Part a. The magnitude of the angular acceleration of the salad spinner as it slows down is 4.00 radians/s².
Part b. It takes 1.00 seconds for the salad spinner to come to rest.
Part A:
The initial angular velocity of the spinner is given by:
ω1 = 20.0 rotations / 5.00 s = 4.00 rotations/s
The final angular velocity of the spinner is zero.
The number of rotations between the initial and final angular velocities is:
Δθ = 6.00 rotations
Using the equation of motion for rotational kinematics with constant angular acceleration:
Δθ = 1/2 α t^2 + ω1 t
where α is the angular acceleration, and t is the time it takes to stop spinning.
At the final angular velocity, ω2 = 0, so we can rearrange the equation to solve for t:
t = ω1 / α
Substituting the given values:
Δθ = 6.00 rotations
ω1 = 4.00 rotations/s
t = (4.00 rotations/s) / α
Solving for α:
Δθ = 1/2 α t^2 + ω1 t
6.00 rotations = 1/2 α (t^2) + (4.00 rotations/s) t
Substituting t = (4.00 rotations/s) / α:
6.00 rotations = 1/2 α [(4.00 rotations/s) / α]^2 + (4.00 rotations/s) [(4.00 rotations/s) / α]
6.00 rotations = 8.00 rotations + 16.00 rotations/s^2 / α
α = 16.00 rotations/s^2 / (6.00 rotations - 8.00 rotations)
α = 8.00 rotations/s^2 / 2.00 rotations
α = 4.00 radians/s^2
Therefore, the magnitude of the angular acceleration of the salad spinner as it slows down is 4.00 radians/s^2.
Part B:
Using the equation of motion for rotational kinematics with constant angular acceleration:
ω2 = ω1 + α t
At the final angular velocity, ω2 = 0, so we can rearrange the equation to solve for t:
t = -ω1 / α
Substituting the given values:
ω1 = 4.00 rotations/s
α = 4.00 radians/s^2
t = -(4.00 rotations/s) / (4.00 radians/s^2)
t = -1.00 s
Since the time cannot be negative, we take the absolute value of t:
t = 1.00 s
Therefore, it takes 1.00 seconds for the salad spinner to come to rest.
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600 is writtena s 2^a x b x c^d
where a , b, c and d are all prime numbers
Find the value of a,b,c and d
Answer:
a = 3
b = 1
c = 5
d = 2
Step-by-step explanation:
To find the prime factorization of 600, we can use trial division by dividing by the smallest prime numbers until we reach a prime factor:
600 ÷ 2 = 300
300 ÷ 2 = 150
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
Therefore, the prime factorization of 600 is:
600 = 2^3 × 3^1 × 5^2
So, a = 3, b = 1, c = 5, and d = 2.
use the given information to solve the triangle
C=135° C = 45₁ B = 10°
4)
5) A = 26°₁ a = 10₁ 6=4
6) A = 60°, a = 9₁ c = 10
7) A=150° C = 20° a = 200
8) A = 24.3°, C = 54.6°₁ C = 2.68
9) A = 83° 20′, C = 54.6°₁ c 18,1
The law of sines is solved and the triangle is given by the following relation
Given data ,
From the law of sines , we get
a / sin A = b / sin B = c / sin C
a)
C = 135° C = 45₁ B = 10°
So , the measure of triangle is
A/ ( 180 - 35 - 10 ) = A / 35
And , a/ ( sin 135/35 ) = sin 35 / a
On simplifying , we get
a = 36.50
Hence , the law of sines is solved
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please show all steps :)
For the following system: Determine how, if at all, the planes intersect. If they do, determine the intersection. [2T/3A] 2x + 2y + z - 10 = 0 5x + 4y - 4z = 13 3x – 2z + 5y - 6 = 0
The planes intersect at the point (-19/21, -11/14, 1).
