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Lostsunrise [7]

2 years ago

14

Naomi invested $4,000 into a fund that is expected to grow by 5.53% per year. How long will it take the fund to be worth $8,000?

1 answer:

Tcecarenko [31]2 years ago

4 0

It will take 13.42 years.

The equation for this is in the form y=a(1+r)ˣ, where a is the initial deposit, r is the interest rate as a decimal number and x is the amount of time. Using our information, we have the equation

8000 = 4000(1+0.053)ˣ
8000 = 4000(1.053)ˣ

Divide both sides by 4000:
8000/4000 = 4000(1.053)ˣ/4000
2 = 1.053ˣ

We will use a logarithm to solve this:
$x=\log_{1.053}2
\\
\\x=13.42$

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Which represents the solution set of 5(x+5)<85

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X<12
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<span>x + 5 < 17 </span>
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If the measure of angle ABC is 57 degrees, what is the measure of arc AB

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NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! THIS IS NOT A TEST OR AN ASSESSMENT!! Please help me with these math questions

Art [367]

Answer:

See below

Step-by-step explanation:

3. What are two ways that a vector can be represented?

Considering a vector $\vec{v}$ in some vector space $\mathbb R^n$ we have

$\vec{v} = \langle a,b\rangle$

This is the component form. I don't like that way. It is probably used in high school, but

$\vec{v} = \begin{pmatrix} a\\ b\\ \end{pmatrix}$

is preferable because the inner product on $\mathbb R^n$ is defined to be

$\langle a,b\rangle := \sum_{i = 1}^n a_i b_i$

You can also write it using linear form such as $\vec{v} = 2i+2j$

4.

For this question, I think you meant

vectors

$\vec{u_1} = (-8, 12)$

$\vec{u_2} = (13, 15)$

Once

$\cos(\theta)=\dfrac{\vec{u_1} \cdot\vec{u_2}}{||\vec{u_1}||||\vec{u_2}||}$

Considering that the dot product is

$\vec{u_1}\cdot \vec{u_2} = (-8)\cdot 13 + 12\cdot 15 = -104+180= 76$

and the norm of $\vec{u_1}$ is $||\vec{u_1}|| = \sqrt{(-8)^2 + 12^2} = \sqrt{64 + 144}= \sqrt{208}$

and the norm of $\vec{u_2}$ is $||\vec{u_2}|| = \sqrt{13^2 + 15^2} = \sqrt{169 + 225}= \sqrt{394}$

Thus,

$\cos(\theta)=\dfrac{76}{\sqrt{208} \sqrt{394}} = \dfrac{19}{\sqrt{13}\sqrt{394}}=\dfrac{19}{\sqrt{5122}}$

$\therefore \theta = \arccos \left(\dfrac{19}{\sqrt{5122}} \right)$

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2 years ago

Explain how to find the mean of a data set

leva [86]

To find mean you add all the values in your data together and divide by the # of values you have.

4 0

3 years ago

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How much does 4 5/7 kg of candy cost if 5/6 kg costs $7.50

Aliun [14]

Answer:

It costs $42.43

Step-by-step explanation:

Lets explain how to solve the problem

- The cost of $\frac{5}{6}$ kilogram of candy is $7.5

- We need to find the cost of $4\frac{5}{7}$ kilogram

We can use the ratio to find the answer

======= Dollar : Kilogram

======= 7.5 : $\frac{5}{6}$

======= c : $4\frac{5}{7}$

By using cross multiplication

∴ c × $\frac{5}{6}$ = 7.5 × $4\frac{5}{7}$

∵ $4\frac{5}{7}$ = $\frac{4*7+5}{7}$

∴ $4\frac{5}{7}$ = $\frac{33}{7}$

∴ c × $\frac{5}{6}$ = 7.5 × $\frac{33}{7}$

∴ c × $\frac{5}{6}$ = $\frac{495}{14}$

Divide both sides by $\frac{5}{6}$

∴ c = $\frac{495}{14}$ ÷ $\frac{5}{6}$

Change the division sign to multiplication sign and reciprocal the

fraction after the division sign

∴ c = $\frac{495}{14}$ × $\frac{6}{5}$

∴ c = $\frac{297}{7}$ = 42.43 dollars

∵ c represents the cost of $4\frac{5}{7}$ kg

∴ It costs $42.43

7 0

3 years ago