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Nat2105 [25]
2 years ago
9

I am F years old and my brother is B years older. What is the sum of our ages? What will be the sum of our ages in three years?

What was the difference of our ages two year ago
Mathematics
1 answer:
dem82 [27]2 years ago
8 0

a) The sum of your ages is F + (F+B) = 2F+B.

b) In 3 years, the sum of your ages will be (F+3)+(F+B+3) = 2F+B+6.

c) The difference of your ages at any time is B.

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Trevor is analyzing a circle, y2 + x2 = 100, and a linear function g(x). Will they intersect?
lakkis [162]
Given a circle described by the equation:
y^2+x^2=100
and a function g(x) given by the table
\begin{center}
\begin{tabular}{ |c |c |c }
 x & g(x) \\
 -1 & -22 \\
 0 & -20  \\
1 & -18   
\end{tabular}
\end{center}

The function g(x) describes a straight line with the equation:
\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}  \\  \\  \frac{y-(-22)}{x-(-1)} = \frac{-20-(-22)}{0-(-1)}  \\  \\ \frac{y+22}{x+1} = \frac{-20+22}{0+1} = \frac{2}{1}  \\  \\ y+22=2(x+1)=2x+2 \\  \\ y=2x-20

To check if the circle and the line intersects, we substitute the equation of the line into the equation of the circle to see if we have a real solution.
i.e.
y^2+x^2=100 \\  \\ (2x-20)^2+x^2=100 \\  \\ 4x^2-80x+400+x^2=100 \\  \\ 5x^2-80x+300=0 \\  \\ x^2-16x+60=0 \\  \\ (x-6)(x-10)=0 \\  \\ x-6=0 \ or \ x-10=0 \\  \\ x=6 \ or \ x=10

When x = 6, y = 2(6) - 20 = 12 - 20 = -8 and when x = 10, y = 2(10) - 20 = 20 - 20 = 0

Therefore, the circle and the line intersect at the points (6, -8) and (10, 0).
8 0
2 years ago
Read 2 more answers
Suppose we have a group of 10 light users and 10 heavy users. what is the probability that exactly 3 of the 20 users are hiv pos
dmitriy555 [2]

Answer: The answer is 30%.


Step-by-step explanation:  Given that there is a group of 10 light users and 10 heavy users. We are to find the probability that exactly 3 of the 20 users are HIV positive.

We have the following four possible cases -

(i) All 3 are light users.

(ii) 1 is a light user and 2 are heavy users.

(iii) 2 are light users and 1 is a heavy user.

(iv) All 3 are heavy user.

Since there is a 45% chance of a light user to be HIV positive and 55% chance of a heavy user to be HIV positive, so the required probability is given by

p\\\\=\dfrac{3\times 0.45+1\times 0.45+2\times 0.55+2\times 0.45+1\times 0.55+3\times 0.55}{20}\\\\=\dfrac{6}{20}\\\\=0.3\\\\=30\%.

Thus, the probability is 30.

4 0
2 years ago
Mike and Krista rent a jet ski while on vacation. The rental cost is represented by the function c(h)=50+20h, where the number o
Step2247 [10]

Answer:

130

Step-by-step explanation:

Given the equation of the relation as c(h) =50 +20 h where c(h) is the total cost for h hours and h is the number of hours of use, then to find the cost of jet ski if 4 hours were used will be;

c(h)=50 +20 h

c(4)=50 +20*4

c(4)=50 +80

=130

5 0
2 years ago
An acute triangle has two sides measuring 8 cm and 10 cm . What is the best representation of the possible range of values for t
Mekhanik [1.2K]

Answer:

the right answer is 2 < s< 18

Step-by-step explanation:

The Third side of the triangle must be greater than the difference of the other two sides which is 10 -8= 2 and smaller than the sum of the other two sides of the triangle which is 10+8= 18.

so third side should be greater than 2 and less than 18.

So right answer is 2 < s< 18

5 0
2 years ago
The theoretical probability of an event occurring is Two-fifths. Which best describes the experimental probability associated wi
erik [133]

Answer:

Out of every 5 trials, the desired outcome will occur approximately 2 times

Step-by-step explanation:

The first statements states that it will happen exactly two times, but probability never guarantee the outcome

The third and fourth statement states out of 7 which cannot be true as 2-5 basically means out of 5

5 0
2 years ago
Read 2 more answers
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