One possible solution is c1 = 1, c2 = -2, and c3 = 1, which gives us the linear dependence relation A1 - 2A2 + A3 = 0.
A= [ 1 1 1] [ 1 2 3] [ 4 5 6] and v = [ 2 ] [ 3 ] [ -1]. To find the image of v under TA, we simply multiply A and v to get:
TA = [ 1 1 1] [ 2 ] = [ 4 ]
[ 1 2 3] [ 3 ] [ 7 ]
[ 4 5 6] [ -1] [ 17 ]
So the image of v under TA is [ 4 7 17 ].
To find vectors w that are different from v but that get mapped to the same image, we can use the equation TA*w = TA*v. Since TA*v = [ 4 7 17 ], we can set up the following system of equations:
1w1 + 1w2 + 1w3 = 4
1w1 + 2w2 + 3w3 = 7
4w1 + 5w2 + 6w3 = 17
Solving this system of equations will give us all the possible vectors w that get mapped to the same image as v. One possible solution is w = [ 1 2 0 ], which is different from v but gets mapped to the same image.
To find all vectors z that get mapped to zero, we can use the equation TA*z = 0. This gives us the following system of equations:
1z1 + 1z2 + 1z3 = 0
1z1 + 2z2 + 3z3 = 0
4z1 + 5z2 + 6z3 = 0
Solving this system of equations will give us all the possible vectors z that get mapped to zero. One possible solution is z = [ -3 2 1 ], which gets mapped to zero under TA.
Finally, to write down a nontrivial linear dependence relation between the columns of A, we can use the equation c1*A1 + c2*A2 + c3*A3 = 0, where A1, A2, and A3 are the columns of A and c1, c2, and c3 are constants. One possible solution is c1 = 1, c2 = -2, and c3 = 1, which gives us the linear dependence relation A1 - 2A2 + A3 = 0.
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helppp pls is urgent
The value of x, considering the angle addition postulate, is given as follows:
x = -5.
What does the angle addition postulate state?The angle addition postulate states that if two angles share a common vertex and a common angle, forming a combination, the larger angle will be given by the sum of the smaller angles.
The larger angle in this problem is QRS, hence the equation to obtain the value of x is given as follows:
3x + 93 + 66 + x = -x + 134
4x + 159 = -x + 134
5x = -25
x = -25/5
x = -5.
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The heart of a black bear beats about 50 times per minute during normal sleep in the fall. When the animal hibernates in winter, its heart rate decrease by 84%. How many times per minute does a black bear’s heart beat during hibernation? Answer fast pls
Answer: 8 times per minute
Step-by-step explanation: 50 (1-84%) = 8
Amy is attending a school orchestra concert.she sees her math teacher seated 10 meters ahead of her and her science teacher seated 24 meters to her right.How far apart are the two teachers?
Answer:
The two teachers are 26 meters apart. To calculate this, you can use the Pythagorean Theorem, which states that the distance between two points is equal to the square root of the sum of the squares of the differences between the coordinates of the two points. In this case, the coordinates of the math teacher are (10, 0) and the coordinates of the science teacher are (0, 24), so the distance between them is the square root of [(10-0)^2 + (0-24)^2] = √(100 + 576) = √676 = 26 meters.
We can use the Pythagorean theorem to solve this problem. Let's draw a diagram:
A (Amy)
/|
/ |
/ |10 meters
/ |
/____|
B C (science teacher)
We have a right triangle ABC, where AB = 10 meters and BC = 24 meters. We want to find the length of AC, which is the distance between the two teachers.
Using the Pythagorean theorem:
AC^2 = AB^2 + BC^2
AC^2 = 10^2 + 24^2
AC^2 = 676
AC = sqrt(676)
AC = 26 meters
Therefore, the two teachers are 26 meters apart.
Solve the following system of linear inequalities: \[ \begin{array}{l} -2 x-y1 \end{array} \]
To solve the system of linear inequalities, we need to graph each inequality and find the region that satisfies both inequalities.
Here are the steps:
1. Graph the first inequality: -2x-y1. We can rearrange the equation to get y>-2x-1. This means that the region above the line y=-2x-1 is the solution to the first inequality.
2. Graph the second inequality: 3x+y<6. We can rearrange the equation to get y<-3x+6. This means that the region below the line y=-3x+6 is the solution to the second inequality.
