Ken runs 12 miles in a marathon. Every 3.5 miles, he stopes to take a drink. How many times does he stop during the marathon ?

Answer:

38 units

Step-by-step explanation:

We can find the perimeter of the shaded figure be finding out the number of unit lengths we have along the boundary of the given figure.

Thus, see attachment below for the number of units of each length of the figure that we have counted.

The perimeter of the figure = sum of all the lengths = 7 + 7 + 10 + 2 + 2 + 6 + 2 + 2 = 38

Perimeter of the shaded figure = 38 units

Answer:

The probability that the sample mean is less than 50 points = 0.002    

Step-by-step explanation:

Step(i):-

Given mean of the normal distribution = 56 points

Given standard deviation of the normal distribution = 12 points

Random sample size 'n' = 36 games

Step(ii):-

Let x⁻ be the random variable of normal distribution

Let x⁻ = 50

[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z = \frac{50-56 }{\frac{12}{\sqrt{36} } }= -3[/tex]

The probability that the sample mean is less than 50 points

P( x⁻≤ 50) = P( Z≤-3)

                = 0.5 - P(-3 <z<0)

               = 0.5 -P(0<z<3)

               =  0.5 - 0.498

               = 0.002

Final answer:-

The probability that the sample mean is less than 50 points = 0.002

Answer:

56

2

.001

Step-by-step explanation:

The Central Limit Theorem for Means states that the mean of any sampling distribution of the means is equal to the mean of the population distribution. The standard deviation is equal to the standard deviation of the population divided by the square root of the sample size. So, the mean of this sampling distribution of the means with sample size 36 is 56 points and the standard deviation is 1236√=2 points. The z-score for 50 using the formula z=x¯¯¯−μσ is −3.

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

-3.0 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001

-2.9 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001

-2.8 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002

-2.7 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003

-2.6 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004

-2.5 0.006 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005

Using the Standard Normal Table, the area to the left of −3 is approximately 0.001. Therefore, the probability that the sample mean will be less than 50 points is approximately 0.001.

Answer:

Step-by-step explanation:

a. The data should be analyzed using paired samples because the economist made two measurements (samples) drawn from the same pair of identical cards. Each data point in one sample is uniquely paired to a data point in the second sample.

b. A pair is made up of two identical cards where one would go into Dutch auction and the other to the first-price sealed bid auction.

c. The explanatory variables are the types of online auction which are the Dutch auction and the first price sealed bid auction. The explanation variable here is categorical: the Dutch auction and the first price sealed bid auction.

d. The response variable which is also known as the outcome variable is prices for the 2 different auction for each pair of identical cards. This variable is quantitative.

e. Null Hypothesis in words: There is no difference in the prices obtained in the two different online auction.

Alternative hypothesis: There is a difference in the prices obtained in the two different online auction.

f. The parameter of interest in this case is the mean prices of pairs of identical cards for both auction and is assigned p.

g. Null hypothesis: p(dutch) = p(first-price sealed auction)

Alternative hypothesis: p(dutch) =/ p(first-price sealed auction)

h. Assuming the p-value is 0.17 at an assed standard 0.05 significance level, our conclusion would be to fail to reject the null hypothesis as 0.17 is greater than 0.05 or even 0.01 and we can conclude that, there is no statistically significant evidence to prove that there is a difference in the prices obtained in the two different online auction.

Answer:

1/2

Step-by-step explanation:

There is a 50/50 chance for the coin to land either heads or tails. Convert that to probability and it is 1/2.

The only time a coin would not be 50/50 chance is if the coin is weighted.

Answer:

1/2 is probability

becoz one side is head or one is tail

Answer:

A≈166.45 in^2

Step-by-step explanation:

A=a^2+2a√(a2/4+h^2)

a = base = 8 in

h = height = 5 in

A = 8^2+16√(8^2/4+5^2) = 166.449... in^2

224

Step-by-step explanation:

because my teacher said it was right

Answer:

  22 m

Step-by-step explanation:

Use the formula for the area of a triangle. Fill in the known values and solve for the unknown.

