If the quarterly interest at 10.5% is $3,150, the principal amount of a loan is

Sequence having rule  f(n) = n² - 5, the first four terms will be -4, -1, 4, and 11.

A sequence in mathematics is a group of integers that adhere to a specific pattern or rule. A sequence of numbers might be infinite or finite, and they are arranged in a certain order.

Every number in the sequence is referred to as a term, and its location within the sequence is referred to as its index. As an illustration, the first term in the series 1, 3, 5, 7, 9, is 1, the second term is 3, the third term is 5, and so on.

Now,

The explicit rule for the sequence is given by f(n) = n² - 5, which means that to find the nth term of the sequence, we need to plug in the value of n into this formula.

To find the first four terms of the sequence, we can simply substitute n = 1, 2, 3, and 4, respectively, into the formula and evaluate the expression.

The first term is f(1) = 1² - 5 = -4.

The second term is f(2) = 2² - 5 = -1.

The third term is f(3) = 3² - 5 = 4.

The fourth term is f(4) = 4² - 5 = 11.

Therefore,

                 the first four terms of the sequence defined by the explicit rule f(n) = n² - 5 are -4, -1, 4, and 11.

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Answer:

a. Using a mortgage calculator with the given information, Marisa's monthly mortgage payment would be $1,088 to the nearest dollar.

b. The total cost of the house, including the down payment and all payments made over the 30-year mortgage period, would be $453,020. This is calculated by adding the $55,000 down payment to the total amount borrowed ($195,000) and then adding the total interest paid over the 30 years ($203,020) to get $453,020.

c. Marisa will have spent $203,020 in interest over the 30-year mortgage period. This is calculated by subtracting the total amount of the loan ($195,000) from the total amount paid over the 30 years ($398,020), which leaves $203,020 in interest paid.

Answer:

The distance between the student and the mirror is 7.5 feet.

Step-by-step explanation:

We can use similar triangles to solve this problem.

Let's call the distance between the student and the mirror "d". We can create a right triangle with the student's height as one leg, the distance "d" as the other leg, and the hypotenuse being the line from the student's eyes to the top of the school. Let's call the length of this line "h".

We can also create a second right triangle with the height of the school as one leg, the distance from the school to the mirror as the other leg, and the hypotenuse being the same line from the student's eyes to the top of the school.

Since these two triangles share an angle (the angle formed by the line from the student's eyes to the top of the school and the ground), they are similar triangles. This means that the ratios of their corresponding sides are equal.

We can set up the following proportion:

(student height) / d = (school height) / (distance from school to mirror)

Plugging in the given values, we get:

4.5 / d = 30 / 50

Simplifying, we get:

4.5 / d = 3 / 5

Cross-multiplying, we get:

3d = 22.5

Dividing by 3, we get:

d = 7.5

Therefore, the distance between the student and the mirror is 7.5 feet.

The distance of the student to the mirror, is 7.5 ft

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given that, a mirror is placed outside a school the distance from the school to the mirror is 50 ft and the height of the school is 30 ft we need to find the distance of the student to the mirror,

This arrangement is creating two similar triangles, here we will use the properties of the similar triangles, to find the distance of the student to the mirror,

Therefore,

30 / 4.5 = 50 / d

d = 50 x 4.5 / 30

d = 225 / 20

d = 7.5

Hence, the distance of the student to the mirror, is 7.5 ft

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The value of x for the given tangent angle is 1.5.

The value of x can be determined by applying the following circle theorem about tangle angles as shown below.

2 x ∠LMN = 16x - 12 ( angle at tangent is half of the angle subtended at the arc)

2 ( 4x ) = 16x - 12

8x = 16x - 12

16x - 8x = 12

8x = 12

x = 12/8

x = 1.5

Thus, if ML is tangent to the circle at L, then the value of x is 1.5 (Written as a decimal)

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The function P(t) = 3.5(0.91)^t is an exponential decay and the percentage rate of change is 9%.

option B.

