Hello,
I hope you and your family are doing well!
Part A)
The given expression is in the form y = -16t^2 + 441, which is a quadratic equation. A quadratic equation can be factored into the form (ax + b)(cx + d) = 0, where a, b, c, and d are constants.
To factor in the given expression, we can start by completing the square. To complete the square, we need to add and subtract the square of half of the coefficient of the x^2 term, which is (1/2)(-16) = -8. This gives us:
y = -16t^2 + 441 = (-16t^2 - 8t^2) + 441 = -24t^2 + 441
Now, we can rewrite the expression as follows:
y = -24t^2 + 441 = (-8t^2) + 441
To complete the square, we need to add and subtract (1/2)^2(-8)^2 = 16:
y = (-8t^2 + 16) + 425
This expression can be rewritten as:
y = (-8t^2 + 16) + (20t)^2
So the expression can be factored as:
y = (-8t + 4)(2t - 5) (this is the answer)
Part B)
To find the time it takes the object to fall to a height of 377 feet, we can set y equal to 377 and solve for t. Substituting the factored form of the expression into the equation and solving for t gives us:
377 = (-8t + 4)(2t - 5)
We can then solve this equation by setting each factor equal to 0 and solving for t. This gives us:
-8t + 4 = 0
2t - 5 = 0
Solving these equations separately gives us:
t = 1/2
t = 5/2
The time it takes the object to fall to a height of 377 feet is t = 1/2 seconds. (or 0.5 in decimal form)
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Kendall set up 15 rows of chairs in the cafeteria for her school's talent competition. In the first 10 rows, she set up 30 chairs on the left side of the middle aisle and x chairs on the right side. In the last 5 rows, she set up 20 chairs on the left side of the middle aisle and y chairs on the right side to make room for the sound crew.
Pick all the expressions that represent how many chairs Kendall set up. Due tomorrow please help
Total number of seats for the center aisle z = 400 + 10x + Y
The cafeteria would have a total of 3z = 1200 + 30 x + 3y chairs.
What is total?The word "total" refers to the addition of numbers or the destruction of something, and a total is a whole or full sum. In mathematics, adding two or more integers yields the sum. When you multiply 8 by 8, you get 16.
If z represents the total number of seats, then z=z1 + z2.
The equation for the first ten rows would be 10 (30 + x)= z1.
The equation for the final five rows would be 5 (20 + y) = z2.
Therefore, there would be z= z1+ z2 seats in the center aisle.
So total number of chairs in the middle aisle would be
z= z1+ z2
z= 10 ( 30 + x)+5 ( 20 + y)
z= 300 + 10x + 100 + y
z= 400 + 10x + y
The total number of chairs in the cafeteria would be z +z +z ( for the 3 aisle right , middle and left)
3z = 3(400 + 10x + y)
3z= 1200 + 30 x+ 3y
Total number of seats for the center aisle z = 400 + 10x + Y
The cafeteria would have a total of 3z = 1200 + 30 x + 3y chairs.
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The value of a farmhouse, in dollars, x years
from the year it was built can by predicted by the
function () = 65500(1.05)^x
The value of a townhouse, in dollars, x years from
the year it was built can be predicted by the
exponential function shown in the table.
How much more will the townhouse be worth than
the farmhouse 5 years after their build date?
After 5 years the value of the farmhouse would be $23675 more than the value of the farmhouse when it was built.
What is the exponential function?
The exponential function is a mathematical function denoted by [tex]f(x)=e^{x}[/tex]. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
The value of a farmhouse, in dollars, x years from the year it was built can be predicted by the function
[tex]g (x) = 65500(1.05)^x[/tex]
Now the given table shows that the value of the farmhouse over the years
Now the value of the farmhouse when it was built = $70000
Now after 5 years, the cost would be
[tex]g(x) = 65500(1.05)^x\\\\g(5)=65500(1.05)^5\\\\g(5) = 93675\\[/tex]
Now the difference would be = 93675 - 70000
= $23675.
