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kodGreya [7K]
3 years ago
9

A science class has 4 girls and 4 boys in the seventh grade and 5 girls and 7 boys in the eighth grade. The teacher randomly sel

ects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both girls?
Mathematics
1 answer:
e-lub [12.9K]3 years ago
7 0

Answer:

<u>The correct answer is 5/24 or 0.21</u>

Step-by-step explanation:

1. Let's review all the information given to answer the question correctly:

Science class in seventh grade = 4 girls and 4 boys

Science class in eighth grade = 5 girls and 7 boys

2. What is the probability that both students selected for the competition are girls,  a seventh grader and an eighth grader?

These are independent events, therefore:

Probability of two independent events = Probability of A * Probability of B

Probability of both students selected for the competition are girls = 4/8 * 5/12

Probability of both students selected for the competition are girls = 20/96 = 5/24

<u>The correct answer is 5/24 or 0.21</u>

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Hannah has to make 25 gallons of punch for a potluck. The punch is made of soda and fruit drink. The cost of the soda is $1.79 p
Rus_ich [418]

Answer:

Hannah needs 10 gallons of soda and 15 gallons of fruit drink

Step-by-step explanation:

Let

x -----> the number of gallons of soda needed

y ----> the number of gallons of fruit drink needed

we know that

x+y=25 -----> equation A

1.79x+2.49y=2.21(25)

1.79x+2.49y=55.25 -----> equation B

Solve the system by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (10,15)

see the attached figure

therefore

Hannah needs 10 gallons of soda and 15 gallons of fruit drink

3 0
3 years ago
Janice receives $.40 per pound for 1 to 99 pounds of aluminum cans he recycles. he receives $.50 per pound if you are cycles mor
Ilya [14]

Answer:

M=\left\{\begin{matrix}0.4x &x\leq99 \\ 0.5x &x>100 \\ \end{matrix}\right.

Step-by-step explanation:

<u>Function modeling</u>

Real-life situations often require the help of mathematics to model numerically what happens when the variables involved can change. It could even be used to predict some expected outcomes from those models.

The problem states Janice receives $.40 per pound when he recycles less or equal than 99 pounds of aluminum. If x is the number of recycled pounds, then the amount of money he receives is

M=0.4x

We also know that if he recycles more than 100 pounds of aluminum, the pay increases to $0.5 per pound. In that case, the amount of money is

M=0.5x

This is a case where the function is defined differently depending on the conditions of the input variable x. It's called a piecewise function. The function can be written as

M=\left\{\begin{matrix}0.4x &x\leq99 \\ 0.5x &x>100 \\ \end{matrix}\right.

Note the function is not well constructed because there is a gap for x=100 where M is not defined. If we establish that for 100 pounds the payment is $0.5, then the second piece would include x=100

5 0
3 years ago
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
steposvetlana [31]
An arithmetic sequence with first term a, and a common distance d si as follows:

m, m+d, m+2d, m+3d, ...

(for example: 3, 8, 13, 18 .... m=3, d=5)


let \displaystyle{ a_n be the n'th term of the arithmeti sequence

m, m+d, m+2d, m+3d, ...


then

a_1=m\\\\a_2=m+d\\\\a_3=m+2d\\\\a_4=m+3d \\\\ .\\\\.

so it is clear that the n'th term, si given by :

a(n)=m+(n-1)d


compare the rule we found with the given rule A(n)=-3+(n-1)(-2.2)

it is clear that m=-3, and d=-2.2, 

so the sequence 

m, m+d, m+2d, m+3d, ...

becomes:

-3, -3-2.2, -3-2*2.2, -3-3*2.2, ....

so
 
-3, -5.2, -7.4, -9.6


the first term is -3, the fourth term is -9.6, the 10th term can be found by plugging in n=10 in the formula:


<span>A(10) = –3 + (10 – 1)(–2.2)=-3+9(-2.2)=-3-19.8=-22.8




remark, we could have use the formula directly and solve for A(1), A(4) and A(10), 

but with the explanations we see how we find derive the formula, and makes it easier to derive, even when we don't remember it properly.



Answer:

1st term=-3

2nd term=-9.6

10th term = -22.8</span>
5 0
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Vedmedyk [2.9K]

Answer:

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Answer:

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