solve the triangle.round to the nearest degree.

Answer:

[tex]4)\ = \frac{5}{\pi}[/tex]

Step-by-step explanation:

Formula:________________

circumference = Diameter × π

_______________________

Then

5 = Diameter × π

Then

[tex]Diameter \ = \frac{5}{\pi}[/tex]

1) (-5, 5), 2) (7, -5), 3) (- 3, 28), 4) (- 12, 0), 5) 10, 6) 14, 7) (- 9, 9), 8) [tex]\sqrt{26}[/tex], 9) - 2, 10) 10, 11) [tex]\left(\frac{\sqrt{26}}{26}, \frac{5\sqrt{26}}{26}\right)[/tex], 12) [tex]\left(\frac{21\sqrt{10}}{10}, -\frac{7\sqrt{10}}{10} \right)[/tex], 13) (0, 7), 14) [tex](- 3\sqrt{3}, - 3)[/tex], 15) The vectors [tex]\vec a[/tex] and [tex]\vec b[/tex] are orthogonal, 16) [tex]7\sqrt{2}[/tex], [tex]135^{\circ}[/tex], 17) [tex]17[/tex], [tex]137^{\circ}[/tex], 18) [tex]12[/tex], [tex]240^{\circ}[/tex], 19) [tex](19.700, 15.392)[/tex]

Vectors are elements that are charaterized for having a magnitude and a direction, whereas scalar are only characterized by magnitude. In this question we must apply different vector properties to obtain the corresponding results.

The first two exercises consist in calculating each vector based on its initial and terminal points, whose results are obtained below by sum of vectors with initial points at origin:

1) (-1, 3) - (4, -2) = (-5, 5)

2) (2, -6) - (- 5, -1) = (7, -5)

The following eight exercises are resolved by applying the operations of addition of vectors and multiplication of a vector by a scalar, and the definition of norm and dot product as well:

3) 3 · (3, 4) + 2 · (- 6, 8) = (9, 12) + (- 12, 16) = (- 3, 28)

4) (- 6, 8) - 2 · (3, 4) = (- 12, 0)

5) [tex]\| \vec v\| = \sqrt{(-6)^{2}+8^{2}}[/tex] = 10

6) [tex]\vec u \,\bullet \,\vec v =[/tex] 3 · (- 6) + 4 · 8 = 14

7) 3 · [(0, 2) - (3, -1)] = 3 · (- 3, 3) = (- 9, 9)

8) [tex]\|\vec v\| = \sqrt{1^{2}+5^{2}} = \sqrt{26}[/tex]

9) [tex]\vec u \,\bullet \,\vec v =[/tex] 3 · 1 + (- 1) · 5 = - 2

10) [tex]\vec w \,\bullet \, \vec v =[/tex] 0 · 1 + 5 · 2 = 10

11) The unit vector is obtained by dividing the vector by its magnitude:

[tex]\vec u_{v} = \frac{1}{\sqrt{26}}\cdot \left(1, 5\right) = \left(\frac{1}{\sqrt{26}}, \frac{5}{\sqrt{26}} \right) = \left(\frac{\sqrt{26}}{26}, \frac{5\sqrt{26}}{26}\right)[/tex]

12) The vector is equal to the product of the magnitude and its unit vector:

[tex]\vec r = 7 \cdot \frac{\vec u}{\|\vec u\|}[/tex]

[tex]\vec r = \frac{7}{\sqrt{10}}\cdot (3, -1) = \left(\frac{21}{\sqrt{10}}, -\frac{7}{\sqrt{10}} \right) = \left(\frac{21\sqrt{10}}{10}, -\frac{7\sqrt{10}}{10} \right)[/tex]

13) and 14) The vector is the product of the magnitude and the directional vector:

13) [tex]\vec r = 7 \cdot (\cos 90^{\circ}, \sin 90^{\circ}) = (0, 7)[/tex]

14) [tex]\vec r = 6\cdot (\cos 210^{\circ}, \sin 210^{\circ}) = (- 3\sqrt{3}, - 3)[/tex]

15) Two vectors are orthogonal if and only if their dot product is zero:

[tex](3.2, 4.8) \,\bullet\,(-3, 2) =[/tex] 3.2 · (- 3) + 4.8 · 2 = 0

The vectors [tex]\vec a[/tex] and [tex]\vec b[/tex] are orthogonal.

The next three exercises are resolved by definitions of norm and direction:

16) [tex]\|\vec v\| = \sqrt{(-7)^{2}+7^{2}} = 7\sqrt{2}[/tex], [tex]\theta = 135^{\circ}[/tex]

17) [tex]\|\vec v\| = 17[/tex], [tex]\theta = 137^{\circ}[/tex]

18) [tex]\|\vec q\| = 12[/tex], [tex]\theta = 240^{\circ}[/tex]

The last exercise consist in defining the vector as a product of magnitude and direction vector:

19) [tex]\vec v = 25\cdot (\cos 38^{\circ}, \sin 38^{\circ}) = (19.700, 15.392)[/tex]

To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13322477

Answer:

9c4

factoring the monomial

(3c2)(-3c2)

Answer:

16.260 (3 d.p.)

Step-by-step explanation:

Divide 50 by 20%

50/20% = 50/0.20 = 250

Answer: 250

Answer: The second histogram a.k.a choice B is correct.

Answer:

18 pi inches

Step-by-step explanation:

Circ of circle = pi * d

                      = 18 pi      exactly

The probability of exactly 1 of the 4 marbles drawn being blue and at least 1 of the 4 marbles drawn being white will be 0.3535 and 0.7454 respectively.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Betty picks 4 random marbles from a bowl containing 3 white, 4 yellow, and 5 blue marbles.

