da = 3.4 years; dl is 1.9 years; total equity is $82 million; total assets is $850 million. duration gap is _1.6833__ years.
Option 1.6833 is correct.
The duration gap measures the difference between the duration of a bank's assets and the duration of its liabilities.
We can calculate the duration gap using the following formula:
[tex]Duration $ Gap = (Duration of Assets\times Market Value of Assets) - (Duration of Liabilities \times Market $ Value of Liabilities)$[/tex]
In this case, we are not given the duration of the assets or liabilities directly, but we can estimate them using the weighted average duration.
To estimate the duration of assets, we can use the formula:
Duration of Assets[tex]= \sum (Duration $ of Asset i \times Market $ Value of Asset i) / Total Market Value of Assets )[/tex]
To estimate the duration of liabilities, we can use the formula:
Duration of Liabilities [tex]= \sum (Duration $ of Liability i \times Market $ Value of Liability i) / Total Market Value of Liabilities[/tex]
We are given that da (duration of asset) is 3.4 years, and dl (duration of liability) is 1.9 years.
We are also given that the total equity is $82 million, and the total assets are $850 million.
We can calculate the total liabilities as follows:
Total Liabilities = Total Assets - Total Equity
Total Liabilities = $850 million - $82 million
Total Liabilities = $768 million
Using these values, we can estimate the duration gap as follows:
Duration of Assets = (3.4 * $850 million) / $850 million = 3.4 years.
Duration of Liabilities = (1.9 * $768 million) / $768 million = 1.9 years
Duration Gap = (3.4 * $850 million) - (1.9 * $768 million) / $850 million
Duration Gap = ($2,890 million - $1,459.2 million) / $850 million
Duration Gap = $1,430.8 million / $850 million
Duration Gap = 1.681 years
Rounding to four decimal places, we get a duration gap of 1.6810 years. Therefore, the closest answer choice is 1.6833.
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To calculate the duration gap, we subtract the duration of liabilities (dl) from the duration of assets (da). In this case, the duration gap is calculated as follows: da - dl = 3.4 - 1.9 = 1.5 years. Therefore, the answer is 1.5325 years, which is closest to option 1 in the multiple-choice question.
The total equity is $82 million, which is the difference between the total assets ($850 million) and the total liabilities. The duration gap measures the sensitivity of a financial institution's net worth to changes in interest rates. A positive duration gap means that the financial institution's net worth will increase with rising interest rates, while a negative duration gap means that the net worth will decrease. The duration gap (DG) is a measure of a financial institution's interest rate risk, calculated as the difference between the duration of its assets (DA) and the duration of its liabilities (DL), weighted by the size of the assets and liabilities. In this case, we are given the following information:
DA = 3.4 years
DL = 1.9 years
Total equity = $82 million
Total assets = $850 million
To calculate the duration gap, follow these steps:
1. Determine the weight of equity (WE) and the weight of liabilities (WL).
WE = Total equity / Total assets = $82 million / $850 million = 0.09647
WL = 1 - WE = 1 - 0.09647 = 0.90353
2. Calculate the duration gap.
DG = DA * WE + DL * WL = 3.4 * 0.09647 + 1.9 * 0.90353 = 0.327998 + 1.718007 = 2.046005 years
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i am good with graphs but not equations, plus i put 30 points for an answer. i need help
Carly reads at a faster rate than Monica. The number of pages in Monica's novel is greater than the number of pages in Carly's novel.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Carly Equation:
y= - 35x + 220
and, Monica equation:
slope = (90- 240)/ 5-0
slope = -150/5
slope= -30
and, the equation is
y- 240 = -30 x
y= -30x + 240
From comparing both cases Carly start with 220 pages and Monica with 240 pages and Carly will complete in 7 hours whereas Monica will complete in 8 hours.
Hence, Carly reads at a faster rate than Monica.
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There are 3 feeder bus services plying to and from the nearby town center. Ahmed can ride on one of these services or walk to the town center. However, he decides that on this way back , he will ride on one of these services. In how many ways can he go to the town center and back ?
