The simplified form of the given expression is 2a+b/2b+a.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is [tex]\frac{\frac{1}{a}+ \frac{2}{b} }{\frac{2}{a}+ \frac{1}{b} }[/tex].
The expression can be simplified as follows
[tex]\frac{\frac{b+2a}{ab} }{\frac{2b+a}{ab} }[/tex]
= 2a+b/2b+a
Therefore, the simplified form of the given expression is 2a+b/2b+a.
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease
The rate of change of the exponential function in this problem represents a decay, and the rate of decrease is of 3.7%.
How to model the exponential function?A decaying exponential function is modeled as follows:
y = a(1 - r)^t.
In which:
a is the initial value.r is the decay rate, as a decimal.The function in this problem is given as follows:
y = 20(0.963)^x.
As 0.963 < 1, this is an exponential decay function, and the decay rate is given as follows:
1 - r = 0.963
r = 1 - 0.963
r = 0.037
r = 3.7%.
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Avery decides to take her puppy for a walk. After 90 feet, they stop to smell some roses. Then, Avery runs into a friend 200 yards up the road. They start talking, and soon it's time for Avery to go home. So, she and her puppy head back to her house. How many feet long was Avery's walk?
Answer:
Below
Step-by-step explanation:
90 feet + 200 yrads = 90 feet + 200 *3 feet = 690 feet EACH direction for a total of 690 * 2 = 1380 ft
Answer:
1380 ft long
Step-by-step explanation:
1. You would convert 200 yds to feet. (3ft in a yd so 600 ft.)
2. Add 600+90 to figure out how far she walked to her friend.
3. Double it because she walked the same distance to get home.
A line has a slope of – 3/5 and a y-intercept of 6. Write its equation in slope-intercept form.
Answer:
y=-3/5x+
Step-by-step explanation:
slope intercept form;
y= mx+c........... mis the gradient while c is the y-intercept
so it will be; y= -3/5x+
the distance from the ground of a person riding on a ferris wheel can be modeled by the equation d equals 20 times the sine of the quantity pi over 30 times t end quantity plus 10 comma where d represents the distance, in feet, of the person above the ground after t seconds. how long will it take for the ferris wheel to make one revolution?
It takes approximately 26.56 seconds for the ferris wheel to make one revolution.
The ferris wheel makes one complete revolution when the distance of the person above the ground returns to the original value after completing a full circle.
This occurs when the sine function returns to its maximum value, which is 1.
Thus, we have the following equation:
20 * sin(π/30 * t) + 10 = 20
Solving for t,
we will get:
sin(π/30 * t) = 0.5
Taking the inverse sine of both sides:
(π/30 * t) = sin^-1(0.5)
Multiplying both sides by 30/π,
we will get the following:
t = (30/π) * sin^-1(0.5)
Now solving the value of t
We will get it as: t ≈ 26.56 seconds.
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you plant two flowers in a garden. The equations y= 13.6x + 21 and y=9.4x+ 21 model the heights y of the flowers, in millimeters, after x days. what does the y-intercept of each equation represent? Will the flowers ever be the same height?
The y-intercept represents the initial height when the were planted.
The height of both plants will never be the same.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The equations y = 13.6x + 21 and y = 9.4x + 21 represent the heights of two flower plants in a garden in millimeters.
We know y-intercept is when x = 0,
Therefore, y = 21 and y = 21 represent the initial height when they were planted.
The height of the plants will never be the same because the initial height was the same but one plant is growing faster than the other.
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suppose that a single die with 6 sides (numbered 1, 2, 3, ... , 6) is rolled twice. what is the probability that the sum of the two rolls equals 4 ?
The probability that the sum of the two rolls equals 4 is 1/12.
Given in the question that a single die with 6 sides is rolled twice, we have to calculate the probability that the sum of the two rolls equals 4.
the set of possible outcomes when we roll a die are {1,2,3,4,5,6}
So when we roll two dice there are 6 × 6 = 36 possibilities
The number of possible combinations that will result in a sum of 4 is (1, 3), (2, 2), and (3, 1). Since there are 6 possible outcomes for each die, the probability of rolling a specific combination is 1/36. There are 3 combinations that will result in a sum of 4, so the probability of rolling a sum of 4 is 3/36 or 1/12.
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Amelia selects a pupil from the list at random 300 times and records the
number of pupils who studies Spanish, Italian, French or German.
