Simplify the complex expression and show work

93÷1.1= 84.545454545

Answer:approximately 30 times

Step-by-step explanation:

The wheel on Carmen's bike circular in shape and has a diameter of 1.1 meter.

Radius = diameter/2 = 1.1/2 = 0.55 meter.

When the wheel completes one revolution, the distance covered is equal to the circumference of the wheel.

The formula for determining the circumference of the wheel is expressed as

Circumference = 2πr

Where π is a constant whose value is 3.14

Circumference = 2 × 3.14 × 0.55 = 3.454 metres.

Carmen races the bicycle for 93m. Therefore, the number of times that the wheel of the bicycle turns as it travels this distance would be

93 / 3.454 = 26.9 times

Answer:

Step-by-step explanation:

Answer:

The answer to your question is  x = 0 and x = 1

Step-by-step explanation:

Equation

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

1)

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

Expand

2)                  x² + x + x² - x - 2x + 2 = -1(x - 2)(x + 1)

Simplify

3)                  2x² -2x + 2 = -1(x² + x - 2x - 2)

4)                  2x² - 2x + 2 = -x² + x + 2

Equal to zero

5)                  2x² - 2x + 2 + x² - x - 2 = 0

6)                  3x² - 3x = 0

Factor

7)                  3x(x - 1) = 0

8)                  3x₁ = 0                   x₂ - 1 = 0

9)                    x₁ = 0/3                x₂ = 1

10)                  x₁ = 0                    x₂ = 1

Answer:

The sale price of the car is $48000.

Step-by-step explanation:

i) let the sale price of the car be = $x

ii) the premium is given as 16%

  therefore the premium of the car will be equal to = 16% of $x

  the premium of the car will be = $0.16x

iii) therefore total price of car in terms of sale price x  = $x + $0.16x

           therefore total price = $1.16x

iv) total price is given as $55,680

Therefore   $55,680 = $1.16x,    therefore $x = [tex]\dfrac{55,680}{1.16} = \$\hspace{0.15cm}48000[/tex].

Therefore the sale price of the car is $48000.

The horizontal distance covered by pilot is 17,972.2 feet.

Step-by-step explanation:

Given,

Distance covered descending = 1000 feet

Diagonal distance = 18,000 feet

The horizontal distance will form a right triangle, therefore, we can find the horizontal distance by using pythagoras theorem.

Here,

a = 1000

b = horizontal distance

c = 18000

[tex]a^2+b^2=c^2\\(1000)^2+b^2=(18000)^2\\1000000+b^2=324000000\\b^2 = 324000000-1000000\\b^2=323000000[/tex]

Taking square root on both sides

[tex]\sqrt{b^2}=\sqrt{323000000}\\b=17972.2[/tex]

The horizontal distance covered by pilot is 17,972.2 feet.

Keywords: pyathoras theorem, square root

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Answer:

1). 875 seats

2). 25 rows in each section

3). $8400

4). Saving of $360

5). 2105 tickets remained unsold

6). x = 16

Step-by-step explanation:

This question is incomplete; here is the complete question.

A stadium has 10,500 seats and 8 VIP boxes. The stadium is divided into 12 equal  sections: 2 premium sections and 10 standard sections. A seat at the premium section  costs $48 per game. A seat at the standard section costs $27 per game.

1. How many seats are there in each section?

2. If there are 35 seats in each row, how many rows are in each section?

3. If all the seats in the premium section are sold out for a game, how much will the  stadium get from those ticket sales?

4. There are 50 games in each season. A season pass costs $2,040. A season pass  holder can go to all the games and have a seat in the premium section. How much can a fan save by buying the season pass?

5. For the night game on Tuesday, 8,395 tickets were sold. How many tickets were  left?

6. Write an equation using “x” and then solve  the equation. Each VIP boxes can seat X  people. If all the seats and VIP boxes are  filled up, there are 10,628 audience in the stadium.