How to find intersection of three planes in three-dimensional space?To determine how, if at all, the planes intersect, we need to solve the system of equations given by the three planes:
[2T/3A] 2x + 2y + z - 10 = 0
5x + 4y - 4z = 13
3x – 2z + 5y - 6 = 0
We can use elimination to solve this system. First, we can eliminate z from the second and third equations by multiplying the second equation by 2 and adding it to the third equation:
5x + 4y - 4z = 13
6x - 4z + 10y - 12 = 0
11x + 14y - 12 = 0
Next, we can eliminate z from the first and second equations by multiplying the first equation by 2 and subtracting the second equation from it:
4x + 4y + 2z - 20 = 0
-5x - 4y + 4z = -13
9x - y - 6z - 20 = 0
Now we have two equations in three variables. To eliminate y, we can multiply the second equation by 14 and subtract it from the first equation:
11x + 14y - 12 = 0
-70x - 56y + 56z = -182
-59x - 42z - 12 = 0
Finally, we can substitute this expression for x into one of the previous equations to find z:
3(59/42)z - 12/42 - 2y - 10 = 0
177z - 60 - 84y - 420 = 0
177z - 84y - 480 = 0
Now we have two equations in two variables, z and y. We can solve for y in terms of z from the second equation:
y = (177/84)z - (480/84)
Substituting this expression for y into the third equation, we can solve for z:
177z - 84[(177/84)z - (480/84)] - 480 = 0
177z - 177z + 480 - 480 = 0
This equation simplifies to 0=0, which means that z can be any value. Substituting z=1 into the expression for y, we get:
y = (177/84)(1) - (480/84) = -11/14
Substituting z=1 and y=-11/14 into the expression for x, we get:
x = (59/42)(1) - (12/42) + 2(-11/14) + 10 = -19/21
Therefore, the planes intersect at the point (-19/21, -11/14, 1).
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Ive been stuck on this one question for a while can someone teach me how to do this?
The value of x is 6 and the perimeter is 52 unints
Calculating the value of x and the perimeterFrom the question, we have the following parameters that can be used in our computation:
The figure
If the lines that appear to be tangent are tangent, then we have the following equation
x + 2 = 8
Evaluate the like terms
x = 6
The perimeter is the sum of the side lengths
So, we have
Perimeter = x + 2 + 8 + 5 + 5 + 9 + 9 + 4 + 4
This gives
Perimeter = 6 + 2 + 8 + 5 + 5 + 9 + 9 + 4 + 4
Evaluate
Perimeter = 52
Hence, the perimeter is 52 unints
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Given the points A: (4,-6,-3) and B: (-2,4,3), find the vector a = AB a = < a >
To find the vector a = AB, we subtract the coordinates of point A from the coordinates of point B:
a = B - A = (-2,4,3) - (4,-6,-3) = (-2-4, 4+6, 3+3) = (-6, 10, 6)
The vector a can be written as a column vector with angle brackets: a = < -6, 10, 6 >.
To find the vector AB (a), we need to subtract the coordinates of point A from the coordinates of point B. Here's the calculation:
a = B - A
a = (-2, 4, 3) - (4, -6, -3)
Now, subtract each corresponding coordinate:
a = (-2 - 4, 4 - (-6), 3 - (-3))
a = (-6, 10, 6)
So, the vector AB (a) is <-6, 10, 6>.
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a
particle moves along a path in the xy-plane. the path is given by
the parametric equations x(t)=sin(3t) and y(t)=cos(3t), help with
steps A-E
a. Find the velocity b. Find the acceleration. c. Find the speed and simplify your answer completely. d. Find any times at which the particle stops. Thoroughly explain your answer. e. Use calculus to
The given set of questions are solved under the condition of parametric equations x(t)=sin(3t) and y(t)=cos(3t) .
Hence, the length of the curve from t= 0 to t= π is 3π.
Now,
A. To evaluate the velocity, we need to perform the derivative of x(t) and y(t) concerning t.
x'(t) = 3cos(3t)
y'(t) = -3sin(3t)
Therefore, the velocity vector is
v(t) = <3cos(3t), -3sin(3t)>
B. To define the acceleration, we need to evaluate the derivative of v(t) concerning t.
a(t) = v'(t) = <-9sin(3t), -9cos(3t)>
C. To describe the speed, we need to calculate the magnitude of the velocity vector.
|v(t)| = √((3cos(3t))² + (-3sin(3t))²)
= 3
D. In order to find the number of times at which the particle stops, to find when the speed is equal to zero.
|v(t)| = 0 when cos(3t) = 0
sin(3t) = 0.
