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It takes 980 bricks to construct a wall that measures 16 feet 8 inches long and 5 feet high. The crew you hire can lay 300 bricks/hour. The cost of the labor is $2500 per eight hour workday, and you can pay for a partial day. You need to build a wall 28 feet 6 inches long and 5 feet high. How much will the new wall cost?  

There could be alternative approaches, but here's how I'd figure it. 

I'll write numbers to two decimal places, but I'm doing calculations  

on my iPhone calculator, which carries out the decimal places a   

lot farther and I'm not rounding them in the calculator, so some  

of the following intermediate totals may seem to be off a small  

amount.  

Using given values, how many bricks per square foot .....

                                  980 / (16.67 * 5)  =  11.76 brk per ft²  

How many bricks will the new wall contain ....  

                                  11.76 * (28.5 * 5)  =  1675.80 brk  

How long will it take the crew to lay that many bricks ....  

                                  1675.80 / 300  =  5.59 hr  

How many days is that many hours ....  

                                  5.59 / 24  =  0.23 day  

How much does the crew earn for that many days ....  

                                  0.23 * 2500  =  581.88 dollars  

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7 / 12 ==58.33% -of people who are bored by cable news

280 / (0.583333333...) ==480 people who are not bored by cable news.

6 is the 6th number in the sequence

Five times a number is divided by 7 more than the number. If the result is 0, then what was the original number?  

Let's call that number "n"  

Five times the number is 5n  

7 more than the number is n + 7  

            5n  

          –––––  =  0  

           n + 7  

The only way this can happen is if n = zero  

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A bag contains yellow, green, blue, and white marbles.  The ratio of yellow, green, blue, and white marbles is 1:2:3:4.  If the bag contains 180 marbles, then how many blue marbles are there?  

Consider:  "The ratio of yellow, green, blue, and white marbles is 1:2:3:4."  

Call the number of yellow marbles X.  

So the number of green marbles is 2X. 

And the number of blue marbles is 3X.  

And the number of white marbles is 4X.  

Add up all the marbles and you have     10X  =  180  

Therefore                                                   X  =  18 yellow marbles  

                                                                 2X  =  36 green marbles  

                                                                 3X  =  54 blue marbles  

                                                                 4X  =  72 white marbles  

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Erm...What is this for ? I don't think it is..allowed to post these stuff here..Right?

Hello,

If 7 out of every 12 people are bored by cable news and there are 280 people at the convention who are bored by cable news, we can set up a proportion to find the total number of people at the convention.

\((b+1)(8b^{2}+1)=2023,\\ 8b^{3}+8b^{2}+b-2022=0,\\b=6,\\b+1=7,\\8b^{2}+1=289,\\(x-7)(x-289)=x^{2}-296x+2023. \)

Hi! I think you made a slight error when you found the product of the roots, I got 8b^3+8b^2+b+1. Other than that your solution is great

The sum of the roots of a quadratic equation is given by -b/a, and the product of the roots is given by c/a. In this case, the sum of the roots is x1 + x2 = b + 1 + 8b^2 + 1 = 8b^2 + b + 2. The product of the roots is x1*x2 = (b + 1)(8b^2 + 1) = 8b^3 + b + 1.

We are given that the sum of the roots is -a/1 and the product of the roots is 2023/1. Setting these equal to the expressions we just derived, we get the following equations:

-a/1 = 8b^2 + b + 2 2023/1 = 8b^3 + b + 1

Multiplying the first equation by 1 and the second equation by -1, we get the following equations:

-a = 8b^2 + b + 2 -2023 = -8b^3 - b - 1

Adding these equations, we get the following equation:

-a - 2023 = -8b^3 - 8b^2 - 3

Combining like terms, we get the following equation:

-a - 2023 = -8b^3 - 8b^2 - 3

Multiplying both sides of the equation by -1, we get the following equation:

a + 2023 = 8b^3 + 8b^2 + 3

Now, we need to find the value of b. We can do this by using the fact that the sum of the roots of a quadratic equation is -b/a. In this case, the sum of the roots is x1 + x2 = b + 1 + 8b^2 + 1 = 8b^2 + b + 2. We are given that this value is equal to 2023. Setting these equal to each other, we get the following equation:

2023 = 8b^2 + b + 2

Subtracting 2 from both sides of the equation, we get the following equation:

2021 = 8b^2 + b

Combining like terms, we get the following equation:

2021 = 8b^2 + b

Factoring out a 1 from the right-hand side of the equation, we get the following equation:

2021 = 1(8b^2 + b)

Dividing both sides of the equation by 1, we get the following equation:

2021 = 8b^2 + b

Now, we can substitute this value of b into the equation a + 2023 = 8b^3 + 8b^2 + 3. Doing so, we get the following equation:

a + 2023 = 8(2021) + 8(1) + 3

Simplifying the right-hand side of the equation, we get the following equation:

a + 2023 = 16168 + 8 + 3

Combining like terms, we get the following equation:

a + 2023 = 16179

Subtracting 2023 from both sides of the equation, we get the following equation:

a = 16179 - 2023

Simplifying the right-hand side of the equation, we get the following equation:

a = 14156

Therefore, the value of a + b is 14156 + 2023 = 16179.

Since triangle \(ABC\) is equilateral, \(PX\) is also a median, bisecting side \(QR\). Thus, \(XR=\frac{9}{2}.\) Note that triangle \(YXR\) is a 30-60-90 triangle with right angle at \(Y\) and 30 degree angle at \(\angle{YXR}\). Thus, \(YR = \frac{\frac{9}{2}}{2} = \frac{9}{4}.\) Since the side opposite the \(60^\circ\) angle in a 30-60-90 triangle is \(\sqrt{3}\) times the side opposite the \(30^\circ\) angle, we have \(XY = \frac{9}{4} \cdot \sqrt{3} = \boxed{\frac{9\sqrt{3}}{4}}.\)

Every season is 3 months, so 9 months ago was 3 seasons ago. Since now is fall, one season ago was summer, two seasons ago was spring, and therefore, three seasons ago was winter. 

45-8=37

The largest possible value of CF is 28.

8 + 2 = 10

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?  

Consider                                                                ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³). 

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

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a = 8/3, b = 12.

The prime numbers less than or equal to 51 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31. We can try all possible combinations of three of these numbers to see which ones add up to 51. There are C(12,3)=220 possible combinations, but some of them add up to the same number. For example, the combinations (2, 17, 32) and (2, 32, 17) both add up to 51. There are 10 different sums that can be obtained by adding three prime numbers less than or equal to 51, and each sum can be obtained in several different ways. The table below shows the different sums and the number of ways to obtain each sum.

Sum Number of ways

2 + 29 + 20 1

2 + 31 + 18 1

2 + 37 + 12 1

3 + 11 + 37 1

5 + 13 + 29 1

7 + 17 + 21 2

11 + 13 + 27 1

17 + 19 + 15 2

23 + 29 + 7 1

There are a total of 10​ different combinations of three prime numbers, not necessarily distinct, that have a sum of 51.

The answer is √2

We can use the Pythagorean Theorem.

We can solve for the hypotenuse of BPC: 1^2 + 1^2 = 2 -> √2 is the length of BC. We can solve for x, a leg of the triangle ABC with the pythagorean theorem again. 1 + 1 = 2 -> 2 + x^2 = 4 -> 4 - 2 = x^2 -> x^2 = 2 -> x = √2

The answer is √2

We can use the Pythagorean Theorem.

We can solve for the hypotenuse of BPC: 1^2 + 1^2 = 2 -> √2 is the length of BC. We can solve for x, a leg of the triangle ABC with the pythagorean theorem again. 1 + 1 = 2 -> 2 + x^2 = 4 -> 4 - 2 = x^2 -> x^2 = 2 -> x = √2

k = 2

m = 0

480. By the way, if you didn't know, the question is basically asking for the cube root of 576000 * 4 * 48

i put it in but it said it was wrong

>> Multiples of 4 from 1 to 15 are 4, 8, 12, which are also multiples of 3. Therefore, there are 3 favorable outcomes. <<

It must be the New Math.  When I went to school, 4 and 8 were not multiples of 3.  

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