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attashe74 [19]
2 years ago
5

What is a trigonometric ratio

Mathematics
1 answer:
Crank2 years ago
5 0

ø=Angle theta

a= length of opposite side a

h=length of hypotenuse h

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The answer to the question is 5
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Tickets to a concert cost $50 for each orchestra seat and $40 for each
Vsevolod [243]

Answer:

H. the number of orchestra seat is 900

Step-by-step explanation:

Step one:

let the number of orchestra seat be x

and balcony seat be y

cost of orchestra= $50 each

cost of balcony =$40 each

total tickets= 1500

x+y= 1500----------1

amount earned= $69000

50x+40y=69000--------2

The system of equation for the situation is

x+y= 1500----------1

50x+40y=69000--------2

from 1, x=1500-y

put this in equation 2

50(1500-y)+40y=69000

75000-50y+40y=69000

-10y=69000-75000

-10y=-6000

divide both sides by -10

y=-6000/-10

y=600

put y= 600 in equation 1

x+600= 1500

x=1500-600

x=900

6 0
3 years ago
On the packaging for a triangular sail, the edge measurements for the sail are listed as 7 ft × 15 ft × 17 ft. Without unfurling
ASHA 777 [7]

Answer:

Shape of Triangular sail is Obtuse Angled Triangle.

Step-by-step explanation:

The triangle is obtuse since the sum of the squares of 2 sides are greater than the square of the third side. (Converse Pythagorean theorem) Hope this helps!

Given: Length of sides of triangular sail = 7 ft , 15 ft , 7 ft

To find: Shape of Sail .i.e., shape of triangle

We use a result which states that

if a , b  , c are sides of triangle where c is greater then a & b.

now, if c² < a² + b² then triangle is Acute angled

if c² = a² + b² then triangle is Right angled

if c² > a² + b² then triangle is Obtuse angled

here a = 7 , b = 7 &  c = 15

c² = 15² = 225

a² + b² = 7² + 7² = 49 + 49 = 98

since, c² > a² + b²

⇒ Triangle must be Obtuse Angled.

Therefore, Shape of Triangular sail is Obtuse Angled Triangle.

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3 years ago
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The answer is c. 64 divided by 4 is 16 and 8 divided by 5 is 16
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The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with me
lisov135 [29]

Answer:

a) <u>0.4647</u>

b) <u>24.6 secs</u>

Step-by-step explanation:

Let T be interval between two successive barges

t(t) = λe^λt where t > 0

The mean of the exponential

E(T) = 1/λ

E(T) = 8

1/λ = 8

λ = 1/8

∴ t(t) = 1/8×e^-t/8   [ t > 0]

Now the probability we need

p[T<5] = ₀∫⁵ t(t) dt

=₀∫⁵ 1/8×e^-t/8 dt

= 1/8 ₀∫⁵ e^-t/8 dt

= 1/8 [ (e^-t/8) / -1/8 ]₀⁵

= - [ e^-t/8]₀⁵

= - [ e^-5/8 - 1 ]

= 1 - e^-5/8 = <u>0.4647</u>

Therefore the probability that the time interval between two successive barges is less than 5 minutes is <u>0.4647</u>

<u></u>

b)

Now we find t such that;

p[T>t] = 0.95

so

t_∫¹⁰ t(x) dx = 0.95

t_∫¹⁰ 1/8×e^-x/8 = 0.95

1/8 t_∫¹⁰ e^-x/8 dx = 0.95

1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t  = 0.95

- [ e^-x/8]¹⁰_t = 0.96

- [ 0 - e^-t/8 ] = 0.95

e^-t/8 = 0.95

take log of both sides

log (e^-t/8) = log (0.95)

-t/8 = In(0.95)

-t/8 = -0.0513

t = 8 × 0.0513

t = 0.4104 (min)

so we convert to seconds

t = 0.4104 × 60

t = <u>24.6 secs</u>

Therefore the time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t is <u>24.6 secs</u>

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3 years ago
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