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Sergio [31]
1 year ago
6

Explain the error a student is asked to find when the value of an investment of $5200 is an account that earns 4.2% annual inter

est compounded quarterly reaches $16,500. The student uses the model V(t)=5200(1.014)^3t and finds that the investment reaches a value of $16,500 after approximately 27.7 years. Fine and correct the students error.
Mathematics
1 answer:
zloy xaker [14]1 year ago
5 0

We are given the following information

Investment = $5200

Annual interest rate = 4.2% = 0.042

Final amount = $16,500

Number of years = 27.7 years

Number of compoudings = quartely = 4

The student uses the following model

V(t)=5200(1.014)^{3t}

The general formula for compound interest is given by

V(t)=P(1+\frac{r}{n})^{nt}

As you can see, the number of compoundings is incorrect (3 vs 4)

The interest rate is also incorrect.

Let us substitute the given values into the above formula

\begin{gathered} V(t)=P(1+\frac{r}{n})^{nt} \\ V(t)=5200(1+\frac{0.042}{4})^{4\cdot27.7} \\ V(t)=5200(1+0.0105)^{110.8} \\ V(t)=5200(1.0105)^{110.8} \\ V(t)=\$16543.5^{} \end{gathered}

Therefore, the final amount is approximately $16,543.5

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Omar rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 98 cents for each mile dr
stiv31 [10]

The given question is incomplete. The complete question is:

Omar rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 98 cents for each mile driven. Omar had to pay $23 when he returned the truck. For how many mile did he drive the truck?

Answer: Omar drove the truck for 5.15 miles

Step-by-step explanation:

Base fee = 17.95 $

Additional charge per mile = 98 cents = 0.98 $     ( 100cents = 1$)

Now Omar payed = 22 $

Let the miles he travelled = x

Now , 17.95+0.98\times x=23

Solvimg for x :

x=5.15miles

Thus Omar drove the truck for 5.15 miles

5 0
2 years ago
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Shkiper50 [21]
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3 0
2 years ago
PLS HELP! GIVING BRAINLIST!
svlad2 [7]

Answer:

We conclude that (4, 2) is NOT a solution to the system of equations.

Step-by-step explanation:

Given the system of equations

y = x - 2

y = 3x + 4

Important Tip:

  • In order to determine whether (4, 2) is a solution to the system of equations or not, we need to solve the system of equations.

Let us solve the system of equations using the elimination method.

\begin{bmatrix}y=x-2\\ y=3x+4\end{bmatrix}

Arrange equation variables for elimination

\begin{bmatrix}y-x=-2\\ y-3x=4\end{bmatrix}

Subtract the equations

y-3x=4

-

\underline{y-x=-2}

-2x=6

Now, solve -2x = 6 for x

-2x=6

Divide both sides by -2

\frac{-2x}{-2}=\frac{6}{-2}

Simplify

x=-3

For y - x = -2 plug in x = -3

y-\left(-3\right)=-2

y+3=-2

Subtract 3 from both sides

y+3-3=-2-3

Simplify

y=-5

The solution to the system of equations is:

(x, y) = (-3, -5)

Checking the graph

From the graph, it is also clear that (4, 2) is NOT a solution to the system of equations because (-3, -5) is the only solution as we have found earlier.

Therefore, we conclude that (4, 2) is NOT a solution to the system of equations.

8 0
3 years ago
In which of the following quadrilaterals are consecutive and opposite angles always congruent?
kati45 [8]
All the angles are congruent in square and rectangle, rhombus has consecutive angles so we can say that all of them have consecutive angles congruent except the parallelogram.
6 0
2 years ago
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Which of the expressions below is equivalent to the expression: 42 + 32 – 13 × 2 + 38? a. 42 + 32 – (26 + 38) b. 42 + 32 – 13 ×
Anika [276]
Using PEMDAS, 42 + 32 - 13 * 2 + 38 can be simplified as,

C. 42 + 32 + 12 = 86

You can check this by inserting the given expression (42 + 32 - 13 * 2 + 38) into a calculator, which should also give you the same answer of 86.
5 0
3 years ago
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