Subject Spanish Italian
Frequency 90
60
French German
30
120
Amelia selects a pupil from the list at random 300 times.
Work out the relative frequency that a pupil studies French.
Submit Answer
The relative frequency that a pupil studies French is 0.1
What is Relative Frequency?This refers to the proportion of one event's frequency to all events' frequencies in a statistical experiment.
Given that:
The total number of data values is 300
The frequency of a pupil that studies French is 30
The relative frequency is 30/300 = 0.1
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the vertices of triangle wxy are located at w(-14,20). x(10,4) and y (-2,-4). what is the approximate length of the midsegment parallel to xy?
The approximate length of the midsegment parallel to xy is 6.63
The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle and has the same length as each of the two sides.
To find the midpoint of a line segment, we average the x-coordinates and the y-coordinates of its endpoints.
Since the question stated that the midsegment is parallel to xy, we need to find midpoint of xw and yw.
First, let's find the midpoint of side xw:
Midpoint of xw : ((-14+10)/2, (20+4)/2) = (-2, 12)
Midpoint of yw : ((-14-2)/2, (20-4)/2) = (-8, 8 )
The length of a line segment between two points (x1, y1) and (x2, y2) in a two-dimensional coordinate system can be calculated using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Length line of midpoint xw and midpoint yw :
√((-2-(-8))^2 + (12-(8))^2) = √(6^2 + 4^2) = √(36 + 8) = √44
So, the length of the midsegment is parallel to XY, which is approximately equal to √44 = 6.63
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The function [tex]f(x)=\sqrt[3]{x+4}[/tex] is transformed to [tex]g(x) = \sqrt[3]{x-1} +3[/tex]
What transformations are performed from function f to function g?
Choose the answers that are correct:
1. Function f is translated up 3 units.
2. Function f is translated to the right 5 units.
3. Function f is translated to the right 3 units.
4. Function f is translated down 1 unit.
Answer:
A) Function f is translated up 3 units.
B) Function f is translated to the right 5 units.
Step-by-step explanation:
Given functions:
[tex]f(x)=\sqrt[3]{x+4}[/tex]
[tex]g(x)=\sqrt[3]{x-1}+3[/tex]
To transform function f to function g, first subtract 5 from the x:
[tex]\begin{aligned}f(x-5)&=\sqrt[3]{x-5+4}\\&=\sqrt[3]{x-1}\end{aligned}[/tex]
Now add 3 to the function:
[tex]f(x-5)+3=\sqrt[3]{x-1}+3[/tex]
When a number "n" is subtracted from the x variable of a function, the function is translated "n" units to the right.
When a number "n" is added to a function, the function is translated "n" units up.
Therefore, the transformations performed from function f to function g are:
Function f is translated to the right 5 units.Function f is translated up 3 units.Which is more, 97 ounces or 6 pounds?
Answer:
97oz
Step-by-step explanation:
16oz per lb
16x6=96
96oz<97oz
Answer: They are equal
Step-by-step explanation:
A sign company is building a sign with the dimensions shown.
What is the area of the sign? Question 4 options:
A. 60 square feet
B. 240 square feet
C. 120 square feet
D. 260 square feet
TLDR: Your answer is D. 260 square feet.
To find the area of a triangle, you must use the formula "1/2 B ⋅ H."
In this problem, your values are the following:
B = 20
H = 26
Now, you just plug these values in and solve.
1/2 (20) ⋅ 26 > 10 ⋅ 26 = 260 ft
Evaluate each expression if d = –24, e = –4, & f = 8.
f+8/-4
Answer:
d=-28 and e=-20
Step-by-step explanation:
d×1=-24×1=e=4
d=-24-4=-28
Logan mows (L) lawns each week for 8 weeks. Eve mows 2 fewer lawns than Logan each week.
a. Write an expression that represents the number of lawns Eve mows in those 8 weeks.
b. Evaluate the expression from part (a) when (L) = 3. Interpret the result
c. Write an expression equivalent to the one from part (a) by using a tabular model.
d. If Logan mows 5 lawns each week, how many lawns does Eve mow in 8 weeks?
(Must show work)
a)
The expression that represents the number of lawns Eve mows in those 8 weeks is 8(L- 2)
b)
The value of the expression is 8.
c)
The tabular table is given above.
d)
Eve mowed 24 lawns in 8 weeks.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Logan:
Number of lawns each week = L
Number of lawns 8 weeks = 8L
Eve:
Number of lawns each week = )L - 2)
Number of lawns 8 weeks = 8(L- 2)
a)
The expression represents the number of lawns Eve mowed in those 8 weeks.
