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2 years ago

I need this answer as fast as you can and explain simple

Mathematics

1 answer:

blondinia [14]2 years ago

4 0

Answer:

Step-by-step explanation:

(b-3)(b-3) would equal (b^2–6b+9), when using the foil method.

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From a square piece of cardboard paper of area size 9 m2 , squares of the same size are cut off from each corner of the paper. T

levacccp [35]

Answer:

Max vol = 2 cubic metres

Step-by-step explanation:

Given that from a square piece of cardboard paper of area size 9 m2 , squares of the same size are cut off from each corner of the paper.

Side of the square = 3m

If squares are to be cut from the corners of the cardboard we have the dimensions of the box as

3-2x, 3-2x and x.

Hence x can never be greater than or equal to 1.5

V(x) = Volume = $V(x) = x(3-2x)^2\\= 9x+4x^3-12x^2$

We use derivative test to find the maxima

$V'(x) = 9+12x^2-24x\\V"(x) = 24x-24\\$

Equate I derivative to 0

$9+12x^2-24x=0\\x=1/2,3/2$

If x= 3/2 box will have 0 volume

So this is ignored

V"(1/2) <0

So maximum when x =1/2

Maximum volume

= $9(1/2)+4(1/2)^3-12(1/2)^2\\=2$ cubic metres

6 0

2 years ago

The inverse of 2x^3+3

Rashid [163]

2/x ^6-3 you do the opposite of everything

6 0

3 years ago

Read 2 more answers

A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selec

VMariaS [17]

Answer:

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

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".

$\bar X=19.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.5 represent the sample standard deviation

n=9 represent the sample size

Solution to the problem

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:

$df=n-1=9-1=8$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that $t_{\alpha/2}=$