compare Grant's account of the meeting the painting.Do you think they are consistent with each other?Why?
Answers
As seen in the attached picture, the account by Grant and the painting are consistent with each other since they both depict a serious and formal situation.
Who was Ulysses S. Grant?Ulysses S. Grant was an American general and statesman who served as the 18th President of the United States. He was born in 1822 in Ohio and graduated from the United States Military Academy at West Point in 1843. He served in the Mexican-American War and later became a leading Union general in the American Civil War.
As we compare his account of Lee's rendition and the painting provided, we can conclude that they are indeed consistent. Both show how serious and formal the meeting was. Grant even describes the way Lee was dressed, which is confirmed by the painting.
The picture and the account appear in the attachment below.
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Related Questions
Determine the value for c so that lim f(x) x -> 4 exists.
f(x) = 1/4x + c, for x < 4 f(x) = -x+6, for x>4 The value of c is ____
Answers
The value of c is 10.
The value of c is 10. To find this, use the limit definition of continuity. This states that for the function to be continuous at x = 4, we must have f(4) = lim f(x) x -> 4. Thus, we can equate f(4) and lim f(x) x -> 4 to get 1/4*4 + c = -4 + 6, giving c = 10.
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27. \( \left\{\begin{array}{c}x+y+z=-1 \\ 2 x+3 y+2 z=3 \\ 2 x+y+2 z=-7 \\ x-3 y+2 z=10 \\ -x+3 y-z=-6 \\ -x+3 y+2 z=6 \\ 6 x-2 y+2 z=4 \\ 3 x-y+2 z=2 \\ -12 x+4 y-8 z=8\end{array}\right. \)
Answers
Using the Gaussian elimination method, the general solution is: [tex]\[ x = -31t + 6 \][/tex], [tex]\[ y = 5 \][/tex], [tex]\[ z = 31t \][/tex].
To solve this system of equations, we can use the Gaussian elimination method. This method involves creating a matrix with the coefficients of the equations and using row operations to reduce the matrix to a form that can be easily solved.
First, we create a matrix with the coefficients of the equations:
[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 2 & 3 & 2 & 3 \\ 2 & 1 & 2 & -7 \\ 1 & -3 & 2 & 10 \\ -1 & 3 & -1 & -6 \\ -1 & 3 & 2 & 6 \\ 6 & -2 & 2 & 4 \\ 3 & -1 & 2 & 2 \\ -12 & 4 & -8 & 8 \end{array} \right) \][/tex]
Next, we use row operations to reduce the matrix to a form that can be easily solved:
[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 0 & 1 & 0 & 5 \\ 0 & -1 & 0 & -5 \\ 0 & -4 & 1 & 11 \\ 0 & 4 & 0 & -5 \\ 0 & 4 & 1 & 7 \\ 0 & -8 & -4 & 10 \\ 0 & -4 & -1 & 5 \\ 0 & 8 & 4 & -4 \end{array} \right) \][/tex]
[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 31 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 27 \\ 0 & 0 & -4 & 50 \\ 0 & 0 & -1 & 25 \\ 0 & 0 & 4 & -44 \end{array} \right) \][/tex]
[tex]\[ \left( \begin{array}{ccc|c} 1 & 0 & 1 & -6 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 1 & 31 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -4 \\ 0 & 0 & 0 & 174 \\ 0 & 0 & 0 & 56 \\ 0 & 0 & 0 & -168 \end{array} \right) \][/tex]
From this reduced matrix, we can see that there are infinitely many solutions to this system of equations. The general solution can be written as:
[tex]\[ x = -31t + 6 \][/tex]
[tex]\[ y = 5 \][/tex]
[tex]\[ z = 31t \][/tex]
Where t is any real number.
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Can someone help me out with the amount deprecating each year? I can’t figure it out.
9th grade algebra
Answers
Answer:
Year 1 Depreciation:$2,000
Depreciation Percentage:20.00%
Total Depreciation:$10,000
Final Year Depreciation:$2,000
Step-by-step explanation:
P.S by teacher told me the answer
Find the fourth proportion to 1 5/7, 2 3/14 and 3 3/5
Answers
The fourth proportion to 15/7,23/14, and 33/5 is 19.25.
To discover the fourth proportion, we require to set up a probability between the 3 presented figures and the fourth unknown variety, which we can name x.
