The tortoise versus the hare: The speed of the hare is given by the sinusoidal function H(t) = sin(t) and the speed of the tortoise is T(t) = cos(t), where t is time measured in hours and the speed is measured in miles per hour. Find the area between the curves from time t = 0 to the first time after one hour when the tortoise and hare are traveling at the same speed. What does this area represent?
a. The total distance traveled by both the hare and tortoise during that time.
b. The difference in the distance traveled by the tortoise and hare during that time.
c. The average difference in velocity between the tortoise and hare during that time.
d. The difference in velocity between the tortoise and hare during that time.

Answer:

x = [tex]\frac{19+\sqrt{365}}{2}, \frac{19-\sqrt{365}}{2}[/tex]

Step-by-step explanation:

1. Move everything to one side of the equation.

x^2 - 19x - 1 = 0

2. Use the quadratic formula where a = 1, b = -19, and c = -1.

x = (-b +- sqrt(b^2-4ac)) / 2a

If you plug those numbers into that formula, you will get the result listed above

Answer:

B

x₁ = [tex]\frac{19-\sqrt{365}}{2}[/tex], x₂ = [tex]\frac{19+\sqrt{365} }{2}[/tex]

Step-by-step explanation:

Answer:

18.04/0.2 = 90.2

Step-by-step explanation:

X = 60 is 1 standard deviation above the mean.

X = 75 is 2.5 standard deviations above the mean.

X = 30 is 2 standard deviations below the mean.

To find the z-score for a particular X value, we use the formula:

z = (X - mean)/standard deviation

where X is the given value, mean is the population mean, and standard deviation is the population standard deviation.

For X = 60:

z = (60 - 50)/10 = 1

Therefore, the z-score for X = 60 is 1.

For X = 75:

z = (75 - 50)/10 = 2.5

Therefore, the z-score for X = 75 is 2.5.

For X = 30:

z = (30 - 50)/10 = -2

Therefore, the z-score for X = 30 is -2.

The z-score represents the number of standard deviations that a particular X value is away from the mean. Since the mean z-score is 0 and a positive z-score means that the X value is above the average.

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Answer:

16/64 and 1/4

Step-by-step explanation:

1/4 x 16/16 = 16/64

1 x 16 / 4 x 16 = 16/64

16/64 = 16/64

Answer:

i think the answer would be 156° .

hope it helps you ^.^

Answer: Car travels 36 miles on 1 gallon of gas

Step-by-step explanation:

[tex]\frac{12}{1}[/tex]   ÷  [tex]\frac{1}{3}[/tex]

12*3 (reciprocal)

36 ( car travels 36 miles on 1 gallon of gas )

Answer:

67

Step-by-step explanation:

complementary mean it equals 90 degrees

90-23 = 67

m<2=67

C. Reflected over the y-axis and translated up 1 unit

Answer:

The answer is C

Step-by-step explanation:

Answer:

10 3/25

Step-by-step explanation:

Answer:

81

Step-by-step explanation:

√x > 9

Squaring both sides, you will get

x > 81

Answer:

25.54

Step-by-step explanation:

somebody say it on the comments :)

The probability that a randomly selected point within the circle falls in the red-shaded area is 75.61%.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We need to find the probability that a randomly selected point within the circle falls in the white area.

We have been given the following parameters;

Radius r = 4 cm

a = 3.2 cm

S = 4.7 cm

The area of the circle A = πr²

A = π(4)²

A = 16π square cm

Here, The total number of outcomes = 16π square cm = 50.26 square cm

The side length of the pentagon a = 4.7 cm

The area of the pentagon can be calculated using:

Area = (1/4)√[5(5+2√5)]a²

Plug a = 4.7

Area = (1/4)√[5(5+2√5)](4.7)²

After calculating, we get;

Area = 38.01 square cm

The Total favorable outcomes = 38.01 square cm

The probability = 38.01/50.26

The probability = 0.7561

In percent,

The probability = 75.61%

Therefore, the probability that a randomly selected point within the circle falls in the red-shaded area is 75.61%.

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9514 1404 393

Answer:

  592 feet

  8.5 seconds

Step-by-step explanation:

The usual equation used for ballistic motion is ...

  h(t) = -16t^2 +h0

Here, we have h0=1168 and t=6, so ...

  h(t) = -16(6^2) +1168 = 592 . . . feet high after 6 seconds

__

For h(t) = 0, the value of t can be found from ...

  0 = -16t^2 +1168

  t^2 = 1168/16 = 73

  t = √73 ≈ 8.5

The object will reach the ground after 8.5 seconds.