Hence, After 5 years the value of the farmhouse would be $23675 more than the value of the farmhouse when it was built.
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If np is greater than mp, which must be true? segment op is longer than segment mq. segment mn has the same length as segment mp. the measure of angle q equals the measure of angle o. angle o is larger than angle q.
Option D is correct since the side opposite the larger angle is larger and you know that MN>NP, so the angle O's measure is more than the angle Q's measure.
What is angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here,
The side that is opposite to the greater angle is greater.
you know that MN>NP.
Then the measure of angle O is larger than the measure of the angle Q.
Because the side opposing the greater angle is larger and you know that MN>NP, option D is true. As a result, the measure of angle O is larger than the measure of angle Q.
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The points (3,r) and (7,-1) lie on a line with slope of -3. Find the missing coordinate r .
Answer:
I'm not sure but x1=3 that's all I know I didn't do it on edge tho
Answer:
r = 11
Step-by-step explanation:
Since we have a slope and one confirmed point, a good approach would be to find the equation of the line that goes through that point. The equation can then be used to find r, for x = 3.
The standard format for an equation of a straight line is y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0). The slope is -3:
y = -3x + b
To find b, enter the given point and solve for b:
-1 = -3*(7) + b [for (7,-1)]
b = 20
The equation for this line is y = -3x + 20
Now enter (3,r)
y = -3x + 20
r = -3(3) + 20
r = 11
The point (3,r) is (3,11)
See the attached graph
which of the following is not the same across classification and regression decision trees? a. type of predicted variable b. impurity measure/ splitting criteria
The following is not the same across classification and regression decision trees is a . type of predicted variable .
Given :
which of the following is not the same across classification and regression decision trees a. type of predicted variable b. impurity measure/ splitting criteria .
What is classification and regression decision trees ?
CART is a predictive algorithm used in Machine learning and it explains how the target variable's values can be predicted based on other matters.
The not same across classification and regression decision trees is type of predicted variable .
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suppose that 60% of adults in district a support a new ballot measure, while 45% of adults in district b support the same measure. polisters take an srs of 200 adults from district a and a separate srs of 100 adults from district b to see the difference between the sample proportions (paps). what will be the shape of the sampling distribution of pa - bb, and why?
120 will be the shape of the sampling distribution.
How do you describe the shape of distribution?Quantitative data's distribution shape may be characterized as having a logical order to the numbers and allowing for the identification of the "low" and "high" end values on the histogram's x-axis. Since qualitative data are not numerical, the distribution shape cannot be specified.
Given that,
Sample size of A, n = 200
Sample size of B, n = 100
Proportion of adults in district A = 60%
Proportion of adults in district B = 45%
In the sample size of 200, the number of adults that support a new ballot measure is:
= (60%) × 200
= 120
Those that oppose is:
= 200 -120
= 80
If 45% supports a new ballot measure in district B, then 55% do not support. The difference between those that support and do not support is:
(55% - 45%) × 100
= 10
Hence, the sampling distribution of p(A) and p(B) is approximately normal, because the number of success in district A is 120.
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Select all of the expressions that could go on the right side of the equation to make the equation have no solutions.
Answer:
c is correct
Step-by-step explanation:
take 8 common bro
Imagine
Math
y =
Slope-Intercept Form - Item 35340
Pre-Quiz
x+
Guided
Learning
Complete the slope-intercept form of the linear equation that represents the
relationship in the table.
Practice
Post-Quiz
Finish
Welcome, Brookly
X
ليا
-2
y
-5
5
CLEAR
с
Please some one answer I’ve been working on this forever
Answer:
353340 + x + 33
Step-by-step explanation:
real life sum situation
what is the reciprocal of 7 3/7?
The reciprocal of 7 3/7 is 7/52
Answer: I'm pretty sure it's 7/52
Step-by-step explanation:
7*7 is 49, plus the 3 is 52, then the reciprocal of that. 7/52 is already in it's simplest form. Hope this helps!
Which of the following are rational numbers?
