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2 years ago

The expression (y-20)(y5)3 is equivalent to ya. What is the value of a?

Mathematics

1 answer:

Leno4ka [110]2 years ago

5 0

Answer:

y¹⁵-20y¹⁴

Step-by-step explanation:

I'm going to assume that your problem looks like this

$(y-20)(y^5)^3$

$(x^n)^y=x^{n*y}$

which means we have

$(y-20)*y^{15}\\\\y^{16}-20y^{15}=ya\\\\*y^{15}-20y^{14}=a$

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-36 as a fraction in simplest form

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Answer:

-1/2

Step-by-step explanation:

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2 years ago

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Suppose you invest $50 a month in an annuity that earns 4% APR compounded monthly. How much money will you have in this account

skelet666 [1.2K]

To solve this we are going to use formula for the future value of an ordinary annuity: $FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]$
where
$FV$ is the future value
$P$ is the periodic payment
$r$ is the interest rate in decimal form
$n$ is the number of times the interest is compounded per year
$t$ is the number of years

We know from our problem that the periodic payment is $50 and the number of years is 3, so $P=50$ and $t=3$ . To convert the interest rate to decimal form, we are going to divide the rate by 100%
$r= \frac{4}{100}$
$r=0.04$
Since the interest is compounded monthly, it is compounded 12 times per year; therefore, $n=12$ .
Lets replace the values in our formula:
$FV=P[ \frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} } ]$
$FV=50[ \frac{(1+ \frac{0.04}{12} )^{(12)(3)} -1}{ \frac{0.04}{12} } ]$
$FV=1909.08$

We can conclude that after 3 years you will have $1909.08 in your account.

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2 years ago

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Recall the equation that modeled the volume of the raised flower bed, y, in terms of the width of the box, y = x3 + 11x2 − 312x.

lakkis [162]

Answer:

48 cubic feet of mulch

Step-by-step explanation:

12 feet long x 4 feet wide x 1 foot deep of mulch= 48 cubic feet of mulch

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2 years ago

Ray industries bought a touchscreen monitor for $1200 it is expected to depreciate at a rate of 25% per year what was the value

max2010maxim [7]

So for this problem, we will be using the exponential equation format, which is y = ab^x. The a variable is the initial value, and the b variable is the growth/decay.

Since our touchscreen starts off at a value of 1200, that will be our a variable.

Since the touchscreen is decaying in value by 25%, subtract 0.25 (25% in decimal form) from 1 to get 0.75. 0.75 is going to be your b variable.

In this case, time is our independent variable. Since we want to know the value 3 years from now, 3 is the x variable.

Using our info above, we can solve for y, which is the cost after x years.

$y=1200*0.75^3\\y=506$

In context, after 3 years the touchscreen will only be worth $506.

7 0

2 years ago

Sample Size for Proportion As a manufacturer of golf equipment, the Spalding Corporation wants to estimate the proportion of gol

Dima020 [189]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56$

And rounded up we have that n=2663

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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 population proportion have the following distribution

$\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$t_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.025$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume an estimated proportion of $\hat p =0.5$ since we don't have prior info provided. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56$

And rounded up we have that n=2663

6 0

2 years ago