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.

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Related Questions

can someone please do this? nit the mini task though, number 8

Answers

1 is C

2 is D

3 is C

4 is A

5 is D

5 is A

7 is B

Please help me with this math problem!! :)

Answers

Step-by-step explanation:

the following things are clear : opposite sides are of equal length, the sum of all angles in a square, rectangle or general parallelogram is 360 degrees, and opposite angles are equal.

so,

y² + 7 = 32

y² = 25

y = 5

2y² = k

2×5² = k

50 = k

the opposite angle of 150 is also 150 degrees.

the opposite angle of x is also x.

so, we have as sum of angles

360 = 150 + 150 + x + x = 300 + 2x

60 = 2x

x = 30 degrees

Two friends, Gabriel and Hudson, had just bought their first cars. Gabriel uses 10 gallons of gas to drive 339 miles in his car. The table below represents the number of miles, yy, that Hudson can drive his car for every xx gallons of gas.

How much farther can Gabriel's car travel on one gallon of gas than Hudson's car?

Answers

Answer- 15.8 Miles

Explanation photo was given above.

The given bar graph shows the number of rooms, bathrooms, fireplaces, and elevators in the building.
Combined, there are 199 rooms, bathrooms, fireplaces, and elevators. The number of rooms exceeds the
number of bathrooms and fireplaces by 68. The difference between the number of fireplaces and elevators is
23. If the number of bathrooms is doubled, it exceeds the number of fireplaces and elevators by 47. Determin
the number of rooms, bathrooms, fireplaces, and elevators in the building.

Answers

Using a system of equations, it is found that there are:

132 rooms.38 bathrooms.26 fireplaces.3 elevators.

For the system, we have that:

The number of rooms is x.The number of bathrooms is y.The number of fireplaces is z.The number of elevators is w.

Combined, there are 199 rooms, hence:

[tex]x + y + z + w = 199[/tex]

The number of rooms exceeds the  number of bathrooms and fireplaces by 68, hence:

[tex]x = y + z + 68[/tex]

The difference between the number of fireplaces and elevators is  23, hence:

[tex]z - w = 23[/tex]

If the number of bathrooms is doubled, it exceeds the number of fireplaces and elevators by 47, hence:

[tex]2y = z + w + 47[/tex]

Replacing the third equation into the fourth:

[tex]z = 23 + w[/tex]

[tex]2y = z + w + 47[/tex]

[tex]2y = 23 + w + w + 47[/tex]

[tex]2y = 2w + 70[/tex]

[tex]y = w + 35[/tex]

Then, from the second equation:

[tex]x = y + z + 68[/tex]

[tex]y + z = x - 68[/tex]

We can solve for w, considering that:

[tex]y = w + 35[/tex]

[tex]z = 23 + w[/tex]

[tex]y + z = x - 68[/tex]

[tex]x = y + z + 68[/tex]

[tex]x = w + 35 + w + 23 + 68[/tex]

[tex]x = 2w + 126[/tex]

[tex]x + y + z + w = 199[/tex]

[tex]2w + 126 + w + 35 + 23 + w + w = 199[/tex]

[tex]5w + 184 = 199[/tex]

[tex]5w = 15[/tex]

[tex]w = \frac{15}{5}[/tex]

[tex]w = 3[/tex]

Then, solving for the other variables:

[tex]x = 2w + 126 = 2(3) + 126 = 132[/tex]

[tex]y = w + 35 = 3 + 35 = 38[/tex]

[tex]z = 23 + w = 23 + 3 = 26[/tex]

There are:

132 rooms.38 bathrooms.26 fireplaces.3 elevators.

A similar problem is given at https://brainly.com/question/17096268

Drag steps and expressions into place to explain and show how to evaluate x⋅y for x=3 and y=9.

Answers

your pics not loading in

Answer:

1. Substitute 9 for y..............................3 x y

2.  Substitute 3 for X .......................................3x 9

3.   multiply ................................... 27                                        

Step-by-step explanation:

the atomic number of arsenic is 33. what is the electron configuration of an arsenic atom

Answers

1s^2 2s^2 2p^6 3s^2 3p^6 3d^10 4s^2 4p^3

The diagram shows a trapezium.
B
D
Diagram NOT accurately drawn
AD = x cm.
BC is the same length as AD.
AB is twice the length of AD.
DC is 4 cm longer than AB.
The perimeter of the trapezium is 38 cm.
Work out the length of AD.