The function P(t) = 3.5(0.91)^t is an exponential decay function because the base, 0.91, is between 0 and 1.

To find the percentage rate of change, we need to find the value of r in the exponential function;

P(t) = P(0) (1 + r)^t or

P(t) = P(0) e^(rt)

where;

In this case, the initial value is 3.5, and the function is P(t) = 3.5 (0.91)^t. Comparing this to the form P(t) = P(0) e^(rt),

we see that P(0) = 3.5 and r = ln(0.91) ≈ -0.094.

Therefore, the percentage rate of change is -9.4%, which means that the value decreases by about 9.4% with each unit of time.

So the correct answer is option B: Exponential decay; 9%.

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The complete question is below:

-Determine whether the function below is exponential growth or exponential decay, and find the percentage rate of

change.

P(t) = 3.5 (0.91)^t

A) Exponential decay; 3.5%

B) Exponential decay; 9%

C) Exponential growth; 9%

D) Exponential growth; 3.5%

The actual perimeter of triangle will be 1.3m

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle. The perimeter is the whole side covered by the all sides.

The sum of all angle of triangle = 180

The blueprint for a new house includes a triangular-shaped room in the attic.

If the blueprint was made using a scale factor of 12

centimeter = 1 meter

The perimeter will be 9cm

12/9 = 1.3m

So the actual perimeter will be 1.3m.

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Based on the table, to the nearest whole number, 7000 people in the total population of 60,000 have green eyes.

We know that;

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Here, We have;

The total number of respondents in the survey is:

= 32 + 14 + 25 + 49

= 120

And, The proportion of respondents with green eyes is:

= 14/120

= 0.1167

Hence, To estimate the number of people in the total population of 60,000 who have green eyes, we can multiply the proportion by the total population:

0.1167 x 60,000 = 7,002

After Rounding this to the nearest whole number gives us:

7,002 ≈ 7,000

Therefore, The answer is, 7,000 people.

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A survey is conducted to investigate the self-identified eye colors of a representative portion of a population. The table shows the results.

Self-Identified Eye Color

Number of Respondents

blue

32

green

14

hazel

brown

25

49

Based on the table, to the nearest whole number, how many people in the total population of 60,000 have green eyes?

O 140 people

O 700 people

O 1,400 people

O 7,000 people

Step-by-step explanation:

f(0):

f(0) = (0^2 - 9) / (0 + 5)

= -9/5

f(-1):

f(-1) = ((-1)^2 - 9) / (-1 + 5)

= (-8) / 4

= -2

f(1/k):

f(1/k) = ((1/k)^2 - 9) / (1/k + 5)

= (1/k^2 - 9) / (1/k) + 5

= (1 - 9k^2) / (k^2 + 5k)

Therefore, f(0) = -9/5, f(-1) = -2, and f(1/k) = (1 - 9k^2) / (k^2 + 5k).

Answer:

Step-by-step explanation:

To find the values of f(x) at the given points, we substitute the values of x into the expression for f(x) and simplify:

f(x) = (x^2 - 9)/(x + 5)

a) To find f(0), we substitute 0 for x:

f(0) = (0^2 - 9)/(0 + 5) = -9/5

Therefore, f(0) = -1.8.

b) To find f(-1), we substitute -1 for x:

f(-1) = (-1^2 - 9)/(-1 + 5) = (-10)/4

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor of 2:

f(-1) = -5/2

Therefore, f(-1) = -2.5.

c) To find f(1/k), we substitute 1/k for x:

f(1/k) = ((1/k)^2 - 9)/(1/k + 5)

We can simplify the numerator by multiplying out the square:

f(1/k) = (1/k^2 - 9)/(1/k + 5)

We can simplify the denominator by multiplying by k/k:

f(1/k) = (1 - 9k^2)/(1 + 5k)

Therefore, f(1/k) = (1 - 9k^2)/(1 + 5k).

The solution for the given system of equations is (1,0) using the addition method.

