Answer:
Step-by-step explanation:
Two lines are perpendicular to each other if their slopes are negative reciprocals of each other. So, The equations i and ii are perpendicular to each other since their slopes are negative reciprocals of each other.
In other words, if the slope of one line is m, then the slope of the other line is -1/m.
To determine the slope of each equation, we can rewrite each equation in slope-intercept form, y = mx + b, where m is the slope and b is the
y-intercept.
i. 3x - 2y = 12
-2y = -3x + 12
y = (3/2)x - 6
The slope of this line is 3/2.
ii. 3x + 2y = -12
2y = -3x - 12
y = (-3/2)x - 6
The slope of this line is -3/2.
iii. 2x - 3y = -12
-3y = -2x - 12
y = (2/3)x + 4
The slope of this line is 2/3.
Therefore, equations i and ii are perpendicular to each other since their slopes are negative reciprocals of each other. Equation iii is not perpendicular to either of the other two equations.
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Is it possible for a rectangle to have a perimeter of 100 feet and an area of 100 square
feet? Justify your response.
No, it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet.
How to find the possibility ?The reason it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet is thanks to the quantity. At some point, the perimeter of a rectangle is larger than the area.
However, as the dimensions increase, it becomes impossible for the perimeter to keep up such that the area keeps increasing. For a rectangle with 100 feet as perimeter, it would not be possible to have an area that is 100 square feet.
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True or false?in an equation with two x’s, the solution is the number that makes the two sides equalwhen put in for both x’s.
The given statement "In an equation with two x’s, the solution is the number that makes the two sides equalwhen put in for both x’s is false because in an equation with two x's, the solution is the number that makes the two sides equal when put in for one or both of the x's.
For example, consider the equation 2x + 3 = 5x - 1. To find the solution, we need to find the value of x that makes both sides of the equation equal. We can do this by simplifying the equation:
2x + 3 = 5x - 1
2x - 5x = -1 - 3
-3x = -4
x = 4/3
So the solution to this equation is x = 4/3. Notice that we only substituted the value of x once in the equation, but we still found the solution.
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Morgan takes a train from London to Bewford and then another train to Agon.
The tree diagram shows the probabilities of Morgan's trains being late or not late.
to Bewford
to Agon
Late
0.24
Late
0.35
0.76
Not late
Late
0.24
0.65
Not late
0.76
Not
late
Morgan will not catch the train to Agon if the train to Bewford is late and the train to Agon is not late.
Work out the probability that Morgan will catch the train to Agon.
Give your answer as a decimal.
The probability that Morgan will catch the train to Agon is 0.578.
To catch the train to Agon, one of the following conditions must be met:
The train to Bewford is not late and the train to Agon is not late.
The train to Bewford is not late and the train to Agon is late.
The probability of the first condition is:
(0.76) x (0.65) = 0.494
The probability of the second condition is:
(0.24) x (0.35) = 0.084
Therefore, the probability that Morgan will catch the train to Agon is:
0.494 + 0.084 = 0.578 (to three decimal places)
So the probability that Morgan will catch the train to Agon is 0.578.
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A cylinder and a cone have the same volume. The cylinder has radius x
and height y
. The cone has radius 2x
. Find the height of the cone in terms of y
.
The height of the cone in terms of y is h = y / 4.
How to find the volume of a cone and a cylinder?The cylinder and the cone have the same volume. The cylinder has radius x and height y. The cone has radius 2x.
Therefore,
volume of a cylinder = πr²h
where
r = radiush = heightVolume of a cone = 1 / 3 πr²h
where
r = radiush = heightTherefore,
πr²h = 1 / 3 πr²h
πx²y = 1 / 3 π (2x)²h
πx²y = 1 / 3 π 4x² h
multiply both sides by 3
πx²y = π 4x² h
divide both sides by π 4x²
Hence,
h = πx²y / π 4x²
h = y / 4
Therefore, the height of the cone is h = y / 4.
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[4 marks) Find the unit tangent vector T and the principal unit normal vector N at t=0 for = r(t) = ti+at+j+ + 3 tk. NI
The unit tangent vector T is (1/√10)i + (3/√10)k
The principal unit normal vector N is j.
vector function r(t) = ti + at²j + 3tk.
