You have 12 cups of granola and 8 1/2 cups of peanuts to make trail mix. What is the greatest number of full batches of trail mix you can make? Explain how you found your answer. ( The Trail Mix Recipe : 2 2/3 cups granola, 1 1/3 cups of peanuts )

3. P(Y | X) = P(Y) and 6. P(X | Y) = P(X)

36 is least number of each for which this was possible.

The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers, or lcm(a, b), in mathematics and number theory.

4 is the LCM of 2 and 4. To get the smallest multiple that is exactly divisible by 2 and 4, i.e. 4, we must first determine the multiples of 2 and 4 (multiples of 2 = 2, 4, 6, 8; multiples of 4 = 4, 8, 12, 16).

Given:

Hot dogs cam in pack of 9.

Buns came in pack of 12.

Now, to find least number of each bought the same number of hot dogs as buns.

So, LCM(9, 12)

9= 3x 3

12= 2 x2 x 3

Thus, LCM(9, 12) = 3 x 3 x 2 x 2 = 36

Hence, 36 is least number of each for which this was possible.

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If 100 envelopes cost $0.70 then it would cost $1.75 for 250 envelopes.

If 100 envelopes cost $0.70, we can set up a proportion to determine the cost of 250 envelopes:

100 envelopes / $0.70 = 250 envelopes / x

Cross-multiplying:

100 × x = 250 × $0.70

Simplifying:

100x = 175

Dividing both sides by 100:

x = 175 / 100

x = $1.75

Therefore, it would cost $1.75 for 250 envelopes.

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Answer:

The y-intecept is [tex](0,-2)[/tex], and the x-intercept is [tex](8,0)[/tex].

Step-by-step explanation:

The interception points with the axes can be foun by making zero one variable.

If you wanna find y-interception, we must make x = 0.

If you wann find x-interception, we must make y = 0.

The given function is

[tex]y=\frac{1}{4}x-2[/tex]

For [tex]x=0[/tex], we have

[tex]y=\frac{1}{4}(0)-2\\y=-2[/tex]

For [tex]y=0[/tex], we have

[tex]y=\frac{1}{4}x-2\\0=\frac{1}{4}x-2\\2=\frac{1}{4}x\\x=8[/tex]

Therefore, the y-intecept is [tex](0,-2)[/tex], and the x-intercept is [tex](8,0)[/tex].

The image attached show this.

The triangle is isosceles.

A triangle is a polygon that has three vertices on each of its three sides. The angle that is created within the triangle is 180 degrees. It indicates that the sum of a triangle's interior angles is 180 degrees. This is a polygon with the fewest sides. At the end of the day, a triangle is characterized as a three-sided two-layered figure whose inside points are equivalent to 180°.

Given a triangle let the triangle be ΔABC

given angles (4x + 8), (5x + 2) and (6x - 10)

let ∠A = (4x + 8), ∠B =  (5x + 2) and ∠C  = (6x - 10)

we know that sum of angle of triangle is 180⁰

∠A + ∠B + ∠C = 180

4x + 8 + 5x + 2 + 6x - 10 = 180

15x = 180

x = 180/15 = 12

∠A = 4x + 8 = 4(12) + 8 = 56⁰

∠B = 5x + 2 = 5(12) + 2 = 62⁰

∠C = 6x - 10 = 6(12) - 10 = 62⁰

since ∠B = ∠C

it is the property of an isosceles triangle, An isosceles triangle is a triangle with any two sides that are the same length and angles on opposite sides that are the same size.

Hence the Given triangle is isosceles.

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Answer:

It is 70

Step-by-step explanation:

Both angles have to add up to 90 and I did the lesson ight

The tip for the cab is close to 10 percent is around $2.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A cab ride from the airport to your home costs $19.50.

Now, The tip given is 10% of the fare so,

= (10/100)×19.50.

= 0.1×19.50.

= 1.95.

So, The exact tip would be $1.95 which is approximately $2.

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The conversion of a percentage to a decimal number, divide the percentage by 100 it means that 275% represents 2.75 times the original quantity.

To convert a percentage to a decimal number,

divide the percentage value by 100.

Here's the step-by-step explanation for converting 275% to a decimal:

Take the percentage value (275%) and divide it by 100.

275 ÷ 100 = 2.75

So, 275% as a decimal is 2.75.

It means that 275% is equal to 2.75 times the whole quantity.

For example, if you have 100 dollars and increase it by 275%, you will end up with 100 + (2.75 × 100) = 375 dollars.

Therefore, the 275% as a decimal number is equal to 2.75.

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Answer:

3(3+4a)(1-2a)

Step-by-step explanation:

Lisa can either sell 100 hard candies or 50 chocolate to make $300.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Lisa wants to make at least $300.00 selling candy. Hard candy cost $3.00 per piece and chocolates cost $6.00 per piece.

Establishing the equation for this problem.

Let,

Hard candy = x

Chocolate = y

Therefore,

3x+6y=300

To find y, let x=0

3(0)+6y =300

6y = 300

y = 50

Similarly,

To find x, put y=0

3x+6(0)=300

3x=300

x=100

Hence, Lisa can sell 100 hard candies or 50 chocolate to make $300.

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Answer:  

[tex]\displaystyle\frac{35}{45}, \frac{49}{63}[/tex] are two equivalent fractions of the given fraction.

Step-by-step explanation:

We are given the following information in the question:

We are given the fraction:

[tex]\displaystyle\frac{7}{9}[/tex]

We have to find an equivalent fraction. This could be done by multiplying both the numerator and the denominator by the same number.

Equivalent fraction:

Multiplying both numerator and denominator by 5

[tex]\displaystyle\frac{7\times 5}{9\times 5} = \frac{35}{45}[/tex]

Multiplying both numerator and denominator by 7

[tex]\displaystyle\frac{7\times 7}{9\times 7} = \frac{49}{63}[/tex]

Hence, [tex]\displaystyle\frac{35}{45}, \frac{49}{63}[/tex] are two equivalent fractions of the given fraction.

The number of  each type of bill or coin the wallet contains is:

                                   4

It is given that:

A wallet holds $ 25 in total.

Also, the number of $ 1 bills,$ 5 bills and qaurters are present in equal number in the wallet.

Let the number of each coin or bill in the wallet be: x

Also, we know that:

1 quarter= 1/4 dollar

i.e.

1 quarter= 0.25 dollar

Hence, we get:

 x+5x+0.25x=25

i.e.

6.25 x=25

On dividing both side of the equation by 6.25 we get:

   x=25/6.25

i.e.

x=4

Hence, the number of each kind of coin or bill are: 4