-1 4/53 47.444... 92.555... 99
Answer:
All are rational except 47.444...
Mai plans to watch 3 movies each month. Write an equation to represent the total number of movies n that she will watch m months.
2 monthly = 2 m, an equation for calculating the total number of movies she will watch over the course of m months.
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
Mai may view the following number of films each month if he watched two per month:
movies available = n
m = months
2 monthly = 2 m
Hence, 2 monthly = 2 m, an equation for calculating the total number of movies she will watch over the course of m months.
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A andwich hop erve 4 ounce of meat and 3 ounce of cheee on each andwich. After making andwiche for an hour, the hop owner ha ued 91 combined ounce of meat and cheee. How many combined ounce of meat and cheee are ued on each (1) andwich?
The combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.
According to the question,
We have the following information:
A sandwich hop serve 4 ounce of meat and 3 ounce of cheese on each sandwich. After making sandwiches for an hour the hop owner has used 91 combined ounce of meat and cheese.
Combined ounces for 1 sandwich:
Ounces of meat + ounces of cheese
4+3
7 ounces
It is given that in an hour 91 ounces of combined cheese and meat are used.
Now, we have:
Number of sandwiches made in 1 hour = 91/7
Number of sandwiches = 13
Ounces of meat used in 13 sandwiches can be found using multiplication as follows:
13*4
Ounces of meat used in 13 sandwiches = 52 ounces
Ounces of cheese used in 13 sandwiches can found using multiplication as follows:
13*3
Ounces of cheese used in 13 sandwiches = 39 ounces
Hence, the combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.
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Match the polynomial with its known factor.
(x+5)
(x-5)
(x+10)
(x-10)
x^3-13x^2+25x+50
x^4+7x^3+13x^2+6x-45
Hello,
I hope you and your family are doing well!
The polynomial x^3-13x^2+25x+50 can be factored as (x+5)(x-5)(x+10).
The polynomial x^4+7x^3+13x^2+6x-45 can be factored as (x+5)(x-5)(x+3)(x-3).
So the correct match is:
(x+5) - x^3-13x^2+25x+50
(x-5) - x^3-13x^2+25x+50
(x+10) - x^3-13x^2+25x+50
(x-10) - x^4+7x^3+13x^2+6x-45
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Happy Holidays!
what is 403.1 rounded to the nearest ten
Answer:
400
Step-by-step explanation:
403.1 rounded is 400
If e 5 x = 24 e 5 x = 24 , then x
The value of x is 0.636.
What is logarithms?
The opposite of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
f(x) = [tex]log_{a}x[/tex] (r) y = [tex]log_{a}x[/tex], where a > 0. It is the inverse of the exponential function a^y = x. Log functions include natural logarithm (ln) or common logarithm (log).
Given equation is
e^(5x) = 24
taking log with base e on both sides:
ln e^(5x) = ln 24
Applying the formula ln e^a = a
5x = ln 24
Divide both sides by 5:
x = 0.636
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A. p = 70
B. p = 140
C. p equals 2 over 140
D. p = 0.0143
The constant of proportionality (p) for the data points on this graph would then be determined as follows: [tex]p = y/xp = 420/6 = 560/8p = 70.[/tex]
How can a proportional relationship be located on a graph?It is proportional if the relationship's graph is a line or ray that passes through the origin.A line or ray is not proportional if it does not pass through the origin.Additionally, if it is not linear, it cannot be proportional.following equation: y = px
Where:
p is the constant of proportionality.
y represents the gems collected.
x represents the game levels.
The constant of proportionality (p) for the data points on this graph would then be determined as follows: [tex]p = y/xp = 420/6 = 560/8p = 70.[/tex]
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Given the following function: f ( x ) = 8 x 2 − 16 a. Factor completely. b. What are the x -intercepts. c. What is f ( − 1 ) d. What is the domain and range? e. Find the inverse of the function. f. What is the domain and range of the inverse? g. What is the relationship between the domains and range of a function and its inverse? h. Will the domain and range of all functions and their inverses follow this same pattern?
