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:

a. 72

b. 816

c. 570

d. 30

Step-by-step explanation:

Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.

Please refer the figure for a better understanding.

a. In a normal distribution, Mean = Median = Mode

Therefore, Median = Mean = 72

b. We have to know that 68% of the values are within the first standard deviation of the mean.

i.e., 68% values are between Mean  Standard Deviation (SD).

Scores between 63 and 81 :

Note that 72 - 9 = 63 and

72 + 9 = 81

This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.

Now, Scores between 63 and 81 =  

= 68 X 12 = 816.

That means 816 students have scored between 63 and 81.

c. We have to know that 95% of the values lie between second Standard Deviation of the mean.

i.e., 95% values are between Mean  2(SD).

Note that 90 = 72 + 2(9) = 72 + 18

Also, 54 = 63 - 18.

Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to  of the values.

Therefore, Scores between 72 and 90 =  

= 570.

That is a total of 570 students scored between 72 and 90.

d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.

In this case, 5 % of the values lie between below 54 and above 90.

Since, we are asked to find scores below 54. It should be 2.5% of the values.

So, Scores below 54 =  

= 2.5 X 12 = 30.

That is, 30 students have scored below 54.

Step-by-step explanation:

It is found that score of 62 is not within one standard deviation of the mean.

The Z-score measures how many standard deviations the measure is from the mean. If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have  [tex]X \sim N(\mu, \sigma)[/tex]then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

In a set with mean and standard deviation, the z- score of a measure X is given by:

[tex]Z = \dfrac{X - \mu}{\sigma},[/tex]

Z-score, we look at the z-score table and find the p-value associated with this z-score.

Given that Mean score of 54 and a standard deviation of 6.

This means to see if a score of 62 is within one standard deviation of the mean.

Is Z between -1 and 1 when X = 62.

[tex]Z = \dfrac{X - \mu}{\sigma},\\Z = \dfrac{62 - 54}{6},[/tex]

Z = 1.33

Therefore, It is found that score of 62 is not within one standard deviation of the mean.

Learn more about z-score here:

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Answer:

18

Step-by-step explanation:

You would divide 48 by 8 and multiply it by 3. Otherwise, you could do

3/8 = x/48

x * 8 = 3 * 48

x * 8 = 144

 /8        /8

x = 18

Answer: He should have 12 lemons left

Step-by-step explanation:

Option:

a. for every 13 dogs, there are 25 cats.

b. there are twice as many cats as dogs at the shelter.

c. the shelter has more dogs than cats.

d. there are 25 animals in the shelter.

Answer:

a. for every 13 dogs, there are 25 cats.

Step-by-step explanation:

Represent Dogs with D and Cats with C;

So;

[tex]\frac{D}{C} = \frac{13}{25}[/tex]

By comparison:

[tex]D=13[/tex]

[tex]C = 25[/tex]

This implies that:

For every 13 D, there are 25 C

Hence: Option A is true

Answer:

1050 fish

Step-by-step explanation:

175(6 tanks) = 1050

Answer:

3

Step-by-step explanation:

X=12 Y=3^2

Y^2=3x3 Which equals 9 therefore it is 12-9 which equals 3

Answer:

I believe the answer would be 3.

Step-by-step explanation:

I hope this helps

Answer:

50 minutes

Step-by-step explanation:

First set up an inequality to find you answer like

800 - 6x = 1000 - 10x

then subtract 800 from both sides leaving you with

-6x = 200 - 10 x

Then add 10 x to both sides giving you

4x = 200

The simplify from here by dividing 200 by 4

200/4 = 50 giving you your answer

Answer:

4.80961924

Step-by-step explanation:

Answer:

ans = 6x4

Step-by-step explanation:

(2x2)(3x2)

first multiply the coefficients

(2*3) = 6

next multiply the variables

(x2*x2) = x2+2 = x4

productofcoeficients,productofvariables

= 6x4

Answer:

The 98% confidence interval of the proportion = (0.312, 0.374)

Step-by-step explanation:

(Give answers accurate to 3 decimal places.)

