Amanda, Bryce, and Corey enter a race in which they have to run, swim, and cycle over a marked course. Their average speeds are given in the table. Corey finishes first with a total time of 1hr 50 min. Amanda comes in second with a time of 2hr 42 min. Bryce finishes last with a time of 3hr 16 min. Find the distance (in mi) for each part of the race.

Amanda, Bryce, And Corey Enter A Race In Which They Have To Run, Swim, And Cycle Over A Marked Course.

Answers

Answer 1

The running distance is 4.23 miles, the swimming distance is 1.98 miles and the cycling distance is 35.64 miles.

Each racer travels the same distance and the sum of the distances travelled ([tex]x[/tex]), in miles. By definition of average speed ([tex]v[/tex]), in miles per hour, we get the following system of equations:

Amanda

[tex]t_{A} = \frac{x_{R}}{v_{A, R}}+\frac{x_{S}}{v_{A,S}}+\frac{x_{C}}{v_{A,C}}[/tex] (1)

Where:

[tex]x_{R}[/tex] - Running distance, in miles.[tex]x_{S}[/tex] - Swimming distance, in miles.[tex]x_{C}[/tex] - Cycling distance, in miles. [tex]v_{A,R}[/tex] - Speed of Amanda in the running distance, in miles per hour.[tex]v_{A,S}[/tex] - Speed of Amanda in the swimming distance, in miles per hour.[tex]v_{A,C}[/tex] - Speed of Amanda in the cycling distance, in miles per hour.[tex]t_{A}[/tex] - Total time of Amanda, in hours.

Bryce

[tex]t_{B} = \frac{x_{R}}{v_{B, R}}+\frac{x_{S}}{v_{B,S}}+\frac{x_{C}}{v_{B,C}}[/tex] (2)

Where:

[tex]v_{B,R}[/tex] - Speed of Bryce in the running distance, in miles per hour.[tex]v_{B,S}[/tex] - Speed of Bryce in the swimming distance, in miles per hour.[tex]v_{B,C}[/tex] - Speed of Bryce in the cycling distance, in miles per hour.[tex]t_{B}[/tex] - Total time of Bryce, in hours.

Corey

[tex]t_{C} = \frac{x_{R}}{v_{C, R}}+\frac{x_{S}}{v_{C,S}}+\frac{x_{C}}{v_{C,C}}[/tex] (3)

Where:

[tex]v_{B,R}[/tex] - Speed of Corey in the running distance, in miles per hour.[tex]v_{B,S}[/tex] - Speed of Corey in the swimming distance, in miles per hour.[tex]v_{B,C}[/tex] - Speed of Corey in the cycling distance, in miles per hour.[tex]t_{B}[/tex] - Total time of Corey, in hours.

If we know that [tex]t_{A} = 2.7\,h[/tex], [tex]v_{A,R} = 10\,\frac{mi}{h}[/tex], [tex]v_{A,S} = 4\,\frac{mi}{h}[/tex], [tex]v_{A, C} = 20\,\frac{mi}{h}[/tex], [tex]t_{B} = 3.27\,h[/tex], [tex]v_{B,R} = 7.5\,\frac{mi}{h}[/tex], [tex]v_{B,S} = 6\,\frac{mi}{h}[/tex], [tex]v_{B,C} = 15\,\frac{mi}{h}[/tex], [tex]t_{C} = 1.833\,h[/tex], [tex]v_{C,R} = 15\,\frac{mi}{h}[/tex], [tex]v_{C,S} = 3\,\frac{mi}{h}[/tex] and [tex]v_{C,C} = 40\,\frac{mi}{h}[/tex], then the solution of the linear system of equations is:

[tex]\frac{x_{R}}{10} + \frac{x_{S}}{4} + \frac{x_{C}}{20} = 2.7[/tex] (4)

[tex]\frac{x_{B}}{7.5}+\frac{x_{S}}{6} +\frac{x_{C}}{15} = 3.27[/tex] (5)

[tex]\frac{x_{R}}{15}+\frac{x_{S}}{3} +\frac{x_{C}}{40} = 1.833[/tex] (6)

[tex]x_{R} = 4.23\,mi[/tex], [tex]x_{S} = 1.98\,mi[/tex], [tex]x_{C} = 35.64\,mi[/tex]

The running distance is 4.23 miles, the swimming distance is 1.98 miles and the cycling distance is 35.64 miles.

We kindly invite to check this question on systems of linear equations: https://brainly.com/question/20379472


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Answer:

4 = a

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Which ordered pair is NOT in the solution set of −2x + 3y  ≥  12?