  A = (1/2)bh

  594 m^2 = (1/2)(54 m)h

  h = (594 m^2)/(27 m) = 22 m

The height of the window is 22 meters.

Answer:

1937.98

Step-by-step explanation:

In the given question, to find the value to be added per year we will use the formula

P= A. r/n/ (1 +r/n)ⁿ - 1

Here A = 50,000

r (rate of interest) = 5 % or 0.05.

n = 1

t = 17

P = value deposit per year

therefore, P = (50,000 X 0.05)/ (1 +0.05)¹⁷ - 1

P =   2500 / 2.29- 1

= 1937.98 $.

therefore, person has to deposit 1937.98 $ per month.

Answer:

(x+9)/(8x+4)

Step-by-step explanation:

Answer:

x^2 - 10x

Step-by-step explanation:

2x^2 - 4x - x^2 +6x

You subtract x^2 from 2x^2 and you get x^2

Then you add 6x and 4x together and get 10x

So then you have x^2 - 10x

(plus I took the test and this was the correct answer.)

Answer:

1 : 500,000

Step-by-step explanation:

The scale of a map scale refers to the relationship (or ratio) between the distance on a map and the corresponding distance on the ground.

In the given map:

1 mm​(map) = 500 m ​(actual)

1 meter = 1000 millimeter

Therefore:

500 meters = 1000 X 500 =500,000 millimeter

Therefore, the scale ratio of the map is:

1:500,000

Step-by-step explanation:

1. 35 + 65

2. y - 14

3. (6 x s) - 3

4. 10(x+8.5).. 6-p

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly selected customer insures exactly one car, and that car is not a sports car?

Answer:

P( X' ∩ Y' ) = 0.205

Step-by-step explanation:

Let X is the event that the customer insures more than one car.

Let X' is the event that the customer insures exactly one car.

Let Y is the event that customer insures a sport car.

Let Y' is the event that customer insures not a sport car.

From the given information we have

70% of customers insure more than one car.

P(X) = 0.70

20% of customers insure a sports car.

P(Y) = 0.20

Of those customers who insure more than one car, 15% insure a sports car.

P(Y | X) = 0.15

We want to find out the probability that a randomly selected customer insures exactly one car, and that car is not a sports car.

P( X' ∩ Y' ) = ?

Which can be found by

P( X' ∩ Y' ) = 1 - P( X ∪ Y )

From the rules of probability we know that,

P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )    (Additive Law)

First, we have to find out P( X ∩ Y )

From the rules of probability we know that,

P( X ∩ Y ) = P(Y | X) × P(X)       (Multiplicative law)

P( X ∩ Y ) = 0.15 × 0.70

P( X ∩ Y ) = 0.105

So,

P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )

P( X ∪ Y ) = 0.70 + 0.20 - 0.105

P( X ∪ Y ) = 0.795

Finally,

P( X' ∩ Y' ) = 1 - P( X ∪ Y )

P( X' ∩ Y' ) = 1 - 0.795

P( X' ∩ Y' ) = 0.205

Therefore, there is 0.205 probability that a randomly selected customer insures exactly one car, and that car is not a sports car.

Question Completion

PIE CHART NUMBERS:

Answer:

0.000063

Step-by-step explanation:

Number of Respondents, n=1400

Probability that they would rate their financial shape as​ excellent = 0.09

Number of Those who would rate their financial shape as excellent

=0.09 X 1400

=126

Therefore:

The probability that 4 people chosen at random would rate their financial shape as​ excellent

[tex]=\dfrac{^{126}C_4 \times ^{1400-126}C_0}{^{1400}C_4} \\=\dfrac{^{126}C_4 \times ^{1274}C_0}{^{1400}C_4}\\=0.000063 $(correct to 6 decimal places)[/tex]

Answer:

3/2y - 5

Step-by-step explanation:

-1/2(-3y+10)

Expand the brackets.

-1/2(-3y) -1/2(10)

Multiply.