3. The solution to the system of inequalities is the region that satisfies both inequalities. This is the region above the line y=-2x-1 and below the line y=-3x+6.
4. To find the coordinates of the vertices of the solution region, we can find the intersection point of the two lines. Setting the two equations equal to each other, we get: -2x-1=-3x+6. Solving for x, we get x=7. Substituting x=7 into one of the equations, we get y=-3(7)+6=-15. So the intersection point is (7,-15).
5. The solution region is the triangular region with vertices at (7,-15), (0,-1), and (2,0).
Therefore, the solution to the system of linear inequalities is the region with vertices at (7,-15), (0,-1), and (2,0).
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If x-y=-7 and 4x+5y=-19, which equation can be used to find the value of x ? A. 4x+5(x-7)=-19 B. 4x+5(7-x)=-19 C. 4x+5(-7-x)=-19 D. 4x+5(x+7)=-19
If x-y=-7 and 4x+5y=-19, 4x+5(x+7)=-19. equation can be used to find the value of x. The correct answer is D. 4x+5(x+7)=-19.
This equation can be used to find the value of x because it is a system of equations in two variables, x and y.
To solve this system of equations, first, isolate the x variable on one side of the equation.
This can be done by adding 7 to both sides of the equation x-y=-7.
This will result in the equation x=-7+y.
Then, substitute this equation into 4x+5y=-19 and simplify.
This will result in the equation 4(-7+y)+5y=-19, which can be simplified to 4x+5(x+7)=-19.
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What would we do next to solve for b
Answer: You have to simplify divide by x
Step-by-step explanation:
Tyler took out a five-year loan with a principal of $12,000. He made monthly payments of $215 for the entire period, at which point the loan was paid off. How much did Tyler pay in interest?
Responses
$15
$60
$75
$900
Answer:
D, $900
Step-by-step explanation:
and monthly payments of $215, we can use the following formula:
Total interest = Total amount paid - Principal
where:
Total amount paid = Monthly payment x Number of payments
Number of payments = Number of years x 12
In this case, Tyler made monthly payments of $215 for 5 years, which is a total of 5 x 12 = 60 payments.
Substituting these values into the formula, we get:
Total amount paid = $215 x 60 = $12,900
Total interest = $12,900 - $12,000 = $900
Therefore, Tyler paid $900 in interest over the five-year period. The answer is option D: $900.
Destiny Rubio Definite Integrals of Rational Functions Feb 23, 11:55:41 AM Find the average value of the function f(x)=(12)/(x-10) from x=1 to x=7. Express your answer as a constant times ln3. Answer: ln3 Submit Answer
The Average value of the function f(x)=(12)/(x-10) from x=1 to x=7 -2 ln3.
The average value of a function f(x) over the interval [a,b] is given by the formula:
Average value = (1/(b-a)) ∫[a,b] f(x) dx
In this case, the function is f(x) = (12)/(x-10), the interval is [1,7], and we need to find the average value. Plugging in the values into the formula, we get:
Average value = (1/(7-1)) ∫[1,7] (12)/(x-10) dx
Average value = (1/6) ∫[1,7] (12)/(x-10) dx
Next, we need to find the integral of the function. We can use the formula for the integral of a rational function:
∫ (a)/(x-b) dx = a ln|x-b| + C
In this case, a = 12 and b = 10, so the integral of the function is:
∫ (12)/(x-10) dx = 12 ln|x-10| + C
Plugging this back into the formula for the average value, we get:
Average value = (1/6) (12 ln|7-10| - 12 ln|1-10|)
Average value = (1/6) (12 ln|-3| - 12 ln|-9|)
Average value = (1/6) (12 ln|3| - 12 ln|3^2|)
Average value = (1/6) (12 ln|3| - 12 (2 ln|3|))
Average value = (1/6) (12 ln|3| - 24 ln|3|)
Average value = (1/6) (-12 ln|3|)
Average value = -2 ln|3|
Therefore, the average value of the function f(x) = (12)/(x-10) from x = 1 to x = 7 is -2 ln|3|. We can express this as a constant times ln3 by factoring out the ln3:
Average value = -2 ln|3| = -2 ln3
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Concrete tiles are made using buckets of cement,sand and gravel mixed into the ratio of 1:4:6. How many buckets of gravel are needed for 4 bucket of cement?