Answers

Perimeter implies the total length of sides of a given figure. Thus the length AD = 4.75 cm.

A plane figure is any type of figure bounded by four straight sides. Examples are square, rectangle, trapezium, rhombus, etc. A trapezium is a type of plane figure which belongs to a family referred to as quadrilaterals.

The perimeter of a given shape is the sum of the length of its boundaries or sides.

Thus the length AD required in the question can be determined by:

AD = x cm

BC = x cm

AB = 2x cm

DC = 4x cm

Perimeter = AD + BC + AB + DC

                 = x + x + 2x + 4x

Perimeter = 8x

But the perimeter of the trapezium has been given as 38 cm.

Thus,

38 = 8x

x = [tex]\frac{38}{8}[/tex]

  = 4.75

Therefore, the length of AD is 4.75 cm.

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Jenny has three times as many new toys as she has favorite toys.

Answers

answer:

3x = y

step-by-step explanation:

૪・ i am inferring you have to create an equation?

・jenny have three times = 3x

・as her fav toys — 3x = y

・new toys = y

・fav toys = x

HELPPPPPPP ME ASAPPPPPP

Answers

Answer:

D

Step-by-step explanation:

Perpendicular lines intersect to create right angles. That rules out A and B because both have a right angle in them. C has two lines that are parallel. The only one left is D which is neither parralell or perpendicualar.

Which coin does Jeff have the most of in his collection?

nickel
penny
dime

Answers

Answer:

dimes

Step-by-step explanation:

Answer: dimes

Step-by-step explanation:

The area of the surface of a ball is equal to the area of the curved surface of a right circular cylinder. If both the height and diameter of the cylinder are 12cm , find the diameter of the ball

Answers

Answer:

D=12 cm

Step-by-step explanation:

please check the image for the answer. Thank you .

Determine whether each equation represents a linear or nonlinear function.
Drag each equation into the appropriate box.
Linear Function Nonlinear Function
y = {x-6
y = (x - 5)2
y = 2* +8
y = 3(x + 7)
y = 4x3 - 1

Answers

Answer:

y=1/2x=6 - linear, written as y=mx+b.

y=(x-5)^2 - nonlinear, x has an exponent greater than 1

y=2^x+8 - nonlinear, x is an exponent

y=3(x+7) - linear, can be written as y=mx+b (y=3x+21)

y=4x^3-1 - nonlinear, x has an exponent greater than 1

Step-by-step explanation:

cody spent 3 hours and 5 minutes looking for his missing cat if he finally found it at 7:35 what time was it when he originally started​

Answers

Answer:

4:30

Explanation:

Three hours before 7:35 is 4:35, but you also have to subtract the extra 5 minutes to make it 4:30

100 POINTS

Given Point P(3,4), what is the resulting point after the following transformations?

Translate 3 up and 2 left
Rotation 180° around origin
Reflection over y-axis

Answers

Answer:

(1, -7)

Step-by-step explanation:

P(3,4)

3 up ---> y = 4 + 3 = 7

2 left ----> x = 3 - 2 = 1

new point (1, 7)

after 180 rotation around origin

point is (-1, -7)

now reflection over y-axis

(1, -7)

Answer:

[tex](1,-7)[/tex]

Step-by-step explanation:

Refer to the image below

On the accompanying grid, draw and label quadrilateral ABCD with points A(1,2), B(6,1), C(7,6), and D(3,7). On the same set of axes, plot and label quadrilateral A′B′C ′D′, the reflection of quadrilateral ABCD in the y-axis. Determine the area, in square units, of quadrilateral A′B′C′D′.

Answers

Answer: Refer to figure 1 for the diagram needed.

A ' = (-1, 2)

B ' = (-6, 1)

C ' = (-7, 6)

D ' = (-3, 7)

Area = 24 square units

============================================================

Explanation:

Start by drawing an xy axis. Plot the given points A,B,C,D on this grid.

To reflect any given point over the y axis, we apply this rule

[tex](x,y) \to (-x,y)[/tex]

which means we change the sign of the x coordinate, but keep the y coordinate the same. For example, a point like A(1,2) moves to A ' (-1,2). The other points are handled in a similar fashion.

After all of the points have been reflected, you'll get what is shown in figure 1.

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

To find the area of quadrilateral ABCD, we can form a bounding box as small as possible around the quadrilateral. Refer to figure 2.

