Milford Company uses the​ percent-of-sales method to estimate uncollectibles. Net credit sales for the current year amount to $ 140 comma 000​, and management estimates 2​% will be uncollectible. The Allowance for Uncollectible Accounts prior to adjustment has a credit balance of $ 3 comma 000. The amount of expense to report on the income statement will be?

Answer with explanation:

To find the common multiple of 45 and 95,we will find HCF of 45 and 95.

45=3 × 3× 5

95=5 × 19

⇒H CF(45,95)

=3 × 3×5×19

=855

→Common multiple of 45 and 95 =855

→There are infinite number of multiple of 855 which are 855, 1710, 2565,.....

You have not written between which two numbers.So, you should write multiple of 855 such that it is smaller than the greater number.

Answer:

y intercept equals 1

Step-by-step explanation:

y= -1/2x+1

the slope is -1/2

the y intercept is 1

Answer:

6 units

Step-by-step explanation:

A rectangle's width is one-fourth of its length.

w = 1/4 l

area is 9 square units

A = l*w = 9

  Replacing w with 1/4l

  l * (1/4l) = 9

1/4 l^2 = 9

Multiply each side by 4 to clear the fraction

4 * 1/4 l^2 = 4*9

l^2 = 36

Take the square root of each side

sqrt (l^2) = sqrt(36)

l =6

Answer:

6 units

Step-by-step explanation:

Let the length = L

Then the width = L/4

area = length * width

area = L * L/4 = 9

L^2/4 = 9

L^2 = 36

L = 6 or L = -6

Since we are dealing with a length, we eliminate the negative answer.

Answer: 6 units

P.S. Your equation is incorrect. L(L) = 9 would work for a square with 4 congruent sides and area 9. Here the sides have different lengths. The equation is L(L/4) = 9.

Answer:

1. [tex]\dfrac{AD}{DB}+1=\dfrac{CE}{EB}+1[/tex]

2. Addition property of equality

Step-by-step explanation:

In triangle ABC,

[tex]\dfrac{AD}{DB}=\dfrac{CE}{EB}.[/tex]

The addition property of equality states that if the same amount is added to both sides of an equation, then the equality is still true.

Use addition property of equality, add 1 to both sides of previouse equality:

[tex]\dfrac{AD}{DB}=\dfrac{CE}{EB}\\ \\\dfrac{AD}{DB}+1=\dfrac{CE}{EB}+1\\ \\\dfrac{AD+DB}{DB}=\dfrac{CE+EB}{EB}[/tex]

Answer:

(AD/DB) +1 = (CE/EB) +1 -----> Addition Property of Equality

Answer:

Attached

Step-by-step explanation:

The conic section you can chose is a parabola

A parabola is a curve where any point on the curve is equidistant from the focus and from a directrix

When you have the vertex and focus points, you can write the equation of the parabola then graph it on a graph tool to visualize the curve.

Assume the vertex is at (3,1) and focus is at (3,5), then you notice here the x-coordinate for vertex and focus is the same , to mean one is top of the other.

This is a regular vertical parabola the x part is squared.

Vertex and focus are 4 units apart. This is by checking the difference in values of y-axis of vertex and focus.This is your p

The equation of the parabola will be

(x-h)²=4p(y-k)

but p=4

(x-3)²=4(4)(y-1)

(x-3)²=16(y-1)

x²-6x+9=16y-16

x²-6x-16y+25=0-----------------equation of the parabola

It is a right-side up parabola

Answer:

I only know question number one; the answer is

A parabola is a curve where any point on the curve is equidistant from the focus and from a directrix.

Step-by-step explanation:

Answer:

[tex]\frac{7}{10}[/tex]

Step-by-step explanation:

Fraction of the amount donated to school library = [tex]\frac{2}{10}[/tex]

Fraction of the amount donated to animal shelter = [tex]\frac{1}{10}[/tex]

Fraction of the amount donated to food bank = [tex]\frac{4}{10}[/tex]

The rest of the amount was saved for next project.