23/1433/5 x
First, we need to transfigure all the mixed figures to unsuitable fragments
= (7/7 * 1)5/7 = 7/75/7 = 12/7
= (14/14 * 2)3/14 = 28/143/14 = 31/14
= (5/5 * 3)3/5 = 15/53/5 = 18/5
Now we're suitable to preference those values into the share
31/1418/5 x
To break for x, we're suitable to cross-multiply
12/7) * x = (31/14) *(18/5)
Simplifying
12x/ 7 = 279/14
Multiplying each aspects via7/12
x = (279/14) *(7/12)
x = 19.25
Thus, the fourth proportion to 15/7,23/14, and 33/5 is 19.25.
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Determine the critical numbers, if any, of the function
f
on the interval
[1,3]
.
f(x)=x 2
3−x
Give your answer as a comma-separated list. Express numbers in exact form. If the function does not have any critical numbers. enter DNE.
Answers
We are only interested in the critical numbers on the interval [1,3], so we can disregard x = 0. Therefore, the critical numbers of the function f(x) on the interval [1,3] are x = 3.
The critical numbers of a function are the points where the derivative of the function is either zero or undefined. To find the critical numbers of the given function f(x) = x^2/(3-x), we need to first find its derivative:
f'(x) = (2x(3-x) - (-1)x^2)/ (3-x)^2 = (6x - x^2 - x^2)/ (3-x)^2 = (6x - 2x^2)/ (3-x)^2
Now, we need to find the values of x for which f'(x) = 0 or f'(x) is undefined. f'(x) is undefined when the denominator (3-x)^2 is equal to 0, which occurs when x = 3. f'(x) is equal to 0 when the numerator 6x - 2x^2 is equal to 0:
6x - 2x^2 = 0
2x(3 - x) = 0
x = 0 or x = 3
However, we are only interested in the critical numbers on the interval [1,3], so we can disregard x = 0. Therefore, the critical numbers of the function f(x) on the interval [1,3] are x = 3.
Answer: 3
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Ah Lee Arithmetic Operations on Functions Feb 20, 8:50:52 PM Given that f(x)=x^(2)-6x-40 and g(x)=x+4, find f(x)-g(x) and express the result as a polynomial in simplest form.
Answers
To find f(x)-g(x), we need to subtract the two given functions.
f(x) = x^(2)-6x-40
g(x) = x+4
f(x)-g(x) = (x^(2)-6x-40) - (x+4)
Next, we need to distribute the negative sign to the terms inside the parentheses:
f(x)-g(x) = x^(2)-6x-40 - x - 4
Then, we can combine like terms: f(x)-g(x) = x^(2)-7x-44
Therefore, the result of f(x)-g(x) is a polynomial in simplest form: x^(2)-7x-44.
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5. About What percent of students said they like Cookie Cake?
How many students answered this survey over their favorite Cake?
Types of Cake
Cookie Cake
Chocolate Cake
Vanilla Cake
Marble Cake
Number of
students
5
6
8
Answers
6. 25 students
5. 20% of students said that they enjoy Cookie Cake.
6. 25 students answered a survey regarding their favorite cake.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The % formula is used to calculate a percentage of a whole in terms of 100.
Percentage = (Value/Total Value) × 100
Percentage of students said they like Cookie Cake:
5/(5 + 6 + 8 + 6) × 100%
5/25 × 100%
20%
The total number of students who answered this survey about their favorite Cake:
5 + 6 + 8 + 6
25
Thus, 25 students answered a survey regarding their favorite cake.
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Solve for the missing variables. Please show your work.
Answers
In the triangle ABC, the value of x, y and z is obtained as 21, 7 and 48 units respectively.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
A triangle ABC is given.
The measure of AB is given as 16 + z units.
The measure of AD is given as 16 units.
The measure of DB is given as z - 16 units.
The measure of BE is given as 21 units.
The measure of BC is given as x units.
The measure of AC is given as 14 units.
According to the midpoint theorem, the length of DE is -
DE = 1/2 (AC)
y = 1/2 (14)
y = 7 units
Therefore, the value of y is obtained as 7 units.
Now according to indirect measurement -
AB / AC = BD / DE
Substitute the values in the equation -
16 + z / 14 = z - 16 / 7
7(16 + z) = 14(z - 16)
112 + 7z = 14z - 224
7z - 14z = -224 - 112
-7z = -336
z = 48
Therefore, the value of z is obtained as 48 units.
