what are the answers to these questions?
The values of the expression are,
⇒ x₂ = - 9.4
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
Given that;
Expression is,
e²ˣ = - 2x - 1
Hence, Function is,
⇒ f (x) = e²ˣ + 2x + 1 = 0
⇒ f' (x) = 2e²ˣ + 2
Now, By newton's method;
⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))
⇒ x₂ = x₁ - f (x₁) / f' (x₁)
⇒ x₂ = - 5 - (e¹⁰ + 10 + 1)/(2e¹⁰ + 2)
⇒ x₂ = - 5 - (e¹⁰ + 11)/(2e¹⁰ + 2)
⇒ x₂ = - 5 (2.6 + 11) / ( 2 x 2.6 + 2)
⇒ x₂ = - 68 / 7.2
⇒ x₂ = - 9.4
⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))
⇒ x₃ = x₂ - f (x₂) / f' (x₂)
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
Thus, The values of the expression are,
⇒ x₂ = - 9.4
⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)
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Consider the following statements:
Which of the statement(s) regarding the "limit" concept in
Mathematics is/are TRUE and which is/are FALSE?
I
A limit is a point or value that a pattern, function or sum of
a series, approaches as the number of terms in the series
increases.
II A limit is a value that a function approximates for a given
input value.
III A limit is a value we get closer and closer to, but never
quite achieve.
I: TRUE - A limit is a value that a function, pattern, or sum of a series approaches as the number of terms or input value increases.
What is a Limit in Mathematics based on the given context?II: TRUE - A limit can also be a value that a function approximates for a specific input value, especially when dealing with continuity or differentiability.
III: FALSE - Although a limit might seem like a value that is never quite achieved, it can be reached or even exceeded, depending on the function and its behavior.
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Please help confused thank you
The solution to the inputs of the given function are:
a) f(0) = 13
b) f(2) = -1
c) f(-2) = 27
d) f(1) + f(-1) = 26
How to solve Function Inputs?The set of input values of a function is referred to as the domain of the function. Then, the set of output values of the function is referred to as the range of the function. Thus, if we possess a set of ordered pairs, we can find the domain by listing all of the input values, which are the x-coordinates.
We are given the function:
f(x) = (-x)³ - x² - x + 13
a) f(0) = (-0)³ - (0)² - 0 + 13
f(0) = 13
b) f(2) = (-2)³ - (2)² - 2 + 13
f(2) = -1
c) f(-2) = (2)³ - (-2)² + 2 + 13
f(-2) = 27
d) f(1) = (-1)³ - (1)² - 1 + 13
f(1) = 10
f(-1) = (1)³ - (-1)² + 1 + 13
f(-1) = 16
f(1) + f(-1) = 10 + 16 = 26
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PLS HELP ME WITH THIS QUESTION PLS
PLS SHOW YOUR WORKING OUT
The value of p is -3/2, the value of q is -1/(t+1), and the value of r is 2.
How did we get these values?Let the first term of the arithmetic series be a, and the common difference be d = 3. Then, we have:
a = 2t + 1
n-th term = a + (n-1)d = 2t + 1 + 3(n-1) = 3n + (2t - 2)
(Notice that the second equation can be found by substituting the expression for a into the formula for the n-th term and simplifying.)
We also know that the n-th term is given by (14t - 5), so we can equate the two expressions:
3n + (2t - 2) = 14t - 5
Simplifying and solving for n, we get:
n = (12t + 3)/3 = 4t + 1
So, the n-th term can also be expressed as:
3n + (2t - 2) = 3(4t + 1) + (2t - 2) = 14t - 5
Simplifying, we get:
14t - 5 = 14t - 5
This confirms that our expressions for the first term, common difference, and n-th term are all consistent with each other.