A. (-3,5)
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Step-by-step explanation:

Factorizing by grouping

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Answers

Answer:

(x+3)(y+2)

Step-by-step explanation:

(xy+2x)+(3y+6)

x(y+2)+3(y+2)

(x+3)(y+2)

solve for x, find the measure of all angles plzzzzz!! ​

Answers

Answer:

∠ H = 22.5°, ∠ I = 45° , ∡ J = 112.5°

Step-by-step explanation:

The 3 angles in a triangle sum to 180° , then

x + 2x + 5x = 180 , that is

8x = 180 ( divide both sides by 8 )

x = 22.5

Then

∠ H = x = 22.5°

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FIND THE SLOPE OF THE LINE

Answers

Answer:

4/1

Step-by-step explanation:

To get from one dot to the next, you go up by four and to the right by one, making the slope 4/1

determine the measurement of segment XV​

Answers

Answer:

Segment XV is equal to 24 mm

Step-by-step explanation:

Both triangles are clearly congruent, both having the same type of angles as well as angle LKJ and angle VKW having the same angle measure, 21 degrees. Lastly, if you were to take out segment JL and WV, the triangles would fold the same. All of this leads to segment XV being the same as segment KL which leads it to be 24 mm. (Sorry if this is confusing, just trying to explain how my brain understood the problem. If you need me to elaborate more let me know).

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Answers

Answer:

$8

Step-by-step explanation:

20% of $40

= [tex]\frac{20}{100}[/tex] × $40

= 0.2 × $40

= $8

$8 is discounted from the regular price

Answer:

$8 off

Step-by-step explanation:

Convert from a percentage to a multiplier by dividing by 100:

[tex]\frac{20}{100}=0.2[/tex]

Then multiply that by the price:

[tex]40*0.2=8[/tex]

meaning the item is $8 off.

You can confirm that like so:

[tex]\frac{8}{40} =0.2\\[/tex]

or 20%

Kaio bought a meal in a town for $20. Sales tax was 6.5% and he left a 15% tip. What was the amount Kaio paid in sales tax?What was the amount Kaio left as a tip?

What was the total cost of the meal?

A.$4.30

B.$21.30

C.$23.00

D.$24.30

Answers

Answer: D. $24.30

Explanation:

$20 • 6.5% = $1.30

$20 • 15% = $3.00

$20 + $3 + $1.30 = $24.30

The length of a planet's orbit around a star is approximately 22,200,000 km. It takes the planet about 1230 Earth days to complete a full orbit. What is the planet's average speed in kmh-1 to 3sf?​

Answers

Answer:

Approximately [tex]12.9\; \rm km \cdot h^{-1}[/tex], assuming that this orbit is circular.

Step-by-step explanation:

The question is asking for a tangential velocity with the unit [tex]\rm km \cdot h^{-1}[/tex]. The unit of the given distance is already in [tex]\rm km[/tex] as required. Convert the unit of the orbital period to hours:

[tex]\begin{aligned}T &= 1230\; \text{day} \times \frac{24\; \rm h}{1\; \text{day}}. = 29520\; \rm h\end{aligned}[/tex].

Calculate the angular velocity [tex]\omega[/tex] of this planet from its orbital period:

[tex]\begin{aligned}\omega &= \frac{2\, \pi}{T} \\ &= \frac{2\, \pi}{29520\; \rm h} \approx 2.1285 \times 10^{-4}\; \rm h^{-1}\end{aligned}[/tex].

Given the radius [tex]r[/tex] of the orbit of this planet, the tangential velocity [tex]v_{\perp}[/tex] of this planet would be:

[tex]\begin{aligned}v_{\perp} &= \omega\, r \\ &\approx 2.1285 \times 10^{-4}\; \rm h^{-1} \times 2.22\times 10^{7}\; \rm km \\ &\approx 4.73 \times 10^{3}\; \rm km \cdot h^{-1}\end{aligned}[/tex].

If the orbit of this planet is circular, the velocity of the planet would be equal to its tangential velocity: [tex]4.73\times 10^{3}\; \rm km \cdot h^{-1}[/tex].

John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck

Answers

Answer:

The answer is not finished but if John is buying the materials and paying for the labor then the answer will be $510.

Step-by-step explanation:

I’m sorry if I didn’t help but the answer is not written out enough…

3
Choose the option(s) that will show the effect (x-2. y+3) has on the figure?
left 2 units
down 2 units
down 3 units
up 2 units
right 3 units
left 3 units
up 3 units
right 2 units
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Answers

Answer:

left 2 units, up 3 units

Step-by-step explanation:

(x-2, y+3)

-2 means 2 to the left

+3 means 3 up

So it would be left 2 units, up 3 units.

Answer:

left 2 units up 3 units

Step-by-step explanation:

Rule:

If  x+b   right in b units

if  x-b    left   in b untits

if  y+b    up   in  b units

if  y-b  down in  b  units

You don 't have to use this rule if you know that on the Ox axis the line goes horizontally (the abscissa axis); And on the Oy axis vertically (the ordinate axis)

Then :

x-2    left in 2 units

y+3   up  in  3 units

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Answers

no there is not at all
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Answers

I would say A, reasoning.

