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3 years ago

Estimate how many times larger 10 x 109 is than 99 x 106.

Mathematics

2 answers:

Yuri [45]3 years ago

6 0

It is C.
I hope i helped!

maw [93]3 years ago

6 0

Answer:

Option C is correct.

Step-by-step explanation:

Given two numbers

$10\times 10^9\text{ and } 99\times 10^6$

we have to estimate about many times a number larger than another.

To estimate we have to divide.

$\frac{10\times 10^9}{99\times 10^6}$ → (1)

As $\frac{x^a}{x^b}=x^{a-b}$

Equation (1) implies

$\frac{10\times 10^{9-6}}{99}$

⇒ $\frac{10\times 10^3}{99}$

⇒ $\frac{10000}{99}=101.01\sim 100\thinspace times$

Hence, 100 times larger.

Option C is correct.

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1. Each kid eats the same amount of food each morning.

Serhud [2]

Answer:

a) One kid eat tubs of yogurt = 1.3 tub of yogurt

b) One kid eat granola = 3.33 ounces

c) cost to feed one kid each morning is $1.12

Step-by-step explanation:

Three kids eat tubs of yogurt = 4

Three kids eat granola = 10 ounces

Cost of one tub of yogurt = 54 cents

Cost of 10 ounces of cereal = $1.26

a) One kid eats how many tubs of yogurt in a morning?

Three kids eat tubs of yogurt = 4

One kid eat tubs of yogurt = 4/3

= 1.3 tub of yogurt

b) How many ounces of granola does a kid eat each morning?

Three kids eat granola = 10 ounces

One kid eat granola = 10/3

= 3.33 ounces

c) How much does it cost to feed one kid each morning?

Cost of 1 tub of yogurt = 54 cents

Cost of 1.3 tub of yogurt = 54*1.3 = 70.2 cents

Converting cents to dollar:

100 cents = 1 dollar

70.2 cents = $0.7

So, Cost of 1.3 tub of yogurt (for one kid)= $0.7

Cost of 10 ounces of cereal = 1.26

Cost of 1 ounce of cereal = 1.26/10

Cost of 3.33 ounces of cereal = (1.26/10)*3.33

= $0.42

Cost of 3.33 ounces of cereal (for one kid) = $0.42

Total cost for each kid = $0.42+$0.7 = $1.12

So, cost to feed one kid each morning is $1.12

7 0

3 years ago

How to do the inverse of a 3x3 matrix gaussian elimination.

nata0808 [166]

As an example, let's invert the matrix

$\begin{bmatrix}-3&2&1\\2&1&1\\1&1&1\end{bmatrix}$

We construct the augmented matrix,

$\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 2 & 1 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 \end{array} \right]$

On this augmented matrix, we perform row operations in such a way as to transform the matrix on the left side into the identity matrix, and the matrix on the right will be the inverse that we want to find.

Now we can carry out Gaussian elimination.

• Eliminate the column 1 entry in row 2.

Combine 2 times row 1 with 3 times row 2 :

2 (-3, 2, 1, 1, 0, 0) + 3 (2, 1, 1, 0, 1, 0)

= (-6, 4, 2, 2, 0, 0) + (6, 3, 3, 0, 3, 0)

= (0, 7, 5, 2, 3, 0)

which changes the augmented matrix to

$\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 7 & 5 & 2 & 3 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 \end{array} \right]$

• Eliminate the column 1 entry in row 3.

Using the new aug. matrix, combine row 1 and 3 times row 3 :

(-3, 2, 1, 1, 0, 0) + 3 (1, 1, 1, 0, 0, 1)

= (-3, 2, 1, 1, 0, 0) + (3, 3, 3, 0, 0, 3)

= (0, 5, 4, 1, 0, 3)

$\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 7 & 5 & 2 & 3 & 0 \\ 0 & 5 & 4 & 1 & 0 & 3 \end{array} \right]$

• Eliminate the column 2 entry in row 3.