Thus, the total fraction of the amount donated will be the sum of fractions of amount donated to school library, animal shelter and food bank.

i.e.

Fraction of the amount donated = [tex]\frac{2}{10}+\frac{1}{10}+\frac{4}{10} = \frac{7}{10}[/tex]

This means, Tyler and Katie donated [tex]\frac{7}{10}[/tex] of their profits.

Answer:−1.825

Step-by-step explanation:

The  probability that all selected transistors are defective is approximately 0.0014, while the probability that none of the selected transistors are defective is 0.1762.

Given:

Transistors = 13

Defective = 4

a. The number of ways to choose 4 defective transistors from the 4 available = [tex]^4C_4[/tex]

               = [tex]\dfrac{4!}{4! 0!}[/tex]

               = 1

and, the total number of ways to choose 4 transistors from the 13 available

[tex]^{13}C_4= \dfrac{13!}{4! * (13-4)!}[/tex]

    = [tex]\dfrac{(13 * 12 * 11 * 10)}{(4 * 3 * 2 * 1)}[/tex]

    = 715

Therefore, the probability of selecting all defective transistors is:

Probability = Number of favorable outcomes / Total number of possible outcomes

                  = 1 / 715

                  = 0.0014

b. The number of ways to choose 4 non-defective transistors from the 9 available is

[tex]^{9}C_4= \dfrac{9!}{4! * (9-4)!}[/tex]

      = [tex]\dfrac{(9 * 8* 7* 6)}{(4 * 3 * 2 * 1)}[/tex]

      = 126

So, the probability of selecting none defective transistors is:

Probability = Number of favorable outcomes / Total number of possible outcomes

                  = 126 / 715

                  = 0.1762

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Final answer:

The probabilities are calculated using combinations: the probability all selected transistors are defective is 1/C(13,4) or 0.13%, and the probability none are defective is C(9,4)/C(13,4) = 17.6%.

Explanation:

The student's question about probabilities can be answered using combinations and the basic principles of probability. We need to calculate the probability that out of 13 transistors, all 4 selected are defective, and then the probability that none are defective.

Probability All Are Defective

To find the probability that all 4 transistors selected are defective, we calculate the number of ways to pick 4 defective ones out of 4 (which is 1 way, since we only have 4 defective ones), and divide it by the number of ways to pick any 4 out of 13. Using combinations, we calculate:

Probability(all defective) = C(4,4) / C(13,4) = 0.13%.

Probability None Are Defective

To find the probability that none of the 4 selected transistors are defective, we calculate the number of ways to pick 4 non-defective ones out of 9 (since 13 total minus 4 defective leaves 9 non-defective), and divide it by the number of ways to pick any 4 out of 13:

Probability(none defective) = C(9,4) / C(13,4) = 17.6%

Answer:

y = 2

Step-by-step explanation:

r tan θ / sec θ = 2

First, simplify tan θ / sec θ:

r (sin θ / cos θ) / (1 / cos θ) = 2

r sin θ = 2

Remember that r cos θ = x and r sin θ = y:

y = 2

Answer:

Answer is A hope that helped

Step-by-step explanation:

Answer:

C. √13

Step-by-step explanation:

The distance between two points is given by

d =sqrt( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( (3-0)^2 + (-3--1)^2)

  = sqrt( 3^2 + (-3+1)^2)

  = sqrt( 9+(-2)^2)

  = sqrt( 9+4)

  = sqrt(13)

To answer this, you basically use Pythagoras' Theroem, but instead of:

[tex]c = \sqrt{a^{2} + b^{2}}[/tex]

it will be :

[tex]distance = \sqrt{(y - y1)^{2} + (x - x1)^{2}  }[/tex]

So you are finding the squareroot of the (difference in y coordinates)² plus (difference in x coordinates) ²:

x is the x-coordinate of (0, -1)      (so x = 0)

y is the y-coordinte of (0, -1)        ( so y = -1)

x1 is the x coordinate of (3, -3)        ( so x1 = 3)

y1 is the y coordinate of (3, -3)        (so y1 = -3)