If he decided that on this way back , he will ride on one of these services then in total 9 ways he can go to the town center and back.
In the given question, there are 3 feeder bus services plying to and from the nearby town center.
Ahmed can ride on one of these services or walk to the town center.
However, he decides that on this way back , he will ride on one of these services.
We have to find in how many ways he can go to the town center and back.
According to the given conditions, we know that there are 3 feeder and we can use these feeder in 3 ways.
So we can write it as;
Number of ways he can go to the town center and back = 3 × 3
Number of ways he can go to the town center and back = 9
Hence, if he decided that on this way back , he will ride on one of these services then in total 9 ways he can go to the town center and back.
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I need help im struggling
Answer:
5
Step-by-step explanation:
You should do cross multiplication.
Multiply 3 by 10 and 6 by 'h'
So 3×10=6h
6h=30
h=30÷6=5
The perimeter of a soccer field is 304 meters. The field is 96 meters long. How wide is it?
The perimeter of a soccer field is 304 meters. The field is 96 meters long. So, its wide becomes: 56 m
What is rectangular perimeter?The length of a two-dimensional shape's perimeter is referred to as its perimeter. The total length of all the sides of the thing is also a definition for it. The perimeter of the form is equal to the algebraic sum of each side's length. For the various geometric forms, there are formulae accessible. The radius of a shape's edge is known as the perimeter. Discover how to calculate a shape's perimeter by multiplying its side lengths.
Given that,
The perimeter of a soccer field is 304 m
length of the field is 96 m
wide = ?
As we know,
perimeter = 2 (length + width)
or, 304 = 2 (96 + width)
or, 304 = 192 + 2 width
or, width = 112 /2
or, width = 56 m
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Mark the points A and B in your book 4 cm apart. Construct and shade the region that is closer to B than to A and within 3 cm of B. You must show all of your construction lines. A• B•
Marking of points A and B in 4 cm apart and shaded the region that is closer to B than to A and within 3 cm of B, in the coordinate plane.
What is Cartesian plane?The cartesian coordinate system includes a two dimensional plane known as the Cartesian Plane. Rene Descartes created the cartesian plane in the 17th century. The cartesian plane's ability to connect Euclidean geometry and algebra is its most significant characteristic.
Numerical coordinates can be used to describe any point on a cartesian plane. An ordered pair is used to express a point's coordinates on a cartesian plane. These points are also signed, and their distance from two perpendicular lines known as axes is fixed.
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reflection across the y-axis
N(-3, 1), G(0, 4), B(-1, 1)
The required reflection of the points N(-3, 1), G(0, 4), B(-1, 1) across the y-axis are N(3, 1), G(0, 4), B(1, 1) .
Explain reflection across y-axis.Point (x, y) is reflected across the x-axis as (x, -y). The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse.
According to question:We have,
N(-3, 1), G(0, 4), B(-1, 1)
While, find reflected points we are considering y-axis as mirror,
Then,
Reflection of point N(-3, 1) across the y-axis
⇒ N(3, 1)
Reflection of point G(0, 4) across the y-axis
⇒ G(0, 4)
Reflection of point B(-1, 1) across the y-axis
⇒ B(1, 1)
Thus, required reflected points are N(3, 1), G(0, 4), B(1, 1) .
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find h (3) if h (x) = 3 - 3/x
Answer:
0
Step-by-step explanation:
h(x) = 3 – 3/x
h(3) = 3 – 3/3
h(3) = 0/3
h(3) = 0
i hope this helped
Debbie's bank offers an online bill pay service. For this, the bank charges $2.25
per month plus $0.10 per bill paid using the service. How many bills does she pay
each month if the charges are always between $3.50 and $5.00? (Note: She is not
allowed to pay part of a bill.)
please write as an inequality and show work
We know that the bank charges $2.25 per month plus $0.10 per bill paid using the service. Let x be the number of bills paid using the service.