Now, we can use the formula for the sum of an arithmetic series to find the sum of the first n terms:
S_n = (n/2)(2a + (n-1)d) = (n/2)(4t + 4t + 1 + 3n - 3) = (3/2)n^2 + (5/2)t - 3n/2 + 1/2
We want to rewrite this expression in the form p(qt - 1)^r. To do this, we can try to complete the square in the n term, like this:
S_n = (3/2)[n^2 - 2n(t+1) + (t+1)^2] + (5/2)t - (3/2)(t+1)^2 + 1/2
S_n = (3/2)[n - (t+1)]^2 - (1/2)(t+1)^2 + (5/2)t + 1/2
Let u = n - (t+1), so that:
S_n = (3/2)u^2 - (1/2)(t+1)^2 + (5/2)t + 1/2
We want to rewrite this in the form p(qt - 1)^r, so let's try to match the terms:
p = -3/2
q = -1/(t+1)
r = 2
Therefore, the value of p is -3/2, the value of q is -1/(t+1), and the value of r is 2.
Note that the assumption that t is greater than 0 was not necessary for the derivation of the sum formula, but it is necessary for the existence of the arithmetic series (since otherwise the first term would be negative).
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The text format of the question in the picture:
22. The first term of an arithmetic series is (2t + 1) where t is > 0 The nth term of this arithmetic series is (14t - 5)
The common difference of the series is 3
The sum of the first n terms of the series can be written as p(qt - 1)^r where p, q and r are integers.
Find the value of p, the value of q and the value of r Show clear algebraic working.
Please help quickly I'm begging!
Assignment details: In this assignment, you will create two graphs and answer questions about Bond's Gym, the business you are supporting.
The functions are f(x) = 600 - 10x & g(x) = 20/3x, and the graphs are added as attachments
Creating the functions of the Bond's GymFrom the question, we have the following parameters that can be used in our computation:
The table of values
For the membership application, we have the following features
Initial value = 600Constant rate of change = (450 - 600)/(15 - 0) = -10So, the function is
f(x) = 600 - 10x
For the membership available, we have the following features
Initial value = 0Constant rate of change = (100 - 0)/(15 - 0) = 20/3So, the function is
g(x) = 20/3x
So, the functions are f(x) = 600 - 10x & g(x) = 20/3x
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I need some assistance with this ? Please
Answer:
I am sorry this is just so new for me like what even is an "imaginary" solution, i am in 6th grade wth
Last week Kristen spent 4 hours gardening over a period of 7 days .she spent the same amount of time gardening each day.about how much time did she spend gardening each day last week
Answer:
28
Step-by-step explanation:
i did 7 times 4
Company B needs to hire 30 new employees. Ten percent (10%) of applicants do not
meet the basic business requirements for the job, 12% of the remaining applicants
do not pass the pre-screening assessment, 23% of those remaining applicants do
not show up for the interview, and 5% of those remaining applicants fail the
background investigation. How many applicants need to apply in order to meet the
hiring target?
Company B needs approximately 55 applicants to apply in order to meet their hiring target of 30 new employees, taking into account the percentages of applicants who do not meet the requirements or pass the various stages of the hiring process.
Let's start with the total number of applicants needed to meet the hiring target of 30 new employees. We can call this number "x". We'll work backwards from there to find the number of applicants that need to apply in order to get 30 new employees.
We know that 5% of the remaining applicants fail the background investigation, which means that 95% pass. We also know that 23% of the remaining applicants do not show up for the interview, which means that 77% do show up.
Similarly, 12% of the remaining applicants do not pass the pre-screening assessment, which means that 88% do pass. Finally, 10% of all applicants do not meet the basic business requirements for the job, which means that 90% do meet the requirements.
Putting all of this information into the following equation;
0.9x × 0.88 × 0.77 × 0.95 = 30
Simplifying and solving for x, we get;
x = 30 / (0.9 × 0.88 × 0.77 × 0.95)
x ≈ 55.24
Therefore, Company B needs approximately 55 applicants.
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HELP PLEASE I REALLY NEED HELP ON THIS QUESTION HELP!
The number for which the theoretical probability matches the experimental probability is 2.
What is experimental and theoretical probability?
Experimental probability and theoretical probability are two different ways to determine the likelihood of an event occurring.
Experimental probability is determined by performing an experiment or conducting observations and collecting data to see how often an event occurs. This method involves counting the number of times an event occurs and dividing that number by the total number of trials or observations.
