Which of these following lies between 6. 3 and 6. 6
6. 2
6. 9
6. 05
6. 41

The average power output of a bike rider at a speed of 20 miles per hour is 556 W

Given, Riding a bike burns 100 Calories per mile. Speed of riding a bike is 20 miles per hour. Power is a measure of the rate at which work is done over time.

Therefore, the formula for average power is given by,

P = W/t

Where, P is power, W is work and t is time.

Now, We know that riding a bike burns 100 Calories per mile, but we have to find out the work done.

So, work done = 100 Calories × distance traveled= 100 × 1.609 × 1000 = 160900 J

Time taken = distance/speed= 1.609/20 = 0.08045 hours

Putting values in the formula of power, we get,

P = W/t= 160900/0.08045= 1999999.9 J/hour

Converting hour to seconds,1 hour = 3600 seconds1 J/s = 1 watt1 J/hour = 1 / 3600 watt

Therefore, power = 1999999.9 / 3600= 555.5556 watts (approx)

Therefore, the average power output of a bike rider at a speed of 20 miles per hour is 556 W (approx). Answer: 556

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The coordinates of your position If we start at the origin, we are moving only along the x-axis  of  a distance of 7 units in positive direction and then only in the negative y-axis direction and  z-coordinate is zero are (7,-6,0).

The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.

The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).

The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).

Therefore, the coordinates of our position are (7, -6, 0)

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Answer: Differential Equation Initial Condition y' + y tan x = sec X + 9 cos x y(0) ... linear differential equation for x > 0 that satisfies the initial condition.

Step-by-step explanation:

4 10 + 40 100 is equivalent to 2/5 + 2/5, which simplifies to 4/5.

To find fractions that are equivalent to 4 10 + 40 100, we need to simplify the given fraction to its lowest terms.

First, we can simplify 4 10 by dividing both the numerator and denominator by the greatest common factor, which is 2. This gives us 2/5.

Next, we can simplify 40 100 by dividing both the numerator and denominator by the greatest common factor, which is 20. This gives us 2/5 as well.

Therefore, 4 10 + 40 100 is equivalent to 2/5 + 2/5, which simplifies to 4/5.

Now, to find fractions that are equivalent to 4/5, we can multiply the numerator and denominator by the same non-zero number.

For option A, 80/100 can be simplified to 4/5 by dividing both the numerator and denominator by 20. Therefore, A is equivalent to 4/5.

For option B, 4/5 is already in its simplest form, so B is equivalent to 4/5.

For option C, 20/100 can be simplified to 1/5 by dividing both the numerator and denominator by 20. Therefore, C is not equivalent to 4/5.

For option D, 8/10 can be simplified to 4/5 by dividing both the numerator and denominator by 2. Therefore, D is equivalent to 4/5.

In summary, options A, B, and D are equivalent to 4 10 + 40 100, while option C is not.

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The z-score for the 25th percentile of a standard normal distribution is approximately -0.625. Here option A is the correct answer.

To find the z-score for the 25th percentile of a standard normal distribution, we need to use a standard normal distribution table or calculator. The 25th percentile corresponds to a cumulative area under the standard normal curve of 0.25.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative area of 0.25 is about -0.68. This means that approximately 25% of the area under the standard normal curve lies to the left of -0.625.

So, among the given options, the correct answer is Option A, -0.625, Option D, -0.50, which is also incorrect. Option E, 0.00, is definitely incorrect because the 25th percentile is to the left of the mean.

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Answer:

x = -2 ,  y = 2

Step-by-step explanation:

hope this helps :)

In order to determine the rate at which the searchlight is rotating when the man is 15 ft from the point on the path closest to the searchlight, the following steps should be performed in this order

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The value of the additional data point is  [tex]$19.17$[/tex].

Let us first find the mean of the given data:

[tex]Mean = \frac{\sum_{i=1}^{n} x_i}{n}=\frac{39 + 45 + 43 + 42 + 44}{5}= 42.6[/tex]

Now let's find the value of the additional data point. Let the value of the additional data point be x. Therefore, the new sum of data is

[tex]$(39+45+43+42+44+x)$[/tex].

Total numbers of data are 6 (five given in the set and one additional data point).So, the mean of the resulting data set is given by:

[tex]32.083 = \frac{(39+45+43+42+44+x)}{6}[/tex]

Multiplying both sides of the equation by 6 we get:

[tex]6 \times 32.083 = (39+45+43+42+44+x)[/tex]

We have the value of [tex]$39+45+43+42+44$[/tex] which is [tex]$213$[/tex].

Therefore, substituting all the values, we get:

[tex]193.83 + x = 213[/tex]

On subtracting [tex]$193.83$[/tex] from both sides, we get the value of

[tex]x. x = 213 - 193.83 = 19.17[/tex]

Therefore, the value of the additional data point is [tex]$19.17$[/tex]

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Answer:

I gave a couple solutions as I wasn't sure if you were asking for graphing purposes or substituting y=-x+6 into the second equation 2x-y=-9. So I gave both solutions just in case.

for the first equation y=-x+6, y intercept is (0,6)

for equation two 2x-y=-9, y intercept is (0,9)

In both of the equations the x value is 1.

Solving for y without graphing. Y=9+2x

and x=-1

Step-by-step explanation:substitute i

HOWEVER, if you are saying that the top equation is the value of y, then you substitute it into the bottom equation. 2x--x+6=-9 which would be x=-5

It really depends on what is expected of the question. I wasn't sure which one, so I gave a couple different approaches. If you could give more information, such as, are you graphing, that would be great. I'll keep an eye out for any comments.

The amount of interest earned on $4,000.00 for 4 years, compounding daily at 4.5% APR, is $1,064.08.

To calculate the amount of interest on $4,000.00 for 4 years, compounding daily at 4.5% APR, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we have P = $4,000.00, r = 0.045, n = 365 (since interest is compounded daily), and t = 4. Plugging these values into the formula, we get:

A = $4,000.00(1 + 0.045/365)^(365*4)

A = $4,000.00(1.0001234)^1460

A = $4,889.68

The final amount is $4,889.68, which means that the interest earned is:

Interest = $4,889.68 - $4,000.00 = $889.68

We are given that the monthly interest table shows that $1.197204 in interest is earned for each $1.00 invested. Therefore, to find the interest earned on $4,000.00, we can multiply the interest earned by the factor:

$1.197204 / $1.00 = 1.197204

Interest earned = $889.68 x 1.197204 = $1,064.08

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The solution to the equation (3√x) - √(9x-17) = 1 is x = 9.

Given the equation in the question (3√x) - √(9x-17) = 1.

To solve for x in the given equation:

(3√x) - √(9x-17) = 1

We can start by isolating the square root term on one side of the equation. Adding √(9x - 17) to both sides, we get:

(3√x) = √(9x - 17) + 1

Squaring both sides of the equation, we get:

(3√x)² = (√(9x - 17) + 1)²

9x = -16 + 2√(9x - 17) + 9x

Solve for 2√(9x - 17)

2√(9x - 17) = 16

36x - 68 = 256

Add 68 to both sides

36x - 68 + 68 = 256 + 68

36x = 324

x = 324/36

x = 9

Therefore, the solution is x = 9.

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The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.

The rate at which the value of the computer system is changing 4 years after it was purchased is "Declining at the rate of $8,803.21 per year". The correct option is D.

We can use the exponential decay formula [tex]V(t) = V0 * e^{-kt}[/tex], where V(t) is the value of the computer system after t years, V0 is the initial value, and k is the decay rate.

We know that V(1) = $15,700 and V(0) = $28,000, so we can solve for k:

[tex]$15,700 = $28,000 * e^{-k*1}[/tex]

[tex]e^{-k} = 0.5607[/tex]

-k = ln(0.5607) ≈ -0.5797

k ≈ 0.5797

Therefore, the decay rate is approximately 0.5797 per year.

To find the rate of change of the value of the computer system 4 years after it was purchased, we can take the derivative of V(t) with respect to t:

dV/dt = -k * V0 * [tex]e^{-kt}[/tex]

Substituting t = 4, V0 = $28,000, and k ≈ 0.5797, we get:

dV/dt = -0.5797 * $28,000 * [tex]e^{-0.5797*4}[/tex] ≈ -$8,803.21 per year

Therefore, the value of the computer system is declining at the rate of approximately $8,803.21 per year 4 years after it was purchased.

The correct answer is (D) Declining at the rate of $8,803.21 per year.

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Hence, 28 toy soldiers are the correct answer.

A group in mathematics is created by combining a set with a binary operation. For instance, a group is formed by a set of integers with an arithmetic operation and a group is also formed by a set of real numbers with a differential operator.

Let's refer to the quantity of toy soldiers as "x".

We are aware that x is within the range of 27 and 54 thanks to the problem.

x can be divided by 4 without any remainders.

The residual is 6 when x is divided by 7.

The leftover after dividing x by five is three.

These criteria allow us to construct an equation system and find x.

Firstly, we are aware that x can be divided by 4 without any residual. As a result, x needs to have a multiple of 4. We can phrase this as:

x = 4k, where k is some integer.

Secondly, we understand that the remaining is 6 when x is divided by 7. This can be stated as follows:

x ≡ 6 (mod 7)

This indicates that x is a multiple of 7 that is 6 more than. We can solve this problem by substituting x = 4k:

4k ≡ 6 (mod 7)

We can attempt several values of k until we discover one that makes sense for this equation in order to solve for k. We can enter k in to equation starting using k = 1, as follows:

4(1) ≡ 6 (mod 7)

4 ≡ 6 (mod 7)

It is not true; thus we need to attempt a next value for k. This procedure can be carried out repeatedly until the equation is satisfied for all values of k.

k = 2:

4(2) ≡ 6 (mod 7)

1 ≡ 6 (mod 7)

k = 3:

4(3) ≡ 6 (mod 7)

5 ≡ 6 (mod 7)

k = 4:

4(4) ≡ 6 (mod 7)

2 ≡ 6 (mod 7)

k = 5:

4(5) ≡ 6 (mod 7)

6 ≡ 6 (mod 7)

k = 6:

4(6) ≡ 6 (mod 7)

3 ≡ 6 (mod 7)

k = 7:

4(7) ≡ 6 (mod 7)

0 ≡ 6 (mod 7)

We have discovered that the equation 4k 6 (mod 7) is fulfilled when k = 7. Thus, we can change k = 7 to x = 4k to determine that:

x = 4(7) = 28

This indicates that there are 28 toy troops. Yet we also understand that the leftover is 3 when x is divided by 5. We don't need to take into account any other values of x because x = 28 satisfies this requirement.

28 toy soldiers are the correct response.

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Answer:30

Step-by-step explanation: the formula is base x height over 2, so (6x10)/2 is 30.

If y is directly proportional to x, when x = 60, y = 6.

Proportional refers to a relationship between two quantities in which one quantity is a constant multiple of the other. In other words, if one quantity increases or decreases by a certain factor, the other quantity will also increase or decrease by the same factor.

Directly proportional is a specific type of proportionality where two quantities increase or decrease by the same factor. In other words, if one quantity doubles, the other quantity also doubles. If one quantity triples, the other quantity also triples, and so on.

In the given question,

If y is directly proportional to x, we can use the formula:

y = kx

where k is the constant of proportionality.

To find the value of k, we can use the given values:

y = kx

50 = k(500)

Solving for k:

k = 50/500

k = 0.1

Now that we know the value of k, we can use the formula to find the value of y when x = 60:

y = kxy = 0.1(60)

y = 6

Therefore, when x = 60, y = 6.

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Answer:

To calculate the distance between each pair of points given, we can use the distance formula which is derived from the Pythagorean theorem. The formula is:

distance = square root of [(x2 - x1)^2 + (y2 - y1)^2]

Using this formula, we can calculate the following distances:

a. Distance between M and P = 13 units

b. Distance between A and B = 5 units

c. Distance between C and D = 10 units

Answer:

2 9/14

Step-by-step explanation:

Answer:

18+m=24, 6

Step-by-step explanation:

You will get the first part by understanding that 24 is the whole and 18 is the part. Part + the other part, m, is the whole. You will then solve this by isolating the variable m, and subtracting 18 on both sides of the equation. Since 24-18=6, that is the final answer.

 The probability of [tex]3X1-1X2 + 3X3[/tex] being greater than 20 is given by[tex]P(3X1-1X2 + 3X3 > 20) = 1- Φ((20-3μ1+μ2-3μ3)/(√3σ11+σ22+3σ33))[/tex].

In this case, [tex]μ1=10, μ2=10, μ3=10, σ11=0.3, σ22=0.3, σ33=0.3,[/tex] so the probability of [tex]3X1-1X2 + 3X3[/tex] being greater than 20 is 1-Φ(-1.0).

1. To answer this question, we can use the formula for a multivariate normal distribution.

The probability of the profit for selling chocolate being greater than 6 million is given by P(X1 > 6) = 1- Φ(6-μ1)/(√σ11). In this case, μ1=10, σ11=0.3, so the probability of the profit being greater than 6 million is 1-Φ(2.667).

2. To answer this question, we need to use the formula for the conditional probability of a multivariate normal distribution.

The probability of the profit for selling chocolate being greater than 6 million, given the sales of marshmallow is 5 million and the sales of graham cracker is 5 million, is given by

[tex]P(X1>6 | X2=5, X3=5) = 1- Φ((6-μ1-Σ12*5-Σ13*5)/(√σ11-Σ12²-Σ13²))[/tex]. In this case,

[tex]μ1=10, σ11=0.3, Σ12=0.3, Σ13=0.3,[/tex]so the probability of the profit being greater than 6 million is 1-Φ(-0.1).

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Answer: 9, 10, and 11

Step-by-step explanation:

If the sum of three consecutive natural numbers is 30, then we can represent the smallest of the three numbers as x. The next two consecutive natural numbers would be x+1 and x+2. Therefore, we can form the equation:

x + (x+1) + (x+2) = 30

Simplifying the left-hand side, we get:

3x + 3 = 30

Subtracting 3 from both sides, we get:

3x = 27

Dividing by 3, we get:

x = 9

Therefore, the three consecutive natural numbers are 9, 10, and 11.

We can be 99% confident that the average number of miles an automobile is driven annually in Alabama is between 21,342.6 and 24,637.4 miles

To answer this question, we need to use the following formula for a confidence interval for the mean: CI = (μ - z*(σ/√n), μ + z*(σ/√n)), Where μ is the population mean, z is the z-score for the given confidence level, σ is the population standard deviation, and n is the sample size. Using the given information, we can calculate the confidence interval for the mean:CI = (23500 - 2.575*(3900/√100), 23500 + 2.575*(3900/√100)), CI = (21342.6, 24637.4)

To summarize, we used the formula for a confidence interval for the mean and the given information to calculate the confidence interval for the average number of miles an automobile is driven annually in Alabama. This confidence interval is (21342.6, 24637.4), which means we can be 99% confident that the average number of miles an automobile is driven annually in Alabama is between 21,342.6 and 24,637.4 miles.

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Answer:

668.376

Step-by-step explanation:

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To simplify 650 – 0.394 + 18.77, we can first add 650 and 18.77 since they're both whole numbers:

650 + 18.77 = 668.77

Then, we can subtract 0.394 from 668.77:668.77 - 0.394 = 668.376

Therefore, 650 – 0.394 + 18.77 simplifies to 668.376.

Step-by-step explanation:

x = +1

x = -2

x = -3

x = -4

Use number line to find the value and fit equation

The nearest hundredth, we get:

C ≈ 12.56 feet.

Circle circumference (or perimeter) = 2R

where R denotes the circle's radius. 3.14 is the approximate (up to two decimal points) value of the mathematical constant. Again, Pi () is a special mathematical constant that represents the circumference to diameter ratio of any circle.

The circumference of a circle is calculated as follows:

C = 2πr

where C is the circumference, (pi) is a constant close to 3.14, and r is the radius of the circle.

When the given values are substituted, the following results are obtained:

C = 2(3.14)(2) \s= 12.56

We get the following when we round to the nearest hundredth:

C ≈ 12.56 feet.

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Answer:

To solve the system of equations:

n + d = 21 ---(1)

0.05n + 0.10d = 1.70 ---(2)

We can use the substitution method by solving for one variable in terms of the other from equation (1) and substituting it into equation (2).

Solving equation (1) for n:

n = 21 - d

Substituting this expression for n into equation (2):

0.05(21 - d) + 0.10d = 1.70

Distributing the 0.05:

1.05 - 0.05d + 0.10d = 1.70

Combining like terms:

0.05d = 0.65

Dividing both sides by 0.05:

d = 13

Substituting this value of d into equation (1):

n + 13 = 21

Solving for n:

n = 8

Therefore, the solution to the system of equations is n = 8 and d = 13.

Answer:The prices of the adult movie tickets and the child movie tickets are $15 and $5 respectively.

Given that, the Jones family spent $45 on movie tickets for 2 adults and 3 children.

Step-by-step explanation:What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let cost of adult tickets be x and the cost of children tickets be c.

The Jones family spent $45 on movie tickets for 2 adults and 3 children.

2a+3c=45 ------(I)

The Smith family spent $40 for 2 adults and 2 children.

2a+2c=40

a+c=20 ------(II)

From equation (II), we have a=20-c

Substitute a=20-c in equation (I), we get

2(20-c)+3c=45

⇒ 40-2c+3c=45

⇒ c=$5

Put c=5 in equation (II), we get

a+5=20

⇒ a=$15

Answer:

2x - 13

Step-by-step explanation:

If x represents the greater number, then the other number is x - 13. The sum of these two numbers is:

x + (x - 13) = 2x - 13

Therefore, the net result of the transaction is a loss of $21.36. The answer is A) $21.36.

Selling price refers to the price at which a product or service is sold to customers or clients. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost of producing or acquiring the product or service, and the difference between the selling price and the cost is the profit earned by the seller. In some cases, the selling price may also include additional charges such as taxes, shipping fees, or handling fees.

by the question.

To calculate the net result of the transaction, we need to determine how many shares were purchased with the $3,200 investment.

$3,200 divided by $11.95/sh = approximately 267.36 shares (rounded to the nearest hundredth)

Therefore, the total cost of purchasing 267 shares at $11.95/sh is:

267 shares x $11.95/sh = $3,195.65

The total revenue from selling 267 shares at $11.87/sh is:

267 shares x $11.87/sh = $3,174.29

To determine the net result of the transaction, we subtract the total revenue from the total cost:

$3,174.29 - $3,195.65 = -$21.36

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