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3 years ago

Find the interest on $4,000 at 3% for 4 months

Mathematics

1 answer:

Sladkaya [172]3 years ago

6 0

Step-by-step explanation:

✧ $\underline{ \underline{ \large{ \tt{G \: I \: V \: E \: N}}}} :$

Principal ( P ) = $ 4000
Rate ( R ) = 3 %
Time ( T ) = 4 months = $\ \frac{4}{12}$

✧ $\underline{ \underline{ \large{ \tt{ T \: O \: \: F\: I\: N \: D}}}} :$

Interest ( I )

✧ $\underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T \: I \:O\: N}}}} :$

☂ $\boxed{ \large{ \sf{Interest \: ( \: I \: ) = \frac{PTR}{100}}}}$

~Plug the known values and then simplify !

➝ $\large{ \bf{ \frac{4000 \times \frac{4}{12} \times 3}{100} }}$

➝ $\large{ \bf{ \frac{4000}{100}}}$

➝ $\large{ \bf{ \frac{4 \: 0 \: \cancel{0 \: 0}}{1 \: \cancel{ 0 \: 0}}}}$

➝ $\boxed{ \large{ \bf{ \$ \: 40}}}$

⟿ $\boxed{ \boxed{ \underline{ \large{ \text{OUR \: FINAL \: ANSWER }: \boxed{ \underline{ \tt{ \$ \: 40}} }}}}}$

----------------------------------------------

☃ $\underline{ \text{Additional \: Info : }}$

Principal ( P ) : The money which is borrowed or deposited is called principal.
Interest ( I ) : The additional amount of money which is paid by borrower to the lender is called interest.
Time ( T ) : The duration of time for which principal is deposited or borrowed is termed as time period.
Rate ( R ) : The condition under which the interest is charged is called rate.
Amount ( A ) : The sum of principal and interest is called an amount.

Hope I helped ! ♡

Have a wonderful day / night ! ♕

Let me know if you have any questions regarding my answer ! ☄

☞ $\underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}$ !! ✎

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

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Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified l

Sloan [31]

Answer:

The integral of the volume is:

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

The result is: $V = 78.97731$

Step-by-step explanation:

Given

Curve: $x^2 + 4y^2 = 4$

About line $x = 2$ --- Missing information

Required

Set up an integral for the volume

$x^2 + 4y^2 = 4$

Make x^2 the subject

$x^2 = 4 - 4y^2$

Square both sides

$x = \sqrt{(4 - 4y^2)$

Factor out 4

$x = \sqrt{4(1 - y^2)$

Split

$x = \sqrt{4} * \sqrt{(1 - y^2)$

$x = \±2 * \sqrt{(1 - y^2)$

$x = \±2 \sqrt{(1 - y^2)$

Split

$x_1 = -2 \sqrt{(1 - y^2)}\ and\ x_2 = 2 \sqrt{(1 - y^2)}$

Rotate about x = 2 implies that:

$r = 2 - x$

So:

$r_1 = 2 - (-2 \sqrt{(1 - y^2)})$

$r_1 = 2 +2 \sqrt{(1 - y^2)}$

$r_2 = 2 - 2 \sqrt{(1 - y^2)}$

Using washer method along the y-axis i.e. integral from 0 to 1.

We have:

$V = 2\pi\int\limits^1_0 {(r_1^2 - r_2^2)} \, dy$

Substitute values for r1 and r2

$V = 2\pi\int\limits^1_0 {(( 2 +2 \sqrt{(1 - y^2)})^2 - ( 2 -2 \sqrt{(1 - y^2)})^2)} \, dy$

Evaluate the squares

$V = 2\pi\int\limits^1_0 {(4 +8 \sqrt{(1 - y^2)} + 4(1 - y^2)) - (4 -8 \sqrt{(1 - y^2)} + 4(1 - y^2))} \, dy$

Remove brackets and collect like terms

$V = 2\pi\int\limits^1_0 {4 - 4 + 8\sqrt{(1 - y^2)} +8 \sqrt{(1 - y^2)}+ 4(1 - y^2) - 4(1 - y^2)} \, dy$

$V = 2\pi\int\limits^1_0 { 16\sqrt{(1 - y^2)} \, dy$

Rewrite as:

$V = 16* 2\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

Using the calculator:

$\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy = \frac{\pi}{4}$

So:

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

$V = 32\pi * \frac{\pi}{4}$

$V =\frac{32\pi^2}{4}$

$V =8\pi^2$

Take:

$\pi = 3.142$

$V = 8* 3.142^2$

$V = 78.97731$ --- approximated

3 0

3 years ago

A treatment is administered to a sample of n = 9 individuals selected from a population with a mean of m = 80 and a standard dev

kupik [55]

Cohen's d is calculated according to the formula:
d = (mean difference) / standard deviation
0.5 = mean difference / 12
Therefore, mean difference = 6
Since we have a population mean of 80, the sample mean must be 80 + 6 = 86.

5 0

3 years ago

Please help me please will give brainliest show all your work thank you

Alika [10]

Answer:

Perimeter: 52 Area: 181-16i?

Step-by-step explanation:

Perimeter

The formula for perimeter is 2l+2w, so you plug in the binomials they give you:

2(11-4i)+2(15+4i)

expand:

22-8i+30+8i

combine like terms (which cancels out 8i and -8i):

22+30=52

Area

"i" is not a real number and thus should not be part of the area here, meaning this answer as it is is wrong and I don't know how one would change that.

Here's what I did to get 181-16i, in any case:

The formula for area is l*w, so I plugged in the numbers:

(11-4i)(15+4i)

expanded:

165+44i-60i-16i*i

and combined like terms:

181-16i

*i is $\sqrt{-1}$ , so $i^{2}$ =-1 and -1*-16=16.