Answer:
We can solve for x by using logarithms.
9^(x + 10) + 3 = 92
9^(x + 10) = 89
Take the log base 9 of both sides:
x + 10 = log9(89)
x = log9(89) - 10
To find the value of log9(89), you can use a logarithm table or calculator.
The solution for x is:
x = log9(89) - 10
Please help! Ordering angles least to greatest as well as side lengths
As side EG is the largest side at 15, and the greatest angle is the opposite side's angle, ∠F.
what is triangle ?Given that it consists of sides and three vertices, a triangle qualifies as a polygon. It connects to the fundamental geometric shapes. Triangle ABC is the term used to refer to such a triangle with the points A, B, and C. When the three points are not collinear, a unique plane and triangle in Geometric forms are discovered. Triangles are polygons because they have three sections and three corners. The points where the four structures of the triangle converge are referenced to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.
given
Find the smallest angle by finding the angle opposite the smallest side, then the medium-sized angle by finding the angle opposite the medium-sized side .
Then the greatest angle by finding the angle opposite the largest side when there are three side lengths available.
As side FG is the smallest side at 7, and the smallest angle is the one across from it, ∠ E.
The opposing angle, ∠G, is the medium-sized angle, just as side EF is a medium-sized side as measured by 12.39.
As side EG is the largest side at 15, and the greatest angle is the opposite side's angle, ∠F.
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The complete question is :-
a) Order the angle measures m∠E , m∠F and m∠EGF from least to greatest ad well as side length .
A cup of coffee contains approximately 95 mg of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how long will it take for half of the caffeine to be eliminated from a person’s body?
What is the percent of increase from 40 to 48
-1+p<15 what is the value of p?
Answer:
-1+p<15
=-1+1+p<15+1
=p<16
Cora is using successive approximations to estimate a positive solution to f(x) = g(x), where f(x)=x2 - 8 and g(x)=2x - 4. The table shows her results for different input values of x. Use Cora's process to find the positive solution, to the nearest tenth, of f(x) = g(x)
The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).
To find the positive solution, to the nearest tenth, of f(x)=g(x) using Cora's process, the steps are as follows:
Input the initial value of x, for example x=0.
Calculate f(x) and g(x):
f(x) = x2 - 8 = 0 - 8 = -8 g(x) = 2x - 4 = 0 - 4 = -4If f(x) is less than g(x), then x should be increased and vice versa.
Increase or decrease x accordingly and calculate the new values of f(x) and g(x).
Keep repeating steps 3 and 4 until the difference between the values of f(x) and g(x) is less than 0.1.
The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).
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the position of the particle as a function of time is given by x(t) = e-(t - 3)2, where x is in meters and t is in seconds. what is the velocity of the particle, in meters per second, at t = 2.9 s?
For a particle having a position of function e^-(t - 3)², the velocity at 2.9s is obtained as 0.198008 m/s.
What is velocity?
The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.
The position of a particle is denoted by a function x(t) = e^-(t - 3)², where x is the distance and t is the time.
Differentiate the function -
v(x) = d/dt(x) = d/dt[e^-(t - 3)²]
v(x) = e^-(t - 3)²[-2(t - 3)]
Now, substitute the value of t = 2.9 in the equation -
v(2.9) = e^-(2.9 - 3)²[-2(2.9 - 3)]
v(2.9) = e^-(-0.1)²[-2(-0.1)]
Use the exponent formula a^-b = 1/a^b -
v(2.9) = 1/e^(-0.1)²[0.2]
Square the digit (0.1) -
v(2.9) = 1/e^(0.01)[0.2]
Substitute the value ofe^0.01 = 1.01005 -
v(2.9) = (1/1.01005)[0.2]
Use the arithmetic operation of division -
v(2.9) = (0.99004)[0.2]
v(2.9) = 0.198008
Therefore, the velocity of the particle is 0.198008 m/s.
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The function h(x) = -x +34 models the height of the roof of a house, where x is the horizontal distance from the center of the house. If a raindrop
falls from the end of the roof, how far from the center of the base does it land? Explain your solution.
The horizontal distance of a raindrop that falls from the end of the roof to the center of the base of the house, obtained from the linear equation for the height of the roof is; x = 18 feet
What is a linear equation?A linear equation is an equation that has one as the highest index, and which when graphed, forms a straight line.