The addition method, also known as the elimination method, is a technique used to solve a system of linear equations by adding the two equations together in such a way that one of the variables is eliminated.

Multiply the first equation by -2:

-10x - 12y = -10

Add the second equation to the first:

-10x - 12y = -10

10x + 12y = 10

0 + 0 = 0

We can solve one of the original equations for x in terms of y and then replace into the equation to represent the solutions in terms of y. For instance, when we solve the first equation for x, we obtain:

5x + 6y = 5

5x = 5 - 6y

x = (5 - 6y)/5

By substituting this into the second equation, we get:

10x + 12y = 10

10((5 - 6y)/5) + 12y = 10

2(5 - 6y) + 12y = 10

10 - 4y = 10

-4y = 0

y = 0

So the solution to the system is (x, y) = ((5 - 6y)/5, y) = (1, 0)

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The exponential function that best models the value of the stock after n weeks is given as follows:

v(n) = 1600(1 + r)^n.

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

The initial investment was of 1600, hence the parameter a is given as follows:

a = 1600.

The rate of change is obtained multiplying two consecutive values on the table, and will have the following format:

b = 1 + r.

In which r is the growth rate.

The problem is incomplete, hence the general procedure to obtain the function is presented.

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Given- Square root of 14 multiplied by square root of 10

To find - which is equivalent to the product below

Explanation - We can write the square root of 14 as

[tex]\sqrt{14} =\sqrt{2} \sqrt{7}[/tex]

and square root of 10 as

[tex]\sqrt{10} =\sqrt{2} \sqrt{5}[/tex]

Now

[tex]\sqrt{14} \sqrt{10} =\sqrt{2} \sqrt{5} \sqrt{2} \sqrt{7} =2\sqrt{35}[/tex]

Hence the choice is equivalent is D

Final answer - The final answer is D

Answer:

y = -3 sin(4x)

or

y = -3 cos(4(x - π/8))

Step-by-step explanation:

We can see that this is a graph of sine or cosine with the following characteristics:

amplitude: 3

period: π/2

vertical shift: 0

We can use these characteristics to form the following equations:

y = -3 sin(4x)

y = -3 cos(4(x - π/8))

Note that we solved for b using the period derivation:

period = 2π / b

[tex]\dfrac{\pi}{2} = \dfrac{2\pi}{b}[/tex]

[tex]b \cdot \dfrac{\pi}{2} = 2\pi}[/tex]

[tex]b = 2\pi \cdot \dfrac{2}{\pi}[/tex]

[tex]b = \dfrac{4\pi}{\pi}[/tex]

[tex]b = 4[/tex]

— sidenote —

These graphs can be infinitely shifted by any integer number of periods left or right, and we can show that using an auxiliary variable multiplied by the period. However, that is clearly not the intent of the problem, so I have not included that in my answer.

Answer:

Coordinates of center: (0, 5)

Radius of circle: 3

Therefore , the solution of the given problem of triangle comes out to be L = 3(√(h²) + ((w/2²))) + 3h .

A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular.

Here,

Given the height and breadth of the top of the frame, we can use the Pythagorean theorem to determine the length of each side of the triangle.

Let's assume the height is h feet and the width of the top of the frame is w feet. The triangle's side lengths can then be calculated as follows:

=> s =√((h²) + ((w/2)²))

We must add up the lengths of all the pipe segments that will be used to build the frame in order to determine the total quantity of steel pipe required.

The following formula can be used to determine how much steel tubing is required:

=>  L = 3s + 3h

where h is the height of the frame and s is the length of each edge of the triangle.

Using the method instead of s, we obtain:

=> L = 3(√(h²) + ((w/2²))) + 3h

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Roger would have 20 workdays in the month if it starts on a Monday and there are at least 20 workdays each week.

Two or more expressions with an Equal sign is called as Equation.

