To verify the generalized Stokes's theorem for the given region M and vector field w, we need to evaluate the surface integral of the curl of w over M and compare it to the line integral of w over the boundary of M.
First, let's find the curl of w:
curl(w) = (d/dy)(x + y + z) - (d/dz)(z) dx + (d/dz)(zdx) + (d/dx)(x) dy
= (1 - 0) dx + (0 - 1) dy + (0 - 1) dz
= dx - dy - dz
Next, let's parametrize the surface M. We can use cylindrical coordinates:
x = cos(theta)
y = y
z = sin(theta)
The unit normal vector N = (x, 0, z) becomes N = (cos(theta), 0, sin(theta)).
The bounds for theta will be from 0 to 2*pi, and for y, it will be from -∞ to 3.
Now, let's evaluate the surface integral of curl(w) over M:
∫∫_M curl(w) · dS
= ∫_0^(2pi) ∫_-∞^3 (cos(theta), 0, sin(theta)) · (dx - dy - dz) dy d(theta)
= ∫_0^(2pi) ∫_-∞^3 (cos(theta) - sin(theta)) dy d(theta)
= ∫_0^(2pi) (3 - (-∞)) (cos(theta) - sin(theta)) d(theta)
= ∫_0^(2pi) 3(cos(theta) - sin(theta)) d(theta)
= 3[ sin(theta) + cos(theta) ] |_0^(2pi)
= 3[ sin(2pi) + cos(2*pi) - (sin(0) + cos(0)) ]
= 3(0 + 1 - 0 - 1)
= 3(0)
= 0
Now, let's calculate the line integral of w over the boundary of M. The boundary curve consists of two parts: the upper circle and the lower circle.
For the upper circle (y = 3):
r = (cos(theta), 3, sin(theta)), theta ∈ [0, 2*pi]
dr = (-sin(theta), 0, cos(theta)) d(theta)
∫_C1 w · dr = ∫_0^(2pi) (sin(theta) d(theta) + (cos(theta) + 3) d(theta) + 0)
= ∫_0^(2pi) (sin(theta) + cos(theta) + 3) d(theta)
= [ -cos(theta) + sin(theta) + 3theta ] |_0^(2pi)
= [-1 + 1 + 6pi - (-1 + 0)] = 6pi
For the lower circle (y = -∞):
r = (cos(theta), -∞, sin(theta)), theta ∈ [0, 2*pi]
dr = (-sin(theta), 0, cos(theta)) d(theta)
∫_C2 w · dr = ∫_0^(2pi) (sin(theta) d(theta) + (cos(theta) + (-∞) + 0)
= ∫_0^(2pi) (sin(theta) + cos(theta) - ∞) d(theta)
= [-cos(theta) + sin(theta) - ∞theta ] |_0^(2pi)
= [-1 + 1 - ∞2pi
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Marcie Ann Weber, age 32, takes out $15,000 of a term insurance for a ten year term.
a. annual premium: $ a0
b. monthly premium: $ a1
Answer:
Step-by-step explanation:
a. annual premium: 79.35
b. monthly premium: 7.14
Marcie Ann Weber, age 32, takes out $15,000 of a term insurance for a ten-year term. Annual premium = $1,500 per year and monthly premium = $125 per month.
What is division?One type of operation is division in mathematics. In this procedure, the phrases or numbers are divided into the same number of components.
Given: Marcie Ann Weber,
insured amount of term insurance plan = $15,000.
Number of year = 10 year
To find the amount of annual premium:
Divide the total insured amount by number of years.
Annual premium = Insured amount of term insurance plan / Number of year
Annual premium = $15,000 / 10
Annual premium = $1,500 per year
To find the amount of monthly premium:
Monthly premium = Insured amount of term insurance plan / Number of month in 10 year
Monthly premium = 15,000 / (10 x 12)
Monthly premium = 15,000 / 120
Monthly premium = $125 per month.
Therefore, annual premium = $1,500 per year and monthly premium = $125 per month.
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What is the area of a circle with a radius of 20 inches?
Group of answer choices
1256 square inches
314 square inches
31.4 square inches
125.6 square inches
Answer:
1256 square inches
Step-by-step explanation:
Area of a circle:
A = πr²
Given:
r = 20
Work:
A = πr²
A=(3.14)20²
A = 3.14(400)
A = 1256
Answer:
1256 square inches.
