Answer: Jenna would have $37,175 in 30 years if she saves $2500 per year with an interest rate of 10% compounded annually.
Step-by-step explanation:
To calculate the total amount Jenna would have after 30 years of saving $2500 per year with an interest rate of 10% compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (principal + interest)
P = the initial principal (the amount Jenna saves each year, $2500 in this case)
r = the interest rate (10% in this case, so 0.10)
n = the number of times interest is compounded per year (annually in this case, so 1)
t = the number of years (30 in this case)
Plugging in the values:
A = $2500(1 + 0.10/1)^(1*30) = $2500(1.10)^30 = $2500(14.87) = $37,175
So, Jenna would have $37,175 in 30 years if she saves $2500 per year with an interest rate of 10% compounded annually.
Answer:
$411,235.06
Step-by-step explanation:
Sydney's Games is selling all games at a 25% discount. However, you also have a membership card at the
store, which gives you an additional 15% off. What will you end up paying for $100 worth of games?
Show your work!
The required selling price of the game after two discount is $63.75.
What is discount?The term discount designates a sum or a percentage subtracted from an item's usual selling price. Make sure you need all of the items you plan to get before waiting until after the holiday to make a purchase. A discount is a decrease in the cost of a commodity or service.
According to question:Discount = 25%,
Additional discount = 15%
Then,
Net discount is = 36.25%
We have,
Price of game = $100
Discount amount = 36.25% of $100 = $36.25
So, the selling price of the game after discount = $100 - $36.25
= $63.75
Thus, required selling price of the game is $63.75.
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In 2010 an item costs $9.00. The price increases by 1.5% each year. How much will it be in 2020?
The term is actually forming an AP.
On 2010 = $9 = a
[tex] \frac{1.5}{100} \times 9 \\ = \frac{13.5}{100} \\ = 0.135[/tex]
d = $0.135
now on 2020, that's 10 years after 2010.
n = 10
[tex]an = a + (n - 1)d \\ = 9 + (10 - 1)0.135 \\ 9 + 9(0.135) \\ = 9 + 1.215 \\ = 10.215[/tex]
THE FINAL ANSWER - $10.125Please don't forget to mark braini if u are satisfied with answerthere might be another ways to solve this problem, but the simplest way is AP.X 3 6 9 12 y 1 5 10 12 What is the r.o.c? Is this linear?
The rate of change is given a 5 / 6. The values we have here are not linear
How to solve for the rate of changeThe rate of change (r.o.c) is the change in y (or the dependent variable) for every unit change in x (or the independent variable). In this case, the r.o.c is
(10-5) / (12-6) = 5/6.
This is not linear because linear is a relationship between a variable and a constant, here the relationship between y and x is not linear because the change in y is not constant with respect to the change in x.
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what is the length of a rectangle that has a perimeter of 48 inches and a width of 18 inches
Answer:
x+x+18+18=48inches
2x+36 = 48 inches
2x = (48-36) inches
2x = 12 inches
x = 6 inches
you know there are 2 boys and an unknown number of girls in a nursery at a hospital. then a woman gives birth a baby, but you dont know its gender, and it is placed in the nursery. then a nurse comes in a picks up a baby and it is a boy. given that the nurse picks up a boy, what is the probability that the woman gave birth to a boy?
The probability that the woman gave birth to a boy, given that the nurse picked up a boy, is 1/3.
There are 2 boys initially and an unknown number of girls in the nursery, so there were a total of 2 + x babies in the nursery, where x is the number of girls.
Since we know that one of those babies is a boy, there are a total of 2 + x - 1 = 1 + x babies left in the nursery.
So the probability of the nurse picking up a boy, given that the woman gave birth to a boy, is 1/(1+x).
P(boy | picked up boy) = P(picked up boy | boy) * P(boy) / P(picked up boy)
= (1/(1+x)) * 1/2 / (1/(1+x) * 1/2 + x/(1+x) * 1/2)
= 1/3
So the probability that the woman gave birth to a boy, given that the nurse picked up a boy, is 1/3.
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Which function has the same graph as f(x) = 2|4x – 6| + 18?
A. f(x) = 2|4x – 6| – 18
B. f(x) = 4|2x – 3| + 18
C. f(x) = 4|2x – 3| + 9
D. f(x) = 4|2x – 3| + 26
The absolute value function that has the same graph as f(x) = 2|4x – 6| + 18 is the one in option B. f(x) = 4|2x – 3| + 18
Which function has the same graph as f(x) = 2|4x – 6| + 18?A function will only have the same graph as f(x) = 2|4x – 6| + 18 if we can rewrite that function into f(x).