The total cost of the service is:
Cost = 2.25 + 0.10x
We also know that the charges are always between $3.50 and $5.00. So we can write this as an inequality:
3.50 <= Cost <= 5.00
To find the number of bills, we can substitute the expression for cost into the inequality:
3.50 <= 2.25 + 0.10x <= 5.00
We can solve this inequality by isolating x on one side:
0.10x >= 1.25
x >= 12.5
So the number of bills paid using the service is greater than or equal to 12.5.
She could pay exactly 12 bills, 13 bills, 14 bills and so on.
The solution is x >= 12.5
Let's call the number of bills paid per month as "x"
We know that the total cost is:
$2.25 (fixed monthly fee) + $0.10x (cost per bill paid)
We also know that the total cost is between $3.50 and $5.00
Therefore, $3.50 <= $2.25 + $0.10x <= $5.00
To solve for x, we can first isolate x by subtracting $2.25 from both sides of the inequality:
$1.25 <= $0.10x <= $2.50
Now we can divide both sides of the inequality by $0.10 to get:
12.5 <= x <= 25
It means that the number of bills paid per month using the service is between 12 and 25 bills, Debbie can pay at least 12 bills and at most 25 bills.
The first five terms of n^2+4 are
Answer: a₁ = 5, a₂ = 6, a₃ = 13 are the only ones I could figure out, I apologize.
Step-by-step explanation: I hope this helps a little!
How do you change the base of an exponential function?
To change the base of an exponential function, we can use the formula:
log_b(a) = log_c(a) / log_c(b).
To change the base of an exponential function, you can use the property that logarithms with different bases are related by the following equation:
log_b(a) = log_e(a) / log_e(b)
Where log_b(a) is the logarithm of a to the base b and log_c(a) is the logarithm of a to the base e.
For example: To change log_3(7) to log_e(x)/log_e(y), we can use the property that logarithms with different bases are related by the following equation:
logb(a) = logc(a) / logc(b)
So log_3(7) = log_e(7) / log_e(3)
To find x and y we can use the logarithm properties and the definition of logarithm:
log_e(x) = log_e(7)
x = 7
log_e(y) = log_e(3)
y = 3
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Casho is deciding between two different movie streaming sites to subscribe to. Plan A costs $40 per month plus $2 per movie watched. Plan B costs $34 per month plus $3 per movie watched. Let AA represent the monthly cost of Plan A if Casho watches xx per month, and let BB represent the monthly cost of Plan B if Casho watches xx movies per month. Write an equation for each situation, in terms of x,x, and determine the number of monthly movies watched, x,x, that would make the two plans have an equal monthly cost.
AA: y=40x+2
BB: y=34x+3
Use a trigonometric ratio to solve for z. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?
When the length of one side and the angle of one corner of a right-angled triangle are provided as 16 and 69°, respectively, trigonometric ratios are used to compute the value of b as 35.38.
what is trigonometric ratios ?The values of all trigonometric functions depending on the side ratio of a right-angled triangle are known as trigonometric ratios. The ratios of a right-angled triangle's sides to any acute angle are the angle's trigonometric ratios.
given
one side = 16
angle = 69°
one angle = 90° as right angle triangle
another angle = 69°+ 90° + x = 180°
= 155° + x = 180°
x = 25°
a / sin69° = 16 / sin25°
a = 35. 38
When the length of one side and the angle of one corner of a right-angled triangle are provided as 16 and 69°, respectively, trigonometric ratios are used to compute the value of b as 35.38.
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Solve using substitution.
Y = 2X + 10
Y = X + 2
Answer:
2+2%2%5+51%895%+8+81%9+61%+5%+8+%15+%
Answer:
(- 8, - 6 )
Step-by-step explanation:
y = 2x + 10 → (1)
y = x + 2 → (2)
substitute y = 2x + 10 into (2)
2x + 10 = x + 2 ( subtract x from both sides )
x + 10 = 2 ( subtract 10 from both sides )
x = - 8
substitute x = - 8 into either of the 2 equations and evaluate for y
substituting into (2)
y = - 8 + 2 = - 6
solution is (- 8, - 6 )
If ALMN=AXYZ, which congruences are true by CPCTC? Check all that
apply.
