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3 years ago

4. A savings account is started with $10,000. Calculate the

Mathematics

1 answer:

Ilya [14]3 years ago

5 0

Answer:

$1217.50

Step-by-step explanation:

<u>Given:</u>

Principal P = $10000
Interest rate r = 2.3% = 0.023
Compound number n = 12
Time t = 5 years

<u>Interest amount is:</u>

I = P(1+ r/n)^(nt) - P
I = 10000(1 + 0.023/12)^60 - 10000 = $1217.50

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PLS HELP IM DESPERATE

katovenus [111]

Answer:

24 square units

Step-by-step explanation:

The area of a parallelogram is given by the formula ...

A = bh

where A represents the area, b the length of the "base", and h the "height" measured at right angles to the base.

Here, it is convenient to use one vertical side of the figure as the base. You can count the grid squares to see that it is 8 units long.

The height is then the distance from one vertical side to the other. Again, you can count the grid squares to see that it is 3 units.

The area is the product of these dimensions:

A = (8 units)·(3 units) = 24 units^2

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3 years ago

Two distinct planes __________ intersect in a pair of lines

hammer [34]

If the planes are parallel to one another then they will never intersect (assuming they are distinct planes as the question states).

Otherwise they will intersect along a single line.

Therefore the answer is NEVER - they can never intersect in a pair of lines.

3 0

3 years ago

What is the product of (x - 9) and (2x - 7)

Crazy boy [7]

2x^2-7x-18x+63

2x^2-25x+63

6 0

3 years ago

Read 2 more answers

The least-squares regression model y =−3.4+5.2x and correlation coefficient r=−0.66 were calculated for a set of bivariate data

Makovka662 [10]

Answer:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

Step-by-step explanation:

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

$\bar x= \frac{\sum x_i}{n}$

$\bar y= \frac{\sum y_i}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

And the model obtained for this case is:

$y = -3.4 +5.2 x$

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

8 0

3 years ago

If $1,000 is invested at 4% simple interest, how much will the investment be worth after 2 years? Please explain how compound an

Novay_Z [31]

<h3>Answer:</h3>

simple interest: $1080.00
compounded annually: $1081.60

<h3>Step-by-step explanation:</h3>

<em>Simple Interest</em>

Simple interest is computed on the principal amount only. Each year, 4% of the principal is added to the balance. So, at the end of 2 years, the balance is ...

... $1000 + 0.04×$1000 + 0.04×$1000

... = $1000×(1 + 0.04×2) = $1000×1.08

... = $1080.00

_____

<em>Comment on the computation</em>

The added interest is the rate (per year) multiplied by the number of years. Here, that is 0.04×2×(principal amount). The formula for the simple interest earned is often seen as ...

... I = Prt . . . . . where I is the amount of interest, P is the principal amount, r is the interest rate for the time period, t is the number of time periods.

The account balance (A) with interest added is ...

... A = P + I = P + Prt

... A = P(1 +rt)

Here, the time period is years, and the rate given is an annual rate.

____

<em>Compound Interest</em>

Compound interest is computed on the <em>account balance</em> at the beginning of the period, not just the <em>principal</em> amount. After the first period, the account balance includes interest earned so far. So, the interest is earning interest. That is why it is called compounded interest.

Here, the balance at the end of the first year is the principal amount plus the interest that has earned:

... $1000 + 0.04×$1000 = $1000×1.04 = $1040.00

The balance at the end of the second year when the interest is compounded is this account balance plus the interest it earns:

... $1040 + 0.04×$1040 = $1040×1.04 = $1081.60

You may notice that the intial principal, $1000, has been multiplied by the factor 1.04 twice. Using exponents, the multiplier for a period of 2 years is 1.04×1.04 = 1.04².

_____

<em>Comment on the computation</em>

The multiplier of the account balance each year is raised to a power that is the number of years. Here, the account balance at the end of 2 years is (1+0.04)² times the principal amount. A formula that is seen for this is ...

... A = P(1 +r)^t . . . . . where A is the final account balance, P is the principal amount, r is the interest rate for the time period, and t is the number of time periods.

7 0

3 years ago