All categories

3 years ago

Please help ASAP

1 answer:

6 0

$A=P(1+ \frac{r}{n})^ \frac{t}{n}$
A=future amount
P=present amount
r=rate in decimal
n=number of times per year compounded
t=time in years

how many years to double
basically
A=2P at t=?
so we can simplify and ignore the pricipal given and do
$2=(1+ \frac{r}{n})^ \frac{t}{n}$
r=7%=0.07
n=2 (semiannualy means 2 times per year)
t=t

$2=(1+ \frac{0.07}{2})^ \frac{t}{2}$
$2=(1+ 0.035)^ \frac{t}{2}$
$2=(1.035)^ \frac{t}{2}$
take the ln of both sides
$ln2=(\frac{t}{2})ln1.035$
divide both sides by ln1.035
$\frac{ln2}{ln1.035} = \frac{t}{2}$
times 2 both sides
$\frac{2ln2}{ln1.035} =t$
use calculator
40.2976=t
nearest tenth
40.3
about 40.3 years

You might be interested in

What is the image point of (–7, 1) after a translation left 4 units and down 5 units?

Marizza181 [45]

<h2>Translating a Point</h2><h3>Answer:</h3>

$(-11,-4)$

<h3>Step-by-step explanation:</h3>

When we first translate the point $(-7,1)$ to the left by $4$ units, we just need to subtract the $x$ -coordinate of the point by $4$ .

$(-7 -4,1) \\ (-11,1)$

Now we have the point $(-11,1)$ . We then translate it down by $5$ units by subtracting the $y$ -coordinate of the point by $5$ units.

$(-11,1 -5) \\ (-11,-4)$

5 0

3 years ago

What is the graph of this function?

jek_recluse [69]

Answer:

You MADE IT EASY

Step-by-step explanation:

${y - 5 \times 9}^{2} \: times \: sevem \\ n \: equals \sec(x + {}^{2} )$

7 0

3 years ago

FAST ASAP!! WILL GIVE BRAINLIST ALOT OF POINTS

Alik [6]

Answer:

= 3 3/4 m^2

or 15/4 m^2

Step-by-step explanation:

The base is the triangle.

A =1/2 bh

A = 1/2 (3 1/3 * 9/4)

Change 3 1/3 to an improper fraction (3*3+1)/3 = 10/3

A = 1/2 * 10/3 *9/4

Re arranging

= 1/2* 9/3 * 10/4

= 1/2 (3) 5/2

=15/4

Now writing as a mixed number

= 3 3/4 m^2

3 0

3 years ago

How do you solve 38.7×10 to the fourth power

faltersainse [42]

ndex Notation and Powers of 10

10 to the Power 2

The exponent (or index or power) of a number says

how many times to use the number in a multiplication.

102 means 10 × 10 = 100

(It says 10 is used 2 times in the multiplication)

Example: 103 = 10 × 10 × 10 = 1,000

In words: 103 could be called "10 to the third power", "10 to the power 3" or simply "10 cubed"

Example: 104 = 10 × 10 × 10 × 10 = 10,000

In words: 104 could be called "10 to the fourth power", "10 to the power 4" or "10 to the 4"

8 0

3 years ago

Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x

Anna11 [10]

Answer:

a) Figure attached

b) $y=1.31 x +98.57$

c) The correlation coefficient would be r =0.47719

d) $y=1.31 x +98.57=1.31*21 + 98.57 =126.08$

Step-by-step explanation:

(a) Draw a scatter diagram for the data.

See the figure attached

(b) Find x, y, b, and the equation of the least-squares line. (Round your answers to three decimal places.) x =__ y =__ b =__ y =__ + __x

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=6576-\frac{300^2}{14}=147.429$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=38186-\frac{300*1773}{14}=193.143$

And the slope would be:

$m=\frac{193.143}{147.429}=1.31$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{300}{14}=21.429$

$\bar y= \frac{\sum y_i}{n}=\frac{1773}{14}=126.643$

And we can find the intercept using this:

$b=\bar y -m \bar x=126.643-(1.31*21.429)=98.571$

So the line would be given by:

$y=1.31 x +98.57$

(c) Find the sample correlation coefficient r and the coefficient of determination r?2. (Round your answers to three decimal places.)

n=14 $\sum x = 300, \sum y = 1773, \sum xy=38186, \sum x^2 =6576, \sum y^2 =225649$

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

$r=\frac{14(38186)-(300)(1773)}{\sqrt{[14(6576) -(300)^2][14(225649) -(1773)^2]}}=0.9534$

So then the correlation coefficient would be r =0.47719

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)

The % of variation is given by the determination coefficient given by $r^2$ and on this case $0.47719^2 =0.2277$ , so then the % of variation explaines is 22.8%.

(d) If a female baby weighs 21 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) ___ lb

So we can replace in the linear model like this:

$y=1.31 x +98.57=1.31*21 + 98.57 =126.08$

7 0

3 years ago