3/2y - 5

Answer:

[tex]= \frac{ 3y}{2} - 5 \\ [/tex]

Step-by-step explanation:

we know that,

[tex]( - ) \times ( - ) = ( + ) \\ ( - ) \times ( + ) = ( - )[/tex]

Let's solve now,

[tex] - \frac{1}{2} ( - 3y + 10) \\ \frac{3y}{2} - \frac{10}{2} \\ = \frac{ 3y}{2} - 5[/tex]

Answer:  a) base = 1 ft          b) height = 4 ft

Step-by-step explanation:

Set this up as a right triangle where base = x, height = 2x + 2, and hypotenuse (length of the ladder) = 13

Use Pythagorean Theorem to create a quadratic equation, factor, then apply the Zero Product Property to solve for x.

(x)² + (2x + 2)² = 13²

x² + 4x² + 8x + 4 = 169

        5x² + 8x - 165 = 0

       (5x + 13) (x - 1) = 0

       x = -13/5   x = 1

We know that distance cannot be negative so disregard x = -13/5.

The only valid answer is x = 1

base = x  --> x = 1

height = 2x + 2    --> 2(1) + 2 = 4

Answer:

The probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 [tex]\mu_{\hat p}=p[/tex]

The standard deviation of this sampling distribution of sample proportion is:

 [tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]

As the sample size is large, i.e. n = 492 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.

The mean and standard deviation of the sampling distribution of sample proportion are:

[tex]\mu_{\hat p}=p=0.07\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.07(1-0.07)}{492}}=0.012[/tex]

Compute the probability that the sample proportion will differ from the population proportion by greater than 0.03 as follows:

[tex]P(|\hat p-p|>0.03)=P(|\frac{\hat p-p}{\sigma_{\hat p}}|>\frac{0.03}{0.012})[/tex]

                           [tex]=P(|Z|>2.61)\\\\=1-P(|Z|\leq 2.61)\\\\=1-P(-2.61\leq Z\leq 2.61)\\\\=1-[P(Z\leq 2.61)-P(Z\leq -2.61)]\\\\=1-0.9955+0.0045\\\\=0.0090[/tex]

Thus, the probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.

Answer: 150

Step-by-step explanation:

How many months are in a year? 12.

The average rate per month is therefore 1800/12 = 150.

Hope that helped,

-sirswagger21

Answer:

Step-by-step explanation:

Let the number be x.

The reciprocal of the number will be 1/x

If the sum of the number and its reciprocal is 41/20, this can be represented as;

[tex]x+\frac{1}{x} = 41/20\\\frac{x^{2}+1}{x} = \frac{41}{20} \\20x^{2} +20 = 41x\\20x^{2} -41x+20 = 0\\[/tex]

Uisng the general formula to get x

x = -b±√b²+4ac/2a

x = 41±√41²-4(20)(20)/2(20)

x = 41±√1681-1600/40

x = 41±√81/40

x = 41±9/40

x = 50/40 or 32/40

x = 5/4 or 4/5

if the value is 5/4, the other value will be 4/5

The numbers are 5/4 and 4/5

The smaller value is 4/5

The larger value is 5/4

Answer:

a=5/4 or 4/5

Therefore, the smaller value = 4/5

The larger value = 5/4

Step-by-step explanation:

Let the number be represented by a

And it's reciprocal be represented by 1/a

So we have

a + 1/a = 41/20

Cross Multiply

20( a +1/a) = 41

20a +20/a =41

Find the LCM which is a

20a² + 20 = 41a

20a² + 20 - 41a =0

20a² - 41a +20 = 0

20a²-25a - 16a + 20 =0

5a(4a - 5) -4( 4a - 5) = 0

(5a - 4)(4a - 5) = 0

5a - 4 = 0

5a = 4

a = 4/5

or

4a - 5 = 0

4a =5

a = 5/4

Therefore, the number which is represented by a is

1) a = 4/5 while it's reciprocal which is 1/a is 5/4

or

2) a = 5/4 which it's reciprocal which is 1/a = 4/5

Therefore, the smaller value = 4/5

The larger value = 5/4

Answer:

If cosine theta < 0 and cotangent theta > 0, then the terminal point determined by theta is in: quadrant 3.