Now according to indirect measurement -
BC / AC = BE / DE
Substitute the values in the equation -
21 + x / 14 = 21 / 7
7(21 + x) = 14 × 21
147 + 7x = 294
7x = 294 - 147
7x = 147
x = 21
Therefore, the value of x is obtained as 21 units.
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Answer:
x = 21
y = 7
z = 32
Step-by-step explanation:
DE = 1/2 (AC)
y = 1/2 (14)
y = 7
AB / AC = BD / DE
Substitute values
16 + z / 14 = z - 16 / 7
7(16 + z) = 14(z - 16)
112 + 7z = 14z - 224
7z - 14z = -224 - 112
-7z = -336
z = 32
BC / AC = BE / DE
Substitute values
21 + x / 14 = 21 / 7
7(21 + x) = 14 × 21
147 + 7x = 294
7x = 294 - 147
7x = 147
x = 21
In the above rectangle, what is the length of each of the longer sides of the perimeter is 36?
Answers
Answer:
Step-by-step explanation:
2(2x+2) + 2(x+4) = 36
4x+4 +2x+8 =36
6x+12= 36
6x = 36-12
6x =24
x = 4
longer side = 10
Line AB contains point A (-4, 1) and point B (-1, 3). Find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point
of dilation at the origin. (1 point)
OA (-8, 2) and B (-2, 6)
OA' (-8, 2) and B (2,-6)
OA (8,-2) and B (2,-6)
OA' (-5, -2) and B (-2, 6)
Answers
The coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin is: OA (-8, 2) and B (-2, 6)
What is the coordinates of A' and B'?To find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin, we can use the following formula:
A' = k * (A - O) + O
B' = k * (B - O) + O
where k is the scale factor, O is the center point of dilation, and A and B are the original points.
In this case, k = 2 and O = (0, 0). So we have:
A' = 2 * (-4, 1 - (0, 0)) + (0, 0) = (-8, 2)
B' = 2 * (-1, 3 - (0, 0)) + (0, 0) = (-2, 6)
Therefore, the coordinates of A' and B' after the dilation are (-8, 2) and (-2, 6), respectively.
So, the answer is option (A) OA (-8, 2) and B (-2, 6).
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A rectangle is 45 cm long and 15 cm wide. What's the ratio of the rectangle's length to its width? A 1:3. B 3:1. C 1:4. D 4:1
Answers
Answer:
Area of a triangle =L*W
A= 45*15
A=270cm²
I WILL GIVE BRAINLIEST TO WHOEVER ANSWER ALL 3 QUESTIONS RIGHT AND MANY POINTS I BEG PLEASE
In theory think about how many sides are on a dice and the numbers that are shown on each side.
it is a six sided dice
In an experiment the dice is rolled 20 times and lands on 1 two times and on 5 four times.
Find each experimental and theoretical probability.
a) landing on 5
Experimental:
Theoretical
b) not landing on 1
Experimental:
Theoretical:
c) landing on 1
Experimental:
Theoretical:
(please help)
Answers
Answer:
c landing on 1 is the answer
hope it helps u mark me BRAINLIST
Big ideas 7.5 question
Answers
Answer:
66.5
Step-by-step explanation:
average the 2 together (57+76)/2
Zeke is building an outdoor rabbit pen in the shape of a square. He places a post of the pen at (2.5, 2.5). What is the location of the corner that reflects (2.5, 2.5) across the y-axis? Express your answer using decimal notation.
Answers
The location of the corner of the rabbit pen that reflects (2.5, 2.5) across the y-axis is (-2.5, 2.5).
What is coordinate plane?The coordinate plane, also called the Cartesian plane, is a two-dimensional grid used to locate points in space. It consists of two perpendicular number lines, one horizontal and one vertical, that intersect at their zero points, called the origin.
Points on the coordinate plane are identified by their coordinates, which are written as ordered pairs of numbers (x, y), where x is the horizontal coordinate and y is the vertical coordinate.
To solve this problem, we need to reflect the point (2.5, 2.5) across the y-axis. When we reflect a point across the y-axis, we keep the y-coordinate the same but change the sign of the x-coordinate.
So, the reflected point will have the same y-coordinate of 2.5, but the x-coordinate will be -2.5. Therefore, the location of the corner of the rabbit pen that reflects (2.5, 2.5) across the y-axis is (-2.5, 2.5).
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find the equation and then find the ordered pair please!
