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3 years ago

A person places $262 in an investment account earning an annual rate of 3.7%,

Mathematics

1 answer:

yaroslaw [1]3 years ago

3 0

Answer:

$315.24

Step-by-step explanation:

Principal, P =$262

Rate, r= 3.7% =0.037

Time, t= 5 Years

The Value of the Investment which is compounded continuously is gotten using the formula:

$V=Pe^{rt}\\=262*e^{0,037*5}\\=\$315.24$

The value of the investment after 5 years is $315.24 to the nearest cent.

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Babby needs some help!

natka813 [3]

Answer:

(5,-3)

Step-by-step explanation:

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3 years ago

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A ladder is leaning against a building so that the distance from the ground to the top of the latter is 1 foot less than the len

masha68 [24]

Answer:

$25\text{ feet}$

Step-by-step explanation:

The ladder, ground, and building form a right triangle where the vertical distance between the top of the ladder and the bottom of the ground is one leg, the horizontal distance between the bottom of the ladder and the building is another leg, and the length of the ladder is the hypotenuse.

For any right triangle, the Pythagorean Theorem states that the sum of the squares of both legs is equal to the hypotenuse squared ( $a^2+b^2=c^2$ ), where $c$ is the hypotenuse.

Let the length of the ladder be $\ell$ (hypotenuse of right triangle). The distance between the top of the ladder and the ground (vertical distance) can be represented as $\ell -1$ .

From the Pythagorean Theorem, we then have:

$7^2+(\ell-1)^2=\ell^2$

Expand using $(a-b)^2=a^2-2ab+b^2$ :

$49+\ell^2-2\ell+1=\ell^2$

Subtract $\ell$ from both sides and add $2\ell$ to both sides:

$49+1=2\ell$

Combine like terms:

$50=2\ell, \\2\ell =50$

Divide both sides by 2:

$\ell=\frac{50}{2}=\boxed{25\text{ feet}}$

Therefore, the length of the ladder is 25 feet.

4 0

3 years ago

24 POINTS!!!!!!!! <br> 6 (4x - 5) <br> and <br> 22x - 33 - 2x

Iteru [2.4K]

6(4x-5)= 24x-30
24x-22x-2x= 2x
-30-33=63

answer is 2x-63

5 0

3 years ago

The function f(x)=50⋅0.8x models the number of ants in Jonathan's ant farm after it is stricken by a deadly ant disease, where x

alina1380 [7]

Answer:

Step-by-step explanation:

In the exponential growth/decay function

$y=a(b)^x$ , in our situation,

y is the number of ants remaining in the colony after the growth or decay,

a is the initial number of ants in the colony, and

b is the growth/decay rate. Rule: if b is greater than 1, the function is growth; if b is greater than 0 but less than 1, the function is decay.

Our equation looks like this (it's given):

$y=50(.8)^x$

a = 50, which is the initial number of ants in the colony.

b = .8 (which actually means that then number of ants is declining by 20% each week). Since .8 is a fraction of 1, this is decay.

So far, we know that 1 and 4 are true. Let's look at 5. We have to do some solving to find out if it's true or not. If the number of ants after x = 2 weeks is 32, then we plug in 2 for x and see if the y we get as the answer is 32:

$y=50(.8)^2$ and

y = 50(.64) so

y = 32

5 is true as well. Let's test 6 by replacing x with 8 and seeing if y = 10:

$y=50(.8)^8$ and

y = 50(.16777216) so

y = 8.388

6 is not true.

1, 4, 5 are true

8 0

3 years ago

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HELP!!!!!!!!!!!!!!!!!!!!!!

borishaifa [10]

Multiplying factors with exponents means you can add the exponents.

So $2^{4} \cdot 2^{-7} = 2^{4-7} = 2^{-3}$

A negative exponent becomes positive when you move it to the denominator, so:

$2^{-3} = \frac{1}{ 2^{3} }$

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3 years ago