--------------------------------------------------

Now, lets find the distance between the two points, by substituting all of this values into the equation at the top:

[tex]distance = \sqrt{(y - y1)^{2} + (x - x1)^{2}  }[/tex]    (substitute in values)

[tex]distance = \sqrt{( 0 -3)^{2} + (-1 - -3)^{2} }[/tex]   (simplify: note -1 - - 3 = -1 + 3)

[tex]distance = \sqrt{( -3)^{2} + (-1 +3)^{2} }[/tex]     (simplify)

[tex]distance = \sqrt{( -3)^{2} + (2)^{2} }[/tex]           (now square the numbers)

[tex]distance = \sqrt{9 + 4 }[/tex]                   (simplify)

[tex]distance = \sqrt{13 }[/tex]

___________________________________________

C.  [tex]\sqrt{13}[/tex]

Answer:

  142°

Step-by-step explanation:

∠3 is an alternate exterior angle with ∠7, so is congruent to ∠7. ∠7 is supplementary to 38°, so has measure 180° -38° = 142°.

The measure of ∠3 is 142°.

Answer:

  a.  F(x) = 1.2(2.5)^(x – 1)

Step-by-step explanation:

The sequence is geometric with first term 1.2 and common ratio 3/1.2 = 2.5. The explicit formula for such a sequence is ...

  a[n] = a[1]·r^(n-1)

For a[1] = 1.2 and r = 2.5, and using x as the term number, the formula is ...

  F(x) = 1.2·2.5^(x-1) . . . . . matches selection A

The formula that could be used for showing the sequence is option A.[tex]F(x) = 1.2(2.5)^{(x - 1)}[/tex]

The sequence should be geometric which means the first term 1.2 and the common ratio is [tex]3\div 1.2[/tex] = 2.5.

Now The explicit formula should be

[tex]a[n] = a[1].r^{(n-1)}[/tex]

Now

Here a[1] = 1.2

and r = 2.5,

So, the formula is

[tex]F(x) = 1.2\times 2.5^{(x-1)[/tex]

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Answer:

  TRUE

Step-by-step explanation:

Changing the mean by adding the same number to every data value does not change the differences those values have from the new mean. Hence the standard deviation remains unchanged. If it was 6, it will be 6.

Answer:

True because standard divination stays the same

Step-by-step explanation:

Answer:

[tex]\large\boxed{\Phi=\dfrac{\pi}{9}+\dfrac{2k\pi}{3}\ or\ \Phi=-\dfrac{\pi}{9}+\dfrac{2k\pi}{3}}[/tex]

Step-by-step explanation:

[tex]\cos3\Phi=\dfrac{1}{2}\qquad\text{substitute}\ 3\Phi=\theta\\\\\cos\theta=\dfrac{1}{2}\iff\theta=\dfrac{\pi}{3}+2k\pi\ or\ \theta=-\dfrac{\pi}{3}+2k\pi\qquad k\in\mathbb{Z}\\\\\text{We're going back to substitution:}\\\\3\Phi=\dfrac{\pi}{3}+2k\pi\ or\ 3\Phi=-\dfrac{\pi}{3}+2k\pi\qquad\text{divide both sides by 3}\\\\\Phi=\dfrac{\pi}{9}+\dfrac{2k\pi}{3}\ or\ \Phi=-\dfrac{\pi}{9}+\dfrac{2k\pi}{3}[/tex]

Answer:

  15.542%

Step-by-step explanation:

For uneven cash flows such as those in this problem, there is no formula for "internal rate of return" (IRR). It must be computed graphically or iteratively. Spreadsheets and financial calculators are equipped to do this calculation. Attached is the result of the calculation done by a graphing calculator.

The sum of "present value" of each of the cash flows is zero when the discount rate is the IRR.

Step-by-step explanation:

Tree A's heights are less spread out than tree B's heights. Tree A has a lower average height than tree Bs

Answer:

No, it is not a linear function. It is an exponential function.

Step-by-step explanation:

You have a secret that you tell to one person.