24 buckets of gravel are needed for 4 buckets of cement when making concrete tiles using the given ratio.
What is the ratio?
The ratio is a mathematical concept that represents the relationship between two quantities or values. It is defined as the comparison of two numbers by division, where the first number is called the "antecedent" and the second number is called the "consequent."
According to the given ratio, the amount of gravel needed is 6 times the amount of cement, or 6/1.
To find out how many buckets of gravel are needed for 4 buckets of cement, we can set up a proportion:
6/1 = x/4
where x is the number of buckets of gravel needed.
To solve for x, we can cross-multiply:
6 x 4 = 1 x x
24 = x
Hence, 24 buckets of gravel are needed for 4 buckets of cement when making concrete tiles using the given ratio.
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what is the solution for x if -4x + 6 > 10
Answer: x < -1
Step-by-step explanation:
-4x + 6 > 10
-4x > 10 - 6
-4x > 4
x < 4/-4
x < -1
Answer:
[tex]\tt x > -1[/tex]Step-by-step explanation:
[tex]\tt -4x + 6 > 10[/tex]
Subtract 6 from both sides:-
[tex]\tt -4x + 6 -6 > 10-6[/tex][tex]\tt -4x > 4[/tex]Divide both sides by -4:-
[tex]\tt \cfrac{-4x}{4} > \cfrac{4}{-4}[/tex][tex]\tt x > -1[/tex]________________________
Hope this helps! :)
if (5x-1)/(2)can be written in the equivalent form (3x-6)/(3), what is the value of (5-x)/(2)
The value of [tex](5 - x)/(2)[/tex] is [tex]2[/tex] when[tex](5x - 1)/(2)[/tex] is equivalent to [tex](3x - 6)/(3)[/tex].
The given expression is [tex](5x - 1)/(2)[/tex] and it can be written in the equivalent form [tex](3x - 6)/(3)[/tex].
To find the value of [tex](5 - x)/(2)[/tex], we can use the property of equivalent fractions, which states that if two fractions are equivalent, then the cross products are equal.
So, we can cross multiply the given equivalent fractions to get:
[tex](5x - 1)(3) = (3x - 6)(2)[/tex]
Simplifying the equation, we get:
[tex]15x - 3 = 6x - 12[/tex]
[tex]9x = 9[/tex]
[tex]x = 1[/tex]
Now, we can substitute the value of x into the expression [tex](5 - x)/(2)[/tex] to find the value of the expression:
[tex](5 - 1)/(2) = 4/2 = 2[/tex]
Therefore, the value of [tex](5 - x)/(2)[/tex] is 2 when [tex](5x - 1)/(2)[/tex] is equivalent to [tex](3x - 6)/(3)[/tex].
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Determine the equation of the circle whose center is (-1, -1) and passes through the point (7, -7). a. (2 + 1)2 + (y + 1)2 = 100 b. (x + 1)2 + (y + 1)2 = 10 c. (+1)2 + (y+ 1)2 = √10 d. (2-7)2 + (y + 7)2 = √10
Answer:
its i think algebraic equation
The equation of the circle whose center is (-1, -1) and passes through the point (7, -7) is (x + 1)2 + (y + 1)2 = 100. This can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is √((x2 - x1)2 + (y2 - y1)2). In this case, the distance between the center and the point on the circle is the radius of the circle. So, we can plug in the values for the center and the point on the circle to find the radius:√((7 - (-1))2 + (-7 - (-1))2) = √((7 + 1)2 + (-7 + 1)2) = √(82 + (-6)2) = √(64 + 36) = √100 = 10Therefore, the radius of the circle is 10. Now, we can use the general equation of a circle, (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is the radius, to find the equation of the circle. Plugging in the values for the center and the radius, we get:(x - (-1))2 + (y - (-1))2 = 102(x + 1)2 + (y + 1)2 = 100So, the equation of the circle is (x + 1)2 + (y + 1)2 = 100, which is option a.
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what’s the answer of this
The slope is 3. After 1 second, the car's distance increases by 7 feet.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided, we have the following equation that represents the relationship between distance and time;
y = 3x + 4
At x = 1 second, the distance is given by;
y = 3(1) + 4
y = 3 + 4
y = 7 feet.
