Consider a machine that exchange quarters for dollar bills. Inserting one dollar bill returns four quarters and you may insert up to five one dollar bills at a time. Is 7 a possible input for the relation this change machine represents ?

The smallest number greater than 100 divisible by 2 is 102, divisible by ten is 110, divisible by four is 104.

It is an easy method of determining the divisibility of a number by a particular divisor, by just observing the number and not actually dividing it.

The number is 100

A smallest number greater than 100 has to be found which is divisible by 2.

All even numbers are divisible by 2, a number which has 0, 2, 4, 6, 8 at its ones position are divisible by 2.

The smallest number from 100 which is divisible by 2 is 102.

A smallest number greater than 100 has to be found which is divisible by 10.

A number is divisible by 10, if it has 0 at its ones position.

The number after 100 which has 0 at its ones position is 110.

A smallest number greater than 100 has to be found which is divisible by 4.

If last two digit of a number forms 00 or are divisible by 4, then the number is divisible by 4.

The smallest number from 100 which is divisible by 4 is 104.

To know more about Divisibility Rule

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First, let us solve for the slope of the line which it intersects with:

m’ = (y2 – y1) / (x2 – x1)

m’ = (-3 – 4) / (-2 – 5)

m’ = 1

The slope of the perpendicular line is the negative reciprocal, therefore:

m = - 1 / m’

m = - 1 / 1

m = -1

So the slope of the line is -1.

To find the slope, we use the formula for slope,

[tex]m=\frac{y_{2}-y_{2}} {x_{2}-x_{1}}[/tex]

Letting the point (2,5) be [tex](x_{1},y_{1})[/tex] and the point (4,10) be [tex](x_{2},y_{2})[/tex].

Now plugging in these values in the formula for slope, we get,

[tex]m=\frac{10-5}{4-2} =\frac{5}{2}[/tex]. The slope is [tex]\frac{5}{2}[/tex].

This basically means 5 mm of rain falls in every 2 hours, or 2.5 mm of rain falls every hour ([tex]\frac{5}{2} =2.5[/tex])

ANSWER: Slope is [tex]\frac{5}{2}[/tex] and 5 mm of rain falls every 2 hours.

7(x-3) = 4(x+5)

distribute:

7x-21 = 4x+20

add 21 to both sides

7x = 4x +41

subtract 4x from both sides

3x = 41

divide both sides by 3

x = 41 /3 = 13.67 ( repeating 6's) so it can be 13 2/3 as a fraction

the answer is 13 2/3

Cliff shot 6 baskets, Lyle shot 18 baskets, and Kyle also shot 18 baskets.

Let's represent the number of baskets Cliff shot as C.

Lyle shot three times as many baskets as Cliff, so Lyle shot 3C baskets.

Kyle shot 12 more baskets than Cliff, so Kyle shot C + 12 baskets.

Since Lyle and Kyle shot the same number of baskets, we can set their expressions equal to each other: 3C = C + 12.

Solving this equation, we find that C = 6.

Therefore, Cliff shot 6 baskets, Lyle shot 3C = 3(6) = 18 baskets, and Kyle shot C + 12 = 6 + 12 = 18 baskets.

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Answer:

i think the answer would be square feet

Step-by-step explanation:

The expanded equivalent of cos(a – b) is  cos(a)cos(b)+sin(a)sin(b).

Given that,

Based on the above information, the calculation is as follows:

= cos (a - b)

=  cos(a)cos(b)+sin(a)sin(b)

Therefore we can conclude that the expanded equivalent of cos(a – b) is  cos(a)cos(b)+sin(a)sin(b).

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Final answer:

A total of 456 sugar cubes touching the box.

Explanation:

To calculate the number of sugar cubes touching the box, we must consider the cubes that lie along each face of the box without double-counting the cubes that touch corners and edges.

The box dimensions are 8 x 6 x 18 inches, and each sugar cube is 1 x 1 x 1 inch.

For the top and bottom faces (6 x 18), we have

6*18 = 108 sugar cubes touching the box on each face, totaling 216 for both the top and bottom.

For the front and back faces (8 x 18), since we must exclude the top and bottom rows, we have

(8-2) x (18-2) = 6 x 16 = 96 sugar cubes for one face and 192 for both.

For the sides (8 x 6), excluding the top and bottom rows again, we have

(8-2) x (6-2) = 6 x 4 = 24 sugar cubes on one side and 48 in total for the two sides.

Adding all these together, we get 216 (top and bottom) + 192 (front and back) + 48 (sides) = 456 sugar cubes touching the box.

Remember, this method assumes a single layer of sugar cubes is in direct contact with the inside surface of the box.

The value of x in the expression (5x+15) (3x-3) is 15x^2 + 30x - 45.

The expression (5x+15) (3x-3) represents the multiplication of two binomials. To find the value of x, we can use the distributive property to simplify the expression:

Putting it all together, we have 15x^2 - 15x + 45x - 45. Combining like terms, the expression simplifies to 15x^2 + 30x - 45.

So, the value for x in the given expression is 15x^2 + 30x - 45.

Answer:

The amount left after 84 years is 59.70 mg.                        

Step-by-step explanation:

Given : If the decay of 742 mg of an isotope is described by the function [tex]A(t)= 742e^{-0.03t}[/tex], where t is time in years.

To find : The amount left after 84 years?

Solution :

The function of decay of 742 mg of an isotope is given by,

[tex]A(t)= 742e^{-0.03t}[/tex]

We have to find the amount left after 84 years.

i.e. put t=84 in the given function,

[tex]A(84)= 742e^{-0.03\times 84}[/tex]

[tex]A(84)= 742e^{-2.52}[/tex]

[tex]A(84)= 59.701[/tex]

Therefore, The amount left after 84 years is 59.70 mg.

f(x) = Ιx+1Ι

x = -5

Ι-5Ι = 5

so equation is 5+1

answer is 6