Step 1: Find the derivative of r(t) with respect to t, which gives us the tangent vector.
r'(t) = (1)i + (2at)j + (3)k
Step 2: Evaluate r'(t) at t=0.
r'(0) = (1)i + (2a*0)j + (3)k = i + 3k
Step 3: Find the magnitude of r'(0).
|r'(0)| = √(1^2 + 3^2) = √10
Step 4: Normalize r'(0) to find the unit tangent vector T.
T = r'(0) / |r'(0)| = (1/√10)i + (3/√10)k
Step 5: Find the second derivative of r(t) with respect to t.
r''(t) = (0)i + (2a)j + (0)k
Step 6: Evaluate r''(t) at t=0.
r''(0) = (0)i + (2a)j + (0)k = 2aj
Step 7: Find the magnitude of r''(0).
|r''(0)| = √(2a)^2 = 2a
Step 8: Normalize r''(0) to find the principal unit normal vector N.
N = r''(0) / |r''(0)| = (2a/2a)j = j
So, at t=0, the unit tangent vector T is (1/√10)i + (3/√10)k, and the principal unit normal vector N is j.
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F(x): (x+7)/(x+5) and g(x): 7x/(x^2-3x-40)
add the functions and show all steps
explain the steps to solve Rational Function
The value of the addition of the functions:
F(x) + g(x) = (8x² + 34x - 56)/(x²-3x-40).
To add the two rational functions F(x) and g(x), we first need to find a common denominator. In this case, the common denominator is (x+5)(x-8), since both denominators can be factored in this way.
F(x) needs to be multiplied by (x-8) on the top and bottom to get a common denominator of (x+5)(x-8), and g(x) needs to be multiplied by (x+5) on the top and bottom to get the same common denominator.
So, we have:
F(x) = (x+7)/(x+5) * (x-8)/(x-8) = (x² - x - 56)/(x² - 3x - 40)
g(x) = 7x/(x²-3x-40) * (x+5)/(x+5) = 7x(x+5)/(x+5)(x-8) = 7x(x+5)/(x²-3x-40)
Now that both functions have the same denominator, we can add them together:
F(x) + g(x) = (x² - x - 56)/(x² - 3x - 40) + 7x(x+5)/(x²-3x-40)
To simplify this expression, we need to combine the two fractions over the common denominator:
F(x) + g(x) = (x² - x - 56 + 7x² + 35x)/(x²-3x-40)
Combining like terms in the numerator:
F(x) + g(x) = (8x² + 34x - 56)/(x²-3x-40)
So, F(x) + g(x) = (8x² + 34x - 56)/(x²-3x-40).
To solve a rational function, we generally follow these steps:
Factor the numerator and denominator as much as possible.Determine any restrictions on the domain of the function (values of x that make the denominator equal to zero).Simplify the function by canceling any common factors.Write the function in lowest terms.Determine any asymptotes (vertical, horizontal, or slant) and intercepts.Graph the function.In the case of F(x) and g(x), we already simplified the sum of the functions. We can see that the denominator factors as (x+5)(x-8), which means that the function is undefined at x = -5 and x = 8. These are vertical asymptotes.
To find any horizontal asymptotes, we can use the fact that the degree of the numerator is greater than or equal to the degree of the denominator. This means that there is no horizontal asymptote; instead, the function approaches infinity as x approaches infinity or negative infinity.
Finally, we can graph the function using this information and any other relevant points, such as intercepts.
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Miguel draws a square on a coordinate plane. One vertex is located at (5, 4). The length of each side is 3 units. Circle the letter by all the ordered pairs that could be another vertex.
To find the other possible vertices of the square, we need to determine the coordinates of the other three vertices. Since we know that the length of each side is 3 units, we can use this information to determine the distance between the given vertex (5, 4) and the other vertices.
First, we can determine the direction of the square by looking at the given vertex and knowing that the sides of a square are equal in length and perpendicular. Since we know that the side length is 3 units, we can move 3 units to the right to find one possible vertex. This gives us the point (8, 4).
Next, we can move 3 units up to find another possible vertex. This gives us the point (5, 7).
Finally, we can move 3 units to the left to find the last possible vertex. This gives us the point (2, 4).
Therefore, the letter that should be circled by all the ordered pairs that could be another vertex is D, which represents the point (2, 4).
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an army has 200 tanks. tanks need maintenance 10 times per year, and maintenance takes an average of 2 days. the army would like to have an average of at least 180 tanks working. how many repairmen are needed? assume exponential interarrival and service times. (hint: use a oneway data table.)
