HELP ME PLEASE!!!

A father leaves his money to his four children the first received 1/3 the second received 1/6 and the third received 2/5 how muc

Eduardwww [97]

Answer:

The remaining child got a fraction of $\frac{1}{10}$ .

Step-by-step explanation:

Lets take the fraction of the money fourth child got is $x$

Addition of all these fractions should be equal to 1.

⇒ $\frac{1}{3} +\frac{1}{6} +\frac{2}{5} +x=1$

⇒ $\frac{10+5+12+30x}{30} =1$ (Taking a common denominator)

⇒ $\frac{27+30x}{30} =1$

⇒ $27+30x=30$

⇒ $30x=3$

⇒ $x=0.1$

Therefore,

The remaining child got a fraction of $\frac{1}{10}$ .

4 0

3 years ago

In 2001, gold was priced at (0.5x + 300) dollars per ounce. Its price tripled in 2008 and then doubled in 2011. In 2016, its pri

zloy xaker [14]

Given:

Price of gold in 2001 = (0.5x+300)

Its price tripled in 2008 and then doubled in 2011. In 2016, its price dropped to $\dfrac{2}{3}$ of the price in 2011.

To find:

An expression for the price of gold per ounce in 2016.

Solution:

We have,

Price of gold in 2001 $= (0.5x+300)$

Its price tripled in 2008.

Price of gold in 2008 $= 3(0.5x+300)$

Then doubled in 2011.

Price of gold in 2011 $= 2\times 3(0.5x+300)$

In 2016, its price dropped to $\dfrac{2}{3}$ of the price in 2011.

Price of gold in 2016 $=\dfrac{2}{3}\times 2\times 3(0.5x+300)$

$=2\times 2(0.5x+300)$

$=4(0.5x+300)$

$=4(0.5x)+4(300)$

$=2x+1200$

Therefore, the required expression for the price of gold per ounce is (2x+1200).

8 0

3 years ago

Lucy had math and reading homework tonight. Lucy can solve each math problem in 5 minutes and she can read each page in 2.5 minu

drek231 [11]

Answer:

$x=18,y=6$ , graph is there for reference.

Step-by-step explanation:

Given,

$x$ is the number of math problem Lucy solved.

$y$ is the number of pages she read.

She can do each math problem in $5$ minutes, therefore she can solve $x$ number of questions into $5 \times x=5x$ minutes.

She can read each page in $2.5$ minutes, therefore she can read $y$ pages in 2.5y minutes.

As per given detail,

$5x+2.5y=105$ equation 1.

And,

It is given that number of math problems Lucy solved is 3 times the number of pages she read.

$x=3y$ equation 2.

We need to find $x$ and $y$ intercept of each of the equation to graph them.

For $x-intercept$ put y=0

We will get $x=\frac{105}{5} =21$

Thus the point is $(21,0)$

Let us find $y-intercept$ by assuming $x=0$

we get $y=\frac{105}{2.5} =42$

Thus the point is $(42,0)$

Join these two points.

Similarly considering the other equation $x=3y$

Here x-intercept would be at $y=0$

We will get $x=0$

Thus the point is $(0,0)$

Let us assume on more point, say $x=30$ , we get $y=10$

Thus the point is $(30,10)$

Join these two points.

We will get a point of intersection at $(18,6)$

Thus $x=18$ and $y=6$

8 0

4 years ago

You have $100 begging on February 1, 2009, you spend $1 each day. On what day do you spend your last dollar?

Leno4ka [110]

Is it a leap year? haha. But for real your anser will be May 11, 2009

7 0

4 years ago

Read 2 more answers

In the United States, 35% of households own a 4K television. Suppose we take a random sample of 150 households. (a) Describe the

sattari [20]

Answer:

(a) The distribution of the sample proportion is Normal distribution.

(b) The probability that in this sample of 150 households that more than 50% own a 4K television is 0.00012.

Step-by-step explanation:

We are given that in the United States, 35% of households own a 4K television.

Suppose we take a random sample of 150 households.

Let $\hat p$ = sample proportion of households who own a 4K television.

The z-score probability distribution for sample proportion is given by;

Z = $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion

p = population proportion of households own a 4K television = 35%

n = sample of households = 150

(a) The distribution of the sample proportion is related to the Normal distribution.

(b) Probability that in this sample of 150 households more than 50% own a 4K television is given by = P( $\hat p$ > 0.50)

P( $\hat p$ > 0.50) = P( $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ > $\frac{ 0.50-0.35}{\sqrt{\frac{0.50(1-0.50)}{150} } }$ ) = P(Z > 3.67) = 1 - P(Z $\leq$ 3.67)

= 1 - 0.99988 = 0.00012

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 3.67 in the z table which has an area of 0.99988.

Therefore, probability that in this sample of 150 households more than 50% own a 4K television is 0.00012.

8 0

3 years ago