L
M
N
☐A. ZX=ZN
B. MLYZ
C. LN = XZ
D. MN = YZ
E. ZY ZM
OF. ZZ = ZL
X
B. MLYZ and C. LN = XZ are not true, since these letters do not correspond to any sides or angles in the given triangles.
What is CPCTC?CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." Given the statement "ALMN = AXYZ," we can assume that triangle ALMN is congruent to triangle AXYZ.
With that in mind, the following congruences are true:
A. ZX=ZN (Corresponding parts of congruent triangles)
D. MN = YZ (Corresponding parts of congruent triangles)
E. ZY ZMo (not a valid statement)
F. ZZ = ZL (not a valid statement)
B. MLYZ and C. LN = XZ are not true, since these letters do not correspond to any sides or angles in the given triangles.
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What are the 3 different slope formulas?
The three different forms of slope formulas are m=(y-b)÷x, m=(y-y₁)÷(x-x₁), and m=(-A)÷B.
The slope gives the steepness of a straight line. The three different forms of the slope of a linear equation are slope-intercept form, point-slope form, and standard form.
From the equation of slope-intercept form y=mx+b, the slope is calculated using the formula, m=(y-b)÷x. Here, the slope is m and the y-intercept is b.
From the equation of the point-slope form (y-y₁)=m(x-x₁), the slope is calculated using the formula, m=(y-y₁)÷(x-x₁). Here, points on the line are x₁ and y₁.
From the equation of standard form Ax+By=C, the slope is m=(-A)÷B. Here, constants or integers are A, C, and B.
In general, the slope is calculated using the formula, m = (Δy)÷(Δx)= (y₂-y₁)÷(x₂-x₁). Here, in the line, the coordinate of the first point is (x₁, y₁), and the second point is (x₂, y₂).
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What is 2y + 8x =
HELP ME!
The solution of equation: 2y + 8x = 2(y + 4)x.
Define the term common factor?A whole number that is a multiplier of at least two numbers is referred to as a common factor. The largest factor that would divide into two or so more numbers is known as the highest common factor (HCF). The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM).In mathematics, the term "common factors" refers to the common divisors that are used when two or more integers are precisely divided by the identical number or numbers.For the stated equation:
= 2y + 8x
As. 2y and 8x both are divisible by 2 .
So, Taking two common from both.
= 2(y + 4x)
Thus, the solution of the equation becomes: 2(y + 4x).
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When 20 is added to a number, the result is 34. What is the number?
What are 4 ordered pairs?
An ordered pair is a refers to the of the x coordinate and the y coordinate of a point. They have two values which is written in a specific order and is quoted by parentheses.
It is used when we need to solve some problems and it also has utilization in the field of statistics.
Ordered pair are also used in coordinate geometry, they are used to portray geometric objects and figures in open space which helps to improve visual perception.
Ordered pairs are used to represent the center, vertices, and length of the sides of a square, circle, rectangle, or polygon with coordinates.
Example: ( 2 , 4).
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Substitution y=2x - 6
y= 5x+8
Answer:
The result can be shown in multiple forms.
Point Form: ( 2, − 2 )
Equation Form: x = 2 , y = − 2
Step-by-step explanation:
1. Eliminate the equal sides of each equation and combine them.
2x − 6 = − 5x + 8
2. Solve 2x − 6 = −5x +8 for x.
x = 2
3. Evaluate y when x = 2.
y = − 2
The solution to the system is the complete set of ordered pairs that are valid solutions.
( 2, − 2 )
The result can be shown in multiple forms.