= 8(L -2)
b)
When L = 3,
8 (L - 2)
= 8 (3 - 2)
= 8 x 1
= 8
c)
Tabular table
Number of weeks Number of lawns
Logan x xL
Eve x x(L - 2)
d)
Logan:
Number of lawns in one week = 5
L = 5
Eve:
Number of lawns in 8 weeks.
= 8 (L - 2)
= 8 (5 - 2)
= 8 x 3
= 24
Thus,
a) 8(L- 2)
b) 8
c) Tabular table is given above.
d) Eve mowed 24 lawns in 8 weeks.
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Bananas cost $0.48 per pound. Which graph correctly shows the relationship between the pounds of bananas and the cost? O A C 52.50 53.00 $1.50 $1.00 50.50 50.00 $8.00 $7.00 $1.50 $1.00 50.50 50.00 Pounds of Bananas 1 1 2 1 Pounds of Bananas 4 B О в D. 3 25 2 15 1 0.5 O $5.00 $4.00 $3.00 $2.00 $1.00 $0.00 0 Pounds of Bananas 1 2 Pounds of Bananas 2 4 10 points S
Equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas and graph is given in attachment.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Given that Bananas cost $0.48 per pound.
Since each pound costs $0.85, the cost of one pound is $0.48,
the cost of two pounds is twice that at $0.96
The equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas.
Hence, equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas and graph is given in attachment.
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HELP
There are 6p+18 fiction books and 4p+12 non-fiction books in a bookcase.
Work out the fraction of the books in the bookcase that are non-fiction.
Give your answer in its simplest form.
The fraction of the books in the bookcase that are non-fiction is 2/5.
What is fraction?A fraction is a part of a whole number, and a way to split up a number into equal parts.
Given that, there are 6p+18 fiction books and 4p+12 non-fiction books in a bookcase, we need to find the fraction of the books in the bookcase that are non-fiction.
Therefore,
Number of fictional books = 6p+18
Number of non-fictional books = 4p+12
Total books = 6p+18+4p+12 = 10p+30
Therefore,
the fraction of the books in the bookcase that are non-fiction is given by,
Number of non-fictional books / Total books
= 4p+12 / 10p+30
= 4(p+3) / 10(p+3)
= 4/10
= 2/5
Hence, the fraction of the books in the bookcase that are non-fiction is 2/5.
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Simplify the expression:
Answer: C!
Step-by-step explanation: Because I'm Him. all jokes aside this is the right answer.
three consecutive even integers are such that the sum of the smaller two is 52 less than three times the largest. what are the integers?
Three consecutives even integers are 42, 44, and 46.
The three consecutives even integers can be represented as x, x+2, and x+4. We can create an equation to solve for x, using the given information.
3(x+4) = 52 + x + (x+2)
3x + 12 = 54 + 2x
x = 42
Therefore, the three consecutives even integers are 42, 44, and 46. To explain this answer, we can use the equation we created. We know that the sum of the smaller two integers is 52 less than three times the largest. We can represent this as 3(x+4) = 52 + x + (x+2). We can then solve for x by subtracting 2x from both sides and adding 12 to both sides, resulting in x = 42. This means that the three consecutives even integers are 42, 44, and 46.
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suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. a sample of 100 steady smokers revealed that the sample mean is $20. the population standard deviation is $5. what is the probability that a sample of 100 steady smokers spend between $19 and $21? 0.0228 0.4772 1.0000 0.9544
The required probability is 0.9544
A z-score is a quantitative measure obtained when a data point from a normal population with mean μ and standard deviation
σ is transformed. It describes the position of the data point representing its distance from the average value of the normal population measured in number of standard deviations. It is given by:
z =(X − μ)/σ
A standard normal table (z-score table) provides the probability to the left of the z-score so obtained.
Number of randomly selected steady smokers is, n=100.
Sample mean is, M=$20.
The population standard deviation is, σ = $5.
To compute the probability that a sample of 100 steady smokers spend between 19 and 21.