The linear function for the height of the roof is, h(x) = -|x| + 34
Where;
h(x) = The height of the roof
x = The horizontal distance from the center of the roof
The minimum height of the roof, obtained from the diagram = 16 feet
Therefore, we get, when h(x) 16, substituting the value h(x) = 16, in the function for the height of the roof, we get;
h(x) = -|x| + 34
h(x) = 16
Therefore, 16 = -|x| + 34 (substitution property)
|x| = 34 - 16 = 18
The distance from the center of the house, which corresponds to the least height of the roof, which is the end of the roof and the location at which the raindrop falls is; x = 18 feet
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how to reccepts 10 integers from the user using an array and a loop. the user will type the input on the console.
The reaccepts 10 integers from the user using an array and a loop is explained below.
To start, you need to declare an array variable that can store 10 integers. For example, you can declare an array variable called "numbers" as follows:
int numbers[10];
Next, you will use a loop to repeatedly ask the user to input an integer. The loop will run 10 times to receive 10 integers. You can use the for loop for this purpose.
Here is an example:
for (int i = 0; i < 10; i++) {
printf("Enter integer %d: ", i + 1);
scanf("%d", &numbers[i]);
}
In this code, the for loop starts with the value of i being 0. It runs until i is less than 10. After each iteration, i is incremented by 1.
After the loop finishes, all 10 integers received from the user are stored in the numbers array. You can access them using the index of the array.
In conclusion, to receive 10 integers from the user using an array and a loop, you need to declare an array variable, use a for loop to repeatedly ask the user for input, and store the input in the array using the scanf function.
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how many faces edges and vertices does a rectangular prism have
A rectangular prism has 6 faces, 8 vertices and 12 edges.
What is rectangular prism?
A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid. A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.
If all the faces of the prism are squares then the rectangular prism is a cube. The volume of a rectangular prism is a measure of the space inside the prism.
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A rectangular field, 400 m long, has an area of 6 hectares. Calculate the perimeter of the field [ 1 hectare=10000m2] What's the answer to this question and what is the way to solve it!
The perimeter of this rectangular field is equal to 1,100 meters.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width of a rectangle.L represents the length of a rectangle.Note: Area = 6 × 10,000 = 60,000 m^2.
Next, we would determine the width of this rectangle:
60,000 = 400W
W = 60,000 /400
Width, W = 150 m.
Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;
Perimeter of a rectangle = 2(L + W)
Perimeter of a rectangle = 2(400 + 150)
Perimeter of a rectangle = 2(550)
Perimeter of a rectangle = 1,100 meters.
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The perimeter of the rectangular field with an area of 6 hectares and length of 400m is 1100 meters.
What is the perimeter of the field?The perimeter of a rectangle is expressed as;
P = 2( length + width )
Given the data in the question;
Length of the field = 400m Area of the field = 60,000m²Width of the field = ?First, we determine the width of the field using the area formula.
Area = Length × width
Plug in the values and solve for width
60,000m² = 400m × width
60,000m² / 400m = Width
Width = 150m
Now, the perimeter will be;
P = 2( 400 + 150 )
P = 2( 550 )
P = 1100 meters.
Therefore, the perimeter is 1100 meters.
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What is the sum?
(9c-8) + (2c-6)
Answer:
The sum is 11c - 14.
plot y = sin(x), x = 0...720 deg, where only the positive values of y are shown on the plot. use loops (for, while) to generate the x and y data, using 1 degree increments of x.
We convert the x value from degrees to radians using math.radians. If the sine value is positive, we append it to the y_values list. If the sine value is negative, we append 0 to the y_values list instead.
Here's a code snippet in Python that generates the x and y data for the sine function with a 1 degree increment of x from 0 to 720 degrees:
import math
x_values = []
y_values = []
for x in range(0, 721, 1):
x_values.append(x)
y = math.sin(math.radians(x))
if y >= 0:
y_values.append(y)
else:
y_values.append(0)
In this code, we use the math.sin function to calculate the sine value for a given x in radians. We convert the x value from degrees to radians using math.radians. If the sine value is positive, we append it to the y_values list. If the sine value is negative, we append 0 to the y_values list instead.
