Answer:
To avoid consecutive b's, the string of b's must be divided into one or more groups of 1, 2, or 3 b's. There are a total of 5 + 1 = 6 possible places to insert the dividers to create these groups. For example, suppose we have a string of 7 b's and we insert dividers between the 3rd and 4th b's, and between the 5th and 6th b's. This would create the following groups of b's: bb|bb|b. In general, the number of possible ways to divide the string of b's into groups of 1, 2, or 3 b's is equal to the number of ways to insert 6 dividers into a string of 7 b's. This is equal to the number of ways to choose 6 of the 8 possible places to insert the dividers, which is equal to $\binom{8}{6} = 28$.
Since the 5 a's and the 1 c must be arranged in a specific order, there is only 1 way to arrange these letters. Therefore, the total number of words consisting of 5 letter a's, 7 letter b's, and 1 letter c is equal to $1 \times 28 = 28$.
Answer:
6 possible words.-----------------------------------------------
According to the question there are 7 'b' s and we can't have them together. We assume more than two consecutive 'b' s contain two consecutive 'b' s and hence not considering any option of having 3, 4, 6 or 7 'b' s.
There is only one way to place 'b' s apart which leaves us with 6 gaps.
There are 5 + 1 = 6 other letters which is just the number to fill in the gaps between 7 'b' s.
We have only an option for 'c' to have any of the 6 gaps, it gives us 6 options and no other options for 'a' s.
Therefore in total we have 6 possible ways.
[tex]y = 2x + 7[/tex]
[tex]y = 3 - \frac{1}{2} x[/tex]
Is this parallel, perpendicular, or neither?
Anjum and Betty spent a total of 9 hours completing the puzzle.
The ratio Anjum’s time : Betty’s time = 7 : 5.
Work out how much time Anjum spent on the puzzle.
solve the given initial-value problem. the de is homogeneous. xy2 dy dx = y3 − x3, y(1) = 1
The particular solution that satisfies the given initial condition is y = 1. This is the solution to the given initial-value problem.
To solve this initial-value problem, we must first note that the given differential equation is homogeneous. This means that if y is a solution to the given equation, then so is cy, where c is an arbitrary constant. Thus, the first step in solving this initial-value problem is to find the general solution of the homogeneous equation. To do this, we can use the method of separation of variables.
This method involves separating the variables x and y on opposite sides of the equation, and then integrating both sides with respect to their respective variables. Doing this yields:
∫xy2 dy = ∫(y3 − x3) dx
Integrating both sides of the equation with respect to y yields:
y3x2/3 + C1 = x4/4 + C2
where C1 and C2 are arbitrary constants. Rearranging this equation yields:
y3 = 4x4/3 − 4C2x2/3 + 4C1
Now, we can use the given initial condition, y(1) = 1, to determine the value of the arbitrary constants. Substituting x = 1 and y = 1 into the equation yields:
13 = 4/3 − 4C2/3 + 4C1
Solving for C1 and C2 yields:
C2 = 0, C1 = 3/4
With the arbitrary constants determined, we can now find the general solution of the homogeneous differential equation. Substituting the values of C1 and C2 into the equation yields:
y3 = 4x4/3 − 3/4
This equation is the general solution of the given homogeneous differential equation. To solve the initial-value problem, we must now find the particular solution that satisfies the given initial condition. To do this, we can substitute the initial condition, y(1) = 1, into the general solution to obtain:
13 = 4/3 − 3/4
Solving for y yields:
y = 1
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please help me with question no. 5
If possible then answer with an explanation would be appreciated.
Answer:
a)
Step-by-step explanation:
additions do not work in general that way when we consider a mixture of positive and negative numbers.
e.g.
x = 3, y = -5
|3 + -5| >= |3| + |-5|
|-2| >= 3 + 5
2 >= 8
is definitely not true.
so, for positive/negative number mixtures a) is wrong.
b) works because
if x >= y, then |x - y| >= |x| - |y|. equal when x and y > 0. larger when x and/or y < 0. correct
if x < y, then |x - y| >= |x| - |y|. larger when x and y > 0.
equal when x and/or y < 0.
c) and d) work because the signs don't change anything. either the result is positive anyway, or if negative just gets converted to the positive result.
