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3 years ago

8

Ms. Lane borrowed $1,000 from her bank for one year at an interest rate of 10 percent. During that year, the price level went up

by 15 percent. Which of the following statements is correct?

1 answer:

Lunna [17]3 years ago

8 0

Answer:

Consider the complete question is,

'Ms. Lane borrowed $1,000 from her bank for one year at an interest rate of 10 percent. During that year, the price level went up by 15 percent. Which of the following statements is correct?

a. Ms. Lane will repay the bank fewer dollars than she initially borrowed.

b. Ms. Lane's repayment will give the bank less purchasing power than it originally loaned her.

c. Ms. Lane's repayment will give the bank greater purchasing power than it originally loaned her.

d. Ms. Lane's repayment will give the bank the same purchasing power that it originally loaned her.'

Solution :

We have,

The borrowed amount, P = $ 1,000,

Interest rate, r = 10% = 0.1,

Time, t = 1 year,

Thus, the returned amount,

$A=P(1+r)^t=1000(1+0.1)^1=1000(1.1) = \$ 1100$

∵ A > P

⇒ Ms. Lane will repay the bank greater dollars than she initially borrowed.

Now, the price level went up by 15 percent,

∵ 1000 + 15% of 1000 = 1000 + 150 = 1500

And, 1500 > 1100

⇒ Ms. Lane's repayment will give the bank less purchasing power than it originally loaned her.

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Quadratics need help making parabola

timama [110]

Answer:

The equation of the parabola is $y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4$ , whose real vertex is $(x,y) = (2, -5.333)$ , not $(x,y) = (2, -5)$ .

Step-by-step explanation:

A parabola is a second order polynomial. By Fundamental Theorem of Algebra we know that a second order polynomial can be formed when three distinct points are known. From statement we have the following information:

$(x_{1}, y_{1}) = (-2, 0)$ , $(x_{2}, y_{2}) = (6, 0)$ , $(x_{3}, y_{3}) = (0, -4)$

From definition of second order polynomial and the three points described above, we have the following system of linear equations:

$4\cdot a -2\cdot b + c = 0$ (1)

$36\cdot a + 6\cdot b + c = 0$ (2)

$c = -4$ (3)

The solution of this system is: $a = \frac{1}{3}$ , $b = - \frac{4}{3}$ , $c = -4$ . Hence, the equation of the parabola is $y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4$ . Lastly, we must check if $(x,y) = (2, -5)$ belongs to the function. If we know that $x = 2$ , then the value of $y$ is:

$y = \frac{1}{3}\cdot (2)^{2}-\frac{4}{3}\cdot (2) - 4$

$y = -5.333$

$(x,y) = (2, -5)$ does not belong to the function, the real point is $(x,y) = (2, -5.333)$ .

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2 years ago

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Furkat [3]

Always do brackets first

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2 years ago

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weqwewe [10]

Answer:

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Step-by-step explanation:

You have to make sure it is a triangle by adding the smallest and the medium sides, if the result is greater than the bigger side then it is a triangle.
you then use the Pythagorean theorem to check if the triangle is a right triangle, acute, or obtuse. If $c^{2}$ = $a^{2} +b^{2}$ then it is a right triangle. If $c^{2} >a^{2} + b^{2}$ then it is an obtuse triangle. if $c^{2} < a^{2} +b^{2}$ then it is an acute triangle.

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DaniilM [7]

Answer:

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