Remember that if A is positive, then we can write:
A*|x| = |A*x|
Now, we can take our absolute value function:
f(x) = 2|4x – 6| + 18
We can rewrite it into:
f(x) = 2|2*2x – 2*3| + 18
f(x) = 2*| 2*(2x - 3)| + 18
f(x) = 2*2*|2x -3 | + 18
f(x) = 4*|2x - 3| + 18
Thhis is what we can see on option B, so that is the correct one.
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How do I solve for the missing value
The missing value in the triangle is given as follows:
28.
How to obtain the missing value?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
As 28 - 16 = 12, the proportional relationship between the side lengths is given as follows:
12/21 = 16/x.
Applying cross multiplication, the value of x is obtained as follows:
12x = 21(16)
Simplifying by 4, we have that:
3x = 21(4)
Simplifying by 3, we have that:
x = 7 x 4
x = 28.
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how many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3, and 4? repetition of digits is allowed.
The integers greater than 999 but not greater than 4000 is 375.
Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers. The examples of integers are, 1, 2, 5,8, -9, -12, etc. The symbol of integers is “Z“.
The smallest number in the series is 1000, a4-digit number.
The largest number in the series is 4000, a4-digit number
The left most digits (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.
The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.
Hence, there are 3×5×5×5 or 375 numbers from 1000 to 3999.
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The play area in a local park ha the dimenion hown at the right. What i the area of the park? 25 m 24 m 30 m What i the bae of the triangle? What i the height of the triangle? PLEASE HELP
The area of parks is 360 m² , base and height are respectively 30m and 24 m.
Given a triangle shaped park with sides 25m, 24m and 30 m.
The total area that is bounded by a triangle’s three sides is referred to as the triangle’s area.
We know that area of triangle = ½ * base * height
Clearly show that base is 30m and height is 24 m.
So, area of triangle = ½ * 30 * 24 = 720/2 = 360 m²
Therefore, area of triangle shaped park is 360m².
Base and height are respectively 30m and 24m.
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Which of the following statements is true?
C
Step-by-step explanation:
c,c is the answer i think so
solve for x
x+19 7x+9
a school locker has a dial lock on which there are 37 numbers from 0 to 36. find the total number of possible passwords, if the lock requires a three digit sequence of left-right-left and the number can not be repeated.
The total number of possible passwords is 46,620, if the lock requires a three digit sequence of left-right-left and the number can not be repeated.
We have to find the total number of possible passwords, if the lock requires a three digit sequence of left-right-left and the number can not be repeated.
A school lock has a lock of 37 numbers from 0 to 36.
The possible different possibilities is;
At the first position have 37 choices.
At the second position have 36 choices because the first number is not be repeated.
At the third position also have 35 choices because the first and second number is not be repeated.
So, The total number of possible passwords = 37 × 36 × 35
The total number of possible passwords = 46,620 ways
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Which tables represent functions? Select all that apply.
Group of answer choices
x y
-2 -2
-1 0
-2 3
2 5
x y
4 -2
1 -1
0 0
4 2
x y
-3 -9
-1 -3
0 0
5 15
x y
0 -2
2 0
3 1
7 5
Answer:
3 and 4
Step-by-step explanation:
numbers don't repeat in the X side
If the demand function for a commodity is given by the equation
p2 + 8q = 1800 and the supply function is given by the equation 700 − p2 + 6q = 0, find the equilibrium quantity and equilibrium price. (Round your answers to two decimal places.)
The equilibrium price is p = 28.
What is price?Price is an amount of money or value that is exchanged for goods & services. It is the amount of money that an individual or business is willing to pay for a product or service. Price is often determined by factors such as the cost of production, supply and demand, and competition. Price is also shaped by factors such as the availability of substitute products, market trends, & the strength of a company's brand.
Equilibrium quantity: q = 200
p2 + 8q = 1800 700 − p2 + 6q = 0
Adding the two equations together: 2500
q = 2500/14 q = 178.57 q ≈ 200
Equilibrium price: p = 28
p2 + 8(200) = 1800
p2 + 1600 = 1800 p2 = 200 p = √200
p ≈ 14.14
Therefore, the equilibrium price is p = 28.
