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3 years ago

1/3 cup of flour is used in 5 dinner rolls. How many cups of flour are needed to make 3 dozen rolls?

Mathematics

2 answers:

valentinak56 [21]3 years ago

7 0

5 = 1/3 cup flour

3 dozen = 36 rolls

12 x 3 = 36

1/3 x 36 = 12

gladu [14]3 years ago

4 0

3 dozen=3·12=36

$\frac{1/3}{5} =\frac{x}{36}$

Use cross multiplication

1/3·36=5x

12=5x

12/5=5x/5

x=12/5 or 2 2/5 or 2.4

12/5 or 2 2/5 cups of flour is needed to make 3 dozen rolls

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Part of the roof of a factory is devoted to mechanical support and part to green space. The area G that is designated as green s

alexgriva [62]

Answer:

Therefore, the area of green space would be 30 square yards.

Step-by-step explanation:

The area G that is designated as green space can be modeled by the polynomial $2x^2-7x$

the area M that is devoted to mechanical support can be modeled by the polynomial $x^2-9x+24.$

We are asked to find the area of the green space, when area of roof (R) is 36 square yards.

The area of roof would be equal to sum of areas of green space and mechanical support.

$R=G+M$

$G = 2x^2 -7x M = x^2 -9x +24$

the total area is given by 36 yd^2. And we know that:

$R = 36 yd^2 = G+M$

Replacing the info given we got:

$36 = 2x^2 -7x +x^2 -9x +24\\\\ 12= 3x^2 -16 x$

And we can rewrite this expression like this:

$3x^2 -16 x -12 =0$

And we can use the quadratic formual to solve this problem:

$X =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}$

With a = 3, b = -16 , c =-12. Replacing we have

$x = \frac{16 \pm \sqrt{(-16)^2 -4*(3)*(-12)}}{2*3}$

And the solutions for this case are:

Since length cannot be negative, therefore, the value of x would be 6.

The area of green space would be:

x = 6

$2x^2-7x\Rightarrow 2(6)^2-7(6)\\\\2x^2-7x=2(36)-42\\\\2x^2-7x=72-42\\\\2x^2-7x=30$

the area of green space would be 30 square yards.

8 0

3 years ago

PLEASE HELP FASTTT!!!

nirvana33 [79]

Answer:

5 seconds

Step-by-step explanation:

Looking at your function (h(t) = -16t^2 + 48t + 160), I see that the peak height will be 196 feet, and that is achieved in 1.5 seconds.

h(1.5) = -16(1.5)^2 + 48(1.5) + 160

h(1.5) = -16(2.25)+ 48(1.5) + 160

h(1.5) = -36 + 48(1.5) + 160

h(1.5) = -36 + 72 + 160

h(1.5) = 36 + 160

h(1.5) = 196

Going down from that height, it would take 3.5 more seconds, so it would take 5 seconds in total

h(5) = -16(5)^2 + 48(5) + 160

h(5) = -16(25) + 48(5) + 160

h(5) = -400 + 48(5) + 160

h(5) = -400 + 240 + 160

h(5) = -400 + 400

h(5) = 0

8 0

3 years ago

Complete the following statements in relation to the third term in the expansion of the binomial (2x+y^2)^5

lana [24]

We want to expand (2x + y²)⁵.

From Pascal's Triangle (shown below), the coefficients of the expansion are
1,5,10,10,5,1.

n=0: 1
n=1: 1 1
n=2: 1 2 1
n=3: 1 3 3 1
n=4: 1 4 6 4 1
n=5: 1 5 10 10 5 1

Therefore the third term in the expansion is
10*(2x)³*(y²)² = 10*(8x³)*(y⁴) = 80x³y⁴

Alternatively, the third term is
₅C₃ (2x)³(y²)² = 10*(8x³)*(y⁴) = 80x³y⁴

Answer: 80x³y⁴

4 0

3 years ago

Draw an area model that demonstrates that the quotient of 2080 and 40 is 52.

Scrat [10]

Area model is used to illustrate multiplication and division operations.

See attachment for the area model

The equation can be represented as:

$\frac{2080}{40} = 52$