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3 years ago

you have $350 in your savings account the account pays an interest rate of 2% how much will you earn in interest this year

Mathematics

1 answer:

Nady [450]3 years ago

7 0

Answer:

if you have $350 in your savings account and you got 2% in interest in one year you will earn $7.00

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Identify the coordinates of triangle ABC when it is dilated by a scale factor of 2 from the origin (0,0).

S_A_V [24]

Answer:

$A' = (-4,4)$

$B' = (2,6)$

$C' = (2,0)$

Step-by-step explanation:

Given [Missing from the question]

$A = (-2,2)$

$B= (1,3)$

$C= (1,0)$

$k = 2$ --- scale factor

Required

The new coordinates

The new coordinate is calculated by:

$New = Old * k$

So, we have:

$A' = A * 2$

$A' = (-2,2) * 2$

$A' = (-4,4)$

$B' = B * 2$

$B' = (1,3) * 2$

$B' = (2,6)$

$C' = C * 2$

$C' = (1,0) * 2$

$C' = (2,0)$

6 0

3 years ago

Find the laplace transform by intergration<br> f(t)=tcosh(3t)

Shkiper50 [21]

$\mathcal L_s\{t\cosh3t\}=\displaystyle\int_0^\infty t\cosh3t e^{-st}\,\mathrm dt$

Integrate by parts, setting

$u_1=t\implies\mathrm du_1=\mathrm dt$
$\mathrm dv_1=\cosh3t e^{-st}\,\mathrm dt\implies v_1=\displaystyle\int\cosh3t e^{-st}\,\mathrm dt$

To evaluate $v_1$ , integrate by parts again, this time setting

$u_2=\cosh3t\implies\mathrm du_2=3\sinh3t\,\mathrm dt$
$\mathrm dv_2=\displaystyle\int e^{-st}\,\mathrm dt\implies v_2=-\frac1se^{-st}$

$\implies\displaystyle\int\cosh3te^{-st}\,\mathrm dt=-\frac1s\cosh3te^{-st}+\frac3s\int \sinh3te^{-st}$

Integrate by parts yet again, with

$u_3=\sinh3t\implies\mathrm du_3=3\cosh3t\,\mathrm dt$
$\mathrm dv_3=e^{-st}\,\mathrm dt\implies v_3=-\dfrac1se^{-st}$

$\implies\displaystyle\int\cosh3te^{-st}\,\mathrm dt=-\frac1s\cosh3te^{-st}+\frac3s\left(-\frac1s\sinh3te^{-st}+\frac3s\int\cosh3te^{-st}\,\mathrm dt\right)$
$\displaystyle\int\cosh3te^{-st}\,\mathrm dt=-\frac1s\cosh3te^{-st}-\frac3{s^2}\sinh3te^{-st}+\frac9{s^2}\int\cosh3te^{-st}\,\mathrm dt$
$\displaystyle\frac{s^2-9}{s^2}\int\cosh3te^{-st}\,\mathrm dt=-\frac1s\cosh3te^{-st}-\frac3{s^2}\sinh3te^{-st}$
$\implies\displaystyle\underbrace{\int\cosh3te^{-st}\,\mathrm dt}_{v_1}=-\frac{(s\cosh3t+3\sinh3t)e^{-st}}{s^2-9}$

So we have

$\displaystyle\int_0^\infty t\cosh3t e^{-st}\,\mathrm dt=u_1v_1\big|_{t=0}^{t\to\infty}-\int_0^\infty v_1\,\mathrm du_1$
$=\displaystyle-\frac{t(s\cosh3t+3\sinh3t)e^{-st}}{s^2-9}\bigg|_{t=0}^{t\to\infty}-\int_0^\infty \left(-\frac{(s\cosh3t+3\sinh3t)e^{-st}}{s^2-9}\right)\,\mathrm dt$
$=\displaystyle\frac1{s^2-9}\int_0^\infty(s\cosh3t+3\sinh3t)e^{-st}\,\mathrm dt$

We already have the antiderivative for the first term:

$\displaystyle\frac s{s^2-9}\int_0^\infty \cosh3te^{-st}\,\mathrm dt=\frac s{s^2-9}\left(-\frac{(s\cosh3t+3\sinh3t)e^{-st}}{s^2-9}\right)\bigg|_{t=0}^{t\to\infty}$
$=\dfrac{s^2}{(s^2-9)^2}$

And we can easily find the remaining term's antiderivative by integrating by parts (for the last time!), or by simply exchanging $\cosh$ with $\sinh$ in the derivation of $v_1$ , so that we have

$\displaystyle\frac3{s^2-9}\int_0^\infty\sinh3te^{-st}\,\mathrm dt=\frac3{s^2-9}\left(-\frac{(s\sinh3t+3\cosh3t)e^{-st}}{s^2-9}\right)\bigg|_{t=0}^{t\to\infty}$
$=\dfrac9{(s^2-9)^2}$

(The exchanging is permissible because $(\sinh x)'=\cosh x$ and $(\cosh x)'=\sinh x$ ; there are no alternating signs to account for.)

And so we conclude that

$\mathcal L_s\{t\cosh3t\}=\dfrac{s^2+9}{(s^2-9)^2}$

8 0

3 years ago

Jamie has 1 7/8 of a pound of ground beef to use for dinner. If she is going to split the dinner between 3 people, how much woul

topjm [15]

0.625 b 1 7/8. Divided by three = 0.625

8 0

3 years ago

In a random sample of 7 residents of the state of Montana, the mean waste recycled per person per day was 2.8 pounds with a stan

galina1969 [7]

Answer:

The 90% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.68 and 2.92 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 7 - 1 = 6

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.9}{2} = 0.95$ . So we have T = 1.9432.

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.9432\frac{0.16}{\sqrt{7}} = 0.12$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.12 = 2.68 pounds.

The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.12 = 2.92 pounds.

The 90% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.68 and 2.92 pounds.

7 0

2 years ago

12-oz of can green beans is sold for $1:45. what is the price per pound?

Natali [406]

Answer:

$1.93 per lb

Step-by-step explanation:

First convert the 12 oz to pounds. There are 16 oz in 1 lb (pound)

So there are 0.75 lbs in 12 oz. To solve this problem you have to use proportions. $\frac{dollar}{lbs} = \frac{dollar}{lbs}$

Make sure both sides match in units (both the numerator and the denominator)

$\frac{1.45 dollars}{0.75 lbs} = \frac{unknown}{1 lbs}$

Use cross multiplication to find the price per pound.

$1.45*1 lbs= (unknown $)*0.75 lbs

Solve $1.45*1= $1.45

Then divide $1.45 by 0.75 lbs to find the unknown $ which equals $1.93

So your answer is $1.93 per lb

4 0

3 years ago

you have $350 in your savings account the account pays an interest rate of 2% how much will you earn in interest this year​

you have $350 in your savings account the account pays an interest rate of 2% how much will you earn in interest this year