Instructions: Fill in the table of values for the exponential function. Insert all answers as fractions, when applicable.
Answers
Given,
The expression is:
[tex]y=-2(\frac{1}{2})^x[/tex]Required:
The value of y at x = -2, -1, 0, 1, 2.
The value of y at x = -2.
[tex]y=-2(\frac{1}{2})^{-2}=-2\times(2)^2=-2\times4=-8[/tex]The value of y at x = -1.
[tex]y=-2(\frac{1}{2})^{-1}=-2\times(2)^1=-2\times2=-4[/tex]The value of y at x = 0.
[tex]y=-2(\frac{1}{2})^0=-2\times(2)^0=-2\times1=-2[/tex]The value of y at x = 1.
[tex]y=-2(\frac{1}{2})^1=-2\times\frac{1}{2}=-1[/tex]The value of y at x = 2.
[tex]y=-2(\frac{1}{2})^2=-2\times\frac{1}{4}=-\frac{1}{2}=-0.5[/tex]The table for the different value of the function:
x y
-2
Related Questions
Suppose that y varies inversely with x, and y = 5/4 when x = 16.(a) Write an inverse variation equation that relates x and y.Equation: (b) Find y when x = 4.y =
Answers
In general, an inverse variation relation has the form shown below
[tex]\begin{gathered} y=\frac{k}{x} \\ k\to\text{ constant} \end{gathered}[/tex]It is given that x=16, then y=5/4; thus,
[tex]\begin{gathered} \frac{5}{4}=\frac{k}{16} \\ \Rightarrow k=\frac{5}{4}\cdot16 \\ \Rightarrow k=20 \end{gathered}[/tex]Therefore, the equation is y=20/x
[tex]\Rightarrow y=\frac{20}{x}[/tex]2) Set x=4 in the equation above; then
[tex]\begin{gathered} x=4 \\ \Rightarrow y=\frac{20}{4}=5 \\ \Rightarrow y=5 \end{gathered}[/tex]When x=4, y=5.
A new statue in a local park has a length (L), width (W), and height (H) (all in feet) that can be expressed by a system of equations. L+W=28L+H=26W+H=22What is the width of the statue?
Answers
To determine the width of the statue:
[tex]\begin{gathered} L+W=28\ldots\ldots..(1) \\ L+H=26\ldots\ldots\ldots(11) \\ W+H=22\ldots\ldots..(111) \end{gathered}[/tex]A local park has a length (L), width (W), and height (H) (all in feet)
Solve equation 1 and 2 simultaneously,
[tex]\begin{gathered} L+W=28 \\ L+H=26 \\ \text{Subtract equation (1) - (11)} \\ W-H=2\ldots\ldots\ldots(IV) \end{gathered}[/tex]Solve equation 3 & 4 simultaneously, make W the subject of formular
[tex]\begin{gathered} W+H=22 \\ W-H=2 \\ \text{Add the two equation} \\ 2W=24 \\ \text{divide both side by 2} \\ \frac{2W}{2}=\frac{24}{2} \\ W=12 \end{gathered}[/tex]Therefore the value of width of the statue = 12 feet
the sum of billiard balls was arranged in an equilateral triangle and 7 balls were extra. Then the same set of billiard balls was arranged into a triangle where each side has one more ball than in the first arrangement but now the new arrangement cannot be completed because there is a shortage of three balls. How many balls are in the set?
Answers
There were 52 billiard balls in the set.
Assume that billiard balls are arranged in rows to form an equilateral triangle, then the first row consists of 1 ball, second row consists of 2 balls, and third row consists of 3 balls, and so on. So there must be n balls in the nth row.
So, the total number of billiard balls that forms the equilateral triangle with n rows is:
1 + 2 + 3 + ... + n = n(n + 1)/2
Let x1 and x2 be the total number of balls in the first and second arrangements respectively.