Answer: reasoning

Step-by-step explanation:

Given m||n, find the value of x.
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t
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Answers

Step-by-step explanation:

due to the laws of symmetry of the angles of 2 crossing lines (and parallel lines are simply repeating and mirroring these angles), both angles must be equal.

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Answer:

(a) 1.0792 x 10³

(b) 3.769 x 10³

(c) 9.985 x 10³

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Tracy has 3/4 pounds of rice to give to 6 of her friends. If each
friends gets an equal amount, how much rice will each friend
receive?

Answers

Answer:

1/8 Pounds

Step-by-step explanation:

Since Tracy gives 3/4 pounds of rice to 6 of her friends, you will need to divide it among 6 people.

3/4 ÷ 6

= 3/4 * 1/6

= 1/4 * 1/2 (cross multiplication)

= 1/8.

Therefore, each of her 6 friends received 1/8 Pounds of rice

I hope this helped!

Leaks can write a 500 word essay in an hour. If she writes an essay in 10 minutes, about how many words do you think the essay contains. PLEASE TELL ME HOW TOU DID IT! WILL MARK BRAINLIEST

Answers

Answer:

83.3

Step-by-step explanation:

Alright so

She can write 500 words per hour

An hour is 60 minutes

500 divided by 6 (because 6x10= 60)

so you get est. 83 words per 10 mins.

To double check, do 83x6= 498, which is because the 83, is 83.3 (repeating)

Alex was thinking of a number. Alex doubles it and adds 0.9 to get an answer of 21.2. Form an equation with x from the information.

Answers

Answer:

2x + 0.9 = 21.2

Step-by-step explanation:

Let x be the number

The number was doubled so it should be 2x, then add 0.9 equals to 21.2

Answer:  2x + 0.9 = 21.2

and x = 10.15

Step-by-step explanation:

A recipe calls for 310 cup of sugar for every 5 cups of water. How many cups of sugar are needed for 25 cups of water?

Answers

Answer:

1550 cups

Step-by-step explanation:

multiply everything by 5

Please help quick! Thanks!

Answers

Answer:

<

Step-by-step explanation:

8^2=64

64+9=73

73-3=70

8*8=64

64+24=88

88-16=72

70<72

list the first six multiples of 6

Answers

Answer: 6, 12,24,30,36

Step-by-step explanation:

Hope this helps! :)

Evaluate the expression for b = 3 and c = 5.

b2c − 11 =

Answers

Answer:

34

Step-by-step explanation:

b = 3 and c = 5

Substitute and evaluate:

b²c - 11 =3²*5 - 11 = 9*5 - 11 =45 - 11 =34

Answer:

[tex]b = 3 \ \: \: : c = 5 \\ \\ b {}^{2} c - 11 = \\ \\ \\ {3}^{2} \times 5 - 11 = \\ \\ 9 \times 5 - 11 = \\ \\ 45 - 11 = \\ \\ = 34[/tex]

The graph of a function is shown on the coordinate plane below. Identify the rate of change of the function.

Answers

Answer:

[tex]\frac{5}{3}[/tex]

Step-by-step explanation:

The slope m is a measure of the rate of change

Calculate m using the slope formula

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

with |(x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (3, 4) ← 2 points on the line

m = [tex]\frac{4-(-1)}{3-0}[/tex] = [tex]\frac{4+1}{3}[/tex] = [tex]\frac{5}{3}[/tex] ← rate of change

Answer:

slope(m) = 7/4

Step-by-step explanation:

You can use Rise over run in order to find out the answer. I just used points (0,-1) and (4,6) and the rise was positive 7 while the run is 4 so the rate of change or the slope is 7/4.

You could also use the long way to figure the slope of the line. You could use (y2 - y1) / (x2, x1) to get the same slope

With a population standard deviation of 10 and a sample size of 4, what is the standard error of the mean

Answers

With a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the mean

Step-by-step explanation:

8.
Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms.

y = (3x + 4)(−2x − 3)

A. linear function; linear term: −17x; constant term: −12

B. quadratic function; quadratic term: 12x^2; linear term: 18x; constant term: −12

C. quadratic function; quadratic term: −6x^2; linear term: −17x; constant term: −12

D. linear function; linear term: −6x^2; constant term: −12

Answers

Answer:

C. quadratic function; quadratic term: −6x^2; linear term: −17x; constant term: −12

Step-by-step explanation:

Answer:

quadratic function; quadratic term: −6x² ; linear term: −17x; constant term: −12

Step-by-step explanation:

The given function is

We need to expand the RHS to get:

We can see that the degree of this polynomial function is 2 and hence it is a quadratic function.

The quadratic term is -6x²

The linear term is -17x

The constant term is -12

Given: 3x < -6.



Choose the solution set.

{x | x > -2}
{x | x < -2}
{x | x > 2}
{x | x < 2}

Answers

Answer:

First divide 3 on both sides to get x by itself, now you have x < -2.

Step-by-step explanation:

Hope this helps :)

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Answer:

3

Step-by-step explanation:

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Yan po correct me if im wrong po.. Salamat po...

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