1). Number of seats in the stadium = 10500

Number of sections = 2 premium + 10 standard = 12

Number of seats in each section = [tex]\frac{10500}{12}=875[/tex]

2). If the number of seats in each row = 35

Then number of rows in each section = [tex]\frac{875}{35}=25[/tex]

3). Number of seats in 2 premium sections = 2×875 = 1750

Cost of 1750 seats at the rate of $48 per game = 1750 × 48 = $84000

4). Cost of one ticket in premium section = $48 per game

If the games planned in one season = 50

Then cost of the tickets = 48×50 = $2400

Cost of the season ticket = $2040

Saving on the purchase of one season ticket = 2400 - 2040 = $360

5). For a night game number of tickets sold = 8395

Total number of seats in the stadium = 10500

Tickets remained unsold = 10500 - 8395 = 2105

6). Number of seats in each VIP box = x

Number of VIP boxes = 8

Number of seats in 8 VIP boxes = 8x

Total number of tickets sold = 10500 + 8x

Total number of audience in the stadium = 10628

Then the equation will be

8x + 10500 = 10628

8x = 10628 - 10500

x = [tex]\frac{128}{8}=16[/tex]

The subject of this question is Mathematics, specifically dealing with seating capacity and pricing in a stadium. To determine the maximum seating capacity of the stadium, add up the number of seats in each section. To calculate the total revenue from a single game, multiply the number of seats in each section by the corresponding ticket price, and then sum up the results.

The subject of this question is Mathematics, specifically dealing with the concepts of seating capacity and pricing in a stadium.

To determine the maximum seating capacity of the stadium, we add up the number of seats in each section: 2 premium sections with 48 seats each, 10 standard sections with 900 seats each, and 8 VIP boxes with a capacity of 12 seats each. This gives us a total of 1116 seats.

To calculate the total revenue from a single game, we multiply the number of seats in each section by the corresponding ticket price, and then sum up the results. For the premium sections, the revenue is $48 per seat multiplied by 96 seats, and for the standard sections, the revenue is $27 per seat multiplied by 900 seats. Adding up these two amounts gives us the total revenue from a single game.

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Answer:

Step-by-step explanation:

A salesperson at a car dealership has a salary of 900 dollars per week plus 3% commission on sales if a salesperson has sales of $72000 in one week, it means that the amount of commission that was received by the salesperson would be

3/100 × 72000 = 0.03 × 72000 = $2160

Therefore, the total amount of pay that the salesperson would receive for the week would be

900 + 2160 = $3060

Answer:

Option C. is correct.

Step-by-step explanation:

Given:

Adrienne's annual take-home pay = $57,000

To find:

The maximum amount that she can spend per month on paying off credit cards and loans and not be in danger of credit overload.

Solution:

Number of months in a year = 12

So, amount she can spend per month =

Annual pay of Adrienne / Number of months in a year = [tex]\frac{57000}{12} =\frac{28500}{6}=\frac{14250}{3}=4750[/tex]

So, option C. is correct.

Answer:

A. $950.00

Step-by-step explanation:

A p e x

Answer:

  15

Step-by-step explanation:

Put the given value of x where x is in the expression and do the arithmetic.

  4^3 -(3 +4)^2 = 64 -49 = 15

The value of the expression for x=4 is 15.

Final answer:

The expression x³ - (3 + x)² for x = 4 simplifies to 64 - 49, resulting in a final answer of 15.

Explanation:

The student has asked to evaluate the expression x³ - (3 + x)² for x = 4. To do this, we will substitute x with 4 and simplify the expression step by step. First, calculate the value inside the parentheses: (3 + 4) = 7. Then, we square this value to get 7² = 49. After that, subtract the squared value from 4³ (which is 64), to get the final answer.

The final answer is 15

Answer:

yes

Step-by-step explanation:

because it is not a whole number so you cant tell

Answer:

3hr 31mins

Step-by-step explanation:

First we convert miles to kilometers

1 miles to km = 1.60934 km

26.2 miles = 26.2 x 1.60934 = 42.164708

A typical marathon approx = 42.165km

If our runner covers 12 km = 1 hr

then he'll cover 42.165km = 42.165/12 = 3.5137 hrs

= 3 hrs + (0.514 * 60 mins) = 3hrs + (30.84mins)

Allan going at that speed would complete the marathon in appox = 3hrs : 31mins.