Step-by-step explanation:

hope this helps you :) my answer is the Step-by-step explanation: and the answer :)

Considering the signals of the sine and the cosine of the trigonometric function, it is found that it's quadrant is given by:

B. Quadrant 3

In this problem, we have that the cosine is negative, and the cotangent is positive. Cotangent is cosine divided by sine, hence if it is positive, both cosine and sine have the same signal, since cos < 0, sine is negative, they are in third quadrant and option B is correct.

More can be learned about the quadrants of trigonometric functions at https://brainly.com/question/24551149

#SPJ2

Answer:

It means in the middle of things, and Homer uses it in the Odyssey at the beginning of the epic because the story starts after the  Trojan War but before Ulysses gets back home.

Explanation:

Media res is a Latin phrase that means a situation where the narration starts in the middle of the story. In simple words, it means when a speaker talks about a story, starting with the middle of the plot but before the ending.

Likewise, Homer used this technique in his epic narrative story The Odyssey when he starts the story after the Trojan War and in the middle of the journey bur before the culmination of the story. Media res allows the middle of the plot to be the starting point and then gradually go back and forth in the narration between the past and the current/ situation.

Thus, the correct answer is the last or fourth option.

Answer:

x2 = 60

Step-by-step explanation:

If the variables x and y are inversely proportional, the product x * y is a constant.

So using x1 and y1 we can find the value of this constant:

[tex]x1 * y1 = k[/tex]

[tex]12 * 15 = k[/tex]

[tex]k = 180[/tex]

Now, we can use the same constant to find x2:

[tex]x2 * y2 = k[/tex]

[tex]x2 * 3 = 180[/tex]

[tex]x2 = 180 / 3 = 60[/tex]

So the value of x2 is 60.

Answer:

Y = 3√2 +4

Step-by-step explanation:

y = acosxº + b

Let's look for the values of a and b first.

Let's get values of x and y and solve simultaneously

When x= 0 ,y=10

When x = 120, y= 1

10 =acos0 + b

10 = a +b..... equation 1

1 = acos120 + b

1= -0.5a + b ..... equation 2

10 = a +b

1= -0.5a + b

10-1= a +0.5a

9 = 1.5a

9/1.5 = a

6 = a

1= -0.5a + b ..... equation 2

1 = -0.5(6) +b

1= -3 + b

1+3 = b

4 =b

So

y = acosxº + b equal to

Y = 6cosx° + 4

So value of y when x= 45 is

Y= 6cos45° +4

Y =6(√2/2) +4

Y = 3√2 +4

The value of y when x = 45 degree is,  [tex]y=3\sqrt{2}+4[/tex]

Given function is,

                            [tex]y = a cos(x)+ b[/tex]

From given table, It is observed that,

          x = 0, y = 10 and x = 90, y = 4

Substitute above values in above equation.

                          [tex]a+b=10\\\\b=4[/tex]

         [tex]a=10-b=10-4=6[/tex]

Now, our equation become,

                                [tex]y = 6 cos(x)+ 4[/tex]

Substitute x = 45 in above equation.

                  [tex]y=6cos(45)+4\\\\y=6*(\frac{\sqrt{2} }{2} )+4\\\\y=3\sqrt{2} +4[/tex]

Learn more:

https://brainly.com/question/13729598

Answer:

Step-by-step explanation:

Answer:

0.989

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they find a job in their chosen field within a year after graduation, or they do not. The probability of a graduate finding a job is independent of other graduates. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation.

This means that [tex]p = 0.53[/tex]

6 randomly selected graduates

This means that [tex]n = 6[/tex]

Probability that at least one finds a job in his or her chosen field within a year of graduating:

Either none find a job, or at least one does. The sum of the probabilities of these outcomes is 1. So

[tex]P(X = 0) + P(X \geq 1) = 1[/tex]

We want [tex]P(X \geq 1)[/tex]

So

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.53)^{0}.(0.47)^{6} = 0.011[/tex]

So

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.011 = 0.989[/tex]

Answer:

Determine if the expressions are equivalent.

when w = 11:

2w + 3 + 4     4 + 2w + 3

2(11) + 3 + 4    4 + 2(11) + 3

22 + 3 + 4      4 + 22 + 3

25 + 4      26 + 3

29        29

Complete the statements.

