and P( BA) = 0.1. Find P(B|Ā), giving answers to within 1% of the exact value. QUESTION 6 + = X is a continuous random variable with probability density function 17/(x + 1), X>0 f(x)= 0, X50. Which of the following is the cumulative distribution function of X? O F(x) = 1-1/(x+1)^7, x>0 O F(x) = 56/(x+1)^9, x>0 O F(x) = -1/(x+1)^7, x>0 =
The probability of both events A and B occurring is 0.3 or 30%.
The cumulative distribution function of X is F(x) = 17 * ln(x + 1) for x > 0.
The probability of event B occurring given that event A does not occur is 0.125 or 12.5%.
ANSWER 4:
We can use the formula P(AB) = P(A) * P(B|A) to find the probability of both events A and B occurring.
P(AB) = P(A) * P(B|A)
P(AB) = 0.5 * 0.6
P(AB) = 0.3
So the probability of both events A and B occurring is 0.3 or 30%.
ANSWER 5:
We can use the formula P(B|A) = P(AB) / P(A) to find the probability of event B occurring given that event A does not occur. We can also use the formula P(A') = 1 - P(A) to find the probability of event A not occurring.
P(A') = 1 - P(A)
P(A') = 1 - 0.2
P(A') = 0.8
P(B|A') = P(BA') / P(A')
P(B|A') = 0.1 / 0.8
P(B|A') = 0.125
So the probability of event B occurring given that event A does not occur is 0.125 or 12.5%.
ANSWER 6:
The cumulative distribution function (CDF) of a continuous random variable X is defined as F(x) = P(X <= x). To find the CDF of X, we need to integrate the probability density function (PDF) of X from 0 to x.
F(x) = ∫ f(t) dt from 0 to x
F(x) = ∫ (17/(t + 1)) dt from 0 to x
F(x) = 17 * ln(t + 1) from 0 to x
F(x) = 17 * ln(x + 1) - 17 * ln(0 + 1)
F(x) = 17 * ln(x + 1)
So the cumulative distribution function of X is F(x) = 17 * ln(x + 1) for x > 0.
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If the transformation from f to g is such that f(x)=e^(x) is verticall shrunk by a factor of ( 1)/(3) to make g(x), what is g(x) ?
After the transformation from f to g, g(x) = eˣ/3.
Vertical shrink refers to a transformation of a function that causes it to be compressed vertically. To perform a vertical shrink, you must multiply the output (y) values of the function by a constant value between 0 and 1.
The transformation of f(x) to g(x) involves a vertical shrink by a factor of 1/3. This means that the value of g(x) will be one third of the value of f(x). We can write this transformation as: g(x) = 1/3 · f(x).
Since f(x) = eˣ, we can substitute this into the equation for g(x) to find the final expression for g(x):
g(x) = (1/3)eˣ
Therefore, the function g(x) after the vertical shrink by a factor of 1/3 is g(x) = (1/3)eˣ or g(x) = eˣ/3.
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(3 points) Problem 5: Determine the value(s) ofasuch that [1a], [aa+2] are linearly independent.
To determine the value(s) of a such that [1 a], [a a+2] are linearly independent, we need to find the values of a that make the determinant of the matrix non-zero. The determinant of a 2x2 matrix is given by:
|1 a|
|a a+2| = (1)(a+2) - (a)(a) = a + 2 - a^2
To make the determinant non-zero, we need to solve the equation:
a + 2 - a^2 ≠ 0
Rearranging the equation, we get:
a^2 - a - 2 ≠ 0
Factoring the equation, we get:
(a - 2)(a + 1) ≠ 0
Therefore, the values of a that make the determinant non-zero are a ≠ 2 and a ≠ -1. These are the values of a that make the vectors [1 a], [a a+2] linearly independent.
So, the value(s) of a such that [1 a], [a a+2] are linearly independent are a ≠ 2 and a ≠ -1.
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What is the measure of "AC"?
