Answer:
To find the resultant of two forces, you can use the following formula:
R^2 = F1^2 + F2^2 + 2F1F2cosθ
Where R is the resultant force, F1 and F2 are the magnitudes of the two forces, θ is the angle between the two forces, and cosθ is the cosine of the angle.
Plugging in the given values, we get:
R^2 = (500 kg)^2 + (875 kg)^2 + 2(500 kg)(875 kg)cos(100 deg)
R^2 = 250000 + 765625 + 767321.98
R^2 = 1788946.98
R = sqrt(1788946.98) ≈ 1337.3 kg
So the magnitude of the resultant force is approximately 1337.3 kg.
To find the angle that the resultant force makes with the smaller force, we can use the following formula:
tanθ = (F2sinθ)/(F1 + F2cosθ)
Where θ is the angle between the resultant force and the smaller force.
Plugging in the given values, we get:
tanθ = (875 kg sin(100 deg))/(500 kg + 875 kg cos(100 deg))
tanθ = 0.768
θ = tan^-1(0.768) ≈ 36.2 deg
So the angle that the resultant force makes with the smaller force is approximately 36.2 degrees.
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Tyler leaves his house at 7:00 a.m. to go to school. He walks for 20 minutes until he reaches his
school, 1 mile from his house. The function d gives the distance d(t), in miles, of Tyler from his
house t minutes after 7:00 a.m.
On snowy days, Tyles's school has a 2 hour delayed start time (120 minutes). The function s
b. gives Tyler's distance s(t), in miles, from home t minutes after 7:00 a.m. with a 120 minute
delayed start time. If d(5) = 0.25, then what is the corresponding point on the function s?
c. Write an expression for s in terms of d.
5(1) -
The function m(t) shifts the time frame by 1hr later the original function d(t).
The function s can be written in terms of d as follows:
s (r) = d × [tex](r+7)^{-1}[/tex]
Define function?The core concept of calculus in mathematics is a function. The relations are certain kinds of the functions. In mathematics, a function is a rule that produces a different result for every input x. In mathematics, a function is represented by a mapping or transformation. Letters like f, g, and h are widely used to indicate these operations.
In this situation, d (5) = 0.25 means that Tyler is 0.25 minutes away from his home at 7:05am. This is because Tyler's distance from his house at time t after 7am is provided by the function d (t).
Tyler's school starts at 9 a.m. with a 120-minute delay. As a result, if d (5) = 0.25, Tyler has walked for 5 minutes, and his distance function s (r) calculates his distance starting at 7 minutes after 7 a.m. with a 120-minute start delay. The matching point, then, indicates Tyler's separation from his home at 7 minutes after 9 a.m. If he started walking at 7 am and took 5 minutes.
The function s can be written in terms of d as follows:
s (r) = d × [tex](r+7)^{-1}[/tex]
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Area and Square Units
Area is amount of surface covered by a figure.
It is measured in square units.
Model each figure.
The area of the given figures is 1) 4 sq. units; 2) 16 sq units; 3) 6 sq units.
Define area and perimeter.
The distance around a closed figure is its perimeter, while the area is the portion of the surface that it occupies. The size of a plane or the space it encloses is expressed in square meters.
1. In this figure, the longest side has 4 units and the smallest one has 1 unit.
Area of the rectangular figure(A) = 4 * 1 = 4 sq units
Perimeter(P) = 4 + 1 + 4 + 1 = 10 units.
2. In this figure, the longest side has 4 units and the smallest one has 4 units.
Area of the rectangular figure(A) = 4 * 4 = 16 sq units
Perimeter(P) = 4 + 4 + 4 + 4 = 16 units.
3. In this figure, the longest side has 4 units, 3 units, then 2 units the smallest one has 1 unit.
Area of the rectangular figures combinely (A) = 4 * 1 + 2 * 1= 6 sq units
Perimeter(P) = 4 + 3 + 2 + 2 + 1 = 12 units.
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Annie is concerned over a report that "a woman over age 40
40
has a better chance of being killed by a terrorist than of getting married." A study found that the likelihood of marriage for a never-previously-wed, 40
40
-year-old university-educated American woman was 3.4%
3.4
%
. To demonstrate that this percentage is too small, Annie uses her resources at the Baltimore Sun to conduct a simple random sample of 407
407
never-previously-wed, university-educated, American women who were single at the beginning of their 40
40
s and who are now 45
45
. Of these women, 20
20
report now being married. Does this evidence support Annie’s claim, at the 0.01
0.01
level of significance, that the chances of getting married for this group is greater than 3.4%
3.4
%
?
The answer is no. As the p-value is more than 0.01, evidence does not support Annie's claim that the chances of getting married for this group is greater than 3.4%.
What is null hypothesis?It assumes that the observed result is due to chance and there is not any difference between specified populations.
To determine this, we must calculate the p-value.
The number of successes in the sample is 20 and the number of observations is 407.
The sample proportion = 0.049. (20/407)
The hypothesis is that the percentage of women who got married is greater than 3.4%.
The null hypothesis is that the percentage is 3.4%.
We can use the z-test statistic to test this hypothesis.
The z-test statistic is calculated as:
z = (0.049-0.034)/(√(0.034(1-0.034)/407))
= 1.66.
The p-value is calculated as:
p-value = Φ/(1.66)
= 0.97.
This is more than 0.01 ,so we can not reject the null hypothesis.
This evidence does not support Annie's claim that the chances of getting married for this group is greater than 3.4%.
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Given lines I and P.
Which of the following statements are TRUE? Select all that apply.
A) The slope of line I is equal to the slope of line P.
B) ABC is congruent to CEF
C) Lines I and P are parallel
D) ABC is similar to CEF
E) Sin (A) = Sin (C)
F) Sin (B) = cos (F)
(explain why each answer choice would be true or false)
Lines I and P can be considered parallel if they have the same slope, and ABC and CEF can be considered similar if they have the same size, but not necessarily the same shape.
What is angle?Angle is a two-dimensional figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. An angle is measured in degrees, which are represented by the symbol °. The size of an angle is determined by the amount of rotation between the two rays, with the vertex being the point of rotation. Angles can be described as acute, obtuse, right, reflex, straight and full.
A) The slope of line I is equal to the slope of line P. - True. If two lines have the same slope, they are parallel.
B) ABC is congruent to CEF - False. Congruent shapes have the same size and same shape. ABC and CEF are not necessarily the same size or shape.
C) Lines I and P are parallel - True. If two lines have the same slope, they are parallel.
D) ABC is similar to CEF - True. Similar shapes have the same size, but not necessarily the same shape.
E) Sin (A) = Sin (C) - False. The sine of an angle is only equal to the sine of another angle if they are the same angle.
F) Sin (B) = cos (F) - False. The sine of an angle is not equal to the cosine of another angle.
In conclusion, lines I and P can be considered parallel if they have the same slope, and ABC and CEF can be considered similar if they have the same size, but not necessarily the same shape. However, the sine of an angle is only equal to the sine of another angle if they are the same angle, and the sine of an angle is not equal to the cosine of another angle.
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Arrange the following from least your greatest 1/3,5/6,3/8
Answer:
Step-by-step explanation:
make them all the same denominator so
the least common denominator for all of them is 24:
1/3 x 8/8=8/24
5/6x4/4=20/24
3/8x3/3=9/24
so from least to greatest it is:
1/3, 3/8, 5/6
twice the difference between two numbers is 44. three times their sum is 96
Answer:
Step-by-step explanation:
Let's say the two numbers are x and y.
From the first statement "twice the difference between two numbers is 44", we can set up the equation:
2(x-y) = 44
Simplifying this equation, we get:
x - y = 22 (dividing both sides by 2)
From the second statement "three times their sum is 96", we can set up the equation:
3(x+y) = 96
Simplifying this equation, we get:
x + y = 32 (dividing both sides by 3)
Now we have two equations:
x - y = 22
x + y = 32
We can solve for x and y by adding the two equations together:
2x = 54
x = 27
Substituting x = 27 in either of the two equations, we get:
y = 5
Therefore, the two numbers are 27 and 5.
x = 27;
y = 5.
Step-by-step explanation:1. Name the number as variables.Say "x" is the first number.
Say "y" is the second number.
2. Form the first equation from the statements.First statement: "twice the difference between two numbers is 44".
Difference of the numbers:[tex]x-y[/tex]
Twice the difference: [tex]2(x-y)[/tex]
Twice the difference between two numbers is 44: [tex]2(x-y)=44[/tex]
3. Form the second equation from the statements.Second statement: "three times their sum is 96".
Sum of the numbers: [tex](x+y)[/tex]
3 times the sum: [tex]3(x+y)[/tex]
3 times the sum is 96: [tex]3(x+y)=96[/tex]
4. Simplify the equations.Use the distributive property of multiplication to simplify each equation as follows (check this property in the attached image).
[tex]2(x-y)=44\\ \\2x-2y=44[/tex]
[tex]3(x+y)=96\\ \\3x+3y=96[/tex]
5. Solve one of the equations for one of the variables.Let's solve the second equation for "x".
[tex]3x+3y-3y=96-3y\\ \\3x=96-3y\\ \\x=\frac{96-3y}{3} \\ \\x=\frac{96}{3} -\frac{3y}{3} \\ \\x=32-y[/tex]
7. Use the calculated value of "x", plug it in the other equation and calculate.[tex]2((32-y)-y)=44\\ \\2(32-y-y)=44\\ \\2(32-2y)=44\\ \\(2)(32)+(2)(-2y)=44\\ \\64+(-4y)=44\\ \\64-4y=44\\ \\-4y=44-64\\ \\-4y=-20\\ \\y=\frac{-20}{-4} \\ \\y=5[/tex]
8. Find the value of "x".Use any equation to find a value for "x" by substituting "y" by "5" and solving for "x".
[tex]3(x+(5))=96\\ \\3(x+5)=96\\ \\3x+15=96\\ \\3x=96-15\\ \\3x=81\\ \\x=\frac{81}{3} \\ \\x=27[/tex]
9. Verify the answers.To see if the answers are correct, plug in the values of "x" and "y" on each formula and see if they return the correct values (44 and 96).
[tex]2(x-y)=44\\ \\2((27)-(5))=44\\ \\2(22)=44\\ \\44=44[/tex]
Correct.
[tex]3((27)+(5))=96\\ \\3(32)=96\\ \\96=96[/tex]
Correct.
The numbers returned the correct values when evaluated in both opf the equation. Therefore, they are the correct answers.
x = 27;
y = 5.
See the graphic solution to this problem in the second attached image.
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Place the slopes in order from steepest to least steep:
(a) m = 4
(b) y = -5x + 3
(c) 2x + 4y = 8
(d) y = 3
35,617 minus by 15,624
Answer:
19, 993
Step-by-step explanation:
35, 617
15, 624
19, 993
Answer:
Step-by-step explanation:
20,047 using simple subtraction
If w=f x d w hitch of the following equations shows work being calculated using correct units
From the given answer choices, the equation that shows work being calculated with the correct unit is C. 113J = (17.4N) x (6.51m)
What is Work Done?In physics, work is defined as the amount of energy transferred by a force when it causes an object to move over a certain distance. Work is a scalar quantity and is expressed in units of joules (J) or foot-pounds (ft-lbs).
Mathematically, work (W) is given by the product of the force (F) applied on an object and the displacement (d) of the object in the direction of the force, as expressed in the formula:
W = F * d * cos(theta)
where theta is the angle between the force vector and the displacement vector.
Thus, the correct units which are Joules, metres and Newton are used.
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solve the area of bottom of tiffin box is 0.30m(sq) and weight is 60n=?
The pressure exerted (in N/m²) by the box on the shelf given that the bottom of the box has an area of 0.30 m² and weighs 60 N, is 200 N/m²
How do i determine the pressure exerted by the box?Pressure is defined a force per unit area. Mathematically, it is written as
Pressure (P) = force (F) / area (A)
P = F / A
With the above formular, we can obtain the pressure exerted by the box as follow:
Area of box (A) = 0.30 m² Weight of box (W) = 60 NPressure exerted (P) =?Pressure exerted (P) = Weight of box (W) / Area of box (A)
Pressure exerted = 60 / 0.30
Pressure exerted = 200 N/m²
Thus, we can conclude that the pressure exerted is 200 N/m²
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Complete question:
The area of the bottom of a tiffin box is 0.30 sq. m and weight is 60 N, Calculate the pressure exerted by the box on the shelf in N/sq. m *
Incorrect Which statement is NOT one of the axioms of Euclidean geometry? XO A. C. D ****? All these pictures i got answers off of Bainly and here are the wrong ones!!
The statement that is NOT one of the axioms of Euclidean geometry is D. If two planes intersect, their intersection is a point.
What are the axioms of Euclidean geometry?Euclidean geometry is a branch of mathematics that deals with the study of two-dimensional and three-dimensional figures using a set of axioms or postulates.
The axioms of Euclidean geometry are a set of five statements that are used as the foundation for all of the theorems and proofs in Euclidean geometry.
The first two axioms are relatively straightforward and intuitive, while the third axiom involves the use of circles to construct geometric figures. The fourth axiom establishes the concept of a right angle, which is a 90-degree angle, while the fifth axiom deals with the concept of parallel lines and their relationship to intersecting lines.
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Please please help
f ₁(x) = x²
Find f(x)
Answer:√x
Step-by-step explanation:
I am assuming the equation says [tex]f^{-1}(x)=x^{2}[/tex]
What you do is put x instead of [tex]f^{-1}(x)[/tex] and y² instead of x²
So x = y²
Rearrange for y
y = √x
Replace y with f(x)
f(x) = √x
A tank in the shape of a hemisphere has a diameter of 12 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
In linear equation, 1161.8 lb is the total weight of the liquid in the tank, to the nearest full pound.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
d = 12 ft
r = 12 ft/2 = 6 ft
volume of sphere = (4/3)πr³
volume of hemisphere = (1/2)(4/3)πr³
volume = (2/3)π(6 ft³) = 12.56 ft³
weight = volume × density
weight = 12.56 ft³ × 92.5 lb/ft³
weight = 1161.8 lb
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HELP PLEASE I DO NOT UNDERSTAND THIS
The simplified expression for x+2x-8+3x+1-2x is 4x - 4.
What is expression?Expression is a term used to describe a wide variety of communication methods such as verbal, nonverbal, written, and artistic. It is the way we communicate our thoughts, feelings, and ideas to others. It is an important part of our lives, from the simplest forms of communication like body language to more complex forms like written literature. Expression is a powerful tool for self-expression, communication, and connection.
The expression x+2x-8+3x+1-2x can be simplified by combining like terms.
First, the x-terms can be combined, resulting in 4x:
x + 2x + 3x - 2x = 4x
Next, the remaining constants can be combined, resulting in -4:
4x - 8 + 1 = -4
Finally, the resulting expression can be written as 4x - 4.
Therefore, the simplified expression for x+2x-8+3x+1-2x is 4x - 4.
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I WILL GIVE BRAINLYEST!! ALGEBRA 1 HW
Answer:☠️☠️☠️☠️do ur hw lil bro u actually need to learn this fr fr dont let me catch u slippin on foenem
Step-by-step explanation:
b. 650 because in the directions it says for groups of more than ( > ) 8 people they charge a FIXED fee of 650 so it's not 75 times 9 which would have been 675
Step-by-step explanation:
C(n) = {
75n, if n <= 8
650, if n > 8 and n <= 12
}
This function states that for groups of 8 people or fewer, the total cost is 75n, while for groups of 9 to 12 people, the total cost is a fixed $650.
b. To determine the total cost of a 1-hour private guided tour with 9 people, we can simply plug n = 9 into the equation we derived in part a:
C(9) = {
75*9, if 9 <= 8
650, if 9 > 8 and 9 <= 12
}
Since 9 is greater than 8 but less than or equal to 12, we use the second case:
C(9) = 650
Therefore, the total cost of a 1-hour private guided tour with 9 people is $650.
ChatGPT
Compare the square root of 32 and twenty one fourths using >, <, or =. twenty one fourths is less than the square root of 32 the square root of 32 is less than twenty one fourths twenty one fourths is equal to the square root of 32 the square root of 32 is less than twenty one fourths
Answer: >
Step-by-step explanation:
Brainliest for helpers asap
Answer: Please provide further information for help so I can assist you.
I need help with this problem please...
The exponential function that describes the amount in the account after time t is:
A(t) = 17509*e^(0.066t).
The balance after 10 years is $39,499.57
The doubling time is approximately 10.48 years.
How to calculate the amounta) The formula for continuously compounded interest is given by:
A = P*e^(rt)
where A is the amount after time t, P is the principal, r is the annual interest rate (as a decimal), and e is the mathematical constant approximately equal to 2.71828.
In this case, P = $17,509, r = 0.066 (6.6% expressed as a decimal), and t is the time in years. So the exponential function that describes the amount in the account after time t is:
A(t) = 17509*e^(0.066t)
b) To find the balance after 1 year, we plug in t=1:
A(1) = 17509e^(0.0661) ≈ $18,693.68
To find the balance after 2 years, we plug in t=2:
A(2) = 17509e^(0.0662) ≈ $19,971.60
To find the balance after 5 years, we plug in t=5:
A(5) = 17509e^(0.0665) ≈ $25,150.24
To find the balance after 10 years, we plug in t=10:
A(10) = 17509e^(0.06610) ≈ $39,499.57
c) The doubling time is the time it takes for the investment to double in value. We can solve for the doubling time by setting A(t) = 2P and solving for t:
2P = P*e^(rt)
2 = e^(rt)
ln(2) = rt
t = ln(2)/r
Plugging in the values for r and solving, we get:
t = ln(2)/0.066 ≈ 10.48 years
So the doubling time is approximately 10.48 years.
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Suppose that the value of a stock varies each day from $10.82 to $33.17 with a uniform distribution. Find the upper quartile; 25% of all days the stock is above what value?
Answer:
The range of the stock prices is from $10.82 to $33.17. To find the upper quartile, we need to find the value of the stock price that is greater than 75% of the data.
The distance between the minimum value and the maximum value is:
$33.17 - $10.82 = $22.35
To find the upper quartile, we need to find the value that is three-quarters of the distance above the minimum value:
$10.82 + 0.75($22.35) = $26.69
Therefore, the upper quartile of the stock price is $26.69.
To find the value above which the stock price is higher 25% of the time, we need to find the value that is 75% of the distance above the minimum value:
$10.82 + 0.25($22.35) = $15.62
Therefore, 25% of the time, the stock price is above $15.62.
To find the upper quartile, we need to first find the median of the stock prices, which is the value that divides the distribution into two equal parts. The midpoint of the distribution is:
Midpoint = (10.82 + 33.17) / 2 = 22.995
Now, we can find the upper quartile, which is the median of the upper half of the distribution. The upper half of the distribution ranges from the midpoint to the highest value of 33.17. Therefore, we calculate the median of this range as follows:
Upper quartile = (22.995 + 33.17) / 2 = 28.0825
So, the upper quartile of the stock prices is $28.08.
To find the value above which the stock is priced 25% of the time, we need to find the 75th percentile of the distribution. Since the distribution is uniform, we can use the formula for the percentile as follows:
Percentile rank = (percentile / 100) = (value - minimum) / (maximum - minimum)
Solving for the value, we get:
value = minimum + percentile rank x (maximum - minimum)
For the 75th percentile, we have:
value = 10.82 + 0.75 x (33.17 - 10.82) = 28.49
Therefore, the stock is priced above $28.49 on 25% of all days.
If f(x) = 2x-3/5 , which of the following is the inverse of f(x)?
5
O A. f¹(x) =
OB. f¹(x) =
O C. f-¹(x) =
OD. f1(x) =
5x+3/
2
2x+3/
5
3x+5/
2
3x+2/
5
The inverse of the linear function, f(x), f(x) = (2x - 3)/5 is f⁻¹(x) = (5·x + 3)/2. The correct option is option A
A. f⁻¹(x) = (5·x + 3)/2
What is the inverse of a function?The inverse of a function is a function that reverses the effect the original function.
The original function is; f(x) = (2·x - 3)/5
The inverse of f(x) can therefore be found by making x the subject of the equation as follows;
f(x) = (2·x - 3)/5
5 × f(x) = (2·x - 3)
5 × f(x) + 3 = 2·x
2·x = 5 × f(x) + 3
x = (5 × f(x) + 3)/2
Plugging in x = f⁻¹(x) and f(x) = x, in the above equation, we get;
f⁻¹(x) = (5 × x + 3)/2
f⁻¹(x) = (5·x + 3)/2The correct option that is an inverse of f(x) is therefore, option A
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What’s the product of 2/8 and3/5
Answer:
3/20
Step-by-step explanation:
To find the product of 2/8 and 3/5, we simply multiply the numerators and the denominators:
(2/8) x (3/5) = (2 x 3) / (8 x 5) = 6/40
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
6/40 = (6 ÷ 2) / (40 ÷ 2) = 3/20
Therefore, the product of 2/8 and 3/5 is 3/20.
Find the 18th term.
-21, -14, -7, 0, 7, ...
18th term = [?]
The 18th term of the sequence is -140
How to determine the term
It is important to note that the formula for the nth term of an arithmetic sequence is expressed with the equation;
an = a + (n - 1) d
Such that the parameters are enumerated as;
an is the nth term of the arithmetic sequencea is the first term of the sequencen is the number of terms in the sequenced is the common differenceFrom the information given, we have;
The sequence is;
-21, -14, -7, 0, 7, ...
Then, the common difference = -14 - (-21) = -14 + 21 = -7
Substitute the value
a18 = -21 + (18 - 1) -7
expand the bracket
a18 =-21 + (17)-7
a18 = - 21 - 119
a18 = - 140
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4. A PMV bus left Mt. Hagen at 07 arrived in Lae at 1850. It covered a distance 840 km. a) How long is this journey? (1 mark) b) What was the average speed of the bus? (1 mark) litre. per c) Diesel fuel was sold for K5.74 Calculate the cost of fuel for the journey if the fuel consumption rate was 1 litre per 20km. (2 marks) a) the total surfac 5. An empty cylinder weighing 0.7 kg has a diameter of 10 cm and a height of 30 cm. It is then filled with water and closed. Find correct to 1 decimal place:
a) the journey took 11 hours and 50 minutes.
b)the average speed of the bus was 70.95 km/hour.
c) the cost of fuel for the journey was K240.08.
Define distanceDistance is the measure of how far apart two objects or points are from each other. It is a scalar quantity, which means it only has magnitude and no direction. Distance is usually measured in units such as meters (m), kilometers (km), feet (ft), miles (mi), or any other appropriate unit of length.
a) convert the times to a 24-hour format to perform the calculation.
07:00 in 24-hour format is 07:00, and 18:50 in 24-hour format is 18:50.
The journey duration is:
18:50 - 07:00 = 11 hours and 50 minutes
Therefore, the journey took 11 hours and 50 minutes.
b) The average speed of the bus can be found by dividing the distance traveled by the time taken:
Average speed = Distance ÷ Time
= 840 km ÷ 11.83 hours (converted from 11 hours and 50 minutes)
= 70.95 km/hour
Therefore, the average speed of the bus was 70.95 km/hour.
c) The fuel consumption rate is 1 liter per 20 km. Therefore, the bus consumed 840 km / 20 = 42 liters of diesel fuel for the journey.
The cost of fuel can be calculated by multiplying the fuel quantity by the cost per liter:
Cost of fuel = Fuel quantity x Cost per liter
= 42 liters x K5.74/liter
= K240.08 (rounded to two decimal places)
Therefore, the cost of fuel for the journey was K240.08.
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A business organization needs to make up a 8 member fund-raising committee. The organization has 6 accounting majors and 7 finance majors. What is the probability that at least 4 accounting majors are on the committee?
a) 0.4079
b) 0.0171
c) 0.1795
d) 0.0163
e) 0.5874
The probability that at least 4 accounting majors are on the committee is E. 0.5874.
How to find the probabilityProbability operates on the principle of dividing the number of expected outcomes by the number of total outcomes. To find the probability that at least 4 accounting majors are on the committee, we can begin by determining the probability of having exactly 4, 5, 6, and 7 accounting majors on the committee. After finding these probabilities, we can then sum up the figures.
First, the total number of ways to choose 8 members from a group of 6+7=13 is:
13! / (8! * 5!) = 1287
Next, we will find the number of ways to choose exactly 4 accounting majors and 4 finance majors is:
6 choose 4 * 7 choose 4 = 15 * 35 = 525
Also, the number of ways to choose exactly 6 accounting majors and 2 finance majors is:
6 choose 6 * 7 choose 2 = 1 * 21 = 21
Finally, the number of ways to choose exactly 7 accounting majors and 1 finance major is:
6 choose 7 * 7 choose 1 = 0 * 7 = 0
Now, we will sum the total number of ways to choose a committee with at least 4 accounting majors as follows:
525 + 210 + 21 + 0 = 756
756 / 1287 = 0.587
Therefore, the probability of selecting a minimum of 4 accounting majors is thus 0.5874.
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A parabola opening up or down has vertex (-1, 2) and passes through (-14, - 153/8)
Write its equation in vertex form.
Simplify any fractions.
The quadratic equation is:
y = (149/1,800)*(x + 1)² + 2
What is the equation of the parabola?Remember that if the parabola has a vertex (h, k) and a leading coefficient a can be written as:
y = a*(x - h)² + k
Here we know that the vertex is (-1, 2), then we will get the following equation:
y = a*(x + 1)² + 2
And we know it passes through (-14, - 153/8), then we will get:
-153/8 = a*(14 + 1)² + 2
-153/8 = a*225 + 2
a = (153/8 - 2)/225 =
a = 149/1,800
The quadratic is:
y = (149/1,800)*(x + 1)² + 2
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Solve x(x-y)dy+y^2dx=0 using
Answer:
the method of exact differential equations:
We need to check if this differential equation is exact. To do that, we check if the partial derivative of the first term with respect to y is equal to the partial derivative of the second term with respect to x:
∂/∂y(x(x-y)) = x(-1) = -x
∂/∂x(y^2) = 0
Since these partial derivatives are not equal, the differential equation is not exact. We can try to make it exact by multiplying the entire equation by a suitable integrating factor.
Let's find the integrating factor (IF) by taking the partial derivative of the IF with respect to y and equating it to the partial derivative of the second term with respect to x:
∂/∂y(IF) = -y^2/(x(x-y)^2)
∂/∂x(y^2) = 0
From the first equation, we can see that an integrating factor of IF = x(x-y)^2 should make the equation exact. Multiplying the entire equation by this integrating factor, we get:
x(x-y)^2dy + y^2x(x-y)dx = 0
Now, we just need to find a function φ(x,y) such that:
∂φ/∂x = x(x-y)^2dy
∂φ/∂y = y^2x(x-y)dx
Integrating the first equation with respect to x, we get:
φ(x,y) = ∫x(x-y)^2dy + f(x)
φ(x,y) = -1/3(x-y)^3x + f(x)
Now, we differentiate this equation with respect to x and equate it to the second equation:
∂φ/∂x = -(x-y)^3 + f'(x)
∂φ/∂y = y^2(x-y)^3
Comparing the two, we can see that f'(x) = 0, which means that f(x) is a constant. We can choose this constant to be zero without loss of generality.
Therefore, the solution to the differential equation is given by:
-1/3(x-y)^3x + C = 0
where C is an arbitrary constant.
Change the following equation of a line into slope-intercept form. X =(y-2)÷2
Equation in the standard slope-intercept form: y = 2X + 2
What is slope-intercept form?The slope intercept form of an equation is represented as follows:
y = mx + c
where, m = slope, c = y-intercept
We want to rewrite the equation X = (y - 2) ÷ 2 in slope-intercept form, which is in the form y = mx + b, where m is the slope and b is the y-intercept.
First, let's isolate y on one side of the equation by multiplying both sides by 2:
2X = y - 2
Next, let's add 2 to both sides:
2X + 2 = y
Finally, let's switch the sides to get the equation in the standard slope-intercept form:
y = 2X + 2
So the slope of the line is 2 and the y-intercept is 2.
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solve the following equations by graphical method: 2x+y=7 and x-y=1
Answer:
Step-by-step explanation:
In a class of 60 students, 40 are Democrats, 10 are business majors, and 4 of the business majors are Democrats. If one student is randomly
selected from the class, find the probability of choosing a Democrat or a business major.
P(Democrat or business major) =
In conclusion, the probability of selecting a Democrat or a business major is 11/15.
How to solve?
To find the probability of selecting a Democrat or a business major, we need to add the probabilities of selecting a Democrat and selecting a business major, and then subtract the probability of selecting a student who is both a Democrat and a business major (since we would be double counting this student).
So, let's calculate each of these probabilities:
Probability of selecting a Democrat: There are 40 Democrats out of 60 students, so the probability of selecting a Democrat is 40/60 = 2/3.
Probability of selecting a business major: There are 10 business majors out of 60 students, so the probability of selecting a business major is 10/60 = 1/6.
Probability of selecting a student who is both a Democrat and a business major: We know that there are 4 business majors who are also Democrats, so the probability of selecting one of these students is 4/60 = 1/15.
Now we can calculate the probability of selecting a Democrat or a business major:
P(Democrat or business major) = P(Democrat) + P(business major) - P(Democrat and business major)
= 2/3 + 1/6 - 1/15
= 11/15
Therefore, the probability of selecting a Democrat or a business major is 11/15.
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The number of years from the start of the Great Depression to the first presidential election of Richard Nixon is six years less than three times Raul’s age. Nixon’s first presidential election happened 39 years after the Great Depression. Using the given information, write an equation to find Raul’s age, r.
Answer:
Raul is 15 years old.
Step-by-step explanation:
The number of years from the start of the Great Depression to Nixon's election is six years less than three times Raul's age: 3r-6
If then Nixon's first election happened 39 years after the Great Depression, then: 3r-6=39
3r-6=39 Add six to both sides so the 6 on the left side gets canceled out (positive and negative cancel each other out) so the equation will now look like this: 3r=45
Then divide 3 on both sides (multiplication and division also cancel each other out), then the equation looks like this: r=15
And so, Raul is 15 years old.