A tortoise challenged a hare to a 100-meter race on a track. The tortoise negotiated a 60-meter head start with the hare. When they passed their respective starting points the hare was running at a constant speed of 3.6 meters per second and the tortoise was crawling at a speed of 0.7 meters per second. (They both maintained these speeds for the entire race.) Our goal is to determine who won the race. Take out a piece of paper and read the above problem statement again. In a couple of sentences, describe how you might determine who won the race. Construct a drawing to represent the 100-meter length of the track. Then place the tortoise and hare's starting points on the track. Define the variable t to represent the number of seconds since the start of the race.

Answer:

Hare wins the race

Step-by-step explanation:

Length of track = 100 m

Let t represent the number of seconds in completing the race.

Speed of tortoise = 0.7 m/s

Distance covered by tortoise in t seconds = Speed \times time = 0.7t

We are given that The tortoise negotiated a 60-meter head start with the hare.

So, Distance covered by tortoise in t seconds = 60+0.7t

Speed of hare = 3.6 m/s

Distance covered by hare in t seconds = 3.6 t

Now

3.6t = 100

[tex]t=\frac{100}{3.6}[/tex]

t=27.77

60+0.7t=100

[tex]t=\frac{100-60}{0.7}[/tex]

t=57.14

So, Hare took less time

So, Hare wins the race

a bag of trail mix contain 3 ounces of peanuts, 6 ounces of cranberries, 2 ounces of almonds and 2 ounces of raisins. what is the ratio of ounces of peanuts to ounces of almonds? write the ratio in the three different ways?​

Tiara is making a new dance outfit. She will need 3 2/3 yards of fabric for a shawl. She also needs 1 3/5 yards of fabric for the dress. She is fortunate enough to already have 2 yards of fabric in her possession. If the current price for fabric is $6.75 per yard, how much money will she need to finish her dance outfit?​

Help asap thanks in advance

Use this chart to help solve the problem.

Tonya's age (yr.)

Tonya's height (in.)

3

36.8

4

40

5

41.25

6

45

7

48.0

8

51.5

Tonya grew 2.25 more inches before her 9 year height was recorded. What is her height at age 9

written with the correct number of significant digits?

Sandra sets the cruise control in her car to 67 miles per hour when she goes on road trips. Which equation can be used to find how many hours, h, it will take her to drive m miles at her constant speed?

Match the pronoun type to the example.

1. personal
many
2. reflexive
those
3. relative
her
4. possessive
whom
5. interrogative
himself
6. demonstrative
what
7. indefinite
we
HELP 100 POINTS

There are 15 students on the debate team. Of these, 3 are boys. Give the ratio of boys to girls on the debate team in simplest form.​

There are 20 circles and 12 triangles. What is the simplest ratio of triangles to total shapes

Daredevil Danny takes a practice jump as shown on the graph below. Complete the steps to determine the equation for the parabolic trajectory of his practice jump.

a) What are the key aspects of any parabola? What do the key aspects tell you about the graph?

(5 points)


It goes all the way up to its max point and comes down. Its max point is 32 and how far it went was from 15 to 35


b) What are the key aspects of Daredevil Danny’s practice jump shown in the graph provided? Describe each value and how it is determined. (10 points)


It is a standard form graph and he needs to figure out the speed he is going to go and the angle


Step 2: Solve for coefficient a.

a) What equation is used to find the vertex form of a parabola with the vertex (h, k)? (5 points)


F(x)=ax2+bx+c

b) Solve for the coefficient a in the vertex form for the parabola in Daredevil Danny’s practice jump using key aspects from step 1. As you solve for the coefficient, explain each step of the process in detail. (15 points)



The picture of the question in the attached figure we know that The equation of a vertical parabola in vertex form is given by where a is the leading coefficient (h,k) is the vertex Looking at the graph we have a vertical parabola open downward (coefficient a is negative)The vertex is a maximum The vertex is the point (25.32) substitute in the equation













c) What is the vertex form of the parabola from Daredevil Danny’s practice jump? (5 points)


f(x)=-12/25(x-25)^2+32

Step 3: Change from vertex form to standard form.

