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cupoosta [38]
1 year ago
5

Mr Davis is creating a spice mixture for a recipe.2/5 of the spice mixture was oregano 1/3 of the spice mixture was basil the re

maining spice mixture was chili powder what fraction of the total amount of spice mixture was oregano and basil
Mathematics
1 answer:
attashe74 [19]1 year ago
7 0

Answer: \frac{11}{15}

Step-by-step explanation:

You know that:

- 2/5 of the spice mixture was oregano.

- 1/3 of the spice mixture was basil.

Then, to find the fraction of the total amount of spice mixture that was oregano and basil, you must add both fractions, as following:

- Find the least common multiply of the denominators:

LCM=5*3=15

- Divide the LCM by each original denominator and multiply the result by each numerator.

- Make the addition.

Then, the result is:

\frac{(2*3)+(1*5)}{15}=\frac{6+5}{15}=\frac{11}{15}

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2 years ago
Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of
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Answer:

Step-by-step explanation:

The two force F1 and F2  are represented by vectors with initial points that are at the origin.

the terminal point of the vector is point P(1, 1, 0)

Therefore, the direction of the vector force is

v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j

The unit vector in the direction of force will be

\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}

The magnitude of the force is 40lb, so the force will be

F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)

The terminal point of its vector is point Q(0, 1, 1)

Therefore, the direction of the vector force is

v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k

\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}

The magnitude of the force is 60lb, so the force will be

F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)

The resultant of the two forces is

F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k

The magnitude force will be

|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68

to (1 decimal place)=55.7lb

b) The direction angle of force F

The angle formed by F and x axis

\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469

The angle formed by F and y axis

\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=

The angle formed by F and z axis

\alpha=\cos^{-1}(\frac{30\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.7620)\\\\=40.359

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Its c, average rate, im sure of it
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Answer:

Step-by-step explanation:

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Ii) Together they scored 39 points. Therefore, the equation which may be used to find the value of × would be

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Answer:

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Step-by-step explanation:

We have the complex number 5-2i and we have to show the location of the point that represents that number in the complex plane

In the complex plane the real numbers are located in the horizontal axis, increasing to the right. The positives real numbers are at the right of the origin and the negatives to the left.

The complex numbers are located in the vertical axis, with the positives over the origin and the negatives below the origin.

This complex number 5-2i is the sum of a real part (5) and a imaginary part (-2i), so the point will be 5 units rigth on the horizontal axis (for the real part) and 2 units down in the vertical axis (for the imaginary part).

8 0
1 year ago
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