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babymother [125]
3 years ago
8

PLEASE HELP ME, THANKS:)

Mathematics
1 answer:
prisoha [69]3 years ago
4 0

<u>First, create M</u> (the set of all perfect square roots less than 100)

1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100 (disregard 10² since it is not LESS THAN 100)

M = {1, 2, 3, 4, 5, 6, 7, 8, 9}  <em>not sure if you want to include the negatives)</em>

<u>Next, create N</u> (the set of all even number less than 30)

N = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

<u>M ∩ N</u> = {2, 4, 6, 8}

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John deposited $2860 in a bank that pays 9% interest, compounded monthly. find the amount he will have at the end of 3 years ?
7nadin3 [17]
To find that you first need to find what 9% is. You can multiply the number, 2,860 by .09 to find out your answer. That should be equal to 257.40. Since you now have that number, you can multiply it by 36. 257.40 is your average per month and you want to know by 3 years. So then your next step is 257.4*36 (there is 36 months in 3 years) which should be equal to 9,266.40.
4 0
3 years ago
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On a certain hot​ summer's day, 645 people used the public swimming pool. The daily prices are $1.75 for children and $2.50 for
VladimirAG [237]

Answer:

327 children and 318 adults

Step-by-step explanation:

The x be the amount of children and y be the amount of adults that were at the swimming pool. We can use this to set up a system of equations:

x+y=645

1.75x+2.50y=1367.25

Move y to the other side in the first equation to isolate x and solve the system using substitution:

x=645-y

  1.75(645-y)+2.50y=1367.25

Distribute

1128.75-1.75y+2.50y=1367.25

         1128.75+0.75y=1367.25

Subtract 1128.75 from both sides

                        0.75y=238.5

Divide both sides by 0.75

                                y=318

x=645-y

x=645-318

x=327

327 children and 318 adults swam at the pool that day

4 0
2 years ago
Approximate area under the curve f(x) =-x^2+2x+4 from x=0 to x=3 by using summation notation with six rectangles and use the the
bekas [8.4K]

Answer:

Summation notation:

\frac{1}{2}\sum_{k=1}^6f((.5k))

or after using your function part:

\frac{1}{2}\sum_{k=1}^6(-(.5k)^2+2(.5k)+4)

After evaluating you get 11.125 square units.

Step-by-step explanation:

The width of each rectangle is the same so we want to take the distance from x=0 to x=3 and divide by 6 since we want 6 equal base lengths for our rectangles.

The distance between x=0 and x=3 is (3-0)=3.

We want to divide that length of 3 units by 6 which gives a length of a half per each base length.

We are doing right endpoint value so I'm going to stat at x=3. The first rectangle will be drawn to the height of f(3).

The next right endpoint is x=3-1/2=5/2=2.5, and the second rectangle will have a height of f(2.5).

The next will be at x=2.5-.5=2, and the third rectangle will have  a height of f(2).

The fourth rectangle will have a height of f(2-.5)=f(1.5).

The fifth one will have a height of f(1.5-.5)=f(1).

The last one because it is the sixth one will have a height of f(1-.5)=f(.5).

So to find the area of a rectangle you do base*time.

So we just need to evaluate:

\frac{1}{2}f(3)+\frac{1}{2}f(2.5)+\frac{1}{2}f(2)+\frac{1}{2}f(1.5)+\frac{1}{2}f(1)+\frac{1}{2}f(.5)

or by factoring out the 1/2 part:

\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))

To find f(3) replace x in -x^2+2x+4 with 3:

-3^2+2(3)+4

-9+6+4

1

To find f(2.5) replace x in -x^2+2x+4 with 2.5:

-2.5^2+2(2.5)+4

-6.25+5+4

2.75

To find f(2) replace x in -x^2+2x+4 with 2:

-2^2+2(2)+4

-4+4+4

4

To find (1.5) replace x in -x^2+2x+4 with 1.5:

-1.5^2+2(1.5)+4

-2.25+3+4

4.75

To find f(1) replace x in -x^2+2x+4 with 1:

-1^2+2(1)+4

-1+2+4

5

To find f(.5) replace x in -x^2+2x+4 with .5:

-.5^2+2(.5)+4

-.25+1+4

4.75

Now let's add those heights.  After we obtain this sum we multiply by 1/2 and we have our approximate area:

\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))

\frac{1}{2}(1+2.75+4+4.75+5+4.75)

\frac{1}{2}(22.25)

11.125

Okay now if you wanted the summation notation for:

\frac{1}{2}(f(3)+f(2.5)+f(2)+f(1.5)+f(1)+f(.5))

is it

\frac{1}{2}\sum_{k=1}^{6}(f(.5+.5(k-1)))

or after simplifying a bit:

\frac{1}{2}\sum_{k=1}^6 f((.5+.5k-.5))

\frac{1}{2}\sum_{k=1}^6f((.5k))

If you are wondering how I obtain the .5+.5(k-1):

I realize that 3,2.5,2,1.5,1,.5 is an arithmetic sequence with first term .5 if you the sequence from right to left (instead of left to right) and it is going up by .5 (reading from right to left.)

6 0
3 years ago
A line passes through the points (1, 4) and (3, –4). which is the slope of the line?
mr_godi [17]

stupid thin wont load

4 0
3 years ago
Which rules define the function graphed below? Edge
valentina_108 [34]

Answer:

B

Step-by-step explanation:

In the first part for every x, y is the value of x plus 2, while in the second part for every x. y is 5

4 0
2 years ago
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