Theoretical probability, on the other hand, is determined by using mathematical principles and calculations to determine the likelihood of an event occurring. It is based on the assumption that all outcomes are equally likely.
In the given table;
For theoretical, P(2) = 1/4
For experimental, P(7) = 7/28 = 1/4
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If you look at these six numbers, you can see they range from 98 all the way to 642. Would the best interval to use for this group be 10 or 100?
If you look at the six numbers (101, 203, 407, 512, 98, 642) you can see they range from 98 all the way to 642. the best interval to use for this group be 100.
What is the range?The right interval to utilize for this set of numbers depends on the aim of the analysis.
If we want to look on the single values and small differences between them, then using interval of 10 would be more better. This would give u room to see small changes that exist between adjacent numbers.
So, in the event that we need to look on the full range and distribution of the numbers, an interval of 100 would be more better. This would permit us to see how the numbers are shared over a larger area of values.
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See full question below
If you look at these six numbers, you can see they range from 98 all the way to 642. Would the best interval to use for this group be 10 or 100?
101, 203, 407, 512, 98, 642
- x²= +x +12=0 .....................................
Therefore, the solutions of the equation -x² + x + 12 = 0 are x = -3 and x = 6.
What is equation?In mathematics, an equation is a statement that shows the equality between two expressions, typically separated by an equal sign (=). An equation can contain one or more variables, which are symbols that represent unknown or varying values. The value of the variable(s) can be found by solving the equation.
Here,
The given equation is:
-x² + x + 12 = 0
To solve for x, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
In this case, we have:
a = -1, b = 1, and c = 12
Substituting these values into the quadratic formula, we get:
x= (-1 ± √(1² - 4(-1)(12))) / 2(-1)
x = (-1 ± √(1 + 48)) / (-2)
x = (-1 ± √(49)) / (-2)
x = (-1 ± 7) / (-2)
There are two solutions:
x = (-1 + 7) / (-2)
= -3
x = (-1 - 7) / (-2)
= 6
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What is the maximum possible product of two numbers that have a sum of -8?
The maximum possible product of two numbers that have a sum of -8 is 16.
How to find the maximum possible product of two numbers that have a sum of -8Let us name the two numbers "x" and "y".
We are aware of the following: x + y = -8
We're looking for the greatest possible product of x and y.
The number we're looking that are as near together as feasible and have a sum of -8.
-4 and -4 are the two numbers that are as near together as possible and have a sum of -8. As a result, x = -4 and y = -4.
The sum of these two figures is:
x * y = (-4) * (-4) = 16
So, the maximum possible product of two numbers that have a sum of -8 is 16.
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The volume of a rectangular prism is 5,890.625cm3 . if the height is 14.5 cm and the length is 25 cm, with is the value of the width ?
A. 16.25 cm B. 16.5 cm C. 16.75cm D. 16.97cm
Answer:
Step-by-step explanation:
The answer is A. 16.25cm.
Explanation:-
We know,
The Volume of Prism =height*width*length;
Here, In the question Height and length is given.
So We have to do a simple calculation to find,width=
(Vol of Prism)/Heigth*length;=> 5890.625/(14.5*25)
=>16.25 cm .
We don't need to worry about dimensions because all are in the same cm dimensions.
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Answer:
A. 16.25 cm
Step-by-step explanation:
To solve for the volume of a rectangular prism, we would use the formula V = l·w·h, where:
"l" is the base length
"w" is the base width
"h" is the height of the prism
In this problem, we are given the volume, height, and length of the rectangular prism. That means we need to find the value of w, the base width. To do this, we plug our known values into the equation and solve for w.
5,890.625 = (14.5)(25)w
To get w by itself, we first divide each side of the equation by 14.5. Remember that when you divide a number by itself, they cancel out.
(5,890.625)/(14.5) = (14.5)(25)w/(14.5)
406.25 = (25)w
Next, we can divide each side of the equation by 25 to get our answer.
406.25/25 = (25)w/25
w = 16.25 cm
In circle
V
V,
V
W
=
2
VW=2 and the length of
⌢
=
2
9
π
WX
⌢
=
9
2
π. Find m
∠
W
V
X
∠WVX.
