1.079 fl qt = ? ml. My book says that 1L = 1.057 fl qt. but how do i get the L to ml.

Solution:

1. 1L = 1.057 fl qt
2. 1L = 1000 ml
3. 1.079 fl qt = 1.079 x 1.057 L = 1.140503 L
4. 1.140503 L = 1140.503 ml

X has 5 base-ten blocks. She models a number that is less than 999. The number she models has a zero in the tens place and a zero in the ones place. What number is she modeling?

Solution:

Base ten blocks are a mathematical manipulative used to learn basic mathematical concepts including addition, subtraction, number sense, place value and counting. You can manipulate the blocks in different ways to express numbers and patterns. Generally, the 3-dimensional blocks are made of a solid material such as plastic or wood and come in four sizes to indicate their individual place value: Units (one’s place), Longs (ten’s place), Flats (hundred’s place) and Big Blocks (thousand’s place). There are also computer programs available that simulate base ten blocks.

Since the number that is being modeled has a zero in the tens place and a zero in the ones place, there are no Longs or Units. Since the number is less than 999, there are no Big Blocks. That leaves only Flats, and there must be five Flats. Since each Flat represents one hundred, the number must be 500.

The ritz carlton hotel used a customer opinion questionare to obtain performing data about its dining and entertainment services. Customers were asked to rate six factors: Welcome, Service, food, menu, appeal, atmosphere and overall experience. Data were recorded for each factor 1 for fair 2 for average and 3 for good and 4 for excellent a) The customers response provided data for six variables. Are the variables quantative or qualitative? b) What measurement of scale if used?

Solution:

1. A quantitative variable is a phenomenon measured in amounts, that is, numerical units. For example, a numerical score is a quantitative variable.
2. The measurement is based on a scale of 1 to 4.

N-3/8=6

Solution:

If Utility Function is Expressed as U(x,y) = x^0.5 y^0.5 What is the Marginal Utility at Point (64,25) and (49,36)? Treat Y as a Constant. Would the Answer be MUx(x,y) = y. MUx(64,25) = 5 ? and MUx(49,36) = 6?

Solution:

MUx(x,y) =     Derivative of U(x,y), treating y constant.

MUx(64,25) =

MUx(49,36) =

Is 288/1155 in Lowest Terms

Solution:

1. First, factorize the numerator using prime numbers: 288 = 2*12*12 = 2*3*4*3*4=2*2*2*2*2*3*
2. Second, factorize the denominator: 1155 = 5*231=5*7*33 = 5*7*3*11
3. Notice that the numerator and denominator have only one factor in common (3).
4. Restate the ratio after removing the common factor
   1. New numerator = 2*2*2*2*2*3 = 96
   2. New denominator = 5*7*11 = 385
   3. Same ratio in lowest terms: 

What Experiment Have 3 Types of Variables?

Solution:

A scientific experiment has three types of variables: independent, dependent and controlled. Please click on this link to get details: http://www.sciencebuddies.org/mentoring/project_variables.shtml.

Factor These: 2w^2-5w-10

Solution:

We can factor the expression  as follows:  

To figure this out, we used the quadratic formula (see http://en.wikipedia.org/wiki/Quadratic_equation):

w = 

We recognized that y=  is a quadratic equation in the form of y=  where a=2, b=-5 and c=-10.

To confirm that our calculation are right, we decided to plot the graph of y = by plugging in various values of w.

As you can see, there is a root at approximately -1.3 and another root at approximately +3.8. So we know approximately what the values of a and b are. We could use a calculator to get closer and closer to the exact values of a and b. For example, if we try w=3.8, we get a value of y = -0.12. If we try a slightly different value, we can see if we’re getting closer to zero or farther away: w=3.81 produces a value of y=-0.018, so we know that 3.81 is a better approximation than 3.8. If we keep calculating closer approximations of the root, we will arrive at the value of b that we calculated using the quadratic formula:

Use Mathematical Induction to Prove That the Statements are true for Every Positive Integer n. 1*3+2*4+3*5+⋯+n(n+2)=n(n+1)(2n+7)/6

Solution:

First, let’s make sure we understand what we mean by “mathematical induction”: “Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers. It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one.” (Wikipedia) We have pasted below another more detailed explanation of how to create a proof using mathematical induction (see “Appendix” below).

Let’s now take the equation you provided: 1*3+2*4+3*5+…+n(n+2)=

We can show that this is true for n=1:         1*3 = = = 3

Now let us assume that the statement is true for n = k. If it is, then we will prove that it has to be true for n=k+1:

WTS è =       +

=    + 

= 

=

=

=

=       QED

In the above proof, WTS means “want to show” and QED means “quod erat demonstratum” (“which was to be demonstrated”).

Appendix

Here’s another more detailed explanation of how to create a proof using mathematical induction:

A Jeweler Needs to mix an Alloy with 16% Gold Content & an Alloy with a 28% Gold Content to Obtain 32oz. of a new Alloy with a 25% Gold Content. How Many oz. of Each of the Original Alloys Must be Used?

Solution:

• A = number of ounces of the first alloy
• B = number of ounces of the second all
• A+B=32
• 0.16 A +0.28 B = 32 x 0.25
• Since A + B = 32, we know that A = 32 – B. You can then re-write the equation above as 0.16 (32-B) + 0.28 B = 32 x 0.25
• This can be simplified to 5.12- 0.16 B + 0.28 B =8
• Or, 0.12 B = 2.88
• Or B = 24
• So A = 8