Every hour, each of the people that know the secret tells one person.

Let N be the people who know the secret.

Let t be the number of hours since you told the first person.

Now, when only you know the secret, means 1 person.

N(0) = 1

Next hour, there are now 2 people that know the secret.  

N(1) = 2

After the next hour, these 2 people will tell 2 more people, so people doubled to 4.

N(2) = 4

One hour later it will be N(3) = 8

We can see the pattern as following.

[tex]N(t)=2^{t}[/tex]

Therefore, the function is exponential not linear.

Answer:

1st problem:

Converges to 6

2nd problem:

Converges to 504

Step-by-step explanation:

You are comparing to [tex]\sum_{k=1}^{\infty} a_1(r)^{k-1}[/tex]

You want the ratio r to be between -1 and 1.

Both of these problem are so that means they both have a sum and the series converges to that sum.

The formula for computing a geometric series in our form is [tex]\frac{a_1}{1-r}[/tex] where [tex]a_1[/tex] is the first term.

The first term of your first series is 3 so your answer will be given by:

[tex]\frac{a_1}{1-r}=\frac{3}{1-\frac{1}{2}}=\frac{3}{\frac{1}{2}=6[/tex]

The second series has r=1/6 and a_1=420 giving me:

[tex]\frac{420}{1-\frac{1}{6}}=\frac{420}{\frac{5}{6}}=420(\frac{6}{5})=504[/tex].

Final answer:

To maximize profit, the hotel management should determine the rate at which the difference in revenue gained from increasing the rate and the cost to service fewer rooms is maximized. By analyzing different rate increases and subtracting the cost of servicing fewer rooms, the management can identify the rate that will generate the highest profit. For example, by increasing the rate to $42 per room, the hotel could maximize profit at $1940.

Explanation:

To determine the price at which the hotel management should charge per room to maximize profit, the management needs to consider the relationship between the price, the number of rented rooms, and the cost to service each room.

First, let's establish the initial conditions:

60 rooms are rented at a rate of $40 per room.

Each rented room costs $8 per day to service.

Next, management determines that for each $2 increase in the nightly rate, five fewer rooms will be rented. To maximize profit, the management should find the rate at which the difference in revenue gained from increasing the rate and the cost to service fewer rooms is maximized.

Here is the step-by-step calculation:

Calculate the initial revenue: $40/room * 60 rooms = $2400

Calculate the initial cost: $8/room * 60 rooms = $480

Calculate the initial profit: $2400 - $480 = $1920

Calculate the new revenue: ($40 + $2)/room * (60 - 5) rooms = $2280

Calculate the new cost: $8/room * (60 - 5) rooms = $440

Calculate the new profit: $2280 - $440 = $1840

Repeat steps 4-6 for different rate increases until the profit is maximized.

Based on this analysis, the management should charge a rate that allows them to profit the most, such as $42/room, which would result in a profit of $1940.

Management should charge $44 per room to maximize profit.

To determine the optimal room rate to maximize profit, we'll utilize concepts from algebra and profit modeling. Let's define the variables:

The revenue, R, can be calculated as:

R = (40 + 2x)(60 - 5x)

The cost, C, of servicing the rooms can be calculated as:

C = 8(60 - 5x)

The profit, P, is given by:

P = R - C

Substituting the revenue and cost formulas:

P = (40 + 2x)(60 - 5x) - 8(60 - 5x)

Let's expand and simplify this equation:

P = (40 + 2x)(60 - 5x) - 8(60 - 5x)

[tex]P = 2400 - 200x + 120x - 10x^2 - 480 + 40x[/tex]

[tex]P = -10x^2 - 40x + 1920[/tex]

To find the value of x that maximizes the profit, we need to find the vertex of the quadratic function. The vertex form of a parabola given by [tex]ax^2 + bx + c[/tex] is at:

[tex]x = \frac{-b}{2a}[/tex]

Substituting a = -10 and b = -40:

[tex]x = -\frac{-40}{2 \times -10} = 40/20 = 2[/tex]

Thus, the management should increase the rate by 2 increments of $2, or $4. Therefore, the optimal room charge is:

$40 + $4 = $44

Answer:

2/9

Step-by-step explanation:

Because there's 2 blue marbles and 9 in total

Answer:

D.