Therefore,
cos(3t) = 0 when t = (π/6) + (nπ/3),
here n = integer.
sin(3t) = 0 when t = (nπ/3),
here n = integer.
E. To calculate the length of the curve from t=0 to t=π by performing calculus
L = ∫[a,b] √((dx/dt)² + (dy/dt)²) dt
Therefore, a=0 and b=π.
L = ∫[0,π] √((3cos(3t))² + (-3sin(3t))²) dt
= ∫[0,π] 3 dt
= 3π
The given set of questions are solved under the condition of parametric equations x(t)=sin(3t) and y(t)=cos(3t) .
Hence, the length of the curve from t=0 to t=π is 3π.
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The complete question is
A particle moves along a path in the xy-plane. the path is given by
the parametric equations x(t)=sin(3t) and y(t)=cos(3t), help with
steps A-E
a. Find the velocity
b. Find the acceleration.
c. Find the speed and simplify your answer completely.
d. Find any times at which the particle stops. Thoroughly explain your answer.
e. Use calculus to find the length of the curve from t=0 to t = π , show your work.
Can someone help me fast!?!?
Trying to get better at doing these kinds of problems.
Graph the line -3x + 5y = 15
Which one would it be? This will help a lot :D
According to the question the graph the line -3x + 5y = 15, we can start by solving for y:
-3x + 5y = 15
5y = 3x + 15
y = (3/5)x + 3
Define graph.As an algebraic framework that depicts a specific function by joining a collection of points, a graph is defined. It establishes a pairwise connection among the items. The graph is made up of nodes (vertices) linked by edges. (lines).
Briefing :
Now we have the equation in slope-intercept form (y = mx + b) where the slope is 3/5 and the y-intercept is 3.
To graph the line, we can start at the y-intercept (the point (0, 3)) and then use the slope to find additional points. Since the slope is 3/5, we can move up 3 units to the right 5 units to get to the point (5, 6), and down 3 units to the left 5 units to get to the point (-5, 0). Connect these points to get the line.
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MarÃa is shopping for party supplies. She finds that paper plates come in packages of 8, napkins come in packages of 10, and paper cups come in packages of 12. What is the least number of packages of plates, napkins, and cups she has to buy so that she has the same number of each item for her party?
The least number of packages of plates, napkins, and cups Maria has to buy is 15 packages .
To find the least number of packages, we need to find the least common multiple (LCM) of the three package sizes: 8 (plates), 10 (napkins), and 12 (cups).
The prime factors of 8 are 2x2x2, of 10 are 2x5, and of 12 are 2x2x3. To find the LCM, we multiply the highest powers of each prime factor: 2³x3x5 = 120.
This means Maria needs 120 of each item. She will buy 120/8 = 15 packages of plates, 120/10 = 12 packages of napkins, and 120/12 = 10 packages of cups.
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Find the equation for the plane through the points Po(-3,- 2,4), Qo(-5, - 1,2), and Ro(1,1,5). C. Using a coefficient of 7 for x, the equation of the plane is (Type an equation.)
The equation for the plane through the points Po(-3,-2,4), Qo(-5,-1,2), and Ro(1,1,5) is:
3x - 3y + 2z - 11 = 0
Using a coefficient of 7 for x, the equation of the plane is:
21x - 3y + 2z - 11 = 0
To find the equation of the plane, we can use the cross product of the vectors formed by the points Qo-Po and Ro-Po.
Let's call the vector formed by Qo-Po "u" and the vector formed by Ro-Po "v". Then, we can find the normal vector to the plane by taking the cross product of "u" and "v":
u = Qo - Po = (-5+3, -1+2, 2-4) = (-2,1,-2)
v = Ro - Po = (1+3, 1+2, 5-4) = (4,3,1)
n = u x v = (1(2) - (-2)(3), (-2)(4) - 1(1), (-2)(3) - 1(4)) = (8,-7,-10)
Now that we have the normal vector to the plane, we can find the equation of the plane by using the point-normal form of the equation of a plane:
n · (P - Po) = 0
where "·" denotes the dot product, P is any point on the plane, and Po is one of the given points on the plane.