The formula for Confidence Interval of Proportion is given as:

p ± z × √p(1 - p)/n

Where p = Proportion = x/n

x = 440

n = 1282

p = 440/1282 = 0.34321372854

Approximately = 0.343

z = z-score of 98 % confidence interval

= 2.326

Confidence Interval =

= 0.343 ± 2.326 × √0.343(1 - 0.343)/1282

= 0.343 ± 2.326 × √0.225351/1282

= 0.343 ± 2.326 × √0.00017578081

= 0.343 ± 2.326 × 0.01325823555

= 0.343 ± 0.03083865589

0.343 - 0.03083865589

= 0.31216134411

Approximately = 0.312

0.343 + 0.03083865589

= 0.37383865589

Approximately to = 0.374

Therefore, the 98% confidence interval of the proportion = (0.312, 0.374)

Answer:

the answer is 7.5

Answer:

2bags= $14 + $5

3bags= $21+ $5

4bags= $28 + $5

5bags= $35 + $5

6bags= $42 + $5

multiply # of bags by 7

and add $5

Answer:

0.5

Step-by-step explanation:

use rise over run, from (-6,0) to (0,3) it rises 3 and runs 6. 3/6 = 1/2.

Answer:

the slope is two

Step-by-step explanation:

rise over run

Answer:

x=22

Step-by-step explanation:

180-77=103

103+55=158

180-158=22

x=22

Answer: the answer is f

Answer:

F

Step-by-step explanation:

the measure of angle one must be equal to the measure of angle five and when doing the math I got x=34 plug that into the equation for angle five i got 48 and the same for plugging it into the equation for angle one.

Here is the complete question

1. State coordinates of x axis

2. State coordinates of y axis

3. State the slope

4. Graph the function

5. Is learning rate increasing or decreasing?

Answer:

1. (50,0)

2. (0,20)

3. Slope = -0.4

4. Check attachment for graph

5. Learning rate is decreasing

Step-by-step explanation:

1.

L(x) = 20-0.4x

20 = 0.4x

x = 20/0.4

x = 50

(50,0)

2

For y coordinate;

L(0) = 20-0.4(0)

= 20

(0,20)

3.

Slope,

Y = -0.4x+20

We compare with

Y = mx+c

m = -0.4

Intercept c = 20

4. Check attachment

5. The slope is negative at m = -0.4 therefore the rate of learning is on a decline. As number of words learnt increases, learning rate falls.

Answer:

Step-by-step explanation:

Answer:

ANSWER IS A I THINK

Step-by-step explanation:

Answer:

32 Horses

Step-by-step explanation:

32-8=24

There are 32 horses and 24 sheep (As you can see there are 8 fewer sheep than horses)

I sort of guess and checked:

Answer:

2 x intercepts

Step-by-step explanation:

math go brrr

Answer: the asnwer is three

Step-by-step explanation: well theres your answer

Answer:

Step-by-step explanation:

Area of a square = Length * Length

Given

Length of garden = 7.4feet

Area of the square = 7.4 * 7.4

Area of the square  = 54.76 ft²

Hence the area of the garden is 54.76 ft²

Answer:

This vector make an angle of 141° with the positive x axis

Step-by-step explanation:

Refer the attached figure

Components of vector :

[tex]A_x=-10 \\A_y = 8[/tex]

We are supposed to find  What angle does this vector make with the positive x axis

[tex]tan \theta =\frac{A_y}{A_x}\\tan \theta =\frac{8}{-10}\\\theta =tan^{-1}(\frac{8}{-10})\\\theta =tan^{-1}(\frac{8}{-10})=-38.65^{\circ}[/tex]

Now ,

[tex]\alpha = 180-38.65=141.35^{\circ}[/tex]

So, this vector make an angle of 141° with the positive x axis

Answer:

13.2 miles/ 1.6 hours= 8.25 miles/hour.Mr. Phillips's speed was 8.25

Answer:

b, c, f are coorrect inequalities

Step-by-step explanation:

hope i helped :D

Answer:

The  value is  [tex]P(A) =  0.133617[/tex]

Step-by-step explanation:

From the question we are told that

  The  mean is  [tex]\mu =  7.5[/tex]

  The standard deviation is  [tex]\sigma  =  0.2[/tex]

  The safest water level is  between  7.2 and  7.8

Generally the probability that the selected pool has a pH level that is not considered safe is mathematically represented as

       [tex]P(A) =  1 - P(7.2 \le X  \le 7.8 )[/tex]

Here  

      [tex]P(7.2 < X  < 7.8 ) = P(\frac{ 7.2 - \mu }{\sigma } <  \frac{X - \mu }{ \sigma } <\frac{ 7.8 - \mu }{\sigma }   )[/tex]

Generally [tex]\frac{X - \mu }{ \sigma } =  Z (The  \ standardized \  value  \  of  X )[/tex]

So

 [tex]P(7.2 < X  < 7.8 ) = P(\frac{ 7.2 - 7.5 }{0.2 } < Z <\frac{ 7.8 - 7.5 }{0.2 }   )[/tex]    

 [tex]P(7.2 < X  < 7.8 ) = P(-1.5 < Z <1.5)[/tex]  

=>  [tex]P(7.2 < X  < 7.8 ) = P(Z <  1.5) - P(  Z < - 1.5) [/tex]

From the z-table the probability of  (Z <  -1.5) and   (  Z <1.5)  are

    [tex]P(Z <  1.5) =  0.93319[/tex]

and  

    [tex]P(Z <  -1.5) =  0.066807[/tex]

So

      [tex]P(7.2 < X  < 7.8 ) =0.93319 - 0.066807 [/tex]

       [tex]P(7.2 < X  < 7.8 ) =0.0866383[/tex]

So

   [tex]P(A) =  1 - 0.0866383[/tex]

=>  [tex]P(A) =  0.133617[/tex]

The probability that the selected pool has a pH level that is not considered safe pool is 0.1336

The given parameters are:

[tex]\mathbf{\mu = 7.5}[/tex]

[tex]\mathbf{\sigma = 0.2}[/tex]

Start by calculating the probability that a pool is safe.

This is represented as: P(7.2 < x < 7.8)

Calculate the z-scores for x =7.2 and 7.8 using:

[tex]\mathbf{z = \frac{x - \mu}{\sigma}}[/tex]

So, we have:

[tex]\mathbf{z = \frac{7.2 - 7.5}{0.2} = -1.5}[/tex]

[tex]\mathbf{z = \frac{7.8 - 7.5}{0.2} = 1.5}[/tex]

So, we have:

[tex]\mathbf{P(7.2 < x < 7.8) = P(-1.5 < z < 1.5)}[/tex]

This gives

[tex]\mathbf{P(7.2 < x < 7.8) = P(z < 1.5) - P(z < -1.5)}[/tex]

Using z table of probabilities, we have:

[tex]\mathbf{P(7.2 < x < 7.8) =0.9332 - 0.0668}[/tex]

[tex]\mathbf{P(7.2 < x < 7.8) =0.8664}[/tex]

The probability that the pool is not safe is calculated using the following complement formula

[tex]\mathbf{P(Not\ Safe) = 1 - P(Safe)}[/tex]

So, we have:

[tex]\mathbf{P(Not\ Safe) = 1 -0.8664}[/tex]

[tex]\mathbf{P(Not\ Safe) = 0.1336}[/tex]

Hence, the probability that the pool is not safe is 0.1336

Read more about probabilities at:

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Answer:

30=-4x+12

Step-by-step explanation:

they both equal -9/2

Answer:

10

Step-by-step explanation:

Answer:

eat well don't forget to eat your dinner okay