Answer:

2.34m2

Step-by-step explanation:

boom

Answer:The faster person will do the job in 7.53hours

Step-by-step explanation:

Let t=faster person

Let t-1= the other person

The job to be done =1

Each person will do a fraction of the job

4/t+4/t-1=1

Multiply both sides wit t(t-1)

4(t+1)+4t=t(t-1)

4t+4+4t=t^2+t

8t+4=t^2+t

0=t^2+t-8t-4

t^2-7t-4=0

Use Almighty formular to solve d quadratic equation

X=-b+- rootb^2-4ac/2a

X=t,a=1,b=-7 c=4

Substituting the values you get:

t=-7 +- root 49+16/2

t=-7 +- root 65/2

t=7 +8.06/2=15.06/2

t=7.53 hours

Answer:

[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

Three red balls, 4 white balls, and 1 green ball are in a bag. A ball is drawn without replacement.

total balls = 3 red + 4 white + 1 green = 8 balls

the number of balls that are not green is 7

pick 3 balls from 7 balls that are not green

[tex]nCr= \frac{n!}{r!(n-r)!}[/tex]

[tex]P(not \ green)=\frac{7C3}{8C3}[/tex]

[tex]7C3= \frac{7!}{3!(7-3)!}=35[/tex]

[tex]8C3= \frac{8!}{3!(8-3)!} =56[/tex]

[tex]P(3 \ balls \ drawn)=\frac{35}{56} =\frac{5}{8}[/tex]

Answer:

B. Median

Step-by-step explanation:

We have been given data about time spent on Internet (min/day). We are asked to determine the best measure of central tendency for the given data.

Data: 75, 38, 43, 120, 65, 48, 52,

We can see that our given data has a very large value outlier (120), so it will increase the mean.

There is no mode for the given data set as no value repeats.

We know that median is best measure for data set with large valued outliers because median is not affected by outliers.

Therefore, option B is the correct choice.

The measure of central tendency that best describes the data is B. Median.

Mean:

= (75 + 38 + 43 + 120 + 65 + 48 + 52) / 7

= 69.86

Median:

We arrange data in ascending order: 38, 43, 48, 52, 65, 75, 120. Since there are seven values, the median is the middle value: 52

Mode: There is no value that appears more than once in the data set.

Therefore, the measure of central tendency that best describes the data is B. Median.

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Answer:

Jacob ran 40 yards more than Ali.

Step-by-step explanation:

Football field is in the shape of a rectangle having dimensions 120 yards × 50 yards

Since Jacob runs around the perimeter of the field from one corner to other corner, therefore, distance run by Jacob = [tex](\text{Length+width})[/tex]

Distance run by Jacob = 50 + 120 = 170 yards

Ali runs through the middle of the field diagonally on a straight line.

Therefore, distance covered by Ali = [tex]\sqrt{\text{length}^{2}+\text{width}^{2}}[/tex]

= [tex]\sqrt{(50)^{2}+(120)^{2}}[/tex]

= [tex]\sqrt{2500+14400}[/tex]

= [tex]\sqrt{16900}[/tex]

= 130 yards

Now difference between the distance covered by Jacob and Ali

= 170 - 130

= 40 yards

Therefore, Jacob ran 40 yards more than Ali.

Answer:

7.5

Step-by-step explanation:

1.25/ (.5) = 2.5

2.5 x 3 = 7.5

Answer:

[tex]r=f\times m-5b[/tex]

Step-by-step explanation:

Given:

Number of boxes of burger meat = [tex]f[/tex]

Number of slices of meat in each box = [tex]m[/tex]

Number of burgers the family eats each week = [tex]b[/tex]

Number of burger meat remaining = [tex]r[/tex]

To write: An equation in terms of [tex]f, m,\ and\ b[/tex] that represents the number of remaining burger meat, [tex]r[/tex], after 5 weeks.

Now, since each box contain 'm' slices.

Therefore, by unitary method, number of slices of meat in 'f' boxes is given as:

[tex]Total\ number\ of\ slices=f\times m[/tex]

Now, each week burger consumption = 'b'

So, 'b' slices of meat are eaten each week. Again by unitary method, the number of slices eaten in 5 weeks is given as:

[tex]\textrm{Number of slices eaten in 5 weeks}=5b[/tex]

Now, Slices remaining = Total number of slices - Number of slices eaten in 5 weeks.

