$10000 in certificate of deposit
$30000 in mutual funds
Step-by-step explanation:
Step 1:
Total amount Stephanie has inherited = $40000
Let x be the amount she should put in certificate of deposit.
So 40000-x is the amount to be deposited in mutual funds
Step 2:
Total interest she wants to earn is 5.4% of $40000 = 5.4*40000/100 = 2160
Interest from certificate of deposit = 2.1% of x = 2.1 * x /100
Interest from mutual funds is 6.5% = 6.5(40000-x)/100
Sum of the interest from both these equals 2160
so 2.1 * x /100 + 6.5(40000-x)/100 = 2160
=> 0.021x/100 + 2600-0.065x = 2160
=> -0.044x = -440 => x= 10000
Step 3 :
Hence Stephaine should invest $10000 in certificate of deposit and (40000-10000) = $30000 in mutual funds
Integrate both sides with respect to <em>t</em> :
∫ d<em>y</em>/d<em>t</em> d<em>t</em> = ∫ -12<em>t</em> ² d<em>t</em>
<em>y(t)</em> = -4<em>t</em> ³ + <em>C</em>
Use the initial condition to solve for <em>C</em> :
5 = -4•0³+ <em>C</em>
<em>C</em> = 5
So
<em>y(t)</em> = -4<em>t</em> ³ + 5
and the answer is D.
Alternatively, you can directly apply the fundamental theorem of calculus:



Answer:
width = 5 in
length = 5+4=9 in
height = 2(5)= 10 in
Step-by-step explanation:
A gift box has a volume of 450 cubic inches.
Let 'w' be the width of the box
The width of the box is 4 inches less than the length.

The height is twice the width.

height = 2w
Volume of box = length times width times height






w=5
, this gives two complex values
so width = 5
length = 5+4=9
height = 2(5)= 10
Answer: h = 17
Step-by-step explanation: As a general rule, if an equation has any fractions in it, try to get rid of those fractions as soon as possible.
The quickest way to get rid of a fraction is to multiply both
sides of the equation by the denominator of the fraction.
So in this problem, we can get rid of the fraction in our
first step by multiplying both sides of the equation by 4.
On the left, the 4's cancel and on the right, 1(4) is 4.
Now we have h - 13 = 4.
Since 13 is being subtracted from <em>h</em>, to get <em>h</em> by itself,
we need to add 13 to both sides of the equation to get h = 17.
Now, we can check our answer by plugging 17 back
into the original equation shown below in italics.