Then,
x1 = n(n + 1)/2 + 7
It has been said that there were 3 lesser balls in the second arrangement:
x2 = (1 + (n + 1))/2 × (n + 1) - 3
x2 = (n + 1) × (n + 2)/2 - 3
Since x1 = x2,
n(n + 1)/2 + 7 = (n + 1) × (n + 2)/2 - 3
We solve above equation to find the value of n,
multiplying both the sides by 2
n(n + 1) + 14 = (n + 1)(n + 2) - 6
n² + n + 14 = n² + 3n + 2 - 6
n - 3n = -4 - 14
-2n = -18
n = 9
So, x1 = 9(9 + 1)/2 + 7
= 9(5) + 7
= 45 + 7
= 52
Therefore, there were 52 billiard balls in the set.
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Jenna bought a package of 2 chicken drumsticks. If the package weighed 0.232 kg, what is the average weight of
each drumstick?
Answers
Answer:
0.116
Step-by-step explanation:
[tex]\frac{0.232}{2}[/tex] = 0.116
An example of an experiment that leads to a uniform probability distribution is...Choose one answer. 1. the sum of rolling two dice 2. measuring the heights of all the students in a school 3. tossing a coin ten times and recording the number of heads 4. selecting a card from a deck of 52 cards
Answers
Solution
A probability distribution in which all of the values of the random variable occur with equal probability is called a uniform probability distribution. Describe an example of an experiment that would produce a uniform distribution. Then find the theoretical probabilities that would result from this experiment. Include a table and graph of the distribution.
Answer:
The theoretical probability experiment of rolling a die would result in a uniform distribution because the probabilities of rolling a 1,2,3,4,5,6 are all equally likely to occur.
Therefore the sum of rolling two dice is an option
Hence the correct answer is
Option 1
please help me work through this homework problem! thank you!
Answers
Given:
Given the function
[tex]y=3+\frac{3}{x}+\frac{2}{x^2}[/tex]and a point x = 3.
Required: Equation of the line tangent to y at x = 3.
Explanation:
The derivative of a function is he slope of the tangent line of the function at a given point. So, finding the derivative gives the slope of the tangent line.
[tex]y^{\prime}=-\frac{3}{x^2}-\frac{4}{x^3}[/tex]Substitute 3 for x into the derivative.
[tex]\begin{gathered} y^{\prime}|_{x=3}=-\frac{3}{3^2}-\frac{4}{3^3} \\ =-\frac{31}{27} \end{gathered}[/tex]Therefore, the slope of the tangent line is -31/27.
Substitute 3 for x into y.
[tex]\begin{gathered} y|_{x=3}=3+\frac{3}{3}+\frac{2}{3^2} \\ =3+1+\frac{2}{9} \\ =4+\frac{2}{9} \\ =\frac{38}{9} \end{gathered}[/tex](3, 38/9) is the only point on the tangent line where it intersects the original graph.
Plug these coordinates along with slope into the general point-slope form to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-\frac{38}{9}=-\frac{31}{27}(x-3) \end{gathered}[/tex]Solving for y will give the equation in slope-intercept form.
[tex]\begin{gathered} y=-\frac{31}{27}(x-3)+\frac{38}{9} \\ =-\frac{31}{27}x+\frac{69}{9} \end{gathered}[/tex]Final Answer: The equation of the tangent line is
[tex]y=-\frac{31}{27}x+\frac{69}{9}[/tex]
6 minus 3 times a number is less than 30. Find the number:
Answers
x > -8
Explanations:Let the number be represented by x:
Three times the number = 3x
Six minus three times the number = 6 - 3x
Six minus three times the number is less than 30:
That can be interpreted mathematically as:
6 - 3x < 30
To find the value of x:
Step 1: Collect like terms
- 3x < 30 - 6
-3x < 24
Step 2: Divide both sides by 3:
[tex]\frac{-3x}{3}=\text{ }\frac{24}{3}[/tex]-x < 8
Multiply both sides by (-1) and change the < sign to >
(-1) (-x) > 8 x(-1)
x > -8
Why would a person pay property taxes?