Step-by-step explanation:
20 squared * π = 1256 square inches
The heights of the female adults in a country can be represented by a random variable that follows the normal distribution N(170,30) Answer these questions:
1. To enter the tallest 20% of the female adults, a man must be at least [....] cm tall.
2. To enter the tallest 1% of the female adults, a man must be at least [....] cm tall.
Given the heights of the female adults in a country is represented by a random variable that follows the normal distribution N(170,30)1. To enter the tallest 20% of the female adults, a man must be at least 184.87 cm tall.
Solution:It is given that, the heights of the female adults in a country can be represented by a random variable that follows the normal distribution N(170,30)Let X be the height of female adults, then X ~ N(170, 30)
Let P be the probability of the tallest 20% female adults.To find the value of x we need to use the standard normal distribution formula which is given byz = (x - μ) / σWhere,z = standard score or z-scorex = the raw scoreμ = the meanσ = the standard deviation
Now, the probability of the tallest 20% female adults is P = 0.20 or 20%We know that the total area under the normal curve is 1 which means P(X < μ) = 0.5So, P( X > μ) = 1 - P(X < μ) = 1 - 0.5 = 0.5Therefore, 0.5 = P(Z < z) at z = 0.84 from standard normal distribution table,0.84 = (x - μ) / σOn substituting the values,0.84 = (x - 170) / 30x - 170 = 0.84 x 30x - 170 = 25.2x = 195.2So, to enter the tallest 20% of the female adults, a man must be at least 184.87 cm tall.2.
To enter the tallest 1% of the female adults, a man must be at least 201.17 cm tall.
Solution: It is given that, the heights of the female adults in a country can be represented by a random variable that follows the normal distribution N(170,30)Let X be the height of female adults, then X ~ N(170, 30)
Let P be the probability of the tallest 1% female adults.
Now, the probability of the tallest 1% female adults is P = 0.01 or 1%We know that the total area under the normal curve is 1 which means P(X < μ) = 0.5So, P( X > μ) = 1 - P(X < μ) = 1 - 0.5 = 0.5Therefore, 0.5 = P(Z < z) at z = 2.33 from standard normal distribution table,2.33 = (x - μ) / σOn substituting the values,2.33 = (x - 170) / 30x - 170 = 2.33 x 30x - 170 = 69.9x = 239.9 cm
So, to enter the tallest 1% of the female adults, a man must be at least 201.17 cm tall.
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To enter the tallest 1% of the female adults, a man must be at least 104.1 cm tall.
The heights of female adults in a country can be represented by a random variable that follows the normal distribution N(170,30).
The questions and their solutions are:
1. To enter the tallest 20% of female adults, a man must be at least [ ] cm tall.
To solve this, we can use the standard normal distribution table.
Let Z be the standard normal distribution.
To find the corresponding Z-score to the 20th percentile, we use the standard normal distribution table.
P(Z < z) = 0.20, where P(Z < z) is the area under the standard normal distribution curve to the left of z.
z = -0.84 (rounded to 2 decimal places).
Using the formula z = (X - µ) / σ, we can solve for X, the height of the woman:
[tex]z = (X - µ) / σX = σz + µX = 30(-0.84) + 170X = 147.8[/tex] (rounded to the nearest tenth of a cm)
Therefore, to enter the tallest 20% of the female adults, a man must be at least 147.8 cm tall.
2. To enter the tallest 1% of female adults, a man must be at least [ ] cm tall.
P(Z < z) = 0.01
z = -2.33 (rounded to 2 decimal places).
Using the formula z = (X - µ) / σ, we can solve for X, the height of the woman:
[tex]z = (X - µ) / σX = σz + µX = 30(-2.33) + 170X = 104.1[/tex] (rounded to the nearest tenth of a cm)
Therefore, to enter the tallest 1% of the female adults, a man must be at least 104.1 cm tall.
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Suppose that a random variable X satisfies E[X] = 0, E[X2] = 1, E[X3] = 0, E[X4] = 3 and let Y = a + bx+cX? Find the correlation coefficient p(X,Y).
Given the random variable X with specific expected values and the equation Y = a + bx + cX, we are asked to find the correlation coefficient p(X,Y).
The correlation coefficient between two random variables X and Y is given by the formula:
p(X,Y) = Cov(X,Y) / sqrt(Var(X) * Var(Y))
To calculate the correlation coefficient, we need to find the covariance (Cov(X,Y)) and the variances (Var(X) and Var(Y)).
Given the expected values, we can calculate the required values as follows:
Cov(X,Y) = E[XY] - E[X]E[Y]
Var(X) = E[[tex]X^2[/tex]] - [tex](E[X])^2[/tex]
Var(Y) = E[tex][(Y - E[Y])^2][/tex]
Using the provided expected values, we can substitute them into the formulas:
Cov(X,Y) = E[XY] - E[X]E[Y] = E[(a + bx + cX)X] - (0)(E[a + bx + cX]) = E[aX + b[tex]X^2[/tex] + c[tex]X^2[/tex]] = a(E[X]) + b(E[[tex]X^2[/tex]]) + c(E[[tex]X^3[/tex]])
Var(X) = E[[tex]X^2[/tex]] - [tex](E[X])^2[/tex] = 1 - [tex](0)^2[/tex] = 1
Var(Y) = E[(Y - [tex]E[Y])^2[/tex]] = E[(a + bx + cX - [tex](E[a + bx + cX]))^2[/tex]] = E[[tex](a + bx + cX)^2[/tex]]
Using the provided values for E[[tex]X^3[/tex]] and E[[tex]X^4[/tex]], we can simplify the expressions further and calculate the values.
Once we have the values of Cov(X,Y), Var(X), and Var(Y), we can substitute them into the correlation coefficient formula to find p(X,Y).
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Please help!!! I’ll mark you as brainliest!!!!!!
0.138613961 as a percent rounded to the nearest tenth
Answer:
13.9%
Step-by-step explanation :
Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.
0.138613961 ------ when multiplying by 100 you move two spots the decimal point: 13.8613961 %
The tenth digit is 8 the number after that is 6
If the digit after tenth is greater than or equal to 5, add 1 to tenth. Else remove the digit.
6 is greater than 5 so we add 1 to 8 and becomes 9
If the digit after the tenth was 4 instead 6, for example,then it would be 13.8%
helpppp plsssss(I’ll give 80 pointssss
Answer:
-4 + -6 = -10
Step-by-step explanation:
From the line at negative 4 it goes to negative 10 you need to add six to four to make ten. Though since it is negative numbers we add a negative 6
how many total elements are in an array with 4 rows and 7 columns?
a. 4
b. 7
c. 28
d. 11
The total number of elements in an array is indeed equal to the product of its number of rows and columns. In this case, since the array has 4 rows and 7 columns, the total number of elements is 4 x 7 = 28.
The total number of elements in an array is equal to the product of its number of rows and columns. In this case, the array has 4 rows and 7 columns, so the total number of elements is:
4 x 7 = 28
Therefore, the answer is (c) 28.
The total number of elements in an array is indeed equal to the product of its number of rows and columns. In this case, since the array has 4 rows and 7 columns, the total number of elements is 4 x 7 = 28.
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simplify this (√7+√3)²
HELP ME ASAP!!!!!!!!
See picture below.
Answer:
Step-by-step explanation:
x+3 - x = 3 = width
2(x+3) = 2x + 6 = length
2x + 6 +2x +6 +3 +3 = 4x + 18 = Perimeter of T
What is the value of a?
A. -18
B. -14
C. 14
D. 18
solve using quadratic formula q^2-2q-1=0
Answer:
1±√2=q
or
q=2.41, -0.41
Step-by-step explanation:
we are given the equation q²-2q-1=0, and we want to use the quadratic equation, which is (-b±√(b²-4ac))/2a
a is 1 (there is a 1 in front of q²)
b is -2
c is -1
substitute into the equation:
q=(2±√(4-4*1*-1))/2
solve for the discriminant:
√(4-4(1*-1))
√8
now the equation:
(2±√8)/2=q
simplify:
1±√2=q
or if your application asks for a decimal:
√2≈1.41
so:
1+1.41=2.41=q
or
1-1.41=-0.41=q
Hope this helps!
PLEASE HELP ME ITS AN EMERGENCY!
Answer:
Number 1 is correct
4.5 x 12 = 54
Number 3 is wrong,
Formula of a triangle:
BH x 1/2(basically dividing by 2)
8 x 15 = 120,
120 DIVIDED BY 2 = 60 is your area, not 120.
Your plug in would be for the triangle:
8 x 15 x 1/2
Number 5 is wrong.
11 + 4 = 15
15 x 6 (you forgot to multiply by the height!) = 90
90 divided by 2 ( x 1/2) = 45 is your area, NOT 90.
Your formula for a trapezoid is:
(b1 + b2) x h x 1/2 Don't forget your height next time!
Plug in: (4 + 11) x 6 x 1/2
C⊃D
~(A∨B)∨C
~B∨D
Show that each of the following arguments is valid by
constructing a proof
The given arguments are proved using logical inference rules.
To show that each of the following arguments is valid, we need to construct a proof using logical inference rules. Here is a proof for the given arguments:
Argument 1:
1. C ⊃ D (Premise)
2. ~(A ∨ B) ∨ C (Premise)
3. ~B ∨ D (Premise)
4. ~(A ∨ B) (Assumption)
5. ~A ∧ ~B (De Morgan's Law, 4)
6. ~B (Simplification, 5)
7. D (Disjunctive Syllogism, 3, 6)
8. ~(A ∨ B) ∨ D (Disjunction Introduction, 7)
9. C (Disjunction Elimination, 2, 8)
10. ~(A ∨ B) ∨ C (Disjunction Introduction, 9)
Therefore, the argument is valid.
Argument 2:
1. C ⊃ D (Premise)
2. ~(A ∨ B) ∨ C (Premise)
3. ~B ∨ D (Premise)
4. ~A ∨ ~B (Assumption)
5. ~(A ∨ B) (De Morgan's Law, 4)
6. C (Disjunction Elimination, 2, 5)
7. C ⊃ D (Premise)
8. D (Modus Ponens, 6, 7)
9. ~B ∨ D (Disjunction Introduction, 8)
10. ~(A ∨ B) ∨ D (Disjunction Introduction, 9)
Therefore, the argument is valid.
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What is the best approximation for √29? 5 5.2 5.9 6
Answer:
Hello, Brainly users, hi hows your day going. Great. Yeah thanks for asking. Anyway, the answer is 5.2.
Step-by-step explanation:
Will provide step-by-step explanation as to how I figured it out if I can get brainliest *HINT HINT*. Have a good day. And keep good vibes amid the pandemic
:D
Answer:
5.2
Plz mark me as brainliest.
write an equation that states (x,y) is the same distance from (4,1) as it is from the x-axis.
The equation that states (x, y) is equidistant from (4, 1) and the x-axis is -8x - 2y + 17 = 0.
To express that the point (x, y) is equidistant from both the point (4, 1) and the x-axis, we can set up an equation using the distance formula.
The distance formula states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, we want the distance from (x, y) to (4, 1) to be equal to the distance from (x, y) to the x-axis. The x-axis can be represented by the equation y = 0.
Let's set up the equation:
√((x - 4)² + (y - 1)²) = √((x - x)² + (y - 0)²)
Simplifying, we get:
√((x - 4)² + (y - 1)²) = √(x² + y²)
To remove the square roots, we can square both sides of the equation:
((x - 4)² + (y - 1)²) = (x² + y²)
Expanding and simplifying further, we have:
x² - 8x + 16 + y² - 2y + 1 = x² + y²
Combining like terms, we obtain:
-8x - 2y + 17 = 0
Therefore, the equation that states (x, y) is equidistant from (4, 1) and the x-axis is -8x - 2y + 17 = 0.
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Five-sixths of the students at a nearby college live in dormitories. If 6000 students at the college live in dormitories, how many students are there in the college?
The number of students that are in college is 7200 if Five-sixths of the students at a nearby college live in dormitories. If 6000 students at the college live in dormitories.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
Five-sixths of the students at a nearby college live in dormitories. If 6000 students at the college live in dormitories
Let x be the number of students that are in college.
Then from the question:
The value of x can be found as follows:
x = (6000/5)×6
x = (1200)×6
x = 7200
Thus, the number of students that are in college is 7200 if Five-sixths of the students at a nearby college live in dormitories. If 6000 students at the college live in dormitories.
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What is the surface area of this right rectangular prism with dimensions of 8 inches by 4 inches by 14 inches?
a. 310
b. 400
c. 525
d. 650
Answer:
400
Step-by-step explanation:
The area of sides and add then up
Mrs. Bruce wants to put in a swimming pool with a deck around the perimeter of the pool. The pool will be rectangular shaped and will have dimensions of 12 feet by 20 feet. The deck around the perimeter will be uniformed in width and have a total area of 68 square feet. Find the width of the deck.
Hint: Draw and accurately label a sketch of the deck and pool in the space below.
Answer:
I think! 3.5 feet wide
Step-by-step explanation:
the area of the pool is 240 square feet. divide by 68 square feet gives you 3.539= 3.5 feet wide. dont shoot me if I'm wrong lol
The width of the deck is approximately 2.65 feet.
To solve the problem, we need to first find the total area of the pool and deck combined, and then subtract the area of the pool to find the area of the deck.
The total area of the pool and deck can be represented as follows:
(12 + 2x) x (20 + 2x)
where x is the width of the deck.
The area of the pool is:
12 x 20 = 240
So, the area of the deck can be found by subtracting the area of the pool from the total area:
(12 + 2x) x (20 + 2x) - 240 = 68
Expanding the left side and simplifying, we get:
4x²+ 64x - 208 = 0
Dividing both sides by 4, we get:
x²+ 16x - 52 = 0
Using the quadratic formula, we get:
x = (-b ± √(b² - 4ac)) / 2a
Where a = 1, b = 16, and c = -52.
Plugging in these values, we get:
x = (-16 ± √(16² - 4(1)(-52))) / 2(1)
x = (-16 ± √(960)) / 2
x = (-16 ± 4√(15)) / 2
x = -8 ± 2√(15)
Since the width of the deck cannot be negative, we can discard the negative solution, and we are left with:
x = -8 + 2√(15)
So, the width of the deck is approximately 2.65 feet.
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PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
The value of ∠FGJ = x⁰ is 45⁰.
What is Linear pair angle?Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
Here, we know that sum of angles on linear pair is 180⁰.
∠FGJ = x⁰ and ∠JGH = 135⁰
∠FGJ + ∠JGH = 180⁰
x⁰ + 135⁰ = 180⁰
x⁰ = 180⁰ - 135⁰
x⁰ = 45⁰
Thus, the value of ∠FGJ = x⁰ is 45⁰.
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I am sorry i am wasting your time please help!
Step-by-step explanation:
True
false
false
true
i think its that I'm sorry if its wrong
The graph of the function is shown below
Which of the following functions best represents the graph ?
A) y= 0.5(2.5)^x
B) y= 3.5x^2 + 0.5
C) y= 0.5(6)^x
D) y= 0.5x+2.5
Answer:
B) y=3.5x^2 +0.5
Step-by-step explanation:
the (0,0.5) tells you what the y-intercept is :)
hope this helps :)
Sophia went to see a play at the theater downtown. 8:30 PM. The first act was 55 minutes long. Intermission lasted for 20 minutes, and the second act was an hour long. What time was it when the play finished?
solve the given differential equation by undetermined coefficients. 1 4 y'' y' y = x2 − 4x
The given second-order linear differential equation, 1y'' + 4y' + y = x^2 - 4x, can be solved using the method of undetermined coefficients. The particular solution is obtained by assuming a form for the solution and determining the coefficients based on the right-hand side of the equation.
To solve the given differential equation by undetermined coefficients, we first consider the homogeneous equation, which is obtained by setting the right-hand side equal to zero: 1y'' + 4y' + y = 0. The characteristic equation associated with this homogeneous equation is [tex]r^2[/tex]+ 4r + 1 = 0, where r represents the roots of the equation. Solving this quadratic equation, we find two complex conjugate roots: r = -2 ± i.
Since the right-hand side of the original equation is a polynomial of degree 2, we assume a particular solution of the form y_p = A[tex]x^{2}[/tex] + Bx + C. Substituting this assumed form into the original equation, we differentiate it twice to obtain the expressions for y''_p and y'_p, and substitute them back into the original equation. This allows us to equate the coefficients of like powers of x on both sides of the equation.
By comparing coefficients, we find that A = 1 and B = -2. However, the term C is a constant and does not contribute to the differential equation. Hence, the particular solution is y_p = [tex]x^{2}[/tex] - 2x.
Finally, the general solution of the differential equation is given by the sum of the homogeneous solution and the particular solution: y = y_h + y_p. Since the homogeneous solution contains complex roots, it can be expressed as y_h =[tex]e^{-2x}[/tex](C_1cos(x) + C_2sin(x)), where C_1 and C_2 are arbitrary constants. Thus, the complete solution is y = [tex]e^{-2x}[/tex]C_1cos(x) + C_2sin(x)) + [tex]x^2[/tex] - 2x.
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How do we find the factors of x2 – 64
Find numbers that multiply to be O but adds to be -64
O Find numbers that multiply to be 1 but adds to be -64
Find numbers that multiply to be -64 but adds to be 1
Find numbers that multiply to be -64 but adds to be 0
Answer:
The factors of x²-64 is equal to (x-8)(x+8).
Step-by-step explanation:
The given expression is:
x²-64
we know that, 8² = 64
So,
(x²-8²) = (x-8)(x+8) [As (a-b)(a+b) = a²-b²]
So, the factors of x²-64 i equal to (x-8)(x+8).
Evaluate the following expression for P = -3 and S = 2
Answer: -9
2 to the power of 0 = 1 then all you have to do is plug in the numbers and simplify
Answer:
-9
Step-by-step explanation:
Well you just subsitute it all and solve from there
s^0= 2^0
p^-2= -3^-2
Anything squared to the power of 0 is 1
so its already 1/smth
the second part is just 3^-2 first which is 1/9 then the negative sign which is -1/9
GIVING BRAINLIEST PLEASE DUE TODAY
A. For babysitting, Nicole charges a flat fee of $3, plus $5 per hour.
Write an equation for the cost, C, after h hours of babysitting.
B. How much money will she make if she babysits for 5 hours?
C. If Nicole earned $48.00, how many hours did she babysit?
After six rolls of a standard die, the experimental probability of rolling a 3 is 26. What do you expect will happen to the experimental probability if the die is rolled 90 more times? Explain.
Answer:
The experimental probability should get closer to the theoretical probability of 1/6 with more trials.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Experimental probability:
The number of desired outcomes is taken from the results of an experiment.
Theoretical probability:
Found before the experiment happens.
For a large number of trials, the experimental probability will be closer to the theoretical probability.
In this question:
A standard die has 6 sides, one which is 3. So the theoretical probability of rolling a 3 is 1/6.
After six rolls of a standard die, the experimental probability of rolling a 3 is 2/6.
The experimental probability, after six rolls, is 2/6 = 1/3.
What do you expect will happen to the experimental probability if the die is rolled 90 more times?
As the number of trials increase, the experimental probability is expected to get closer to the theoretical probability, which in this case is 1/6.
In the figure below, m<3 = 136. Find m <1, m<2, and m<4 please explain
Answer:
angle 3=angle (vertical opposite angle)
angle 3 +angle 2=180°(by linear pair)
136°+angle 2=180°
angle 2=180°-136°
angle 2=44°
angle 2=angle 4(by vertical opposite angle)
choose the correct simplification of (4x3 − 3x − 7) (3x3 5x 3).
a. 7x3 − 2x − 4
b. x3 − 8x − 10
c. 7x3 2x − 4
d. x3 8x 10
The answer is not provided in the given options.
To simplify the expression (4x^3 - 3x - 7)(3x^3 + 5x + 3), we can use the distributive property of multiplication.
Multiplying each term in the first expression by each term in the second expression, we get:
(4x^3)(3x^3) + (4x^3)(5x) + (4x^3)(3) + (-3x)(3x^3) + (-3x)(5x) + (-3x)(3) + (-7)(3x^3) + (-7)(5x) + (-7)(3)
Simplifying each term, we have:
12x^6 + 20x^4 + 12x^3 - 9x^4 - 15x^2 - 9x - 21x^3 - 35x - 21
Combining like terms, we get:
12x^6 + (20x^4 - 9x^4) + (12x^3 - 21x^3) + (-15x^2) + (-9x - 35x) + (-21)
Simplifying further, we have:
12x^6 + 11x^4 - 9x^3 - 15x^2 - 44x - 21
Therefore, the correct simplification of (4x^3 - 3x - 7)(3x^3 + 5x + 3) is:
12x^6 + 11x^4 - 9x^3 - 15x^2 - 44x - 21.
Therefore, the answer is not provided in the given options.
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One year of classes at the University of Texas at Austin costs $10,700.
Georgio has received a grant that will pay $700 and a scholarship for
$5,500. He wants to get a job to pay 40% of the remainder of the costs
and borrow the rest of the money. How much does he need to earn on
his job, and how much will he need to borrow?
O
Georgio has to earn $1,600 and borrow $2,700.
Georgio has to earn $1,800 and borrow $2,700.
Georgio has to earn $1,800 and borrow $2,300.
Georgio has to earn $1,600 and borrow $2,300.
Answer:
Georgio has to earn $1,800 and borrow $2,700.