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Alisiya [41]
3 years ago
5

A mother earned ​$7500.00 from royalties on her cookbook. She set aside​ 20% of this for a down payment on a new home. The balan

ce will be used for her​ son's future education. She invests a portion of the money in a bank certificate of deposit​ (CD account) that earns​ 4% and the remainder in a savings bond that earns​ 7%. If the total interest earned after one year is ​$360.00​, how much money was invested at each​ rate?
Mathematics
2 answers:
Kruka [31]3 years ago
3 0

The amount of money deposited in the CD = 2000$
The amount of money deposited in the saving account = 4000$


Hope this helps. :D

Arisa [49]3 years ago
3 0

Answer:

$2000 was invested in cd at 4% and $4000 was invested in bonds at 7%.

Step-by-step explanation:

20% of 7500 = 0.20\times7500=1500 dollars

Balance remained =7500-1500=6000 dollars

Let she invests in cd = x

So, she will invest in bond = 6000-x

Now, the cd earns 4% and bond earns 7% and total interest earned is $360.

0.04x+0.07(6000-x)=360

=> 0.04x+420-0.07x=360

=> 0.03x=60

So, x = 2000 (amount in cd)

And amount in bonds = 6000-2000 = $4000.

Therefore, $2000 was invested in cd at 4% and $4000 was invested in bonds at 7%.

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Artist 52 [7]

9514 1404 393

Answer:

  a.  yes; AA similarity

  b.  maybe 8, (or 30)

Step-by-step explanation:

a. The missing angle of ∆ABC is 180° -60° -20° = 100°. So, two of the angles of ∆ABC match those of ∆DEF, meaning the triangles are similar by the AA theorem.

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b. We notice the side ratios to be ...

  DE/AB = 12/9 = 4/3

Using that same ratio for corresponding sides ...

  EF/BC = 4/3

  EF = BC(4/3) = 6(4/3) = 8

Using the marked side lengths, we find EF = 8.

__

We note that two angles and the side between them are sufficient information to solve ∆DEF with no reference to the markings of ∆ABC. Doing that, we find EF ≈ 30.4. We credit the discrepancy to the fact that ∆ABC is mis-marked. The longer side cannot be opposite the smaller angle.

4 0
3 years ago
25 point for this question:
KonstantinChe [14]

Answer:

a=\frac{13}{11}   b =\frac{-2}{11}

Step-by-step explanation:

  • By equating coefficients on both sides of respective terms.

Given,

\frac{x-4}{x^2+7x-18} = \frac{a}{x+9} + \frac{b}{x-2}

<u>Now take  </u><u>lcm</u><u> on right hand side </u>

\frac{x-4}{x^2+7x-18} =\frac{a(x-2)+b(x+9)}{x^2+7x-18}

By equating coefficients of respective terms

x-4 = a(x-2)+b(x+9)

a+b=1  -----1 ; 9b-2a=-4  -----2

Substitute b=1-a in 2

9(1-a)-2a=-4

11a=9+4=13

a=\frac{13}{11}

As b=1-a=1- \frac{13}{11}=\frac{-2}{11}

3 0
3 years ago
A nickle 5% of a dollar. Write the value of a nickel as a decimal and as a fraction.
kkurt [141]
Decimal= 0.05
fraction=5/100 or 1/20
3 0
3 years ago
The amounts of plastic waste generated in a region during two years were 32,400,000 tons and 20,300,000 tons. What was the total
Alik [6]
Just assume this two numbers 

32400000 +
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52700000 what expressed in scientific notation will be 5,27 * 10^7

hope this will help you 
4 0
3 years ago
Read 2 more answers
Normal line to the curve y=ln(2x+a) at x=1 is perpendicular to x-4y+2 = 4ln3. Find the value of a.
Nesterboy [21]
Hello,

The normal perpendicular to x-4y+2=4ln(3) or y=(x+2-4ln(3))/4
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So y'=(ln(2x+a))'=1/(2x+a) *2 if x=1 , y'=1/(2+a)
Thus
1/(2+a)=-4 ==>2+a=-1/4==>a=-1/4-2==>a=-9/4

7 0
3 years ago
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