Answers
Kuta Software Infinie Algebra ? Absolute Value Inequalities Salve each inequality and graph its solution. 61 1 laulsis * -36043 3) m-2/
Answers
Prob 22
7 + | 6v + 7| ≤ 60
then
| 6v + 7| ≤ 53
now eliminate lines ||
6v + 7 ≤ 53
and
6v + 7 ≤ - 53,. 6v ≤ -60
Now solve for x
6v ≤ 47,. v≤ 46/6
also
6v ≥ -47,. v≥ -46/6
Then answer is
-10 ≤ v ≤ -46/6
Graph for problem 22
Given the formula for the perimeter of a rectangle, p=2l+2wwhich answer would you get if you solve for l? p−2w 2 p/w-2 p/2−2w p−2l/2
Answers
If we have:
[tex]p=2w+2l[/tex]To solve for l we can start by inverting the sides and substracting 2w from both sides so that the term with l becomes alone in the left side:
[tex]\begin{gathered} p=2w+2l \\ 2w+2l=p \\ 2w-2w+2l=p-2w \\ 2l=p-2w \end{gathered}[/tex]Now, we can divide both sides by 2 so thay the 2 in 2l gets canceled:
[tex]\begin{gathered} 2l=p-2w \\ \frac{2l}{2}=\frac{p-2w}{2} \\ l=\frac{p-2w}{2} \end{gathered}[/tex]So, the answer we would get is
[tex]\frac{p-2w}{2}[/tex]Use the words to complete the sentences :1) Downards,2) 15,3) Ascending,4) does,5) upwards,6) Positive,7) Does not,8) Negative,9) Descending,10) 16,11) 3, 12) 3.51) The Graph a plane -----. 2) The line is slanting ------- and therefore has a ------ slope.3) It takes the plane ------ seconds to touch the ground.4) The plane starts at ------- kilometers in the sky .5) Graph ------ touch the origin (0, 0) .
Answers
According to the given graph, we have the following:
1) The graph represents a plane descending.
2) The line is slanting downwards and therefore has a negative slope.
3) It takes the plane 15 seconds to touch the ground.
4) The plane starts at 3 kilometers in the sky.
5) Graph does not touch the origin (0,0).
The given graph shows a decreasing line, starting at y = 3, and reaching y = 0 when x = 15.
100 POINTS AND BRAINLY FOR THE CORRECT ONLY ANSWER IF U UNDERSTAND THE QUESTION!
A line includes the points (10,6) and (2,7). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
PLEASE AND THANK U
Answers
Answer:
[tex]y-6=-\dfrac{1}{8}(x-10)[/tex]
Step-by-step explanation:
To find the equation of a line that passes through two points, first find its slope by substituting the given points into the slope formula.
Define the points:
(x₁, y₁) = (10, 6)(x₂, y₂) = (2, 7)Substitute the points into the slope formula:
[tex]\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-6}{2-10}=\dfrac{1}{-8}=-\dfrac{1}{8}[/tex]
Therefore, the slope of the line is -¹/₈.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:
[tex]\implies y-6=-\dfrac{1}{8}(x-10)[/tex]
The confidence interval on estimating the heights of the students is given as (5.5, 6.5). Find the sample proportion of the confidence interval.
Answers
Answer:
Step-by-step explanation:
A pizza is to be cut into halves. Each of these halves is to be cut into fourths. What fraction of the pizza is each of thefinal pieces?
Answers
Given:
Each of these halves is to be cut into fourths.
So:.
A pizza is to be cut into halves
since half is represented by 1/2.
So each piece is now
[tex]\frac{1}{2}\text{ of the original.}[/tex]If each of these halves is to be cut into fourths, then the fraction of final pieces is:
[tex]\begin{gathered} =\frac{1}{2}\times\frac{1}{4} \\ =\frac{1}{8} \end{gathered}[/tex]
Answer:
1/8
Step-by-step explanation:
Fractions
We have 1/2
!/2 is to be cut in 1/4
1/2 * 1/4 = 1/8
Araceli filled a cone-shaped container with a variety of colored sand to give as a gift to a friend. The volume of a cone is represented by the expression below, where r is the radius of the base of the cone and h is the height of the cone.radius = 3 1/23 5/3 is the height
Answers
The volume of the cone is 45.28 cubic inches.