Assuming a month has four weeks, each with at least 20 workdays, we can calculate the total number of workdays in the month starting on a Monday as follows:

Week 1: Monday to Friday = 5 workdays

Week 2: Monday to Friday = 5 workdays

Week 3: Monday to Friday = 5 workdays

Week 4: Monday to Friday = 5 workdays

So the total number of workdays in the month is:

5 + 5 + 5 + 5 = 20

Therefore, Roger would have 20 workdays in the month if it starts on a Monday and there are at least 20 workdays each week.

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Answer: 9g+10

Step-by-step explanation:

Simple addition 6+3=9

Since 10 doesnt have a variable you just add it to the end of the equation, make sure to keep the sign = 9g-10

Emma's profit from selling the stock is $743.44.

To find out Emma's profit from selling the stock, we need to calculate the total cost of purchasing the stock and the total revenue from selling the stock. Then we can subtract the total cost from the total revenue to get the profit.

Total cost of purchasing the stock:

Emma bought 300 shares of the stock for $39.22 per share plus a 1 percent commission.

Commission = 1% of (300 x $39.22) = $117.66

Total cost = (300 x $39.22) + $117.66 = $11,871.66

Total revenue from selling the stock:

Emma sold 300 shares of the stock for $46.54 per share plus a commission of $49.95 plus $24 per share.

Commission = $49.95 + (300 x $24) = $7,449.95

Total revenue = (300 x $46.54) - $7,449.95 = $12,665.05

Profit:

Profit = Total revenue - Total cost - Commission

Profit = $12,665.05 - $11,871.66 - $49.95 = $743.44

Therefore, Emma's profit from selling the stock is $743.44.

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Emma received $6,512.05 after selling the 300 shares of stock in the fast food company.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

To calculate the total amount Emma paid for the stock, we first need to calculate the commission she paid when she purchased it:

1% commission = 0.01 * 39.22 = 0.3922

Total cost per share = 39.22 + 0.3922 = 39.6122

So, Emma paid $39.6122 per share when she bought the stock.

To calculate the total amount she received for selling the 300 shares, we need to first calculate the commission she paid for selling it:

Commission per share = 24

Total commission = 300 * 24 + 49.95 = 7,449.95

The total amount she received for selling the shares is:

300 * 46.54 = 13,962

Therefore, the total amount of money Emma received after selling the shares and paying the commission is:

13,962 - 7,449.95 = 6,512.05

Therefore, emma received $6,512.05 after selling the 300 shares of stock in the fast food company.

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The correct equation represents the relationship in the table is,

⇒ w =  d - 1.25

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The table shows the relationship between d, the amount of money Alice has at the beginning of each day, and w, the amount of money she has after riding the bus to work.

Hence, By all the options;

The correct equation satisfy the given values in table.

For first option;

w = d + 1.25

Put  d = 15.75;

w = 15.75 + 1.25

w = 17

Hence, It is wrong.

For fourth equation;

w =  d - 1.25

Put  d = 15.75;

w = 15.75 - 1.25

w = 14.50

Hence, It is correct equation.

Thus, The correct equation represents the relationship in the table is,

⇒ w =  d - 1.25

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The total cost of painting his basement floor is $51.70.

To find the total cost of the paint including HST, we first need to calculate the total area of the basement floor that needs to be painted. We can do this by multiplying the length by the width:

Area of basement floor = length x width

Area of basement floor = 2.5 m x 2.3 m + 1.8 m x 2.3 m

Area of basement floor = 5.75 m² + 4.14 m²

Area of basement floor = 9.89 m²

Now, we can calculate the number of cans of paint needed:

Number of cans = Area of basement floor / Area covered by each can

Number of cans = 9.89 m² / 3.5 m²

Number of cans = 2.8257

Number of cans = 3

The total cost of the paint without HST would be:

Total cost = Number of cans x Cost per can

Total cost = 3 x $15.25

Total cost = $45.75

To calculate the HST, we need to multiply the total cost by the HST rate (13% or 0.13):

HST = Total cost x HST rate

HST = $45.75 x 0.13

HST = $5.95 (rounded to two decimal places)

Finally, we can find the total cost including HST by adding the total cost and the HST:

Total cost including HST = Total cost + HST

Total cost including HST = $45.75 + $5.95

Total cost including HST = $51.70

Therefore, the total cost of the paint including 13% HST is $51.70.

