∫1.5 T(h) dh = 9.573, rounded to three decimal places. (a) To evaluate ∫1.5 T(h) dh, we need to integrate T(h) with respect to h from 0 to 1.5: ∫1.5 T(h) dh = ∫0.1.5 (9.43h^3 - 15.41h^2 + 17.34h - 9.83) dh
Using the power rule of integration, we can integrate each term of the polynomial: ∫0.1.5 (9.43h^3 - 15.41h^2 + 17.34h - 9.83) dh
= (9.43/4)h^4 - (15.41/3)h^3 + (17.34/2)h^2 - 9.83h |0.1.5
= [(9.43/4)(1.5)^4 - (15.41/3)(1.5)^3 + (17.34/2)(1.5)^2 - 9.83(1.5)] - [(9.43/4)(0)^4 - (15.41/3)(0)^3 + (17.34/2)(0)^2 - 9.83(0)] = 9.573
Therefore, ∫1.5 T(h) dh = 9.573, rounded to three decimal places.
(b) The answer to part (a) represents the total change in temperature during the hour and a half after the beginning of the thunderstorm. This means that the temperature increased by an average of 9.573 degrees per hour during this time period.
This integral gives us a measure of the total effect of the thunderstorm on the temperature, which is useful for predicting the weather and understanding the behavior of natural phenomena.
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What is the area of the polygon?
The area of the polygon is 42 metres squared.
How to find the area of a figure?The figure is a composite figure. The area of the figure is the sum of the area of the individual shapes.
Therefore,
area of the figure = area of the rectangle + area of trapezium
Hence,
area of the rectangle = lw
where
l = lengthw = widthTherefore,
area of the rectangle = 6 × 4
area of the rectangle = 24 m²
area of trapezium = 1 /2 (a + b)h
area of trapezium = 1 / 2 (4 + 8)3
area of trapezium = 1 / 2 (36)
area of trapezium = 18 m²
Therefore,
area of the figure = 18 + 24
area of the figure = 42 m²
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According to the Rational Root Theorem, the following are potential roots of f(x) = 2x² + 2x - 24.
-4,-3, 2, 3, 4
Which are actual roots of f(x)?
O-4 and 3
O-4, 2, and 3
O-3 and 4
O-3, 2, and 4
Answer: The actual roots of f(x) = 2x² + 2x - 24 are -3 and 4.
Step-by-step explanation:
math problem help fast!!!!!!!!!!!!!!!!! write the answer on a paper please
Answer:
1. the lateral is 4.4 the total is 8.2
2. the lateral is 132 and the total is 41
1. Exercise 4E Write the following scales in the form of 1:n, where n is a whole number. (a) 5 cm represents 4 m (c) 5 cm represents 4 km (d) 4 cm represents 5 km
The scales in the ratio of 1 : n are:
a) 1 : 80
c) 1 : 80000
d) 1 : 100000
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
a)
5 cm and 4 m
1 m = 100 cm
So,
4 m = 4 x 100 cm
4 m = 400 cm
Ratio.
= 5 cm : 4 m
= 5 cm : 400 cm
= 1 : 80
c)
5 cm and 4 km
1 km = 100000 cm
So,
4 km = 400000 cm
Ratio.
= 5 cm : 400000 cm
= 1 : 80000
d)
4 cm and 5 km
1 km = 100000 cm
So,
5 km = 500000 cm
Ratio.
= 5 cm : 500000 cm
= 1 : 100000
Thus,
The scales in the ratio of 1 : n are:
1 : 80
1 : 80000
1 : 100000
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-3x - 2y = 5
12x + 8y = -20
Answer:
y=-1
x=-1
Step-by-step explanation:
Convert 3.5 kilograms to grams
3.5 kilograms is 3500 grams
Answer: 3500
Step-by-step explanation: one kilogram is 1000 gram so multiply 3.5 x 1000
Please select the best answer from the choice provided.
Answer:12
Step-by-step explanation:
n*11=4*33
n=4*33/11=3*4=12
What is the relative change in tuition? (Give your answer as a percent between 0 and 100, not a decimal between 0 and 1. Round to ONE decimal place and remember the absolute value).