Combine -5 times row 2 and 7 times row 3 :

-5 (0, 7, 5, 2, 3, 0) + 7 (0, 5, 4, 1, 0, 3)

= (0, -35, -25, -10, -15, 0) + (0, 35, 28, 7, 0, 21)

= (0, 0, 3, -3, -15, 21)

$\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 7 & 5 & 2 & 3 & 0 \\ 0 & 0 & 3 & -3 & -15 & 21 \end{array} \right]$

• Multiply row 3 by 1/3 :

$\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 7 & 5 & 2 & 3 & 0 \\ 0 & 0 & 1 & -1 & -5 & 7 \end{array} \right]$

• Eliminate the column 3 entry in row 2.

Combine row 2 and -5 times row 3 :

(0, 7, 5, 2, 3, 0) - 5 (0, 0, 1, -1, -5, 7)

= (0, 7, 5, 2, 3, 0) + (0, 0, -5, 5, 25, -35)

= (0, 7, 0, 7, 28, -35)

$\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 7 & 0 & 7 & 28 & -35 \\ 0 & 0 & 1 & -1 & -5 & 7 \end{array} \right]$

• Multiply row 2 by 1/7 :

$\left[ \begin{array}{ccc|ccc} -3 & 2 & 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 1 & 4 & -5 \\ 0 & 0 & 1 & -1 & -5 & 7 \end{array} \right]$

• Eliminate the column 2 and 3 entries in row 1.

Combine row 1, -2 times row 2, and -1 times row 3 :

(-3, 2, 1, 1, 0, 0) - 2 (0, 1, 0, 1, 4, -5) - (0, 0, 1, -1, -5, 7)

= (-3, 2, 1, 1, 0, 0) + (0, -2, 0, -2, -8, 10) + (0, 0, -1, 1, 5, -7)

= (-3, 0, 0, 0, -3, 3)

$\left[ \begin{array}{ccc|ccc} -3 & 0 & 0 & 0 & -3 & 3 \\ 0 & 1 & 0 & 1 & 4 & -5 \\ 0 & 0 & 1 & -1 & -5 & 7 \end{array} \right]$

• Multiply row 1 by -1/3 :

$\left[ \begin{array}{ccc|ccc} 1 & 0 & 0 & 0 & 1 & -1 \\ 0 & 1 & 0 & 1 & 4 & -5 \\ 0 & 0 & 1 & -1 & -5 & 7 \end{array} \right]$

So, the inverse of our matrix is

$\begin{bmatrix}-3&2&1\\2&1&1\\1&1&1\end{bmatrix}^{-1} = \begin{bmatrix}0&1&-1\\1&4&-5\\-1&-5&7\end{bmatrix}$

6 0

3 years ago

The sum of three numbers is 104. The first number is 10 less than the second. The third number is 4 times the second. What are t

Shalnov [3]

Answer:

The numbers are 9, 19 and 76.

Step-by-step explanation:

Let's take the second number and make it a variable, like x. Now let's find all the other numbers in terms of x.

The first number in terms of x:

$x - 10$

The second number in terms of x:

$4x$

If we add them all up, these 3 numbers in terms of x must be equal to 104, so:

$x + (x - 10) + (4x) = 104 \\ x + x - 10 + 4x = 104 \\ 6x - 10 = 104 \\ 6x = 114 \\ x = 19$

Now that we know the second number, we can find the other numbers since we already figured out their values in terms of x:

$19 - 10 = 9$

$4 \times 19 = 76$

The first number is 9, second number 19 and the third number 76.

6 0

3 years ago

Which angles are adjacent to each other?

alexdok [17]

Answer:

(c). Angle 12 and 9

Step-by-step explanation:

7 0

3 years ago

A intercept of 2 and slope of 1/6

Mekhanik [1.2K]

I’m assuming you want it in slope intercept form so it’s y=1/6x-2

6 0

3 years ago