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Answer:

To find the integer that describes the change in temperature, we can divide the total temperature drop by the number of hours:

32 ÷ 4 = 8

Therefore, the temperature dropped by 8 degrees Fahrenheit each hour. The integer that describes the change is -8, since the temperature decreased.

Answer: To find the integer that describes the change in temperature, we need to divide the total change in temperature (32° F) by the number of hours over which the temperature dropped (4 hours). This will give us the amount that the temperature dropped by each hour.

So, dividing 32 by 4, we get:

32 ÷ 4 = 8

Therefore, the temperature dropped by 8 degrees Fahrenheit each hour.

Step-by-step explanation:

The function values increase in size in a positive direction and decrease in size in a negative direction.

The following two statements can be used to describe how the function in the given graph ultimately behaves:

The function gets closer to positive infinity as x gets closer to negative infinity. This is the case since the graph's left end is pointed upward, showing that as x decreases, the function values increase in size in a positive direction.

The function becomes closer to negative infinity as x gets closer to positive infinity. This is the case since the graph's right end is pointing downward, showing that as x increases in value, the function values decrease.

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F1 = 1167.35N and F2 = 1932.65N are the contact support forces on the beam

For the torques, let the axis be at support 2 and consider torques and the counterclockwise rotation is positive.

Let m = mass of athlete and M = mass of beam.

Thus, the equilibrium of torques will be:

Mg(1.96) - mg(0.54m) - F1(3.92) = 0

Substitute the values and solve for F1:

(250 * 10 * 1.96) - (60 * 10 * 0.54) - 3.92F1 = 0

3.92F1 = 4900 - 324

3.92F1 = 4576

F1 = 1167.35N

Note: The weight of the beam is acting at the center and the distance from center to axis at support 2 is 1.96m.

Balancing forces in the vertical direction, we have:

F1 + F2 - Mg − mg = 0

1167.35 + F2 - (250 * 10) − (60 * 10) = 0

1167.35 + F2 - 2500 - 600 = 0

F2 = 1932.65N

Note: upward forces (supports) are positive and downward forces are negative.

Thus, the contact support forces on the beam are F1 = 1167.35N and F2 = 1932.65N.

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Answer:

0<b<=12

Step-by-step explanation:

Answer:

4 + 36x

Step-by-step explanation:

4(1 + 9x)

= 4 + 36x

So, the answer is 4 + 36x

The statement missing in the proof is option D. m ∠ ⁢ 3 + m ∠ ⁢ 5 = 180 ∘.

A triangle is classified as a geometric shape with three sides and three angles. It is one of the basic shapes in geometry, and is typically characterized by its three interior angles, which must add up to 180 degrees. The most common types are the equilateral triangle (all sides equal), the isosceles triangle (two sides equal), and the scalene triangle (no equal sides).

A proof involves logical deduction of the statements in order to arrive at a conclusion. In this case, the conclusion is that the angles 3, 5, and 7 are all congruent. To do this, the proof must show that the angles add up to 180 degrees, which is the sum of the angles in a triangle. Option D, m ∠ ⁢ 3 + m ∠ ⁢ 5 = 180 ∘, is the statement that must be included in the proof to show that the angles are congruent. Without this statement, it is impossible to prove that the three angles are congruent. Therefore, Option D is the missing statement in the proof.

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To have an effective safeguarding system, specific and detailed training of workers must also be included.

What constitutes the foundation of the safety system?

 Any portion of the operator's body, including the hands, arms, and other body parts, must not come into touch with potentially harmful moving parts.

                              A strong safety system completely avoids the chance of the operator or another worker putting their bodies in close proximity to dangerous moving parts.

What are the two main sorts of protection strategies?