Answers
Note that the pair of numbers that solves the system of equations:
y=11x+40; and
y= -7x+9
are, x = -31/18 ; and y = 379/18.
What is the rationale for the above response?
To solve the system of equations, we need to find the values of x and y that satisfy both equations simultaneously. One way to do this is to set the expressions for y equal to each other, since both expressions represent the same value of y.
So we have:
11x + 40 = -7x + 9
Simplifying and solving for x, we get:
18x = -31
x = -31/18
Now that we have found the value of x, we can substitute it into either equation to find the corresponding value of y. Let's use the first equation:
y = 11(-31/18) + 40
y = -341/18 + 720/18
y = 379/18
Therefore, the pair of numbers that solves the system of equations is (-31/18, 379/18).
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Susan opens a savings account with $900. She earned $54 in 1.5 years. What is the annual interest rate?
Answers
The annual interest rate on Susan's savings account is 4%.
What is the annual interest rate on Susan account?Annual interest rate, also known as annual percentage rate is the yearly interest generated by a sum that's charged to borrowers or paid to investors We can use the simple interest formula to calculate the annual interest rate which is Simple Interest = (Principal x Rate x Time)
By plugging our values, we get.
$54 = ($900 x Rate x 1.5)
Simplifying the equation:
Rate = $54 / ($900 x 1.5)
Rate = 0.04
Rate = 4%.
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5 out of the 10 employees at the water slides are temporary employees. What percentage of the employees at the water slides are temporary?
Write your answer using a percent sign (%).
Answers
Answer: 50%
Step-by-step explanation: There are 5 out of 10 employees at the water slide. 10 in this situation is going to be 100%
since there is only 5 out of 10 employees that are temporary
it would be 50%
Answer: 50%
Step-by-step explanation:
Two ladders are places at different locations on a coconut palm tree so that lights can be
installed, as pictured below. The length of the taller ladder is three times the length of the shorter ladder. The shorter ladder is placed 3.5 feet from the base of the tree while the taller ladder is placed 7.5 feet from the base of the tree. What is the distance on the tree between the two ladders?
Answers
Therefore, [tex]h = \sqrt{(12.25 - x^2)} = 3.73[/tex] feet represents the distance between the two staircases on the tree. Thus, option c is correct.
what is Pythagoras theorem ?The Pythagorean theorem states that the square length of the hypotenuse, or the side that faces the right angle, of a right triangle is equal to the sum of the square lengths of the other two sides. The following can be expressed mathematically: [tex]a^2 + b^2 = c^2[/tex] where "c" represents the length of the hypotenuse and "a" and "b" represent the measurements of the two sides of the right triangle.
given
Assume the tree is h feet tall, the higher ladder is 3 feet long, and the lower ladder is x feet long.
Using the Pythagorean formula, we can create two equations:
With regard to the narrower staircase, x² + h² = (3.5)
Use the formula for the higher ladder. (3x)²+ h²= (7.5)².
The formulas are as follows, simplified: 12.25 x² + 9.25 x² + 56.25
To remove h2, we can solve for x in the first equation and y in the second equation: 8x² = 44.
Finding the value of x is as follows: [tex]x = \sqrt{(5.5) } = 2.34[/tex]
Therefore, [tex]h = \sqrt{(12.25 - x^2)} = 3.73[/tex] feet represents the distance between the two staircases on the tree.
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Complete question:
Two ladders are placed at different locations on a coconut palm tree so that lights can be installed, as pictured below. The length of the taller ladder is three times the length of the shorter ladder. The shorter ladder is placed 3.5 feet from the base of the tree while the taller ladder is placed 7.5 feet from the base of the tree. What is the distance on the tree between the two ladders?
O 4.59 feet
O 9.78 feet
O 3.73 feet
O 8.96 feet
At Frome International train station, 35% of trains were late in a week.
! In that week there were 440 trains.
! Calculate how many trains were on time. My
Answers
Answer:
Step-by-step eEIKxplanation:
What is the area of the following circle?
Either enter an exact answer in terms of
�
πpi or use
3.14
3.143, point, 14 for
�
πpi and enter your answer as a decimal.
Answers
The area of the following circle is A ≈ 153.86 square units.
Describe Circle?A circle is a two-dimensional geometric shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter.
The circumference of a circle is the distance around the edge of the circle, and it is calculated using the formula C = 2πr, where r is the radius and π (pi) is a mathematical constant approximately equal to 3.14159. The area of a circle is the region enclosed by the circle, and it is calculated using the formula A = πr².