Triangle KLM repreent a ection of a park et aide for picnic table. The picnic area will take up approximately 400 quare yard in the park. Triangle K L M i hown. The length of K M i 45 yard and the length of L M i 20 yard. Angle L K M i 25 degree. Trigonometric area formula: Area = One-half a b ine (C)
To the nearet yard, what amount of fencing i needed to urround the perimeter of the picnic area?
95 yard
107 yard
160 yard
190 yard
The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.
In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.
We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.
We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.
Using this in the given triangle KLM, we get:
Area = (1/2)(KL)(KM)(sin K),
or, 400 = (1/2)(KL)(45)(sin 25°),
or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.
Thus, we get KL = 42 yards.
Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.
Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.
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Answer: b
Step-by-step explanation:
Solve each problem. Explain or show your reasoning.
a. What is 25% of 160?
b. What is 39% of 200?
c. What is 150% of 32?
d. 13 is 50% of what number?
e. 18 is 120% of what number?
f. 21 is what percentage of 30?
Answer:
Step-by-step explanation:
a. 40 because 25 percent is 1/4th and 160 times 1/4=40
b. 78 because 200 times 39/100 is 78
c. 48 because 32 times 150/100=48
d. 26 because if it is 50 percent it is 1/2 of a number so just multiply
e. 15
f. 70 percent, simplify both numbers to the lowest number possible equal to 21/30 so 7/10 and that is 70 percent
A swimming club has three types of members: adults, juniors and children.
The ratio of juniors to children is 1 : 3.
The ratio of children to adults is 5 : 2.
What is the ratio of juniors to adults in its simplest form?
The ratio of junior to adult = 6/5
What is proportion?
An equality between two ratios. According to proportion, if 2 sets of given numbers area unit increasing or decreasing within the same quantitative relation, then the ratios area unit aforesaid to be directly proportional to every different.
Main body:
Given - data in the question
To find answer the question
Solution - Let no of junior, children and adults be x, y, z respectively.
Now, ratio of junior to children = 1/3
So, x = 3y
Ratio of children to adult = 5/2
So, 5y = 2z
.(2)
So, from (1) we get, y = x / 3
So, 5x / 3 = 2z
⇒5x = 6z
⇒ x/z=6/5
Hence, the ratio of junior to adult = 6/5
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a shipment of 16 televisions contains 7 regular and 9 deluxe models. the manufacturer failed to mark the model designation on the cartons. if 4 cartons are selected at random, what is the probability that exactly 3 of them are the deluxe model? (round your answer to three decimal places.)
If 4 cartons are selected at random, the the probability that exactly 3 of them are the deluxe model is 0.3231.
A shipment of 16 televisions contains 7 regular and 9 deluxe models.
The manufacturer failed to mark the model designation on the cartons.
If 4 cartons are selected at random, then we have to find the probability that exactly 3 of them are the deluxe model.
Now 4 cartons selected at random from 16 cartoons of televisions can be selected in ways = [tex]^{16}C_{4}[/tex]
Now simplifying
4 cartons selected at random from 16 cartoons of televisions can be selected in ways = [tex]\frac{16!}{4!12!}\\[/tex]
After simplification
4 cartons selected at random from 16 cartoons of televisions can be selected in ways = 1820
Now 3 of them are the deluxe model, can be selected in ways = [tex]^{9}C_{3}[/tex]
Now simplifying
3 of them are the deluxe model, can be selected in ways = [tex]\frac{9!}{3!6!}\\[/tex]
After simplification
3 of them are the deluxe model, can be selected in ways = 84
Remaining 1 selected from 7 regular model in ways = [tex]^{7}C_{1}[/tex]
Remaining 1 selected from 7 regular model in ways = 7
Therefore the probability that exactly 3 of them are the deluxe model = 84*7/1820
The probability that exactly 3 of them are the deluxe model = 0.3231
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The length of a rectangular house is two-and-a-half times its width. Solve the problem
using x to denote the shorter side of the rectangle.