(a) This is the factored form of the equation.
(b) The x - intercepts are (√2, 0) and (-√2, 0).
(c) The value of f(-1) is -8.
What is x - intercept?
We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to find the y-intercept.
(a) Consider, the given equation
f(x) = 8x^2 - 16
First to factor the equation.
Take 8 common from both the terms,
f(x) = 8(x^2 - 2)
This is the factored form of the equation.
(b) Now to find the x- intercept.
Let y = 8x^2 - 16
Set y = 0
So,
0 = 8x^2 - 16
8x^2 - 16 =0
x^2 - 2 = 0
x^2 = 2
x = ±√2
Hence, the x - intercepts are (√2, 0) and (-√2, 0).
(c) Now to find the value of f(-1)
plug x = -1 in the given equation.
f(-1) = 8(-1)^2 - 16
f(-1) = 8(1) - 16
f(-1) = 8 - 16
f(-1) = -8
Hence, the value of f(-1) is -8.
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For each system of equations, drag the true statement about its solution set to the box under the system.
Therefore ,the answer that states, "Infinitely many solutions, both sides are equivalent expressions" is the one that should be selected in this case.
What is equation ?Equations are mathematical expressions that have two algebraic expressions on either side of an equals (=) sign. For an unknown quantity represented by an unknown variable, equations can be solved to determine its value.
Here,
The number of solutions is unlimited if there are more variables than linear independent equations.
A single solution or no solution is possible if there are the same number of linearly independent equations and variables.
In the following scenarios, we are at a loss for solutions:
y = x + 3
y = x - 3
this causes:
x + 3 = x - 3
+3 = -3
Consequently, this system lacks a solution.
The first set of equations is
y = x + 5
y = 2x + 5
You can see that there is only one solution for this system because there are only two variables and two linear independent equations.
Thus, "One solution, the graph of these lines should connect at one point" is what we have here. The key idea is (0, 5)
Another system is:
y =x+x+5 = 2x + 5
y = 2x+ 5
Since both equations are identical and there are just two variables in this situation, there are an endless number of solutions to the system.
The answer that states, "Infinitely many solutions, both sides are equivalent expressions" is the one that should be selected in this case.
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Identify where the new point A goes after
a 270° rotation about the origin (-4,2)
Answer: point A will stay where it is.
Step-by-step explanation: point A is the point of rotation
contains two base angles measuring 110g degrees.
3.) Hot Air Balloon You are in a hot air balloon that is 600 feet above the ground where you
can see two people.
600 ft
Not drawn to scale
If the angle of depression from your line of sight to the person at B is 30°, how far is
the person from the point on the ground below the hot air balloon?
The distance from the the point on the ground bellow the hot air balloon is 1039 feet
How to calculate the distance?Distance here talks about how far the person stands from a point
The given parameters are
The angle of depression from the point 30⁰
Height of the air balloon = 600 feet
The distance from the the point on the ground bellow the hot air balloon = x
To find x we use the trigonometric ratio:
TanB = opposite/Adjacent
Tan30 = 600/x
This implies that x*tan30 = 600
Making x the subject we have 600/tan30
⇒x = 600/0.5774
x=1034 feet
In conclusion, the distance from the the point on the ground bellow the hot air balloon is 1039 feet
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Angles W and X are complementary. Determine the degree measure of
55. 1°
60. 2°
90°
150. 2°
The degree measure of ∠W if m∠X = 29.8° is 60.2 °.
Given:
Angles W and X are complementary, determine the degree of measure of ∠W if m∠X = 29.8° .
Let x be the measure of angle w.
we know that ,
Complementary angles :
When the sum of two angles is equal to 90 degrees, they are called complementary angles.
m <X + m <W = 90°
substitute angle x value
29.8 ° + x = 90 °
x = 90 ° - 29.8 °
x = 60.2 °
Therefore the degree measure of m <W = 60.2 °.
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Full question :
Angles W and X are complementary. Determine the degree measure of m <W if m∠X = 29.8°.