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Use the function below to find f(-2) f(x)=3^x
By evaluating the exponential function on x = -2 we will get:
f(-2) = 1/9
How to evaluate the exponential function?Here we have the exponential function below:
f(x) = 3^x
And we want to find f(-2), this means that we just need to evaluate the exponential function in x = -2 (so we just replace the variable x by the number -2)
f(-2) = 3^(-2)
Remember that the negative exponent means that we need to take the inverse, then:
f(-2) = 3^(-2) = 1/3^2
f(-2) = 1/9
That is the value we wanted to find.
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Move a number to each box to create an equation to solve 8/100+9/10 =
The solution of the given fraction can be gotten through filling the boxes with the following values respectively;
8/100 + 9/10 = 98/100
What is a fraction?A fraction is defined as the representation of a part of a whole value in the form of a numerator and denominator.
The given fraction;
8/100 + 9/10 = ?
Find the lowest common multiple of the denominator = 100.
= 8/100 + 9/10
= 8 + 90/100
= 98/100
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I need help asap with this question
In the right-angle triangle RQS the measure of m∠R = 90°, m∠Q = 59° and m∠S = 31°.
What is a right-angled triangle?
Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.
A right-angled triangle RQS is given.
The measure of ∠R is given as = 90°.
The measure of ∠Q is given as = (2x + 33)°.
The measure of ∠S is given as = (5x - 34)°.
According to the properties of the triangle, the sum of all angles of a triangle equals 180°.
So, the equation will be -
∠R + ∠Q + ∠S = 180°
Substituting the values into the equation -
90° + (2x + 33)° + (5x - 34)° = 180°
Combining the like terms -
90° + 2x + 33° + 5x - 34° = 180°
7x + 89° = 180°
7x = 180° - 89°
7x = 91°
x = 13°
The measure of ∠Q - (2x + 33)°
∠Q = 2(13°) + 33°
∠Q = 26° + 33°
∠Q = 59°
The measure of ∠S - (5x - 34)°
∠S = 5(13°) - 34°
∠S = 65° - 34°
∠S = 31°
Therefore, the measures of angles are 90°, 59° and 31°.
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El departamento de teatro de la escuela está organizando una producción y planea cobrar $10 por entrada y $5 por una entrada para niños. Necesitan ganar por lo menos $3,000 cada noche para cov s. El auditorio tiene capacidad para 400 personas.
The four inequalities are a + c ≤ 400, 10a + 5c ≥ 3000, a ≥ 0 and c ≥ 0. The club must sell 200 children tickets and 200 adult tickets.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The value for one ticket is - $10
The value for one children's ticket is - $5
The total amount that need s to be earned is - $3000
The number of seats in the auditorium is - 400
Let the number of children be = c and the number of adults be = a.
Then the inequality will be -
a + c ≤ 400
10a + 5c ≥ 3000
a ≥ 0
c ≥ 0
The inequalities will have a straight line as (≤,≥) symbols are used in the inequalities.
Write the two inequalities in equation form -
a + c = 400....(1)
10a + 5c = 3000 or 2a + c = 600....(2)
Subtract equation (1) from (2) -
2a + c - (a + c) = 600 - 400
2a + c - a - c = 200
a = 200
a = 200
Substitute the value of a in equation (1) -
200 + c = 400
c = 400 - 200
c = 200
So, the intersection point is (200,200) and the number of children is 200 whereas the number of adults is 200.
Therefore, the graph is obtained.
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The school drama department is putting on a production and plans to charge $10 per ticket and $5 for a children's ticket. They need to earn at least $3,000 each night for cover the cost. The auditorium has a capacity for 400 people.
Write and graph a system of four inequalities that describe how many of each type of ticket the club must sell to meets its goal.
Three siblings have a gift of $169 to split in the ratio of 1/2 : 1/3 : 1/4. What is the greatest number of dollars that any of the siblings will receive?
The greatest amount of dollar shared is $78
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls
The ratio of the three sibling is 1/2 : 1/3 : 1/4. Firstly, we multiply all the terms with the l.c.m which is 12
therefore the ratio = 6: 4: 3
The total money to be share is 169
The total ratio is 13
The share of the first sibling = 6/13 × 169
= $ 78
The share of the second sibling = 4/13 × 169 = $52
The share of the third sibling = 3/13 × 169 = $ 39
Therefore the highest number of dollars shared is $78
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Curated Practice Problem Set #9
1.
It takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box which holds 15
cups of sugar. Double the dimensions of the box. Approximately how much paint would the new
box need? How much sugar would it hold?
As per the given ratio, the amount of paint is 8 ounces needed is and the amount of sugar it will hold 120 ounces.
In math then term ratio is defined as an ordered pair of numbers a and b, written a / b where b does not equal 0
Here we have given that it takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box which holds 15 cups of sugar.
And then here we have know that they double the dimensions of the box.
Let us consider that the dimension be a.
And as we all know that double the dimensions of the box then dimensions are 2a
Then the ratio of paint and the area of the box remains constant and it can be calculated as,
=> paint / area = 2/x
=> 2/x = 6a² / 6(2a)²
When we simplify this one then we get then x is 8 ounces.
Here we know that the ratio of sugar and the volume of the box remains constant.
Then the sugar volume is calculated as,
=> 15 / X = a³ / (2a)³
When we simplify this then we get the value of x is 120
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the cover charge for entering mandi's dance hall is $5. drinks are then $6 each. what equation, in point-slope form, will give the total cost for the cover charge and drinks?
The equation of the total cost for the cover charge and drinks in point-slope form is y = 6x + 5.
The point-slope form of a linear equation is given by -
[tex]y - y_1 = m(x- x_1)[/tex]
where m is the slope and [tex](x_1, y_1)[/tex] is a point on the line.
Here, the total cost for the cover charge and drinks can be represented by the equation y = mx + b, where y is the total cost, x is the number of drinks, m is the cost per drink, and b is the cost of the cover charge.
We know that the cover charge is $5 and drinks are $6 each, so, we can find the slope (m) of the equation by using the cost per drink which is m = 6.
We can also find the point [tex](x_1, y_1)[/tex] by using the cover charge cost which is (0,5).
Therefore, the equation in point-slope form of the total cost for the cover charge and drinks will be -
y - 5 = 6(x-0)
y - 5 = 6x
y = 6x + 5
Where x is the number of drinks and y is the total cost i.e. cover charge + drinks.
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Read the passage and examine the text in bold. Then, answer the question.
I always loved my grandfather's explanations of our seasons, "This is the country of three seasons. From June on to November, it lies hot, still, and unbearable, sick with violent and unrelenting storms; then on until April, it is chill, quiet, and drinks its scant rain and scanter snows. From April to the hot season again, it is blossoming, radiant, and a seductress." His months were only approximate, later or earlier the rain-laden wind may drive up the water gate of the Colorado River from the Gulf and bring to us our heat, chill, or radiance. In the desert, we see the land set its seasons by the rain.
Does the bolded portion contain an error? Choose the correction if one is needed.
A. and drank its scant rain
B. and thirsty for its scant rain
C. and, drinks its scant rain
D. No correction is needed
The context clues show that the bolded portion contain doesn't contain an error. Therefore, D. No correction is needed
What are context clues?When determining a word's meaning, context clues take into account the words that immediately precede the unknown word and lead us to infer its meaning.
These words, also known as visual indices, are explained or defined by other words that are used in the same sentence.
From June on to November, it lies hot, still, and unbearable, sick with violent and unrelenting storms; then on until April, it is chill, quiet, and drinks its scant rain and scanter snows. From April to the hot season again, it is blossoming, radiant, and a seductress.
In this case, it is grammatically correct. The correct option is D.
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Interest is compounded semianually. Find the amount in the account after the given time. Principal Rate of Interest Time $2000 6% 3 years The amount in the account is $? (Round to the nearest cent)
Answer:
$2837.04
Step-by-step explanation:
semi-annually = every 6 month
p=2000
i=6%
t=3 years = 6 periods
compound 6 times in 3years = (1+6%)^6 =1.418519
multiply principal of $2000 = 2837.04
X+3y=14 and 2x-3y=-8
To solve this system of equations, we can use the method of elimination. The goal is to eliminate one of the variables, such as x or y, by adding or subtracting the equations.
First we can eliminate the y variable by adding the two equations together:
X + 3y = 14
2x - 3y = -8
3x = 6
Dividing both sides by 3:
x = 2
Now we have the value of x, we can substitute it back into one of the original equations:
X+3y=14
2 + 3y = 14
Subtracting 2 from both sides:
3y = 12
Dividing both sides by 3:
y = 4
So the solution of the system of equations is (x,y) = (2,4)
To check the solution, we can substitute the values back into the original equations:
x + 3y = 14
2 + 3(4) = 14
2 + 12 = 14
14 = 14
and
2x - 3y = -8
2(2) - 3(4) = -8
4 - 12 = -8
-8 = -8
As the equation holds true, the solution (2,4) is correct.
Does anyone know the answer?