Construct the expression for the area of the rectangle in terms of x.
Answer:
Let x be the shorter side of the rectangular house. Since the length of the house is two-and-a-half times its width, we can write this as 2.5x. The area of a rectangle is given by the formula length * width, so the area of the rectangular house in terms of x is 2.5x * x = 2.5x^2. This is the expression for the area of the rectangular house in terms of the shorter side x.
Answer:
[tex]2.5x^2[/tex]
Step-by-step explanation:
Let x be the shorter side of the rectangle, which is also its width (w), so:
[tex]w=x[/tex]
Given that the length of the rectangle is two-and-a-half times its width, this means the length (l) can be expressed as:
[tex]l=2.5x[/tex]
The area of a rectangle (A) is the product of its length (l) and width (w):
[tex]A =l \cdot w[/tex]
Substitute the expressions for length and width into the formula for area:
[tex]A=2.5x \cdot x[/tex]
Simplify this expression:
[tex]A=2.5x^2[/tex]
Therefore, the expression for the area of the rectangle in terms of x is:
[tex]\Large\boxed{\boxed{2.5x^2}}[/tex]
Abdullah and Amna bought a car for $9000, Abdullah paid 45% of the $9000 and Amna paid
the rest.
b) Write down the ratio of the payments Abdullah: Amna in its simplest form.
Answer:
9 : 11
is your a nswer in it's simplest form
Step-by-step explanation:
Abdullah and Amna bought a car for $9000, Abdullah paid 45% of the $9000 and Amna paid
the rest.
b) Write down the ratio of the payments Abdullah: Amna in it's simplest form.
Abdullah paid 45% means Amna paid 55% (100% - 45% = 55%), so the Abdullah : Amna ratio is 45 : 55, let's simplify by dividing the two parts by 5 and we will have the ratio in its simplest form.
45 : 55
let's simplify
9 : 11 is your answer
What is the value of x?
Answer:
in Right triangles you can use this formula to find altitude by using two parts which altitude has made on the base
H² = b¹ × b²
So using this formula (which can be proven by triangle similarity) can help us to find x
10² = 4x × x ===>> x =5
5. Find the range of values of x for which (3x-7)(x-5) ≥x+5.
Answer: Therefore, the range of values of x for which (3x-7)(x-5) ≥x+5 is x<5 or x>5, or x∈(-∞,5)∪(5,∞).
Step-by-step explanation: To find the range of values of x for which (3x-7)(x-5) ≥x+5, we first need to find the values of x for which the inequality is satisfied. We can do this by setting each factor equal to 0 and solving for x.
Setting (3x-7) equal to 0 gives us x=7/3. Setting (x-5) equal to 0 gives us x=5.
Next, we need to consider the signs of the factors. If both factors are positive or both are negative, the inequality will be satisfied. If one factor is positive and the other is negative, the inequality will not be satisfied.
For x<5, both factors are negative, so the inequality is satisfied. For x>5, both factors are positive, so the inequality is satisfied.
Therefore, the range of values of x for which (3x-7)(x-5) ≥x+5 is x<5 or x>5, or x∈(-∞,5)∪(5,∞).
the angle of elevation of the sun is decreasing at a rate of 0.25 radyh. how fast is the shadow cast by a 400-ft-tall building increasing when the angle of elevation of the sun is ?y6?
The shadow of a 400ft tall building is increasing at a rate of 100ft /hr
The angle of elevation of the sun is decreasing at a rate of 0.25 rad/hr
The height of the building is 400 ft tall
We need to find the rate at which the shadow is increasing
d/dθ = 1/4 rad/hr at θ = π/4
400/x = tan θ
x = 400/ tan θ
Upon derivation with t
dx/dt = 400 sec²θ/tan ²θ dθ/dt
at θ = π/4 and dθ/dt = 0.25 rad/hr
dx/dt = 400 (2x3)x0.25
dx/dt = 100ft/hr
Therefore, the shadow is increasing at the rate of 100ft/hr
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Which graph represents the inequality y > 3-x?