The diameter of the circle is 14, so the radius is half of that, which is 7.
The area of the circle is given by the formula A = πr², where r is the radius. Substituting in the values we get:
A = π(7)²
A = 49π
Therefore, the area of the circle is 49π square units. If you want to use an approximation, you can use 3.14 as an estimate for π and get:
A ≈ 153.86 square units.
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The complete question is -
44+1 44+2 44+3 which table represents inputs and
outputs that follow the same rule
Answers
Table that represent input & output value would be:
Input Output
44 45
45 46
46 47
To determine which table represents inputs and outputs that follow the same rule as 44+1, 44+2, and 44+3, we can simply evaluate each of the expressions and look for a pattern.
44 + 1 = 45
44 + 2 = 46
44 + 3 = 47
Therefore, the rule appears to be adding 1 to each subsequent number. We can check this by evaluating additional terms:
44 + 4 = 48
44 + 5 = 49
Based on this pattern, the correct table would be:
Input Output
44 45
45 46
46 47
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(1×1,000)+(3×100)+(5×10)+(9×
10
1
)+(8×
100
1
)left parenthesis, 1, times, 1, comma, 000, right parenthesis, plus, left parenthesis, 3, times, 100, right parenthesis, plus, left parenthesis, 5, times, 10, right parenthesis, plus, left parenthesis, 9, times, start fraction, 1, divided by, 10, end fraction, right parenthesis, plus, left parenthesis, 8, times, start fraction, 1, divided by, 100, end fraction, right parenthesis
Answers
The value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100) is 1,350.98.
To find the value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100), we need to simplify and perform the arithmetic operations.
Multiplying each term in the expression, we get:
1 × 1,000 = 1,000
3 × 100 = 300
5 × 10 = 50
9 × 1/10 = 0.9
8 × 1/100 = 0.08
Adding up all the terms, we get:
1,000 + 300 + 50 + 0.9 + 0.08 = 1,350.98
In summary, to find the value of the expression, we multiply each term by its respective coefficient, then add up all the terms. In this case, the result is 1,350.98.
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Complete question is:
Find the value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100)?
Module 06: Project Option 1
You guys got me on this right I need this done by 4:30 pm tomorrow please help me the assignment is below
Answers
An expression that looks like Sarah's expression but is not equivalent is:
10(5j + j + 3).
What can you say about expressions?A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Let's examine the writing style of expressions. A number is 6 times larger than the other number, x, by a factor of 2. This statement is represented mathematically by the expression x/2 + 6. Using mathematical expressions, complex puzzles can be solved.
now in the question,
We can write a look alike expression which is not equivalent is:
10(5j + j + 3).
Now translating the new expression into verbal:
Sarah gets paid $10 for every shark tooth she finds. After finding 3, she asked Jhon for help. When Jhon finds a tooth, by that time Sarah finds 5 of them.
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. Ricardo is measuring the height of a plant. The starting height of the plant was 3 centimeters. He then took measurements once a week and found an average growth of 0.5 cm per week. Write an equation that describes the plant's height, y, after x weeks.
Answers
The equation that describes the plant's height is y = 3 + 0.5x .
What is the equation that describes the plant's height?The equation that describes the plant's height is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.
The general form of a linear equation is:
y = mx + c
Where:
m = slope
c = intercept
Plant's height = starting height + (rate of growth x number of weeks)
y = 3 + (0.5 x x)
y = 3 + 0.5x
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-12 Correct answer=Brainly
Answers
If g(v)=11v^(4)+29v^(3)+19v^(2)+22v+39, use synthetic division to find g(-2). Submit
Answers
The answer is g(-2) = 15.
To find g(-2) using synthetic division, we need to follow these steps:
Write down the coefficients of the polynomial in descending order. The coefficients are 11, 29, 19, 22, and 39.
Write down the value of the divisor in the leftmost column. In this case, the divisor is -2.
Bring down the first coefficient (11) to the bottom row.
Multiply the bottom row value (11) by the divisor (-2) and write the result (-22) in the next column.
Add the coefficient in that column (29) to the result (-22) and write the sum (7) in the bottom row.
Repeat steps 4 and 5 until you reach the last column. The final result in the bottom row is the remainder.
The synthetic division should look like this:
-2 | 11 29 19 22 39
| -22 -14 -10 -24
-------------------
11 7 9 12 15
Therefore, g(-2) = 15.