The amount of sand inside the cone is measured by its volume.
Based on the numbers for the radius and height, the cone's volume is 45.28 cubic inches.
The volume of a cone is the measure of how much space a cone takes up. Cone height and base radius both affect how much space the cone takes up.
The volume of the cone is given by V = [tex]\frac{1}{3}\pi r^{2} h[/tex]
The value of the radius is r = [tex]3\frac{1}{23} = \frac{70}{23}[/tex]
The value of Height is h = [tex]3\frac{5}{3} = \frac{14}{3}[/tex]
So, the Volume of the cone =[tex]V =\frac{1}{3}\pi r^{2} h[/tex]
[tex]V =\frac{1}{3}\pi r^{2} h\\\\V = \frac{1}{3}\pi (\frac{70}{23}) ^{2} \frac{14}{3} \\\\V = 45.28[/tex]
The volume of the cone is 45.28 cubic. inches
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help me please I love when I can get help
Answers
To determine in how many pices of 2/3ft can a 9ft long ribbon be cut, you have to divide 9 by 2/3:
[tex]9\div\frac{2}{3}[/tex]To divide both fractions, first turn the 9 into a fraction by adding 1 as a denominator
[tex]\frac{9}{1}\div\frac{2}{3}[/tex]Now you have to invert the fraction that is the denominator of the division
[tex]\frac{2}{3}\to\frac{3}{2}[/tex]And multiply it by the first fraction
[tex]\frac{9}{1}\cdot\frac{3}{2}=\frac{9\cdot3}{1\cdot2}=\frac{27}{2}\cong13.5[/tex]She can divide the ribbon in 13 pieces of 2/3ft each
Isolate one radical on one side of the equation.Raise each side of the equation to a power equal to the index of the radical and simplify. Check all proposed solutions in the original equation.
Answers
The given equation is
[tex]\sqrt[]{3\text{ - 2x}}\text{ - 4x = 0}[/tex]The first step is to add 4x to both sides of the equation. We have
[tex]\begin{gathered} \sqrt[]{3\text{ - 2x}}\text{ - 4x + 4x = 0 + 4x} \\ \sqrt[]{3\text{ - 2x}}\text{ = 4x} \\ \text{Squaring both sides of the equation, we have} \\ (\sqrt[]{3-2x)}^2=(4x)^2 \\ 3-2x=16x^2 \end{gathered}[/tex]3 - 2x = 16x^2
Adding 2x to both sides of the equation, we have
3 - 2x + 2x = 16x^2 + 2x
3 = 16x^2 + 2x
Subtracting 3 from both sides of the equation, we have
3 - 3 = 16x^2 + 2x - 3
0 = 16x^2 + 2x - 3
16x^2 + 2x - 3 = 0
This is a quadratic equation. We would solve for x by applying the method of factorisation. The first step is to multiply the first and last terms. We have 16x^2 * - 3 = - 48x^2. We would find two terms such that their sum or difference is 2x and their product is - 48x^2. The terms are 8x and - 6x. By replacing 2x with with 8x - 6x in the equation, we have
16x^2 + 8x - 6x - 3 = 0
By factorising, we have
8x(2x + 1) - 3(2x + 1) = 0
Since 2x + 1 is common, we have
(2x + 1)(8x - 3) = 0
2x + 1 = 0 or 8x - 3 = 0
2x = - 1 or 8x = 3
x = - 1/2 or x = 3/8
We would substitute these values in the original equation to check. We have
[tex]\begin{gathered} For\text{ x = }-\text{ }\frac{1}{2} \\ \sqrt[]{3\text{ - 2}\times-\frac{1}{2}}\text{ - 4}\times-\text{ }\frac{1}{2}\text{ = 0} \\ \sqrt[]{3\text{ - - 1}}\text{ + 2 = 0} \\ \sqrt[]{4}\text{ + 2 = 0} \\ 2\text{ + 2 }\ne0 \end{gathered}[/tex][tex]\begin{gathered} \text{For x = }\frac{3}{8} \\ \sqrt[]{3\text{ - 2}\times\frac{3}{8}}\text{ - 4}\times\frac{3}{8}\text{ = 0} \\ \sqrt[]{3\text{ - }\frac{3}{4}}\text{ - }\frac{3}{2}=\text{ 0} \\ \sqrt[]{\frac{9}{4}}\text{ - }\frac{3}{2}\text{ = 0} \\ \frac{3}{2}\text{ - }\frac{3}{2}\text{ = 0} \end{gathered}[/tex]The solution is x = 3/8
Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
Answers
The derivative of the function y = -1/x-2 is 1/(x-2)².
