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3 years ago

32 ft2 of carpet costs $477.84. What is the cost of the carpet per square foot?

Mathematics

1 answer:

Genrish500 [490]3 years ago

3 0

Divide the total amount of money by the total amount of feet.

477.84/32 = $14.93

hope this helps :)

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How much of the 8% solution should we use to make 100g of a 3% solution?

sp2606 [1]

Suppose x grams of 8% solution should be mixed to make 100 g of 3% solution.
here we shall have:
the amount of 3% solution in the 100 g will be:
3/100*100=3 grams
the the equation will be, 8% of what quantity becomes 3g?
(8/100)*x=3
hence solving for x we shall have:
0.08x=3
x=3/0.08
x= 37.8 grams
The implication of this is that, when you have 37.5 grams of 8% solution, that will contain 3 of pure chemical and hence when you add more solvent on top of 37.5 g until you reach 100g, that will be 3% solution.

8 0

3 years ago

Read 2 more answers

A concert hall has three sections: the main floor, the balcony, and the gallery. For a recent concert, 1020 tickets were sold. T

Angelina_Jolie [31]

Answer:

Let the number of balcony seats be b

Let the number of gallery tickets be g

Let the number of main floor tickets be m

b + g + m = 1020

b = 2g

m = b + 225

The number of balcony tickets = 318

The number of gallery tickets = 159

The number of main floor tickets = 543

Step-by-step explanation:

Let the number of balcony seats be b

Let the number of gallery tickets be g

Let the number of main floor tickets be m

i) Therefore we can write b + g + m = 1020

ii) there were twice as many balcony tickets sold as gallery tickets

therefore b = 2g $\Rightarrow$ g = 0.5b

iii) there were 225 more main floor tickets than balcony tickets

therefore m = b + 225

iv) using equation ii) and equation iii) in equation i) we can write

b + g + m = b + 0.5b + b + 225 = 1020 $\Rightarrow$ 2.5b = 795 $\Rightarrow$ b = 318

v) g = 0.5 b = 0.5 $\times$ 318 = 159

vi) m = b + 225 = 318 + 225 = 543

5 0

4 years ago

Read 2 more answers

Which graph shows the result of dilating this figure by a factor of 4 about the origin? On a coordinate plane, rectangle A B C D

Andrei [34K]

Answer:

Second option: On a coordinate plane, rectangle A'B'C'D' prime has points $(-4,4),(12,4),(12,-4),(-4,-4)$

(See the graph attached)

Step-by-step explanation:

For this exercise it is importnat to know that a Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) has the same shape as the Pre-Image (which is the original figure before the transformation), but they have different sizes.

In this case, you know that the vertices of the rectangle ABCD ( The Pre-Image) are the following:

$A(-1,1)\\\\B(3,1)\\\\C(3,-1)\\\\D(-1,-1)$

Therefore, to find the vertices of the rectangle A'B'C'D' (The Image) that results of dilating the rectangle ABCD by a factor of 4 about the origin, you need to multiply the coordinates of each original vertex by 4. Then, you get:

$A'=((-1)(4),(1)(4))=(-4,4)\\\\B'=((3)(4),(1)(4))=(12,4)\\\\C'=((3)(4),(-1)(4))=(12,-4)\\\\D'=((-1)(4),(-1)(4))=(-4,-4)$