A retired woman has $90,000 to invest but needs to make $3,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%. If we let x be the amount the woman invests in the 15% bond, how much in dollars will she be able to invest in the CD?

 any amount from 0 to 90000 USD

Step-by-step explanation:

x USD will be paid for 15% bonds that makes x*0.15 USD /per year

So 90000-x will be paid for 7% bonds , that makes (90000-x)*0.07 USD/per year= 6300-0.07x   USD / per year.

So the total amount the woman gets from both investments yearly should be not less than 3000 USD/per year

Otherwise

0.15*x+6300-0.07*x>=3000

0.08*x+6300>=3000

The inequation is correct for any x>=0

The woman will be able invest in CD any amount from 0 to 90000 USD.

If we suppose that investments in CD more safe we'd recommend to the lady to invest all money to CD.

see below

Step-by-step explanation:

$3000 is not a right number or $90000

Assume n instead of $3000, then

is required equation

x= (n-6300)/0.08 is the amount invested in the 15% bond

Consider n> $6300

Then 90000 -x will be the amount invested in the CD

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.