Therefore, [tex]r=f\times m-5b[/tex]

Hence, the equation that represents the number of slices of burger meat remaining in terms of 'f', 'm', and 'b' is given as:

[tex]r=f\times m-5b[/tex]

Answer: 9:11

Step-by-step explanation:

Let x be the total number of students.

If 3/4 of students study a language That mean 3x/4 students study a language.

Number of students that don't study a language becomes

x - 3x/4 = x/4.

and 3/5 of those who study language study French, that means 3x/4 * 3/5 of students study French.

This gives 3x/4 * 3/5 = 9x/20 Studying French.

Number of students that study language but do not study French becomes

3x/4 - 9x/20 = 6x/20

Total number of students that do not study French becomes

[total number of students not studying any language] + [total number of students studying a language but do not study French ]

Which becomes

x/4 + 6x/20 = 11x/20

Hence ratio of those that study French to those that do not study French Becomes

9x/20 : 11x/20

9:11.

Answer:

a) Domain = [tex](-\infty,400)\cup (400,\infty)[/tex]

b) [tex]x \in [0,100][/tex]

c) 53.03 worker hours

d) 83.33 worker hours

e) 83.33 worker hours

Step-by-step explanation:

We are given the following in the question:

[tex]W(x) = \dfrac{250x}{(400-x)}[/tex]

where W(x) is the number of worker-hours required to distribute new telephone books to x% of the households in a certain rural community.

a) Domain of function.

The domain is the all the possible values of x that the function can take.

Domain = [tex](-\infty,400)\cup (400,\infty)[/tex]

b) Values of x

Since x is a percentage in reference to context, it can only take value upto 100. Also it cannot take any negative value.

So domain n reference to context will be

[tex]x \in [0,100][/tex]

c) worker-hours were required to distribute new telephone books to the first 70% of the households

[tex]W(70) = \dfrac{250(70)}{(400-70)} = 53.03[/tex]

53.03 worker hours were required to distribute new telephone books to the first 70% of the households.

d) Worker hour for entire community

For entire community, x = 100

[tex]W(100) = \dfrac{250(100)}{(400-100)} = 83.33[/tex]

83.33 worker hours were required to distribute new telephone books to the entire households.

e) Percentage of the households in the community for 3 worker hours

[tex]3 = \dfrac{250x}{(400-x)}\\\\1200-3x = 250x\\253x = 1200\\\\x = \dfrac{1200}{253} = 4.74\%[/tex]

Thus, 4.74% of the households in the community had received new telephone books by the time 3 worker-hours had been expended.

Final answer:

The domain of the function W(x) is (-∞, 400) U (400, +∞). The values of x that have a practical interpretation in this context are in the interval [0, 100]. Approximately 53.03 worker-hours were required to distribute new telephone books to the first 70% of households, and approximately 83.33 worker-hours were required to distribute to the entire community. After 3 worker-hours, approximately 4.73% of the households had received new telephone books.

Explanation:

(a) The domain of the function W is the set of all possible values of x that make the function defined and meaningful. In this case, the function W(x) is defined except when the denominator 400-x is equal to zero. So, we need to find the values of x that make the denominator zero.

To do that, we solve the equation 400-x = 0, which gives x = 400.

Therefore, the domain of the function W is the set of all real numbers except x = 400. We can express this in interval notation as (-∞, 400) U (400, +∞).

(b) In this context, the function W(x) represents the number of worker-hours required to distribute new telephone books to x% of the households in the rural community. A practical interpretation is only meaningful when x represents a valid percentage, meaning that it is between 0% and 100%, inclusive. So, the values of x that have a practical interpretation in this context are in the interval [0, 100].
(c) To find the worker-hours required to distribute new telephone books to the first 70% of households, we substitute x = 70 into the function W(x). Evaluating the expression, we get: W(70) = 250(70) / (400 - 70) = 17500 / 330 = 53.03.

Therefore, approximately 53.03 worker-hours were required to distribute new telephone books to the first 70% of households.

(d) To find the worker-hours required to distribute new telephone books to the entire community, we substitute x = 100 into the function W(x). Evaluating the expression, we get: W(100) = 250(100) / (400 - 100) = 25000 / 300 = 83.33.

Therefore, approximately 83.33 worker-hours were required to distribute new telephone books to the entire community.