There are primarily two types of safeguarding: hard guards and safeguarding gadgets. Hard guards act as a physical barrier between workers and moving parts.

                            Safeguarding devices, however, stop unintentional access to dangers. A machine that needs two hands to operate it, for instance, ensures that neither hand may enter the danger zone.

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P(-2.33 ≤ z ≤ 2.33) = 0.98 for a standard normal random variable Z.

We are aware that the area under the curve between - and - is equal to 1 for a standard normal random variable Z.

The task of finding a number for z0 such that P(-z0 z z0) = 0.98 is given to us.

We can divide the area of 0.98 evenly between the two tails of the distribution since the normal distribution is symmetric around the mean.

(1 - 0.98 / 2) = 0.01 would be the area in each tail.

We can determine the z-score that corresponds to the area of 0.01 by using a calculator or a conventional normal distribution table. An area of 0.01 equates to a z-score of roughly -2.33.

Thus, z0 would have the value:

z0 = -(-2.33) = 2.33

Hence, for a typical normal random variable Z, P(-2.33 z z 2.33) = 0.98.

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The statement that cannot be true is "length RW is a midsegment of the triangle".

option D.

The midsegment of a triangle is a line segment that connects the midpoints of two sides of a triangle. More specifically, if a triangle has sides of lengths a, b, and c, then the midsegment connects the midpoints of the two sides of length a and is parallel to the side of length c.

The length of the midsegment is half the length of the third side (c/2).

In other words, if a triangle has sides AB, BC, and AC, then the midsegment connects the midpoint of AB (denoted as M) to the midpoint of BC (denoted as N) and is parallel to AC. The length of the midsegment MN is equal to half the length of AC (MN = 1/2 * AC).

For the given diagram, the midpoint is S, so the length RW cannot be the length of the midsegment.

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Answer:

Step-by-step explanation:

Let's simplify - 4 - (-5):-

[tex]\tt -4 - (-5)[/tex]

[tex]\tt -4+5[/tex]

[tex]\tt 1[/tex]

Now, let's see which expression has the same value:-

F. -4 + (-5)

[tex]\tt -4 + (-5)[/tex]

[tex]\tt -4-5[/tex]

[tex]\boxed{\tt -9}[/tex]

________________

G. -4 +5

[tex]\tt -4 +5[/tex]

[tex]\boxed{\tt 1}[/tex]

_________________

H. -5 + (-4)

[tex]\tt -5 + (-4)[/tex]

[tex]\tt -5-4[/tex]

[tex]\boxed{\tt -9}[/tex]

_________________

J. -5-(-4)

[tex]\tt -5-(-4)[/tex]

[tex]\tt -5+4[/tex]

[tex]\boxed{-1}[/tex]

Therefore, we can say that G. -4 +5 has a similar value as

-4 - (-5).

________________________

Hope this helps! :)

The total distance driven during the 4-hour trip is approximately 294.05 miles

An element of a number or any number of equal pieces is represented by a fraction. There is a fraction with an upper value (numerator) and a lower value (denominator) (lower value).

We must sum up the distances for each hour of the 4-hour journey to get the overall mileage.

1 hour's worth of driving covered 55.25 miles.

64 3/4 miles were covered in Hour 2 of driving.

52 3/10 miles were covered in Hour 3 of driving.

67.89 miles were covered in Hour 4 of driving.

We must transform the mixed number from Hour 2 into an improper fraction in order to sum these distances:

Driving distance in hour two: 64 3/4 = (4 x 64 + 3) / 4 = 259 / 4

We can now calculate the distances:

55.25 + 259/4 + 52.3 + 67.89

We need to find a common denominator so that we can add these numbers:

55.25 = 221/4

259/4 = 259/4

52.3 = 523/10

67.89 = 6789/100

We may now multiply the fractions:

221/4 + 259/4 + 523/10 + 6789/100 = 5881/20

5881/20 = 294 1/20 is the result of converting this improper fraction to a mixed number.

As a result, the 4-hour trip's total mileage came to about 294.05 miles.

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