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Lera25 [3.4K]
3 years ago
9

Find n(A) for the set A = {300, 301, 302, ..., 3000}

Mathematics
1 answer:
sergiy2304 [10]3 years ago
5 0

Answer:

  n(A) = 2701

Step-by-step explanation:

If we subtract 299 from the numbers in the set, we get the counting numbers ...

  {1, 2, 3, ..., 2701}

The number of elements in the set is 2701:

  n(A) = 2701

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Solve the problem.A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course. At that t
Mice21 [21]

Given:

A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course.

The distance between plan and mountain is 10 km.

A short time later, the bearing to the mountain becomes 45°.

Here NM is the distance between the plane from the mountain when the second bearing is taken.

We need to find the measure of NM.

We\text{ know that }\angle INM\text{ and }\angle\text{XNM are supplementary angles.}

The sum of the supplementary angles is 180 degrees.

\angle INM+\angle XNM=180^o\text{Substitute }\angle XNM=45^o\text{ in the equation.}

\angle INM+45^o=180^o

\angle INM=180^o-45^o

\angle INM=135^o

We know that the sum of all three angles of the triangle is 180 degrees.

\angle INM+\angle NIM+\angle INM=180^o\text{Substitute }\angle INM=135^o\text{ and }\angle NIM=35^o\text{ in the equation.}

135^o+35^o+\angle INM=180^o

170^o+\angle INM=180^o

\angle INM=180^o-170^o

\angle INM=10^o

Consider the sine law.

\frac{\sin N}{IM}=\frac{\sin M}{IN}=\frac{\sin I}{NM}

Take the equation to find the measure of NM.

\frac{\sin N}{IM}=\frac{\sin I}{NM}\text{Substitute }\angle N=135^o,\angle I=35^o,\text{ and IM=10 in the equation.}

\frac{\sin 135^o}{10}=\frac{\sin35^o}{NM}

NM=\frac{\sin 35^o}{\sin 135^o}\times10NM=8.11

Hence the measure of NM is 8.1 km.

The plane is 8.1 km far from the mountain when the second bearing is taken.

5 0
1 year ago
216 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as
Semenov [28]

Answer:

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Step-by-step explanation:

Given, the number of student enrolled= 216

Let us suppose number of student failed = x

Given,

no. of student passed is 5 times no. of student failed.

Then, no. of student passed = 5x

x +5x = 216

6x = 216

x = 216/6

x = 36

Thus, the no. of student failed is 36.

6 0
2 years ago
What is the slope of the line that contains the points (-3,5)and (-5,6)
tigry1 [53]
<span>(-3,5) (-5,6)
slope = 5-6 / -3 --5
</span><span>slope = -1 / 2

</span>
6 0
3 years ago
Brielle’s piggy bank has all nickels and dimes. The total value of the money in her piggy bank is $7.80. If Brielle
deff fn [24]

66*0.5=3.30

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ANSWER: 45 dimes

8 0
3 years ago
PLEASEE HELPP!!!! ASAPP PLEASE PLEASEE!!!
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Answer:

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3 years ago
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