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The chart shows the average time spent reading per day for students in an 8th grade class.
The line plot is titled minutes of reading per day, and the horizontal axis is labeled minutes of reading per day. There are 5 dots at 30, 1 dot at 33, 5 dots at 35, 1 dot at 36, 1 dot at 37, 3 dots at 40, 1 dot at 44, one dot at 46, 1 dot at 47, and 1 dot at 50.
Which of the following describes this data set?
Categorical and bivariate
Categorical and univariate
Numerical and bivariate
Numerical and univariate
This data collection may be characterized as numerical and univariate.
What is numerical and univariate?
If the collection of all potential values for a numerical univariate data is finite or countably infinite, the data is discrete. Usually, discrete univariate data are used in counting (such as the number of books read by a person). If the range of all potential values is a set of numbers, then a numerical univariate data is continuous.
Categorical data:
Categorical variables represent different sorts of data that may be categorized. Race, sex, age group, and educational level are some examples of categorical variables.
Data types that may be kept and recognized based on the names or labels assigned to them are referred to as categorical data.
Numerical data refers to the data that is in the form of numbers, and not in any language or descriptive form. Also known as qualitative data as it qualifies data before classifying it.
Over here we have the data for the average time spent reading per day for students in an 8th grade class.
Average Time is a numerical data
Bivariate data deals with two variables univariate data, which is one variable data we have numerical data and one variables so its Numerical and univariate.
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Evaluate m³ for m= 3/2.
Answer:8
Step-by-step explanation: isaid it is
PLEASE HELP I NEED THIS RIGHT NOW!!
Two pools are being filled with water. To start, the first pool had 972 liters of water and the second pool was empty. Water is being added to the first pool at a rate of 17 liters per minute. Water is being added to the second pool at a rate of 44 liters per minute.
Let x be the number of minutes water has been added.
Answer: To find the number of liters of water in the first pool after x minutes have passed, we can use the formula:
972 + 17x
To find the number of liters of water in the second pool after x minutes have passed, we can use the formula:
44x
Note that both of these formulas assume that the pools are being filled continuously, without any interruptions. If the flow of water into either pool is interrupted at any point, the actual amount of water in the pools may be different from what these formulas predict.
Answer:
a)
17x + 972
44x
b)
972 + 17x = 44x
Step-by-step explanation:
Explain the connection between <2 and
From Properties of Triangles , both figures are connected and angle ∠B or ∠2 is 65°
What are some basic Properties of triangles?Basic properties of triangles are:
1)A triangle's (of all varieties) total sum of angles is 180°.
2)The length of a triangle's two longest sides added together is longer than the third side.
3)Similar to this, the length of the third side of a triangle's third side is shorter than the difference between its two sides.
4)The longest of a triangle's three sides is the side that faces the larger angle.
5)A triangle's exterior angle is always equal to the product of its inner and exterior opposite angles. The outer angle attribute of a triangle refers to this characteristic.
Calculation:As sum of angles in a triangle is 180° and sum of angles on a line is also 180°, both the figures are related.
Sum of angles=180°;
[tex]50+B+65=180;\\B=65[/tex]
∠B=65°
Similarly angle 2 is also 65°
From Properties of Triangles , both figures are connected and angle ∠B or ∠2 is 65°
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State all integer values of x in the interval (1, 8) that satisfy the following inequality:
4x - 5 4
Integers lying in between in interval (1, 8) are 3, 4, 5, 6, 7, which satisfy the given inequality.
Explain the term closed interval?Any interval that contains all the limit points is said to be closed. The symbol for it is []. For instance, [2, 5] denotes a value greater or equal to 2 and lower or equal to 5. If one of an open interval's endpoints is present, it is referred to as a half-open interval. These intervals are regarded as closed since the endpoints create a boundary.4x - 5 > 4
4x > 9
x > 2.25
Integers lying in between in open interval (1, 8) are 3, 4, 5, 6, 7
Thus, integers lying in between in interval (1, 8) are 3, 4, 5, 6, 7, which satisfy the given inequality.