Find the coordinates of h if x(11, -6) is the midpoint of gh and g(15, 4).
Answer:
h (7, - 16 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is
M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula
let the coordinates of h be (x, y )
here (x₁, y₁ ) = g (15, 4 ) and (x₂, y₂ ) = h (x, y )
use the midpoint formula on g, h and equate to the coordinates x (11, - 6 )
[tex]\frac{15+x}{2}[/tex] = 11 ( multiply both sides by 2 )
15 + x = 22 ( subtract 15 from both sides )
x = 7
and
[tex]\frac{4+y}{2}[/tex] = - 6 ( multiply both sides by 2 )
4 + y = - 12 ( subtract 4 from both sides )
y = - 16
then
coordinates of h = (7, - 16 )
anyone know how to do this
From the triangle, the values of a and b are 5.1 units and 4.4 units respectively
How to find the lengths of a triangle?You should know that a triangle is a polygon with three sides, three vertices, three angles whose sum of angles is 180⁰
Using the trig ratio of Cosine
CosY=Adjacent/Hypothenuse
cos31=w/6
Cross multiplying we have
6*cos31=w
w=5.1 units
Then to find b, note that /VW/=/VY/=5.1
<VYX=<VWX............... base angles of isosceles triangle WVY
Using cosine again from trig.
Cos31=b/5.1
5.1*cos31=b
simplify to get b=4.4 units
Therefore b= 4.4 units
a=90-31 (remaining 2 angles of a right angled triangle)
a=59⁰
In conclusion, the value of a=59⁰ and the value of b=4.4 units
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If I wa aked to think of a number and multiply it by 2 I could write thi Algebraically a 2x write the following algerbraically uing X a your unknown. I think of a number multiply it by 3 and add 1 to the reult
If a number is assumed then multiply it by 3 and added the result to 1 then its algebraic equation will be 3x+1
According to the question
Assume a Number and multiply it by 2.
To Find:
to write it algebraically
Let the number that was asked to think to be x.
Then it is multiplied by 2 which becomes 2x.
Now the number is multiplied by 3
So, x multiplied by 3 will become 3x.
Then, 3x is added to 1
So, we can write it as 3x+1
Therefore, the equation can be written as 3x+1 algebraically.
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I need help with my math please
Answer:
B) y = 3x + 2-----------------------------------
Perpendicular lines have opposite-reciprocal slopes.
Given line has a slope of - 1/3, so the perpendicular slope is 3.
The matching choice is B.
Answer:
[tex]\textsf{B.} \quad y=3x+2[/tex]
Step-by-step explanation:
If two lines are perpendicular to each other, their slopes are negative reciprocals.
The negative reciprocal of a number is -1 divided by the number.
Given equation:
[tex]y=-\dfrac{1}{3}x+4[/tex]
The slope of the given equation is -¹/₃
Therefore, the slope of the perpendicular line is:
[tex]\implies -1 \div -\dfrac{1}{3}=-1 \times -3=3[/tex]
Therefore, the equation of the line that is perpendicular to the given equation is:
[tex]\textsf{B.} \quad y=3x+2[/tex]For each relation, decide whether or not it is a function.
Domain
sky
tree
leaf
cloud
Function
Not a function
Relation 1.
Function
Not a function
Range
7
Relation 3
{(m, m),(m, d),(v, v), (v, r)}
Domain
-2
Function
Not a function
Relation 2
Function
Not a function
Range
Relation 4
{(4, z),(4, e), (3, f), (9, z)}
Answer:
Relation 1 & 2 are functions
Relation 3 & 4 are not functions
Step-by-step explanation:
For a relation to be a function every x must have one and only one y
This is not true for relation 3 which has 2 y's at x = m and 2 y's at x = v
This is also not true for relation 4 which has 2 y's at x = 4
Write 6 1/5 as an improper fraction in its simplest
form
The mixed fraction in simplest improper fraction is 31/5.