Enter your answer in the box.
Will give Brainiest if right. and to help other people thx.
Answer: 21 degrees
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Question 5 If \( A \) and \( B \) are \( 3 \times 3 \) matrices satisfying \( \operatorname{det} A=12 \) and \( \operatorname{det} B=3 \), then \( \operatorname{det}\left(2 A^{-1} B^{2}\right)= \) A 1
\( \operatorname{det}\left(2 A^{-1} B^{2}\right) = \frac{18}{12} = \frac{3}{2} \)Explanation: We are given that \( \operatorname{det} A=12 \) and \( \operatorname{det} B=3 \). We need to find the determinant of \( 2 A^{-1} B^{2} \). We can use the properties of determinants to simplify the expression. Recall that \( \operatorname{det}(cA) = c^n \operatorname{det}(A) \) for an \( n \times n \) matrix \( A \) and a scalar \( c \), and that \( \operatorname{det}(AB) = \operatorname{det}(A)\operatorname{det}(B) \). Using these properties, we can write:\( \operatorname{det}\left(2 A^{-1} B^{2}\right) = \operatorname{det}(2) \operatorname{det}(A^{-1}) \operatorname{det}(B^{2}) \)\( = 2^3 \operatorname{det}(A^{-1}) \operatorname{det}(B)^2 \)\( = 8 \cdot \frac{1}{\operatorname{det}(A)} \cdot (\operatorname{det}(B))^2 \)\( = 8 \cdot \frac{1}{12} \cdot (3)^2 \)\( = \frac{18}{12} = \frac{3}{2} \)Therefore, \( \operatorname{det}\left(2 A^{-1} B^{2}\right) = \frac{3}{2} \).
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4. Show how you find the average rate of change off(x)=2 x^{2}-9over the interval [4,6] .
The average rate of f(x), in [4,6], is equal to 20.
To find the average rate of change of a function over an interval, we use the formula:
Average rate of change = (f(b) - f(a))/(b - a)
Where f(x) is the function, a and b are the endpoints of the interval, and f(a) and f(b) are the values of the function at those endpoints.
In this case, our function is f(x) = 2x² - 9, and our interval is [4, 6]. So, we plug in the values into the formula:
Average rate of change = (f(6) - f(4))/(6 - 4)
First, we find f(6) and f(4):
f(6) = 2(6²) - 9 = 2(36) - 9 = 72 - 9 = 63
f(4) = 2(4²) - 9 = 2(16) - 9 = 32 - 9 = 23
Now we plug these values back into the formula:
Average rate of change = (63 - 23)/(6 - 4) = 40/2 = 20
In conclusion, the average rate is worth 20.
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Let a, b, and c be elements of a field F.Prove:
(1) If a + b = c + b, then a = c.
(2) If ab = cb and b doesn't equal 0, then a = c.
Answer:
The given statements can be proved as follows:
(1) If a + b = c + b, then a = c.
Proof:
- Start with the given equation: a + b = c + b
- Subtract b from both sides of the equation: a + b - b = c + b - b
- Simplify the equation: a = c
- Therefore, if a + b = c + b, then a = c.
(2) If ab = cb and b doesn't equal 0, then a = c.
Proof:
- Start with the given equation: ab = cb
- Divide both sides of the equation by b: ab/b = cb/b
- Simplify the equation: a = c
- Therefore, if ab = cb and b doesn't equal 0, then a = c.
In both cases, the elements a and c are equal when the given conditions are met.
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calculate the areas of the rectangles having the following measurements
Perimeter(p)=220cm and breadth(b)=45cm
Answer:
it is 2,475
Step-by-step explanation:
In his motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing spot, a distance of 90 mi, in 3 hr. Returning, he finds that the trip downstream, still at top speed, takes only 2.5 hr. Find the rate of Bill's boat and the speed of the current. Let x = the rate of the boat in still water and y = the rate of the current.
The rate of Bill's boat in still water is 33 mph and the speed of the current is 3 mph.