Let's use the point Po(-3,-2,4) to find the equation of the plane:
n · (P - Po) = 0
(8,-7,-10) · (x+3, y+2, z-4) = 0
8(x+3) - 7(y+2) - 10(z-4) = 0
8x - 7y - 10z + 11 = 0
So the equation of the plane through the points Po, Qo, and Ro is:
3x - 3y + 2z - 11 = 0
To use a coefficient of 7 for x, we can simply multiply both sides of the equation by 7:
21x - 21y + 14z - 77 = 0
Simplifying, we get:
21x - 3y + 2z - 11 = 0
Therefore, the equation of the plane with a coefficient of 7 for x is 21x - 3y + 2z - 11 = 0.
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will mark brainlist to the correct person who does the step by step correctly and also the correct answer
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
Answer:
answer choice C
Step-by-step explanation:
The playground is a rectangle.
To find the area of a rectangle, we use the formula:
Area = Length x Width
The length is 25 yards.
The width is 68 yards.
Plugging these into the area formula:
Area = 25 x 68 = 1,700 square yards
Of the options, the closest choice is:
1,710 square yards
The area is 1,710 square yards.
What is true about the constant of variation for an inverse variation relationship?
Answer:
it is the product of the independent and dependent variables
Step-by-step explanation:
I took a quiz and got that answer right
The constant of variation for an inverse variation relationship is always a fixed value.
What is a characteristic of the constant of variation in an inverse variation relationship?Inverse variation is a relationship between two variables where an increase in one variable results in a decrease in the other variable, while a decrease in one variable results in an increase in the other variable.
Mathematically, this relationship is expressed as y = k/x, where k is the constant of variation.
The constant of variation represents the ratio of the two variables in the inverse variation relationship. It is a fixed value because it remains the same regardless of the values of the variables.
For example, if y varies inversely with x, and y = 4 when x = 2, then the constant of variation is k = xy = 4(2) = 8. This means that y will always be equal to 8/x in this inverse variation relationship.
Therefore, the constant of variation for an inverse variation relationship is always a fixed value, and it represents the ratio between the two variables in the relationship.
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Your doing practice 3
Based on the information, the three numbers are 14, 34, and 70.
What are the numbers?Based on the information, the second number = 3x - 8
The third number is five times the first number, which can be written as:
third number = 5x
The sum of the three numbers is 118, so we can write an equation:
x + (3x - 8) + 5x = 118
9x - 8 = 118
Adding 8 to both sides:
9x = 126
x = 236 / 914
Now we can use this value of x to find the other two numbers:
second number = 3x - 8 = 3(14) - 8 = 34
third number = 5x = 5(14) = 70
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Find angle C
SinC/4=sin104/8
Answer:
C = 52
Step-by-step explanation:
sin(c/4) = sin(104/8)
sin(c/4) = 0.22495
c/4 = 13
c = 52
Give an example of a Benchmark fraction and an example of a mixed number
The benchmark fractions are the most common fraction.
Such as 1/2, 0, 3/8 etc.
What is a mixed fraction?Mixed fractions are a type of fraction in which there is a whole number part and a fractional part. for example 17/3 would be 5 2/3 as a mixed fraction
Brian has two cubes.
. The first cube has a volume of 125 cm3.
. The second cube has a volume of 343 cm3.
What is the difference in the area of one face of the second cube and the area of one face of the first cube?
A. 2 cm2
B. 24 cm2
C. 49 cm2
D. 218 cm2
Help asap
If the first cube has a volume of 125 cm³ and the second cube has a volume of 343 cm³, the difference in the area of one face of the second cube and the area of one face of the first cube is 24cm². The answer is B. 24 cm².
To find the difference in the area of one face of each cube, we first need to find the side length of each cube. Since the volume of a cube is equal to the side length cubed (V = s³), we can find the side length by taking the cube root of the volume.
For the first cube:
Volume = 125 cm³
Side length = cube root of 125 = 5 cm
For the second cube:
Volume = 343 cm³
Side length = cube root of 343 = 7 cm
Next, we find the area of one face of each cube. The area of one face of a cube is equal to the side length squared (A = s²).
Area of one face of the first cube:
A1 = 5² = 25 cm²
Area of one face of the second cube:
A2 = 7² = 49 cm²
Finally, find the difference in the area of one face of each cube:
Difference = A2 - A1 = 49 cm² - 25 cm² = 24 cm²
The answer is B. 24 cm².
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What is the FICA tax on an income of $47,000? Remember that FICA is
taxed at 7.65%
The FICA tax will be $3595.5 on an income of $47,000.
Given that the principal amount = $47,000
Given that the FICA is taxed at the percentage of 7.65%
To findout the FICA tax we have to findout the 7.65% of money from the principal money $47,000.
The formula for finding the Y% of money from Z amount is = [tex]\frac{y}{100}[/tex] * Z
From the above formula, we can find the FICA tax.
FICA tax = [tex]\frac{7.65}{100}[/tex] * 47000 = 0.0765 * 47000 = 3595.5.
From the above solution, we can conclude that the FICA tax on an income of $47,000 is $3595.5
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Suppose the surface area for a can having a particular volume is minimized when the height of the can is equal to 22 cm. If the surface area has been minimized, what would you expect the radius of the can to be? (Round your answer to the nearest tenth if
necessary. You do not need to include the unit.)
If the surface area of a can with a particular volume is minimized when the height of the can is 22 cm, we would expect the radius of the can to be the same as the height, given that a cylinder has the smallest surface area when its height and radius are equal.
The surface area of a can with height h and radius r can be given by the formula:
A = 2πr² + 2πrh
The volume of the can is given by:
V = πr²h
If we differentiate the surface area with respect to r and equate it to zero to find the critical point, we get:
dA/dr = 4πr + 2πh(dr/dr) = 0
Simplifying this expression, we get:
2r + h = 0
Since we know that the height of the can is 22 cm, we can substitute h = 22 in the equation to get:
2r + 22 = 0
Solving for r, we get:
r = -11
Since the radius of the can cannot be negative, we discard this solution. Therefore, the radius of the can should be equal to its height, which is 22 cm.
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the height and age of each child in a random sample of children was recorded. the value of the correlation coefficient between height and age for the children in the sample was 0.8 . based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement? responses on average, the height of a child is 80% of the age of the child. on average, the height of a child is 80% of the age of the child. the least-squares regression line of height versus age will have a slope of 0.8 . the least-squares regression line of height versus age will have a slope of 0.8 . the proportion of the variation in height that is explained by a regression on age is 0.64 . the proportion of the variation in height that is explained by a regression on age is 0.64 . the least-squares regression line will correctly predict height based on age 80% of the time. the least-squares regression line will correctly predict height based on age 80% of the time. the least-squares regression line will correctly predict height based on age 64% of the time.
The least-squares regression line of height versus age will have a slope of 0.8 . Was true statement option (2)
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, in this case, height and age. A correlation coefficient of 0.8 indicates a strong positive linear relationship between height and age. The slope of the least-squares regression line represents the change in the height of a child for each one-unit increase in age.
Therefore, a slope of 0.8 indicates that for each one-year increase in age, the expected increase in height is 0.8 units. The other options are not correct or relevant based on the given information.
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Full Question: the height and age of each child in a random sample of children was recorded. the value of the correlation coefficient between height and age for the children in the sample was 0.8 . based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?
responses on average,
the height of a child is 80% of the age of the child. on average, the height of a child is 80% of the age of the child. the least-squares regression line of height versus age will have a slope of 0.8 . the least-squares regression line of height versus age will have a slope of 0.8 . the proportion of the variation in height that is explained by a regression on age is 0.64 . the proportion of the variation in height that is explained by a regression on age is 0.64 .1) Figure HIDE has vertices at coordinates H(1,4), I(2, -1), D(4, -3), and E(5, 3). What are the coordinates for H’I’D’E’ if H’I’D’E’=R (HIDE)? You can edit the drawing below to plot the points if you prefer.