The relative change in tuition tells us the tuition in 2016/17 decreased by — %
The relative change in tuition tells us the tuition in 2016/17 decreased by 9.99 %.
What is relative change?The indicator's value in the earlier period is used to calculate the relative change, which expresses the absolute change as a percentage. Additionally, indicators that are expressed as percentages, such as the unemployment rate, are subject to the concepts of absolute and relative change.
Given:
The tuition in University if Washington in 2015-16 = 10,203
and, The tuition in University if Washington in 2016-17 = 9,183
so, the relative change is
= (10203 - 9183)/ 10203
= 1020/ 10203
= 0.0999
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this was the attendance at 3 football matches one day, each round to the three nearest 1,000. what's the largest total number of people who attended 3 matches on the day
The largest total number of people who attended 3 matches on the day was 17, 000 people.
How to find the number of people ?The largest total number of people who attended 3 matches on the day would be the sum of the largest rounded attendance numbers for each match:
Match 1: 5,000
Match 2: 8,000
Match 3: 4,000
Rounding each attendance number to the nearest 1,000 gives us:
Match 1: 5,000
Match 2: 8,000
Match 3: 4,000
Adding these rounded numbers together gives us:
5,000 + 8,000 + 4,000 = 17,000
Therefore, the largest total number of people who attended the three matches on the day was 17,000.
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The full question is:
Match 1 - 5, 000 people
Match 2 - 8, 000 people
Match 3 - 4, 000 people
This was the attendance at 3 football matches one day, each round to the three nearest 1,000. what's the largest total number of people who attended 3 matches on the day
Assume that T is a linear transformation. Find the standard matrix of T. T: R2→R2 first reflects points through the line x2-x1 and then reflects points through the line x2-x1 A= (Type an integer or simplified fraction for each matrix element)
the standard matrix of T. T: R2→R2 is [ 0 1 ]
[ 1 0]
We must locate the pictures of the standard basis vectors of R2 under T and translate those images into columns of a 2x2 matrix in order to get the standard matrix of T.
Let's start by thinking about the reflection along the line x2 - x1. The point (x1, x2) is mapped to the point via this reflection (x2, x1).
We apply T to the first standard basis vector, e1 = (1,0), to determine its image:
T(e1) = (0,1) (0,1)
We also use T: to determine the image of the second standard basis vector, e2 = (0,1).
T(e2) = (1,0) (1,0)
Hence, (0,1) and (1,0) are the images of the standard basis vectors, These photos can now be expressed as columns in a matrix:
[0 1]
[1 0]
This is the standard matrix of T.
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Please help me answer this question ASAP!!
The total distance driven by Ryan is given as follows:
20.5 miles.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
Considering that 12 minutes = 12/60 = 0.2 hours, the distance for the first customer was of:
40 = d/0.2
d = 40 x 0.2
d = 8 miles.
Considering that 15 minutes = 15/60 = 0.25 hours, the distance for the second customer was of:
50 = d/0.25
d = 0.25 x 50
d = 12.5 miles.
Hence the total distance was of:
8 + 12.5 = 20.5 miles.
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Differentiate y=x4 -x
Answer:
Step-by-step explanation:
To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).
So, for y = x^4 - x, we can find the derivative as follows:
y' = 4x^3 - 1
So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.
I need the answer like now
Answer:
1. 0 10 20 30 40 50
10 14 18 22 26 30
2. (the immage)
3. Yes this is a liner equation
Step-by-step explanation:
Write a extended metaphor poem about Tennis
Answer:
Tennis, a game of skill and grace,
A dance upon a court of green.
Racquets are partners in this space,
A symphony of motion seen.Each stroke a crescendo to the ear,
A harmony of speed and spin.
The ball, a fleeting, flashing sphere,
A fleeting moment to win.The court is life, a battlefield,
Of challenges and victories.
A test of strength, both heart and mind,
Of courage, skills, and agility.The net, a barrier, divides,
Two opponents in their quest.
A symbol of the tension that resides,
In every match, every test.But when the final point is served,
And winner takes the day.
The court transforms, a stage, preserved,
For celebration in its way.
Step-by-step explanation:
Determine all zeros for the function () = (2 + 2 − 8) ( − 6). Show all work.
The function's two zeros are: x = -1 and x = 6.
What is function?In mathematics, a function is a set of ordered pairs (input, output), where each input is associated with exactly one output. The input is commonly referred to as the independent variable, and the output is referred to as the dependent variable. A function can be represented algebraically, graphically, or verbally. Algebraically, a function is often represented by an equation that defines the relationship between the independent variable and the dependent variable. For example, the equation y = 2x + 1 defines a linear function, where x is the independent variable and y is the dependent variable.
Here,
The zeros of a function are the values of the independent variable for which the function equals zero. To determine all zeros for the function f(x) = (2x + 2)(x - 6), we need to find the solutions to the equation f(x) = 0.
To do this, we can set the two factors equal to zero and solve for x:
2x + 2 = 0
x = -1
x - 6 = 0
x = 6
These are the two zeros of the function: x = -1 and x = 6.
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Using your calculus skills derive the equations for the critical saturation ratio and the critical radius. (Hint: the critical point on the Kohler curve represents a maximum value). The equations you should end up with are as follows: r* = V3b/a and S* = 1+V4a3/27b Where r is the critical radius and S is the critical saturation ratio
The derivation of the critical radius(r*) as and critical saturation(S*) as is explained below .
To derive the critical saturation ratio (S*) and critical radius (r*),
We use calculus to find the maximum value of the saturation ratio for a given radius on the Kohler curve.
First, let us consider the equation for the saturation ratio, S, as a function of radius, r:
that is : S = 1 + ar²/3b ;
where a and b are constants.
Next, we find the derivative of S with respect to r:
On differentiating Curve "S" with respect to "r" ;
⇒ dS/dr = 2ar/3b ;
Equating the derivative = 0 , we can find the critical points:
⇒ dS/dr = 0 = 2ar/3b ;
On Solving for r, we have ;
⇒ r* = √(3b/a)
Next , to find the critical saturation ratio(S*) , we substitute r* back into the original equation for S:
⇒ S* = 1 + ar²/3b = 1 + a×(3b/a)/3b = 1 + √(4a³/27b)
Therefore , the critical saturation ratio and critical radius are written as r* = √(3b/a) and S* = 1 + √(4a³/27b) .
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The given question is incomplete , the complete question is
Using your calculus skills derive the equations for the critical saturation ratio and the critical radius. (Hint: the critical point on the Kohler curve represents a maximum value).
The equations you should end up with are as follows:
r* = √(3b/a) and S* = 1 + √(4a³/27b) Where r* is the critical radius and S* is the critical saturation ratio .
An airline has two flights traveling from CVG to ORD on a busy Friday evening. Flight A is scheduled to leave at 6:30 p.m. The airplane for flight A has a capacity of 96 passengers. The second flight, Flight B, leaves one hour later and has a capacity of only 68 passengers. Based on historical data, the airline knows that the probability that a passenger on Flight A will be a no-show is 0.03 and the probability that a passenger will be a no-show on Flight B is 0.02. For this exercise, we will assume that passenger no-shows are independent events. Round all answers to four decimal places. 6. If the airline chooses not to oversell flight A and sells exactly 96 tickets, what is the probability that it will have a full flight (i.e. all 96 passengers show up)? 7. If the airline oversells flight A with 99 tickets sold, what is the probability that all passengers that show up will have a seat on the flight (i.e. 3 or more no-shows)? 8. If the airline oversells flight B with 70 tickets sold, what is the probability that the flight will have exactly 68 customers show up? 9. If the airline oversells flight B with 72 tickets, what is the probability that all passengers that show up will have a seat on the flight?
6. The probability that Flight A will have a full flight is 0.4163.
7. The probability that all passengers who show up will have a seat on the flight is 0.5731.
8. The probability that Flight B will have exactly 68 customers show up is 0.0904.
9. The probability that all passengers that show up will have a seat on the flight is 0.9707.
6. If the airline chooses not to oversell flight A and sells exactly 96 tickets, the probability that it will have a full flight can be calculated using the binomial distribution. Let X be the number of passengers who show up for the flight.
Then, X follows a binomial distribution with n = 96 and p = 0.97 (since the probability that a passenger shows up is 1 - 0.03 = 0.97). Thus, the probability that all 96 passengers show up is:
P(X = 96) = (96 choose 96) × [tex]0.97^{96}[/tex] × [tex]0.03^0[/tex] = 0.4163
So, the probability that Flight A will have a full flight is 0.4163.
7. If the airline oversells Flight A with 99 tickets sold, the probability that all passengers who show up will have a seat on the flight (i.e. 3 or more no-shows) can be calculated using the binomial distribution again. Let Y be the number of no-shows for the flight. Then, Y follows a binomial distribution with n = 99 and p = 0.03. We want to find the probability that Y is greater than or equal to 3 (i.e. there are 3 or more no-shows), which can be calculated as:
P(Y >= 3) = 1 - P(Y <= 2) = 1 - ((99 choose 0) × [tex]0.03^0[/tex] × [tex]0.97^{99}[/tex] + (99 choose 1) × [tex]0.03^1[/tex] × [tex]0.97^{98}[/tex] + (99 choose 2) × [tex]0.03^2[/tex] × [tex]0.97^{97}[/tex]) = 0.5731
So, the probability that all passengers who show up will have a seat on the flight is 0.5731.
8. If the airline oversells Flight B with 70 tickets sold, the probability that the flight will have exactly 68 customers show up can be calculated using the binomial distribution with n = 70 and p = 0.98 (since the probability that a customer shows up is 1 - 0.02 = 0.98). Let Z be the number of customers who show up for the flight. Then, the probability that exactly 68 customers show up is:
P(Z = 68) = (70 choose 68) × [tex]0.98^{68}[/tex] × 0.02² = 0.0904
So, the probability that Flight B will have exactly 68 customers show up is 0.0904.
9. If the airline oversells Flight B with 72 tickets sold, the probability that all passengers who show up will have a seat on the flight can be calculated using the binomial distribution again. Let W be the number of no-shows for the flight. Then, W follows a binomial distribution with n = 72 and p = 0.02. We want to find the probability that W is less than or equal to 3, which can be calculated as:
P(W <= 3) = (72 choose 0) × [tex]0.02^0[/tex] × [tex]0.98^{72}[/tex] + (72 choose 1) × [tex]0.02^1[/tex] × [tex]0.98^{71}[/tex] + (72 choose 2) × [tex]0.02^2[/tex] × [tex]0.98^{70}[/tex] + (72 choose 3) × [tex]0.02^3[/tex] × [tex]0.98^{69}[/tex] = 0.9707.
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Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.) Let f(x) : (cos(12x) - cos(3x))/x^2 We want to find the limit lim x=0 from (cos(12x) - cos(3x))/x^2 Start by calculating the values of the function for the inputs listed in this table. x fx 0.2 24.987664 0.1 -98.998848 0.05 -19.923683 0.01 -99.853172 0.001 -998.62855 0.0001 -9989.29525 0.00001 -99862.9534' Based on the values in this table, it appears : lim x=0 from (cos(12x) - cos(3x))/x^2=
my answers don’t match when I put in calculator the cos of any x value
Answer: The value of the limit of the function may not be equal to the value of the function evaluated at a particular x-value. In other words, just because a function takes on a certain value at a particular x-value doesn't mean that the limit of the function at that x-value is equal to that value. To determine the limit of the function, you may need to use different methods such as L'Hopital's Rule or other limit laws. Additionally, it's important to keep in mind that the limit of the function may not exist, in which case it wouldn't be equal to any specific value.
Step-by-step explanation:
If a town with a population of 10,000 doubles in size every 17 years, what will the population be 68 years from now?
The population after 68 years from now is 160, 000.
What is Exponential Function?A relation of the form y = [tex]a^x[/tex], with the independent variable x ranging over the entire real number line as the exponent of a positive number a.
Given:
10000 is the initial population
2 is the rate at which the population grows
68/17 is the number of periods that the population grows
Now, using Exponential function the population can be represented as
= 10000 x [tex]2^{(68/17)}[/tex]
= 10000 x [tex]2^{(4)}[/tex]
= 10000 x 16
= 160, 000
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y = k x Try it! 1. y is inversely proportional to x. If y = 5 when x = 3, find an equation connecting y and x.
An equation connecting y and x.is given as y = 15/x
What is inverse variation?
In Maths, inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases
y∞1/x
This implies that y=k/x where k is a constant
5 = k/3
Making k the subject of the relation
therefore, k = 15
The equation connecting y and x would be y = 15/x
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4(x - 1)(3x - 1) = 0 answer?
Answer:
[tex]x = 1 \ \ \ \text{OR} \ \ \ x = \dfrac{1}{3}[/tex]
Step-by-step explanation:
First, multiply out the set of parentheses and simplify the resulting quadratic expression.
[tex]4(x - 1)(3x - 1) = 0[/tex]
[tex]4(3x^2-x-3x+1) = 0[/tex]
[tex]4(3x^2-4x+1) = 0[/tex]
Then, factor out a 3 from the parentheses to get rid of the coefficient on the quadratic's first term.
[tex]4(3(x^2-\dfrac{4}{3}x+\dfrac{1}{3})) = 0[/tex]
[tex]12(x^2-\dfrac{4}{3}x+\dfrac{1}{3}) = 0[/tex]
Finally, complete the square.
[tex]12\left(x^2-\dfrac{4}{3}x + \left(\dfrac{-\dfrac{4}{3}}{2}\right)^2\right) = 12\left(-\dfrac{1}{3}\right) + 12\left(\dfrac{-\dfrac{4}{3}}{2}\right)^2[/tex]
[tex]12\left(x^2-\dfrac{4}{3}x + \dfrac{4}{9}\right) = -4 + \dfrac{16}{3}[/tex]
[tex]12\left(x - \dfrac{2}{3}\right)^2 = \dfrac{4}{3}[/tex]
[tex]\left(x - \dfrac{2}{3}\right)^2 = \dfrac{1}{9}[/tex]
↓ take the square root of both sides
[tex]x - \dfrac{2}{3}\right = \pm \sqrt{\dfrac{1}{9}}[/tex]
[tex]x = \dfrac{2}{3} \pm \sqrt{\dfrac{1}{9}}[/tex]
[tex]x = \dfrac{2}{3} \pm\dfrac{1}{3}[/tex]
↓ split into two equations
[tex]x = \dfrac{2}{3} + \dfrac{1}{3} \ \ \ \text{OR} \ \ \ x = \dfrac{2}{3} - \dfrac{1}{3}[/tex]
[tex]\boxed{x = 1 \ \ \ \text{OR} \ \ \ x = \dfrac{1}{3}}[/tex]
How can 1% of 800 be used to
determine 28% of 800?
1% of 800 is
SO 28% of 800 is
Find the value of k so that the given differential equation is exact. (y3 + kxy4 − 2x) dx + (3xy2 + 24x2y3) dy = 0
The value of k for the given differential equation is exact is,
⇒ k = 12
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The given differential equation is,
⇒ (y³ + kxy⁴ - 2x) dx + (3xy² + 24x²y³) dy = 0
And, The given differential equation is exact.
Now, We know that;
For the differential equation M dx + N dy = 0;
The condition of exactness is,
⇒ dM / dy = dN / dx .. (i)
Here, We have;
M = y³ + kxy⁴ - 2x
N = 3xy² + 24x²y³
Hence, We get;
M = y³ + kxy⁴ - 2x
dM / dy = 3y² + 4kxy³
N = 3xy² + 24x²y³
dN / dx = 3y² + 48xy³
From (i);
⇒ dM / dy = dN / dx
⇒ 3y² + 4kxy³ = 3y² + 48xy³
⇒ 4kxy³ = 48xy³
⇒ 4k = 48
⇒ k = 48/4
⇒ k = 12
Thus, The value of k = 12
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is it possible to have a function f defined on [ 2 , 4 ] and meets the given conditions? f is continuous on [ 2 ,4 ] and the range of f is an unbounded interval.
No, it is not possible to have a function f defined on [2,4] that is continuous and has an unbounded range. This is because of the Extreme Value Theorem, which states that a continuous function on a closed interval must have a maximum and minimum value within that interval. If the range of f is unbounded, then there is no maximum or minimum value, which contradicts the Extreme Value Theorem. Therefore, it is not possible to have such a function.
If we modify the condition to allow for an unbounded range in only one direction (either unbounded from above or unbounded from below), then it is possible to have a function that is continuous on [2,4] with an unbounded range.
For example, consider the function f(x) = 1/(x-4) defined on the interval [2,4]. This function is continuous on [2,4] and has an unbounded range in the negative direction, as f(x) approaches negative infinity as x approaches 4 from the left.
Another example is the function g(x) = x^2 defined on the interval [2,4]. This function is continuous on [2,4] and has an unbounded range in the positive direction, as g(x) approaches infinity as x approaches 4 from the right.
So, it is possible to have a continuous function on [2,4] with an unbounded range in one direction, but not in both directions simultaneously.
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Rearrange for n
m = n² + 3
Answer:
Step-by-step explanation:
EVALUATE
n(m ^5+m−n) divided by
m(m−n)
EXPAND
m^2mn Divided by
mn-n^2+nm^5
Which dotted line segment correctly represents the perpendicular bisector of line segment XY?
AB
CD
GF
TW
AB dotted line segment correctly represents the perpendicular bisector of line segment XY
What is Straight Line?A line is an infinitely long object with no width, depth, or curvature.
A perpendicular bisector can be defined as a line segment which bisects another line segment at 90 degrees.
In other words, a perpendicular bisector intersects another line segment at 90° and divides it into two equal parts.
In the given figure the XY is a straight line.
The perpendicular bisector to this line is AB.
Hence, AB dotted line segment correctly represents the perpendicular bisector of line segment XY
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Una empresa minera compra un terreno en
Perú. Los estudios determinaron las siguientes
probabilidades previas:
a.
P(encontrar oro de buena calidad)=0.50
b. P(encontrar oro de mala calidad)=0.30
C. P(no encontrar oro)=0.20
Calcular la probabilidad de encontrar oro en dicho
The probability of finding gold in that land is 0.8.
What is Probability?Probability of a event measures the chances of that event to happen. The only difference is that probability gives a mathematical explanation of the event. Probability of a event lie between zero and one.Given is that a mining company buys a piece of land in Peru. The studies determined the following prior probabilities -
P(find good quality gold)=0.50P(find poor quality gold)=0.30P(find no gold)=0.20We can write the probability of finding gold in that land as -
P{E} = P(find good quality gold) + P(find poor quality gold)=0.30
P{E} = 0.5 + 0.3
P{E} = 0.8
Therefore, the probability of finding gold in that land is 0.8.
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{QUESTION IN ENGLISH -
A mining company buys a piece of land in
Peru. The studies determined the following
prior probabilities:
to.
P(find good quality gold)=0.50
b. P(find poor quality gold)=0.30
C. P(find no gold)=0.20
Calculate the probability of finding gold in that}
Is the theoretical probability that the coin lands head up all three times is the same value as the theoretical probability that the coin lands tails up all three times? Explain.
Yes, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row. This is because each flip of a fair coin is an independent event and has an equal chance of landing on either heads or tails.
What is theoretical probability about?The probability of getting heads on a single coin flip is 0.5 (or 1/2), and the same is true for getting tails on a single coin flip. The probability of getting three heads in a row is calculated by multiplying the probability of getting heads on each of the three flips together, which is"
(1/2) x (1/2) x (1/2) = 1/8.
Similarly, the probability of getting three tails in a row is also:
(1/2) x (1/2) x (1/2) = 1/8.
Therefore, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row, both of which are 1/8.
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find the value of x. SIMPLEST RADICAL FORM
Step-by-step explanation:
Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle). a and b are the legs.
so, in our case,
27² = 16² + x²
729 = 256 + x²
473 = x²
x = sqrt(473)
473 = 11×43 and has therefore no squared factors.
therefore, it cannot be further simplified.
Admission to a baseball game is $2.00 for general admission and $3.50 for reserved seats. The receipts were $2716.00 for 1139 paid admissions. How many of each ticket were sold?
Let G be the number of general seats sold.
Let R be the number of reserved seats sold.
The total number of seats sold is G + R = 1139
Since general seats costs $2 each, 2G is the total receipts from general tickets sales.
Since reserve seats costs $3.50 each, 3.5R is the total receipts from reserved ticket sales.
The total receipts is 2G + 3.5R = 2716
We now have two equations in two unknowns and can solve for G and R.