Define the term improper fraction?A fraction that has the numerator higher than or equal to a denominator is said to be inappropriate.Proper fractions are those that are higher than 0 but a little less than 1. The numerator is lower than the denominator in appropriate fractions. An improper fraction is one that has a numerator that is greater or equal to the denominator.A wrong fraction is always bigger than or equal to one.For the stated mixed fraction;
6 1/5
To convert this in improper fraction;
= (6x5 + 1)/5
= (30 + 1)/5
= 31/5
This, the mixed fraction in simplest improper fraction is 31/5.
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You notice that the row labels in your spreadsheet are 1, 2, 3, 8, 9. Row labels 4 through 7 are missing. What could cause this?.
The various reasons why rows 4 to 7 could be missing are mentioned.
Explain the term spreadsheet?A spreadsheet is a piece of software that can store, display, and edit data that has been organized into rows and columns. One of the most used tools for personal computers is the spreadsheet. In general, a spreadsheet is made to store numerical data plus short text strings.Rows 4 to 7 may be missed for the following reasons:
Rows 4 through 7 have a chance of having incorrect or improperly structured data.Probability that rows 4 through 7 are concealed.There is a chance that the users shown in rows 4 through 7 are different from the users you are currently logged in as.Rows 4 through 7 had a chance of being erased from the sheet.Thus, these are various reasons why rows 4 to 7 could be missing.
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Todd caught at least three times as many fish this year as he did last year. He caught 63 fish this year. Write an inequality that represents how many fish he caught last year
The requirement is represented by the inequality y≥3x, and he caught at least 21 fish last year.
What is inequality?In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. Inequality originates from a lack of equilibrium. To solve an inequality, isolate the variable on one side from the other constants. To do so, use opposing procedures to modify the inequality. To begin, separate the x by multiplying each side by two. Whatever you do on one side must equally be done to the other.
Here,
Let y is fishes caught in this year and x be the fishes caught in last year.
y≥3x
63≥3x
x≥21
The inequality that represent the condition is y≥3x and he caught at least 21 fishes last year.
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Aarushi formed the polynomial below: If she assumed that y ≠ 0, what is the CONSTANT term in the polynomial?
Answer:
1w
Step-by-step explanation:
I want points
use this model to determine the answer what is 6÷1/5
Answer: 30
Step-by-step explanation:
6 divided by 1/5 is the same as 6/1 * 5/1
6/1 * 5/1 = 30/1
=30
30/5 = 6
Answer:
30
Step-by-step explanation:
There are a couple of ways to do this. One way is the traditional way.
[tex]\frac{6}{1}[/tex]÷[tex]\frac{1}{5}[/tex] Then multiply by the reciprocal
[tex]\frac{6}{1}[/tex] x [tex]\frac{5}{1}[/tex] = [tex]\frac{30}{1}[/tex] = 30
Another way that is more intuitive:
[tex]\frac{6}{1}[/tex]÷[tex]\frac{1}{5}[/tex] Get a common denominator of 15
[tex]\frac{90}{15}[/tex]÷[tex]\frac{3}{15}[/tex] = [tex]\frac{\frac{90}{3} }{\frac{15}{15} }[/tex]= [tex]\frac{30}{1}[/tex] = 30
given regular pentagon $abcde,$ a circle can be drawn that is tangent to $\overline{dc}$ at $d$ and to $\overline{ab}$ at $a.$ in degrees, what is the measure of minor arc $ad$?
The measure of minor arc is 108°
Pentagon:
A pentagon is a geometrical shape, which has five sides and five angles. Here, “Penta” denotes five and “gon” denotes angle.
If a pentagon is regular, then all the sides are equal in length, and five angles are of equal measures. If the pentagon does not have equal side length and angle measure, then it is known as an irregular pentagon.
The sum of all the interior angles for a regular pentagon is 540°.
hence,
Value of each interior angle = 540°/5
= 108°
From figure,
we have to find ∠AED
we can see ∠AED is one of the internal angle of pentagon.
so,
∠AED = 108°
The measure of minor arc is 108°
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Write this statement out as an equation and solve.