Given, the function is y = -1/x-2
Differentiate the function with respect to x.
dy/dx = d/dx (-1/x-2)
the function is in the form of :
d/dx [f(x)g(x)] = f(x)d/dx((x)) + g(x)d/dx(f(x))
here d/dx [f(x)g(x)] = d/dx [(-1)(1/x-2)]
therefore, d/dx [(-1)(1/x-2)] = (-1)d/dx(1/x-2) +(1/x-2)d/dx(-1)
⇒ d/dx [(-1)(1/x-2)] = (-1)(-1)(x-2)⁻¹⁻¹ + (1/x-2)d/dx(0)
⇒ d/dx [(-1)(1/x-2)] = 1(x-2)⁻² + 0
⇒ d/dx [(-1)(1/x-2)] = 1/(x-2)²
Hence the derivative of the function is 1/(x-2)²
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Convert 255 to base 2
Answers
We can count the number of zeros and ones to see how many bits are used to represent 255 in binary i.e. 11111111. Therefore, we have used 8 bits to represent 255 in binary.
Convert 255 to base 2?
255 = 8 bits
255 in Binary: 255₁₀ = 11111111₂
Binary is a system used in mathematics and computer science where values and numbers are stated as 0 or 1.Binary is base-2, which means that there are just two digits or bits used.For computers, 1 denotes truth or "on," while 0 denotes falsehood or "off." Computers communicate and represent information using binary code.Everything you see on a computer, including letters, numbers, and pictures—basically everything—is made up of multiple 0s and 1s combinations. One of the four different kinds of number systems is the binary number system.When used in computer programs, binary numbers are solely represented by the digits 0 (zero) and 1. (one).Here, the base-2 numeral system is used to represent the binary numbers.One binary number is (101)2, for instance. The modern binary number system was first suggested and refined by Gottfried Leibniz in the 17th century in his article Explication de l'Arithmétique Binaire [1].The system was created by Leibniz about 1679, although it wasn't published until 1703.He had already used 0 and 1.To learn more about binary refer
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I need to explain the mistake he made and show my work and I need the answer
Answers
The problem is;
-2(x-1) - 2 > 8 - 5x +4+ x
open the parenthesis
-2x + 2 -2 > 8- 5x + 4+ x
collect the like-term
-2x+5x-x > 8+4
2x > 12
divide both-side of the inequality by 2
x>6
The first mistake that was made is adding of the x-variables
It is 2x and not -6x
Determine weather it is a function, and state it’s domain and range.
Answers
Find the inverse of:
[tex]f(x)=(3x-24)^2[/tex]The variable x can take any real value and the function f(x) exists. This means
the domain of f(x) is (-∞, +∞).
Now find the inverse function.
[tex]\begin{gathered} y=(3x-24)^2 \\ \pm\sqrt[]{y}=3x-24 \\ \pm\sqrt[]{y}+24=3x \\ x=\frac{\pm\sqrt[]{y}+24}{3} \\ x=\pm\frac{1}{3}\sqrt[]{y}+8 \end{gathered}[/tex]Swapping letters, we get the inverse function:
[tex]y=\pm\frac{1}{3}\sqrt[]{x}+8[/tex]For each value of x, we get two values of y, thus this is not a function.