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Name the seven types of quadrilaterals?
Different Quadrilateral Types
Trapezium.Parallelogram.Rectangle.Rhombus.Square.Kite.What is meant by quadrilateral?A polygon with four sides, four vertices, and four angles is called a closed quadrilateral. A polygon with four sides, such as a square, rectangle, or rhombus, is referred to as a quadrilateral.You are most likely currently staring at a computer screen that resembles a quadrilateral. Geometry lessons cover the quadrilateral as a geometrical shape.A polygon with four sides exactly is referred to as a quadrilateral. The fact that a quadrilateral has exactly four vertices and four angles is also implied by this. When discussing 2-D figures, it's common to talk about both the inside and the boundary (the line segments that make up the figure's edges).To learn more about quadrilaterals, refer to:
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I need help seeing if I’m correct with my answers .please and thank you
Answer:
Step-by-step explanation:
13) 5.38 Slightly off
14) 10.4 Correct
15) Can't read the numbers
16) 11.7 slightly off
17) Can't read (be careful with which side goes where in the Pythagorean Theorem calculation. a^2 + b^2 = c^2 where a and b are the two sides and c is the hypotenuse (across from the right angle).
18) 16.46
19) 10.57
20) 7.04
21) 4.87 It seems that the hypotenuse is given as 7.2, so the equation should be 5.3^2 + x^2 = 7.2^2
22) Same as in 21: 2.7^2 + x^2 = 6.5^2 x = 5.91
[But I'm having difficulty reading the problems due to fuzziness]
solve for x
2x-24 4x+6
Answer:
x=33
Step-by-step explanation:
[tex]180=2x-24+4x+6[/tex]
[tex]180=6x-18[/tex]
[tex]198=6x[/tex]
[tex]x=33[/tex]
Solve for x in the diagram below
The value of the variable x in the given right angle expression is; x = 11
How to solve right angle problems?We know that a right angle simply means an angle that is equal to 90 degrees.
Now, we see that the sum total of the angle in the diagram is 90 degrees and as such the sum of the two internal angles will be 90 degrees.
Thus;
5x + 35 = 90
Subtract 35 from both sides to get;
5x = 55
x = 55/5
x = 11
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What are the patterns?
(Please help I have no idea)
Line 1:
Line 2:
Line 3:
The patterns are:
Line 1: T A C G T T T A A T G A G G C C C T A G T G
Line 2: T C C C C T A G T C G T G G C C T A A A G T C
Line 3: A C T G C T A G C T A C G T T A T C G T C C G
What is base pairing?Base pairing rule refers to the specific pairing of nitrogenous bases in DNA. According to this rule, adenine (A) pairs with thymine (T) and cytosine (C) pairs with guanine (G) through hydrogen bonds. This base pairing results in a complementary sequence of nucleotides on the two strands of DNA, forming a stable double helix structure.
The base pairing rule ensures the accurate replication and transmission of genetic information from one generation to the next. The DNA strands become:
a. Original: A T G C A A A T T A C T C A C C G G G A T C A C
Complementary: T A C G T T T A A T G A G G C C C T A G T G
b. Original: A G G G G A T C A G C A C C G G A T T T C A T G
Complementary: T C C C C T A G T C G T G G C C T A A A G T C
c. Original: T G A C G A T C G A T G C A C A T G C A T G G C
Complementary: A C T G C T A G C T A C G T T A T C G T C C G.
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a rectangular bin with a square base, an open top, and a volume of 62,500 cm3 is to be made. what is the minimum surface area for the bin? enter only the minimum surface area, and do not include units in your answer.
Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm^2.
What is rectangle ?