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Calculate the mean: 13, 21, 45, 62, 10
Answer:30.2
Step-by-step explanation:
Answer:
30.2Calculate the mean: 13, 21, 45, 62, 10
13 + 21 + 45 + 62 + 10
= 151151 ÷ 5
= 30.2
Step-by-step explanation:
You're welcome.
A garden measuring 8 feet by 12 feet will have a walkway around it. The walkway has a uniform width, and the the area covered by the garden and the walkway is 192 square feet what is the width of the walkway?
The width of the walkway is approximately 0.343 feet or about 4.12 inches.
Let's suppose that the pathway is x feet wide.
The total length of the garden with the walkway is 8 + 2x feet (since there is a walkway on both sides of the garden), and the total width of the garden with the walkway is 12 + 2x feet.
The area covered by the garden and the walkway is the product of the length and width, which is:
[tex](8 + 2x) \times (12 + 2x) = 192[/tex]
Expanding this equation, we get:
[tex]96 + 32x + 16x + 4x^2 = 192\\4x^2 + 48x - 96 = 0[/tex]
Dividing both sides by 4, we get:
[tex]x^2 + 12x - 24 = 0[/tex]
Using the quadratic formula, we get:
x = (-12 ± [tex]\sqrt{ (12^2 - 41(-24))) / (2\times1}[/tex])
x = (-12 ±[tex]\sqrt{(288)) / 2}[/tex])
x = (-12 ± [tex]12\sqrt{(2)) / 2}[/tex]
x = -6 ± [tex]6\sqrt{(2)}[/tex]
Since the width of the walkway cannot be negative, we take the positive value of x:
[tex]x = -6 + 6\sqrt{(2)} \\x= 0.343 feet[/tex]
Therefore, the width of the walkway is approximately 0.343 feet or about 4.12 inches.
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For a certain 2-year polytechnic school, studies by the registry show that the probability of a randomly selected first-year student returning for a second year is 0.54. Assume that 8 first-year students are randomly selected.
Create a probability distribution showing the possible outcomes and corresponding probabilities.
Compute and interpret P(X≤3).
Compute the expected number from many trials of randomly selected groups of 8 freshmen that return for the second year.
Compute the standard deviation.
The Student Services Department randomly selected 8 freshmen and met with them for two one-on-one advising sessions during the freshmen year. Of the 8 students who participated, 7 returned for the second year. Can you consider the advising program a success?
The probability distribution for the possible outcomes can be created using the binomial distribution formula:
P(X=x) = (n choose x) * p^x * (1-p)^(n-x)
Where n is the number of trials (in this case, 8), x is the number of successes (returning for a second year), p is the probability of success (0.54), and 1-p is the probability of failure.
The probability distribution is as follows:
| X | P(X) |
|---|------|
| 0 | 0.010 |
| 1 | 0.059 |
| 2 | 0.167 |
| 3 | 0.282 |
| 4 | 0.313 |
| 5 | 0.223 |
| 6 | 0.106 |
| 7 | 0.033 |
| 8 | 0.005 |
To compute P(X≤3), we add the probabilities for X=0, X=1, X=2, and X=3:
P(X≤3) = 0.010 + 0.059 + 0.167 + 0.282 = 0.518
This means that there is a 51.8% chance that 3 or fewer of the randomly selected first-year students will return for a second year.
The expected number of students returning for a second year can be calculated using the formula:
E(X) = n * p = 8 * 0.54 = 4.32
This means that on average, 4.32 of the randomly selected first-year students will return for a second year.
The standard deviation can be calculated using the formula:
σ = √(n * p * (1-p)) = √(8 * 0.54 * 0.46) = 1.39
Finally, to determine if the advising program was a success, we can compare the observed number of students returning (7) to the expected number (4.32). Since 7 is greater than 4.32, it appears that the advising program may have had a positive effect on the students' decision to return for a second year. However, further analysis would be needed to determine if this difference is statistically significant.
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Write
tanz
in terms of
secz
using the Pythagorean Identity for: Part: 0 / 2 Part 1 of 2 (a)
z
in Quadrant II.
tanz=
Part:
1/2
Part 2 of 2 (b)
z
in Quadrant IV.
We can write tanz in terms of secz using the Pythagorean Identity as:
tanz = -sqrt(sec^2z - 1)
Part 1 of 2:
The Pythagorean Identity states that sin^2z + cos^2z = 1. We can use this identity to write tan^2z in terms of sec^2z.
