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4 years ago

When Θ = 5 pi over 6, what are the reference angle and the sign values for sine, cosine, and tangent?

1 answer:

7 0

Ф =5π/6
The reference angle is the smallest angle that the terminal side of the angle makes with the x-axis.

Given that here π/2 < Ф < π, the angle is in the second quadrant.

In the second quadrant the signs are:

sine positive
cosine negative
tangent negative.

Furthermore, the reference angle is π - Ф = π - 5π/6 = π/6.

Then,

sin Ф = sin π/6 = 1/2
cos Ф = - cos π/6 = -√(3) / 2
tan Ф = - tan π/6 = -√(3) /3

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Derek wants to practice playing the guitar for 9 hours in 8 days. What is the

bonufazy [111]

Answer:

1 hour and 7.5 minutes or 67.5 per day will help him reach his goal of 9 hours per 8 days.

Step-by-step explanation:

9 hours

- 8 days

________

8 hours

1 hour left

1 hour is 60 minutes and 60/8 is 7.5 so each day will have added to it 7.5 minutes wish makes the answer 1 hour and 7.5 minutes or 67.5 minutes.

7 0

4 years ago

The equation 3.2p=16 represents the total cost of p of fruit that jamal bought at a farmers market. Solve for p yo find the numb

andre [41]

Answer:

p=5

Step-by-step explanation:

Let p represent the total cost of fruit purchased by Jamal at the farmers market.

It is given that $3.2p = 16$

Solving for p from the given equation:

$p = \frac{16}{3.2}$

=> p = 5

Hence,We can conclude that Jamal bought 5 pounds of fruit at the market.

Verification:

3.2 p = 3.2 * 5 = 16

Hence the left hand side of the equation is equal to the right hand side when p=5.

6 0

4 years ago

A sequence is defined by g(1) = 3 and g(n) = 2 • g(n-1) for n > 0. Which statement defines the nth term of g?

Anastasy [175]

Answer:

because g(n) = 2.g(n - 1) => this is a geometric progression

=> g(n) = 3.2^(n-1)

Step-by-step explanation:

7 0

3 years ago

A federal report found that a lie detector test given to someone telling the truth will suggest that they lied in about 20% of c

aleksley [76]

Answer:

$0.055$

Step-by-step explanation:

Let $p$ be the probability of lying an applicant, so, $p=20 \%$ .

$\Rightarrow p=\frac {20}{100}=\frac {1}{5}\;\cdots (i)$

Any applicant will either lie or will tell the truth.

Let $q$ be the probability of telling the truth, so, $q= 1-\frac {1}{5}$

$\Rightarrow q=\frac {4}{5}$

As for every applicant $p+q=1$ , so this is Bernoullies trials, for which

the probability of success of exactly $x$ times of an event out of $n$ trials is $P(x)=\binom {n}{x} p^xq^{n-x}\; \cdots (iii)$ .

Now, let $E$ be the event of at least one of the applicants is lying out of $11$ applicants, here the total number of applicants, $n=11$ .

So, $P(E)= P(x=1)+ P(x=2)+\cdots+ P(x=11)$

This is equivalent to

$P(E)=1-P(x=0)$ as $[P(x=0)+P(x=1)+ P(x=2)+\cdots+ P(x=11)=1]$

Now, from equation (iii),

$P(E)=1-\binom {11}{0} p^0q^{11-0}$

$\Rightarrow P(E)=1-11\left(\frac {1}{5}\right)^0\left(\frac {4}{5}\right)^{11}$ [from equations s (i) and (ii)]

$\Rightarrow P(E)=1-11\times 1 \times \left(\frac {4}{5}\right)^{11}$

$\Rightarrow P(E)=1-0.945$ (approx)

$\Rightarrow P(E)=0.055$

Hence, the probability that the lie detector indicates that at least one of the applicants is lying is $0.055.$

7 0

3 years ago

Solve for t.

vova2212 [387]

Answer:

-5

Step-by-step explanation:

From your knowledge of multiplication tables, you know that ...

-35 = -(7×5) = 7×(-5)

Then comparing to the given equation, you realize ...

t = -5

_____

Or, you can recognize 7 as the coefficient of t and divide both sides of the equation by that:

-35/7 = (7t)/7

-5 = t

5 0

3 years ago

Read 2 more answers