To find the rate of Bill's boat and the speed of the current, we can use the distance formula, which states that distance = rate × time. Since we know the distance and time for both the upstream and downstream trips, we can set up two equations and solve for the rate of the boat and the speed of the current.
Let x = the rate of the boat in still water and y = the rate of the current.
For the upstream trip:
90 = (x - y) × 3
For the downstream trip:
90 = (x + y) × 2.5
Simplifying the equations gives us:
90 = 3x - 3y
90 = 2.5x + 2.5y
Multiplying the first equation by 2.5 and the second equation by 3 gives us:
225 = 7.5x - 7.5y
270 = 7.5x + 7.5y
Adding the two equations together eliminates the y variable:
495 = 15x
Solving for x gives us:
x = 33
Substituting x back into the first equation gives us:
90 = (33 - y) × 3
90 = 99 - 3y
3y = 9
y = 3
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real zero, Including any repeated zeroes? Choose your answ f(x)=x^(6)+8x^(5)+9x^(4)-2x^(2)-7x+4
The real zeroes of the function f(x)=x^(6)+8x^(5)+9x^(4)-2x^(2)-7x+4 are -4, -1, and 1.
The real zeroes of the function f(x)=x^(6)+8x^(5)+9x^(4)-2x^(2)-7x+4 can be found by using the Rational Zero Theorem and synthetic division.
The Rational Zero Theorem states that the possible rational zeroes of a polynomial are the factors of the constant term divided by the factors of the leading coefficient. In this case, the constant term is 4 and the leading coefficient is 1, so the possible rational zeroes are ±1, ±2, and ±4.
We can use synthetic division to test these possible zeroes and find the actual zeroes of the function. Synthetic division is a method of dividing a polynomial by a linear factor of the form x-a. The result of synthetic division is a quotient and a remainder, and if the remainder is 0, then x-a is a factor of the polynomial and a is a zero of the function.
Using synthetic division, we find that the real zeroes of the function are -4, -1, and 1. These are the values of x that make the function equal to 0. There are no repeated zeroes in this case.
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Si al salario por semana se le rebaja el 9. 5% para ccss y el salario es de 50. 000 ¿cuánto me pagan?
If the weekly salary is reduced by 9.5% for CCSS and the salary is 50000, then they would pay $45250.
The percent reduction in the weekly salary is = 9.5% = 0.095,
So, the amount of the reduction is;
⇒ reduction = 9.5% of 50,000
⇒ reduction = 0.095 x 50,000
⇒ reduction = 4750
So, the reduction in the weekly salary is 4750,
Now, we subtract the reduction from the original salary to get the new salary after the reduction,
⇒ new salary = 50000 - 4750
⇒ new salary = 45250
Therefore, the new salary after the 9.5% reduction for CCSS is $45250.
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Big ideas 7.5 (question)
1) A perpendicular bisector in kite ABCD is; BD
2) An isosceles triangle in kite ABCD is; ΔABC
3) A right triangle in kite ABCD is; ΔABM
What is a Kite?In geometry, a kite is defined as a quadrilateral with reflection symmetry across a diagonal.
here, we have,
1) A perpendicular bisector is defined as a line segment which bisects another line segment at 90 degrees.
Looking at the diagram, Line BD bisects Line AC and as such BD is the perpendicular bisector.
2) An Isosceles triangle is defined as a a triangle in which two sides have the same length.
In this case, in Triangle ABC, AB and BC have the same length and as such Triangle ABC is the Isosceles Triangle.
3) A right triangle is defined as a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.