Answer:
Step-by-step explanation:
In a circle, the measure of an inscribed angle is equal to half the measure of its intercepted arc. In this case, the inscribed angle is ∠WVX and its intercepted arc is ⌢WX.
Since the length of ⌢WX is (9/2)π, its measure in degrees is (9/2)π * (180/π) = 810/2 = 405 degrees.
Therefore, the measure of ∠WVX is half the measure of its intercepted arc, which is 405/2 = 202.5 degrees.
Solve for 10 and 12 please and thank you
Answer:
10. 120 Degrees 12. 60 Degrees
Step-by-step explanation:
#12. Since CAD is 30, and BAD is a 90 degree angle, angle BAF is 60 degrees. Since BAF is 60 degrees and FAE and BAF are vertical angles, they have the same angle measure. 60 Degrees.
#10. Since BAF is 60, and FAE and BAF are on a line, we can do 180-60 to get the measure in degrees of that angle. FAE = 120 Degrees.
Answer:
Step-by-step explanation:
10. somewhere between 126 and 129, i feel its 128
12. between 60 and 65
Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4. 31.4n + 8.4 = 24 –8.4n + 31.4 = 24 24 = 31.4n + (–8.4) 24 – 31.4 = –8.4n
The correct equation for the following sentence is 24 = 31.4n + (–8.4) . Option C
What are algebraic expressions?Algebraic expressions are simply described as those expressions that are made up of factors, coefficients, constants, terms and variables.
Additionally, algebraic expressions are made up of arithmetic or mathematical operations, such as;
BracketDivisionSubtractionMultiplicationParenthesesAdditionFrom the information given, we have that;
24 is the constant
Let the number be represented as n
Then, the expression is given as;
24 = 31.4(n) - 8.4
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1. A sample of 250 high-school students in a city results in an average number of text messages sent per month of 172.6, with a margin of error of + 4.8. If there are 3000 high-school students in the city, what is the estimated number of text messages sent in a month? between______ and____text messages
Answer:
Step-by-step explanation:
1) Find the upper bound of the confidence interval:
Upper bound = sample mean + margin of error
= 172.6 + 4.8
= 177.4
2) Find the lower bound of the confidence interval:
Lower bound = sample mean - margin of error
= 172.6 - 4.8
= 167.8
3) Estimate the total number of text messages sent in a month:
Total number of text messages sent = (number of students in the population / number of students in the sample) x sample mean
= (3000 / 250) x 172.6
= 2071.2
Therefore, the estimated number of text messages sent in a month is 2071.2, with a 95% confidence interval between 167.8 and 177.4 text messages.
Answer:
Between 503400 and 532200 text messages----------------------------
Determine the average number of text messages sent per student within the margin of errorFind lower bound:
172.6 - 4.8 = 167.8 text messagesFind upper bound:
172.6 + 4.8 = 177.4 text messages Estimate the total number of text messages for all 3000 studentsLower bound:
167.8 text messages × 3000 students = 503400 text messagesUpper bound:
177.4 text messages × 3000 students = 532200 text messagesThe estimated number of text messages sent in a month for all 3000 high-school students in the city is:
Between 503400 and 532200 text messagesA chef has 5 containers of rice. Each container has 2 cups of rice in it. If the chef uses cup of rice for a recipe, how many cups of rice do they have left?
Answer:10-x
Step-by-step explanation:5 containers 2 cups in each. 5 x 2= 10. we don't know how many cups of rice he uses for a recipe so we call it x. Then we subtract it from the 10 cups of rice.
50 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
Answer:
the answer for this question is x=8
Find the surface area of each composite figure. Use 3.14 for π. Round to the nearest tenth. 12m. 6cm. 6cm. 4cm.
The Surface area of the composite figure is calculated as approximately: 234 sq. cm
How to Find the Surface Area of a Composite Figure?The surface area of the composite figure is the area surrounding the faces of the solid as a whole. Therefore, we have:
Surface area (SA) = Surface area of the square prism + surface area of the square pyramid - 2(area of base)
Area of base = area of square = 6 * 6 = 36 sq. cm.