A rectangle is a two - dimensional shape with four sides, where each pair of opposite sides are equal in length and parallel to each other
Let's say the length, width and height of the rectangular bin are l, w and h respectively. The volume of the bin can be expressed as:
V = l * w * h = 62500 cm^3 (Given)
Since the base is a square, have w = l. Therefore,
V = l^2 * h
h = V / l^2 = 62500 / l^2
The surface area of the bin can be expressed as:
A = 2lw + 2lh + 2wh
Substituting the value of w = l and h = V / l^2, get:
A = 2l^2 + 2l * (V / l^2) + 2l * l = 2l^2 + 2V / l + 2l^2 = 4l^2 + 2V / l
To minimize the surface area, differentiate A with respect to l and set it to zero:
dA/dl = 8l + 2V / l^2 = 0
4l^3 = V
l^3 = V / 4
Taking the cube root of both sides,
l = (V / 4)^(1/3)
Substituting the value of V,
l = (62500 / 4)^(1/3) = (15625)^(1/3) = 125 cm
Since w = l,
w = 125 cm
h = V / l^2 = 62500 / (125)^2 = 250 cm
The minimum surface area is then given by,
A = 2lw + 2lh + 2wh = 2 * 125 * 125 + 2 * 125 * 250 + 2 * 125 * 125 = 31250 cm^2
Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm^2.
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Minimum surface area of rectangular bin with 62,500 cm³ volume and square base is 31250 cm^2.
A rectangle is a two - dimensional shape with four sides, where each pair of opposite sides are equal in length and parallel to each other
Let's say the length, width and height of the rectangular bin are l, w and h respectively. The volume of the bin can be expressed as:
V = l * w * h = 62500 cm³ (Given)
Since the base is a square, have w = l. Therefore,
V = l² * h
h = V / l² = 62500 / l²
The surface area of the bin can be expressed as:
A = 2lw + 2lh + 2wh
Substituting the value of w = l and h = V / l^2, get:
A = 2l² + 2l * (V / l²) + 2l * l = 2l²+ 2V / l + 2l² = 4l² + 2V / l
To minimize the surface area, differentiate A with respect to l and set it to zero:
dA/dl = 8l + 2V / l² = 0
4l³ = V
l³ = V / 4
Taking the cube root of both sides,
l = (V / 4)^(1/3)
Substituting the value of V,
l = (62500 / 4)^(1/3) = (15625)^(1/3) = 125 cm
Since w = l,
w = 125 cm
h = V / l² = 62500 / (125)²= 250 cm
The minimum surface area is then given by,
A = 2lw + 2lh + 2wh = 2 * 125 * 125 + 2 * 125 * 250 + 2 * 125 * 125 = 31250 cm²
Minimum surface area of rectangular bin with 62,500 cm^3 volume and square base is 31250 cm².
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A rectangle has sides measuring (3x + 5) units and (6x + 11) units. Part a: what is the expression that represents the area of the rectangle? show your work to receive full credit. Part b: what are the degree and classification of the expression obtained in part a? part c: how does part a demonstrate the closure property for polynomials?.
Part a: The expression that represents the area of the rectangle is A = (3x + 5)(6x + 11). To calculate the area, we must multiply the two sides of the rectangle together. The length of the rectangle is 3x + 5 units and the width of the rectangle is 6x + 11 units. Therefore, the area is (3x + 5)(6x + 11).
Part b: The degree of the expression obtained in part a is 2 and the classification is a binomial.
Part c: The closure property for polynomials states that the result of combining two polynomials is also a polynomial. In part a, we combined two polynomials, 3x + 5 and 6x + 11, to form the expression (3x + 5)(6x + 11). This expression is also a polynomial, demonstrating the closure property for polynomials. The closure property for polynomials allows us to combine two polynomials and still have a polynomial as the result. This is important in mathematics because it allows us to simplify equations and solve problems more quickly and efficiently.
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Inverse Variation
Independent Practice
Suppose a camper took 2 h to ride around a resevoir at 10 mi/h at the beginning of the summer. By the end of the summer, she can ride around the resevoir in 1
h. What is her rate at the end of the summer?
A. 30 mi/h
B. 0.35 mi/h
C. 13.3 mi/h
D. 9.5 mi/h
Her rate at the end of the summer is 20 miles per hour.
What is her rate at the end of the summer?We can define the rate in this case as the change in position as a function of the time.
So, the rate would be something like a speed (exactly a speed, actually).
Initially, the camper travles at a rate of 10mi/h in 2 hours, so the total distance is:
d = (10mi/h)*2h = 20mi
And at the end of the sumer, the camper travels that distance in one hour, so the rate at the end of the summer is:
R = 20mi/1h = 20mi/h
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Please help me outtt
Hey there!
|2x + 1| < -4
Since you have an absolute value that is LESS than 0, we can say that it doesn’t have any solutions.