Now, check another value for the variable.

When w = 2, the first expression is  

11

.

When w = 2, the second expression is  

11

.

Therefore, the expressions are  

equivalent

.

Step-by-step explanation:

i did the math hope this helps

Answer:

Hii its Nat here to help! :)

Step-by-step explanation: A is 11 and b is 11.

C is Equal

Screenshot included.

Answer:

The diagram of the question is missing, I found a matching diagram, and it is attached to this answer

The 3D object produced is a cone with height 8 and diameter 8 (radius 4)

Step-by-step explanation:

A 3 dimensional solid figure can be formed when a 2 dimensional object is rotated about a line without displacing the object.

when the object in the diagram is rotated about line m, the rotation forms an object with a circular base of diameter 8 units (radius 4) from the base of the triangle and height 8 units, and the 3D object formed is called a cone.

Answer:

Step-by-step explanation:

-6y+4x=z

-6y=z-4x

y=(z-4x)/-6

Answer:

[tex]y=\frac{z-4x}{-6}[/tex]

Step-by-step explanation:

Answer:

[tex]7.98 \:m[/tex]

Step-by-step explanation:

Area of a triangle is base times height divided by 2.

[tex]A= \frac{bh}{2}[/tex]

[tex]69.6= \frac{b \times 17.45}{2}[/tex]

[tex]69.6 \times 2= b \times 17.45[/tex]

[tex]139.2=b \times 17.45[/tex]

[tex]\frac{17.45b}{17.45}=\frac{139.2}{17.45}[/tex]

[tex]b=\frac{2784}{349}[/tex]

[tex]b=7.97707[/tex]

The appropriate unit is meters.

Answer:

7.98 m

Step-by-step explanation:

Answer:

When you say that two numbers are relatively prime, it means that both numbers do not have a common factor except 1. Stephen is incorrect because 38 and 40 are both multiples of 2.

Answer:

Prime numbers are number that has its factors to be 1 and itself

38 and 40 are not prime because they have more than one factor

38 = { 1 , 2 , 19 , 38} and

40 = { 1 , 2 , 4 , 5 , 8 , 10 , 20 , 40 }

This make his statement incorrect.

Hope this helps.

Answer:

1) A = 0.79

B = 0.4708

2) CI = (0.7728, 0.8072)

3) CI = (0.4481, 0.4935)

b. It appears that the proportion of adults who feel this way in country A is more than those in country B.

Step-by-step explanation:

1) Sample proportions for both Population A and B

For country A:

Sample size,n = 1500

Sample proportion = [tex] \frac{1185}{1500} = 0.79 [/tex]

For Country B:

Sample size,n = 1302

Sample proportion = [tex] \frac{613}{1302} = 0.4708 [/tex]

2) Confidence interval for country A:

Given:

Mean,x = 1185

Sample size = 1500

Sample proportion, p = 0.79

q = 1 - 0.79 = 0.21

Using z table,

90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]

Confidence interval, CI:

[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]

[tex] = \frac{0.79 - 1.64}{\sqrt{(0.79 * 0.21)/1500}}, \frac{0.79 + 1.64}{\sqrt{(0.79 * 0.21)/1500}} [/tex]

[tex] CI = (0.7728, 0.8072) [/tex]

3) Confidence interval for country A:

Given:

Mean,x = 613

Sample size = 1302

Sample proportion, p = 0.4708

q = 1 - 0.4708 = 0.5292

Using z table,

90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]

Confidence interval, CI:

[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]

[tex] = \frac{0.4708 - 1.64}{\sqrt{(0.4708 * 0.5292)/1302}}, \frac{0.4708 + 1.64}{\sqrt{(0.4708 * 0.5295)/1302}} [/tex]

[tex] CI = (0.4481, 0.4935) [/tex]

From both confidence interval, we could see that that the proportion of adults who feel this way in country A is more than those in country B.

Option B is correct.