Step-by-step explanation:

You could find the 8 terms and then add them up.

Let's do that.

Luckily we have the common ratio which is -5.   Common ratio means it is telling us what we are multiplying over and over to get the next term.

The first term is -11.

The second term is -5(-11)=55.

The third term is -5(55)=-275.

The fourth term is -5(-275)=1375.

The fifth term is -5(1375)=-6875.

The sixth term is -5(-6875)=34375.

The seventh terms is -5(34375)=-171875.

The eighth term is -5(-171875)=859375.

We get add these now. (That is what sum means.)

-11+55+-275+1375+-6875+34375+-171875+859375

=716144 which is choice D.

Now there is also a formula.

If you have a geometric series, where each term of the series is in the form [tex]a_1 \cdot r^{n-1}[/tex], then you can use the following formula to compute it's sum (if it is finite):

[tex]a_1\cdot \frac{1-r^{n}}{1-r}}[/tex]

where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio. n is the number of terms you are adding.

We have all of those. Let's plug them in:

[tex]a_1=-11[/tex], [tex]r=-5[/tex], and [tex]n=8[/tex]

[tex]-11 \cdot \frac{1-(-5)^{8}}{1-(-5)}[/tex]

[tex]-11\cdot \frac{1-(-5)^{8}}{6}[/tex]

[tex]-11 \cdot \frac{1-390625)}{6}[/tex]

[tex]-11 \cdot \frac{-390624}{6}[/tex]

[tex]-11 \cdot -65104[/tex]

[tex]716144[/tex]

Either way you go, you should get the same answer.

Final answer:

The sum of the 8-term geometric series with the given first term and common ratio is calculated using the geometric series sum formula, resulting in a sum of 716,144, Which is option D.

Explanation:

The sum of a geometric series is determined by the formula Sₙ = a(1 - rⁿ)/(1 - r), where Sₙ is the sum of the first N terms, a is the first term, r is the common ratio, and N is the number of terms. Since we have an 8-term geometric series with a first term of -11 and a common ratio of -5, we can calculate the last term (-11 x (-5)⁷) to ensure it is indeed 859,375, confirming the ratio and the number of terms.

The sum can then be calculated as follows: S₈ = -11 x (1 - (-5)⁸) / (1 - (-5)) = -11 x (1 - 390625) / (1 + 5) = -11 x (-390624) / 6 = -11 x -65104 = 716,144, which corresponds to option D.

Answer: 0.25

Step-by-step explanation:

Given : The  future lifetime of Gary is uniformly distributed with interval [0 years , 60 years].

Then the probability density function for Gary's future lifetime will be:-

[tex]f(x)=\dfrac{1}{60-0}=\dfrac{1}{60}[/tex]

The future lifetime of Eric is uniformly distributed with interval [0 years , 40 years].

Then the probability density function for Erin's future lifetime will be:-

[tex]f(x)=\dfrac{1}{40-0}=\dfrac{1}{40}[/tex]

Now, the joint density function for Gary and Eric's future lifetime :-

[tex]f(x,y)=f(x)f(y)=\dfrac{1}{40\times60}=\dfrac{1}{2400}[/tex]  [∵Their future lifetimes are independent. ]

Now, the probability that Gary dies first is given by :-

[tex]\int^{60}_{0}\int^{40}_{x}f(x,y)\ dy\ dx\\\\=\int^{60}_{0}\int^{40}_{x}\dfrac{1}{2400}\ dy\ dx\\\\=\int^{60}_{0}\dfrac{40-x}{2400}\ dx\\\\=\dfrac{1}{2400}[40x-\dfrac{x^2}{2}]^{60}_{0}\\\\=\dfrac{1}{2400}(2400-\dfrac{3600}{2})=0.25[/tex]

Hence, the probability that Gary dies first =0.25

Answer:

Step-by-step explanation:

looks like it's about 1/2

Looks approximately like x = 0.6 ish

are there MCQ choices?

