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3 years ago

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Below, you are given the 2012 value of a product and the rate at which the value is expected to change during the next 5 years.

Use this information to write a linear equation that gives the dollar value V of the product in terms of the year. (Let t = 12 represent 2012.) 2012 Value Rate $48,000 $2200 decrease per year

1 answer:

beks73 [17]3 years ago

6 0

Answer:

$y = 48000 - 2200x$ --- equation

$y = 37000$ --- value at 5th year

Step-by-step explanation:

Given

$Value = \$48000$

$Rate = \$2200$ decrease

Required

Determine the linear equation

Determine the value at the 5th year

Represent years with x.

If the rate in 1 year is 2200,

in x years, it'll be 2200x (decrement)

So, the value (y) at x years is.

$y = 48000 - 2200x$

The value at the 5th year is when x = 5.

So, we have:

$y = 48000 - 2200 * 5$

$y = 48000 - 11000$

$y = 37000$

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A person invests 9000 dollars in a bank. The bank pays 6% interest compounded monthly. To the nearest tenth of a year, how long

il63 [147K]

Answer:

$7.4\ years$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=?\ years\\ P=\$9,000\\ r=0.06\\n=12\\ A=\$14,000$

substitute in the formula above

$14,000=9,000(1+\frac{0.06}{12})^{12t}$

$(14/9)=(1.005)^{12t}$

Apply log both sides

$log(14/9)=(12t)log(1.005)$

$t=log(14/9)/[(12)log(1.005)]$

$t=7.4\ years$

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4 years ago

Find the area of the figure

djverab [1.8K]

Answer:

Top- 28cm

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3 years ago

Round 218 to the nearest hundred

Sergio [31]

When rounding to the nearest hundred, if the number in the tens place is less than 5, you should round downwards (keep the same number shown in the hundreds place). However, if the number in the tens place is 5 or greater, than you have to round up, which means adding one to the number currently in the hundreds place. So, for this problem, the digit 1 is in the tens place. Because 1 is less than 5, we know that we have to round down. Thus, 218 rounded to the nearest hundred is 200. Hope this helps!!

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3 years ago

3. Using the sample size of 800 and the proportion 0.47, calculate the margin of error associated with the estimate of the propo

salantis [7]

Answer:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346$

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

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

Solution to the problem

We assume for this case a confidence level of 95%. 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 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

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

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 if we replace the values obtained we got this:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346$

6 0

3 years ago

Solve by the substitution method <br><br> y=3x-12<br> 2x-3y=-13

Neporo4naja [7]

<span>y=3x-12
2x-3y=-13
substitute </span>y=3x-12 into <span>2x-3y=-13

</span><span>2x-3y=-13
</span>2x-3(3x-12)=-13
2x - 9x + 36 = -13
-7x = -49
x = 7

y=3x-12 = y=3(7) -12 = 21 - 12 = 9

answer
solution
x = 7 and y = 9

3 0

4 years ago

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