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What is the area of the shaded part of the following composite figure? Round your answer to the nearest whole. I NEED THIS LIKE YESTERDAY PLEASE HELP.
Answers
The area of the dark region is 164.15 square feet because it is equal to the sum of the areas of the circles and rectangles.
what is circle ?In geometry, a circle is a closed object made up of all the points in a plane that are equally spaced from the circle's centre. The radius and diameter of a circle are measured from the centre to any spot on the circle, respectively. The circumference, which is equivalent to pi times the diameter, is the distance around the circle.
given
[tex]area of circle = π * r * r[/tex]
= 22/7 * 2 * 2 = 88/7 ft2
area of rectangle = length * breadth
= 9.4 * 18.8
= 176.72 ft2
area of shaded region
176.72 - 12.57
= 164.15 ft 2
The area of the dark region is 164.15 square feet because it is equal to the sum of the areas of the circles and rectangles.
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What is E(Y | X<=1/2) ?
expectation of Y given that X is less than or equal half
Answers
The conditional expectation of Y given that X is less than or equal to 1/2 is calculated by taking the weighted average of the possible values of Y, with the weights being the probabilities of X being less than or equal to 1/2 for each value of Y.
The formula for E(Y | X<=1/2) is:
E(Y | X<=1/2) = ∑y P(Y=y | X<=1/2) * y
To find P(Y=y | X<=1/2), we can use the formula:
P(Y=y | X<=1/2) = P(X<=1/2 | Y=y) * P(Y=y) / P(X<=1/2)
We can then plug in the values for each possible value of Y and calculate the conditional expectation.
For example, if Y can take on the values 0, 1, and 2, and the probabilities of X being less than or equal to 1/2 for each value of Y are 0.2, 0.5, and 0.3, respectively, and the probabilities of Y being 0, 1, and 2 are 0.4, 0.3, and 0.3, respectively, then:
E(Y | X<=1/2) = (0.2 * 0.4 / 0.5) * 0 + (0.5 * 0.3 / 0.5) * 1 + (0.3 * 0.3 / 0.5) * 2
E(Y | X<=1/2) = 0 + 0.3 + 0.36
E(Y | X<=1/2) = 0.66
Therefore, the conditional expectation of Y given that X is less than or equal to 1/2 is 0.66.
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 20
Blue 9
Green 19
Yellow 14
Purple 14
Based on these results, express the probability that the next spin will land on red or green or purple as a decimal to the nearest hundredth.
Answers
The spinner probability that the next spin will land either red or green or purple is found 0.70 as a decimal to the nearest hundredth.
Explain about the probability in spinner?The possibility or likelihood that a spinner could land on a specific value when spun is known as spinner probability. The spinner probability, for instance, would be 1/10, or 10%, if there were a spinner with 10 separate parts and you wanted to know the chance of landing on just one of them.Spinner Results
Color Frequency
Red 20
Blue 9
Green 19
Yellow 14
Purple 14
Total outcomes: 20 + 9 + 19 + 14 + 14
Total outcomes: 76
spinner probability = favorable outcome / total outcome
favorable outcome (red or green or purple) = 20 + 19 + 14 = 53
spinner probability = 53 / 76 = 0.69
spinner probability = 0.70
Thus, the probability that the next spin will land either red or green or purple is found 0.70 as a decimal to the nearest hundredth.
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VIII. Determine whether the vectors u = (2,1,0) v = (-4,3,1), and w=(0,-2,-5) are linearly dependent or linearly independent
Answers
The vectors are linearly independent.
The vectors u = (2,1,0), v = (-4,3,1), and w=(0,-2,-5) are linearly dependent if there exists scalars c1, c2, and c3 such that c1u + c2v + c3w = 0. To determine if this is the case, we can form a matrix with the vectors as columns and find its determinant. If the determinant is 0, then the vectors are linearly dependent. If the determinant is not 0, then the vectors are linearly independent.
The matrix formed by the vectors is:
```
| 2 -4 0 |
| 1 3 -2|
| 0 1 -5|
```
The determinant of this matrix is:
```
2(3(-5) - (-2)(1)) - (-4)(1(-5) - (0)(-2)) + 0(1(1) - (0)(3))
= 2(-15 + 2) + 4(5) + 0
= 2(-13) + 20 + 0
= -26 + 20
= -6
```
Since the determinant is not 0, the vectors are linearly independent.
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