Using the definition of a z-score, computing the z-score for X =$19,
z =(X − μ)/σ /[tex]\sqrt{n}[/tex]
[tex]z = \frac{19-20}{5}/\sqrt{100}[/tex]
z = -2
Again using the definition of a z-score to compute the z-score for X = $21,
z =(X − μ)/σ /[tex]\sqrt{n}[/tex]
[tex]z = \frac{21-20}{5}/\sqrt{100}[/tex]
z = 2
The probability that a sample of 100 steady smokers spend between 19 and 21 is obtained as:
P(19< X < 21) = P(-2 < X < 2)
= P(z< 2) - P(z < -2)
= P(z < 2) − [1 − P (z < 2)]
= 0.9772 - (1 - 0.9772)
= 0.9772 - 0.0288
= 0.9544
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In ΔKLM, m = 63 inches, mm∠K=24° and mm∠L=42°. Find the length of l, to the nearest inch.
Check the picture below.
[tex]\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(\measuredangle M)}{m}=\cfrac{\sin(\measuredangle L)}{l}\implies \cfrac{\sin(114^o)}{63}=\cfrac{\sin(42^o)}{l} \\\\\\ l\sin(114^o)=63\sin(42^o)\implies l=\cfrac{63\sin(42^o)}{\sin(114^o)}\implies l\approx 46~inches[/tex]
East Middle’s football team has 20.9 liters of sports drink on the field during the game. Each player receives the same amount of sports drink.
If East Middle’s football team consists of 22 players, how much sports drink, in liters, does each player receive?
(Write the answer as a decimal to the nearest hundredth.)
Taking the quotient between the volume of sports drink and the number of players we will see that each player gets 0.95 liters.
How much sports drink, in liters, does each player receive?We know that East Middle’s football team has 20.9 liters of sports drink on the field during the game. Now we want to divide that evenly among all the players of the team, and we know that the team has 22 players.
Then we just need to take the quotient between these two numbers, it is:
20.9/22
We can rewrite that as:
(209/10)*(1/22)
(209/220)
Each player receives (209/220) liters of sports drink.
We can also simplify that as (209/220) liters = 0.95 liters.
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jim has received scores of 69 and 82 on his first two 100 point tests. what score must he get on his third 100 point test to keep an average of 85 or greater?
Jim needs a score of 97 on his third test to keep an average of 85 or greater.
Average refers to the sum of a set of numbers divided by the count of numbers in the set. It gives a typical or central value that represents the set of numbers.
Given,
The average of his first two tests is (69 + 82) / 2 = 75.5.
To get an average of 85,
he needs the sum of his three tests to be 3 * 85 = 255.
So, the sum of his first two tests is 255 - x, where x is the score he needs on the third test.
Therefore, x = 255 - (69 + 82) = 255 - 151 = 104.
So, he needs a score of 104 on his third test.
Jim needs a score of 97 on his third test to keep an average of 85 or greater.
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Write an explicit formula for a,, the nth term of the sequence 14,16,18,….
The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.
What is the explicit formula for the nth term of the sequence?Since the sequence increases by 2, it is an arithmetic sequence.
The formula the nth term an arithmetic sequence is expressed as;
aₙ = a₁ + d( n - 1 )
Given the sequence; 14,16,18,….
First term a₁ = 14
Common difference d = 16 - 14 = 2
Now, plug the values into the above formula and simplify.
aₙ = a₁ + d( n - 1 )
aₙ = 14 + 2( n - 1 )
aₙ = 14 + 2n - 2
aₙ = 14 - 2 + 2n
aₙ = 2n + 12
Therefore, the explicit formula is aₙ = 2n + 12.
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Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 74.5 Mbps. The complete list of 50 data speeds has a mean of x= 17.34 Mbps and a standard deviation of s= 20.79 Mbps. a. What is the difference between carrier's highest data speed and the mean of all 50 data speeds? b. How many standard deviations is that [the difference found in part (a)]?
a. The difference between the highest data speed (74.5 Mbps) and the mean of all 50 data speeds (17.34 Mbps) is:
74.5 - 17.34 = 57.16 Mbps
b. To find the number of standard deviations, divide the difference by the standard deviation:
57.16 / 20.79 = 2.75
So, the difference of 57.16 Mbps is 2.75 standard deviations from the mean.
Mbps known as for “Megabits per second.” This is the standard measure of “speed” or “bandwidth” on home internet connections.
It finds how many bits (units of digital information) can be transferred each second. You’ll normally see speeds ranging from 10-1,000 Mbps advertised for home internet plans.
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Compare the y-intercepts for the two linear functions represented below.