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The correct question is-
State all integer values of x in the interval (1, 8) that satisfy the following inequality:
4x - 5 > 4
John nee 20 gram of a 54% acid olution for hi cience project. Hi chool' cience laboratory ha bottle of 30% olution and bottle of 60% olution. How much of each hould john ue?
By solving equations we know that he should mix 4 grams and 16 grams of the 30% and 60% bottles, respectively.
What are equations?In mathematical equations, the equals sign is used to show that two expressions are equal.
According to algebra, an equation is a statement that shows the equality of two mathematical expressions.
For instance, the formulas 3x + 5 and 14, which together make the equation 3x + 5 = 14, are separated by the word "equal."
So, John requires a total of 20 grams.
Let x equal the 30% that he requires.
Let 20-x equal 60% of what he needs.
So, we have:
(x/20 * 30) + (20-x/20 * 60) = 54
Evaluate as follows:
1.5x + 60 -3x = 54
-1.5x = -6
x = 4 grams
20-x = 16 grams
Therefore, by solving equations we know that he should mix 4 grams and 16 grams of the 30% and 60% bottles, respectively.
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please help me! thank you.
The value of side JK in the Rhombus JKLM is 3√41.
What is rhombus?A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape.
Given that,
JKLM is a rhombus,
And side MN = 15 and diagonal JL = 24,
Since, In rhombus diagonal bisects each other at equally at 90°.
Therefore, ∠JNK = 90°, and JN = JL/2 = 12
Also, NK =MN = 15
Use Pythagorean formula to find side JK,
JK² = JN² + NK²
= (12)² + (15)²
= 144 + 225
JK² = 369
JK = 3√41
The required value of side JK is 3√41.
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PLEASE HELP ASAP!!!
Dontaya is at the top of a lighthouse
which is 250 feet above sea level. From the top, the measure of the angle of depression to Brace's boat on the water is 48 degrees. How far is Brace's boat from the bottom of the lighthouse? (round your FINAL
answer to the nearest whole foot)
Brace's boat is 225 feet from the bottom of the lighthouse.
What do you mean by trignoemtry?
Trigonometry (“triangles” and “measures”) is the branch of mathematics that studies the relationship between the side lengths and angles of triangles.
Trigonometry is one of the important branches in the history of mathematics that studies the relationship between the sides and angles of right triangles.
Trigonometric ratios of triangles are also called trigonometric functions. Sine, cosine, and tangent are three important trigonometric functions, abbreviated sin, cos, and tan.
It is given that Dontaya is at the top of a lighthouse which is 250 feet above sea level. From the top, the measure of the angle of depression to Brace's boat on the water is 48 degrees
Let Brace's boat is x feet from the bottom of the lighthouse.
Using trignometric ratios,
tan 48 = [tex]\frac{P}{B}=\frac{250}{x}[/tex]
1.11 = [tex]\frac{250}{x}[/tex]
x = [tex]\frac{250}{1.11} = 225.23[/tex] ≈ 225 feet
Therefore, Brace's boat is 225 feet from the bottom of the lighthouse.
To learn more about the trignometry from the given link.
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A truck company charges $30 to rent a moving truck for the day, plus 5 cents for every mile driven during the day. The function f(x)=0.05x+30 represents the total cost for the moving truck for one day's rental where x is the number of miles driven.
Part A: Jada rents the moving truck for one day and drives a total of 42 miles. What would be her costs for the rental? To earn full credit, show your work using a method explained in the Orientation.
Part B: Kimmy rented the same moving truck and spent a total of $37.80. How many miles did she drive during the rental period? To earn full credit, show your work using a method explained in the Orientation.
Answer:
Part A: $32.10
Part B: 156 miles
Step-by-step explanation:
Part A:
$0.05 per mile. 0.05 times 42 = $2.10
30 + 2.10 = $32.10
Part B:
The rent cost a day is $30
37.80 - 30 = $7.80
7.80 is the money for miles
7.80 divided by 0.05 = 156 miles