To get Daredevil Danny through the Flaming Hoop Jump of Awesome, you will need to know the values of a, b, and c, which are the coefficients of the quadratic equation in standard form.

a) What is the equation for a parabola in standard form? (5 points)

y = ax^2 + bx + ct




b) Convert the vertex form of the equation you wrote above to standard form. (10 points)







c) What are the values for coefficients a, b, and c in the quadratic equation for Daredevil Danny’s practice jump? (5 points)






Step 4: Calculate the equation for the flaming hoop jump.

Using the same method for the practice jump, write the standard form of the equation that will get Daredevil Danny safely through the Flaming Hoop Jump of Awesome!

a) Write the vertex form by substituting in values for x, y, h, and k, and then solve for a. Show your work. (10 points)










b) Determine the values of a, b, and c. Show your work. (10 points)



c) Using your values of a, b, and c, did Daredevil Danny successfully pass through the Flaming Hoop Jump of Awesome? If not, describe what happened. Then, go back to critique your work and revise it. Write about your revision. (5 points)



d) Once you have determined the correct values of a, b, and c, verify algebraically that Daredevil Danny will successfully pass through the Flaming Hoop Jump of Awesome. (5 points)


Please help I only need help with steps 2 and 3!

 Which ordered pair is in the solution set of the system of linear inequalities graphed below?​

 

(0,2)

 

(2,4)

 

(-2,-4)

 

(-1,2)

4(1-x)+2x=-3(x+1) solve for X

Evaluate functions from their graph

Write an equation of the line that passes through (2, 7) and (0, −5).

estimated answer for 3 3/7 x 1 3/4 simplify and type a whole number​

25x 10 ^ 6 in standard form ​

The reciprocal of - 4 3/4 is

During game play, Juan threw 2 darts onto the board. Determine the likelihood of the scores Juan could get with his two throws. 4 or greater: 14: 16:

The Insurance Institute for Highway Safety publishes data on the total damage suffered by compact automobiles in a series of controlled, low-speed collisions. The cost for a sample of 9 cars, in hundreds of dollars, is provided below: 10,6,8,10,4,3.5,7.5,8,9 (a) What is the median cost of the total damage suffered for this sample of cars? (b) What is the first quartile for the above data? (c) What is the interquartile range of the above data? (d) What is the mean of the total damage suffered for this sample of cars? (e) Using the correct units, what is the value of the variance?

HELP ME PLEASE I ALREADY GRAPHED IT BUT PLEASE ANSWER THE QUESTION BELOW

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Jacob ordered 4 pizzas to be delivered.



Each pizza costs $12.75.
Jacob gave the driver an $8 tip when the pizzas were delivered.


Which of the following expressions could be used to determine Jacob’s total cost?


A. 4(12.75 + 8)
A., , 4(12.75 + 8)

B. 4(12.75 )+ 8
B., , 4(12.75 )+ 8

C. 4(8) + 12.75
C. , , 4(8) + 12.75

D. 4(12.75 − 8)
D. , , 4(12.75 − 8)

A large manufacturing company models the number of workers it hired each year after 2010 using the function shown on the graph.

Patricia and Emma work together. They both have the same amount of money invested in their portfolios. Their investments are listed in the table. Two months ago, the company Patricia and Emma work for started incurring losses, and now its share price has started falling. Which statement is correct given the scenario?

Patricia’s Investmentscompany stocks, bonds, mutual funds, domestic stocks, and international stocksEmma’s Investmentscompany stocks

A. 

Patricia’s portfolio will be affected the most because she has too many assets in her portfolio.

B. 

Emma’s portfolio will be affected the most because it is limited to company stock.

C. 

Neither portfolio will be significantly affected because both have a good mix of assets.

D. 

Both portfolios will be equally affected because both have an equal amount of company stock.



​

what is the branch of mathematics that uses variables and operations?

what is the slope of (-3,4) (-2,0)

Every Sunday, Tamika sells pieces of homemade fudge at a local carnival. Each piece of fudge weighs 34 pound. Next Sunday, Tamika plans on

bringing 712 pounds of homemade fudge to sell.

How many pieces of fudge will Tamika be able to sell at the carnival next Sunday?

There are 8 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible

Melissa averages a rate of 1.5 steps per second while walking. How many steps will she take in an hour if this rate continues?

What the area of 149m and 76m

. It takes 11 widgets to assemble one motor. Your team can assemble four motors in one day. If you need to order parts for next week (5 working days), how many widgets should you order?