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3 years ago

18. Write an expression to represent the area of the shaded region in simplest form. Please help it's due tomorrow

Mathematics

1 answer:

IgorC [24]3 years ago

7 0

Answer:

(x^2 + 2x - 21) sq units

Step-by-step explanation:

Area of the shaded region = Area of the larger rectangle - Area of smaller rectangle

Area of the larger region = x(x+2)

Area of the larger region =x^2 + 2x

Area of the smaller rectangle = 3 * 7

Area of the smaller rectangle = 21 sq. units

Area of the shaded region = x^2 + 2x - 21

Hence the required expression is (x^2 + 2x - 21) sq units

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Which statements are true about the polynomial function?<br><br> f(x)=x4+5x3−x2−5x

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Answer:

f(5) is NOT 0.

When x=-5, f(x) IS 0.

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But x-5 is NOT a factor of x.

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3 years ago

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In one community, a random sample of 26 foreclosed homes sold for an average of $443 comma 555 with a standard deviation of $

alexandr1967 [171]

Answer:

i) a) Normality : We assume that the data follows approximately a normal distribution

ii) Random sample: The data comes from a random sample

iii) The sample size represent <10% of the population size

We assume that all the conditions are satisfied for this case.

b) $443555-2.06\frac{195381}{\sqrt{26}}=364621.22$

$443555+2.06\frac{195381}{\sqrt{26}}=522488.775$

So on this case the 95% confidence interval would be given by (364621.22;522488.775)

c) We are confident at 95% that the true mean of foreclosed homes sold's are between (364621.22;522488.775)

d) Since the lower value for the 95% confidence interval is higher than 300000 we can conclude that yes differes significantly and the true mean is different from 300000 at 5% of significance.

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".

$\bar X=443555$ represent the sample mean

$\mu$ population mean (variable of interest)

s=195381 represent the sample standard deviation

n=26 represent the sample size

Part a

We need some conditions:

a) Normality : We assume that the data follows approximately a normal distribution

b) Random sample: The data comes from a random sample

c) The sample size represent <10% of the population size

We assume that all the conditions are satisfied for this case.

Part b

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=26-1=25$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,25)".And we see that $t_{\alpha/2}=2.06$

Now we have everything in order to replace into formula (1):

$443555-2.06\frac{195381}{\sqrt{26}}=364621.22$

$443555+2.06\frac{195381}{\sqrt{26}}=522488.775$

So on this case the 95% confidence interval would be given by (364621.22;522488.775)

Part c

We are confident at 95% that the true mean of foreclosed homes sold's are between (364621.22;522488.775)

Part d

Since the lower value for the 95% confidence interval is higher than 300000 we can conclude that yes differes significantly and the true mean is different from 300000 at 5% of significance.

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3 years ago

for the parent function what effect does the values k = 5 have on the graph? vertical shift of five units up. vertical shift of

Tresset [83]

The value k = 5 will shift the parent function 5 units up. i.e. vertical shift of 5 units up.

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3 years ago