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german
3 years ago
12

Amy's grandmother gave her 3 identical chocolate chip cookies and 4 identical sugar cookies. In how many different orders can Am

y eat the cookies such that either she eats a chocolate chip cookie first, she eats a chocolate chip cookie last, or both?
Mathematics
1 answer:
Dmitrij [34]3 years ago
6 0

Answer:

chocolate chip cookie first: 15 ways

chocolate chip cookie last: 15 ways

chocolate chip cookie first and last: 5 ways

Step-by-step explanation:

There is a total of 7 cookies.

Is she eats a chocolate cookie first, she will have 2 chocolate cookies and 4 sugar cookies (6 in total).

So, to find the number of different orders that Amy can eat the remaining cookies, we just need to calculate a combination of 6 choose 2 (that is, the number of ways we can put the 2 chocolate cookies among the 6 cookies) or a combination of 6 choose 4 (same thing, but for the sugar cookies):

C(6,2) = 6! / (2! * 4!) = 6 * 5 / 2 = 15 ways

Is she eats a chocolate cookie last, she will have 2 chocolate cookies and 4 sugar cookies (6 in total), so the problem is solved again with a combination of 6 choose 2:

C(6,2) = 15 ways

Is she eats a chocolate cookie first and last, she will have just 1 chocolate cookie left and 4 sugar cookies (5 in total), so the problem is solved with a combination of 5 choose 1 or a combination of 5 choose 4:

C(5,1) = 5! / (1! * 4!) = 5 ways

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Jane has 3 ¾ cups of yogurt that she wants to split into smaller containers. Each container can hold ¾ cup of yogurt.
den301095 [7]

Answer:

5 containers

Step-by-step explanation:

Converting to a decimal can make questions like this easier to solve.

3 3/4 = 3.75

3/4= .75

3.75 cups divided by .75 cup containers results in 5 containers needed.

7 0
3 years ago
Help plz I need this answer
meriva
The y-intercept is (0, 2). Only choices C and D will give that value. Of those, choice C is a decreasing exponential, while choice D is an increasing one (as shown in the graph).

The best selection is
  D. F(x) = 2(2.1)^(2x)
4 0
3 years ago
Use differentials to estimate the amount of material in a closed cylindrical can that is 60 cm high and 24 cm in diameter if the
alexira [117]

Answer:

dV=542.9 cm^{3}    

Step-by-step explanation:

Let's start with the equation of the volume of a cylinder:

V=\pi r^{2}*h

Where:

  • r is the radius of the cylinder (r=D/2=24/2=12 cm)
  • h is the high of the cylinder (h = 60 cm)

We can us partial derivatives to find the differential of this volume. So we will have:

dV=\frac{\partial V}{\partial r}dr+\frac{\partial V}{\partial h}dh (1)

Now:

\frac{\partial V}{\partial r}=2\pi r*h=2\pi 12*60=4523.9 cm^{2}

\frac{\partial V}{\partial h}=\pi 12^{2}=452.4 cm^{2}

dr is a differential of the radius, so in our case it is 0.1 cm and dh, differential of the high, is 0.1*2 cm. We multiply by 2 because we need to consider the top and the bottom of the cylinder.

Now we just need to put all of this definitions in the equation (1).

dV=4523.9*0.1+452.4*0.2=542.9 cm^{3}    

I hope it helps you!

6 0
4 years ago
Find an equation of the circle that has center (-4,3) and passes through (6,-4).
kumpel [21]

Answer:

(x+4)^2+(y-3)^2=149

Step-by-step explanation:

The equation of a circle is (x-h)^2+(y-k)^2=r^2 where (h,k) is the center of the circle and r is the radius of the circle.

Given that (h,k)\rightarrow(-4,3) and it passes (6,-4), their distance between each other must the radius of the circle, so we can use the distance formula to find the radius:

d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\d=\sqrt{(-4-3)^2+(6-(-4))^2}\\\\d=\sqrt{(-7)^2+10^2}\\\\d=\sqrt{49+100}\\\\d=\sqrt{149}

Therefore, if the length of the radius is r=\sqrt{149} units, then r^2=149, making the final equation of the circle (x+4)^2+(y-3)^2=149

5 0
3 years ago
Here is my question: -7 times x = 189
RSB [31]
Hey buddy
This is not complete can you please ask complete question
Thanks
8 0
3 years ago
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