A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in

Write a function that represents the situation. Let t represent the time in years. You deposit $800 in an account that earns 7%

Anna35 [415]

Answer:

pretty sure it's 56 I could be wrong though

3 0

2 years ago

A school wants to put on a dance recital Middle School dancers have short programs that run 4 minutes long High School performer

sp2606 [1]

Answer: The answer is $\textup{M}+\textup{H}\leq 10~~\textup{and}4\textup{M}+7\textup{H}\leq 90.$

Step-by-step explanation: Given that a school wants to put on a dance recital. The programs of Middle school dancer will be short of 4 minutes each and programmes of High school performers will be long of 7 minutes each.

Number of middle school dances is "M" and number od high school dances is "H".

Since there cannot be more than 10 dances all together, so fisrt inequality can be written as

$\textup{M}+\textup{H}\leq 10.$

Also, the entire recital must take maximum 90 minutes, so the second inequality can be written as

$4\textup{M}+7\textup{H}\leq 90.$

Thus, the pair of inequalities is

$\textup{M}+\textup{H}\leq 10,\\\\4\textup{M}+7\textup{H}\leq 90.$

6 0

2 years ago

18 is what percent of 20?

velikii [3]

divide it

18/20 = 0.9

18 is 90% of 20

5 0

3 years ago

Read 2 more answers

Find the value of x. if necessary, round to the nearest tenth.

irina [24]

This looks blury can you get it a little more clear or I think it is just me!

6 0

2 years ago

Consider the case of a triangle with sides 5, 12, and the angle between them 90°.

Daniel [21]

Answer:

a) Applying Pithagoras Theorem

b) Trigonometric relations

c) No we can not

d) No we can not

e) See step-by-step explanation

f) See step-by-step-explanation

Step-by-step explanation:

a) The easiest method for calculating the missing side is applying Pithagoras Theorem

c² = a² + b²

c² = (5)² + (12)² ⇒ c² = 25 + 144 ⇒ c² = 169 ⇒ c = 13

b) The easiest method to find the missing angles, is to calculate the sin∠ and then look for arcsin fuction in tables.

sin ∠α = 5/13 sin ∠α = 0.3846 ⇒ arcsin (0.3846 ) α = 23⁰

Now we can either get the other angle subtracting 180 - 90 - 23 = 67⁰

Or calculating sinβ = 12 /13 sinβ = 0.9230 arcsin(0.9230) β = 67⁰

c) The law of cosines should not be applied to right triangles, in fact for instance in our particular case we have:

Question a)

c² = a² + b² - 2*a*b*cos90⁰ (law of cosines ) but cos 90⁰ = 0

then c² = a² + b² which is the expression for theorem of Pithagoras

In case you look for calculating the missing angles

c² = a² + b² - 2*5*13*cos α

169 = 25 + 144 - 2*5*13* cos α

As you can see 169 - 25 - 144 = 0

Then we can not apply law of cosine in right triangles, we shoul apply trigonometric relations and Pithagoras theorem, and as we saw you can get the expression of Pithagoras theorem from cosine law

c² = a² + b² - 2*a*b*cos∠90° cos ∠ 90° = 0

Then c² = a² + b²

3 0

2 years ago