It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear .Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear:1. (1+y2)(d2y/dt2)+t(dy/dt)+y=et2. t2(d2y/dt2)+t(dy/dt)+2y=sin t3. (d3y/dt3)+t(dy/dt)+(cos2(t))y=t34. y''-y+y2=0You have 10 choices to choose for each problem:a. 1st. order linear differential equationb. 2nd. order linear differential equationc. 3rd. order linear differential equationd. 4th. order linear differential equatione. 5th. order linear differential equationf. 1st. order non-linear differential equation=g. 2nd. order non-linear differential equationh. 3rd. order non-linear differential equationi. 4th. order non-linear differential equationf. 5th. order non-linear differential equation
The coefficient of the second derivative (t2) is constant, so the equation is linear.
1. (1+y2)(d2y/dt2)+t(dy/dt)+y=et2 -> 2nd. order non-linear differential equation
2. t2(d2y/dt2)+t(dy/dt)+2y=sin t -> 2nd. order linear differential equation
3. (d3y/dt3)+t(dy/dt)+(cos2(t))y=t3 -> 3rd. order non-linear differential equation
4. y''-y+y2=0 -> 2nd. order non-linear differential equation
The order of a differential equation is the highest derivative involved in the equation. For example, in the equation 1 + y2(d2y/dt2) + t(dy/dt) + y = et2, the highest derivative is the second derivative (d2y/dt2), so this equation is of 2nd order. Linearity is determined by whether the coefficients of each derivative are constants, or whether they depend on the function y and its derivatives. In this equation, the coefficient of the second derivative (1+y2) is not constant, so the equation is non-linear. Similarly, in equation t2(d2y/dt2)+t(dy/dt)+2y=sin t, the coefficient of the second derivative (t2) is constant, so the equation is linear.
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Justin has a savings account.
• He started with $50 in his account.
• He deposits $12 into the account each week.
• Let b represent the amount Justin has in the bank after w weeks.
Which equation can be used to determine the total amount in Justin's account?
Answer: The equation that can be used to determine the total amount in Justin's account is:
b = 50 + (12 * w)
This equation represents the total amount in Justin's account, b, after w weeks. The equation starts with the initial amount, $50, which is the amount Justin had in his account before making any deposits. Then, it adds the amount deposited each week, $12, multiplied by the number of weeks, w. This results in the total amount in the account after w weeks.
In this equation the variable "w" represents the number of weeks that have passed and "b" represents the total balance.
Step-by-step explanation:
A 3-yard piece of cotton cloth costs $2.61. What is the price per foot?
The price per foot is $0.29
Given,
A 3-yard piece of cotton cloth costs = $2.61
1 Yard = 3 Foot
so, 3 Yard = 9 Foot
The Cost of cotton cloth per foot,
= 2.61/9
= 0.29
Therefore, the price per foot is $0.29
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The random variable K has a geometric distribution with mean 16. Which of the following is closest to the standard deviation of random variable K ?a. 0.0625b. 0.9375c. 4d. 15.49e. 240
The standard deviation of random variable K is 15.49 (option D ) and this can be determined by using the formula of mean and standard deviation.
Given,
The mean of geometric distribution of random variable K = 16
Formulae for finding mean,
mean = 1/p
Substitute the value of the mean in the above formula in order to determine the value of 'p'.
[tex]16 =\frac{1}{p}[/tex]
[tex]p = 0.0625[/tex]
The formulae for standard deviation :
S.D.=[tex]\frac{\sqrt{1-p} }{p}[/tex]
Now substitute the value of p in the above equation,
S.D. [tex]= \frac{\sqrt{1-0.0625} }{0.0625}[/tex]
[tex]= 15.49[/tex]
Hence, the answer is option D.
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during the last 3 years consolidated oil company expanded its gasoline stations into convenience food stores (cfss) in an attempt to increase total sales revenue. the daily sales (in hundreds of dollars) from a random sample of 10 weekdays from one of its stores are:
One kind of average is the mean. It is calculated by dividing the total number of values in a list of values, such as measurements or numbers, by the total number of values in the list.
What is the mean in maths?There are various mean types in mathematics, particularly in statistics. Each mean helps to summarise a certain set of data, frequently to help determine the overall significance of a specific data set.The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.Only numerical variables—regardless of whether they are discrete or continuous—can be used to determine the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it.Given data :
a ) Mean =
x = [tex]\frac{\left \{ {{i=10} \atop {i=1}} \right.}{n} Xi[/tex] = 101 / 10 = 10.1 hundreds of dollars
The median is the 50th percentile To determine the location index for the median (2nd
quartile (p =50) we do the following:
The index is
i = [tex]\frac{p}{100}[/tex] (n) = [tex]\frac{50}{100}[/tex] (10) = 5 integer
Since the index, 5, is an integer, the 2nd quartile is determined by finding the average of
the 5th and 6th values from the lower or higher end of the sorted data. This is:
Median = [tex]Q_{2}[/tex] = [tex]\frac{10 + 11}{2}[/tex] = 10.5 hundreds of dollar
Mode = most frequently occurring observation = 11 hundreds of dollars ( two times )
Here i attached graph
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"
evaluate the functions at 0, -2, and 1. f (x )equals x cubed minus 3 x squared plus 4
The functions are 0, -2 and 1 for the mentioned function is 4, - 16 and 2.
Firstly we will represent the function in equation form. Then we will calculate the result by keeping each value of function.
f(x) = x³ - 3x² + 4
Calculating result when function is 0
f(x) = 0³ - 3×0² + 4
f(x) = 0 - 0 + 4
f(x) = 4
Calculating result when function is -2
f(x) = (-2)³ - 3×(-2)² + 4
Finding square and cube
f(x) = -8 - 3×4 + 4
Performing multiplication
f(x) = - 8 - 12 + 4
Performing addition
f(x) = - 20 + 4
Performing subtraction
f(x) = - 16
Calculating result when function is 1
f(x) = 1³ - 3×1² + 4
f(x) = 1 - 3 + 4
Performing addition
f(x) = 5 - 3
Performing subtraction
f(x) = 2
Thus, functions are 4, -16 and 2.
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IMC 2018 5th grade question 14
Answer: 69
Step-by-step explanation:
I need help, please, I didn't understand you very well.
Answer:
30
Step-by-step explanation:
Answer: 30
Step-by-step explanation:
Use Pythagorean theorem a^2 + b^2 = c^2:
18^2 + 24^2 = c^2
324 + 576 = c^2
900 = c^2
c = 30
refer to the above table. if the consumer buys both product x and product y, how much will the consumer buy of each in order to maximize utility?
If the consumer buys both product X and product Y, the consumer buy of each to maximize utility will be 3X and 4Y.
Product X Product Y
Quantity MUx Quantity MUy
1 32 1 24
2 28 2 20
3 24 3 16
4 20 4 12
5 16 5 8
If the consumer can only buy product X, consumer buy and the total utility will be 5X and 120.
If the consumer buys both product X and product Y, the consumer buy of each to maximize utility will be 3X and 4Y.
When the consumer purchases the utility-maximizing
combination of product X and product Y, total utility will be 156.
A consumer is in equilibrium and is spending income in such a way that the marginal utility of product X is 40 units and Y is 16 units. The unit price of X is $5. The price of Y is: $2 per unit.
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The complete question is :
Based on the table below showing the marginal utility schedules for product X and product Y for a hypothetical consumer. The price of product X is $4 and the price of product Y is $2. The income of the consumer is $20. how much will the consumer buy of each in order to maximize utility?
Recognizing the measurement scale of the data collected on each variable is important because the type of data dictates the appropriate data summary methods and statistical procedures. Which variable(s) in the data set are measured using a nominal scale?
The data set's environment variable(s) are quantified on a nominal scale.
Describe data sets?
A data set is created from collected data. When working with tabular data, a data set is equivalent to one or more database tables, each of whose columns and rows correspond to various variables and each of which corresponds to a particular record of the corresponding data set. A data set is a collection of interconnected, unique pieces of interconnected data that can be accessed separately, together, or under a single control.A particular type of data structure is used to organize a data set. A few examples of the enormous amount include numerous medical data, various measures, financial data, statistical data, demographic data about specific populations, and insurance data.To learn more about data sets refer to:
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If G is a group of order pq, where p and q are primes. How could I prove that any nontrivial subgroup of G must be cyclic?
Let H be a nontrivial subgroup of G.
Since p and q are coprime, the only possible divisors of pq are p and q. Thus we must have either |H|=p or |H|=q. Now, by Cauchy's theorem, H must contain an element of order p or q respectively. Then, by Lagrange's theorem, the order of any element in H must divide p or q, i.e. H must be cyclicThen, H has an order of m, where m is a divisor of pq. By Lagrange's Theorem, m divides both p and q. Since p and q are prime, m must be equal to either p or q. This implies that the order of H is either p or q.
Therefore, H must be cyclic, because the order of a cyclic group is always equal to its number of elements. Thus, any nontrivial subgroup of G must be cyclic.
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Complete question:If G is a group of order pq, where p and q are primes, how could I prove that any nontrivial subgroup of G must be cyclic?
el cociente de 5 y un número
Using Algebraic Expressions, The ratio of any two numbers is five: 5/x
What is algebra?Many students find algebra intimidating since it's the first math course they take where they have to deal with variables, abstract ideas, and problem-solving skills. Additionally, not enough is frequently done in the classroom to relate algebra to students' daily lives and explain why it is important to comprehend.
We take into consideration a number "x" for the algebraic expression.
Two numbers are divided to produce the quotient. The ratio between five units and any number "x" is what we have here.
a mathematical expression
Quantile = 5/x
We will get various quotient outcomes depending on the value we provide to the variable "x."
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Full question"
The ratio of 5 between any number.
A certain drug is made from only two ingredients: compound A and compound B. There are 7 millimeters of compound A used for every 5 millimeters of compound B. If a chemist wants to make 900 millimeters of the drug, how many millimeters of compound A are needed?
Answer: The answer is: 525 millimeters of compound A are needed.
Step-by-step explanation:
You have to put it in equation form to solve for compound A. To do this use variables.
7(x) + 5(x) = 900
12(x) = 900
x = 900/12
x = 75
When we get 75 you have to plug it into compound A to get this:
7(75) = 525
To confirm our answer we plug in 75 to both variables.
7(75) + 5(75) = 900
I hope this was able to help you :D
Felipe has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
Answer: 20 different total voting combination
Step-by-step explanation: So we have 5 bands. Lets called them A, B, C, D, and E.
If John has to vote on his favorite and second favorite that means we will be selecting 2 bands out of the 5 possible to choose from.
To find the TOTAL amount of different combinations we need to pair up bands and find all the combo's.
Here are the results/totals:
AB
AC
AD
AE
BA
BC
BD
BE
CA
CB
CD
CE
DA
DB
DC
DE
EA
EB
EC
ED
So this is 20 different total voting combinations.
If you want to do it simpler without listing you can take the the 5 bands and multiple by 4 since you know each initial band (A, B, C, D, and E) will be paired with another band other than itself.
Let S be the set of all positive integers having at most 4 digits and such that each of the digits is 0 or 1. What is the greatest prime factor of the sum of all the numbers in S ?
A. 11
B. 19
C. 37
D. 59
E. 101
The greatest prime factor of 2516 is 11, so the answer is A. 11
What is the prime factor?
A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11,
We can use the process of counting to find the sum of all the numbers in S.
For one-digit numbers, there are 2 possibilities (0 or 1).
For two-digit numbers, there are 2 x 2 = 4 possibilities (00, 01, 10, 11).
For three-digit numbers, there are 2 x 2 x 2 = 8 possibilities (000, 001, 010, 011, 100, 101, 110, 111).
For four-digit numbers, there are 2 x 2 x 2 x 2 = 16 possibilities (0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111).
So, the sum of all the numbers in S is
2 + 4(1+2+3+4) + 8(1+2+3+4+5+6+7+8) + 16(1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16)
We can simplify this expression as
2 + 4(10) + 8(36) + 16(136)
The sum of all the numbers in S is equal to 2 + 40 + 288 + 2176 = 2516.
Hence, The greatest prime factor of 2516 is 11, so the answer is A. 11
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graphing y ≥ |x| - 4?
The graph for the given mode function, y ≥ |x| - 4 is attached below.
What is a modulus function?In mathematics, the modulus function is a function for which any input value of x, output will be always positive
Given that,
The modulus function,
y ≥ |x| - 4
We can write given function in a following two ways-
y ≥ x - 4
y ≥ -x - 4
So, for any value of x
y should be greater than modulus functions value
Plotting graph for y ≥ x - 4
So first draw line x - 4
Now, here we have inequality sign
So left side region will be our desired space
Similarly, Plotting graph for y ≥ -x - 4
So first draw line -x - 4
Now, here we have inequality sign
So right side region will be our desired space
Hence, Graph is drawn for the given function
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An ice cream cone with a 2cm radius has a volume of 75.36 cubic cm how tall is the ice cream cone
Step-by-step explanation:
reading the question thoroughly, we find out that volume (V) and radius (r) of the cone is given, and we just have to find out the length (h) of the cone
V = πr²h/3
Putting the given values in place,
V = 75.36 cm³
V = 75.36 cm³r = 2 cm
V = 75.36 cm³r = 2 cmπ = 3.14
Now, since we calculating for h, we can interpret the formula in the terms of h, i.e.
h = 3V/(πr²)
h = 3×75.36/(3.14×2²)
h = 226.08/12.56
h = 18 cm
Thus, the height of the ice cream cone is 18cm
Hope this helped!
Tamela compared the rates of three cable companies. TV Watchers—$30.80 for 70 channels Tel-EVision—$46.40 for 145 channels Channels Galore—$40.80 for 120 channels Which cable company has the best rate of price per channel?
The cable company with the best rate of price per channel is
Tel-EVision.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
TV Watchers—$30.80 for 70 channels.
The unit rate.
= 30.80/70
= 0.44
Tel-EVision—$46.40 for 145 channels.
The unit rate.
= 46.40/145
= 0.32
Channels Galore—$40.80 for 120 channels
The unit rate.
= 40.80/120
= 0.34
Thus,
Tel-EVision cable company has the best rate of price per channel.
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PLEES HELP ME WITH MY HOMEWORK
Answer:
Step-by-step explanation:
2. 63
3. 0
4. 6
5. 9
6. 10
7. 4
8. 8
9. 0
10. 5
11. 10
12. 7
13. 9
14. 5
15. 5
16. 3
17. 8
18. 0
Mid topic checkpoint chapter 4 for questions 3,and 4
Equation that represents the Marks and study hours of Adams is y = 7.5x + 60.
What is Linear equation?A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given a linear regression graph that has a linear equation.
Slope intercept form of a line
y = mx + c
where,
m is the slope
c is the y-intercept(Where x is zero)
In our case,
y-intercept = 60
Thus, the equation of line will be:
y = mx + 60
Coordinates of the line are given (4, 90). So, these points will Satisfy the equation.
90 = 4*m + 60
4.m = 30
m = 7.5
Thus, equation of the line will be:
y = 7.5x + 60
Adam's test score after studying for 6 hours:
y = 7.5 * 6 + 60
y = 45 + 60
y = 105
therefore, Equation that represents the Marks and study hours of Adams is y = 7.5x + 60.
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Timmykat wants to start losing some weight. He goes to the doctor and the doctor tells him that he needs to burn off 600 calories a day or more. TK loves riding his bike but he only burns 10 calories a minute that way. When TK runs he loses 15 calories a minute.
a) Make an inequality where x represents the number of minutes biking and y represents the number of minutes running. b) If Timmykat bikes for 30 minutes and doesn’t run at all will he burn enough calories?
c) If Timmykat runs for 30 minutes and doesn’t bike at all will he burn enough calories?
d) Graph the inequality.
e) What are three different scenarios where Timmykat will burn at least 600 calories a day?
The total number of calories burned can be represented by the inequality 10x + 15y ≥ 600
Timmykat will not burn enough calories in the two scenariosThe graph is attachedThe three different scenarios are explained belowThe inequality of the scenarioUsing the following parameters:
x represents the number of minutes biking y represents the number of minutes runningThe inequality is
10x + 15y ≥ 600
Will he burn enough calories?In this case, x = 30 and y = 0.
Plugging in these values into the inequality:
10(30) + 15(0) = 300
Since 300 is less than 600, Timmykat will not burn enough calories if he only bikes for 30 minutes and doesn't run at all.
Will he burn enough calories?In this case, x = 0 and y = 30.
Plugging in these values into the inequality:
10(0) + 15(30) = 450
Since 450 is less than 600, Timmykat will not burn enough calories if he only runs for 30 minutes and doesn't bike at all.
The graph of the inequalitySee attachment
Three different scenariosThree different scenarios where Timmykat will burn at least 600 calories a day are:
Biking for 40 minutes and running for 20 minutes: 10(40) + 15(20) = 400 + 300 = 700, which is greater than 600.Biking for 45 minutes and running for 15 minutes: 10(45) + 15(15) = 450 + 225 = 675, which is greater than 600.Biking for 50 minutes and running for 10 minutes: 10(50) + 15(10) = 500 + 150 = 650, which is greater than 600.Read more about inequality at
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to help tyler identify the heights of the peaks, write down what you know about each peak from the first page of this activity (3 points: 1 point for each completed row).
The heights and locations of the three peaks in this activity are: Peak 1 is 4,064 meters (13,320 feet) and located in Ladakh, India; Peak 2 is 8,848 meters (29,029 feet) and located in Nepal; and Peak 3 is 8,611 meters (28,251 feet) and located in Pakistan.
Peak 1: Height: 4,064 m (13,320 ft), Location: Ladakh, India
Peak 2: Height: 8,848 m (29,029 ft), Location: Nepal
Peak 3: Height: 8,611 m (28,251 ft), Location: Pakistan
Peak 1: Height: 4,064 m (13,320 ft), Location: Ladakh, India
This means that the height of Peak 1 is 4,064 meters (13,320 feet) and it is located in Ladakh, India.
Peak 2: Height: 8,848 m (29,029 ft), Location: Nepal
This means that the height of Peak 2 is 8,848 meters (29,029 feet) and it is located in Nepal.
Peak 3: Height: 8,611 m (28,251 ft), Location: Pakistan
This means that the height of Peak 3 is 8,611 meters (28,251 feet) and it is located in Pakistan.
The heights and locations of the three peaks in this activity are: Peak 1 is 4,064 meters (13,320 feet) and located in Ladakh, India; Peak 2 is 8,848 meters (29,029 feet) and located in Nepal; and Peak 3 is 8,611 meters (28,251 feet) and located in Pakistan.
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A submarine is 575 feet below sea level. It is ascending at a rate of 325 feet per minute
If a submarine is 575 feet below sea level and is ascending at a rate of 325 feet per minute, we can use that information to determine how long it will take for the submarine to reach the surface.
The distance the submarine needs to travel to reach the surface is:
Distance = Sea level - Current depth
Distance = 0 feet - (-575 feet) = 575 feet
We can use the rate of ascent and distance to find the time it will take for the submarine to reach the surface.
Time = Distance / Rate
Time = 575 feet / 325 feet per minute
Time = 1.77 minutes
So it will take the submarine 1.77 minutes to reach the surface, assuming it continues to ascend at a rate of 325 feet per minute.
A doctor prescribes an ointment that is 4% hydrocortisone. A pharmacist has 1% and 5% concentrations in stock. How many ounces of each should the pharmacist use to make a 1-ounce tube?
To make a 1-ounce tube of the ointment that is 4% hydrocortisone, the pharmacist needs to use 0.04 ounces of the active ingredient (hydrocortisone).
The pharmacist has 1% and 5% concentrations in stock, therefore he needs to use 0.96 ounce of the 1% concentration and 0.04 ounces of the 5% concentration.
The pharmacist should use 0.96 ounces of the 1% concentration and 0.04 ounces of the 5% concentration to make a 1-ounce tube of the ointment with the correct percentage of hydrocortisone.
It's important to note that it's important that the pharmacist needs to mix the correct amount of hydrocortisone to get the desired percentage, and also that the pharmacist needs to check the final percentage of the ointment before dispensing to ensure the safety and efficacy of the medication.
what is the slope through the line of (5, -6) and (2, 3)
Hello:
--> this problem wants us to calculate the slope between (5, -6) and (2, 3)
So we are given two points:
--> (x1, y1): (5, -6)
--> (x2,y2): (2, 3)
Let's consider our formula needed:
[tex]\text{Slope} = \dfrac{y2-y1}{x2-x1}=\dfrac{3--6}{2-5} =\dfrac{9}{-3} =-3[/tex]
Thus our slope is -3
Answer: -3
Help pls! The question is in the the photo.
Step-by-step explanation:
after mixing 1 can of concentrate and 3 cans of water, we will have 4 cans of juice.
the volume of 1 can is (as for any cylinder or regular 3D object)
base area × height
for a cylinder the bar area is the area of a circle
pi×r²
r is the radius, which is half of the diameter.
in the picture it is not fully clear what is 2.25 in long : the diameter of the radius ?
I suspect it is the diameter.
so, the radius of our cans is 2.25/2 = 1.125 in
the volume of 1 can is
pi×1.125²×4.25
and the volume of all 4 cans of juice is then
4×pi×1.125²×4.25 = 17×3.14×1.265625 = 67.5590625 in³
≈ 68 in³
so, your answer is 68.
It cost the concession stand $1.25 for each nacho sold. If the concession stand marks up the nachos 80%, how much do they charge for each nacho?
The concession stand charges $2.25 for each nacho.
What is the percentage?
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.
To find out how much the concession stands charge for each nacho, we need to calculate the markup percentage.
The markup percentage is calculated by:
(Markup Amount / Cost) * 100 = Markup Percentage
In this case, the markup amount is 80% of the cost of each nacho, which is:
(80/100) * $1.25 = $1
So, the markup amount is $1.
To calculate the final price of each nacho, we need to add the markup amount to the cost:
$1.25 (cost of nacho) + $1 (markup amount) = $2.25
Therefore, the concession stand charges $2.25 for each nacho.
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the length of a rectangle is seven more than triple the width. if the perimeter is 166 inches , find the dimension
Answer:
Width = 3.773 inches
Length = 79.227 inches-
Step-by-step explanation:
g = 7(3w) Eq. 1
166 = 2(g+w) Eq. 2
g = length
w = width
From Eq, 1:
g = 21w Eq. 3
Replacing Eq. 3 in Eq. 2
166 = 2(21w + w)
166 = 2(22w)
166 = 44w
166/44 = w
w = 3.773
From Eq. 3
g = 21(3.773)
g = 79.227
Check:
From Eq. 2:
166 = 2(79.227 + 3.773) = 2 * 83
A florist divided f flowers equally among 6 vases. Choose the expression that shows how many flowers were in each vase.
Answer:
42 divided by 6=7 so in each vase there are 7 flowers
Step-by-step explanation:
The sports program has a balance of $500 Kenny needs to buy basketballs that cost $25 per practice Kenny hopes to have at least $200 after purchasing the necessary basketballs which inequality represents Kenny’s situation.
The inequality that represents Kenny's situation is 25x ≤ 500 − 200
What is inequality ?In mathematics, inequality is describe about the relative size or order of two values.
It states that one value is either greater than, less than, or not equal to the other value.
It is usually represented by symbols such as > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), and ≠ (not equal to).
In this question ,
Let x be the number of basketballs Kenny needs to buy.
The inequality that represents Kenny's situation is:
25x ≤ 500 − 200
This inequality states that the total cost of purchasing the basketballs (25x) must be less than or equal to the available balance minus the desired amount after purchase (500 − 200 = 300).
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