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goblinko [34]
3 years ago
7

Last year alvina contributed 85$ per month toward her 401k account if her employer matched 20% of her contributions, what was th

e total amount contributed to the 401 k at the end of the year?
Mathematics
1 answer:
julsineya [31]3 years ago
3 0
So, first let's solve for the total amount that Alvina contributed to her 401k account, by multiplying the amount contributed per month ($85) times the number of months (12):
85*12=1020
So, Alvina contributed $1020 to her 401k account.

Her employer contributed 20% of that, which we can find by multiplying the amount Alvina contributed by .2:
1020*.2=204
So we know that Alvina's employer contributed $204 to her 401k account.

We can add these two numbers to get the total:
1020+204=1224
And that's our final answer of $1224 total contributed to the account!

Hope I helped, and let me know if you have any questions! :)
You might be interested in
An insurance company has 25,000 automobile policy holders. If the yearly claim of a policy holder is a random variable with mean
telo118 [61]

Answer:

P(T>8300000)=1-P(T

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Data given

n = 25000 represent the automobile policy holders

\mu= 320 represent the population mean

\sigma =540 represent the population standard deviation

Let T the variable that represent the total of interest on this case. We can assume that the random variable for an individual policy holder is given by:

X\sim N(\mu = 540, \sigma=540)

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

Solution to the problem

First we need to find the distribution for the random variable T like this:

\bar X = \frac{\sum_{i=1}^n x_i}{n}

And the total T is given by:

T=\sum_{i=1}^n X_i =n \bar X

We can find the expected value, variance and deviation for this random variable like this:

E(T)= n E(\bar X) = n \mu = 25000*320=8000000

Var(T)= Var(n\bar X)= n^2 Var(\bar X) = n^2 \frac{\sigma^2}{n}=n \sigma^2 =25000*(540^2)=7290000000

Sd(T)=\sqrt{7290000000}=85381.497

And we are interested on this probability:

P(T>8300000)

And we can use the Z score formula given by:

Z=\frac{T-E(T)}{\sigma_T}

P(T>8300000)=1-P(T

6 0
3 years ago
Y<br> 45°<br> 30°<br> N<br> 17<br> I need help pls
melisa1 [442]

Answer:

x=29.4

Step-by-step explanation:

To help find the sides of a triangle, I use SOHCAHTOA.

SOH - CAH - TOA

S=O/H (Sine=\frac{opposite}{hypotenuse} )

C=A/H (Cosine=\frac{adjacent}{hypotenuse} )

T=O/A (Tangent =\frac{opposite}{adjacent} )

Let's find x first. We know 2 parts of the triangle: the adjacent leg, and the angle that is opposite of that.

So it would be tangent (tan).

opposite = 17

adjacent = 30°

Plug these numbers into the calculator and you should get your answer.

\frac{17}{tan(30)} = 29.44486372...

x=29.4

Try to do <em>y</em> on your own and let me know if you have any questions!

Also correct me if I'm wrong on anything.

Hope this information helps!

4 0
2 years ago
The population of deer forest is currently 800 individuals. Scientists predict that this population will grow at a rate of 20 pe
jonny [76]

Answer:

<em>C. 3.8 years</em>

Step-by-step explanation:

<u>Exponential Growth </u>

The natural growth of some magnitudes can be modeled by the equation:

P(t)=P_o(1+r)^t

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

The actual population of deer in a forest is Po=800 individuals. It's been predicted the population will grow at a rate of 20% per year (r=0.2).

We have enough information to write the exponential model:

P(t)=800(1+0.2)^t

P(t)=800(1.2)^t

It's required to find the number of years required for the population of deers to double, that is, P = 2*Po = 1600. We need to solve for t:

800(1.2)^t=1600

Dividing by 800:

(1.2)^t=1600/800=2

Taking logarithms:

t\log 1.2=\log 2

Dividing by log 1.2:

t=\frac{\log 2}{ \log 1.2}

Calculating:

t = 3.8 years

Answer: C. 3.8 years

6 0
3 years ago
Is 6 squared plus 9 sqaured <br> rational?
iris [78.8K]
Simplify the expression

6² + 9²

6² = 6 x 6 = 36
9² = 9 x 9 = 81

36 + 81 = 117

117 is a rational number ∴ <span>6</span>²<span> plus 9</span>² is rational


hope this helps
5 0
3 years ago
Which order pair could be removed so that the set of ordered pairs is a function (4,-2) (-3,2) (3,4) (1,1)
Masja [62]
<span> (4,-2) (-3,2) (3,4) (1,1)
In reality, it is already a function, because for every x only one corresponding value of y.
We do not see any repeating values of x, so this set is already function. We do not have to remove anything.</span>
6 0
3 years ago
Read 2 more answers
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