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.

Answers

Answer 1

Answer:

b. The difference in the distance traveled by the tortoise and hare during that time.

Step-by-step explanation:

First the intersection points are found out on the graph. Then the area between the curves is found out.

Putting the values

H(t) = sin(t)

H(t) = sin(1) = 0.01745

T(t) = cos(t),

T(t) = cos(1)= 0.9998

As T(t) ≥ H(t)

Area is found out by taking the integral of it.

Area = Integral ( limit 0 to 0.998)  T(t)-H(t) dt

The difference represents how far the turtle is from the hare.

So it represents the difference in the distance traveled by the tortoise and hare during that time.


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You and your friend skate at the same rate. You complete 7 laps in 9 minutes. How long does your friend take to complete 14 laps?

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Answer: 10=8 11=9 12=10 13=11 14=12 15=13 16=14 17=15

Step-by-step explanation:

Using complete sentences, explain the key features of the graph of the cosine function. (10 points)

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E⁣⁣⁣xplanation i⁣⁣⁣s i⁣⁣⁣n a f⁣⁣⁣ile

bit.[tex]^{}[/tex]ly/3a8Nt8n

A die and a coin are tossed together . Probability of getting a head on the coin is

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what? im very confused...i honestly dont know

Find the area of this parallelogram. Be sure to include the correct unit in your answer.

Answers

Answer:

66 sq.yd

Step-by-step explanation:

Given,

Base of the parallelogram = 11 yd

Height of the parallelogram = 6 yd

Therefore,

Area of the parallelogram = base × height

= 11 yd × 6 yd

[tex] = 66 {yd}^{2} [/tex]

Hence,

Area of the parallelogram is 66 sq. yd

Find the volume of a cone with a base diameter of 10 cm and a height of 9 cm

Answers

Answer:

235.71cm^2

Step-by-step explanation:

Volume of cone = 1/3 pie r^2 h

1/3*22/7*5*5*9

= 235.71cm^2

Volume of a cone is 235.6 cm³.

Why is the volume of a cone?The volume of a cone with height h and radius r is 1/3πr2h, which is exactly one third the volume of the smallest cylinder that it fits inside. This can be proved easily by considering a cone as a solid of revolution, but I would like to know if it can be proved or at least visual demonstrated without using calculus.  

The volume of a cone is calculated the using the formula:

[tex]V = \frac{1}{3} \pi r^{3} h[/tex]

Given,

         height of the cylinder is, h=9cm.

         The diameter of the base is 10cm. r = 5 cm

    put the values into the formula to get -

          V = [tex]\frac{1}{3} * \pi * 5^{2} * 9[/tex]

         [tex]V = 75 \pi[/tex]

Put value of π = 3. 14 ,

          V = 75 * 3.14

           V =  235.6 cm³

Therefore, Volume of a cone is 235.6 cm³.

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Need help on em punett sqaures

Answers

Answer:

Black Fur: 100%    White Fur: 0%

Step-by-step explanation:

    B     B

b  Bb  Bb              (all dominant)

b  Bb  Bb

Black Fur: 100%  White Fur: 0%

Answer:

B B

______

b | Bb | Bb |

b | Bb | Bb |

_____

Phenotype Probability (%):

Black Fur: 100%

White Fur: 0%

_____________________

Calculate the volume of the figure.
2 cm
3 cm
F
|
-
-
-
3 cm
3 cm
O 15 cm
33 cm
O 45 cm
O 54 cm
What is the value of x, if the volume of the sone i

Answers

Answer:

33 cm

Step-by-step explanation:

volume of the under the pyramid Is 3×3×3=27

volume of pyramid is 3×3×2=18

divide 18 ÷3 =6

27+6=33

the reason why we divide by 3 because ti's is the formula

Answer:

1. B 130 2/3ft^3

2. B 226 in^3

3. B 33 cm^3

4. A 4 m

5. D 15m

Step-by-step explanation:

I got a 100! For connexus students, hope this helps!!

Which statement is true about angle DCB and angle ACF

Answers

Answer: C. They are complementary but not necessarily congruent.

Answer: they are complementary but not necessarily congruent

Step-by-step explanation:

Find the slope of 3y = 6x + 4

Answers

Answer:
The slope or m is 2

Explanation:
The full answer is y = 2x + 4/3

Slope being 2 as y = mx + b

And the slope is m

VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.

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Answer: (4,-11)

Step-by-step explanation: To perform a 180 degree rotation we switch the signs of the coordinates

Answer:

4,-11

Step-by-step explanation:

The answer is 4,-11 because if you think that you go over -4 and go up 11. Now switch the negative sign to the y coordinate because it is a 180 degree turn then you have your answer. 4,-11

pls mark as brainliest!!

Halle el perimetro de las siguientes figuras. ​

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English please ?I can’t understand

What is the equation relating x and
y together?
X
1
2
3
4
5
-9
-8
-7
-6
-5
y=X-[ ?]

Answers

Answer:

If y=x-?, it'd have to be something like y=X-(1-10) etc.

Step-by-step explanation:

I don't think you're giving us enough, but that should be what it is, try to associate that with the full problem or format.

3
S
1+ 305
[tex]3 - \sqrt{5 } \div 1 + \sqrt[3]{5} [/tex]

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Step-by-step explanation:

can you throw more light on what you want us to find?

What number should be added to both sides of the equation to complete the square? x-^2+8x=4

Answers

Answer:

2.

