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3 years ago

Find the simple interest rate if $1,200 earns $81 interest in 9 months.

Mathematics

2 answers:

andreyandreev [35.5K]3 years ago

7 0

Answer: the simple interest rate is 9%

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount invested.

P represents the principal or amount invested.

R represents interest rate

T represents the duration of the investment in years.

From the information given,

P = $1200

T = 9 months = 9/12 = 0.75 year

I = $81

Therefore,

81 = (1200 × R × 0.75)/100

81 = 900R/100 = 9R

R = 81/9

R = 9%

Elina [12.6K]3 years ago

5 0

1) Plug the numbers into the equation for a simple interest rate. The equation is I = Prt, where P is the initial amount, r is the interest rate, and t is the time in years. 2) You have to turn the time into years, so put it over 12 (the months in a year) to turn it into a fraction for the unit of years, and plug in the equation to get I = 1200*0.81*(9/12). 3) Multiply this equation out to get 729.00, this is the answer. Answer: $729.00 interest. **TAKE THIS WITH A GRAIN OF SALT, you wrote the interest as dollars, but in this equation I assumed you meant to write it was a percent. If you did make a mistake and the 81 interest is a percent, then the math in this equation is correct. If it is an amount of money, then don’t copy it because it would be incorrect.

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Vesna [10]

Answer:

Find below the calculations of the two areas, each with two methods. The results are:

Upper triangle:

$Area=5000\sqrt{3}units^2$

Lower triangle:

$Area=14,530m^2$

Explanation:

A) Method 1

When you are not given the height, but you are given two sides and the included angle between the two sides, you can use this formula:

$Area=side_1\times side_2\times sin(\alpha)$

Where, $\alpha$ is the measure of the included angle.

1. Upper triangle:

$side_1=200units\\ \\ side_2=100units\\ \\ \alpha =60\º\\ \\ Area=200units\times 100units\times sin(60\º)/2\\ \\ Area=5000\sqrt{3}units^2$

2. Lower triangle:

$side_1=231m\\ \\ side_2=150m\\ \\ \alpha =123\º\\ \\ Area=231m\times 150m\times sin(123\º)/2\\ \\ Area=14,529.96m^2\approx14,530m^2$

B) Method 2

You can find the height of the triangle using trigonometric properties, and then use the very well known formula:

$Area=(1/2)\times base\times height$

Use it for both triangles.

3. Upper triangle:

The trigonometric ratio that you can use is:

$sine(\alpha)=opposite\text{ }leg/hypotenuse$

Notice the height is the opposite leg to the angle of 60º, and the side that measures 100 units is the hypotenuse of that right triangle. Then:

$sin(60\º)=height/100units\\ \\ height=sin(60\º)\times100units\\ \\ height=50\sqrt{3}units$

$Area=(1/2)\times base\times height=(1/2)\times 200units\times 50\sqrt{3}units=5,000\sqrt{3}units^2$

3. Lower triangle:

$sin(180\º-123\º)=height/231m\\ \\ height=sin(57\º)\times 231m\\ \\ height=193.7329m^2$

$Area=(1/2)\times base\times height=(1/2)\times 150m\times 193.7329m^2\\\\ Area=14,529.96m^2\approx 14,530m^2$

5 0

3 years ago

The graph represents the normal distribution of recorded weights, in pounds, of cats at a veterinary clinic.

marshall27 [118]

Please consider the graph.

We have been given that graph represents the normal distribution of recorded weights, in pounds, of cats at a veterinary clinic. We are asked to choose the weights, which are within 2 standard deviations of the mean.

We can see from our graph that mean of the weights is 9.5 and standard deviation in 0.5.

The data point that would be below two standard deviation is: $9.5-2\times 0.5$ that is $9.5-1=8.5$ .