Thus, your answer should be:
NO SOLUTIONS
REMEMBER: If your absolute value is smaller/less than 0, you would NOT have any solutions to the particular equation (like this one you have provided just now)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Neil rents a bike that costs $12 for 4 hours and $18 for 7 hours. Whats the slope?
Answer: 2
Step-by-step explanation:The slope of a line is the ratio of the change in y-values to the change in x-values between two points on the line.
To find the slope, we first need to find two points on the line, for example (4,12) and (7,18).
Then, the slope can be calculated as:
(18 - 12) / (7 - 4) = 6 / 3 = 2.
The slope is 2.
Assume 2. 0 kg of apples is 1 dozen and that each apple has 8 seeds. How many seeds are in 14 kg of apples?.
Answer:56
Step-by-step explanation:
You divide 14kg by 2kg and get 7kg. So then you times 7kg by 8 seeds.
Hope this helps :)
Ellen has maxed out her credit card at $19,500 and vows not to make any other credit card purchases. Her credit card company charges 1. 5% interest per
month, and the minimum monthly payment is all interest due plus 3% of the principal balance. How much of the balance can Ellen pay down if she pays the
minimum payment only for 3 months? Round the answer to the nearest cent.
After three months, Alan would have paid off how many dollars?
Answer:
$538
Step-by-step explanation:
The minimum payment in the first month would be:
Minimum payment = 1.5% * $19,500 + 3% * $19,500 = $292.25
At the end of the first month, the balance would be:
Balance = $19,500 + $19,500 * 1.5% - $292.25 = $19,318.375
In the second month, the minimum payment would be:
Minimum payment = 1.5% * $19,318.375 + 3% * $19,318.375 = $291.26
At the end of the second month, the balance would be:
Balance = $19,318.375 + $19,318.375 * 1.5% - $291.27 = $19,138.89
In the third month, the minimum payment would be:
Minimum payment = 1.5% * $19,138.89 + 3% * $19,138.89 = $290.26
At the end of the third month, the balance would be:
Balance = $19,138.89 + $19,138.89 * 1.5% - $290.26 = $18,961.62
So, Ellen would have paid off $19,500 - $18,961.62 = $538.38. The answer rounded to the nearest cent is $538
-1 = 2x - y, 8x - 4y = -4 using substitution
Answer:
Infinitely many solutions
Explanation:
1) subtract “1” from both sides to get y by itself
Y=-2x-1
2) 4y+8x=-4 share a gcf of “4” so you can divide the whole equation by 4
y+2y=-1
Now substitute “-2x-1” as y
(-2x-1)+2x=-1
-2x and 2x cancel each other and so does -1 and -1
Hence, this system has infinitely many solutions
Answer:
x = 0, y = 1.
Step-by-step explanation:
We can solve for the variables x and y by using substitution. Let's start by solving the first equation for one of the variables:
-1 = 2x - y
y = 2x + 1
Next, we'll substitute y = 2x + 1 into the second equation:
8x - 4y = -4
8x - 4(2x + 1) = -4
Expanding the second equation:
8x - 8x - 4 = -4
-8x - 4 = -4
-8x = 0
x = 0
Finally, we can use one of the equations to find y:
y = 2x + 1
y = 2(0) + 1
y = 1
So, the solution is x = 0, y = 1.
What can you infer about non-Euclidean geometry
Non-Euclidean geometries provide a different and more general view of geometry that can help better understand the nature of space and the relationships between objects in the world .
What is Non-Euclidean geometry ?Non-Euclidean geometry is a branch of mathematics that studies the properties and characteristics of geometries that are different from Euclidean geometry, which is the traditional study of geometry and the one most people are familiar with .
Non-Euclidean geometries differ from Euclidean geometry in that they have different postulates , or basic assumptions , about the relationships between points, lines, and angles .
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The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system. [1 0 0 -2 1 0 0 0 -3 1 0 0 0 -1 1 4 -5 4 3] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The solution has infinitely many elements.
O B. The solution set is empty.
