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Stolb23 [73]
3 years ago
10

A retired couple has up to $50,000 to invest. As their financial adviser, you recommend that they place at least $35,000 in Trea

sury bills yielding 1% and at most $10,000 in corporate bonds yielding 3%. Write and graph the system of equations of linear inequalities that describes the possible amounts of each investment.
Mathematics
1 answer:
patriot [66]3 years ago
3 0

Answer:

See Explanation

Step-by-step explanation:

According to the Question,

Given that, A retired couple has up to $50,000 to invest. As their financial adviser, you recommend that they place at least $35,000 in Treasury bills yielding 1% and at most $10,000 in corporate bonds yielding 3%.

Therefore,

Let, x be the amount of money invested in Treasury bills

y be the amount invested in corporate bonds

Thus, the system of equations of linear inequalities is

x + y ≤ 50000

x ≥ 35000

0 ≤ y ≤ 10000

For, the graph of the system of equations of linear inequalities describes the possible amounts of each investment.

(Please find in the attachment)

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Write a equation of a hyperbola given the foci and the asymptotes
professor190 [17]

Solution:

The standard equation of a hyperbola is expressed as

\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\text{ \lparen parallel to the x-axis\rparen} \\ \frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\text{ \lparen parallel to the y-axis\rparen} \end{gathered}

Given that the hyperbola has its foci at (0,-15) and (0, 15), this implies that the hyperbola is parallel to the y-axis.

Thus, the equation will be expressed in the form:

\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\text{ ----equation 1}

The asymptote of n hyperbola is expressed as

y=\pm\frac{a}{b}(x-h)+k

Given that the asymptotes are

y=\frac{3}{4}x\text{ and y=-}\frac{3}{4}x

This implies that

a=3,\text{ and b=4}

To evaluate the value of h and k,

undefined

3 0
1 year ago
A copy machine makes 28 copies per minute. How many copies does it make in 3 minutes and 45 seconds?
lina2011 [118]
<u>Convert minutes and seconds to minutes:</u>
\text{3 mins 45 seconds} \longrightarrow 3 \dfrac{3}{4} \text{mins}


<u>FInd 3 3/4 mins:</u>
\text{1 min} \longrightarrow 28 \text{ copies}

3  \dfrac{3}{4} \text{ min} \longrightarrow 28 \times 3\dfrac{3}{4} \text{ copies}

3  \dfrac{3}{4} \text{ min} \longrightarrow 28 \times \dfrac{15}{4} \text{ copies}

3  \dfrac{3}{4} \text{ min} \longrightarrow 105 \text{ copies}

Answer: It can make 105 copies.

4 0
4 years ago
Pleaseee i need help!! and the working!
zaharov [31]
Hey! $1.96 x £25,000 = $49,000
Then to change it back you:
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6 0
4 years ago
Jerry starts a new career making $32,000 annually. Each year for a total of 30 years
LUCKY_DIMON [66]

Step-by-step explanation:

if your asking how much money will he make for 30 years it will be 960,000. if your asking how much money will he make for 1 year it will be 8,000 I think I'm not sure

6 0
3 years ago
The cost of purple dye has been increasing over the last few months, and Robyn uses this dye as part of her tie dye scarf busine
joja [24]

The lowest percentage increase in the cost of dye that would make the scarves unprofitable is 42%

<h3>How to calculate the percentage?</h3>

(Price- Unit Cost)/Price= 20% or 0.2

Price- Unit Cost= 0.2 Price

0.8 Price = Unit Cost

Let Unit Cost be x

Price = x/0.8= 1.25x

Dye is 60% of unit costs= 0.6x

Cost of remaining material= 1 - 0.6x = 0.4x

Unit Cost= Cost of Dye+ Cost of remaining material

So, in order to become unprofitable, Unit Cost must be 1.25x

Therefore

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Percentage change in cost of dye= {(0.85x-0.6x)/0.6x}*100= 41.66 or 42%

Therefore, theowest percentage increase in the cost of dye that would make the scarves unprofitable is 42%.

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

6 0
1 year ago
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