Surface area of the square prism = 2a² + 4ah
a = 6 cm
h = 4 cm
Plug in the values:
Surface area of the square prism = 2(6²) + 4*6*4
= 72 + 96
= 168 sq. cm.
Surface area of the square pyramid = 2bs + b²
b = side length = 6 cm
s = slant height = √(8² + 3²) = 8.5 cm
Plug in the values:
Surface area of the square pyramid = 2 * 6 * 8.5 + 6² = 138 sq. cm.
Surface area of the composite figure = 168 + 138 - 2(36) = 234 sq. cm
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How do I solve this?
The 99% confidence interval estimate of the population standard deviation is [12.54, 54.62] mi/h.
What is a confidence interval?A confidence interval is the mean of your estimate plus and minus the variation in that estimate. This is the range of values you expect your estimate to fall between if you redo your test.
x = [64, 60, 56, 60, 52, 59, 58, 59, 70, 68]
s = 5.963
n = 10
CI = [(n-1)*s²/chi2_upper, (n-1)*s²/chi2 lower]
CI = [(9*5.963^m²)/19.022, (9*5.963²)/2.700]
CI = [12.54, 54.62]
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ACTIVITY 1: Complete the table below by computing the unknown component of simple interest.
Answer:
what arecrosses on line 2
What is the solution of x=9y and 3y - 3x =24
Answer:
Step-by-step explanation:
The solution to the system of equations `x=9y` and `3y - 3x =24` can be found by substituting the value of `x` from the first equation into the second equation. This gives us `3y - 3(9y) = 24`, which simplifies to `-24y = 24`. Solving for `y`, we get `y = -1`. Substituting this value of `y` into the first equation, we get `x = 9(-1) = -9`. So the solution to the system of equations is `(x,y) = (-9,-1)`.
Is there anything else you would like to know?
A new car sells for 25000 the value of the car decreases by 15% each year what is the approximate value of the car 5 years
The answer is $11,092.63.
This could be calculated using the proportion. If the value of the car decreases by 15% each year, that means that after each year the value of the car is 85% of the value from the first year.
After 1st year:
$25,000 : 100% = x1 : 85%
x1 = $25,000 · 85% ÷ 100%
x1 = $21,250
After 2nd year:
$21,250 : 100% = x2 : 85%
x2 = $21,250 · 85% ÷ 100%
x2 = $18,062.5
After 3rd year:
$18,062.5 : 100% = x3 : 85%
x3 = $18,062.5 · 85% ÷ 100%
x3 = $15,353.12
After 4th year:
$15,353.12 : 100% = x4 : 85%
x4 = $15,353.12 · 85% ÷ 100%
x4 = $13,050.15
After 5th year:
$13,050.15 : 100% = x5 : 85%
x5 = $13,050.15 · 85% ÷ 100%
x5 = $11,092.63
Therefore, the value of the car 5 years after it is purchased is $11,092.63.
Use the quadratic formula to solve -2x^2+2x+1
The solutions for -2x²+2x+1 are x = 1 + √(3)/2 and x = 1 - √(3)/2.
To use the quadratic formula to solve -2x²+2x+1, we first identify the coefficients a, b, and c of the quadratic equation in standard form: ax²+bx+c=0. In this case, a=-2, b=2, and c=1. We then plug these values into the quadratic formula
x = (-b ± √(b²-4ac)) / 2a
Substituting the values, we get
x = (-2 ± √(2²-4(-2)(1))) / 2(-2)
Simplifying the expression inside the square root
x = (-2 ± √(4+8)) / (-4)
x = (-2 ± √12) / (-4)
Simplifying the radical
x = (-2 ± 2√3) / (-4)
Reducing the fraction
x = (1 ± √3/2)
Therefore, the two solutions are x = (1 + √3/2) and x = (1 - √3/2).
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one two 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Answer:
31
Step-by-step explanation:
the next number is 31 in this series
Oak and Maple streets are parallel to each other. Main Street has a traffic
light at (5, 1) and is perpendicular to Oak and Maple. What is the equation
of the line representing Main Street?
