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3 years ago

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.

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

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

$NM=\frac{\sin 35^o}{\sin 135^o}\times10$ $NM=8.11$

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:

The no. of student failed is 36.

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

7.80-3.30=4.50

4.50/0.10=45

ANSWER: 45 dimes

8 0

3 years ago

PLEASEE HELPP!!!! ASAPP PLEASE PLEASEE!!!

Darya [45]

Answer:

two are correct: side ED is equal to DC, and ABCDE is a pentagon

Step-by-step explanation:

pentagon is a polygon having 5 sides

You can find the length of BC by using the distance formula

5 0

3 years ago

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