Answer:

The cost of the bench is $475

Step-by-step explanation:

Let cost of garden table= x and cost of bench= y

x + y = 996 (eqn 1)

x - y = 46 (eqn 2)

eqn 1 + eqn 2

2x = 1042

2x/2 = 1042/2

x = 521

The cost of the garden table is $521.

Substitute x = 521 into eqn 1

x + y = 996

521 + y = 996

y = 996 - 521

y = 475

The cost of the bench is $475.

Answer: The correct answer is C

x-1/8y^2=0

Step-by-step explanation: i took the test and got it right

Answer:

P (F or C)  = 27/36= 0.75

Step-by-step explanation:

There are 36 vehicles in all.

There are total 26 cars.

There are total Ford vehicles which are 15 in number out of which 14 are cars. The results can be summarized as follows.

                           Cars                   Trucks            Total Vehicles

Ford                           14                           1                      15

Toyota                      7                              3                     10

Gm                            5                              6                     11                    

Total                        26                            10                     36      

As the events are composite

The probability of randomly selecting vehicle is either a Ford or a car is given by  P (F or C) = P(F) + P(c)- P(FC)

where P(F) is the probability of the Ford car and P (C) is the probability of the car.

P(F)= 15/ 36

P(C)= 26/36

P(FC)= 14/36

This is the additive rule applied for composite events.

P (F or C) = P(F) + P(c)- P(FC)

             = 15/36 + 26/36- 14/36

                = 27/36=0.75

Answer:

x=56º

Step-by-step explanation:

The cube tells us that 34º and x must equal 90º

So we use what we know to find the missing piece

90º=34º+x

-34º -34º

56º=x

Answer:56

Step-by-step explanation:90+34+x=180 because triangles angels sums up to 180 degrees

180-124=x

56=x

Answer:

73 is the correct answer

Step-by-step explanation:

I would pick 3 and 6

or C and F

Answer:

f=160

Step-by-step explanation:

all you really need to do is multiply 20 and 8 and you end up with 160

Answer:

32

Step-by-step explanation:

a door is rectangular in shape

area = length × breadth

8 × 4

32

answer:

The area of the door is 32 square ft

Answer:

0.73

Step-by-step explanation:I use khan too 0.7 is 10 times as great as 0.07

Answer:

r = 1.41 mm

Step-by-step explanation:

Given that,

The circumference of the flower, C = 8.9 mm

We need to find its radius. We know that,

Circumference, [tex]C=2\pi r[/tex]

Where

r is the radius of the object

[tex]r=\dfrac{C}{2\pi}\\\\r=\dfrac{8.9}{2\pi}\\\\r=1.41\ mm[/tex]

So, the radius of the object is equal to 1.41 mm.

Answer:

6,656 rabbits

Step-by-step explanation:

Population of rabbits = 26

Population doubles every 30 days

how many rabbits will be on the farm after 240 days?

t = 240 days / 30 days

= 8

Future Amount = 26(2)^t

=26(2)^8

= 26(256)

= 6,656

Therefore, the population of rabbits on the farm after 240 days is 6,656

Answer:

try to multiply the $400 to the interest and divided by $22.40

Answer:

10

Step-by-step explanation:

5+9+10+11+12+13=60 divided by 6 = 10

Mean = Sum of all observations/Number of observations

Mean = 12 + 13 + 9 + 5 + 11 + 10/6

=60/6

= 10

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Answer:

Perimeter of base = 18 ft

Height = 7 ft

Base area = 12ft²

SA= 150 ft² *

Step-by-step explanation:

Perimeter of base = 8+5+5=18 ft

Height = 7 ft

Base area = 1/2x8x3=12ft²

SA= (8x7)+(12+12)+2(5x7)=56+24+70=150 ft²

*There are several different way to figure out the surface area, so I’m not sure exactly how they want it displayed.  150 is the answer though.  Plus, I think there was supposed to be an addition sign between the first two parentheses.

Answer:

2923.34

Step-by-step explanation:

π×r²×h

3.14 ×7 ²×19 2923.34

2923.34

Step-by-step explanation:

the formula for the volume of a cylinder is V = 3.14 × radius squared × h. So 3.14 × 49 × 19 which equals 2924.82

Answer:

The defendant has offered to make annual payments of $23,000, $29,000, $56,000, and $84,000 to you each year over the next four years,

Answer:

a.) 4

Step-by-step explanation:

a.)4

Answer:

3 units

Step-by-step explanation:

There are 3 squares between them.