Oak St.: y =
A. Y
1
22
+3 Maple St.: y = 22
C. y = -2x + 11
B.y=2x-9
D. y = -2x + 15
+6
The equation of the line representing Main Street is option C. y = -2x + 11
How did we arrive at this equation?The slope of the parallel lines is ½. The Main Street is perpendicular to Oak and Maple. So, the slope of Main Street is -2.
[The product of slopes of perpendicular Lines is -1.)
y - 1 = -2 (x -5)
y - 1 = -2x +10
y = -2x + 10 + 1
y = -2x + 11
Therefore, the best choice is option C. y = -2x + 11
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Since Main Street is perpendicular to Oak and Maple, its slope will be the negative reciprocal of the slope of Oak and Maple. Let's first find the equation of Oak Street.
We don't have enough information to determine the equation of Oak Street, so we need to make an assumption about its equation. Let's assume that Oak Street passes through the point (0,3) and has a slope of 2 (since the options suggest that Oak Street has a positive slope).
Using the point-slope form of a line, we have:
y - 3 = 2(x - 0)
y - 3 = 2x
y = 2x + 3
Now we can find the slope of Maple Street by noticing that it is parallel to Oak Street. Since parallel lines have the same slope, Maple Street also has a slope of 2.
To find the equation of Main Street, we need to use the fact that it passes through the point (5,1). Using the point-slope form of a line, we have:
y - 1 = -1/2(x - 5)
y - 1 = -1/2x + 5/2
y = -1/2x + 7/2
Therefore, the equation of the line representing Main Street is y = -1/2x + 7/2. The answer is (D).
A company makes paper labels for paint cans. As shown below, each can is in the shape of a cylinder with a height of 5 in and a diameter of 6in . The paper label is wrapped around the can and covers only the side of the can (not the top or bottom). If the company has a total of 4521.6in^2 of paper available, how many labels can be made? Use 3.14 for n , and do not round your answer.
48 labels can be made if the company has a total of 4521.6in² of paper available.
We can calculate the number of labels by finding the surface area of the side of the can.
What is the surface area of the side of the can?The surface area of the side of the can is the circumference of the base times the height:
C = πd
C = 3.14 x 6
C = 18.84 in
Area = C x h
Area = 18.84 x 5
Area = 94.2 in²
Therefore, each label requires 94.2 in² of paper.
To find the number of labels that can be made, we divide the total amount of paper by the amount needed per label:
Number of labels = Total area of paper / Area per label
Number of labels = 4521.6 / 94.2
Number of labels = 48
Therefore, 48 labels can be made using a total of 4521.6in² of paper.
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Seven days a year, Tiger Stadium becomes the fifth largest city in the state of Louisiana. Over 92,000 fans pack the stadium to watch the Tigers play. After the game, if the fans leave at a rate of 10% per minute, how long will it take before the stadium is half empty?
1. Find the data using at least 10 numbers in the x column.
2. Create a scatter plot. Label the graph and show increments.
3. Write an exponential equation.
4. Interpret the meaning of the "a" and "b" in your function y=ab^x including the units.
5. Find out how long it will take before the stadium is half empty and all the way empty.
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
A. The expression that represents the total amount of canned food they have collected so far is: 4x² + 2xy + 3
B. Number of canned food still remaining to be collected is: 2x² - 4xy + 5
How to Solve Polynomial Expressions?A polynomial expression is a mathematical expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication of non-negative integer exponents.
Part A: To find the expression that represents the total amount of canned food they have collected so far, add the expression for each person given together.
3x² - 2 + x² + 2xy + 5
Combine like terms:
4x² + 2xy + 3
Part B: Number of canned food still remaining to be collected is calculated below.
(6x² - 2xy + 8) - (4x² + 2xy + 3)
Open bracket:
6x² - 2xy + 8 - 4x² - 2xy - 3
Combine like terms:
2x² - 4xy + 5
Learn more about polynomial expressions on:
https://brainly.com/question/2833285
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