The solution set contains one solution:
The solution to the original system is:x1 = 0, x2 = 0, x3 = -1, x4 = -3, x5 = 1
How to find the solution to the original system?The given matrix is in row echelon form, meaning that the leading entry of each non-zero row is to the right of the leading entry of the previous row. In this form, the solution to the linear system can be found by back substitution.
Starting from the bottom row, we have the equation:
-1 * x4 + 4 * x5 = -1
Solving for x4, we have:
x4 = -4 * x5 + 1
Moving up to the next row, we have:
0 * x1 + 0 * x2 + 3 * x5 = 3
Solving for x5, we have:
x5 = 1
So, x4 = -4 * 1 + 1 = -3.
Next, the third row gives us:
0 * x1 + 0 * x2 - 3 * x3 + 4 * x4 = 4
Substituting the value of x4, we have:
0 * x1 + 0 * x2 - 3 * x3 + 4 * (-3) = 4
Solving for x3, we have:
x3 = -1
Since there are no more non-zero rows in the matrix, we have found a complete solution for the linear system.
The solution set of the original system is the set of all possible values of (x1, x2, x3, x4, x5) that satisfy the system of equations represented by the matrix. Since the given matrix is in row echelon form, this solution set is unique and consists of a single point in the 5-dimensional space.
The solution to the original system is:
x1 = 0, x2 = 0, x3 = -1, x4 = -3, x5 = 1
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4. You are painting the roof of a
boathouse. You are going to
place the base of a ladder
3.2 feet from the boathouse.
How long does the ladder
need to be to reach the
roof of the boathouse?
K
3.2 ft
12.6 ft
Answer:
ladder has to be at least 13 ft long
Step-by-step explanation:
l = length of the ladder
12.6² + 3.2² = l²
l² = 158.76 + 10.24 = 169
√l² = l = √169 = 13
The ladder is the hypotenuse of a right triangle with sides 12.6 and 3.2
ten people are sitting in a row of ten chairs, chewing gum. each person spits out their gum and places it either under their own chair or under an immediately adjacent chair. how many ways can this happen such that every chair ends up with exactly one piece of gum under it?
There are 512 ways that every chair can end up with exactly one piece of gum under it.
This problem can be solved using the Principle of Inclusion-Exclusion.
Let's call the number of ways that gum is placed under a chair i "Ai". Then we have:
A1 = 1
A2 = 2
A3 = 4
...
A10 = 1024
Now, we want to calculate the number of ways that gum is placed under every chair such that exactly one piece of gum is placed under each chair. To do this, we need to subtract the number of ways that gum is placed under two chairs and add the number of ways gum is placed under three chairs, and so on.
The number of ways that gum is placed under two chairs can be calculated as:
C(10, 2) * 2^8 = 45 * 256 = 11520
The number of ways that gum is placed under three chairs can be calculated as:
C(10, 3) * 2^7 = 120 * 128 = 15360
Continuing this process, we have:
A = 1024 - 11520 + 15360 - 14336 + 8192 - 2048 + 256 - 16 + 1 = 512
So there are 512 ways that every chair can end up with exactly one piece of gum under it.
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There are 512 ways that every chair can end up with exactly one piece of gum under it.
This problem can be solved using the Principle of Inclusion-Exclusion.
Let's call the number of ways that gum is placed under a chair i "Ai". Then we have:
A1 = 1
A2 = 2
A3 = 4
...
A10 = 1024
Now, we want to calculate the number of ways that gum is placed under every chair such that exactly one piece of gum is placed under each chair. To do this, we need to subtract the number of ways that gum is placed under two chairs and add the number of ways gum is placed under three chairs, and so on.
The number of ways that gum is placed under two chairs can be calculated as:
C(10, 2) * 2^8 = 45 * 256 = 11520
The number of ways that gum is placed under three chairs can be calculated as:
C(10, 3) * 2^7 = 120 * 128 = 15360
Continuing this process, we have:
A = 1024 - 11520 + 15360 - 14336 + 8192 - 2048 + 256 - 16 + 1 = 512
So there are 512 ways that every chair can end up with exactly one piece of gum under it.
To learn more about Subtract
brainly.com/question/2346316
#SPJ4
−4( w + 1) = −24
Thanku