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Troyanec [42]
3 years ago
7

How many of the first 1000 positive integers are multiples of both 4 and 5 but not 6 ?

Mathematics
1 answer:
castortr0y [4]3 years ago
5 0
Let's begin by breaking  each number down into its prime factors:    4 = 2 x 2    5 = 5    6 = 2 x 3 Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4, 5, and 6 by multiplying all common and unique prime factors of each number:    common prime factors: 2    unique prime factors:  2,5,3    LCM = 2 x 2 x 5 x 3 = 60 Next, let's determine how many times 60 goes into 10,000 (excluding remainder):    10,000/60 = 166 and 2/3    Multiples of ALL 3 numbers (4,5,6) = 166  Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4 and 5 by multiplying all common and unique prime factors of each number:    common prime factors:  none
    unique prime factors:  2 x 2 x 5
    LCM = 2 x 2 x 5 = 20 Next, let's determine how many times 20 goes into 10,000:
    10,000/20 = 500
    Multiples of BOTH numbers (4 and 5) = 500 Finally, let's subtract the multiples of ALL three numbers (4,5,6) from the multiples of BOTH numbers (4 and 5) to get our answer:   Multiples of ONLY numbers 4 and 5 (excluding 6):       500 - 166 = <span>334</span>
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The Interest on $2,000 for 2 years is $320 what is the simple interest rate?
Ronch [10]

Answer:

It would be 20

Step-by-step explanation:because you have to divide 320 by 2 which equals $160 for 1 year and then divide that by 2 again would be $80 for 6 months then divide it by 2 again which would be $40 and 3 months for it then divide it by 2 again and 1 and a half months equal $20

6 0
2 years ago
Enter an inequality that represents the description, and then solve.
kondaur [170]

Answer:

X > 9

Step-by-step explanation:

2x > 18

x > 18/2

x > 9

4 0
3 years ago
A rectangular cow pasture is enclosed on three sides by a fence and the fourth side is part of the side of a barn that is $400$
Rudiy27

Let us list out the given information:

Cost per foot = $5

Total fencing cost = $1200

Let L be the length of the barn that will maximize the area of the pasture and W be the width of the rectangular cow pasture.

From the given information, we need to do the fencing for three sides covering 1 L and 2 W's because other L will be the fourth side is part of the side of a barn. We need to write the equation based on the cost information.

If cost/foot is $5, then cost of length ' L ' will be 5L dollars and cost of '2W' width equals 10W dollars. Total cost is $1200. We can set up second equation as

5L + 10W = 1200. This can be simplified by dividing throughout the equation by 5 to get L+ 2W= 240. Solving for L we get L = 240 - 2W

Area of a rectangle is given by A = L ×W.

Substituting 240 - 2W for L we get the area function as..

A=(240 - 2W)×W= 240W-2W²

A = -2W²+240W.

When we have a function of the form f(x) = ax^2 + bx + c, then maximum value of the function can be obtained for x = -b/2a. Using that idea we can find the maximum area.

Here in the area function a = -2 and b = 240

For W = -b/2a = -240/2(-2) = -240/-4 = 60 feet, we get maximum area.

The question is asking us to find Length. We can substitute W = 60 in the equation L = 240 - 2W to find the Length.

L = 240 - 2(60) = 240 - 120 = 120 feet.

Conclusion: The length of the side parallel to the barn that will maximize the area of the pasture is 120 feet.

Note: Here the information 400 feet in the sentence "the fourth side is part of the side of a barn that is 400 feet long" given to distract us, we might not require that information to find the Length.

3 0
3 years ago
Please Help!
Vitek1552 [10]

Answer:

2. It will be a 7 3/4in x 12 1/4in rectangle

4.  31,987 in^2

6. 30 547/640 in^3

Step-by-step explanation:

2. This is a cross-section. In order to get the cross-section, you take your shape. (a 7 3/4 x 12 1/4 x 3 3/4 rectangle) and essentially you remove the last dimension (Height).

4. Take your surface area value (319 35/64) and multiply it by 100 (10 per dimension length and width). This leaves you with 319.87x100 = 31,987 in^2

6. (308 35/64)/10. Pretty easy, take 308.546875, divide by 10, and you get 30.8546875, which is 30 547/640 in^3 in fractions.

4 0
2 years ago
Read 2 more answers
Please help me thank you
BlackZzzverrR [31]

\frac{9}{2}  \div by \: 3
5 0
3 years ago
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