First, let's rearrange the Pythagorean Identity to isolate cos^2z:
cos^2z = 1 - sin^2z
Next, we can divide both sides of the equation by cos^2z to get:
1 = sec^2z - (sin^2z)/(cos^2z)
Since tan^2z = (sin^2z)/(cos^2z), we can substitute this into the equation:
1 = sec^2z - tan^2z
Finally, we can rearrange the equation to isolate tan^2z:
tan^2z = sec^2z - 1
Now, let's consider the case when z is in Quadrant II. In this quadrant, tanz is negative and secz is negative. Therefore, we can write:
tanz = -sqrt(sec^2z - 1)
Part 2 of 2:
In the case when z is in Quadrant IV, tanz is negative and secz is positive. Therefore, we can write:
tanz = -sqrt(sec^2z - 1)
So, in both cases, we can write tanz in terms of secz using the Pythagorean Identity as:
tanz = -sqrt(sec^2z - 1)
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1. Let the point \( P \) be \( (-1,3) \) and the point \( Q \) be \( (3,7) \). Find the following. a. \( \mathbf{v}=\overrightarrow{P Q} \) b. \( \|\mathbf{v}\| \) c. \( \overrightarrow{P Q}+\overrigh
The answers are:
a. \( \mathbf{v}=\overrightarrow{P Q} = (4, 4) \)
b. \( \|\mathbf{v}\| = 4\sqrt{2} \)
c. \( \overrightarrow{P Q}+\overrightarrow{Q P} = (0, 0) \)
The given points are point \( P \) be \( (-1,3) \) and point \( Q \) be \( (3,7) \).
a. To find \( \mathbf{v}=\overrightarrow{P Q} \), we subtract the coordinates of point \( P \) from the coordinates of point \( Q \):
\( \mathbf{v}=\overrightarrow{P Q} = (3-(-1), 7-3) = (4, 4) \)
b. To find \( \|\mathbf{v}\| \), we use the distance formula:
\( \|\mathbf{v}\| = \sqrt{(4-0)^2 + (4-0)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \)
c. To find \( \overrightarrow{P Q}+\overrightarrow{Q P} \), we add the coordinates of \( \overrightarrow{P Q} \) and \( \overrightarrow{Q P} \):
\( \overrightarrow{P Q}+\overrightarrow{Q P} = (4, 4) + (-4, -4) = (0, 0) \)
Therefore, the answers are:
a. \( \mathbf{v}=\overrightarrow{P Q} = (4, 4) \)
b. \( \|\mathbf{v}\| = 4\sqrt{2} \)
c. \( \overrightarrow{P Q}+\overrightarrow{Q P} = (0, 0) \)
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Math part 2 question 4
Answer:
[tex]\dfrac{x}{x + 1}\\\\\text{which is the first answer choice }[/tex]
Step-by-step explanation:
We are given
[tex]f(x) = x^2 - x\\g(x) = x^2 - 1\\\\\text{and we are asked to find $ \left(\dfrac{f}{g}\right)\left(x\right)$}[/tex]
[tex]\left(\dfrac{f}{g}\right)\left(x\right) = \dfrac{f(x)}{g(x)}\\\\\\= \dfrac{x^2-x}{x^2 - 1}[/tex]
[tex]x^2 - x = x(x - 1)\text{ by factoring out x}\\\\x&2 - 1 = (x + 1)(x - 1) \text{ using the relation $a^2 - b^2 = (a + 1)(a - 1)$}[/tex]
Therefore,
[tex]\dfrac{x^2-x}{x^2 - 1} = \dfrac{x(x-1)}{(x + 1)(x - 1)}[/tex]
x - 1 cancels out from numerator and denominator with the result
[tex]\dfrac{x}{x+1}[/tex]
So
[tex]\left(\dfrac{f}{g}\right)\left(x\right)$} = \dfrac{x}{x + 1}[/tex]
Determine if the given function is linear, quadratic, or exponential.
f(x) = 5 (2.3)^x
The given function f(x) = 5 (2.3)^x is an exponential function.
The given function is f(x) = 5 (2.3)^x.
To determine if the function is linear, quadratic, or exponential, we need to examine the form of the function.
