What is the greatest common factor of a^6b^3 and a^4b^7

r 27 is the answer....

The number of cups of raisins needed to make 1/2 of the recipe is equal to [tex]1\frac{1}{3}[/tex] cups of raisins.

What is the unitary method ?

The unitary method is a method in which you find the value of one unit and then the value of required no. of units.

It is given that a full recipe asks for [tex]2\frac{2}{3}[/tex] cups of raisins.

We have to find the number of cups of raisins needed to make 1/2 of the recipe.

1 full recipe needs =  [tex]2\frac{2}{3}[/tex] cups of raisins.

So , the number of cups of raisins needed to make 1/2 of the recipe can be calculated by :

1/2 of recipe needs =  [tex]2\frac{2}{3}[/tex]  × [tex]\frac{1}{2}[/tex] cups of raisins

or

1/2 of the recipe needs :

= [tex]\frac{8}{3}[/tex]  × [tex]\frac{1}{2}[/tex] cups of raisins

= [tex]\frac{4}{3}[/tex]

or [tex]1\frac{1}{3}[/tex] cups of raisins

Therefore , the number of cups of raisins needed to make 1/2 of the recipe is equal to [tex]1\frac{1}{3}[/tex] cups of raisins.

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Answer:

10:4 On dividing both the number by 2 and 15 : 6

On dividing both the number by 3

Step-by-step explanation:

Given  : ratios 10:4 and 15:6 .

To find : you show that the ratios 10:4 abd 15:6 are equivalent.

Solution : We have given 10:4 and 15:6 .

For 10 : 4

On dividing both the number by 2

5 : 2

For 15 : 6

On dividing both the number by 3

5 : 2.

So, we can  see both are equal in ratio 5 : 2 .

Therefore, 10:4 On dividing both the number by 2 and 15 : 6

On dividing both the number by 3

Answer:

We know that:

[tex]C_{(N)}=15000+8000N[/tex]

So first we need to substitute the next equation in the C(N) equation

[tex]N_{(t)} = 100t-5t^{2}[/tex]

And therefore we have:

[tex]C_{(t)}=15,000 + 8000*(100t-5t^{2})\\C_{(t)}=15,000 + 800000t-40000t^{2}[/tex]

Finally we replace at t = 5 in the equation above and we have:

[tex]C_{(5)}=15,000 + 800000*5-40000*5^{2}\\C_{(5)}= 3015000[/tex]

The interpretation is that after 5 hours of operation, we have wasted 3015000 dollars producing cars.  

To calculate the cost of production as a function of time, substitute the production function N(t) into the cost formula C(N). After simplifying, the cost function is C(t) = 15,000 + 800,000t - 40,000t². At 5 hours, the cost is 3,015,000 dollars.

To find the cost C as a function of the time t of operation of the factory, we first use the formula for the number of cars produced N(t) = 100t - 5t². Then we substitute the expression for N(t) into the cost function C(N) = 15,000 + 8000N.

Substituting N(t) into C(N), we get:

This is the cost C as a function of time t.

When t = 5 hours, the function becomes:

This result means that the cost of production after 5 hours of operation is 3,015,000 dollars.

Answer:

The equation of line is y = 2x.

Step-by-step explanation:

Consider the provided information.

A coordinate grid is shown. The x axis values are from negative 5 to positive 5 in increments of 1 for each grid line, and the y axis values are from negative 10 to positive 10 in increments of 2 for each grid line.

The slope intercept form of an equation of line is: y = mx + c

Where m is the slope and c is the y intercept.

[tex]Slope = m = \frac{Rise}{Run}[/tex]

Increments or decrements in x axis value represent the Run. Increments or decrements in y axis value represent the Rise.

It is given that "y axis values are from negative 10 to positive 10 in increments of 2 for each grid line."

Thus the Rise is 2 unit.

The x axis values are from negative 5 to positive 5 in increments of 1 for each grid line,

Thus the Run is 1 unit.

Hence the slope is: [tex] Slope=m=\frac{Rise}{Run}=2[/tex]

It is given that line passing through (0,0) it means the y intercept is 0.

Now substitute the value of m and y intercept in slope intercept form..

y = 2x + 0

y = 2x

Hence, the equation of line is y = 2x.

Yes, 3.6 repeating is equal to 11 /3 .

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Number is,

⇒ 11 /3

Now, We know that;

⇒ 11 / 3

After divide we get;

⇒ 3.666666...

Thus, 3.6 repeating is equal to 11 /3 .

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The density of the brick, calculated by dividing its mass of 100g by its volume of 25cm3, is 4 g/cm³.

The density of a substance can be calculated using the formula density = mass/volume. In this case, the brick has a mass of 100g and a volume of 25cm3. Therefore, its density would be 100g / 25cm3 = 4 g/cm³. This means that the density of the brick is 4 grams per cubic centimeter.

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Answer:

division property of equality

Step-by-step explanation:

7q= 49

To solve this equation we  need to get 'q' alone

In order to get 'q' alone, we need to remove 7 from 'q'

Here 7 is multiplied with 'q'

To remove any number we always do opposite operation

Opposite operation of multiplication is division

So we divide both sides by 7

q= 7

Here we used division property of equality

Final answer:

By applying the equations of motion for an object in free fall, it's determined that the stone was dropped from 404 feet above the ground, considering its positions at two separate times and using the acceleration due to gravity.

Explanation:

To find the original height from which the stone was dropped, we can use the equations of motion under constant acceleration due to gravity. Since we are dealing with a vertical motion and we are given the stone's positions at two different times, the most appropriate equation to use is:

h = h0 + v0t - ½gt²

Where:

We know that the stone is 250 feet above the ground at a certain instant and 10 feet above the ground 3 seconds later. Thus, we can use these values to solve for h0 in two steps. Firstly, convert the given heights to the same unit of measurement if necessary (in this case, they are already in feet). Then, substitute the given values into the equation:

At t = 3 seconds, h = 10 feet:

10 = h0 - ½(32)(3)²

Solving this equation gives us:

h0 = 10 + ½(32)(3)² = 10 + 144 = 154 feet

However, this calculation only accounts for the latter part of the fall. To find the total height from which it was dropped, we need to consider the height above the 250 feet mark.

Since we initially observed the stone at 250 feet and then at 10 feet above the ground, it implies the stone was dropped from 250 feet + 154 feet = 404 feet above the ground.

To find the number when 5/3% of it is 4.75, you can set up the equation (5/3%) x N = 4.75 and solve for N.

To find the number when 5/3% of it is 4.75, we can set up the equation:

(5/3%) x N = 4.75

To solve for N, we need to convert the percentage to a decimal:

5/3% = 5/3 x 1/100 = 5/300 = 1/60

Now we can rewrite the equation:

(1/60) x N = 4.75

To isolate N, we can multiply both sides of the equation by 60:

N = 4.75 x 60 = 285

Therefore, the number is 285.