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Evaluate the expression below when x = 2 and z = 12. z + 5x^3

Answers

Answer:

52

Step-by-step explanation:

z + 5x ^3

12 + 5*(2^3)

12 + 5 * 8

12 + 40

52

You can get 6 tickets for $39 at the local movie theater. How much is each ticket? ​

Answers

Answer:

$6.50

Step-by-step explanation:

39 / 6 = 6.5

Answer:

$6.50

Step-by-step explanation:

Hi,

To get the cost per ticket, all you have to do is divide 39 by 6. When you do that you get, 6.5 which means each ticket costs $6.50.

I hope that helps :)

Solve 58 - 10x * 20 * 9x.
O A rs-2
B. X-2
C. XS2
O D. x22

Answers

The answer to your question might be B

In a recent survey by the National Association of Colleges and Employers, the average starting salary for college graduate with a computer and information sciences degree was reported to be $62,194.40 You are planning to do a survey of starting salaries for recent computer science majors from your university. Using an estimated standard deviation of $11,605, what sample size do you need to have a margin of error equal to $5000 with 95% confidence

Answers

Answer:

A sample size of 21 is needed.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

Using an estimated standard deviation of $11,605

This means that [tex]\sigma = 11605[/tex]

What sample size do you need to have a margin of error equal to $5000 with 95% confidence

A sample size of n is needed. n is found when M = 5000. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]5000 = 1.96\frac{11605}{\sqrt{n}}[/tex]

[tex]5000\sqrt{n} = 1.96*11605[/tex]

[tex]\sqrt{n} = \frac{1.96*11605}{5000}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*11605}{5000})^2[/tex]

[tex]n = 20.69[/tex]

Rounding up,

A sample size of 21 is needed.

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Examine the following equation.
2x² – 5x – 7 = 0
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0 5+787
4
-5+781
4
0 -53731
4
5:31
4

Answers

The expression which can be used to find the solutions of the given equation is option (a) [5 ± √81] / 4.

What are Quadratic Equations?

Quadratic equations are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

The given quadratic equation is,

2x² - 5x - 7 = 0

The solutions of a quadratic equation can be found using the quadratic formula.

Quadratic formula for ax² + b x + c = 0 is,

x = [-b ± [tex]\sqrt{b^2-4ac}[/tex] ] / 2a, where [tex]\sqrt{b^2-4ac}[/tex] is called discriminant.

From the given equation,

a = 2, b = -5 and c = -7.

Solution can be found as,

x = -(-5) ± [tex]\sqrt{(-5)^2-(4*2*-7)}[/tex] ] / (2 × 2)

  = [5 ± √(25 + 56) ] / 4

  = [5 ± √81] / 4

Hence the solution can be found as [5 ± √81] / 4.

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MAFS.4.0A.1.2
2. Eddie has 50 marbles. Manny has m marbles. If Eddie
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E = 10 * m
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Simplify 15 – 3(6 – 4)

Answers

Answer:

9

Step-by-step explanation:

15-3(6 -4)

=15-3(2)

=15-6

=9

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Answer:

9

Step-by-step explanation:

Solve for x. Assume that lines which appear tangent are tangent.

Answers

Answer:

Step-by-step explanation:

In a scale drawing, Matt's dining room measures 6 inches long by 4 inches wide. The actual length of the dining room is 12 feet. What is the actual width of the dining room?

Answers

Answer:

8

Step-by-step explanation:

make a ratio

length of scale/width of scale=length of real/width of real

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x=8

Hope that helps :)

4.
In order to purchase a new CD player, Rosa must
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Answers

M >= 85. The >= sign means greater than or equal to.

ORDER THE SIDE LENGTHS FROM LEAST TO GREATEST


help pls asap

Answers

Answer:

m<K, m<J, m<I

Step-by-step explanation:

The size of angles and sides correspond. The larger the side, the larger the angle must be. So, this means the largest angle will be directly across from the longest side. Since <K is across from the smallest side, it is the smallest angle. Additionally, <I is across from the longest side so it is the largest.

HELP ME Look at the photo,

Answers

Answer:

I believe... x=12

Step-by-step explanation:

5x = 4x + 12

5x - 4x = x

therefore, x = 12

hope this helps :)

Simone asked her classmates, "How many days do you floss your teeth in a
typical week?" The table shows Simone's data.
Days of Flossing per Week
6
3
1
4
3
3
5
6
6
7
7
6
5
3
2.
4
0
4.
5
7
1
2
6
7
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Answers

Answer:

24

Step-by-step explanation:

Count the amount of answers she got.

Can someone help me? A: How long did it take Diane to complete her route on Thursday if, on average, it took her 46 minutes?

Answers

Answer: B.) 43

I just did it on usatestprep and I got 43

Step-by-step explanation:

The solution is Option B.

The time it took for Diane to complete her route on Thursday is given by the equation T = 43 minutes

What is Mean?

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the mean of the data be represented as M = 46 minutes

The time it took for Diane to complete her route on Thursday be T

Now , the total time for all the 7 days be represented as S

And , the value of S is

S = 58 + 39 + 42 + 46 + T + 49 + 45

S = 279 + T

Substituting the values in the equation , we get

Mean = Sum of Values / Number of Values

46 = ( 279 + T ) / 7

Multiply by 7 on both sides of the equation , we get

322 = 279 + T

Subtracting 279 on both sides of the equation , we get

T = 322 - 279

T = 43 minutes

Hence , the value of T is 43 minutes

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Which ordered pair is a solution to the system

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Answer:

I think it might be this one(-2,0)

i believe the answer is either one or third option. good luck.

Find the future value and interest eared if $8906.54 is invested for 8 years at 5% compounded semiannually

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Answer:

ummm yes 19293

Step-by-step explanation:

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