X Y
-1 -1
0 1
1 3 y = 4x - 1
2 5
3 7
A.
The y-intercept of function A is same as the y-intercept of function B.
B.
The y-intercept of function A is greater than the y-intercept of function B.
C.
The y-intercept of function A is less than the y-intercept of function B.
B. The y-intercept of function A is greater than the y-intercept of function B.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
from the given data, we get,
the 1st line's equation is, y=2x+1
i.e. y-intercept = 1
and,
the 2nd equation is,
1 3 y = 4x - 1
i.e. y-intercept = -1/13
=-0.77
as, 1> -0.77
Hence, B. The y-intercept of function A is greater than the y-intercept of function B.
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The triangle on the right is a scaled copy of the triangle on the left. Identify the scale
factor. Express your answer as a whole number or fraction in simplest form.
Scale-factor of copy to original is 3/2.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given,
Right side triangle is scaled copy of left side triangle
Ratio of side of copy to side of original = (57/2) / 19 = 3/2
So, Scale factor = 3/2
Hence, 3/2 is the scale-factor in making copy of original triangle.
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Find the slope of a line parallel to the line whose equation is 3x+18y=-4863x+18y=−486. Fully simplify your answer.
The slope of the parallel line is given by the equation m = ( -1/6 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
3x + 18y = -486 be equation (1)
On simplifying the equation , we get
Subtracting 3x on both sides of the equation , we get
18y = -3x - 486
Divide by 18 on both sides of the equation , we get
y = ( -3/18 )x - ( 486/18 )
On further simplification , we get
y = ( -1/6 )x - 27
Now , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
Slope m = -( 1/6 )
Hence , the slope of the line is m = -1/6
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to start her old lawn mower, rita has to pull a cord and hope for some luck. on any particular pull, the mower has a 20% chance of starting. what is the probability that it takes her exactly 3 pulls to start the mower?
Rita's old lawn mower will start after exactly three pulls 12.8% of the time,
The binomial probability formula states that the probability of success occurring precisely x times in n trials is equal to the product of the probability of success (p) and the probability of failure (1-p) raised to the power of n-x. This can be used to calculate this. The probability of success occurring exactly three times is equal to 0.2 x 0.8 x 0.8, or 12.8%, given that the number of trials (n) and the probability of success (p) is both 20 percent.
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Can someone help me ive been stuck on this for a bit
Keenan opens a savings account with $740
that earns 6% interest per year, not compounded.
How much money, to the nearest penny, will Keenan have in 8 years? Give your answer in dollars.
Answer: $1095.20
Step-by-step explanation: Multiply 6% by 740 and then times that number by 8 and add it to 740, lmk if it is wrong though.
Answer:
1095.20
Step-by-step explanation:
Take the 8 for the amount of time and multiply it by .06 because .06 is repeating each year.
You get .48 when you multiply it. Take that decimal and multiply it by 740.
He will get an extra 355.20. Add that with 740.
He has $1095.20 in his account.
Dottie went to the movies with her friends. She bought a soda for $2.35, a pack of bubble gum for $1.15, and a chocolate bar for $1.65. How much did Dottie spend in total?
Answer:
Step-by-step explanation:
The candy bar cost, in dollars, is $1.05
Say the price of a piece of bubble gum is x.
This means that we can represent our scenario with the equation (x+1)+x=1.10, with (x+1) representing the price of a candy bar.
We can then solve from there.
We have given that,
(x+1)+x=1.10
Simplify above expression
2x+1=1.10
2x=0.10 - Subtract From Both Sides
x=0.05 - Divide From Both Sides
So now we have the price of the piece of bubble gum, but we want the cost of the candy bar.
What is the cost?
Cost is the value of money that a company had to spend to produce its goods or services.
Fortunately, we know it costs one dollar more than the piece of bubble gum, so just do 0.05 + 1. This means our candy bar costs $1.05.
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Answer:
Soda = 2.35
Pack of bubble gum = 1.15
Chocolate bar = 1.64
2.35 + 1.15 + 1.64 = 5.15
Answer: Dottie spent a total of $5.15.
3.35x + 115 = 3.25x + 125
For the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.
What is an equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
The given expression is:
3.35x + 115 = 3.25x + 125
Regroup all the terms with variable x on one side of the equation:
3.35x - 3.25x = 125 - 115
0.1x = 10
x = 100
Hence, for the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.
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