All categories

3 years ago

A cyclist travels at an average speed of 15 mph for 3 hours. How far did she travel in miles?

Mathematics

1 answer:

vazorg [7]3 years ago

7 0

Answer:

Step-by-step explanation:

3 hours × 15 miles/hour = 45 miles

You might be interested in

A plane has an airspeed of 111 km/h. It is flying on a bearing of 79 degrees while there is a 25 km/h wind out of the northeast

qwelly [4]

Answer: Ground Speed = 91 km/hr, Bearing = 189°

Step-by-step explanation:

Step 1: Draw a picture (see attached) to determine the angle between the given vectors. Notice that I moved the wind vector 180° so the head of the wind vector would line up with the tail of the plane vector. This created an angle of 34° between the plane and wind vectors. Why?

the dashed line is 45°
79° (plane) - 45° (wind) = 34°

Step 2: Solve for the length of the resultant vector using Law of Cosines

c² = a² + b² - ab cos C

c² = (111)² + (25)² - (111)(25) cos 34°

c² = 12,946 - 4601

c² = 8345

c = 91

Ground speed is 91 km/hr

Step 3: Solve for the bearing of the resultant vector using Law of Sines

$\dfrac{sin\ A}{a}=\dfrac{sin\ C}{c}$

$\dfrac{sin\ A}{25}=\dfrac{sin\ 34}{91}$

$sin\ A=\dfrac{25\ sin\ 34}{91}$

$A=sin^{-1}\bigg(\dfrac{25\ sin\ 34}{91}\bigg)$

A = 9°

Reminder that we moved the wind vector 180° to create the resultant vector so we need to add 180° to our answer.

Bearing = A + 180°

= 9° + 180°

= 189°

7 0

3 years ago

If you’re good with probability math 30 please help with questions 33 and 35! real answers only

drek231 [11]

Answer: 33) b 34) a 35) none

Step-by-step explanation:

33)

Filling in the Venn Diagram (from Left to right, including outside of circles):

T only = 13

(T ∩ F)only = 6

F only = 21

(T ∩ D) only = 3

T ∩ F ∩ D = 5

(F ∩ D) only = 8

D only = 15

(T ∪ F ∪ D)' = 11

TOTAL = 82

$P(D'\cap F) = \dfrac{6+21}{13+6+21+3+5+8+15+11}\quad =\large\boxed{\dfrac{27}{82}}$

34)

Red = 26

Face = 12

Red ∩ Face = 6

Total cards = 52

R ∪ F = R + F - (R ∩ F)

= 26 + 12 - 6

= 32

$P(R\cup F)=\dfrac{R\cup F}{Total}\quad =\dfrac{32}{52}\quad \rightarrow \quad \large\boxed{\dfrac{8}{13}}$

35) Note that the total is 34 + 17 + 8 + 3 + 9 + 4 + 5 = 80

I think the teacher made an error, if so, then the answer is "d".

$P(C) = \dfrac{34+17+3+9}{Total} =\dfrac{53}{80}\quad \bigg(not\ \dfrac{34}{75}\bigg)\qquad \text{This is False.}\\\\\\P(S\cap T)=\dfrac{9+0}{Total}=\dfrac{9}{80}\quad \bigg(not\ \dfrac{12}{75}\bigg)\qquad \text{This is False.}\\\\\\\\P(C\cup T)\cup S = \dfrac{17+9+3+4}{Total}= \dfrac{33}{80}\quad \bigg(not\ \dfrac{38}{75}\bigg)\qquad \text{This is False.}\\\\\\P(C\cup T)\cap S'=\dfrac{34+17+8}{Total}=\dfrac{59}{80}\quad \bigg(not\ \dfrac{59}{75}\bigg)\quad \text{This is False.}$

7 0

3 years ago

Is 33/3 a natural, whole, integer, or rational number??????

Orlov [11]

Answer: All of it (natural, whole, integer, and rational)

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

A stadium has two sections, A and B.

Alekssandra [29.7K]

ANSWER: a=12 b=15
Explanation: (look at work below)

4a + 1b = 63 (eq1)
5a + 3b = 105 (eq2)
-12a + -3b = -189 (subt. eq1 from eq2)
————————-
-7a = -84
a = 12
4(12) + 1b = 63 (plug in the a value)
48 + 1b = 63
b = 15

5 0

3 years ago

Solve x^3 = 1/8. A. 1/2 B. ą1/ 2 C. 1/4 D. ą1/4

drek231 [11]

X equals 1/2. I got that answer by taking the root of both sides of the equation

5 0

3 years ago