(e) To find the percentage of households that had received new telephone books after 3 worker-hours, we rearrange the function W(x) to solve for x. We have:

W(x) = 250x / (400 - x)

3 = 250x / (400 - x)

3(400 - x) = 250x

1200 - 3x = 250x

1200 = 253x

x = 1200 / 253 ≈ 4.73

Therefore, approximately 4.73% of the households in the community had received new telephone books after 3 worker-hours.

Answer:

x= −5621/201

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3 /7x+5 =  812/7772/7-7

3 /7x+5=  1/67+−7

3 /7x+5=(  1/67+-7)(Combine Like Terms)

3 /7x+5=  −468 /67

3 /7x+5= −468/67

Step 2: Subtract 5 from both sides.

3 /7x+5−5=−468/67−5

3 /7x=−803/67

Step 3: Multiply both sides by 7/3.

(  7/3)*(3/7x)=(7/3)*(−803/67)

x= −5621/201

Answer:

I pick the reasoning of option A

Step-by-step explanation:

I like the reasoning given in B, however, there are many cases of Athletes that, after reaching the top, maintain supremacy and improve over the years, adapting to their old age. Usually speed and physical resistance are replaced by technique and experience in the case of the top athletes.

I dont like C and D argument too much because being the best in a sport doesnt mean either that you reach the maximum level possible (in many cases you can keep growing) or that you dont have more motivations. Many athletes are super competitive people and they try to improve themselves all the time to reach, and stay, in the top.

I choose option A as answer because people on the cover doesnt neccesarily mean that they are the absolute best. Their performance was way better than their usual performance, and that may be due to either real skill growth, heavy training or a lucky streak. If it is a lucky streak, it is natural for that player's performance to go down into more terrenal levels for him. On the other hand, If he trained heavily, then he might have big injuries on later seasons and his performance wont be able to keep up for long. Thats why 'surprises' (that also sell better due to be a novelty) tend to go downhill after they reach the cover of sports illustrated.

The decrease in performance after an athlete's phenomenal season could be due to a statistical phenomenon called regression to the mean. This principle suggests that if a variable (e.g., athletic performance) is extreme on its first measurement, it will tend to be closer to the average on its subsequent measurement, which could explain why some athletes have less stunning seasons after achieving outstanding performances.

A better explanation for the decrease in performance of the Sports Illustrated cover athlete could be option A. People on the cover are usually highlighted for their outstanding performances, which are far from the mean. Due to a phenomenon called regression to the mean, it is likely that their performance in the next season would be closer to the mean (average).

Regression to the mean is a statistical concept that suggests that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement, and vice-versa.

This has nothing to do with a jinx, but rather with the statistical principle that performances, both good and bad, tend to cluster around the mean over time. So, outstanding performance is often followed by less exceptional performance, not necessarily because the player got worse, but because the original performance was likely above their true average.

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Answer:

Step-by-step explanation:

The number of questions on a math test is represented (3x+1). The number of questions on the spelling test is represented by (x+12).

An expression to find how many more questions were on the math test would be

= 3x + 1 - (x + 12)

= 3x + 1 - x - 12

= 3x - x + 1 - 12

= 2x - 11

When the value of x = 8, then the expression becomes

2× 8 - 11 = 16 - 11 = 5

Final answer:

To find how many more questions are on the math test compared to the spelling test, you subtract the spelling test expression from the math test expression. Simplifying this gives 2x - 11. Evaluating this expression for x = 8 shows there are 5 more questions on the math test.

Explanation:

The question asks you to write an expression to find out how many more questions are on the math test compared to the spelling test, and then evaluate this expression for x = 8.

Step 1: Write the expression

To find how many more questions are on the math test, you subtract the number of questions on the spelling test from the number of questions on the math test. Therefore, the expression is:

(3x + 1) - (x + 12)

Step 2: Simplify the expression

First, distribute the negative sign: 3x + 1 - x - 12. Simplify by combining like terms: 2x - 11. This simplified expression represents how many more questions are on the math test compared to the spelling test.

Step 3: Evaluate the expression for x = 8

Plug in x = 8 into the simplification, 2x - 11. So, you get: 2(8) - 11 = 16 - 11 = 5.

Therefore, there are 5 more questions on the math test than on the spelling test when x = 8.