The total number of the marbles will be

Total marble = 3 + 4 + 5

Total marble = 12

Then the probability of exactly 1 of the 4 marbles drawn being blue will be

[tex]\rm P(B) = \dfrac{^5C_1 \times ^7C_3}{^{12}C_4}\\\\P(B) = \dfrac{35}{99} = 0.353535[/tex]

Then the probability of at least 1 of the 4 marbles drawn being white will be

[tex]\rm P(W) = \dfrac{^{3}C_1\times \ ^{9}C_3}{^{12}C_4} + \dfrac{^{3}C_2\times \ ^{9}C_2}{^{12}C_4} + \dfrac{^{3}C_3\times \ ^{9}C_1}{^{12}C_4} \\\\\\P(W) = \dfrac{252}{495} + \dfrac{108}{495} + \dfrac{9}{495}\\\\\\P(W) = \dfrac{369}{495}\\\\\\P(W) = 0.745454[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

Answer:

A. 0.3535.

B. 0.7455.

Step-by-step explanation:

The probability that exactly 1 of the 4 marbles drawn is blue is 0.3535. The probability that at least 1 of the 4 marbles drawn is white is 0.7455.

so he got for £95 and sold it for £133, so  hmmmm the difference is simply £38.

if we take 95 to be the 100%, what is 38 off of it in percentage?

[tex]\begin{array}{ccll} \pounds&\%\\ \cline{1-2} 95 & 100\\ 38& x \end{array} \implies \cfrac{95}{38}=\cfrac{100}{x}\implies \cfrac{5}{2}=\cfrac{100}{x} \\\\\\ 5x=200\implies x=\cfrac{200}{5}\implies x=40[/tex]

Answer:

42°

Step-by-step explanation:

Angles on one side of a straight line always add up to 180.

Therefore: 180° - 123° = 57°

So, 57° + 81° =138°

x=180° -138° = 42°

Answer:

There would be 5.5 or 5 1/2 classes

Step-by-step explanation:

Turn fractions into decimals

Multiply each by 60

Then Divide

Answer:

C

Step-by-step explanation:

Multiplying the sequence by 2 gives us the next term. Therefore it has to be the formula a1 x r^n-1. If we substitute the values it would end up as the answer C

Answer:

The correct answer would be option C; 12 x 2ⁿ⁻¹

Step-by-step explanation:

You can check this using any number

since n is the term number we can check it;

let's say we have to find out the answer to the third term number, so we will substitute the n by 3 in the equation from option C and solve

term = 12 x 2ⁿ⁻¹

term = 12 x 2 ³ ⁻¹

term = 12 x 2 ²

term = 12 x 4

term = 48

The term does match the third number in the series given above and hence the equation works!

Hope this helps!

Answer: 4

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation: Im going to guess the dice has 6 sides, rolling any number on that 1 dice would be a 1/6 chance. I hope this helps!

Answer:

-33.6

Step-by-step explanation:

1. Solve inside the brackets = 4.2

2. Multiply that by -8 = -33.6

Answer:

-33.6

Step-by-step explanation:

Answer:

Less than

Step-by-step explanation:

1/3 * 7/15 is less than 1/3 because 1/3 * 7/15 is being multiplied by a number that is less than 1.

Answer:

The answer is C.

Step-by-step explanation:

C. 50-59 since it has the same number of employees as 10-19.

Answer:

$ 1.65 per gallon

Step-by-step explanation:

4 quarts in 1 gallon so 8 quarts in 2 gallons.

Cost for 2 gallons $13.20 so $13.20 ÷ 8 =  $1.65

Answer:

x=13

Step-by-step explanation:

<FGA is a vertical angle to <EGB, so both = to 77. Then since < CGB=90, we do 90-77=13

Answer:

6.

Step-by-step explanation:

That is the number of permutations of 2 from 3

= 3P2

= 3!/(3-2(!

= 3*2

= 6.

Answer:

A

Step-by-step explanation:

The Y-intercept is -3.

The gradient is -3/4 since it goes down 3 every 4 tiles.

Answer:

[tex]y=-\frac{3}{4}x -3[/tex]

Step-by-step explanation:

Hey there!

We can form this equation in slope-intercept form

This means, we have to find the slope and the y intercept of the line

First lets find the slope

The equation for slope is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In order to find y and x, we need to take two points on the line

(-4, 0) and (0, -3)

x1   y1        x2  y2

Plug it in:

[tex]\frac{-3-0}{0-(-4)} \\\\\frac{-3}{4} \\\\-\frac{3}{4}[/tex]

This means, the slope is -3/4

Now we have to find the y-intercept

The y-intercept is where the line intercepts the y-axis

The line intercepts the y-axis at the point (0, -3)

So now that we have the slope and the y-intercept, we can form the equation

[tex]y=-\frac{3}{4}x-3[/tex]

Answer:

See below ~

Step-by-step explanation:

First 3 blanks

Final blank

Answer:

Step-by-step explanation:

Answer:

maria: $2,500
henry:$750

Step-by-step explanation:

all you have to do is multiply them each by 6

Answer:

Maria will have $1500

Henry will have $750

Step-by-step explanation:

Maria - Multiply 250 x 6

Henry- Multiply 125 x 6

Answer:

PO

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

1/3 = x/12

12 * 1/3 =x      x = 4  

Answer:

  3/7

Step-by-step explanation:

Write the division of the pizzas as a ratio, and you will have it.

  (3 pizzas)/(7 persons) = (3/7) pizza/person

__

Each person gets 3/7 of a pizza.

Answer:

Step-by-step explanation:

so the dvd player is 984 dollars so now we multiply it by three and our total would be 2,952