The coordinates for H’I’D’E’ after a reflection over the y-axis include the following:
H' (-1, 4).
I' (-2, -1).
D' (-4, -3).
D' (-5, 3).
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to the coordinate of the given quadrilateral HIDE, we have the following coordinates:
(x, y) → (-x, y).
Coordinate H = (1, 4) → Coordinate H' = (-(1), 4) = (-1, 4).
Coordinate I = (2, -1) → Coordinate I' = (-(2), -1) = (-2, -1).
Coordinate D = (4, -3) → Coordinate D' = (-(4), -3) = (-4, -3).
Coordinate E = (5, 3) → Coordinate D' = (-(5), 3) = (-5, 3).
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Suppose that the demand for a product is given by 2p²q = 10000 + 9000p² (a) Find the elasticity when p = $50 and q = 4502. (b) What type of elasticity is this? (elastic, unitary or inelastic?)
(c) How would the revenue be affected by an increase in price?
(a) The elasticity at p = $50 and q = 4502 is 2.778.
(b) The elasticity is elastic.
(c) An increase in price would result in a decrease in revenue.
How to determined the elasticity of demand?(a) To find the elasticity when p = $50 and q = 4502, we first need to find the partial derivatives of q with respect to p and then use the elasticity formula:
Demand: 2p²q = 10000 + 9000p²
Partial derivative of q with respect to p: 4pq = 18000p
When p = $50 and q = 4502:
4(50)(4502) = 900800
Elasticity:
e = (p/q) * (dq/dp) = (50/4502) * (900800/18000) = 2.778
(b) To determine what type of elasticity this is, we look at the value of the elasticity calculated in part (a). Since the elasticity is greater than 1, we know that this is an elastic demand.
(c) To determine how the revenue would be affected by an increase in price, we need to look at the relationship between elasticity and revenue. If demand is elastic,
Then an increase in price will result in a decrease in total revenue, and if demand is inelastic, then an increase in price will result in an increase in total revenue.
Since we know that the demand is elastic (from part (b)), we can conclude that an increase in price will lead to a decrease in revenue.
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Given the exponential decay function f (t) = 2(0. 95) find the average
rate of change from x =0 to x =4. Show your work.
The average rate of change is -0.1295, under the condition the given exponential decay function is f (t) = 2(0. 95).
In order to find the average rate of change from x=0 to x=4 for the given exponential decay function [tex]f(t) = 2(0.95)^{t}[/tex], we need to find the slope of the line that passes through the points (0,f(0)) and (4,f(4)).
f(0) = 2(0.95)⁰ = 2
f(4) = 2(0.95)⁴ ≈ 1.482
The slope of the line passing through these two points is:
(f(4) - f(0))/(4 - 0)
= (1.482 - 2)/4
≈ -0.1295
Therefore, the average rate of change from x=0 to x=4 is approximately -0.1295.
An exponential decay function is a form of a function that reduces at a constant rate over time. It is a type of mathematical model used to present many real-world phenomena such as radioactive decay, population growth, and the depreciation of assets.
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Two scout patrols start hiking in opposite directions. Each patrol hikes 5 kilometers. Then the scouts turn 90 degrees to their right and hike another 6 kilometers. How many kilometers are there between the two scout patrols?
The distance between the two scout patrols is approximately 11.66 kilometers.
We can see that the situation forms a right triangle with the hypotenuse representing the distance between the two scout patrols. Let's call this distance d.
Each patrol initially hikes 5 kilometers in opposite directions. This means that the distance between them at this point is 10 kilometers (5 km + 5 km).
Then, each patrol turns 90 degrees to their right and hikes 6 kilometers. This means that they travel along the legs of the right triangle, which have a length of 6 kilometers.