The area of rectangle FEHG is 6*6 = 36 square units

Then we subtract off the areas of these four outer triangles

Triangle AED = 5*2/2 = 5Triangle AFB = 1*5/2 = 2.5Triangle BCG = 1*5/2 = 2.5Triangle CDH = 1*4/2 = 2

Meaning we'll end up with 36-5-2.5-2.5-2 = 24 as the area of quadrilateral ABCD. Because a reflection is a mirror copy, quadrilateral A'B'C'D' will have the same area as ABCD.

A toy rocket is launched from the ground, the equation

h= -16t^2+ 80t, models the height of the rocket h in feet at any timet

in seconds.

For which interval of time will the rocket be higher than 64 feet off the

ground?

Answers

Answer:

Step-by-step explanation:

We can graph the function and determine the points where the y value line is greater than 64 feet.  We could also solve the equation for h = 64.

Graphing:

A graph is attached.  The intersections of the line at height = 64 feet are at (1,64) and (4,64).  The first is going up and the second coming down.  The period of time the rocket is above 64 feet is from 1 to 4 seconds.

Solving:

h= -16t^2+ 80t

64 = -16t^2+ 80t

-16t^2+ 80t - 64 = 0

Solve using the quadratic formula:

We get two answers:  1 and 4 (seconds)

FOR 3 graders learn and pay attention in class its important Ask me any multiplacation equation or time tables

Answers

Answer:

c

Step-by-step explanation:

Complete the following proof. Given: (BD) is the perpendicular bisector of (AC) Prove: ∢A≅∢C
Statement Reason
1. (BD) is the perpendicular bisector of (AC) 1. Given
2. Point B is the midpoint of (AC) 2. Definition of perpendicular bisector
3. 3. Definition of midpoint
4. ∢ABD and ∢CBD are right angles 4. Definition of perpendicular bisector
5. ∢ABD and ∢CBD are congruent 5. All right angles are congruent.
6. 6. Reflexive property of congruence
7. 7.
8. ∡A≅∡C 8.

Answers

Answer:

I dont know if this is right but... i tried XD

Step-by-step explanation:

Angle A is congruent to angle C.

What is Triangle?

A triangle in geometry is a polygon with three sides and three angles. The sum of the interior angles of a triangle is 180°.

If XYZ is a triangle, it is represented as ΔXYZ

Here, it is given that BD is the perpendicular bisector of AC.

Then by the definition of perpendicular bisector, B is the midpoint of AC.

Consider ΔABD and  ΔCBD

ΔABD and  ΔCBD are right triangles with  ∡ABD =  ∡CBD = 90°.

So,  ∡ABD ≅  ∡CBD   (∵ all right angles are congruent)

Now, by the reflexive property of congruence, every side or angles are congruent to itself.

So BD ≅ BD

Since B is the midpoint of AC, AB = BC.

Hence AB ≅ BC

By SAS theorem, if two sides and an angle of a triangle are congruent to two sides and angles of another triangle, then both triangles are congruent.

Hence ΔABD ≅ ΔCBD

So, Angle A is congruent to angle C.

Hence ∡A ≅ ∡C if BD is perpendicular bisector of AC.

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What is the dividend when the divisor is 8 and the quotient is 96 with a remainder of 3?
dividend:
Explain how you found the dividend.

Answers

Answer:

13

Step-by-step explanation:

13÷8=96r3 आओऋअःनबभसजहलव

The required dividend would be 765 when the divisor is 8 and the quotient is 96 with a remainder of 3.

What is the Quotient?

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

Let the required dividend would be x

The divisor is 8 and the quotient is 96 with a remainder of 3 which is given in the question

As per the given question, the solution would be as:

⇒ x ÷ 8 = 96 r3

⇒ x  + 3 = 96 × 8

⇒ x + 3 = 768

⇒ x = 768 - 3

⇒ x = 765

Therefore, the required dividend would be 765.

Learn more about the quotient here:

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What is the value of x in the equation ?

Answers

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

This is our equation

[tex]2.5\left(6x-4\right)=10+4\left(1.5+0.5x\right)[/tex]

First off we can distribute the 2.5 and the 4

Now our equation is [tex]15x-10=10+6+2x[/tex]

subtract [tex]2x[/tex] from both sides

[tex]13x-10=16[/tex]

add [tex]10[/tex] to both sides

[tex]13x=26[/tex]

Divide both sides by [tex]13[/tex]

[tex]x=2[/tex]

Can someone tell me which one is the answer? Am I wrong or correct?

