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1 year ago

6

How much should you put in an investment paying a simple interest rate of 5% if you needed $4000 in eighteen mont

1 answer:

Eddi Din [679]1 year ago

6 0

now, there are 12 months in a year, so 18 months is really 18/12 of a year, thus

$~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$4000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{18}{12}\dotfill &\frac{3}{2} \end{cases} \\\\\\ 4000=P[1+(0.05)(\frac{3}{2})]\implies 4000=P(1.075) \\\\\\ \cfrac{4000}{1.075}=P\implies 3720.93\approx P$

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Select the number line that correctly shows the calculation for |−3|.

Oxana [17]

It is the third answer. Absolute value just means the distance from that number (-3 in your case) to 0 on a number line. Choice 3 shows just that.

7 0

3 years ago

Read 2 more answers

The curves r1(t) = 2t, t2, t4 and r2(t) = sin t, sin 5t, 2t intersect at the origin. Find their angle of intersection, θ, correc

masya89 [10]

Answer:

Therefore the angle of intersection is $\theta =79.48^\circ$

Step-by-step explanation:

Angle at the intersection point of two carve is the angle of the tangents at that point.

Given,

$r_1(t)=(2t,t^2,t^4)$

and $r_2(t)=(sin t , sin5t, 2t)$

To find the tangent of a carve , we have to differentiate the carve.

$r'_1(t)=(2,2t,4t^3)$

The tangent at (0,0,0) is [ since the intersection point is (0,0,0)]

$r'_1(0)=(2,0,0)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{2^2+0^2+0^2} =2$

Again,

$r'_2(t)=(cos t ,5 cos5t, 2)$

The tangent at (0,0,0) is

$r'_2(0)=(1 ,5, 2)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{1^2+5^2+2^2} =\sqrt{30}$

If θ is angle between tangent, then

$cos \theta =\frac{r'_1(0).r'_2(0)}{|r'_1(0)|.|r'_2(0)|}$

$\Rightarrow cos \theta =\frac{(2,0,0).(1,5,2)}{2.\sqrt{30} }$

$\Rightarrow cos \theta =\frac{2}{2\sqrt{30} }$

$\Rightarrow cos \theta =\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =cos^{-1}\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =79.48^\circ$

Therefore the angle of intersection is $\theta =79.48^\circ$ .

8 0

2 years ago

Shawna and her best friend Keisha go shopping. The function p(t) = 3x +2x-4x2+ 21 represents how much money each girl spent base

NNADVOKAT [17]

Answer:

$\$30$

Step-by-step explanation:

we have

$p(t)=3x+2x-4x^{2}+21$

<em>Find the amount of money that each girl spent</em>

For t= 2 hours

$p(2)=3(2)+2(2)-4(2)^{2}+21$

$p(2)=10-16+21$

$p(2)=\$15$

<em>Find the amount of money that they spend together</em>

Multiply by 2 the amount of money that each girl spent

$(2)\$15=\$30$

3 0

2 years ago

-4(6x+3)= -12(x+ 10)

Lilit [14]

Answer:

9

Step-by-step explanation:

-4(6x+3)= -12(x+10)

<u><em>Let's do the first part:</em></u>

-4(6x+3)

<em>**distribute**</em>

-4 x 6x = -24x; -4 x 3 = -12 ->>> -24x - 12

<u><em>Let's do the second part:</em></u>

-12(x+10)

<em>**distribute**</em>

-12 x x = -12x; -12 x 10 = -120 ->>> -12x -120

-24x -12 = -12x - 120

<em>**Move variable to the left-hand side and change its sign**</em>

-24x +12x -12 = -120

-12x - 12 = -120

-12x = 108

x = 108/-12

x=9

3 0

3 years ago

Please help me due soon

alexira [117]

He bought 20 pounds of pet food

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2 years ago