The power (P) required to run a motor is equal to the voltage (E) applied to that motor times the current (I) supplied to the motor. If the motor data says the motor uses 180 watts of power and the voltage applied to the motor is 120 volts, how much current will the motor require?
Answer:
1.5A
Step-by-step explanation:
To find the current that the motor will require, we can use the formula for power, which is given by:
P = E * I
where P is the power, E is the voltage, and I is the current. Substituting the values for the power and voltage into the formula, we get:
180 = 120 * I
Dividing both sides of the equation by 120, we get:
1.5 = I
Therefore, the current that the motor will require is 1.5 amps.
Step-by-step explanation:
The formula for power is P = E x I, so the current required by the motor is equal to the power divided by the voltage. In this case, the current required by the motor is 180 watts / 120 volts = 1.5 amps.
Find the value of the variable
A. 74 degree
B. 64 degree
C. 32 degree
D. 180 degree
Please help!!!
Answer:
A, 74°
Step-by-step explanation:
Both of the angles are named y, so this means they are the same/have the same value!
Remember, all triangles equal 180°
To find y...
First, we subtract 32° from 180° to see what the Y angles total up to!
180° - 32° = 148°
the two y angles on the left side of the triangle equal 148°, but what does just one of them equal?
Divide by 2 to find out!
148° ÷ 2 = 74°
one y angle = 74°
y = 74°
Help me with this question please
2
A normal die, numbered 1 to 6, is rolled 50 times.
The results are shown in the frequency table.
Score
Frequency
(b) Find the median score.
(a) Write down the modal score.
(c) Calculate the mean score.
(d) The die is then rolled another 10 times.
The mean score for the 60 rolls is 2.95.
Calculate the mean score for the extra 10 rolls.
The mean, median, mode and the mean of the extra ten rolls are
2.96,2.5,1 and 2.9 respectively
What is mean, median and mode of a frequency distribution?The mean represents the average of the dataset, the median represents the middle value of the data set, and the mode represents the repeated value in the dataset.
Using the given information we construct the following table
Score frequency Cumulative Frequency (frequency*score)
1 15 15 15
2 10 25 20
3 7 32 21
4 5 37 20
5 6 43 30
6 7 50 42
thus N= 50 (even) The Median is the average of the 25th and 26th observations. The 25th and 26th observations corresponds to the value 3.
The Median is = 2.5
The modal score = 1
Mode = 3×(median) – 2×(mean)
mean = 2.96
The mean score for the 60 roles is 2.95×60 = 148+sum of the extra ten
sum of the extra ten =29
Thus mean of the extra ten roles is
= 29/10
= 2.9
Hence the mean, median, mode and the mean of the extra ten rolls are
2.96,2.5,1 and 2.9 respectively
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A new gaming chair costs $455.95. You have already saved $155.95 and earn $37.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
37.5 + 155.95w = 455.95; w = 8
37.5w + 155.95 = 455.95; w = 8
37.5w − 155.95 = 455.95; w = 16
37.5w − 455.95 = 155.95; w = 16
Answer:
You must babysit for 8 weeks to earn enough money to buy the new gaming chair.
Step-by-step explanation:
To determine how many weeks you must babysit to earn enough money to buy the new gaming chair, we need to write and solve an equation that represents the relationship between the money you have saved, the money you earn each week, and the cost of the gaming chair.
First, we can let w represent the number of weeks you must babysit. Then, we can set up the equation:
Earnings + Savings = Total Cost
Substituting the known values into the equation, we have:
Earnings + Savings = Total Cost
$37.50w + $155.95 = $455.95
To solve the equation, we can first subtract $155.95 from both sides of the equation:
$37.50w + $155.95 - $155.95 = $455.95 - $155.95
$37.50w = $300.00
Next, we can divide both sides of the equation by $37.50 to find the value of w:
$37.50w / $37.50 = $300.00 / $37.50
w = 8
Therefore, you must babysit for 8 weeks to earn enough money to buy the new gaming chair.