Answer:

[tex]m =-\frac{1}{2}[/tex]

Step-by-step explanation:

The equation of a line in the pending intersection form is:

[tex]y = mx + b[/tex]

Where m is the slope of the line and b is the intersection with the y axis.

In this case we have the following equation

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

To find the slope of this line you must rewrite it in the form

[tex]y = mx + b[/tex]

Then we solve the equation for y.

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

[tex]y=-\frac{1}{2}(x-2)+3[/tex]

[tex]y=-\frac{1}{2}x-2*(-\frac{1}{2})+3[/tex]

[tex]y=-\frac{1}{2}x+1+3[/tex]

[tex]y=-\frac{1}{2}x+4[/tex]

Note that [tex]m =-\frac{1}{2}[/tex]

Finally the slope is: [tex]m =-\frac{1}{2}[/tex]

The slope of the line with equation; y-3 = -1/2(x-2) is; slope, m = -1/2.

According to the question, the equation of the line in discuss is; y-3 = -1/2(x-2).

To determine the slope of the line, we need to rearrange the equation such that it resembles the slope-intercept form of the equation of a straight line as follows;

The equation of a straight line; y = mx + c.

Now, we expand the equation of the line and rearrange as follows;

By comparison, the slope of the line given bey the equation, y-3=-1/2(x-2) is; slope, m = -1/2.

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Answer:  a. reject the null hypothesis, church attendance and marital status are dependent

Step-by-step explanation:

Given : A Chi square test has been conducted to assess the relationship between marital status and church attendance. The obtained Chi square is 23.45 and the critical Chi square is 9.488.

Null hypothesis : There is no relationship between the variables.

Alternative hypothesis : There is a relationship between the variables.

Here we can see that the obtained chi-square (23.45) value is greater than the critical chi square value (9.488) , then we have to reject the null hypothesis.

So the correct answer is reject the null hypothesis, church attendance and marital status are dependent.

Given the obtained Chi-square 23.45 is greater than the critical Chi square 9.488, we reject the null hypothesis, implying there is a significant relation or dependence between marital status and church attendance.

In a Chi square test, if the obtained Chi square value is higher than the critical Chi square value, it means that the observed data significantly deviates from what is expected under the null hypothesis. Therefore, in this case, where the obtained Chi square is 23.45 and the critical number is 9.488, we would reject the null hypothesis. Considering that the null hypothesis is generally posed under the assumption of no relation or independence between the variables being tested, rejecting it thus implies that there is a significant relationship or dependence between marital status and church attendance. Therefore, the correct answer to the question is a. reject the null hypothesis, church attendance and marital status are dependent

.

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[tex]6x[/tex]

............................................

Answer:

1, 2, 3, 6, 7, 14, 21, 42 [start from the outer ends, then come inner, placing negative symbols on either or]

Step-by-step explanation:

Just like what "dashabo123" said, you can hand each number a negative one at a time before moving to the next set of factors.

I am joyous to assist you anytime.

Answer:

a. x-intercept = 3 , y-intercept = 9.

Step-by-step explanation:

-6x - 2y = -18

Convert to slope-intercept form:

-2y = 6x - 18

y = -3x + 9

So the y-intercept  (when x = 0) is  when y = 9..

Solving for x to find the x-intercept:

0 = -3x + 9

3x = 9

x = 3.

Answer:

Step-by-step explanation:

The problem statement tells you that x represents the horizontal distance in feet that the airplane is from the building. The domain is the set of useful values of x, which will be from 0 to 50 feet. Values of x less than 0 or more than 50 make no sense in this scenario.

Answer:

  168 km

Step-by-step explanation:

Let x represent the distance Tyler drives at the slower speed, and let y represent the distance at the higher speed. Using time = distance/speed, we can write equations for the total travel time:

  x/42 +y/105 = 2.5

  x/28 +y/60 = 4.0 . . . . . 1.5 hours more than the usual 2.5 hours

Multiplying the first equation by 210, we have ...

