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earnstyle [38]
3 years ago
6

An amount of $40,000 is borrowed for 11 years at 7 5% interest compounded annually. If the loan is paid in full at the end of th

at period, how much myst be paid back?
​
Mathematics
1 answer:
valina [46]3 years ago
6 0

Amount to be paid back = $ 88,624.36

<u>Step-by-step explanation:</u>

Principal amount = $ 40,000

Rate of interest = 7.5%

Number of years = 11

A=P\left(1+\frac{r}{n}\right)^{n t}

Plugin the values as,

A=40000\left(1+\frac{7.5}{100}\right)^{11}

A=40000(1+0.075)^{11}

A=40000(1.075)^{11}

A=\$ 88,624.36

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The following data represent the pH of rain for a random sample of 12 rain dates in Tucker County, West Virginia. A normal proba
Sphinxa [80]

Answer:

Step-by-step explanation:

n = 12

Mean = (4.58 + 5.72 + 4.77 + 4.76 + 5.19 + 5.05 + 4.80 + 4.77 + 4.75 + 5.02 + 4.74 + 4.56)/12 = 4.8925

Standard deviation = √(summation(x - mean)²/n

Summation(x - mean)² = (4.58 - 4.8925)^2 + (5.72 - 4.8925)^2 + (4.77 - 4.8925)^2 + (4.76 - 4.8925)^2 + (5.19 - 4.8925)^2 + (5.05 - 4.8925)^2 + (4.80 - 4.8925)^2 + (4.77 - 4.8925)^2 + (4.75 - 4.8925)^2 + (5.02 - 4.8925)^2 + (4.74 - 4.8925)^2 + (4.56 - 4.8925)^2 = 1.122225

Standard deviation = √(1.122225/12

s = 0.31

a) Point estimate = sample mean = 4.8925

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

Margin of error = z × s/√n

Where

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 12 - 1 = 11

b) Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 2.201

Margin of error = 2.201 × 0.31/√12

= 0.197

95% confidence interval = 4.8925 ± 0.197

Upper limit = 4.8925 + 0.197 = 5.0895

Lower limit = 4.8925 - 0.197 = 4.6955

We are 95% confident that the population mean of the rain water ph lies between 4.6955 and 5.0895

c) For 99% confidence level, z = 3.106

Margin of error = 3.106 × 0.31/√12

= 0.278

99% confidence interval = 4.8925 ± 0.278

Upper limit = 4.8925 + 0.278 = 5.1705

Lower limit = 4.8925 - 0.278 = 4.6145

We are 99% confident that the population mean of the rain water ph lies between 4.6145 and 5.1705

d) The interval gets wider as the confidence level is increased. This is logical since the test score is higher for 99% and therefore, increases the range of values. Since we want to be more confident, the range of values must be extended.

3 0
3 years ago
In an experiment examining the effects Tai Chi on arthritis pain, Callahan (2010) selected a large sample of individuals with do
Volgvan

Answer:

a) Participants in Tai Chi course

b) Nominal

c) Magnitude of arthritis pain

d) Ordinal

Step-by-step explanation:

TYPES OF VARIABLES:

  • Independent Variable:

An independent variable is the one controlled or changed in an experiment to test the effects on the dependent variable. If this variable is changed, there shall be effects on the experiment.

In this case, number of participants in the course was independent.

  • Dependent Variable:

Dependent variable is the one being tested and measured. If the independent variable changes, this variable will show the effect of the changes.

<em>The variables can be determined by their cause and effect on the experiment.</em>

TYPES OF SCALES:

<em>There are two variations in types of scales; Quantitative and Qualitative.</em>

<em>Qualitative variables are measured by either nominal or ordinal scale, while quantitative variables are measured by ratio or interval.</em>

  • Nominal scale:

Nominal scales assign identifiers as labels to objects or classes of objects. The  assigned numbers carry no additional meaning except as identifiers for example: patient A, patient B etc.  

  • Ordinal scale:

Ordinal scales assign numbers to objects to rank  an attribute. For example: Level of pain 1 - 10, Level of satisfaction etc.

  • Interval:

In an interval scale, numbers are  assigned to objects such that the interval helps in interpretation of the variables. For example: age of patients: 30 - 40, 40 - 50 etc.

  • Ratio:

Ratio scales includes an absolute “zero” point. For example, Rate of arthritis in patients of a particular age etc.

4 0
3 years ago
Write the ratio of apples to oranges in simplest form please explain. Thanks
Nadya [2.5K]
There are 6 apples and 2 oranges.
So the ratio of apples to oranges would be 6:2.
However this can be simplified, because these number have a common factor, which is 2. So you divide 2 by 2, and 6 by 2, and get 1 and 3. So the ratio of apples to oranges in simplified form is 1:3. Hope this explains it :)
7 0
3 years ago
Read 2 more answers
Simplify 18/5 to get the answer
Inga [223]
5\frac{3}{5}
4 0
3 years ago
please help! 20 points. if you guess or just comment to take points i will make sure ur account gets banned, thanks! i want a si
alina1380 [7]

Answer: x=15

Step-by-step explanation: Since 3x+5 is equal to 50, you can write 3x+5=50, and 3x=45, x=15.

7 0
3 years ago
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