Here is the expected number of broken machines or tanks and K is the total number of tanks. So (K-L) gives the number of tanks in working condition.
The number of repairmen (R) needed to have an average of at least 180 tanks working is to be determined. Thus as observed from the results obtained for one-way data table, the value of R such that (K-L) is at least 180 is R = 11 repairmen
The Expected number of broken or bad machines (L) is
[tex]L=\sum j\pi_i[/tex]
The Expected number of machines waiting for service (1) is
[tex]L=\sum (j-R)\pi_i[/tex]
An expected number of words is often used as a guideline to ensure that the content is neither too long nor too short. In this case, the expected number is 150 words. A 150-word piece of writing can be considered a short composition. It is long enough to convey a basic idea or message, but not so long that it becomes tedious to read. This length is often used in blog posts, news articles, and social media updates.
When writing a 150-word piece, it is important to make every word count. The writing should be clear and concise, with each sentence contributing to the overall message. It may also be helpful to outline the main points before starting to write to ensure that the piece stays focused.
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Given the following demand function, q = D(x) = 1536 - 2x², find the following: a. The elasticity function, E(x). b. The elasticity at x = 20. c. At x = 20, demand (circle one) is elastic has unit elasticity is inelastic d. Find the value(s) of x for which total revenue is a maximum (assume x is in dollars).
a. The elasticity function: E(x) = -8x²/(1536-2x²)
b. The elasticity at x = 20 is -2.78.
c. At x = 20, demand is elastic.
d. The value of x for which total revenue is a maximum is $12.
a. The elasticity function, E(x), can be calculated using the formula:
E(x) = (dQ/Q) / (dx/x)
where Q is the quantity demanded and x is the price. In this case, we have:
Q = D(x) = 1536 - 2x²
Taking the derivative with respect to x, we get:
dQ/dx = -4x
Using this, we can calculate the elasticity function:
E(x) = (dQ/Q) / (dx/x) = (-4x/(1536-2x²)) * (x/Q) = -8x²/(1536-2x²)
b. To find the elasticity at x = 20, we substitute x = 20 into the elasticity function:
E(20) = -8(20)²/(1536-2(20)²) = -3200/1152 = -2.78
So the elasticity at x = 20 is -2.78.
c. To determine whether demand is elastic, unit elastic, or inelastic at x = 20, we can use the following guidelines:
If E(x) > 1, demand is elastic.
If E(x) = 1, demand is unit elastic.
If E(x) < 1, demand is inelastic.
Since E(20) = -2.78, demand is elastic at x = 20.
d. To find the value(s) of x for which total revenue is a maximum, we use the formula for total revenue:
R(x) = xQ(x) = x(1536 - 2x²)
Taking the derivative of R(x) with respect to x, we get:
dR/dx = 1536 - 4x²
Setting this equal to zero to find the critical points, we get:
1536 - 4x² = 0
Solving for x, we get:
x = ±12
To determine whether these are maximum or minimum points, we take the second derivative of R(x):
d²R/dx² = -8x
At x = 12, we have d²R/dx² < 0, so R(x) is maximized at x = 12. Therefore, the value of x for which total revenue is a maximum is $12.
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Find the inverse for each relation: 4 points each
1. {(1,‐2), (2, 3),(3, ‐3),(4, 2)}
2. {(4,2),(5,1),(6,0),(7,‐1)}
Find an equation for the inverse for each of the following relations.
3. Y=-8x+3
4. Y=2/3x-5
5. Y=1/2x+10
6. Y=(x-3)^2
Verify that f and g are inverse functions.
7. F(x)=5x+2;g(x)=(x-2)/5
8. F(x)=1/2x-7;g(x)=2x+14
The inverse relation is {(‐2,1), (3, 2),(‐3, 3),(2, 4)}, {(2, 4),(1, 5),(0, 6),(‐1, 7)}, the inverse equation is: y = (-x + 3)/8, y = (3/2)x - (15/2), y = (1/2)x + 10,
x = sqrt(y) + 3 or x = -sqrt(y) + 3 and f(g(x)) = g(f(x)) = x, f and g are inverse functions.
1.To find the inverse of the relation, we need to switch the x and y values of each point and solve for y:
{(‐2,1), (3, 2),(‐3, 3),(2, 4)}
2. Following the same process as above:
{(2, 4),(1, 5),(0, 6),(‐1, 7)}
So the inverse relation is {(2, 4),(1, 5),(0, 6),(‐1, 7)}.
3.To find the equation of the inverse, we can solve for x:
y = -8x + 3
x = (-y + 3)/8
So the inverse equation is: y = (-x + 3)/8.
4. Following the same process as above:
y = (2/3)x - 5
x = (3/2)y + 5
So the inverse equation is: y = (3/2)x - (15/2).
5. Following the same process as above:
y = (1/2)x + 10
x = 2(y - 10)
So the inverse equation is: y = (1/2)x + 10.
6.To find the inverse equation, we need to solve for x:
y = (x-3)^2
x = sqrt(y) + 3 or x = -sqrt(y) + 3
So the inverse equation is: x = sqrt(y) + 3 or x = -sqrt(y) + 3.
7,To verify that f and g are inverse functions, we need to show that f(g(x)) = x and g(f(x)) = x.
f(x) = 5x + 2
g(x) = (x-2)/5
f(g(x)) = 5((x-2)/5) + 2 = x - 2 + 2 = x
g(f(x)) = ((5x + 2)-2)/5 = x/5
Since f(g(x)) = g(f(x)) = x, f and g are inverse functions.
8.Following the same process as above:
f(x) = (1/2)x - 7
g(x) = 2x + 14
f(g(x)) = (1/2)(2x+14) - 7 = x
g(f(x)) = 2((1/2)x - 7) + 14 = x
Since f(g(x)) = g(f(x)) = x, f and g are inverse functions.
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A line includes the points (0,-7) and (n, -8) has a slope of -1/6. What is the value of n?
Answer:
n = 6.
Step-by-step explanation:
The slope of the line = (y2 - y1) / (x2 - x1) where the 2 points are (x1, y1) and (x2, y2).
So, (-8 - (-7)) / (n - 0) = -1/6
-1/n = -1/6
n = 6.
Square $ABCD$ has side length 7. What is the length of the diagonal $AC?$ (its a square also)
The length of the diagonal AC in square ABCD is approximately 9.899 units.
To find the length of the diagonal AC, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In our case, since ABCD is a square, angle ABC is a right angle. Therefore, triangle ABC is a right-angled triangle with sides AB and BC both equal to 7 units. We can apply the Pythagorean theorem to find the length of diagonal AC (the hypotenuse):
AC² = AB² + BC²
Plugging in the side lengths:
AC² = 7² + 7² = 49 + 49 = 98
Now, we take the square root of both sides to find the length of AC:
AC = √98 ≈ 9.899
So, the length of the diagonal AC in square ABCD is approximately 9.899 units.
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C C
A student believes that a certain number cube is unfair and is more likely to land with a six facing up. The student rolls
the number cube 45 times and the cube lands with a six facing up 12 times. Assuming the conditions for inference
have been met, what is the 99% confidence interval for the true proportion of times the number cube would land with a
six facing up?
0. 27 2. 58
0. 221-0. 27)
45
0. 7342. 33
0. 731-0. 73)
45
0. 27 2. 33
0. 271 -0. 20)
45
0. 73 +2. 58
0. 73(10. 73)
45
Mix
Save and Exit
The answer is option B: (0.221-0.27).
Using the formula for a confidence interval for a proportion:
p± z*√(p(1-p)/n)
where p is the sample proportion (12/45 = 0.267), z* is the z-score for the desired confidence level (99% corresponds to a z-score of 2.576), and n is the sample size (45).
Substituting the values, we get:
0.267 ± 2.576*√(0.267(1-0.267)/45)
which simplifies to:
0.267 ± 0.195
Therefore, the 99% confidence interval for the true proportion of times the number cube would land with a six facing up is (0.072, 0.462).
So the answer is option B: (0.221-0.27).
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If a and b, then c. given: the if-then statement's reverse isalso correct. if a is true, b is true, what is c?
If a and b, then c means that if both a and b are true, then c must also be true. This is an example of a conditional statement, where the truth of one proposition (c) is dependent on the truth of the other two propositions (a and b).
Now, given that the reverse of the if-then statement is also correct, we can conclude that if b is true, then a is also true. This means that both a and b are true. Therefore, according to the original statement, c must also be true.
In other words, if a and b are both true, then c must also be true. This is because the conditional statement "if a and b, then c" holds true in this scenario. Therefore, we can conclude that the value of c is true.
Overall, understanding the logic behind conditional statements and their reverses can help us make logical conclusions about the truth of propositions based on the truth of other propositions.
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HELP DUE TOMORROW!!!!!!!!
Answer:
The third choice is the correct answer.
Moe wants to get to the restaurant at 8:30 a.m. It takes him 20 minutes to drive there. What time should Moe leave for the restaurant? Move numbers to the clock to show the time.
8:10
subtract 20min from 30 min
30-20=10
Answer: He should move at 8:10
Explanation: 10 + 20 = 30 / 30 - 20 = 10
Therefore he should leave at 8:10
Enter the y coordinate of the solution to this system of equations. 3x+y=-2 x-2y=4
The y coordinate of the solution to this system of equations is -2
Calculating the y coordinate of the solution to this system of equations.From the question, we have the following parameters that can be used in our computation:
3x+y=-2 x-2y=4
Express properly
So, we have
3x + y = -2
x - 2y = 4
Multiply the second equation by -3
so, we have the following representation
3x + y = -2
-3x + 6y = -12
Add the equations to eliminate x
7y = -14
Divide both sides by 7
y = -2
Hence, the value of y is -2
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Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.
Vertex at (0,0); axis of symmetry the y-axis; containing the point (6,4).
What is the equation of the parabola? Find the two points that define the latus rectum.
The equation of the parabola is:
x = ay²The two points that define the latus rectum are (±9/64, 4).
How to find the equation of the parabola?The equation of the parabola with vertex at (0,0) and axis of symmetry the y-axis can be written in the form x = ay^2, where a is a constant. Since the parabola contains the point (6,4), we can substitute these values to solve for a:
6 = a(4²)
6 = 16a
a = 6/16 = 3/8
So the equation of the parabola is x = (3/8)y².
To find the two points that define the latus rectum, we need to determine the focal length, which is the distance from the vertex to the focus.
Since the axis of symmetry is the y-axis, the focus is located at (0, f), where f is the focal length. We can use the formula f = a/4 to find f:
f = a/4 = (3/8)/4 = 3/32
So the focus is located at (0, 3/32). The two points that define the latus rectum are the intersections of the directrix, which is a horizontal line located at a distance of f below the vertex, with the parabola. The directrix is located at y = -3/32.
To find the intersections, we can substitute y = ±(16/3)x^(1/2) into the equation of the directrix:
y = -3/32
±(16/3)[tex]x^(^1^/^2^)[/tex]= -3/32
x = 9/64
So the two points that define the latus rectum are (±9/64, 4).
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Ms. Griffin has 0. 8 liters of hot tea and 4 teacups. She will divide the tea evenly among the cups. Which model represents 0. 8 divide by 4
The model that represents Ms. Griffin's situation is 0.8 divided by 4, which equals 0.2 liters of hot tea in each teacup.
To find the amount of tea in each teacup, you need to divide the total amount of tea (0.8 liters) by the number of teacups (4). The model for this is 0.8 ÷ 4. Follow these steps:
1. Divide 0.8 by 4:
0.8 ÷ 4 = 0.2
2. Interpret the result:
Each teacup will have 0.2 liters of hot tea.
So, the model that represents Ms. Griffin's situation is 0.8 divided by 4, which equals 0.2 liters of hot tea in each teacup.
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PLEASEEEEEEEEEEEEEEE HEEEEEEEEEEEELP
If a force of 1500 N is applied on a cart with a mass of 500 Kg, calculate the
acceleration of the cart
Answer:
3 m/s²
Step-by-step explanation:
We can use Newton's Second Law of Motion. The Second Law of Motion states that acceleration is calculated by dividing the force by the mass.
[tex]A=\frac{F}{m}[/tex] with f being the force and m being the mass
We know that the force is 1,500 N and the mass is 500 kg.
So, let's substitute:
[tex]A=\frac{1500}{500}\\A=3[/tex]
So the acceleration of the cart is 3 m/s²
Hope this helps :)
Two factories blow their whistles at exactly the same time. If a man hears the two blasts exactly
4. 2 seconds and 5. 9 seconds after they are blown and the angle between his lines of sight to the two
factories is 40. 8°, how far apart are the factories? Give your result to the nearest meter. (Use the fact
that sound travels at 344 m/sec. )
A) 2903 meters
B) 3263 meters C) 1329 meters D) 1997 meters
The distance between the factories is approximately 1704 meters.
To solve this problem, we can use the Law of Cosines. Let's denote the distance between the man and Factory 1 as x, the distance between the man and Factory 2 as y, and the distance between the factories as z.
Given that the time difference for the man to hear the blasts from Factory 1 and Factory 2 is 4.2 seconds and 5.9 seconds respectively, we can calculate x and y using the speed of sound (344 m/s):
x = 4.2 seconds * 344 m/s = 1444.8 meters
y = 5.9 seconds * 344 m/s = 2030.4 meters
Now, we apply the Law of Cosines using the given angle of 40.8°:
z² = x² + y² - 2xy * cos(40.8°)
z² = 1444.8² + 2030.4² - 2(1444.8)(2030.4) * cos(40.8°)
z² ≈ 2904106.33
Take the square root to find the distance between the factories:
z ≈ √2904106.33 ≈ 1704.14 meters
Rounded to the nearest meter, the distance between the factories is approximately 1704 meters. However, this answer is not included in the given options. There might be an error in the question or the provided options.
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The mass of the Rock of Gibraltar is 1. 78 ⋅ 1012 kilograms. The mass of the Antarctic iceberg is 4. 55 ⋅ 1013 kilograms. Approximately how many more kilograms is the mass of the Antarctic iceberg than the mass of the Rock of Gibraltar? Show your work and write your answer in scientific notation
The mass of the Antarctic iceberg is approximately 2.56 × 10¹more kilograms than the mass of the Rock of Gibraltar.
To find out, we can subtract the mass of the Rock of Gibraltar from the mass of the Antarctic iceberg:
4.55 × 10¹³ kg - 1.78 × 10¹² kg = 4.37 × 10¹³ kg
Therefore, the mass of the Antarctic iceberg is about 2.56 × 10¹ (or 25.6) times greater than the mass of the Rock of Gibraltar.
This is because the mass of the Antarctic iceberg is much larger than the mass of the Rock of Gibraltar, as it is a massive block of ice floating in the ocean while the Rock of Gibraltar is a solid rock formation on land.
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Given the side lengths 5 inches and 8 inches, what is the RANGE for possible lengths of the missing side, X?
Since X cannot be negative (as it is a side length), we only need to consider the inequalities X > 3 and 13 > X. Therefore, the range of possible lengths for the missing side, X, is between 3 inches and 13 inches (not inclusive).
To find the range of possible lengths for the missing side, X, we need to use the Triangle Inequality Theorem.
This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two given side lengths are 5 inches and 8 inches.
Let's find the range of possible lengths for the missing side, X, using the theorem:
1. 5 + 8 > X
13 > X
2. 5 + X > 8
X > 3
3. 8 + X > 5
X > -3.
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Which describes the intersection of the plane and the solid? a: triangleb: rectanglec: parallelogram d: trapezoid
The solid being referred to is a cuboid and the plane that intersects it creates a triangular shape, then the intersection of the plane and the solid would be described as Triangle. Option A is the correct answer.
If a cuboid is being sliced by a plane that creates a triangular shape within the solid, then the intersection of the plane and the solid would take the form of a triangle.
However, it's important to note that this answer only applies to the specific scenario in which a cuboid is being sliced and the resulting intersection appears triangular.
In general, the intersection of a plane and a solid could take on a variety of shapes, including rectangles, parallelograms, or trapezoids, depending on the specific solid and plane in question.
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Find the range and mean of each data set. Use your results to compare the two data sets.
Set A:
1 10 7 17 20
Set B:
10 17 16 18 12
Answer:
Set A: 1, 7, 10, 17, 20
Range: 19
Mean: 11
Set B: 10, 12, 16, 17, 18
Range: 8
Mean: 14.6
How to find...
Mean: Divide the sum of all values in a data set by the number of values.
Range: Find the largest observed value of a variable (the maximum) and subtract the smallest observed value (the minimum).
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Tina is standing at the bottom of a hill. Matt is standing on the hill so that when Tina's line of sight is
perpendicular to her body, she is looking at Matt's shoes.
a. If Tina's eyes are 5 feet from the ground and 14. 5 feet from Matt's shoes, what is the angle of elevation of
the hill to the nearest degree? Explain.
