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sasho [114]
2 years ago
7

How far will a wheel of radius 7 cm travel in two revolutions

Mathematics
1 answer:
Svetllana [295]2 years ago
5 0

Answer:

  • 87.92 cm

Step-by-step explanation:

<u>The travel is 2 circumferences:</u>

  • 2C = 2*2πr = 4πr = 4*3.14*7 = 87.92 cm
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A bag contain 3 black balls and 2 white balls.
Troyanec [42]

Answer:

Step-by-step explanation:

Total number of balls = 3 + 2 = 5

1)

a)

Probability \ of \ taking \ 2 \ black \ ball \ with \ replacement\\\\ = \frac{3C_1}{5C_1} \times \frac{3C_1}{5C_1} =\frac{3}{5} \times \frac{3}{5} = \frac{9}{25}\\\\

b)

Probability \ of \ one \ black \ and \ one\ white \ with \ replacement \\\\= \frac{3C_1}{5C_1} \times \frac{2C_1}{5C_1} = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}

c)

Probability of at least one black( means BB or BW or WB)

 =\frac{3}{5} \times \frac{3}{5} + \frac{3}{5} \times \frac{2}{5} + \frac{2}{5} \times \frac{3}{5} \\\\= \frac{9}{25} + \frac{6}{25} + \frac{6}{25}\\\\= \frac{21}{25}

d)

Probability of at most one black ( means WW or WB or BW)

=\frac{2}{5} \times \frac{2}{5} + \frac{3}{5} \times \frac{2}{5} \times \frac{2}{5} + \frac{3}{5}\\\\= \frac{4}{25} + \frac{6}{25} + \frac{6}{25}\\\\=\frac{16}{25}

2)

a) Probability both black without replacement

  =\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}

b) Probability  of one black and one white

 =\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}

c) Probability of at least one black ( BB or BW or WB)

 =\frac{3}{5} \times \frac{2}{4} + \frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{6}{20} + \frac{6}{20} \\\\=\frac{18}{20} \\\\=\frac{9}{10}

d) Probability of at most one black ( BW or WW or WB)

 =\frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{1}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{2}{20} + \frac{6}{20} \\\\=\frac{14}{20}\\\\=\frac{7}{10}

6 0
3 years ago
Mr. brown bought a television set and paid $110 as the first install ment if he unscreases each payment by $20 and pays a totall
vampirchik [111]

Answer:

The answer should be 960

Step-by-step explanation:

110+130+150+170+190+210

8 0
2 years ago
Read 2 more answers
Jack is flying his kite . He runs 100 feet away from his house and lets out 45 feet of string . The angle of elevation from the
fiasKO [112]

Answer: 125.80 ft

Step-by-step explanation:

Asuming the described situation is as shown in the figure below, we need to find the distance h between the kite and Jacks house, but first we need to find the x, y and then d.

How?

We will use trigonometry, especifically the trigonometric functions sine and cosine:

For y:

sin(65 \°)=\frac{y}{45 ft} (1)

Where y is the opposite side to the angle and 45 ft the hypotenuse.

Isolating y:

y=40.78 ft (2)

For x:

cos(65 \°)=\frac{x}{45 ft} (3)

Where x is the adjacent side to the angle.

Isolating x:

y=19.017 ft (4)

Finding d:

d=x+100 ft (5)

d=19.017 ft +100 ft

d=119.017 ft (6)

Now that we have found these values, we have to work with a bigger triangle, where the hypotenuse is the distance between the kite and Jack's house h and the sides are the values calculated in (4) and (6).

So, in this case we will use the <u>Pithagorean theorem</u>:

h^{2}=y^{2} +d^{2} (7)

Isolating h and writing with the known values:

h=\sqrt{y^{2} +d^{2}} (8)

h=\sqrt{(19.017 ft)^{2} +(119.017 ft)^{2}} (9)

h=125.80 ft This is the distance between the kite and the house

3 0
3 years ago
What is the solution to the system of equations?
kaheart [24]
Substitution would be a great approach to solving this system, because the first equation defines y as x - 10 and you can thus substitute x - 10 for y in the second equation:

2x + (x - 10) = 4

Then 3x - 10 = 4, and 3x = 14.  Solving for x:  x = 14/3.

Since y = x-10, subst. 14/3 for x to find y:  y = 14/3 - 30/3 = -16/3

The solution is (14/3, -16/3).
6 0
3 years ago
Read 2 more answers
Which lengths could be the side lengths of a triangle?
Natali [406]
A triangle is a triangle is two of the side lengths is greater than the third side. A- (18+6= 24). (24>23). (13+6=19). (19>18). This is a triangle. B- (13+22=35). (35>7). (22+7=29). (29>13). (13+7=20). (20<22) This is not a triangle. C- (22+13=35). (35>8). (13+8=21). (21<8). This is not a triangle. D- (6+18=24). (24>12). (12+6=18). (18=18) This is not a triangle. The correct answer is A.
7 0
3 years ago
Read 2 more answers
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