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3 years ago

10

Debbie studies for 12.5 hours, John studies for 6 hours, and Ashley studies for 1.5 hours. what is the average number of hours t

he 3 students study?

1 answer:

ale4655 [162]3 years ago

6 0

you can answer it six point six six six six six infinity or you can answer it 6.7 depending upon how they want

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Write the trigonometric expression sin(sin−1u−tan−1v) as an algebraic expression in u and v. Assume that the variables u and v r

igomit [66]

Answer:

[u – v√(1 – u²)]/√(1 + v²)

Step-by-step explanation:

Let sin^-1(u) = A, therefore sinA = u.

We know that sin(theta) = opposite/hypothenuse

Therefore, sinA = u/1 and u is the opposite side to angle A while 1 is the hypotenuse. Draw an acute triangle placing u opposite to angle A and 1 as the hypotenuse. By Pythagoras theorem the adjacent would be √(1 – u²).

By doing this, it means cosA = adjacent/hypotenuse = √(1 – u²)/1 = √(1 – u²)

Also, let tan^-1(v) = B, therefore tanB = v.

We know that tan(theta) = opposite/adjacent

Therefore, tanB = v/1 and v is the opposite side to angle B while 1 is the adjacent. Draw an acute triangle placing v opposite to angle B and 1 as the adjacent. By Pythagoras theorem the hypothenuse would be √(1 + v²).

Therefore, sinB = opposite/hypotenuse = v/√(1 + v²) and cosB = adjacent/hypotenuse = 1/√(1 + v²)

Now,

sin[sin^–1(u) – tan^–1(v)] =

sin(A – B) =

sinAcosB – sinBcosA =

u[1/√(1 + v²)] – [v/√(1 + v²)][√(1 – u²)] =

[u/√(1 + v²)] – [v√(1 – u²)/√1 + v²)] =

[u – v√(1 – u²)]/√(1 + v²).

8 0

3 years ago

Adam exchanged British pounds for Swiss franc He changed £400 into 592 francs What was the exchange rate of British pounds to Sw

OLEGan [10]

Answer: 1 : 1.48

Step-by-step explanation:

Adam was able to change £400 into 592 francs which means that the British pound is stronger because it was able to buy more Swiss francs.

The exchange rate can be gotten using direct proportion:

400 : 592

1 : x

Cross multiply:

400x = 592

x = 592/400

x = 1.48

Exchange rate is:

= 1 : 1.48

5 0

3 years ago

A university's freshman class has 5000 students. 80% of those students are majoring

icang [17]

Answer:

4000

Step-by-step explanation:

5000 * .8 is 4000

3 0

3 years ago

Read 2 more answers

Members of a softball team raised $1513.50 to go to a tournament. They rented a bus for $961.50 and budgeted $46 per player for

aniked [119]

Answer: 1513.50=961.50+46x

The number of players the team can bring to the tournament = 12.

Step-by-step explanation:

Let x= the number of players the team can bring to the tournament.

Total money raised = Rent of bus + (Cost per player) (Number of players)

$1513.50=961.50+46x\\\\\Rightarrow\ 46x=1513.50-961.50\\\\\Rightarrow\ 46x = 552\\\\\Rightarrow x=\dfrac{552}{46}\\\\\Rightarrow x=12$

Hence, the number of players the team can bring to the tournament = 12.

6 0

3 years ago

Suppose there is a 1.2°F drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on

Nesterboy [21]

Answer: $49.7^{\circ}F$

Step-by-step explanation:

Given

The temperature on the ground is $56.9^{\circ}F$

temperature drop observed is $1.2^{\circ}F\ \text{per 1000 ft}$

The height of the plane is $6000\ ft$

The total increase in height per $1000\ ft$ is $6$ units

Temperature drop is

$\Rightarrow 1.2\times 6=7.2^{\circ}F$

The temperature at that altitude is

$\Rightarrow 56.9-7.2=49.7^{\circ}F$

5 0

3 years ago