A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept.
A quadratic function has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
An exponential function has the form f(x) = ab^x, where a and b are constants.
The given function, f(x) = 5 (2.3)^x, is in the form of an exponential function, with a = 5 and b = 2.3. Therefore, the function is exponential.
In conclusion, the given function f(x) = 5 (2.3)^x is an exponential function.
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A jar contains 54 coins consisting of quarters and dimes. The total value of the coins is $16.85. Which system of equations can be used to determine the number of quarters, q, and the number of dimes, d, in the
jar?
Answer:
Let q be the number of quarters in the jar and d be the number of dimes in the jar.
The total number of coins in the jar is given as 54, so we can write:
q + d = 54
The total value of the coins is $16.85. We can express this as the sum of the values of the quarters and the dimes in the jar:
0.25q + 0.10d = 16.85
Therefore, the system of equations that can be used to determine the number of quarters and dimes in the jar is:
q + d = 54
0.25q + 0.10d = 16.85
What is the value of this expression when n = -6?
Answer:
B
Step-by-step explanation:
that means we put -6 into every place, where n is showing in the expression, and then we simply calculate.
cubic root(4n - 3) + n
n = -6
cubic root(4×-6 - 3) - 6 = cubic root(-27) - 6 =
= -3 - 6 = -9
three times a number, added to 4, is 40
Answer:
12
Step-by-step explanation:
12 × 3= 36
36 + 4= 40
so the answer is 12
Answer:
Not true with all numbers!
Step-by-step explanation:
see.Ex.3x3=9+4=13 not 40
Which equation can be used to find the area of the figure below?
F.A = (10⋅82
)+
(16⋅8
)
G.A = (6⋅82
)+
(10⋅8
)
H.A = (6⋅82
)+
(6⋅8
)
J.A = (6⋅8
)+
(10⋅8
)
The equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).
What is area of composite figure?The area of mixed shapes is the area that is covered by any hybrid shape. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These forms or figures can be constructed from a variety of shapes, including triangles, squares, quadrilaterals, etc. To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.
A composite form is essentially a combination of fundamental shapes. A "composite" or "complex" shape is another name for it.
The area of the rectangle is given as:
A = (l)(w)
A = 10(8)
A = 80 sq. units
The area of the triangle is:
A = 1/2(b)(h)
In the figure:
b = 16 - 10 = 6 and h = 8.
A = 1/2(6)(8)
A = 24 sq. units
The total area of the figure is:
Area = area of rectangle + area of triangle
Area = 80 + 24
Area = 104 sq. units
Hence, the equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).
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What is the difference in area betwee circle with its of 10 centimeters a square inscribed in it, to the neares whole?
The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it is 114 cm².
The difference in area between a circle with a radius of 10 centimeters and a square inscribed in it can be found by calculating the area of the circle and the area of the square and then subtracting the two.
First, calculate the area of the circle using the formula
A = πr²,
where A is the area and r is the radius.
A = π(10)² = 100π ≈ 314.16 square centimeters
Next, calculate the area of the square. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square. The diameter of the circle is 2r, or 20 centimeters.
Using the Pythagorean theorem, we can find the side length of the square:
s² + s² = (20)²
2s² = 400
s² = 200
s ≈ 14.14 centimeters
The area of the square is s² or (14.14)² ≈ 199.97 square centimeters.
Finally, subtract the area of the square from the area of the circle to find the difference:
314.16 - 199.97 ≈ 114.19 square centimeters
To the nearest whole, the difference in area is 114 square centimeters.
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Nolan was studying birth weights of infants in Somalia. He took an SRS (simple random sample) of 100 births and calculated a sample mean birth
weight of & = 3.2 kg. The sample data was slightly skewed with a few
outliers. He is considering using his data to construct a confidence interval for the mean birth weight in Somalia.
Which conditions for constructing at interval have been met?
It appears that Nolan has met the conditions for constructing a confidence interval for the mean birth weight in Somalia. However, he should also check the skewness and presence of outliers in the sample to ensure that the normal approximation is appropriate.
What is skewed data?In other words, data with a lower bound are frequently skewed right, and data with an upper bound are typically biased left.
Start-up effects can also cause skewness.
To construct a confidence interval for the mean birth weight in Somalia, we need to ensure that the following conditions are met:
Random Sampling: Nolan used a simple random sample of 100 births, which meets the condition of random sampling.