In this case if Mis the intersection of BD and AC, then the right angle triangle is ABM
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I need help with these maths questions
Answer:
see explanation
Step-by-step explanation:
(a)
• the opposite sides of a rectangle are congruent
then
4x + 1 = 2x + 12
(b)
solving
4x + 1 = 2x + 12 ( subtract 2x from both sides )
2x + 1 = 12 ( subtract 1 from both sides )
2x = 11 ( divide both sides by 2 )
x = 5.5
(c)
the perimeter (P) is the sum of the 4 sides of the rectangle , that is
P = 4x + 1 + x + 2x + 12 + x ( collect like terms )
= 8x + 13 ( substitute x = 5.5 )
= 8(5.5) + 13
= 44 + 13
= 57
Answer:
a) Because two opposite sides of the rectangle have the same sizes
B)
[tex]x = \frac{11}{2} [/tex]
c)
[tex]57[/tex]
Step-by-step explanation:
b)
[tex]4x + 1 = 2x + 12 \\ 4x - 2x = 12 - 1 \\ 2x = 11 \\ \frac{2x}{2} = \frac{11}{2} \\ x = \frac{11}{2} [/tex]
c) Perimeter
[tex]p = 2(x + y) \\ 2( \frac{11}{2} + 23) \\ 2( \frac{57}{2} ) \\ 57[/tex]
23 comes from
[tex]2x + 12 \\ x = \frac{11}{2} \\ 2( \frac{11}{2} ) + 12 \\ 11 + 12 \\ \\ 23[/tex]
What should be reason 8 in the following proof?
Answer: I think putting Prop of ║lines might work. I haven't done this in a long time, so I'm most likely wrong, but that might help. I'm so sorry.
Curt and Melanie are mixing blue and yellow paint to make seafoam green paint.use the percent equation to find how much yellow paint they should use
The percentage of yellow paint that has to be used is given as 0.45
How to find the amount of yellow paint that is to be used hereThe amount of seafoam paint is given as 1.5 quartz
The percentage of yellow paint in the seafoam paint is 30 percent
Hence the amount that would be in it that would be made of yellow paint is given as
1.5 x 30%
1.5 x 0.30
= 0.45
Hence we would conclude by saying that the amount of yellow paint that has to be used in order to make the paint should be 0.45
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Curt and Melanie are mixing blue and yellow paint to make seafoam green paint. 1.5 quarts of seafoam paint is made of 70% blue, 30% yellow. Use the percent equation to find how much yellow paint they should use.
1- Indicate the transformations to f(x)
a) y = −0.5f(−0.5x) − 1
b) y = 2f(x − 5) + 4
c) y = 3f (−2(x + 1))
2- Indicate the transformations to f(x) = √x
It is a vertical stretching by a factor of 2 followed by a vertical shift of 1 unit.
1- To transform f(x) in the given equations, the following transformations need to be done:
a) y = −0.5f(−0.5x) − 1 is a transformation by vertical stretching by a factor of 0.5, followed by a horizontal compression by a factor of 0.5, and then a vertical shift of 1 unit.
b) y = 2f(x − 5) + 4 is a transformation by horizontal shifting of 5 units to the left, followed by a vertical stretching by a factor of 2, and then a vertical shift of 4 units.
c) y = 3f (−2(x + 1)) is a transformation by horizontal shifting of 1 unit to the right, followed by a horizontal compression by a factor of 2, and then a vertical stretching by a factor of 3.
2- To transform f(x) = √x, it is a vertical stretching by a factor of 2 followed by a vertical shift of 1 unit.
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3
The drama club at Hawthorne Middle School is selling tickets to their spring musical. Student tickets
cost $10 and adult tickets cost $15. Last week, they sold 120 tickets for the Sunday matinee show. If those
ticket sales totaled to $1,400, how many adult tickets were sold? How many student tickets were sold?
40 adult tickets were sold and 80 student tickets were sold.
What is an equation?
An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations.
Let's use algebra to solve this problem.
Let's call the number of student tickets sold "s" and the number of adult tickets sold "a".
From the problem, we know two things:
The total number of tickets sold was 120:
s + a = 120
The total amount of money made from ticket sales was $1,400:
10s + 15a = 1400
Now we have two equations with two variables, so we can solve for "a" and "s".
Let's start by solving for "s" in the first equation:
s + a = 120
s = 120 - a
Now we can substitute this expression for "s" into the second equation:
10s + 15a = 1400
10(120 - a) + 15a = 1400
1200 - 10a + 15a = 1400
5a = 200
a = 40
So 40 adult tickets were sold.
Now we can substitute this value of "a" into the first equation to find "s":
s + a = 120
s + 40 = 120
s = 80
So 80 student tickets were sold.
Therefore, 40 adult tickets were sold and 80 student tickets were sold.
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Gemma makes a conjecture that in the sum of an eye and the jersey, and is selfish, always an even integer. Which choice is the best proof of her conjecture
As per the concept of integer, the best proof of her conjecture is Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2. Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even. (option b)
Now, let's look at the given choices to find the best proof for Gemma's conjecture.
Choice B) Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2. Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.
This choice provides a proof by using algebraic equations. It begins by defining an odd integer as 2n + 1, where n is any integer. Then, it uses algebraic manipulation to show that the sum of this odd integer and itself results in an even integer. Specifically, (2n + 1) + (2n + 1) simplifies to 4n + 2, which is equal to 2(2n + 1). This proves that the sum of an odd integer and itself is always even.
This choice is a tautology, which means that it's always true, but it doesn't provide any evidence or proof to support Gemma's conjecture.
The best proof for Gemma's conjecture is choice B.
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Complete Question:
Gemma makes a conjecture that the sum of an odd integer and itself is always an even integer. Which choice is the best proof of her conjecture?
A) Look at these different examples: 7 + 7 = 14, 13 + 13 = 26, 23 + 23 = 46. So the sum of an odd number and itself must be even
B) Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2. Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.
C) Let n represent an odd number, and let n + n be an even number. Therefore, n + n = n + n, which shows that the sum of an odd number and itself is even.
D) Every time you add an odd number and itself, the sum is an even number.
Aisling runs 2km on Monday and three times that many on Tuesday. If she wants to run 20km this week. How many km does she need to run
Answer:12km
Step-by-step explanation:
She ran 2km on Monday, and three times as much on Tuesday so we do 2 x 3 which equals 6. So 6km, plus the original 2km is 8km (6+2) is she wants to run 20km this week, then she needs to subtract what shes already ran to find out how many more km she needs to run. 20-8=12 so 12km.
Find the area of the trapezoid. Leave your answer in simplest radical form.
a) 156 ft^2
b) 78 ft^2
c) 78 √ 2 ft^2
d) 13 ft^2
The area of the trapezoid in simplest radical form is 78 feet².
Given a trapezoid.
Length of the bases are 10 feet and 16 feet.
We have to find the height.
Consider the smaller right triangle formed by the height of the trapezoid.
Triangle base length or one leg = 16 - 10 = 6 feet
Since one of the angle is 45°, the other angle in the right triangle is also 45°.
Since it is isosceles, opposite sides for 45° angles are same.
Other leg = 6 feet, which is the height.
Area of the trapezoid = 1/2 (a + b)h, where a and b are bases and h is the height.
A = 1/2 (10 + 16) 6
= 78 feet²
Hence the correct option is b.
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The yearly income of a family is Rs. 500000. The ratio of the expenditure and saving of the family is 4 : 1. Find the amount of expenditure and saving.
Answer:
Let's assume that the amount of saving is x.
According to the problem, the ratio of expenditure to saving is 4:1, so the amount of expenditure can be expressed as 4x.
The total income of the family is Rs. 500000, and it can be expressed as the sum of expenditure and saving:
Expenditure + Saving = 500000
Substituting the values of expenditure and saving, we get:
4x + x = 500000
Simplifying this equation, we get:
5x = 500000
Dividing both sides by 5, we get:
x = 100000
Therefore, the amount of saving is Rs. 100000, and the amount of expenditure is 4 times this value, which is Rs. 400000.
