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pshichka [43]
2 years ago
13

cho used 2 1/3 cups of flour to bake a cake. she used 3 1/4 cups of flour to bake a loaf of bread. how much more flour did cho u

se to bake the loaf of bread than to bake the cake?
Mathematics
2 answers:
nata0808 [166]2 years ago
8 0
<h2>Answer:</h2>

Hence, she used 11/12 cups of more flour  to bake the loaf of bread than to bake the cake.

<h2>Step-by-step explanation:</h2>

It is given that:

Cho used 2 1/3 cups of flour to bake a cake.

i.e. in simple fraction the amount of flour she used to baker the cake is given by:

2\dfrac{1}{3}=\dfrac{2\times 3+1}{3}\\\\i.e.\\\\2\dfrac{1}{3}=\dfrac{7}{3}\ cups

and  she used 3 1/4 cups of flour to bake a loaf of bread

and in simple fraction the amount of cups of flour she used to bake a loaf of bread is:

3\dfrac{1}{4}=\dfrac{3\times 4+1}{4}\\\\i.e.\\\\3\dfrac{1}{4}=\dfrac{13}{4}\ cups

Hence, the extra quantity of flour that she use to bake the loaf of bread than to bake the cake is:

=\dfrac{13}{4}-\dfrac{7}{3}\\\\\\=\dfrac{13\times 3-7\times 4}{4\times 3}\\\\\\=\dfrac{39-28}{12}\\\\\\=\dfrac{11}{12}\ cups

OlgaM077 [116]2 years ago
4 0
3 1/4 - 2 1/3 = 
13/4 - 7/3 = 
39/12 - 28/12 = 
11/12

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The equation 9+12m=6+15(m-1) models the following situation: Movie-rental company A charges a sign-up fee of $9 plus $12 per mon
Ganezh [65]

Answer:

3m = 18

Step-by-step explanation:

9 + 12m = 6 + 15(m - 1)

9 + 12m = 6 + 15m - 15

3m = 18

6 0
2 years ago
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Performance task: A parade route must start And and at the intersections shown on the map. The city requires that the total dist
GaryK [48]

Answer:

Part A: The proposed route does not meet requirement because it is longer than the maximum required length of 3 miles

Part B: For the total distance is as close to 3 miles as possible, the start point of the parade should be at the point on Broadway with coordinates (9.941, 4.970)

Part C: The coordinates of the cameras stationed half way down each road are;

For central avenue; (4, 2)

For Broadway; (7.97, 2.49)

Step-by-step explanation:

Part A: The length of the given route can be found using the equation for the distance, l, between coordinate points as follows;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

Where for the Broadway potion of the parade route, we have;

(x₁, y₁) = (12, 3)

(x₂, y₂) = (6, 0)

l_1 = \sqrt{\left (0 -3\right )^{2}+\left (6-12 \right )^{2}} = 3 \cdot \sqrt{5}

For the Central Avenue potion of the parade route, we have;

(x₁, y₁) = (6, 0)

(x₂, y₂) = (2, 4)

l_2 = \sqrt{\left (4 -0\right )^{2}+\left (2-6 \right )^{2}} = 4 \cdot \sqrt{2}

Therefore, the total length of the parade route =-3·√5 + 4·√2 = 12.265 unit

The scale of the drawing is 1 unit = 0.25 miles

Therefore;

The actual length of the initial parade =0.25×12.265 unit = 3.09 miles

The proposed route does not meet requirement because it is longer than the maximum required length of 3 miles

Part B:

For an actual length of 3 miles, the length on the scale drawing should be given as follows;

1 unit = 0.25 miles

0.25 miles = 1 unit

1 mile =  1 unit/(0.25) = 4 units

3 miles = 3 × 4 units = 12 units

With the same end point and route, we have;

l_1 = \sqrt{\left (0 -y\right )^{2}+\left (6-x \right )^{2}} = 12 - 4 \cdot \sqrt{2}

y² + (6 - x)² = 176 - 96·√2

y² = 176 - 96·√2 - (6 - x)²............(1)

Also, the gradient of l₁ = (3 - 0)/(12 - 6) = 1/2

Which gives;

y/x = 1/2

y = x/2 ..............................(2)

Equating equation (1) to (2) gives;

176 - 96·√2 - (6 - x)² = (x/2)²

176 - 96·√2 - (6 - x)² - (x/2)²= 0

176 - 96·√2 - (1.25·x²- 12·x+36) = 0

Solving using a graphing calculator, gives;

(x - 9.941)(x + 0.341) = 0

Therefore;

x ≈ 9.941 or x = -0.341

Since l₁ is required to be 12 - 4·√2, we have and positive, we have;

x ≈ 9.941 and y = x/2 ≈ 9.941/2 = 4.97

Therefore, the start point of the parade should be the point (9.941, 4.970) on Broadway so that the total distance is as close to 3 miles as possible

Part C: The coordinates of the cameras stationed half way down each road are;

For central avenue;

Camera location = ((6 + 2)/2, (4 + 0)/2) = (4, 2)

For Broadway;

Camera location = ((6 + 9.941)/2, (0 + 4.970)/2) = (7.97, 2.49).

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Serhud [2]
<h3>Answer:</h3>
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<h3>Step-by-step explanation:</h3>

The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.

If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...

... x -sin(x) @ x=π/3

... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812

You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.

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If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...

... (x+1-π/4)/√2 -sin(x) @ x=π/3

... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620

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2 years ago
Sin(11∘)cos(19∘)+cos(11∘)sin(19∘)
sergij07 [2.7K]
Recall that:

sin(A + B) = sinAcosB + cosAsinB

Therefore:

sin11°cos19° + cos11°sin19° = sin(11° + 19°)

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The square of a number decreased by 3 times the number 28 find all possible values for the number
stealth61 [152]

Question:

The square of a number decreased by 3 times the number is 28 find all possible values for the number  

Answer:

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Solution:

Given that the square of a number decreased by 3 times the number is 28

To find: all possible values of number

Let "a" be the unknown number

From given information,

square of a number decreased by 3 times the number = 28

a^2 - 3a = 28

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x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

Using the above formula,

\text { For } a^{2}-3 a-28=0 \text { we have } a=1, b=-3, c=-28

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Thus the possible values of number are 7 and -4

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