The domain of the inverse is restricted to values of x that make the square root exist, thus the domain is x ≥ 0, or [0, +∞)
The range of the inverse is the domain of the original function, that is, (-∞, +∞)
Function: No
Domain: [0, +∞)
Range: (-∞, +∞)
The choice to select is shown below.
A batting cage charges a flat fee of $5 to practice and th Write an equation that models the charges (C) in terms of the number of bucket balls (b) that you use: O C = 1.50 b + 5 O C = 5 b + 1.50 6 Ob = 1.60 C + 5 Ob = 5 C + 1.50
Answers
we have
C -----> total charge
b -----> number of buckets of balls
Remmeber that
the equation of the line in slope intercept form is equal to
y=mx+b
where
m is the slope and b is the initial value or y-intercept
In this problem
m=$1.50 per buckey
b=$5
therefore
y=1.50x+5
or
C=1.50b+5
answer is first optionI need help simplify each expression look for the terms first
Answers
8k + 3 +4k
________________
First, add the k
8k + 4k = (8+4) k = 12 k
________________
you add if there are other variables or numbers
3
________________
12k + 3
Do you have any questions regarding the solution?
Sample SpaceFind the number of outcomes in the following experiments. 1. Selecting a letter from the English alphabet
Answers
The English Alphabet consist of 26 letters. The number of outcome of the experiment therefore is 26 which consist of the sample space.
S = {A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}
What is the factor 24/28 in simplest form
Answers
Answer:
6/7
Step-by-step explanation:
24/28 they both are commonly divisible by 4,
making them 6/7
how do i use a graphing calculator to solve the system.
Answers
Given:
[tex]\begin{gathered} 0.4x\text{ + }\sqrt{2}y\text{ = 1} \\ \sqrt{5}\text{ x + 0.8y = 1} \end{gathered}[/tex]Using a graphing calculator, we have the graph shown below:
The point of intersection of the equations represents the solution to the system.
Hence, the solution to the system is:
x = 0.216
y = 0.646
Solve the inequality and write the solution using:
Inequality Notation:
Answers
The answer of the given inequality is x < 16
Difference between equality and inequality equations
Both mathematical phrases, equations and inequalities, are created by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.
The inequality expression is ,
(1 * x) /4 < 4 or x/4 < 4
=> x < 4 * 4
=> x < 16
Therefore, the answer is x < 16.
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Find area and perimeter of the shape identify the shape
Answers
Part A
The dimensions of the shape shown are given as
length, l = 12 in
breadth (b) = width, w = 4 in
The area of the shape is given as;
[tex]\begin{gathered} A=l\times b \\ A=12\times4 \\ A=48in^2 \end{gathered}[/tex]Therefore, the area of the shape is 48 square inches.
Part B
The perimeter of a shape is the sum of all the outer sides enclosing the shape
From the above shape, we add all four sides together
[tex]\begin{gathered} P=12+12+4+4 \\ P=32in \end{gathered}[/tex]Consequently, we can get the perimeter using formula method as well
[tex]\begin{gathered} P=2(l+b) \\ P=2(12+4) \\ P=2(16) \\ P=2\times16 \\ P=32in \end{gathered}[/tex]Therefore, the perimeter of the shape is 32 inches.
Part C
From the dimension given in the question, since the shape has a length and width, and the length and width are not equal, then the shape is a rectangle.
The shape, therefore, is a rectangle.
1 pointThe 5 consecutive integers below add up to 175. What is the value of x?x-3x-2X - 1ХX + 1
Answers
Then x=36.
Kayla has $37.99 in her checking account. she uses her debit card to make purchases of $26.29 and $22.98 which overdraws her account. her bank charges her account an overdraft fee of $25.00. She then deposits her paycheck for $55.07 from her part time job. what is the balance in her account?
Answers
Aye itz just me, this is the solution:
Initial balance = $ 37.99
Purchase 1 = ($ 26.29)
Purchase 2 = ($ 22.98)
Overdraft fee = ($ 25.00)
Deposit = $ 55.07
______________________
New balance = 37.99 - 26.29 - 22.98 - 25 + 55.07
New balance = $ 18.82