Point Form: ( 2, − 2 )
Equation Form: x = 2 , y = − 2
Answer:
x = 2
y = -2
Step-by-step explanation:
Substitute equation 1 into equation 2 then solve for x:
2x - 6 = -5x + 8
7x = 14
x = 14/7 = 2
Now substitute x=2 into either equation to solve for y:
y = 2(2) - 6 = -2
HELPP this is the last question I need to answer asap
Answer:
x = 5, -5, 3, -3
Step-by-step explanation:
First, substitute u = x^2 into the equation, and we have
u^2 - 34u + 225 = 0
u = x^2
Factor u^2 −34u +225 using the AC method, and we get
( u - 25) ( u - 9) = 0
We know If any individual factor on the left side of the equation is equal to
0, the entire expression will be equal to 0, so
u - 25 = 0
u - 9 = 0
Next, we set u - 25 equal to 0 and solve for u, and we get
u = 25
Then set u - 9 equal to 0 and solve for u, and we get
u = 9
The final solution is all the values that make (u−25)(u−9) = 0 true.
u =25,9
Substitute the real value of u=x^2 back into the solved equation.
x^2 = 25
(x^2)^1 = 9
x^2 = 25
x = 5, -5
Now we solve the second equation
(x^2)^1 = 9
x = 3, -3
So, the answers are: 5, -5, 3, -3
A tree that is 3 feet tall is growing at a rate of 1 foot per year. A 5-foot tree is growing at a rate of 0. 75 foot per year. The ordered pair (t, h) represents the time in years, t, at which the trees are at height, h. Which ordered pair represents the number of years elapsed when the trees are at the same height?.
the ordered pair that represents the number of years elapsed when the trees are at the same height is (8,5). We were then asked to find the number of years elapsed when the trees are at the same height.
In this problem, we were given two different trees, one that is 3 feet tall and growing at a rate of 1 foot per year, and another that is 5 feet tall and growing at a rate of 0.75 feet per year. The ordered pair (3,1) represents the 3-foot tall tree growing at a rate of 1 foot per year and the ordered pair (5,0.75) represents the 5-foot tall tree growing at a rate of 0.75 feet per year.
To find the number of years elapsed when the trees are at the same height, we need to solve the equation:
3 + 1t = 5 + 0.75t
t = (5 - 3)/(1 - 0.75) = 2/0.25 = 8
So the ordered pair that represents the number of years elapsed when the trees are at the same height is (8,5).
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help me cause its due today
Answer:
(-2, 1)
Step-by-step explanation:
x = -2
-2(-2) + 2y = 6
4 + 2y = 6
2y = 2
y = 1
Is the triangle with sides 25 cm 5 cm and 24 cm a right angle triangle give reasons for your answer?
It is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm because the sum of two sides are greater than third sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.
To check this we firstly add the 25 and 5
25 + 5 > 24
30 > 24
Now we add 25 and 24
25 + 24 > 5
49 > 5
Now we add 5 and 24
5 + 24 > 25
29 > 25
It is possible to construct a triangle whose sides are 25 cm 5 cm and 24 cm because the sum of two sides are greater than third sides.
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How many prime numbers are twins?
Total number of prime numbers which are twin are infinite and its general form is given ( 6n - 1 , 6n + 1 ) apart from ( 3, 5 ) where 'n' represents the natural number.
As given in the question,
Prime numbers are those numbers which have only two factors one and the number itself.
Prime numbers which are twins are defined as when the difference between two prime number is equal to 2.
Example of twin prime numbers are as follow :
( 3, 5 ) , ( 5, 7 ) , ( 11 , 13 ) , ( 17 , 19 ) , ( 29 , 31 ), ( 41, 43 ) ,...........,(6n - 1 , 6n + 1 )
where 'n' represents the natural number.
5 is the only prime number which exist in two pairs of twin prime numbers.
Apart from ( 3,5 ) all the twin prime numbers divided by 12.
Therefore, there are infinite prime numbers which are representing as a twin prime numbers.
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Pablo has 21 coins in his coin collection. 9 of the coins are gold and the rest are silver. What is the ratio of the number of silver coins to the number of gold coins? 4) Write your answer as a fraction. Use a slash (/) to separate the numerator and denominator.
Answer:12/9
Step-by-step explanation:
subtract 9 from 21 and 21 will give you 12 silver coins which will be 12 silver coins to 9 gold coins
Choose the number line that represents the fraction equivalent to three-twelfths.
A number line with zero, one twelfth, two twelfths, three twelfths, four twelfths, five twelfths, six twelfths, seven twelfths, eight twelfths, nine twelfths, ten twelfths, eleven twelfths, and one marked on it. A red line is drawn from the zero mark to the three twelfths mark.