How do I draw a parabola when given the directix and focus
The distance between any point on the parabola and the directrix is equal to the distance between that point and the focus. This property is what defines a parabola.
How to draw a parabola when given the directix and focus?To draw a parabola given the directrix and focus, follow these steps:
Draw the directrix as a straight line.Mark the focus point on the opposite side of the directrix from the vertex.Find the midpoint between the focus and the directrix, which is also the vertex of the parabola.,Draw a perpendicular line from the vertex to the directrix. This is the axis of symmetry of the parabola.Measure the distance between the focus and the vertex. This distance is called the focal length and is denoted by "p".From the vertex, mark a point "p" units above and below the vertex along the axis of symmetry. These points are called the "endpoints of the latus rectum."Draw lines through each endpoint of the latus rectum perpendicular to the axis of symmetry, extending to intersect the directrix. These two lines will be parallel to each other and equidistant from the axis of symmetry.Finally, draw a smooth curve through the focus point that passes through each endpoint of the latus rectum. This curve is the parabola.Learn more about parabola here: https://brainly.com/question/25651698
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For A-C, choose Yes or No to indicate whether or not each expression has a value greater than 6.
29
√9
B. 4+ √3
A.
C. 6.4 -
D. 27
18
√27
OYes ONO
OYes No
OYes No
OYes No
3)(9pts)Use Cramer's rule to find the values of the variablesx,y, andz( 3 points each). Show the determinants involved clearly and expand the numerator determinants as follows to get any credit: For variablex, expand along the first column; for variabley, expand along the second column; for variablez, expand along the third column. You will receive 0 points if you expand these determinants any other way, even if your answer is correct.−3x+0y−6z8x−2y+3z2x−y−4z=11=17=3
The values of the variables x, y, and z obtained by using Cramer's rule are 83/105, -277/105, and -99/105, respectively.
To find the values of the variables x, y, and z using Cramer's rule, we need to find the determinant of the coefficient matrix and the determinants of the matrices obtained by replacing the first, second, and third columns of the coefficient matrix with the constant terms.
The coefficient matrix is:
|−3 0 −6|
| 8 −2 3|
| 2 −1 −4|
The determinant of the coefficient matrix is:
|−3 0 −6| = (−3)(−2)(−4) − (0)(3)(2) − (−6)(8)(−1) − (−3)(−1)(3) − (0)(−4)(8) − (−6)(−2)(2)
= −24 − 0 − 48 − 9 − 0 − 24
= −105
The matrix obtained by replacing the first column with the constant terms is:
|11 0 −6|
|17 −2 3|
| 3 −1 −4|
The determinant of this matrix is:
|11 0 −6| = (11)(−2)(−4) − (0)(3)(3) − (−6)(17)(−1) − (11)(−1)(3) − (0)(−4)(17) − (−6)(−2)(3)
= 88 − 0 − 102 − 33 − 0 − 36
= −83
The matrix obtained by replacing the second column with the constant terms is:
|−3 11 −6|
| 8 17 3|
| 2 3 −4|
The determinant of this matrix is:
|−3 11 −6| = (−3)(17)(−4) − (11)(3)(2) − (−6)(8)(3) − (−3)(3)(3) − (11)(−4)(2) − (−6)(17)(2)
= 204 − 66 − 144 − 9 + 88 + 204
= 277
The matrix obtained by replacing the third column with the constant terms is:
|−3 0 11|
| 8 −2 17|
| 2 −1 3|
The determinant of this matrix is:
|−3 0 11| = (−3)(−2)(3) − (0)(17)(2) − (11)(8)(−1) − (−3)(−1)(17) − (0)(3)(8) − (11)(−2)(2)
= 18 − 0 + 88 − 51 − 0 + 44
= 99
Now we can use Cramer's rule to find the values of the variables x, y, and z:
x = (−83)/(-105) = 83/105
y = (277)/(-105) = -277/105
z = (99)/(-105) = -99/105
83/105, -277/105, and -99/105 are the values of x,y and z respectively.
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