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3 years ago

7

Mrs. Van Sant is using 1 scoop of lemonade mix for every 2 liters of water to make some lemonade. She is having a party and want

s to make 12 liters of lemonade. How much lemonade mix should she use?

1 answer:

sesenic [268]3 years ago

6 0

6 scoops of mix = 12 liters.

1 scoop = 2 liters, multiply both sides by 6 and that will give your answer.

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5. Let A = (x, y), B = {1,2). Find the Cartesian products of A and B: A x B? (Hint: the result will be a set of pairs (a, b) whe

hichkok12 [17]

Answer: A x B = {(x,1), (x,2), (y,1), (y,2)}

Step-by-step explanation:

The Cartesian product of any two sets M and N is the set of all possible ordered pairs such that the elements of M are first values and the elements of N are the second values.

The Cartesian product of sets M and N is denoted by M × N.

For Example : M = {x,y} and N={a,b}

Then , M × N ={(x,a), (x,b), (y,a), (y,b)}

Given : Let A = {x, y}, B = {1,2}

Then , the Cartesian products of A and B will be :

A x B = {(x,1), (x,2), (y,1), (y,2)}

Hence, the Cartesian products of A and B = A x B = {(x,1), (x,2), (y,1), (y,2)}

8 0

3 years ago

How would you go about finding the solution to this system of three equations in three variables? Be specific. For example, you

kupik [55]

I:2x – y + z = 7
II:x + 2y – 5z = -1
III:x – y = 6

you can first use III and substitute x or y to eliminate it in I and II (in this case x):
III: x=6+y
-> substitute x in I and II:
I': 2*(6+y)-y+z=7
12+2y-y+z=7
y+z=-5

II':(6+y)+2y-5z=-1
3y+6-5z=-1
3y-5z=-7

then you can subtract II' from 3*I' to eliminate y:
3*I'=3y+3z=-15

3*I'-II':
3y+3z-(3y-5z)=-15-(-7)
8z=-8
z=-1

insert z in II' to calculate y:
3y-5z=-7
3y+5=-7
3y=-12
y=-4

insert y into III to calculate x:
x-(-4)=6
x+4=6
x=2

so the solution is
x=2
y=-4
z=-1

3 0

3 years ago

an Carlos County Health Department reported 17 new cases of tuberculosis in the first half of 2001 and 18 additional cases durin

Tpy6a [65]

Answer:

San Carlos County

Step-by-step explanation:

a) Data and Calculations:

Number of cases of tuberculosis reported in the first half of 2001 = 17

Number of cases of tuberculosis reported in the second half = 18

Total number of cases reported = 35 (17 + 18)

Population of the county at the beginning of 2001 = 204,500

Population of the county at the end of the year = 215,000

Average population for the year = 209,750 (204,500 + 215,000)/2

Therefore, the incidence rate of tuberculosis in the county = 35/209,750 * 100

= 0.000167

b) Since the incidence rate is <1, it suggests that the population of San Carlos County is at a very reduced risk of exposure to tuberculosis. This means that only 1 in 6,000 (209,750/35) people are exposed to the disease in the county.

5 0

2 years ago

There is a bag filled with 5 blue and 6 red marbles.

Afina-wow [57]

Answer:

The probability of getting two of the same color is 61/121 or about 50.41%.

Step-by-step explanation:

The bag is filled with five blue marbles and six red marbles.

And we want to find the probability of getting two of the same color.

If we're getting two of the same color, this means that we are either getting Red - Red or Blue - Blue.

In other words, we can find the independent probability of each case and add the probabilities together*.

The probability of getting a red marble first is:

$\displaystyle P\left(\text{Red}\right)=\frac{6}{11}$

Since the marble is replaced, the probability of getting another red is: $\displaystyle P\left(\text{Red, Red}\right)=\frac{6}{11}\cdot \frac{6}{11}=\frac{36}{121}$

The probability of getting a blue marble first is:

$\displaystyle P\left(\text{Blue}\right)=\frac{5}{11}$

And the probability of getting another blue is:

$\displaystyle P\left(\text{Blue, Blue}\right)=\frac{5}{11}\cdot \frac{5}{11}=\frac{25}{121}$

So, the probability of getting two of the same color is:

$\displaystyle P(\text{Same})=\frac{36}{121}+\frac{25}{121}=\frac{61}{121}\approx50.41\%$

*Note:

We can only add the probabilities together because the event is mutually exclusive. That is, a red marble is a red marble and a blue marble is a blue marble: a marble cannot be both red and blue simultaneously.

4 0

2 years ago

Select yes or no to indicate whether a zero must be written in the dividend to find the quotient

neonofarm [45]

Answer:

2.25 divided by 0.6 : Yes and 5.2 divided by 8, 3.63 divided by 3, 71.1 divided by 9 : No

Step-by-step explanation:

We have that when two numbers are divided, they can be written in the form $\frac{p}{q}$ , where p is the dividend and q is the divisor.

Now, when we divide 5.2 by 8, we can write $\frac{5.2}{8}$

Also, the division 3.63 by 3, can be written as $\frac{3.63}{3}$ = 1.21

Further, when we divide 71.1 by 3, we can write $\frac{71.1}{3}$ = 23.7

We can see that above divisions are easy divisions and do not require to write any type of 0 in the numerator.

Moreover, when we divide 2.25 by 0.6, we can write $\frac{2.25}{0.6}$ = $\frac{2.25\times 10}{6}$ .

So, we get that in the last division, we need to write a zero in order to multiply the numerator with 10 for easy division.

Hence, 2.25 divided by 0.6 : Yes and 5.2 divided by 8, 3.63 divided by 3, 71.1 divided by 9 : No

3 0

3 years ago