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2 years ago

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One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years’ time, I wil

l be twice as old as my brother.” How old are they each now?
Good Luck!!

2 answers:

aleksklad [387]2 years ago

5 0

Answer:

17

Step-by-step explanation:

Let us suppose two years ago my brother's age was x years

Then, my age was 3x

Three years from now, my brother's age will be (x +2+3) = (x+5) years

And my age will be (3x+2+3) = (3x+5) years

But it is given that i will be twice as old as my brother.

So, 2(x+5)= (3x+5)

or, x= 5 years

So my brother's present age is 5+2= 7 years

And my age is 5*3+2= 17 years

Crank2 years ago

4 0

Pretty sure that the answer is 17

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2 years ago

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2 years ago

Need help please!! Will give points

Nataly [62]

Answer:

1. $\bar X=5.10$

2. $\sigma=0.47$

3. $\sigma^2=0.22$

Step-by-step explanation:

<u>QUESTION 1</u>

The given data set for the expenditure is

$4.85,5.10,5.50,4.75,4.50,5.00,6.00$

The formula for calculating the mean is given by,

$\bar X=\frac{\sum x}{n}$

We need to add all the expenditure and divide by the total number of days.

$\bar X=\frac{4.85+5.10+5.50+4.75+4.50+5.00+6.00}{7}$

This gives us,

$\bar X=\frac{35.7}{7}$

$\Rightarrow \bar X=5.10$ to the nearest hundredth.

<u>QUESTION 2</u>

The standard deviation of the data set is given by the formula;

$\sigma =\sqrt{\frac{\sum(x-\bar X)^2}{n} }$

This implies that,

$\sigma =\sqrt{\frac{(4.85-5.10)^2+(5.10-5.10)^2+(5.50-5.10)^2+(4.75-5.10)^2+(4.50-5.10)^2+(5.00-5.10)^2+(6.00-5.10)^2}{7} }$

This will give us,

$\sigma =\sqrt{\frac{(-0.25)^2+(0.00)^2+(0.40)^2+(-0.35)^2+(-0.60)^2+(-0.10)^2+(0.90)^2}{7} }$

$\sigma =\sqrt{\frac{0.0625+0+0.16+0.1225+0.36+0.01+0.81}{7} }$

$\sigma =\sqrt{\frac{61}{280} }$

$\sigma =0.466775$

to the nearest hundredth,

$\sigma =0.47$ .

<u>QUESTION 3</u>

The variance is the square of the standard deviation.

$\sigma^2 =(0.46675)^2$

$\sigma^2 =0.217857$

To the nearest hundred gives,

$\sigma^2 =0.22$

3 0

3 years ago

Solve the quadratic equation by using a graphic approach. Round your answer to the hundredths place.

den301095 [7]

Answer:

x = 3.24, x = -1.24

Step-by-step explanation:

The standard form for a quadratic equation is $ax^2+bx+c=0$ . For your equation a = 1, b = -2, c = -4. The quadratic formula you will be using is $x=\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}$ .

Plug in a = 1, b = -2, and c = -4 into the formula.

$=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}$

We'll do the top part first:

$\sqrt{\left(-2\right)^2-4\cdot \:1\cdot \left(-4\right)}$

Apply rule $- (-a) = a$

$=\sqrt{\left(-2\right)^2+4\cdot \:1\cdot \:4}$

Apply exponent rule $(-a)^{n} =a^n$ if $n$ is even

$(-2)^2=2^2$

$=\sqrt{2^2+4\cdot \:1\cdot \:4}$

Multiply the numbers

$=\sqrt{2^2+16}$

$2^2=4$

$=\sqrt{4+16}$

Add

$=\sqrt{20}$

The prime factorization of 20 is $2^2*5$

20 divides by 2. <em>20 = 10 * 2</em>

<em /> $=2*10$ <em />

10 divides by 2. <em>10 = 5 * 2</em>

<em /> $=2* \:2*5$ <em />

2 & 5 are prime numbers so you don't need to factor them anymore

$=2*2*5$

$=2^2*5$

$=\sqrt{2^2\cdot \:5}$

Apply radical rule $\sqrt[n]{ab} =\sqrt[n]{a} \sqrt[n]{b}$

$=\sqrt{5}\sqrt{2^2}$

Apply radical rule $\sqrt[n]{a^{n} } =a$ ; $\sqrt{2^2} =2$

$=2\sqrt{5}$

$=\frac{-\left(-2\right)\pm \:2\sqrt{5}}{2\cdot \:1}$

Because of the $\pm$ you have to separate the solutions so that one is positive and the other is negative.

$x=\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1},\:x=\frac{-\left(-2\right)-2\sqrt{5}}{2\cdot \:1}$

Positive x:

$\frac{-\left(-2\right)+2\sqrt{5}}{2\cdot \:1}$

Apply rule $-(-a)=a$

$=\frac{2+2\sqrt{5}}{2\cdot \:1}$

Multiply

$=\frac{2+2\sqrt{5}}{2}$

Factor $2+2\sqrt{5}$ and rewrite it as $=2\cdot \:1+2\sqrt{5}$ . Factor out 2 because it is the common term. $=2\left(1+\sqrt{5}\right)$ .

$=\frac{2\left(1+\sqrt{5}\right)}{2}$

Divide 2 by 2

$x=1+\sqrt{5}$ or $x=3.24$ (You'll probably have to use a calculator for the square root of 5)

^Repeating the process of positive x for negative x in order to get $x=1-\sqrt{5}$ or $x=-1.24$

4 0

2 years ago