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raketka [301]
1 year ago
8

2. A store is to pack pencils in boxes of 10 and 12 pieces. What is the smallest number of pencils that can be packed using the

boxes?​
Mathematics
1 answer:
Taya2010 [7]1 year ago
3 0

Answer:

2

Step-by-step explanation:

Obtain the greatest common factor of both 12 and 10

Factors of 10 = 1, 2, 5, 10

Factors of 12 = 1, 2, 3, 4, 6, 12

From the above, the greatest common factor of 10 and 12 is 2

Hence, smallest number of pencils using the boxes is 2

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Juan put three square tiles with sides 8 centimeters, 10 centimeters, and x centimeters together so that they form a right trian
Elan Coil [88]
Since the area of a square is equal to the square of one of its side's length, then the area should be equivalent to x^{2}.
A = x^{2} ---> equation (1)
By using pythagoras rule which states that the x^{2} = hyp^2 - opposite^2---> equation (2)
where the opposite side's length is 8 and the hypotenuse side's length is 10
by substituting by the values in equation (2) therefore,
x^{2} = 10^{2} - 8^{2} substitute this value in equation (1) then
A = x^{2} = 10^{2} -8^{2}
where A is the area of the square whose side is x
6 0
1 year ago
Read 2 more answers
Find the value of cosAcos2Acos3A...........cos998Acos999A where A=2π/1999
Lady bird [3.3K]
Hello,

Here is the demonstration in the book Person Guide to Mathematic by Khattar Dinesh.

Let's assume
P=cos(a)*cos(2a)*cos(3a)*....*cos(998a)*cos(999a)
Q=sin(a)*sin(2a)*sin(3a)*....*sin(998a)*sin(999a)

As sin x *cos x=sin (2x) /2

P*Q=1/2*sin(2a)*1/2sin(4a)*1/2*sin(6a)*....
         *1/2* sin(2*998a)*1/2*sin(2*999a) (there are 999 factors)
= 1/(2^999) * sin(2a)*sin(4a)*...
     *sin(998a)*sin(1000a)*sin(1002a)*....*sin(1996a)*sin(1998a)
 as sin(x)=-sin(2pi-x) and 2pi=1999a

sin(1000a)=-sin(2pi-1000a)=-sin(1999a-1000a)=-sin(999a)
sin(1002a)=-sin(2pi-1002a)=-sin(1999a-1002a)=-sin(997a)
...
sin(1996a)=-sin(2pi-1996a)=-sin(1999a-1996a)=-sin(3a)
sin(1998a)=-sin(2pi-1998a)=-sin(1999a-1998a)=-sin(a)

So  sin(2a)*sin(4a)*...
     *sin(998a)*sin(1000a)*sin(1002a)*....*sin(1996a)*sin(1998a)
= sin(a)*sin(2a)*sin(3a)*....*sin(998)*sin(999) since there are 500 sign "-".

Thus
P*Q=1/2^999*Q or Q!=0 then
P=1/(2^999)

       








7 0
1 year ago
Read 2 more answers
<>) Melinda
Vanyuwa [196]

Answer:

The statement "500 divided by 50 is 10" is a true statement

Step-by-step explanation:

In mathematics, we have a term that we refer to as Place Value.

Place Value in mathematics can be defined as the value that a digit has based on its position or place in a number.

Examples of place value is:

Thousands represented by Th

Hundreds represented by H

Tens represented by T

Units represented by U

In the above question,

500 ÷ 50 gives us 10.

This is true because, 500 as a number, the Digit 5 has a place value of hundreds

50 as a number , the digit 5 has a place values of Tens.

10 as a number, the digit 1 has a place value of Tens.

In mathematics, the multiplication of 2 numbers in a place value of Tens always gives us a place value of hundreds.

For example, 10 × 50 = 500

Likewise, when we divide, a number with a place value of hundreds by a number with a place value of tens, we have a number with a place value of tens.

For example: 500 ÷ 50 = 10.

Therefore, the statement "500 divided by 50 is 10" is a true statement

7 0
1 year ago
Sean’s age and Helen’s age are in the ratio of 3:5. Two years ago, Helen was twice as old as Sean was then. Find their present a
PolarNik [594]
Lets Sean's age be x
Helen's age by y
x/y=3/5
x=3/5y

Second equation
2(x-2)=y-2

on solving u get Helen as 10 and Sean as 6
3 0
2 years ago
Resistors are labeled 100 Ω. In fact, the actual resistances are uniformly distributed on the interval (95, 103). Find the mean
Zinaida [17]

Answer:

E[R] = 99 Ω

\sigma_R = 2.3094 Ω

P(98<R<102) = 0.5696

Step-by-step explanation:

The mean resistance is the average of edge values of interval.

Hence,

The mean resistance, E[R] = \frac{a+b}{2}  = \frac{95+103}{2} = \frac{198}{2} = 99 Ω

To find the standard deviation of resistance, we need to find variance first.

V(R) = \frac{(b-a)^2}{12} =\frac{(103-95)^2}{12} = 5.333

Hence,

The standard deviation of resistance, \sigma_R = \sqrt{V(R)} = \sqrt5.333 = 2.3094 Ω

To calculate the probability that resistance is between 98 Ω and 102 Ω, we need to find Normal Distributions.

z_1 = \frac{102-99}{2.3094} = 1.299

z_2 = \frac{98-99}{2.3094} = -0.433

From the Z-table, P(98<R<102) = 0.9032 - 0.3336 = 0.5696

5 0
2 years ago
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