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3 years ago

Roger served 5/8 pound of crackers, which was 2/3 of the entire box. what was the weight of the crackers originally in the box

1 answer:

4 0

5/8 = 2/3 the entire box

Half of 2/3 is 1/3, and 2/3 + 1/3 = 1

So find half of 5/8 and add it to 5/8.

5/8 * 1/2 = 5/16

5/8 + 5/16

Change 5/8 to a fraction with a denominator of 16:

10/16 + 5/16 = 15/16

So the original weight is 15/16 pounds.

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Building a is 160160 feet shorter than building

Serjik [45]

I assume the heights are 160 ft and 1480 ft.

The two heights are unknown, so we will use variable h to help solve the problem.
The shorter building, building A, has height h.
Since building A is shorter by 160 ft, then building B is taller by 160 ft, so the height of building B is h + 160.

Now we add our two heights to find the total height.

h + h + 160 is the total height.
We can write it as 2h + 160

We are told the total height is 1480 ft, so we let 2h + 160 equal 1480, and we have an equation.

2h + 160 = 1480

Subtract 160 from both sides

2h = 1320

Divide both sides by 2

h = 660

h + 160 = 820

Building A measures 660 ft.
building B measures 820 ft.

7 0

3 years ago

Which is a perfect square ?

barxatty [35]

Answer:

6^2 Is perfect square which is 36.

3 0

3 years ago

Read 2 more answers

I have many students are represented in the data set?

nalin [4]

Answer:

a) 19 students

b) the mean 3 9/19

the median 3

the mode 3

c) the range 6

Step-by-step explanation:

The data set shows that

0 points gets 1 student,

1 point gets 1 student,

2 points get 2 students,

3 points get 6 students,

4 points get 4 students,

5 points get 3 students and

6 points get 2 students.

a) There are 1+1+2+6+4+3+2=19 students.

b) The mean is

$\dfrac{1\cdot 0+1\cdot 1+2\cdot 2+6\cdot 3+4\cdot 4+3\cdot 5+2\cdot 6}{19}=\dfrac{66}{19}=3\dfrac{9}{19}.$

The average score is 3 9/19 points.

The median is 10th term in the data set - 3 points (means the middle score in the data set)

The mode is 3 points (means most happened score)

c) The range of the data is 6-0=6 points.

7 0

3 years ago

determine the point of intersection of the following pair of lines ............2x-3y-4=-13 and 5x=-2y+25. 3x+2y-7=0 and 2x=12-5y

grandymaker [24]

Answer:

(x, y) = (3, 5)
(x, y) = (1, 2)

Step-by-step explanation:

A nice graphing calculator app makes these trivially simple. (See the first two attachments.) It is available for phones, tablets, and as a web page.

The usual methods of solving a system of equations involve elimination or substitution.

There is another method that is relatively easy to use. It is a variation of "Cramer's Rule" and is fully equivalent to elimination. It makes use of a formula applied to the equation coefficients. The pattern of coefficients in the formula, and the formula itself are shown in the third attachment. I like this when the coefficient numbers are "too messy" for elimination or substitution to be used easily. It makes use of the equations in standard form.

_____

1. In standard form, your equations are ...

2x -3y = -9
5x +2y = 25

Then the solution is ...

$x=\dfrac{-3(25)-(2)(-9)}{-3(5)-(2)(2)}=\dfrac{-57}{-19}=3\\\\y=\dfrac{-9(5)-(25)(2)}{-19}=\dfrac{-95}{-19}=5\\\\(x,y)=(3,5)$

2. In standard form, your equations are ...

3x +2y = 7
2x +5y = 12

Then the solution is ...

$x=\dfrac{2(12)-5(7)}{2(2)-5(3)}=\dfrac{-11}{-11}=1\\\\y=\dfrac{7(2)-12(3)}{-11}=\dfrac{-22}{-11}=2\\\\(x,y)=(1,2)$

_____

Note on Cramer's Rule

The equation you will see for Cramer's Rule applied to a system of 2 equations in 2 unknowns will have the terms in numerator and denominator swapped: ec-bf, for example, instead of bf-ec. This effectively multiplies both numerator and denominator by -1, so has no effect on the result.

The reason for writing the formula in the fashion shown here is that it makes the pattern of multiplications and subtractions easier to remember. Often, you can do the math in your head. This is the method taught by "Vedic maths" and/or "Singapore math." Those teaching methods tend to place more emphasis on mental arithmetic than we do in the US.

7 0

3 years ago

Twenty times a square of a positive integer plus 50 equals negative 40 times the square of the positive integer plus one-hundred

rusak2 [61]

20x^2+50 = -40x^2+110x [ Taking x as the unknown positive integer ]

4 0

3 years ago