A Ferris wheel with a radius of 13 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when the rider is 18 m above ground level?

Answer:

a). 9 weeks

b). 4 more weeks

Step-by-step explanation:

a). The cost of new bicycle = $155.75

     Amount I have with me   = $30

Therefore remaining amount = 155.75 - 30

                                                 = $ 125.75

Amount I will save in one week = $ 5

Amount my aunt will give me one week  = $ 10

Therefore total amount i will save in one week = 5 + 10

                                                                              = $ 15 in one week

Therefore number of weeks required to collect the remaining amount of $125.75 is  = 125.75 / 15

                   = 8.38 weeks

                  = 9 weeks

Thus 9 weeks are required to save money to buy a bicycle that cost $155.75

b). New cost the bicycle = $ 203.89

    From above at the end of 9 weeks I will have = $ 125.75

    Amount I have with me before = $ 30

   Therefore by the end of 9 weeks I have total amount = 125.75 + 30

                                                                                              = $ 155.75

  Therefore amount less = 203.89 - 155.75

                                         =  $ 48.14

  Number of weeks require to collect the remaining amount of $ 48.14 by saving  $ 15 in one week is = 48.14 / 15

                                             = 3.20 week

                                              = 4 weeks

Thus,  4 more weeks  is required to save money to buy a new bicycle that cost $ 203.89

It will take approximately 9 weeks to save enough money to buy the bicycle. It would take approximately 12 more weeks to save enough money for a bicycle that costs $203.89.

To determine how many weeks it will take to save enough money to buy a bicycle, we can set up an equation:

$30 + ($5 + $10)  imes x = $155.75

Where x represents the number of weeks. Now, we can solve for x:

$30 + $15x = $155.75

$15x = $125.75

x = $125.75 / $15 = 8.38

Since we can't have a fraction of a week, we can round up to the nearest whole number. So, it will take approximately 9 weeks to save enough money.

To determine how many more weeks you would have to save to buy a bicycle that costs $203.89, we can again set up an equation:

$30 + ($5 + $10)  imes x = $203.89

Now, we can solve for x:

$30 + $15x = $203.89

$15x = $173.89

x = $173.89 / $15 = 11.59

Rounding up to the nearest whole number, it would take approximately 12 more weeks to save enough money.

Answer:

40% of 20

Step-by-step explanation:

Final answer:

To solve this problem, you can set up a system of equations. There are 4 finches and 14 parrots.

Explanation:

To solve this problem, we can set up a system of equations based on the given information. Let's assume that the number of finches is 'x'. According to the problem, there are 2 more than 3 times as many parrots as finches. This can be written as:

Parrots = 3x + 2

Since the total number of parrots and finches is 18, we can set up another equation:

Parrots + Finches = 18

Substituting the first equation into the second equation, we get:

(3x + 2) + x = 18

Combining like terms, we have:

4x + 2 = 18

Subtracting 2 from both sides, we get:

4x = 16

Dividing both sides by 4, we find that:

x = 4

So, there are 4 finches and 3(4) + 2 = 14 parrots.

The unit is converted in new scale as 1 inch is equal to 9 feet.

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

For the given situation,

A rectangular sidewalk has a length = 21 feet

Scale factor, 1 inch = 7 feet.

So, 21 feet = [tex]\frac{21}{7}[/tex]

⇒ [tex]3[/tex] inches

The length of the actual side walk changes to 27 feet.

The length of actual side walk in inches = 3 inches.

Now, 1 inch = [tex]\frac{27}{3}[/tex]

⇒ [tex]1 inch = 9 feet[/tex]

Hence we can conclude that the unit is converted in new scale as 1 inch is equal to 9 feet.

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divide:

8/40 = 0.2

0.2 = 20%

Hi, here we want to "finish" a delta-epsilon proof.

We will find that the maximum delta is: δ = 0.02

We just want to find the value of δ such that:

[tex]|x - 1| < \delta[/tex]

Implies that:

[tex]|5x - 5| < \epsilon[/tex]

Well, let's start with the second expression:

[tex]|5x - 5| < \epsilon[/tex]

We can take the 5 out of the absolute value:

[tex]5*|x - 1| < \epsilon[/tex]

Now we can divide both sides by 5:

[tex]|x - 1| < \epsilon/5[/tex]

Now, if you look at the above expression, in the left side we have the same thing as in the delta inequality.

So for now we have:

[tex]|x - 1| < \epsilon/5[/tex]

[tex]|x - 1| < \delta[/tex]

From this is easy to conclude that the maximum value that delta can take is:

δ = ε/5

And we know that ε = 0.1, then we have:

δ = 0.1/5 = 0.02

δ = 0.02

The maximum value that delta can take is 0.02

Then we need to repeat it for ε = 0.01, so we get:

δ = 0.01/5 = 0.002

δ = 0.002

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divide 3 1/2 by 4

3 1/2 = 7/2

7/2 / 4 = 7/8 foot each

Answer:

[tex]\frac{7}{8}[/tex] feet.

Step-by-step explanation:

Four sister bought a total of ribbon = [tex]3\frac{1}{2}[/tex] feet

                                                           = [tex]\frac{7}{2}[/tex] feet

The sisters want to share the ribbon equally.

So we will divide the total length of the ribbon by 4.

= [tex]\frac{7}{2}[/tex] ÷ 4

= [tex]\frac{7}{2}[/tex] × [tex]\frac{1}{4}[/tex]

= [tex]\frac{7}{8}[/tex] feet.

Each sister will receive [tex]\frac{7}{8}[/tex] feet of ribbon.

Answer:

The correct option is B.

Step-by-step explanation:

In the given diagram, we have 6 boxes of -x and 6 box of 1 on the left hand side. It means,

[tex]LHS=6(-x)+6(1)=-6x+6[/tex]

We have 2 boxes of x and 9 box of -1 on the right hand side. It means,

[tex]RHS=2(x)+9(-1)=2x-9[/tex]

So, the equation represented by the given diagram is

[tex]-6x+6=2x-9[/tex]

[tex]-6x-2x=-9-6[/tex]

[tex]-8x=-15[/tex]

Dived both sides by -8.

[tex]x=\frac{-15}{-8}[/tex]

[tex]x=\frac{15}{8}[/tex]

The value of x is [tex]\frac{15}{8}[/tex]

Therefore the correct option is B.

Answer:

Step-by-step explanation:

They have 30 gallons of paint and for each hour that passes, they use 3 gallons of paint. Therefore, we can express that as a function:

y = -3x + 30

where y = gallons left

and x = hours passed

Therefore, the end points are (0, 30) and (10, 0)

Using our function when 0 hours has passed:

y = -3(0) + 30

y = 30

Therefore one endpoint is when x = 0 y = 30 or (0,30)

Using our function when 10 hours has passed:

y = -3(10) + 30

y = -30 + 30

y = 0

Therefore one endpoint is when x = 10 y = 0 or (10, 0)

The graph can be seen in the picture below.

The value of all things required to create a good or service are called inputs or factors of production. These include resources such as labor, materials, and machinery. Other related terms include productive efficiency, utility, sunk costs and physical capital per person.

The value of all things needed to create a good or service is referred to as the inputs or factors of production. These include resources like labor, materials, and machinery. For instance, to produce a car, the inputs would include the metal for the body, the labor to assemble the car, and the machinery to manufacture parts. Physical capital per person refers to the machinery and equipment available to help a person produce a good or service. The concept of productive efficiency comes in when it is impossible to produce more of one good without decreasing the quantity produced of another good. Utility represents the satisfaction, usefulness, or value one obtains from consuming goods and services. Sunk costs are costs that have been incurred in the past and cannot be recovered.

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The value of all things needed to create a good or service is referred to as the inputs or factors of production.

These consist of manpower, supplies, and equipment. For example, the inputs needed to construct an automobile would be labor to assemble the vehicle, machinery to make parts, and metal for the body.

The tools and machinery that can be used to assist a person in producing a good or service is referred to as physical capital per person. When it is difficult to generate more of one good without producing less of another good, the idea of productive efficiency enters the picture.

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Final answer:

Joyce read 1/6 of her book on Monday, 2/5 on Tuesday, and 1/3 on Wednesday. After converting to a common denominator and adding the fractions, she read 27/30 of her book, which simplifies to 9/10 or 90% of her book in total.

Explanation:

To find out how much of her book Joyce has read over three days, we need to add up the fractions of the book she read each day.

To calculate the total, we can first find a common denominator for the fractions, which in this case is 30. We then convert each fraction and sum them up:

After adding the fractions, we find that Joyce has read 27/30 of her book over the three days, which can be simplified to 9/10 if we divide both the numerator and the denominator by 3.

Therefore, Joyce has read 90% of her book by the end of Wednesday.

To find the Jacobian of the given transformation, we need to compute the partial derivatives of x and y with respect to u and v. The Jacobian matrix is a matrix that represents these partial derivatives.

To find the Jacobian of the transformation x = u^2 + uv and y = uv^2, we need to compute the partial derivatives of x and y with respect to u and v. Let's start with the partial derivative of x:

∂x/∂u = 2u + v

Now let's find the partial derivative of x with respect to v:

∂x/∂v = u

Using the same process, we can find the partial derivatives of y:

∂y/∂u = v^2

∂y/∂v = 2uv

Putting it all together, the Jacobian matrix is:

J(u, v) = [∂x/∂u, ∂x/∂v; ∂y/∂u, ∂y/∂v]

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The Jacobian of the transformation is [tex]\( uv(4u + v) \)[/tex].

The Jacobian of the transformation given by [tex]\( x = u^2 + uv \) and \( y = uv^2 \)[/tex] is determined by finding the determinant of the matrix of partial derivatives. The matrix of partial derivatives, known as the Jacobian matrix, is given by: [tex]J = \begin{bmatrix} \frac{\partial x}{\partial u} \frac{\partial x}{\partial v} \\ \frac{\partial y}{\partial u} \frac{\partial y}{\partial v} \end{bmatrix}[/tex]

We calculate each of the partial derivatives:

 [tex]\frac{\partial x}{\partial u} = \frac{\partial}{\partial u}(u^2 + uv) = 2u + v[/tex]

[tex]\frac{\partial x}{\partial v} = \frac{\partial}{\partial v}(u^2 + uv) = u[/tex]

[tex]\frac{\partial y}{\partial u} = \frac{\partial}{\partial u}(uv^2) = v^2[/tex]

[tex]\frac{\partial y}{\partial v} = \frac{\partial}{\partial v}(uv^2) = 2uv[/tex]

Now we can construct the Jacobian matrix: [tex]J = \begin{bmatrix} 2u + v u \\ v^2 2uv \end{bmatrix}[/tex]

The determinant of this matrix gives us the Jacobian of the transformation:

[tex]\text{Jacobian} = \text{det}(J) = (2u + v)(2uv) - (u)(v^2)[/tex]

[tex]\text{Jacobian} = 4u^2v + 2uv^2 - uv^2[/tex]

[tex]\text{Jacobian} = 4u^2v + uv^2[/tex]

[tex]\text{Jacobian} = uv(4u + v)[/tex]

Therefore, the Jacobian of the transformation is [tex]\( uv(4u + v) \).[/tex]

Using the equation, 98 hamburgers were sold on Saturday.

An equation is an equality relationship between two expressions written on both sides of the equal to sign.

Let the number of hamburgers sold be h and number of cheeseburgers sold be c.

Then we can formulate an equation

c = 3h

c + h = 392

3h + h = 392

4h = 392

h = 98

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Final answer:

To divide 0.4 by 0.02, transform the division problem into 40 divided by 2 by moving the decimal places to the right, resulting in the answer 20.

Explanation:

To solve the division of two decimal numbers, 0.4 divided by 0.02, you can follow these steps:

The division now looks like 40 ÷ 2, which equals 20.

So, 0.4 divided by 0.02 equals 20. This method allows us to divide decimal numbers by converting them into whole numbers, simplifying the calculation.

Answer:

80 women

Step-by-step explanation:

A ratio of men to women of 3:2 means that for 3 men that use the gym 2 women use the gym, so using a rule of three we can determinate how many women were on the gym that day if 120 men were there, like this:

  3 men   ------ 2 women

120 men  ------       X

[tex]X = \frac{(120men)(2women)}{3men}=80 women[/tex]

Then, there were 80 women for the 120 men that were in the gym.

1/2 is twice the sum of -2 and a number is the same as the number decreased by 7/2.

Given that we need to find the sum of -2 and a number is the same as the number decreased by 7/2.

Let's break down the problem and solve it step by step.

The problem states that twice the sum of -2 and a number is the same as the number decreased by 7/2.

Step 1: Assign a variable to the unknown number.

Let's say the unknown number is "x".

Step 2: Write the equation based on the given information.

Twice the sum of -2 and the unknown number is the same as the number decreased by 7/2.

This can be written as:

2(-2 + x) = x - 7/2

Step 3: Simplify the equation.

Multiply 2 by each term inside the parentheses:

-4 + 2x = x - 7/2

Step 4: Isolate the variable on one side of the equation.

To do this, we can subtract x from both sides of the equation:

-4 + 2x - x = x - 7/2 - x

Simplifying:

-4 + x = -7/2

To solve for x, we need to isolate it on one side of the equation.

We can do this by adding 4 to both sides:

-4 + 4 + x = -7/2 + 4

Simplifying:

x = 1/2

Therefore, the unknown number is 1/2.

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