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3 years ago

In what positive integral number base is 231 double 113

Mathematics

1 answer:

ad-work [718]3 years ago

5 0

Answer:

Base 5

Step-by-step explanation:

We want to determine the base at which:

113 X 2 =231

We consider the last number of the result (231).

The base must be a number such that:

3 X 2 will have a remainder of 1.

3 X 2 = 6 = 5 Remainder 1

Therefore:

113 X 2 =231 in positive integral number base 5.

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How mamy ways can you add three differemt numbers to get a sum of 20

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You can do 5+5+10, 6+6+8, 9+9+2, 4+4+12, 3+3+14, 2+2+16, 1+1+18. I believe these are all of them, so there are 7 ways.

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4 years ago

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Write 5 Expressions that are equivalent to 20x + 100

lapo4ka [179]

1st. x times 20+100
2nd. 100+20x
3rd. 100+x times20
4th. 20x+100
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3 years ago

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For her presentation on the Wonders of the World, Mary baked a square pyramid-shaped cake as pictured below. The slant height of

mihalych1998 [28]

Answer:

$V=196in^3$

Step-by-step explanation:

The volume of a pyramid is:

$V=\frac{A_{b}h}{3}$

where $A_{b}$ is the area of the base and $h$ is the height (the perpendicular measurement between base and highest point, not the slant height)

Since the base is a square, the area is given by:

$A_{b}=l^2$

where $l$ is the length of the side: $l=8in$ , thus:

$A_{b}=(8in)^2\\A_{b}=64in^2$

Now we need to find the height, for this we use the right triangle that forms with half of a square side (8in/2 = 4in), the slant height (10in), and the height.

In this right triangle, the slant height is the hypotenuse, the leg 1 is the unknown height, and leg 2 is half of the square side.

Using pythagoras:

$hypotenuse^2=leg1^2+leg2^2$

substituting our values, and indicating that leg 1 is height h:

$(10in)^2=h^2+(4in)^2$

$100in^2=h^2+16in^2$

and solving for the height:

$h^2=100in^2-16in^2\\h^2=84in^2\\h=\sqrt{84in^2}\\ h=9.165in$

and finally we calculate the volume using this height and the area of the base:

$V=\frac{A_{b}h}{3}$

$V=\frac{(64in^2)(9.165in)}{3} \\V=195.5in^3$

rounding to the nearest cubic inch: $V=196in^3$

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4 years ago

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dlinn [17]

Step-by-step explanation:

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3 years ago

There are 10 employees in a particular division of a company. Their salaries have a mean of 570,000, a median of $55,000,and a s

harkovskaia [24]

Answer:

a) $160,000

b) $55,000

c) $332264.804

Step-by-step explanation:

We are given that there are 10 employees in a particular division of a company and their salaries have a mean of $70,000, a median of $55,000, and a standard deviation of $20,000.

And also the largest number on the list is $100,000 but By accident, this number is changed to $1,000,000.

a) Value of mean after the change in value is given by;

Original Mean = $70,000

$\frac{\sum X}{n}$ = $70,000 ⇒ $\sum X$ = 70,000 * 10 = $700,000

New $\sum X$ after change = $700,000 - $100,000 + $1,000,000 = $1600000

Therefore, New mean = $\frac{1600000}{10}$ = $160,000 .

b) Median will not get affected as median is the middle most value in the data set and since $1,000,000 is considered to be an outlier so median remain unchanged at $55,000 .

c) Original Variance = $20000^{2}$ i.e. $20000^{2}$ = $\frac{\sum x^{2} - n*xbar }{n -1}$

Original $\sum x^{2}$ = ( $20000^{2}$ * (10-1)) + (10 * 70,000) = $3,600,700,000

New $\sum x^{2}$ = $3,600,700,000 - $100,000^{2} + 1,000,000^{2}$ = 9.936007 * $10^{11}$

New Variance = $\frac{new\sum x^{2} - n*new xbar }{n -1}$ = $\frac{9.936007 *10^{11} - 10*160000 }{10 -1}$ = 1.103999 * $10^{11}$ Therefore, standard deviation after change = $\sqrt{1.103999 * 10^{11} }$ = $332264.804 .

7 0

4 years ago