The angle of elevation of the hill to the nearest degree is 44°.
The angle of elevation is the angle formed between the horizontal and an observer's line of sight to an object that is located above the observer. In this case, Tina is standing at the bottom of the hill and looking up at Matt who is standing on the hill. When Tina's line of sight is perpendicular to her body, she is looking at Matt's shoes.
This means that the line of sight forms a right angle with the ground.
To find the angle of elevation, we can use trigonometry. We know that the opposite side is the height of the hill (from Matt's shoes to the top of the hill), which is not given in the problem. However, we can use the Pythagorean theorem to find it.
Let h be the height of the hill. Then,
h^2 = (14.5)^2 - (5)^2
h^2 = 198.25
h ≈ 14.1 feet
Now, we can use the tangent function to find the angle of elevation.
tan θ = opposite/adjacent = h/14.5
tan θ = 14.1/14.5
θ ≈ 44.2°
Therefore, the angle of elevation of the hill to the nearest degree is 44°. This means that the hill slopes upward at an angle of 44° from the ground, as viewed from Tina's position at the bottom.
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A particle is moving along the x-axis on the interval 0 ≤ t ≤ 10, and its position is given by x of t equals one third times x cubed minus five halves times x squared plus 6 times x minus 10. at what time(s), t, is the particle at rest?
answers:
t = 0
t = 2 and 3
t = 1 and 5
t = 6
The particle is at rest at t = 3. Therefore, the particle is at rest at t = 2 and t = 3.
To find when the particle is at rest, we need to find the values of t where the velocity of the particle is zero.
The velocity function is obtained by taking the derivative of the position function: v(t) = x'(t) = x²(t) - 5x(t) + 6
Setting v(t) = 0, we get a quadratic equation in x(t): x²(t) - 5x(t) + 6 = 0. Factoring the quadratic, we get: (x(t) - 2)(x(t) - 3) = 0
Therefore, x(t) = 2 or x(t) = 3. We now need to check which values of t correspond to these values of x(t).
At x(t) = 2, we get: v(t) = x²(t) - 5x(t) + 6 = 4 - 10 + 6 = 0. Thus, the particle is at rest at t = 2. At x(t) = 3, we get: v(t) = x²(t) - 5x(t) + 6 = 9 - 15 + 6 = 0
Thus, the particle is at rest at t = 3. Therefore, the particle is at rest at t = 2 and t = 3.
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What occurs when a white dwarf in a binary star system if it gains mass beyond the chandrasekhar limit?.
If a white dwarf in a binary star system gains mass beyond the Chandrasekhar limit (approximately 1.4 solar masses), it undergoes a runaway nuclear reaction, causing it to collapse and explode in a Type Ia supernova.
A white dwarf is a dense stellar remnant that is left behind after a star has exhausted all its nuclear fuel and has shed its outer layers. In a binary star system, the white dwarf may gain mass from its companion star, either through accretion or a merger. If the mass of the white dwarf exceeds the Chandrasekhar limit, the gravitational forces become so strong that the electrons in the atoms are forced to combine with the atomic nuclei, forming neutrons. This process is called electron capture, and it releases a tremendous amount of energy.
The energy released is enough to ignite a runaway nuclear reaction, causing the white dwarf to collapse and explode in a Type Ia supernova. Type Ia supernovae are important cosmic events because they are used as standard candles to measure the distance to distant galaxies. These explosions are also believed to play a significant role in the chemical evolution of the universe, as they produce heavy elements such as iron and nickel that are scattered into the interstellar medium.
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Can someone please answer the question below (Level: Year 8 (7th Grade) ) about algebra equations?
Thanks ^^
Arturo has completed 27 math problems, which is 75% of the assignment. How many problems total did he have to complete?
I need help!
The total number of problems he solved is 36 if after completion of 27 problems he has completed 75% of the assignments.
Percentage of completion = 75 % of the work
The percentage can be converted to decimal by dividing the percentage by 100.
Thus, the part that has been completed = 75% = 0.75 of the work
The number of questions done = 27
Let the total number of questions be x
Thus, 75% of x is given as 27
75% of x = 27
0.75 * x = 27
0.75x = 27
x = 27/0.75
x = 36
Thus, the total number of questions is 36.
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