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4 years ago

Solve each proportion. If necessary, round to the nearest hundredth. Show your work.

Mathematics

1 answer:

Pachacha [2.7K]4 years ago

6 0

Answer:

1) m = 21

2) f = 8

3) m = 42

Step-by-step explanation:

1) 12/7 = 36/m

12m/7 = 36

12m = 36(7)

m = 36(7)/12

m = 21

2) 42/56 = 6/f

42f/56 = 6

42f = 6(56)

f = 6(56)/42

f = 8

3) 10/14 = 30/m

10m/14 = 30

10m = 30(14)

m = 30(14)/10

m = 42

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The magnitude and direction of two vectors are shown in the diagram. What is the magnitude of their sum?

VLD [36.1K]

Separate the vectors into their x- and y-components. Let u be the vector on the right and v the vector on the left, so that

u = 4 cos(45°) x + 4 sin(45°) y

v = 2 cos(135°) x + 2 sin(135°) y

where x and y denote the unit vectors in the x and y directions.

Then the sum is

u + v = (4 cos(45°) + 2 cos(135°)) x + (4 sin(45°) + 2 sin(135°)) y

and its magnitude is

||u + v|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)

… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))

… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))

… = √(16 + 16 cos(135° - 45°) + 4)

… = √(20 + 16 cos(90°))

… = √20 = 2√5

5 0

3 years ago

Read 2 more answers

Please do this question for me, I don’t get it, all it wants you to do is convert.

IgorC [24]

9514 1404 393

Answer:

$6.80/fortnight

Step-by-step explanation:

You need to know there are 13 weeks in a quarter, and 2 weeks in a fortnight. The conversion is straightforward.

$\dfrac{\$44.20}{\text{quarter}}\times\dfrac{1\text{ quarter}}{13\text{ weeks}}\times\dfrac{2\text{ weeks}}{1\text{ fortnight}}=\dfrac{\$44.20\times2}{13\text{ fortnight}}\\\\=\boxed{\$6.80\text{/fortnight}}$

4 0

3 years ago

Please help, thanks!

Westkost [7]

Answer:

$x=99^{\circ},\\y=81^{\circ}$

Step-by-step explanation:

The sum of the interior angles of a polygon with $n$ sides is $180(n-2)$ . Since the shape in the figure has 5 sides, the sum of its interior angles is $180(5-2)=180\cdot 2=540^{\circ}$ .

Therefore, we can set up the following equation:

$95+125+105+116+x=540,\\441+x=540,\\x=\boxed{99^{\circ}}$

Since $\angle x$ and $\angle y$ make up one side of a line, they are supplementary, as each side of a line is $180^{\circ}$ .

Thus, we have:

$x+y=180,\\99+y=180,\\y=\boxed{81^{\circ}}$

4 0

3 years ago

James has 6 stamps in his stamp collection. Roy has 12 stamps in his stamp collection. James adds 2 stamps to his stamp collecti

Alina [70]

2:3

it was originally 8:12, but it has to be simplified. 2/3 can also work as an answer.

6 0

4 years ago

The Pick 4 games in many state lotteries announce a four‑digit winning number each day. Each of the 10,000 possible numbers 0000

barxatty [35]

Answer:

a) P(a)= 0.0001

b) P(b)= 0.0024

Step-by-step explanation:

Given:

Chosen number = 3079

Possible numbers that have chance of winning from 0000 to 9999= 10,000

Winning condition= if made choice matches the winning digits

Now

a)What is the probability that the winning number matches your number exactly?

From 0000 to 9999, only one time can the number 3079 can be the winning number, so

P(a)= 1/10000

= 0.0001

b)What is the probability that the winning number has the same digits as your number in any order?

Winning numbers from 0000 to 10000 that have same digits as 3079 are

4 x 3 x 2 x 1 = 24 ways

Following are the 24 numbers from 0000 to 9999 that have matching digits to 3079:

0379

0397

0973

0937

0793

0739

3079

3097

3970

3907

3790

3709

7039

7093

7930

7903

7390

7309

9073

9037

9370

9307

9730

9703

P(b)= 24/10000

=0.0024 !

8 0

4 years ago