Using the Pythagorean theorem, we can solve for the hypotenuse:
d² = 10² + 6²
d² = 136
d ≈ 11.66 km
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help I want to get this done
Answer:
j: 0, m: (-4)
Step-by-step explanation:
RECALL:
Rational function is the func. expressed by polynomials p(x) and q(x) as:
p(x)/q(x) where q(x) is non-zero
j(m+4) must be non zero, or
j(m+4)≠0
j≠0 and m+4≠0
j≠0 and m≠(-4)
One measure of student success for colleges and universities is the percent of admitted students who graduate. Studies indicate that a key issue in retaining students is their performance in so-called gateway courses. These are courses that serve as prerequisites for other key courses that are essential for student success. One measure of student performance in these courses is the DFW rate, the percent of students who receive grades of D, F, or W (withdraw). A major project was undertaken to improve the DFW rate in a gateway course at a large midwestern university. The course curriculum was revised to make it more relevant to the majors of the students taking the course, a small group of excellent teachers taught the course, technology (including clickers and online homework) was introduced, and student support outside the classroom was increased. The following table gives data on the DFW rates for the course over three years. In Year 1, the traditional course was given; in Year 2, a few changes were introduced; and in Year 3, the course was substantially revised.
Year DFW Rate Number of Students Taking Course
Year 1 42. 1% 2408
Year 2 24. 3% 2325
Year 3 19. 4% 2126
1. Do you think that the changes in this gateway course had an impact on the DFW rate? (Use α = 0. 1. )
2. State the null and alternative hypotheses.
3. State the Ï2 statistic, degrees of freedom, and the P-value.
Yes. The null hypothesis is that the changes in the course did not have a significant impact on the DFW rate. The chi-squared statistic is 44.63, with 2 degrees of freedom, and the p-value is less than 0.001.
1. Yes, it is likely that the changes in the gateway course had an impact on the DFW rate, as the rate decreased from 42.1% in Year 1 to 19.4% in Year 3.
2. The null hypothesis is that the changes in the course did not have a significant impact on the DFW rate, while the alternative hypothesis is that the changes did have a significant impact on the rate.
3. The chi-squared statistic is 44.63, with 2 degrees of freedom, and the p-value is less than 0.001. This indicates that there is a significant relationship between the year the course was given and the DFW rate, providing evidence to reject the null hypothesis in favor of the alternative hypothesis that the changes made to the course had a significant impact on the DFW rate.
The p-value of less than 0.001 indicates strong evidence against the null hypothesis, as it is less than the significance level of 0.1.
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Y=1/3x-3 and y=-x+1 what the answer pls i really need this
The point of intersection between the two given equations is (3, -2).
The problem is asking to find the point of intersection between the two given equations:
y = (1/3)x - 3 ............... (equation 1)
y = -x + 1 ............... (equation 2)
To solve for the intersection point, we can set the two equations equal to each other:
(1/3)x - 3 = -x + 1
Simplifying and solving for x:
(1/3)x + x = 1 + 3
(4/3)x = 4
x = 3
Now that we know x = 3, we can substitute it into either of the two original equations to find y:
Using equation 1: y = (1/3)x - 3 = (1/3)(3) - 3 = -2
Using equation 2: y = -x + 1 = -(3) + 1 = -2
Therefore, the intersection point is (3, -2).
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Please answer the question correctly and neatly. Will upvote if
correct.
Using a Table of Integrals with the appropriate substitution, find e3r + 6e2x + 7e et - 64 peste da Answer: ] +0
The equation provided, "e3r + 6e2x + 7e et - 64 pestle da," is not an integral expression and does not have a variable of integration.
Additionally, the requested answer, "] +0," does not make sense in the context of the question. Please provide a complete and accurate question for me to assist you with. Hi! Based on your terms provided ("Integrals", "substitution", and "find"), I understand that you are looking to solve an integral using substitution. However, the integral you provided appears to have some typographical errors. Please provide the correct integral, and I'll be happy to help you solve it.
