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allochka39001 [22]
4 years ago
5

Tickets prices for a science museum are $18 for adults and $12 for students. If $162 is collected from a group of 12 people, how

many adults and students are in a group?
Mathematics
1 answer:
riadik2000 [5.3K]4 years ago
6 0
X=number of adults, y= number of students

x+y=12
18x+12y=162

You can simplify the second equation by dividing by six: 3x+2y=27
Rearrange the first equation: y= 12-x. Plug y into the simplified second equation:

3x+2(12-x)=27
3x-2x+24=27
x=3.

Plug the now known x value into y=12-x. So y= 9.
Therefore, there are 3 adults and 9 students.

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A grocery store chain has been tracking data on the number of shoppers that use coupons. the data shows that 71% of all shoppers
sashaice [31]

The confidence interval comes out to be (0.685,0.735).

Calculating the Confidence Level and Other Terms

The confidence level can be calculated as follows,

z = \frac{36}{40} * 100%%  

z = 90 %

The margin error is given as, E= 0.025

The p value in this case is 0.71

Calculating the Confidence Interval

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

Confidence interval can be obtained by using the following formula,

(p-E, p+E) = (0.71-0.025, 0.71+0.025).

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3 0
2 years ago
What is the simplified version of 10x(426)
Effectus [21]
4260 is the answer

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3 0
4 years ago
Read 2 more answers
Mrs. Grubb bought some shirts for $4 each and some hats for $12 each. She bought 9 pieces of clothing for $100. Write a system o
Lana71 [14]

Answer:

Mrs. grub bought total number of shirts = 1

Mrs. grub bought total number of hats = 8

Step-by-step explanation:

Let Mrs. grub bought total number of shirts = x

Let Mrs. grub bought total number of hats = y

As given,

Price of 1 shirt = $4

Price of 1 hat = $12

⇒ Price of x shirts = $ 4x

   Price of y hats = $ 12y

Given that,

Mrs. Grubb bought total piece of clothes = 9

⇒ x + y = 9     .......(1)

Also given,

She bought all clothing for $100

⇒ 4x + 12 y = 100       ........(2)

Divide equation (2) by 4 we get

x + 3y = 25     .......(3)

Now,

Subtract equation (1) from equation (3) , we get

x + 3y  - ( x + y ) = 25 - 9

⇒ x + 3y - x - y = 16

⇒2y = 16

⇒y = \frac{16}{2} = 8

⇒ y = 8

Put value of y in equation (3), we get

x + 3(8) = 25

⇒x + 24 = 25

⇒x = 25 - 24 = 1

⇒x = 1

∴ we get

Mrs. grub bought total number of shirts = x = 1

Mrs. grub bought total number of hats = y = 8

8 0
3 years ago
In the year 1995, there were 1200 students at pine elementary school. In the year 2010 there were 1500 students. Find the rate o
AnnZ [28]

The rate of change from 1995 to 2010 is 20 students per year and the linear function that models the data will be: y=20x-38700

<em><u>Explanation</u></em>

In the year 1995, there were 1200 students and in the year 2010, there were 1500 students.

If x represents the year and y represents the number of students, then two points in form of (x,y) will be: (1995, 1200) and (2010, 1500)

So, the rate of change or slope = (change in value of y / change in value of x) =\frac{1500-1200}{2010-1995}= \frac{300}{15}=20

Now, plugging  slope(m) = 20 and first point (x_{1}, y_{1}) =(1995,1200)  into <u>point slope form of linear equation</u> y-y_{1} =m(x-x_{1}) , we will get.....

y-1200=20(x-1995)\\ \\ y-1200=20x-39900\\ \\ y= 20x-39900+1200\\ \\ y= 20x-38700



4 0
3 years ago
Question4..........................
belka [17]

Answer:

see explanation

Step-by-step explanation:

Given

- (\frac{2}{5} )²

The negative is outside the bracket and is not squared, that is

= - \frac{2}{5} × \frac{2}{5}

= - \frac{2(2)}{5(5)} = - \frac{4}{25}

Given

\frac{5^3}{3} = \frac{5(5)(5)}{3} = \frac{125}{3}

4 0
3 years ago
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