You have already invested $400 in a stock with an annual return of 11%. How much of an additional $1,200 should be invested at 12% and how much at 6% so that the total return on the entire $1,600 is 9%? (Round each answer to the nearest cent.)

To solve this problem, we have to find the multiples of 3 and then find the probability of selecting them. The probability of having a multiple of 3 is 1/3.

The probability of tossing a six-sided dice and a eight-sided dice.

When we toss them together, the maximum value will be

[tex]6 * 8 = 48[/tex]

The multiplies of 3 will be

Data;

The probability of having a multiple of 3 will be

[tex]P(multiple of 3) = \frac{16}{48} = \frac{1}{3}[/tex]

The probability of having a multiple of 3 is 1/3

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Answer:

-17 - (-8)

Option 3 is correct.

Step-by-step explanation:

Phrase: "the difference between -17 and -8"

Expression: To write the phrase into algebraic form with a variable or constant.

Difference: write two number using subtraction between them.

"the difference between -17 and -8"

First number is -17 and second number is -8

Expression: -17 difference -8

Now using minus sign write as expression.

[tex]\Rightarrow -17-(-8)[/tex]

Hence, The correct expression is -17-(-8)

Answer: The answer is (A) -5.

Step-by-step explanation:  We are given to find the element [tex]a_{23}[/tex] in the following matrix:

[tex]A=\begin{bmatrix}8 & -4 & -3\\ 3 & -9 & -5\\ -8 & 8 & 8\end{bmatrix}[/tex]

We know that [tex]a_{mn}[/tex] is an element of a matrix present in the m-th row and n-th column.

So, [tex]a_{23}[/tex]  will be the element present in the second row and third column.

Since the element in the second row and third column is - 5, so we have

[tex]a_{23}=-5.[/tex]

Thus, (A) -5 is the correct option.

In the given two column proof two sides and included angles are equal.

Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles .In the figure sides BD≅BD , AB≅ BC and <ABD ≅,BDD Therefore triangle ABD and triangle CBD are congruent by SAS property of congruence.

The correct  option for missing statement is D. ΔABD ≅ ΔCBD .

Answer:

ΔABD ≅ ΔCBD

Step-by-step explanation:

Guys this is the right answer,  ΔABD ≅ ΔCBD. I got it right on my test!

The cost that's necessary to pay the loan will be $31,616.16.

First, we need to calculate the effective monthly interest rate. This will be:

i = 0.053/12

= 0.0044

The effective annual interest rate will then be:

i = (1 + 0.0044)^12 - 1

I = 0.0543

Next thing will be to calculate the present worth of all the loans which will be:

P = 6125 + 6125 (1 + 0.0543) + 6125 (1 + 0.0543)² + 6125(1 + 0.0543)³

P = $22,671.40

The worth of the loans after four years will be:

P = 22671.40 (1 + 0.0543)⁴

= $31,616.16

In conclusion, the correct option is $31,616.16.

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To calculate the total cost of Toby's 4 Stafford loans, the monthly amount for one loan is first calculated and then multiplied by four and by the number of months. The correct total lifetime cost is approximately $31,569.60.

To determine the total lifetime cost that Toby will pay to pay off his 4 Stafford loans, each with a principal of $6,125, an interest rate of 5.3% compounded monthly, and a loan duration of ten years, we need to calculate the monthly payment for a single loan and then multiply by the number of loans and the duration. The formula for the monthly payment on an installment loan is:

P = P[r(1+r)^n] / [(1+r)^n - 1]

where:

Using the data given:

P = $6,125 * [0.004417(1 + 0.004417)^120] / [(1 + 0.004417)^120 - 1]

Calculating this gives us a monthly payment of approximately $65.77 for each loan. Toby took out 4 loans, so his total monthly payment is 4 * $65.77 = $263.08.

The total lifetime cost for a single loan is the monthly payment * number of payments (120), which is:

Total cost for one loan = $65.77 * 120 = $7,892.40

And the total lifetime cost to pay off all 4 loans:

Total cost for all loans = $7,892.40 * 4 ≈ $31,569.60

Therefore, rounding each loan's payment to the nearest cent, the total lifetime cost to pay off all 4 of Toby's loans is roughly $31,569.60, making the answer option b the correct one.

We are given that the slope is half the y-intercept and their sum is 1. Using these conditions we can solve for b and m (which represent y-intercept and slope) and we find that b=2/3 and m=1/3. Therefore, the equation of the line is y = 1/3x + 2/3.

The question is about finding the equation of a line from given conditions. We know that the equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. We are given two conditions: the slope is half the y-intercept, and their sum is 1.

Let's assume that the y-intercept is b and the slope is m. Now we can substitute the value of m from the first equation into the second. This gives us: b + b/2 = 1. Solving this, we get b = 2/3 and therefore, m = 1/3.

So, the equation of the line is y = 1/3x + 2/3.

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The simplified product of 3/7 multiplied by 14 is 6.

To multiply 3/7 by 14, you can follow these steps:

Multiply the numerators: 3 x 14 = 42.

Multiply the denominators: 7 x 1 = 7.

Therefore, the product of 3/7 multiplied by 14 is 42/7.

However, we can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 7.

= 42/7

= 6/1

= 6.

So, the simplified product of 3/7 multiplied by 14 is 6.

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Arc DB measure less than 180 degrees,  is called a minor arc.

Option (b) is correct

A minor arc is an arc whose angle is less than 180 degrees.

From given figure, It is observed that, arc DB measure less than 180 degrees is called a minor arc.

Hence, option (b) is correct.

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