A number line with zero, one eighth, two eighths, three eighths, four eighths, five eighths, six eighths, seven eighths, and one marked on it. A red line is drawn from the zero mark to the three eighths mark.
A number line with zero, one fourth, two fourths, three fourths, and one marked on it. A red line is drawn from the zero mark to the one fourth mark.
A number line with zero, one fifth, two fifths, three fifths, four fifths, and one marked on it. A red line is drawn from the zero mark to the one fifth mark.
A number line with zero, one sixth, two sixths, three sixths, four sixths, five sixths, and one marked on it. A red line is drawn from the zero mark to the one sixth mark.
A number line marked with zero, one twelfth, two twelfths, three twelfths, four twelfths, five twelfths, six twelfths, seven twelfths, eight twelfths, ten twelfths, eleven twelfths, and one. From the zero point to the three twelfths mark, a red line is painted.
What is fraction?A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
Here,
Multiply one times three, and four by three.
It will equal to three out of twelve or 3/12.
=1/4
A number line marked with zero, one twelfth, two twelfths, three twelfths, four twelfths, five twelfths, six twelfths, seven twelfths, eight twelfths, ten twelfths, eleven twelfths, and one. From the zero point to the three twelfths mark, a red line is painted.
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A company rents paddleboards by charging a rental fee plus an hourly rate. Write an expression that represents the cost (in dollars) of renting a paddleboard for h hours.
The expression that represents the cost (in dollars) of renting a paddleboard for h hours is r + xh
How to determine the cost for h hoursFrom the question, we have the following parameters that can be used in our computation:
Cost of rents:
Charging a rental fee plus an hourly rate.
Using the above as a guide, we have the following:
Initial rental fee = r
Hourly rate = x
The cost for h hours can then be represented as
C(h) = Initial rental fee + Hourly rate * Number of hours
Substitute the known values in the above equation, so, we have the following representation
C(h) = r + x * h
Evaluate
C(h) = r + xh
Hence, the expression is r + xh
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(Two-Step Linear Inequalities MC)
Which graph represents the solution to the inequality 2(b + 2) > 24?
number line with open point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing right
number line with open point at 10 with arrow pointing right
The graph that represents the solution to the inequality is a number line with closed point at 10 with arrow pointing left
What is an inequality?You should be aware that inequality is is a mathematical statement showing that two opposite things are not equal. The graph is a diagram that illustrates the statement.
The given inequality is 2(b + 2) > 24
Opening the brackets to get
2b+4≥24
2b≥24-4
This implies that 2b≥20
Making b the subject
b≥20/2
b≥10
Conclusively the graph is a number line with closed point at 10 with arrow pointing left
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1) Marisol works for a florist that sells two types of bouquets, as shown below. On Monday, Marisol used
96 tulips to make the bouquets. On Tuesday, she used 192 tulips to make the same number of Spring Mix
bouquets as Monday, but 3 times as many Garden Delight bouquets.
a. Write a system of equations that you can use to find how many bouquets of each type Marisol made.
b. Find the total number of tulips Marisol used to make Garden Delight bouquets on Monday and Tuesday.
To calculate how many flowers of each kind Marisol created, use the formulae x+y=96 and x+3y=192. Marisol used 48 tulips in total to produce Garden Delight bouquets on Monday and Tuesday.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Here,
Let x be Spring Mix bouquets and y be the Garden Delight bouquets.
x+y=96
x+3y=192
2y=96
y=48
x=48
The system of equations that you can use to find how many bouquets of each type Marisol made is x+y=96 and x+3y=192. The total number of tulips Marisol used to make Garden Delight bouquets on Monday and Tuesday is 48.
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Find the distance between points (-5,4) and (9,4
Answer:
9 units
Step-by-step explanation:
The y values are the same, this means that this is a horizontal line. The distance from -5 to 9 is 14 units.
Answer:
14
Step-by-step explanation:
using the distance formula to determine the distance between the two points