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Inessa05 [86]
3 years ago
10

Dillon plans to invest $16,000 part at 4% simple interest and the rest at 5% simple interest what is the most he can invest at 4

% and still be guaranteed at least 700 per year
Mathematics
1 answer:
marishachu [46]3 years ago
5 0

Answer:

Step-by-step explanation:

The simple interest formula is P * r * t = I, where P is the initial investment, r is the interest rate in decimal form, t is the time in years.  This problem would be best solved by making a table, one row for account 1 and one row for account 2 with the formula along the top:

              P     *     r     *     t     =     I

acct 1

acct 2

First let's fill in our years.  The words "per year" were used, so the time in each row is a 1:

            P     *      r      *      t       =      I

acct 1                                 1

acct 2                                1

Now let's fill in the interest rates as decimals:

         P     *     r     *     t     =     I

acct 1            .04          1

acct 2           .05          1

Now for the principle amount.  If all we have to invest is 16000 and we put x into one account, then all we have left to put into the other account is what's left after taking x out of 16000, or 16000 - x.

                     P      *      r      *      t      =      I

acct 1             x           .04           1

acct 2   16000 - x       .05          1

The formula tells us that we multiply the P times the r times the t to get I, so lets do that.  Multiply straight across the top to get an interest of .04x.  Multiply straight across the bottom to get an interest of .05(16000 - x) which, after distributing, is 800 - .05x:

                 P      *      r      *      t      =      I

acct 1         x           .04            1      =    .04x

acct 2   16000-x    .05            1      =   800 - .05x

We need the amount of interest that we earn from both of these accounts to equal 700, so add the last column and set it equal to 700:

.04x + 800 - .05x = 700.  Combine like terms to get

-.01x = -100 so

x = 10,000

That means that the account which has an interest rate of 4% can have 10,000 in it while the other account has 6,000 in it.

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6. Find the values for each of the following: a. 3 times 5 in Z1o b. 3 times 5 in Zs c. 3 times 5 in Z3 e. 5 3 in Z1o
Anettt [7]

Answer:  The calculations are done below.

Step-by-step explanation:  We are given to find the values for each of the following :

(A) 3 times 5 in \mathbb{Z}_{10}.

We know that

\mathbb{Z}_{10}=\{0,1,2,3,4,5,6,7,8,9\}(\textup{mod}10).

Therefore, we get

3\times5=15(\textup{mod}10)=5.

(B) 3 times 5 in \mathbb{Z}_{5}.

We know that

\mathbb{Z}_{5}=\{0,1,2,3,4\}(\textup{mod}5).

Therefore, we get

3\times5=15(\textup{mod}5)=0.

(C) 3 times 5 in \mathbb{Z}_{3}.

We know that

\mathbb{Z}_{3}=\{0,1,2\}(\textup{mod}3).

Therefore, we get

3\times5=15(\textup{mod}3)=0.

(D) 5 times 3 in \mathbb{Z}_{10}.

We know that

\mathbb{Z}_{10}=\{0,1,2,3,4,5,6,7,8,9\}(\textup{mod}10).

Therefore, we get

5\times3=15(\textup{mod}10)=5.

Thus, the required values are evaluated.

8 0
3 years ago
Alexandra savings account balance is $95.65. She writes a check for $107.85. How much money is in her account now? Answer should
777dan777 [17]

Answer:

-12.2

Step-by-step explanation:

95.65-107.85=-12.2

7 0
2 years ago
PLSSS HELP I GIVE BRAINLIEST
Mumz [18]

Answer:

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Step-by-step explanation:

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2 years ago
andrews book collection contains 60 books.he donates 15% of his books yo the national library,sells 1/4 of his books to a book d
Vitek1552 [10]

Answer:

Books remaining in  Andrews book collection = 29 books

Explanation:

 Andrews book collection contains 60 books.

 He donates 15% of his books to the national library,

        Number of books to library = 60 x 15/100 = 9

 Sells 1/4 of his books to a book dealer,

        Book sold to book dealer = 60 x 1/4 = 15

 Sells 7 books on amazon.

 Books remaining = 60 - (9 + 15 + 7)

                              = 60 - 31

                              = 29

Books remaining in  Andrews book collection = 29 books

3 0
3 years ago
Use the substitution u = tan(x) to evaluate the following. int_0^(pi/6) (text(tan) ^2 x text( sec) ^4 x) text( ) dx
Rudiy27
If we use the substitution u = \tan x, then du = \sec^2 {x}\ dx. If you try substituting just u and du into the integrand, though, you'll notice that there's a \sec^2x left over that we have to deal with.

To get rid of this problem, use the identity \tan^2 x + 1 = \sec^2 x and substitute in the left side of the identity for the extra \sec^2x, as shown:

\int\limits^{\pi/6}_0 {tan^2 x \ sec^4 x} \, dx
\int\limits^{\pi/6}_0 {tan^2 x \ (tan^2 x + 1) \ sec^2 x} \, dx

From there, we can substitute in u and du, and then evaluate:

\int\limits^{\pi/6}_0 {tan^2 x \ (tan^2 x + 1) \ sec^2 x} \, dx
\int\limits^{\frac{1}{\sqrt{3}}}_0 {u^2(u^2 + 1)} \, du
\int\limits^{\frac{1}{\sqrt{3}}}_0 {u^4 + u^2} \, du
= \left.\frac{u^5}{5} + \frac{u^3}{3}\right|_0^\frac{1}{\sqrt{3}}
= (\frac{(\frac{1}{\sqrt{3}})^5}{5} + \frac{(\frac{1}{\sqrt{3}})^3}{3}) - (\frac{(0)^5}{5} + \frac{(0)^3}{3})
= \frac{1}{45\sqrt{3}} + \frac{1}{9\sqrt{3}} = \frac{6}{45\sqrt{3}} = \bf \frac{2}{15\sqrt{3}}


8 0
3 years ago
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