Answer:
b or c
Step-by-step explanation:
126+6x=180
180-126=54
54/6=9
x= 9
If triangle NPQ is congruent to triangle RSQ the perimeter of triangle NPQ= 7x+2, and the perimeter of triangle RSQ=10x-4, find the perimeter of triangle NPQ
The perimeter of triangle NPQ is calculated to be 72 when NPQ is given congruent to RSQ.
Perimeter of triangle NPQ = 7x + 2
Triangle perimeter: RSQ = 10x - 4
As triangle NPQ is given congruent to triangle RSQ, we have,
NQ / RQ = PQ / SQ = 24 / 32 = 21 / 28 = 3 / 4
The above ratio can be equated to the ratio of perimeters of the triangles NPQ and RSQ.
Perimeter of triangle NPQ/Perimeter of triangle RSQ = 7x + 2/10x - 4 = 3/4
7x + 2/10x - 4 = 3/4
On cross multiplication and solving, we have, x = 10.
The perimeter of triangle NPQ = 7x + 2 = 70 + 2 = 72
The question is incomplete. The complete question has the picture of two congruent triangles given in the below attachment.
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Rewrite one fourteenthx3y + eight fourteenthsxy2 using a common factor.
one seventhxy(2x2 + 8y)
one seventhx2y(2x + 8y)
one fourteenthxy(x2 + 8y)
one fourteenthx3y2(y + 8)
The expression 1/14 x³y + 8/14 xy² can be rewritten as one fourteenth xy (x² + 8y).
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is [tex]\frac{1}{14}[/tex] x³y + [tex]\frac{8}{14}[/tex] xy².
We have to take the common factor of both the terms [tex]\frac{1}{14}[/tex] x³y and [tex]\frac{8}{14}[/tex] xy² outside.
The common factor of both terms is [tex]\frac{1}{14}[/tex] xy.
[tex]\frac{1}{14}[/tex] x³y + [tex]\frac{8}{14}[/tex] xy² = [tex]\frac{1}{14}[/tex] xy (x² + 8y)
Hence the given expression can be rewritten as [tex]\frac{1}{14}[/tex] xy (x² + 8y).
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how many ways are there to list the digits { 1 , 2 , 2 , 3 , 4 , 5 , 6 } so that identical digits are not in consecutive positions?
2880 ways are there to list the digits { 1, 2, 2, 3, 4, 5, 6 } so that identical digits are not in consecutive positions.
The list of the digits is: { 1, 2, 2, 3, 4, 5, 6 }
Here we have to determine how many ways are there to list the digits { 1, 2, 2, 3, 4, 5, 6 } so that identical digits are not in consecutive positions
We have one number in consecutive positions in this question
That is: (2, 2)
Number of ways that (2,2) are in consecutive positions = [tex]$\frac{6!}{2!}[/tex] = 360
The permutation of 1, (2, 2), 3, 4, 5, 6 = 6!
6! = 720
To get the total number of permutations
= [tex]$\frac{7!}{2!}[/tex]
= [tex]$\frac{5040}{2}[/tex]
= 2520
The number of ways that 2 identical digits are not consecutively positioned
= 2520 - 360 + 720
= 2880
There are 2880 ways to list the digits { 1, 2, 2, 3, 4, 5, 6 }.
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Please Help! View the picture below
The order of the angles from least to greatest are given as follows:
<N , <R, <Q.
How to order the angles?The law of sines states that the ratio between the sine of the angle and the length of the opposite side of the triangle is equals.
This means that the higher the side length, the greater the opposite angle will be.
Hence:
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Ani bought a bag to hold her dive weights. the bags manufacturer claims that it can hold 53 pounds without breaking. ani has placed 29 pounds in the bag. how many more pounds can she place in the bag before it breaks? What is the inequality to represent the situation. Solve the inequality and graph your solution.
The bag can hold a maximum of 53 pounds before breaking, and Ani has already placed 29 pounds in the bag. To find out how many more pounds she can place in the bag, we can subtract the weight already in the bag from the maximum weight the bag can hold:
53 - 29 = 24
So Ani can place 24 more pounds in the bag before it breaks.
The inequality to represent this situation is:
weight in bag + x <= 53 (x represents the amount of weight Ani can put in the bag before it breaks)
To find the solution, we can substitute the value of weight in bag and get
29 + x <= 53
Now we can solve the inequality for x
x <= 24
The solution is x <= 24, which means Ani can place 24 more pounds or less in the bag before it breaks.
To graph the solution, we can start with the number line, and plot the point 24 to the right of the origin, and shade the region to the left of the point. This represents the solution set of x <= 24, which means Ani can place 24 more pounds or less in the bag before it breaks.