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Stella [2.4K]
3 years ago
9

How much more interest will Maria receive if she invests $1,000 for one year at x percent annual interest, compounded semiannual

ly, than if she invests $1,000 for one year at x percent annual interest, compounded annually?
Mathematics
1 answer:
notka56 [123]3 years ago
3 0

Answer:

  $0.025x² . . . where x is a number of percentage points

Step-by-step explanation:

The multiplier for semi-annual compounding will be ...

  (1 + x/2)² = 1 + x + x²/4

The multiplier for annual compounding will be ...

  1 + x

The multiplier for semiannual compounding is greater by ...

  (1 + x + x²/4) - (1 + x) = x²/4

Maria's interest will be greater by $1000×(x²/4) = $250x², where x is a decimal fraction.

If x is a percent value, as in x = 6 when x percent = 6%, then the difference amount is ...

  $250·(x/100)² = $0.025x² . . . where x is a number of percentage points

_____

<u>Example</u>:

For x percent = 6%, the difference in interest earned on $1000 for one year is $0.025×6² = $0.90.

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Suppose that two small cities have the same longitude, which gives the east-west position of a point on Earth's surface. One has
wel

Answer:

Distance between A and B is 2672 km.

Step-by-step explanation:

Since one city B is having latitude of 23° and other town is having latitude of 47°.Radius of Earth has been given as 6380 km.

Therefore arc A from x-axis will be A = 2πr(∅/360) = 2×3.14×6380×(47/360)

= 5230.90 km

Now arc B from x-axis = 2πr(∅'/360) = 2×3.14×6380(23/360) = 2559.80 km

Therefore distance between them = 5230.9-2559.8 = 2671.9 ≅ 2672 km

Now we will rewrite the arc length formula in radians.

arc A = r×(∅×π/180)

arc A = 6380×(47×π/180) = 1665.9π

arc B = 6380×(23×π/180) = 815.22π    

Now the distance between A and B =  850.68π

6 0
3 years ago
Which events are independent? Choose all that apply.
Mila [183]

Answer:

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6 0
3 years ago
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Suppose a company's revenue R (in dollars) from the sale of x units of its product is given by R = 260x. Suppose further that th
Arada [10]

Answer:

C(x) = R(x) - P(x)

C(x) = 260x - P(x)

Step-by-step explanation:

I think some information is missing in the question. However, symbolically, the answer for Total Cost (C(x)) = 260x - P(x), where P(x) is the profit.

Basically, we derived that from:

P(x) = C(x) - R(x).,

By making C(x) subject of formula, we have:

C(x) = R(x) - P(x)

Since, we only know the value of R = 260x, then, we have;

                            C(x) = 260x - P(x)

6 0
3 years ago
Plz answer ASAP need help
Aleks04 [339]

Answer:

4 hours

Step-by-step explanation:

Let the number of hours = x.

Jay reads 55 pages per hour, so in x hours, he reads 55x pages.

After reading for x hours, he has 278 - 55x pages left to read.

Odhran reads 45 pages per hour, so in x hours, he reads 45x pages.

After reading for x hours, he has 238 - 45x pages left to read.

Since we want to know when they have the same number of pages left, we set the expressions equal and solve for x.

278 - 55x = 238 - 45x

Add 45x to both sides.

278 - 10x = 238

Subtract 278 from both sides.

-10x = -40

Divide both sides by -10.

x = 4

Answer: 4 hours

6 0
3 years ago
 2x- 3y=9   5x+3y=12   How would i solve this? I dont understand this and i really need help with it!Also I have to graph the an
dedylja [7]
\begin{cases} 2x- 3y=9 \\5x+3y=12 \end{cases}\\ + \ \ ------- \\ 7x=21 \ \ /: 7\\ \\x=\frac{21}{3}\\ \\ x=3 \\ \\2x- 3y=9

2*3-3y=9\\ \\6-3y =9\\ \\-3y=9-6\\ \\-3y=3 \ \ / :(-3)\\ \\x=-1\\ \\ \begin{cases} x=3\\y= -1 \end{cases}

graph\\ \\\begin{cases} 2x- 3y=9 \\5x+3y=12 \end{cases}\\ \\ \begin{cases} - 3y=-2x+9\ \ /:(-3) \\ 3y=-5x+12 \ \ /:3 \end{cases}\\ \\ \begin{cases} y= \frac{2}{3}x-3 \\ y=-\frac{5}{3}x+4 \end{cases}


7 0
3 years ago
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