Answer:

0.5

Step-by-step explanation:

The slope m of a linear equation y = mx + b that goes through point (-9,6) and point (-3, 9) would have the following formula

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 6}{-3 - (-9)} = \frac{3}{6}= \frac{1}{2}[/tex] or 0.5

Where [tex](x_1,y_1), (x_2, y_2)[/tex] are the coordinates of the 2 points that this line goes through

Answer:

Side of 40 and height of 20

Step-by-step explanation:

Let s be the side of the square base and h be the height of the box. Since the box volume is restricted to 32000 cubic centimeters  we have the following equation:

[tex]V = hs^2 = 32000[/tex]

[tex]h = 32000/ s^2[/tex]

Assume that we cannot change the thickness, we can minimize the weight by minimizing the surface area of the tank

Base area with open top [tex]s^2[/tex]

Side area 4hs

Total surface area [tex]A = s^2 + 4hs[/tex]

We can substitute [tex]h = 32000/ s^2[/tex]

[tex]A = s^2 + 4s\frac{32000}{s^2}[/tex]

[tex]A = s^2 + 128000/s[/tex]

To find the minimum of this function, we can take the first derivative, and set it to 0

[tex]A' = 2s - 128000/s^2 = 0[/tex]

[tex]2s = 128000/s^2[/tex]

[tex]s^3 = 64000[/tex]

[tex]s = \sqrt[3]{64000} = 40[/tex]

[tex]h = 32000/ s^2 = 32000/ 40^2 = 20[/tex]

Answer:

0.6826

Step-by-step explanation:

Mean(μ) = 37

Standard deviation (σ) = 9

P(28 < x < 46) = ???

Using normal distribution

Z = (x - μ)/σ

For x = 28

Z = (28 - 37)/9

Z = -9/9

Z = -1

For x = 46

Z = (46 - 37)/9

Z = 9/9

Z = 1

We now have

P(-1 < Z < 1)

= P(Z < 1) - P(Z < -1)

From the table, Z = 1 = 0.3413

φ(Z) = 0.3413

Recall that

When Z is positive, P(x<a) = 0.5 +φ(Z)

P(Z<1)= 0.5 + 0.3413

= 0.8413

When Z is negative, P(x<a) = 0.5 - φ(Z)

P(Z< -1)= 0.5 - 0.3413

= 0.1587

We now have

0.8413 - 0.1587

= 0.6826

Answer:The procedure to use the find the value of x calculator is as follows:

Step 1: Enter the values in the divisor and the product field

Step 2: Now click the button “Solve” to get the output

Step 3: The dividend or the x value will be displayed in the output field

Step-by-step explanation: In algebra, it is easy to find the third value when two values are given. Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication, and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Answer:

x ≥ 120

Step-by-step explanation:

i) Let x be the number of packages of cards

ii) we know that Pablo currently has 1200 cards.

iii) Therefore the equation required is

15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards

iv) Solving the equation we get

    15x + 1200 ≥ 3000

⇒  15x ≥ (3000 - 1200)

⇒ 15x ≥ 1800

⇒ x ≥ (1800 ÷ 15)

∴ x ≥ 120

answer

x ≥ 120

Step-by-step explanation:

Step-by-step explanation:

i) Let x be the number of packages of cards

ii) we know that Pablo currently has 1200 cards.

iii) Therefore the equation required is

15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards

iv) Solving the equation we get

   15x + 1200 ≥ 3000

⇒  15x ≥ (3000 - 1200)

⇒ 15x ≥ 1800

⇒ x ≥ (1800 ÷ 15)

∴ x ≥ 120

Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle shown,

AB represents the hypotenuse of the right angle triangle.

With 45 degrees as the reference angle,

AC represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine QR, we would apply trigonometric ratio

Sin θ = opposite side/hypotenuse side. Therefore,

Sin 45 = BC/6√2

√2/2 = BC/6√2

BC = √2/2 × 6√2

BC = 6

Answer:

  16 mph

Step-by-step explanation:

The relationship between distance, speed, and time is ...

  speed = distance/time . . . . . "miles per hour"

Malcom's distance was 32 miles each way, for a total of 64 miles. Then his average speed was ...

  speed = (64 mi)/(4 h) = 16 mi/h

See the attached picture: