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3 years ago

If sin⁡ θ>0 and tan⁡ θ<0, in which quadrant does the terminal side of θ lie?

Mathematics

1 answer:

AlladinOne [14]3 years ago

8 0

Answer:

Quadrant IV

Step-by-step explanation:

For an angle in the fourth quadrant the point P has positive x coordinate and negative y coordinate. Therefore: In Quadrant IV, cos(θ) > 0, sin(θ) < 0 and tan(θ) < 0 (Cosine positive). The quadrants in which cosine, sine and tangent are positive are often remembered using a favorite mnemonic.

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The quality assurance engineer of a receiving-sets manufacturer inspects receiving-sets in lots of 50. He selects 4 of the 50 re

Mariana [72]

Answer:

0.0430 = 4.30% probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.

Step-by-step explanation:

Sets are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

Lots of 50 means that $N = 50$

5 are defective, which means that $k = 5$

4 are selected, which means that $n = 4$

Find the probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.

This is $P(X = 2)$ . So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,50,4,5) = \frac{C_{5,2}*C_{45,2}}{C_{50,4}} = 0.0430$

0.0430 = 4.30% probability that exactly 2 of the 4 receiving-sets selected by the engineer are defective.

4 0

3 years ago

What is m∠D?<br><br> m∠D = °

Alex Ar [27]

Answer:

angle d would be 63 degrees since angle B and A would form a same side interior angle, which adds to 180 so angle A has to be 117. angle D also forms a same side interior with angle A, so 180-117=63.

4 0

3 years ago

Read 2 more answers

A total of 937 people attend the play. Admission was $2.00 for adults and $0.75 for students. The totral ticket sales amounted t

a_sh-v [17]

Answer:

x = students

y = adults

Linear Systems of Equations :

x + y = 937

0.75x + 2y = 1,109

Step-by-step explanation:

Step 1 : eliminate one of the variables

x + y = 937

0.75x + 2y = 1,109

-2(x + y = 937) = -2x - 2y = -1874

-2x - 2y = -1874

0.75x + 2y = 1109

We can eliminate y since -2y + 2y = 0

Step 2: Find x number of students.

-2x = -1874

+0.75x = 1109

____________

-1.25x = -765

____________ = 612 students attended

-1.25

937 - 612 = 325 adults

Check Answer :

612 x 0.75 = $459

325 x 2 = $650

$650 + $459 = $1,109

Therefore, there will be 612 students attending and 325 adults.

6 0

3 years ago

Two people are randomly chosen from an office with 4 managers and 8 office workers. If the first person, a manager, is not repla

Lisa [10]

Answer:

8/11 or 73%

Step-by-step explanation:

# of office workers to whole

Find the percentage of 8/11

Hopefully this helps, good luck!

6 0

2 years ago

X^2+12=40 what number must you add to complete the square?

posledela

Answer:

Step-by-step explanation:

1) If you really meant X^2+12=40, then this simplifies to x^2 = 28, and therefore x = ±√28, or x = ±2√7.

2) If you meant X^2+12x=40:

a) Take half of the coefficient of x: that would be (1/2)(12), or 6.

b) Square this result, obtaining: 6² = 36

c) Add this 36 to x^2 + 12x + 40, and then subtract it: We get:

x² + 12x + 36 - 36 = 40, or x² + 12x + 36 = 76

We have to add 36, as indicated above, to "complete the square."

4 0

3 years ago