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AveGali [126]
3 years ago
12

How many elements are in the set {whole numbers between 3 and 15}? 11 12 13

Mathematics
2 answers:
igor_vitrenko [27]3 years ago
7 0
Let S be the set of whole numbers between 3 and 15 then <span>S={3,4,5,6,7,8,9,10,11,12,13,14,15}</span> so How many elements are in the set ? just count them..
Softa [21]3 years ago
7 0

Whole numbers between 3 and 15 are given by:

{4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

Therefore, to answer the question, what we must do is to count the number of whole numbers that we have inside the set.

We note that, without including number 3 and including number 15, the number of integers is equal to 11.

Answer:

There are 11 elements in the set of whole numbers between 3 and 15.

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y =
miss Akunina [59]

Answer:

381.18 cubic units

Step-by-step explanation:

Graph the region:

desmos.com/calculator/iwvreqjz2m

The region is a trapezoid.  When we rotate it about x = 1, we get a hollow cylinder shape.  We can either use washer method or shell method to find the volume.

If we find the volume using washer method, we'll have to use two integrals, one for the triangular part of the trapezoid and one for rectangular part.  If we use shell method, we only need one integral.  So let's use shell method.

Cut a thin, vertical slice of the region.  The width of this slice is dx.  The height of the slice is y₂ − y₁ = x − 0 = x.  The radius of the shell is x − 1.

The volume of the shell is:

dV = 2π (x − 1) (x) dx

dV = 2π (x² − x) dx

The total volume is the sum of all the shells from x=5 to x=7.

V = ∫ dV

V = ∫₅⁷ 2π (x² − x) dx

V = 2π ∫₅⁷ (x² − x) dx

V = 2π (⅓ x³ − ½ x² + C) |₅⁷

V = 2π [(⅓ 7³ − ½ 7² + C) − (⅓ 5³ − ½ 5² + C)]

V = 2π [⅓ 7³ − ½ 7² − ⅓ 5³ + ½ 5²]

V = 2π [⅓ (7³ − 5³) + ½ (5² − 7²)]

V = 2π [⅓ (218) + ½ (-24)]

V = 2π (72⅔ − 12)

V = 121⅓ π

V ≈ 381.18

The volume is approximately 381.18 cubic units.

6 0
3 years ago
a company is offering a job with a salry of 30000 for the first year and a 5% raise each year after that If the 5% raise continu
stellarik [79]

Figure out 5% of 30,000: .05 x 30,000 = 1,500

Multiply 1,500 by the number years, but subtract the first year (as you don't receive a bonus) : 1,500 x 39 =  58,500

Now add the bonus with the initial salary: 58,500 + 30,000 = 88,500.

THE ANSWER IS $88,500!!! :)

5 0
3 years ago
What is the next term in the sequence below? -324,108,-36,12,...
liq [111]
This is a geometric sequence with a common ratio of -1/3 and an initial term of -324.  Any geometric sequence can be expressed as:
a(n)=ar^(n-1), in this case a=-324 and r=-1/3 so
a(n)=-324(-1/3)^(n-1)  so the 5th term will be
a(5)=-324(-1/3)^4
a(5)=-324/81
a(5)= -4
5 0
4 years ago
Read 2 more answers
n a jar of coins, the ratio of nickels to dimes is 5:7. If the jar contains 350 dimes, how many nickels are there?
irina1246 [14]

Answer:

250 nickles

Step-by-step explanation:

Nickles and dimes are coins with different currency values. One nickel(N) is equal to 5 cents while one dime(D) is equal to 10 cents. The ratio of nickel:dime is 5:7, to put into the equation it will be:

N/D= 5/7

7N=5D   ---> 1st equation

There are 350 dimes, the equation will be:

D=350   ----> 2nd equation

We can find out the number of nickels by substitute the 2nd equation into the first. The calculation will be

7N=5D

N= 5D/7

N=5(350)/7

N=  250

4 0
3 years ago
The Questions above.
Sergeeva-Olga [200]

Answer:

It's B.9

Step-by-step explanation:

Because

11+9=20

20+9= 29

29+9= 38

The common difference is positive because the arithmetic sequence is increasing.

8 0
3 years ago
Read 2 more answers
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