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Will mark brainliest (to whoever explains this clearly)
Lizzie came up with a divisibility test for a certain number m that doesn't equal 1:
-Break a positive integer n into two-digit chunks, starting from the ones place. (For example, the number 354764 would break into the two-digit chunks 64, 47, 35. )
- Find the alternating sum of these two-digit numbers, by adding the first number, subtracting the second, adding the third, and so on. (In our example, this alternating sum would be 64-47+35=52. )
- Find m, and show that this is indeed a divisibility test for m (by showing that n is divisible by m if and only if the result of this process is divisible by m)
Lizzie's divisibility test states that a number n is divisible by a certain number m if and only if the alternating sum of its two-digit chunks is divisible by m.
How does Lizzie's divisibility test work?Lizzie's divisibility test involves breaking a positive integer into two-digit chunks, finding the alternating sum of these chunks, and then determining if the result is divisible by a certain number m.
To apply the test:
Break the positive integer n into two-digit chunks from right to left.Calculate the alternating sum of these two-digit numbers, adding the first number, subtracting the second, adding the third, and so on.Find m, the divisor for which you want to test divisibility.If the result of the alternating sum is divisible by m, then n is also divisible by m.To prove that this is a divisibility test for m, you need to show that n is divisible by m if and only if the result of the alternating sum is divisible by m.
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(a) Determine the critical value(s) for a right-tailed test of a population mean at the
α=0. 10
level of significance with
20
degrees of freedom.
(b) Determine the critical value(s) for a left-tailed test of a population mean at the
α=0. 10
level of significance based on a sample size of
n=15.
(c) Determine the critical value(s) for a two-tailed test of a population mean at the
α=0. 01
level of significance based on a sample size of
n=11
The critical value for a right-tailed test of a population mean at α=0.10 level of significance with 20 degrees of freedom is 1.325.
The critical value for a left-tailed test of a population mean at the α=0.10 level of significance based on a sample size of n=15 is -1.345.
The critical value(s) for a two-tailed test of a population mean at the α=0.01 level of significance based on a sample size of n=11 is -2.718 and 2.718.
To find the critical values, we need to use a t-distribution table or a statistical software that provides the critical t-values for a specific level of significance and degrees of freedom.
For part (a), since it's a right-tailed test, the critical value will be positive, and we need to look for the t-value that corresponds to an area of 0.10 to the right of the mean in the t-distribution table. With 20 degrees of freedom, the critical value is 1.325.
For part (b), since it's a left-tailed test, the critical value will be negative, and we need to look for the t-value that corresponds to an area of 0.10 to the left of the mean in the t-distribution table. With 15 degrees of freedom, the critical value is -1.345.
For part (c), since it's a two-tailed test, we need to split the significance level equally between the two tails. We need to find the t-values that correspond to an area of 0.005 to the left of the mean and 0.005 to the right of the mean in the t-distribution table. With 11 degrees of freedom, the critical values are -2.718 and 2.718.
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a student aimed to get a mean mark of 80% in his mathematics test after 9 tests his mean mark is 79%. Calculate the lowest mark he requires in his last test to enable him to achieve his target.
Answer:
89
Step-by-step explanation:
construct the formula to obtain the total of marks in first 9 tests:
79 = x/9
79 * 9 = 711
x = 711
so to get 80% in the next test we construct this formula:
80 = 711 + y / 9 + 1
the value we get for y is 89
to confirm the answer, 711+89/10 gives us 80, which is the correct value we want
PLEASE HELP ME WITH THIS MATH PROBLEM!!! WILL GIVE BRAINLIEST!!! 25 POINTS!!!
Answer: In bold
Step-by-step explanation:
The formula they gave is a rate
Let's solve for the rate first.
This equation is done for 3 years 2018-2021 that's why ^3
3.55 = 2.90(1+x)³ >divide both sides by 2.90
1.224 = (1+x)³ > take cube root of both sides
1.0697 = 1+x
x= .0697
so let's make our generic formula
[tex]y = 2.90(1+.0697)^{t}[/tex] let t be years and let y= price
Let's calculate 2018, so this would be year 0
[tex]y = 2.90(1+.0697)^{0}[/tex]
y=$2.90 this is for 2018
They already gave you 2021 price
y=$3.55 this is for 2021
Rate of increase is .0697
In 2025
That's 7 years=t
[tex]y = 2.90(1+.0697)^{7}[/tex]
y=$4.65 for 2025