Answers

Answer:

I don't believe your wrong mate

Ashley has 10 skirts in her closet.




2 skirts are blue

3 skirts are red

4 skirts are green

1 skirt is pink



Ashley randomly selects 2 skirts without replacement. The outcome of the second skirt is —

Answers

Answer:

the highest choices are red and green

(☞╹◡╹)☞ Enjoy ☜(╹◡╹☜)

Answers

Step-by-step explanation:

hey.....

how are uh

PLEASE ANSWER QUICK AND SHOW WORK

Miss Johnson borrow $8,300 to buy a car. She agreed to a
4% interest rate and payments for 5 years.
How much will her interest be?
What is her total debt for buying the car?

Answers

Answer:

Interest: $402.20

Total Debt owed: $9,302.00

Step 1: Multiply the principal (the original amount borrowed) by the interest rate (%):  

$8,300 x 4% = 360.00 (interest for one year)

Step 2: Find out how many years she will be paying back the loan and add that number of years to the first payment year ($360). ($360 + 5years = 365 total payments) Then multiply the total number of payments by the interest rate ($365 x .04 = $14.60 interest per payment).

Step 3: Add up all the yearly interests ($14.60 per payment x 12 months = $181.20 yearly interest)

Step 4: Add the yearly interest to the total debt owed.  

$9,302 + $181.20 = $9,483.20 total debt

Total amount owing after 5 years = $8,300+($365 x .04 interest rate per payment for 60 months)=10,605.00 dollars owed in 5 years of payments. Interest owed is 10,605 x .04=$410.20 for a grand total of 10,915.20 dollars owed overall for this 4% loan which was paid back over a period of five years with twelve monthly payments per year at four percent interest rate per month ($410.20/12=$34.02).

What is the equation of the line that passes through the point (4,7) and has a slope
of -1/4

Answers

Answer:

See answer below.

Step-by-step explanation:

y - 7 = -1/4(x - 4)

y - 7 = -1/4(x - 4)   in point slope form  

In slope intercept form: y - 7 = -1/4x + 1

                                       y = -1/4 x + 8

1. The expression 2p - 15 represents the number of lilies left in the zoo's garden after a storm. If p = 223, how many lilies are left in the garden after the storm? 431 lilies 223 lilies 193 lilies 208 lilies​

Answers

2(223)-15
446-15=431lilies


At the craft store, Patty bought a bag of yellow and brown marbles. The bag contained 85
marbles, and 60% of them were yellow. How many yellow marbles did Patty receive?

Answers

Answer:

51 yellow marbles

Step-by-step explanation:

60% of 85 can be found by multiplying 85 and 0.6 to get 51

Answer:

i got 51 marbles! simple.

Which of the following is NOT classified as nonverbal communication a. Signs b. Eye Contact c. Body language d. Gestures

Answers

Answer:

american sign language (ASL)

can i have help on this q plz

Answers

Answer:

14.8

Step-by-step explanation:

7.4 * 2 = 14.8.

hope this helps

Answer:

54.76[tex]cm^{2}[/tex]

Step-by-step explanation:

The area of a shape is base times height. bh

Since this is a square, all of the sides are the same length. Meaning 7.4*7.4 to make 54.76cm^2.

What are complex integers ?

Answers

Answer:

In mathematics, a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a symbol, called the imaginary unit, that satisfies the equation i² = −1. Because no real number satisfies this equation, i was called an imaginary number by René Descartes.

Step-by-step explanation:

Complex Integer

(or Gaussian integer), a number of the form a + bi, where a and b are integers. An example is 4 – 7i. Geometrically, complex integers are represented by the points of the complex plane that have integral coordinates.

Complex integers were introduced by K. Gauss in 1831 in his investigation of the theory of biquadratic residues. The advances made in such areas of number theory as the theory of higher-degree residues and Fermat’s theorem through the use of complex integers helped clarify the role of complex numbers in mathematics. The further development of the theory of complex integers led to the creation of the theory of algebraic integers.

The arithmetic of complex integers is similar to that of integers. The sum, difference, and product of complex integers are complex integers; in other words, the complex integers form a ring.

Answer:

An immediate consequence of the definition of arithmetical operations on complex numbers is that the sum, the difference, and the product of two or more complex numbers.

Step-by-step explanation:

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