Applying equations, the number of each type of pancake are originally: 81 blueberry pancakes, 27 plain pancakes, and 42 chocolate chip pancakes.
How to Solve Word Problems Using Equations?Let's use the following variables to represent the number of each type of pancake:
Let x be the number of blueberry pancakes.Let y be the number of plain pancakes.Let z be the number of chocolate chip pancakes.From the problem statement, we know that:
x + y + z = 150 (total number of pancakes)
1/3 x blueberry pancakes are left
4/5 y plain pancakes are left
1/2 z chocolate chip pancakes are left
There are now an equal number of each type of pancake
From the last statement, we can set up the following equations:
1/3 x = y = 1/2 z
Multiplying all sides of each equation by the least common multiple of the denominators, we get:
2x = 6y = 3z
Dividing all sides of each equation by 2, we get:
x = 3y = 3/2 z
Now we can use the equation x + y + z = 150 to substitute for x in terms of y and z:
3y + y + 2/3(3/2z) = 150
Simplifying and solving for z, we get:
5z = 270
z = 54
Substituting z = 54 into x = 3/2 z, we get:
x = 81
Substituting z = 54 into y = x/3, we get:
y = 27
Therefore, there were originally 81 blueberry pancakes, 27 plain pancakes, and 42 chocolate chip pancakes.
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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.
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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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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please answer it asap.
Answer:
8^2
Step-by-step explanation:
Name two pairs of adjacent angles.
Answer:
the definition of adjacent mathematically means two angles if they have a common side and a common vertex.
Step-by-step explanation:
a would b adjacent to d. c would be adjacent to d.
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:
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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How do you convert 72 kilograms to pounds? show the mathmatical steps
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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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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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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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.
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
A circular path 2feet wide has an inner diameter of 550 feet . How much farther is it around the outer edge of the path than around the inner edge?
Answer:
[tex]L_c=12.56 \ \text{feet}[/tex]
Step-by-step explanation:
From the question we are told that
Width of circular path [tex]w_c=2 \ \text{feet}[/tex]
Inner Diameter [tex]d_{in}=550 \ \text{feet}[/tex]
Outer diameter [tex]d_{out}=550+2\times2[/tex] (inner diameter + 2 circular path width)
[tex]d_{out}=550+4[/tex]
[tex]d_{out}=554 \ \text{feet}[/tex]
Generally the equation for inner circumference of the circle is mathematically given by
[tex]C_1=\pi d_{in}[/tex]
[tex]C_1=3.14\times550[/tex]
[tex]C_1=1727 \ \text{feet}[/tex]
Generally the equation for outer circumference of the circle is mathematically given by
[tex]C_2=\pi d_{out}[/tex]
[tex]C_2=3.14\times554[/tex]
[tex]C_2=1739.56 \ \text{feet}[/tex]
Generally the difference in length of the two circumference is mathematically given by
[tex]L_c=C_2-C_1[/tex]
[tex]L_c=1739.56-1727[/tex]
[tex]L_c=12.56 \ \text{feet}[/tex]
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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Place the slopes in order from steepest to least steep:
(a) m = 4
(b) y = -5x + 3
(c) 2x + 4y = 8
(d) y = 3
The following equation involves multiple angles. Solve the equation on the interval [0, 2π). cos 4x= 1/2
[tex]\cos(4x)=\cfrac{1}{2}\implies 4x=\cos^{-1}\left( \cfrac{1}{2} \right)\implies 4x= \begin{cases} \frac{\pi }{3}\\\\ \frac{5\pi }{3} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 4x=\cfrac{\pi }{3}\implies \boxed{x=\cfrac{\pi }{12}}~\hfill 4x=\cfrac{5\pi }{3}\implies \boxed{x=\cfrac{5\pi }{12}}[/tex]
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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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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Part 1
Use the Pythagorean theorem to find the unknown side of the right triangle.
Answer:
Hypotenuse length = 37Step-by-step explanation:
According to the question we are given with a right traingle Where base is 35 and the perpendicular is 12.
We need to find the unknown side that is the longest side (Hypotenuse) .
By using pythagoras theorem :
[tex]\longrightarrow \rm \: \: (H)^2 = (B)^2 + (P)^2 \\ [/tex]
here,
H represents hypotenuseB represents base P represents Perpendicular.Putting the required values in the Pythagoras theorem we will get,,
[tex]\longrightarrow \rm \: \: (H)^2 = (35)^2 + (12)^2 \\ \\ \longrightarrow \rm \: \:(H)^2 =1225 + 144 \\ \\ \longrightarrow \rm \: \:(H)^2 = 1369 \\ \\ \longrightarrow \rm \: \:H = \sqrt{1369} \\ \\ \longrightarrow \rm \: \:H = 37 \\ [/tex]
Therefore, Unknown side of the right triangle i.e hypotenuse is 37 .
Solve the equation 101 = k +33 for k
K=
Answer:
101 = k + 33
101 - 33 = k + 33 - 33
68 = k
this is your required answer
what is μ (∠FNL)? this is crazy stuff
The angle ∠FNL in the given trapezium shows that ∠FNL is 122°
What are the opposite angles of a trapezium?The opposite angles of a trapezium are not necessarily equal, unlike in a parallelogram.
However, the opposite angles of a trapezium are supplementary, which means that the sum of one pair of opposite angles equals 180 degrees.
In other words, if we label the angles of a trapezium as F, D, N, and L (with F and L being opposite angles, and D and N being opposite angles), then we have:
∠F + ∠L = 180 degrees
∠D + ∠L = 180 degrees
Thus, ∠FDL + ∠FNL = 180
4x - 14 + 9x - 40 = 180
13x - 54 = 180
13x = 234
x = 18
∠FNL = 9x - 40
∠FNL = 9(18) - 40
∠FNL = 122°
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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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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTSp
Answer:
f(x) = 3x-5
Step-by-step explanation:
Plug in the domain 0, in the other answer options
f(x) = -3x + 4 turns into f(x) = -3(0) + 4 and thats equal to 4, there is no value set to 4 in the range so that option is cancelled out
f(x) = x+2 turns into f(x) = 0+2 =2, there is no value set to 2 in the range so that option is cancelled out
f(x) = -5x + 3 turns into f(x) = -5(0) + 3, and thats equal to 3, there is no value set to 3 in the range so that option is cancelled out
f(x) = 3x-5 turns into f(x) = 3(0) - 5, and thats equal to -5, there is a value in the range that equals -5, you could also try any domain value into this equation and it would result into either -11, -5, 1, 7, or 13.
keep in mind f(x) is the range
PLEASE ANSWER THIS ASAP What is the exact surface area of a cylindrical propane tank with a radius of 1 m and a height of 10 m?
2π m²
20π m²
22π m²
24π m²
22π m² is the exact surface area of a cylindrical propane tank.
What are volume and surface area?
The entire area of all the faces makes up the surface area of a three-dimensional form. We measure the areas of each face and put them together to determine the surface area of a shape.
The surface-area-to-volume ratio, also known as the surface-to-volume ratio or abbreviated as SA:V, refers to how much surface area there is in each unit volume of an object or collection of objects.
A=2πrh+2πr²
=2π * 1* 10 +2π* 1²
= 2π( 10 + 1)
= 2π * 11
= 22π m²
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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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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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Kayne runs a specialty running store. Last year, he earned $50,000 in revenue and had explicit costs of $20,000. Kayne could have made $42,000 selling video games on the Internet and received an additional $5,000 if he rented out the store and equipment. Calculate Kayne’s implicit costs.
Brainliest for helpers asap
Answer: Please provide further information for help so I can assist you.
Of 10 test scores, seven are less than or equal to 85. What is the percentile rank of a test score of 85?
Thus, the percentile rank of just an 85 on a test is: 70 percentile for the given test scores.
Explain about the Percentile?A percentile in statistics refers to a score's position in relation to other scores in a given set. Although percentile has no one fixed meaning, it is frequently described as the proportion of numbers within a collection of data scores that are lower than a particular value.
Percentile shows the proportion of persons who fall below a given value. When we declare that a score of 365 out of 400 represents the 90% percentile on an exam, it means that 90% of test-takers received scores that were lower than or equal to 365.
Give: Seven of the ten test results are inside the 85th percentile.
The percentage of those who received less than or equal to 85 is just as follows: 7/10 = 0.7.
percentile rank:
0.7*100 = 70
Thus, the percentile rank of just an 85 on a test is: 70 percentile for the given test scores.
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