  5x +2y = 525

Multiplying the second equation by 420, we get ...

  15x +7y = 1680

Subtracting 3 times the first of these equations from the second, we have ...

  (15x +7y) -3(5x +2y) = (1680) -3(525)

  y = 105

Putting this into the very first equation, we get ...

  x/42 + 105/105 = 2.5

  x/42 = 1.5 . . . . . . subtract 1

  x = 63 . . . . . . . . .multiply by 42.

The total distance to Tyler's parents' house is ...

  63 km + 105 km = 168 km

Tyler's total travel distance is approximately 168 km.

Calculating Total Distance Traveled

To determine the total distance Tyler traveled, let du be the distance through urban areas and dm be the distance on the motorway.

→ The total distance is:

[tex]D = d_u + d_m[/tex]

First, using the normal journey:

→ Urban Area:

Speed = 42 km/h

Time = [tex]t_u[/tex] / 42,

→ Motorway:

Speed = 105 km/h

Time = [tex]t_m[/tex] / 105,

→ Total time for normal journey:

→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]

We have:

→ [tex]d_u[/tex] = 42 * [tex]t_u[/tex]

→ [tex]d_m[/tex] = 105 * [tex]t_m[/tex]

When there is fog:

→ Urban Area:

Speed = 28 km/h

Time = [tex]t__uf}[/tex] / 28

→ Motorway:

Speed = 60 km/h

Time = [tex]t_{um[/tex] / 60

Total time for foggy journey:

→ [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60

Given that he leaves 1 hour early and arrives 30 minutes late, the total journey time in foggy conditions is:

→ 2.5+1+0.5=4 hours

Thus,

→  [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60 = 4

Solving the Equations

We now have two equations:

→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]

→ [tex]t_{uf}\ /\ 28\ + t_{mf} \ /\ 60 = 4 hours[/tex]

Let's solve these equations step-by-step.

First, let's multiply the first equation by 210 (the least common multiple of 42 and 105):

→ [tex]210(t_u/42 + t_m/105) = 210*2.5[/tex]

→ [tex]5t_u+2t_m=525[/tex] (eq. 1)

Next, let's multiply the second equation by 420 (the least common multiple of 28 and 60):

→ [tex]420( t_u/28+ t_m /60)=420*4[/tex]

→ [tex]15t_u +7t_m =1680[/tex] (eq. 2)

We now solve these two linear equations:

→ [tex]5t_u+2t_m=525[/tex]

→ [tex]15t_u +7t_m =1680[/tex]

First, let's solve Equation 1 for [tex]t_m[/tex] in terms of  [tex]t_u[/tex]:

→ [tex]d_m=(525-5d_u)/2[/tex]

Substitute this expression into Equation 2:

→ [tex]15t_u+7((525-5d_u)/2)=1680[/tex]

Multiply through by 2 to clear the fraction:

→ [tex]30t_u +7(525-5t_u )=3360[/tex]

→ [tex]30t_u +3675-35t_u =3360[/tex]

→ [tex]-5t_ u +3675=3360[/tex]

→ [tex]-5t_u=3360-3675[/tex]

→ [tex]-5t _u=-315[/tex]

→ [tex]t_u=63[/tex]

Now substitute [tex]t_u=63[/tex] back into Equation 1 to find [tex]t_m[/tex]:

→ [tex]5(63)+2t_m =525[/tex]

→ [tex]315+2t_m =525[/tex]

→ [tex]2t_m =210[/tex]

→ [tex]t_m=105[/tex]

Thus, the total distance Tyler travels is:

[tex]= t _u +t_m[/tex]

[tex]=63+105[/tex]

[tex]=168\ kilometers[/tex]

Answer:

$98.47

Step-by-step explanation:

1. 2(9.5) + 3 (7.95) + 49.95 = $92.80

6% • $92.80 = $5.57

$92.80 + $5.57 = $98.47