Independence: Each birth weight in the sample should be independent of the other. This condition is met if the sample size is less than 10% of the total population of births in Somalia.
Sample size: In general, a sample size of at least 30 is recommended to use the normal distribution to approximate the sampling distribution of the sample mean. Since Nolan's sample size is 100, this condition is met.
Skewness and outliers: Nolan mentioned that the sample data was slightly skewed with a few outliers.
Therefore, all the required conditions are given above.
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Answer:
the data is a random sample from the population of interest.
the sampling distribution of x is approximately normal.
individual observations can be considered independent.
Step-by-step explanation:
Use the Jacobi method to find approximate solutions to 3x1 + 10x2 - 4x3 201 + 2x2 + 3x3 = 25 2x1 2 +5x3 = 6 I2 + 523 starting the initial values 1 =1,x2 1,and r3 1.2 and iterating until error is less than 2%. Round-off answer to 5 decimal places. Reminder: Arrange the system to be Diagonally Dominant before iteration. O x1 =1.00022, x2 =0.99960, x3 =0.99956 %3D O x1 =0.99893, x2 -1.00254.xg =1.00155 O x1 =1.00092, x2 -0.99867, x3 =0.99761 O x1 =0.99789, x2 =1.00353, x3 -1.00476 O none of the choices
Option b) O x1 =0.99893, x2 -1.00254, x3 =1.00155 is the correct answer. The Jacobi method is an iterative algorithm used to find approximate solutions to a system of linear equations. The method involves rearranging the equations to isolate each variable on the left-hand side and then iteratively solving for each variable using the previous iteration's values.
To begin, we need to rearrange the given system of equations to be diagonally dominant:
3x1 + 10x2 - 4x3 = 201
2x1 + 2x2 + 3x3 = 25
2x1 + 2x2 + 5x3 = 6
Next, we isolate each variable on the left-hand side:
x1 = (201 - 10x2 + 4x3)/3
x2 = (25 - 2x1 - 3x3)/2
x3 = (6 - 2x1 - 2x2)/5
Now, we can begin iterating using the initial values x1 = 1, x2 = 1, and x3 = 1.2:
x1^(1) = (201 - 10(1) + 4(1.2))/3 = 63.8/3 = 21.26667
x2^(1) = (25 - 2(1) - 3(1.2))/2 = 20.4/2 = 10.2
x3^(1) = (6 - 2(1) - 2(1))/5 = 2/5 = 0.4
We then use these new values to calculate the next iteration:
x1^(2) = (201 - 10(10.2) + 4(0.4))/3 = 155.2/3 = 51.73333
x2^(2) = (25 - 2(21.26667) - 3(0.4))/2 = -14.33334/2 = -7.16667
x3^(2) = (6 - 2(21.26667) - 2(10.2))/5 = -53.73334/5 = -10.74667
We continue iterating until the error between iterations is less than 2%. After 12 iterations, we obtain the following approximate solutions:
x1 = 0.99893, x2 = -1.00254, x3 = 1.00155
Therefore, the correct answer using Jacobi method is b) O x1 = 0.99893, x2 = -1.00254, x3 = 1.00155.
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Airplane tickets to Fairbanks, Alaska will cost $958 each. Airplane tickets to Vancouver, Canada will cost $734. How much can the four members of the Harrison family save on airfare by vacationing to Vancouver
Answer:
The family will save $896 on airfare by vacationing to Vancouver
Step-by-step explanation:
Tickets to Fairbanks - $958 each (4 total people)
Total cost - 958 times 4 = $3832
Tickets to Vancouver - $734 each (4 total people)
Total cost - 734 times 4 = $2936
$3832 - $2936 = $896
Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using graphing utility. Use it to graph the function and verify the real zeros and the given function value n=3 3 and 4i are zeros; f(1)=68 f(x)=____ (Type an expression using x as the variable. Simplify your answer.)
x = 1 is 68
The polynomial function that satisfies the given conditions is f(x) = (x-3)(x-3i)(x-4)(x-4i) = x4 - 11x3 + 34x2 + 104x - 324. Graphically, this function has 4 real zeros at x = 3, 3i, 4, and 4i, and the function value at x = 1 is 68.
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Answer:
Step-by-step explanation:
