This question involves using the binomial distribution.
Let X be the number of male high school lacrosse players who will play at the college level out of the 20 selected players . We can model X as a binomial random variable with parameters n=20 and p=0.128, where p is the probability of success (i.e., a player going on to play at the college level).
The probability of exactly 4 players playing at the college level is given by the formula:
P(X=4) = (20 choose 4) * (0.128)^4 * (1-0.128)^(20-4)
Using a calculator, we can evaluate this expression to find:
P(X=4) = 0.155
Therefore, the probability that exactly four of the 20 male high school lacrosse players selected at random will end up playing at the college level is 0.155, or between C and 1 (inclusive).
Note that we rounded to three decimal places as requested .
An end behavior model for f(x) = [tex](8x^6-16x^3+8)/4x^2-4x-24)[/tex]
2x^2.
2x^3.
2x^4.
2x^6.
This given function does not have an end behavior since it is not a polynomial.
What is the end behavior of a function?The end behavior of a function describes the behavior or trend of the function as the input values (x) approach positive or negative infinity. It helps us understand what happens to the function's values as x becomes very large or very small.
We have three possible cases of end behavior of a function which are;
When the value of x approaches positive infinityWhen the value of x approaches negative infinityWhen a function may have different behaviors for positive and negative infinity. In such cases, we specify the end behavior separately for positive and negative infinity.The end behavior of a function is often determined by using the leading term of the function, which is the term with the highest power of x.
In the given problem;
[tex]f(x) = \frac{8x^6 - 16x^3 + 8}{4x^2 - 4x - 24}[/tex]
The end behavior of this function does not exist because this function is not a polynomial
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What is the approximate perimeter of the triangle shown below?
Last question is 19.8…
The perimeter of the given triangle is: 19.2 units
What is the Perimeter of the Triangle?The formula for the distance between two coordinates is:
D = √[(y₂ - y₁)² + (x₂ - x₁)²]
Thus: (0, 3)(4, -2)
Slant distance on left side of triangle = √[(-2 - 3)² + (-3 - 0)²] = 5.8 units
Slant distance on right side of triangle = √[(-2 - 3)² + (4 - 0)²] = 6.40 units
Length of horizontal part of triangle = 7 units
Thus:
Perimeter of triangle = 5.83 + 6.40 + 7 = 19.2 units
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please help i cant fail this
Answer:20%
Step-by-step explanation:
I need assistance for 1b
The two numbers are 15 and 15. The product of the two numbers is 225.
Let x and y be the two numbers we are searching for. We know that x + y = 30, so we can settle for y to get y = 30-x. The result of x and y is then, at that point:
[tex]P(x, y) = x(30 - x) = 30x - x^2[/tex]
To find the greatest item, we can take the subsidiary of P(x, y) concerning x and set it equivalent to 0:
dP(x, y)/dx = 30 - 2x = 0
Settling for x, we get x = 15. Subbing x = 15 into y = 30-x, we get y = 15. Hence, the two numbers that have an amount of 30 and produce the biggest conceivable item are 15 and 15.
The result of the two numbers is:
P(15, 15) = 15 * 15 = 225
So the result of the two numbers is 225.
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what is the addictive inverse of 36
Answer:
Step-by-step explanation: -36
I need some help with this problem please
(a) The result of row 1 and row 2 interchange is [3 -2 3]
[2 3 1]
(b) The result of multiplying and adding the matrix is [-1 5 -2]
[3 -2 3]
What is the row operation of the matrix?
The row operation of the matrix is calculated as follows;
The given matrix;
[2 3 1]
[3 -2 3]
To interchange row 1 and row 2, we determine it as follows;
R₁ ↔ R₂ = [3 -2 3]
[2 3 1]
The product of row 2 and -1 is calculated as;
-1 (R₂) = [-3 2 -3]
The addition of -1(R₂) + R₁ is calculated as;
-1(R₂) + R₁ = [-3 2 -3] + [2 3 1]
-1(R₂) + R₁ = [-1 5 -2]
new matrix = [-1 5 -2]
[3 -2 3]
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Find the area of the composite figure ?
The area of the composite figure is 81 yd². Option D
How to determine the areaThe composite figure is made up of a rectangle, a triangle and a trapezoid
The formula for the area of a rectangle is expressed as;
Area = length × width
Substitute the values
Area = 7(6)
Multiply the values
Area = 42 yd²
Area of the triangle = 1/2 base ×height
Area of the triangle = 1/2 × 6 ×5 = 30/2 = 15yd²
Area of the trapezoid = a+b/2 h
Substitute the values
Area = 7 + 9/2 (3) = 16/2(3) = 8(3) = 24yd²
Total area = 24 + 15 + 42 = 81 yd²
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The area of the composite figure is 81 cm²
What is area of composite figure?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Any figure that we can break and form more than one basic shape from is called a composite figure.
The figure consist of two trapezoid
Area of trapezoid 1 = 1/2( a+b) h
= 1/2 ( 12 + 7) 6
= 1/2 × 19 × 6
= 19 × 3
= 57cm²
area of trapezoid 2
= 1/2(a+b) h
= 1/2 ( 7+9) 3
= 1/2 × 16 × 3
= 8 × 3
= 24 cm²
Therefore the area of the composite figure
= 57 +24 = 81 cm²
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pls answer me fast rapidly:
The next day you take Zeek to the Arizona State Fair. His mom gives him $30 to
spend. It costs $13 to get in and the $2 for every ride. How many rides can he ride?
● Define a variable, ex: x = ________.
● Write an equation to model this situation.
● Solve the equation for your variable.
● Write your answer in a complete sentence.
● Give the page a relevant title.
Answer:
Step-by-step explanation:
Let’s define the number of rides that Zeek can ride as “r”.
To determine how many rides Zeek can ride, we need to first subtract the cost of admission from his total budget:
$30 - $13 = $17
This means that Zeek has $17 left to spend on rides. Since each ride costs $2, we can set up the following equation:
$2r = $17
To solve for “r”, we divide both sides of the equation by $2:
r = $8.50
So Zeek can ride a maximum of 8 rides with the $17 he has left after paying for admission. However, since he cannot ride a fraction of a ride, he may be limited to only 8 rides or fewer.
Is x-1
a factor of
x^5-3x^4-2x^3-5x^2+5x+12?
Correct The remainder when you divide is
The remainder theorem indicates that remainder when the polynomial x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) is 8
What is the remainder theorem?The remainder theorem specifies the relationship between the division of a polynomial by a linear factor to the value of the polynomial at a specified point
The remainder when the polynomial expression; x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by x - 1, can be found using the remainder theorem by plugging in x = 1 in the function as follows;
f(1) = 1⁵ - 3 × 1⁴ - 2 × 1³ - 5 × 1² + 5 × 1 + 12 = 8
The remainder when x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) therefore is 8
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I need help urgently on this problem, please and thank you
The inverse of function f is [tex]f^{-1}(x)=\frac{4}{x}-3[/tex].
The domain of f is (-∞, -3) U (-3, ∞).
The range of f = (-∞, 0) U (0, ∞)
The domain of f⁻¹ = (-∞, 0) U (0, ∞).
The range of f⁻¹ = (-∞, -3) U (-3, ∞).
How to determine an inverse function?In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value or domain) and dependent value (y-value or range) as follows;
f(x) = y = 4/(3 + x)
x = 4/(3 + y)
3 + y = 4/x
f⁻¹(x) = 4/x - 3
[tex]f^{-1}(x)=\frac{4}{x}-3[/tex]
By critically observing the graph of this rational expression (function) and its inverse shown in the image attached below, we can reasonably and logically deduce the following domain and range:
Domain of f = (-∞, -3) U (-3, ∞); {x|x ≠ -3}.
Range of f = (-∞, 0) U (0, ∞); {y|y ≠ 0}.
Domain of f⁻¹(x) = (-∞, 0) U (0, ∞); {y|y ≠ 0}.
Range of f⁻¹(x) = (-∞, -3) U (-3, ∞); {x|x ≠ -3}.
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What is -4 ≥ k - 2 I can not find it so please help...
Is x-7
a factor of
x^5+5x^4-2x^3+4x^2+8x+3976
?
Correct The remainder when you divide is
x-7 is a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$[/tex], we can use the Factor theorem which states that if f(a) = 0, then x-a is a factor of f(x).the remainder when we divide [tex]x^5+5x^4-2x^3+4x^2+8x+3976$[/tex] by x-7 is 4054.
To check if x-7 is a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$,[/tex] we can use the factor theorem which states that if f(a) = 0, then x-a is a factor of f(x).
To check if x-7 is a factor, we evaluate the polynomial at x=7:
[tex]f(7) = 7^5+5\cdot7^4-2\cdot7^3+4\cdot7^2+8\cdot7+3976 = 384004$.[/tex]
Since [tex]$f(7)\neq 0$[/tex], we can conclude that x-7 is not a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$.[/tex]
To find the remainder when we divide [tex]$x^5+5x^4-2x^3+4x^2+8x+3976$[/tex]by x-7, we can use polynomial long division or synthetic division. Using polynomial long division, we get:
[tex]x^4 + 12x^3 + 82x^2 + 578x + 4046\\x-7 | x^5 + 5x^4 - 2x^3 + 4x^2 + 8x + 3976\\- x^5 + 7x^4[/tex]
------------
[tex]12x^4 - 2x^3 + 4x^2 + 8x\\ 12x^4 - 84x^3[/tex]
-------------
[tex]82x^3 + 4x^2 + 8x\\ 82x^3 - 574x^2[/tex]
--------------
[tex]578x^2 + 8x\\ 578x^2 - 4046[/tex]
------------
4054
Therefore, the remainder when we divide [tex]$x^5+5x^4-2x^3+4x^2+8x+3976$ by $x-7$ is $4054$.[/tex]
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What is the surface area of a sphere with diameter 8 cm?
Answer:
A≈201.06cm²
Step-by-step explanation:
A=4πr2
d=2r
Solving forA
A=πd2=π·82≈201.06193cm²
Please help I’ll mark you as brainliest if correct
Answer:
5, 3
Step-by-step explanation:
What is the surface area of this cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth. 18 yd 9 yd
The surface area of the given cylinder is approximately 1758.4 square yards.
To find the surface area of a cylinder, we need to calculate the sum of the areas of its curved surface (lateral surface area) and its two circular bases.
Given:
Height (h) = 18 yards
Radius (r) = 10 yards
π (pi) ≈ 3.14
Lateral Surface Area:
The lateral surface area of a cylinder can be calculated using the formula 2πrh, where r is the radius and h is the height.
Lateral Surface Area = 2πrh
Substituting the given values, we have:
Lateral Surface Area = 2 × 3.14 × 10 × 18
Lateral Surface Area = 1130.4 square yards (rounded to the nearest hundredth)
Circular Bases:
The area of a circle can be calculated using the formula πr^2, where r is the radius.
Area of a Circular Base = π[tex]r^2[/tex]
Substituting the given radius, we have:
Area of a Circular Base = 3.14 × [tex]10^2[/tex]
Area of a Circular Base = 314 square yards
To find the total surface area, we need to add the lateral surface area and the areas of the two circular bases.
Total Surface Area = Lateral Surface Area + 2 × Area of a Circular Base
Substituting the values, we get:
Total Surface Area = 1130.4 + 2 × 314
Total Surface Area = 1758.4 square yards (rounded to the nearest hundredth)
Therefore, the surface area of the given cylinder is approximately 1758.4 square yards.
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Question
'What is the surface area of this cylinder? What is the surface area of this cylinder? Use I ~ 3.14 and round your answer to the nearest hundredth_ 18 yd 10 yd square yards'
4.1.2 Calculate the total number of deaths for all the countries.
Calculating the total number of deaths for all countries requires collecting data from various sources and summing up the individual death counts. Here is a step-by-step guide on how to approach this calculation:
Identify reliable sources: Look for reputable sources that provide updated and accurate information on global death counts.
Gather country-specific data: Access the data provided by these sources and collect the individual death counts for each country.
Validate and verify data: Cross-reference the data from multiple sources to ensure consistency and accuracy.
Sum up the death counts: Add up the individual death counts for each country to obtain the total number of deaths.
Regularly update the data: As the situation evolves, keep track of new data releases and updates.
Calculating the total number of deaths for all countries requires collecting data from various sources and summing up the individual death counts. Here is a step-by-step guide on how to approach this calculation:
Identify reliable sources: Look for reputable sources that provide updated and accurate information on global death counts. Examples include official government health agencies, international health organizations (e.g., WHO), and reputable databases (e.g., Worldometer, Johns Hopkins University).
Gather country-specific data: Access the data provided by these sources and collect the individual death counts for each country. Ensure the data is recent and covers a comprehensive list of countries.
Validate and verify data: Cross-reference the data from multiple sources to ensure consistency and accuracy. Different sources may have slight variations, so it's important to verify the data and use the most reliable figures.
Sum up the death counts: Add up the individual death counts for each country to obtain the total number of deaths. Use a spreadsheet or calculator to perform the calculations accurately.
Regularly update the data: As the situation evolves, keep track of new data releases and updates. Update the total number of deaths accordingly to maintain accuracy.
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The question probable may be:
How to calculate the total number of deaths for all the countries?
An archaeologist finds a barren land with a large number of fossils of Dinosaurs. The number N(t) of fossils that can be found per cubic meter after t years can be determined by solving the equation:
Assuming that the initial number of fossils is 100, estimate the number of fossils after 10 years.
The assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.
To estimate the number of fossils after 10 years, we need to solve the given equation. However, since the equation is not provided, we'll assume a simple exponential decay model for the population of fossils.
Let's assume the equation for the population of fossils is:
N(t) = N0 * e^(-kt)
where:
N(t) is the number of fossils after t years,
N0 is the initial number of fossils,
k is a decay constant, and
e is the base of the natural logarithm (approximately 2.71828).
Since the initial number of fossils is given as 100, we have N0 = 100. Now, we need to find the value of the decay constant (k) to estimate the number of fossils after 10 years.
Without further information, it's challenging to determine the exact decay constant. However, let's assume a hypothetical value of k = 0.1 for this example.
Plugging the values into the equation, we get:
N(10) = 100 * e^(-0.1 * 10)
= 100 * e^(-1)
≈ 100 * 0.36788
≈ 36.788
So, with the assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.
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Answer:
B. 2333.59
Step-by-step explanation:
We have been given the following differential equation:
[tex]\dfrac{dN}{dt}=\dfrac{5000}{6+5t}[/tex]
To find the number of fossils N(t) after t = 10 years, we first need to solve the differential equation using integration and the given parameters to create an equation for N(t) in terms of t.
Solving a differential equation means using it to find an equation in terms of the two variables, without a derivative term.
Rearrange the equation so that all the terms containing N are on the left-hand side, and all the terms containing t are on the right-hand side:
[tex]1\;dN=\dfrac{5000}{6+5t}\; dt[/tex]
Integrate both sides:
[tex]\displaystyle \int 1 \;dN=\int \dfrac{5000}{6+5t}\; dt[/tex]
Use the following integration rules:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Integration rulest}\\\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\;\;(where $n$ is any constant value)\\\\\\$\displaystyle \int \dfrac{n}{a+bx}\:\text{d}x=\dfrac{n}{b}\ln |a+bx|+\text{C}$\\\\ \end{minipage}}[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int 1\;dN&=\int \dfrac{5000}{6+5t}\; dt\\\\\implies N&=\frac{5000}{5}\ln \left|6+5t\right|+C\\\\N&=1000\ln \left|6+5t\right|+C\end{aligned}[/tex]
As the initial number of fossils is 100, then N = 100 when t = 0.
Substitute these values into the equation and solve for C:
[tex]100=1000\ln \left|6+5(0)\right|+C[/tex]
[tex]C=100-1000\ln (6)[/tex]
Therefore, the equation for N in terms of t is:
[tex]N=1000\ln \left|6+5t\right|+100-1000\ln(6)[/tex]
Use the quotient log rule to simplify:
[tex]N=1000\ln \left|6+5t\right|-1000\ln(6)+100[/tex]
[tex]N=1000\ln \left(\dfrac{\left|6+5t\right|}{6}\right)+100[/tex]
To estimate the number of fossils after 10 years, substitute t = 10 into the equation:
[tex]N=1000\ln \left(\dfrac{\left|6+5(10)\right|}{6}\right)+100[/tex]
[tex]N=1000\ln \left(\dfrac{56}{6}\right)+100[/tex]
[tex]N=2333.59\; \sf (2\;d.p.)[/tex]
Therefore, the number of fossils after 10 years is 2333.59.
Which is a whole number?
0.86
2/5
98
35%
Answer:
98 is a whole number
Step-by-step explanation:
0.86 is a decimal
2/5 is a fraction
35% is a percentage
Write the number 0.08 in scientific notation
The scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex] where 10 raised to an exponent (-2).
In scientific notation, a number is expressed as the product of a coefficient and a power of 10.
To write the number 0.08 in scientific notation, it as a decimal number multiplied by a power of 10.
So, 0.08 can be written in scientific notation as 8 x [tex]10^{(-2)[/tex].
In scientific notation, the number is written as the product of a coefficient (8) and a power of 10 raised to an exponent (-2), indicating the decimal's position relative to the coefficient.
Therefore, the scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex].
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Help, what is the value of x if the volume is 133 1/3
If the volume is 133 1/3 in³, the value of x is equal to 5 inches.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;
133 1/3 = 10 × x × 2 2/3
400/3 = 10 × x × 8/3
400/3 = 80x/3
80x = 400
x = 400/80
x = 5 inches.
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Which of the following statements are true?
Select all that apply.
A. 4 is a perfect cube.
B. 16 is a perfect square.
C. 2,197 is both a perfect square and a perfect cube.
D. 8 is a perfect cube.
E. 18 is neither a perfect square nor a perfect cube.
Answer:
B and D
Step-by-step explanation:
4²= 16
it's a perfect square
2³= 8
it's a perfect cube
A lion can run 1.89 miles in distance. If 1 mile is the
same as 5,280 feet, what is the distance that a lion
can run in feet?
PLEALSLE ANSWER FOR 70 POINTS
prove: the square of a number that is two more than a multiple of 3 is one more than a multiple of 3
Prove in below steps:
(3n + 2)² = 9n² + 12n + 4 = 9n² + 12n + 3 + 1 = 3(3n² + 4n + 1) + 1 = 1 more than a multiple of 3Proved
18.3% of the animals in the local shelter are neither cats nor dogs. 2% of those animals that are not cats or dogs are rabbits. If there are 267 animals in the shelter, approximately how many of them are rabbits? Do not round any numbers until you finish the problem
what would The number of discharge days for a patient admitted January 23 to February 15 is _____.
Answer:
The number of discharge days for a patient admitted January 23 to February 15 is 31 - 23 + 15 = 23
Exponent
T-Table
Coincident (Consistent
Dependent)
Systems of Equations
Inconsistent
Consistent Independent
1.
2.
3.
4.
5.
6.
A set of two or more equations
with the same variables.
A system of linear equations with
EXACTLY ONE solution.
A system of linear equations with
INFINITELY MANY solutions.
A system of equations with NO
solution.
A number representing how many
times the Base number should be
multiplied by itself.
A chart of the different values for
an equation or graph.
A set of two or more equations with the same variables.
A system of linear equations with EXACTLY ONE solution.
A system of linear equations with INFINITELY MANY solutions.
A system of equations with NO solution.
A number representing how many times the Base number should be multiplied by itself.
A chart of the different values for an equation or graph.
Systems of Equations:
A set of two or more equations with the same variables.
These equations are solved simultaneously to find the values of the variables.
Consistent Independent:
A system of linear equations with EXACTLY ONE solution.
This means that the lines represented by the equations intersect at a single point.
Consistent Dependent (Coincident):
A system of linear equations with INFINITELY MANY solutions.
In this case, the equations represent the same line or overlapping lines, and every point on the line is a solution.
Inconsistent:
A system of equations with NO solution.
This occurs when the lines represented by the equations are parallel and never intersect.
Exponent:
A number representing how many times the base number should be multiplied by itself.
For example, in the expression[tex]2^3,[/tex] the exponent is 3, which means 2 should be multiplied by itself 3 times [tex](2 \times 2 \times 2 = 8).[/tex]
T-Table:
A chart of the different values for an equation or graph.
It typically includes two columns: one for the input values (usually x) and one for the corresponding output values (usually y).
T-tables are helpful for understanding the relationship between the variables in an equation and for plotting points on a graph.
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Use substitution to solve the system of equations. How many solutions are there? 12 x − 13 y = 5 x = 23 y + 10 There are no solutions. There is one solution. There are infinitely many solutions.
Answer: there is one solution
Step-by-step explanation:
12x − 13y = 5
x = 23y + 10
lets substitute x into the first equation.
12(23y + 10) - 13y = 5
276y + 120 - 13y = 5
263y = -115
y = -115/263
substituting for x:
x = 23(-115/263) + 10
x = -2645/263 + 10
x = -15/263
As we can see, we get one value of x;
this means there is one solution
Given WX is tangent to ⊙S at point V, select all the statements that must be true.
A. m∠TVX =m∠TVX
B. m∠TSV =m∠UVX
C. m∠TVW = m∠TSV
D. m∠TUV =m∠TVW
E. m∠UVX =m∠VTU
Given WX is tangent to OS at point V, the statements that must be true include:
A. m∠TVX =m∠TVX
C. m∠TVW = m∠TSV
D. m∠TUV =m∠TVW
How to explain the tangentIn mathematics, a tangent is a line that touches a curve at exactly one point, without intersecting it at that point. The tangent line at a point on a curve represents the slope of the curve at that point. The concept of tangent is important in calculus, where it is used to calculate derivatives of functions.
TUV = 1/2MTU = TVW
TUV = TVW
Also, MTV = TSV = 2TVW
TVW = TSV
The correct options are A, C and D.
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A high school is building a new gym in the shape off a pyramid. Its base is a square with each side 500 feet long and has a slant height of 60 feet. What is the surface area of this pyramid?
The surface area of the pyramid is approximately 393,560 square feet.
To find the surface area of the pyramid, we need to find the area of each of the four triangular faces and the area of the square base.
The area of the square base is simply the area of a square with side length 500 feet:
Area of base =[tex](side length)^2 = (500 feet)^2[/tex]= 250,000 square feet.
To find the area of each triangular face, we need to know the length of one of the sides of the base and the slant height of the pyramid.
Since the base is a square, all sides have the same length of 500 feet.
Using the Pythagorean theorem, we can find the height of each triangular face:
height = √(slant heigh[tex]t^2[/tex] - base lengt[tex]h^2[/tex]/4)
height = √([tex]60^2 - (500/2)^2[/tex])
height = √(3600 - 62500/4)
height = √(3600 - 15625)
height = √20375
height ≈ 142.76 feet
Now we can find the area of one of the triangular faces:
Area of triangular face = (1/2) x (base length) x (height)
Area of triangular face = (1/2) x 500 feet x 142.76 feet
Area of triangular face ≈ 35,690 square feet
Since there are four triangular faces, the total surface area of the pyramid is:
Total surface area = 4 x (Area of triangular face) + (Area of base)
Total surface area = 4 x 35,690 square feet + 250,000 square feet
Total surface area ≈ 393,560 square feet
for such more question on surface area
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