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3 years ago

Aiden measures a book with paper strips. It is actually 10 paper strips long, but he gets an answer of 8. What is his mistake ?

Mathematics

2 answers:

Korolek [52]3 years ago

8 0

I think the best possibility that could lead Aiden's mistake are the following, First, it must be that the length of the paper strips are not the same. Second, it would be that she miscounted the strips. I hope you are satisfied with my answer and feel free to ask for more

VladimirAG [237]3 years ago

7 0

Since no options are provided, there could be several reasons for this.

<em><u>Among these reasons are:</u></em>

1- He did not measure from the beginning of the first strip till the end of the last one.

Now, check the attached picture please.

For the measurement to be correct, he should measure from the beginning of the first strip till the end of the last one as represented by the red line.

If he measured otherwise, say for example, from the end of the first strip till the beginning of the last as represented by the blue line, he will be getting the wrong measurement.

2- The strips may be of different width. This would lead to an error in measurement.

3- He might have simply miscounted the strips.

4- He did not follow the precision or accuracy rules stated for the measurements using paper strips (if they were stated)

Hope this helps :)

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Express the system as AX = B; then solve using matrix inverses

Wittaler [7]

Answer with explanation:

1. The given equations are

3x -5 y=2

-x+2 y= 0

⇒The matrix in the form of , AX=B, is

$A=\left[\begin{array}{cc}3&-5\\-1&2\end{array}\right] ,\\\\ X=\left[\begin{array}{c}x&y\end{array}\right],\\\\B=\left[\begin{array}{c}2&0\end{array}\right]$

$\rightarrow X=A^{-1}B\\\\\rightarrow X=\frac{Adj.A}{|A|}\times B$

Adj.A=Transpose of cofactor of Matrix A

$Adj.A=\left[\begin{array}{cc}2&1\\5&3\end{array}\right] ,\\\\ |A|=6-5\\\\|A|=1\\\\\left[\begin{array}{c}x&y\end{array}\right]=\left[\begin{array}{cc}2&5\\1&3\end{array}\right] \times \left[\begin{array}{c}2&0\end{array}\right]\\\\x=4, y=2$

The given equations are

x+y-z=2

x+z=7

2 x +y+z=13

⇒The matrix in the form of , AX=B, is

$A=\left[\begin{array}{ccc}1&1&-1\\1&0&1\\2&1&1\end{array}\right]\\\\ X=\left[\begin{array}{ccc}x\\y\\z\end{array}\right]\\\\B= \left[\begin{array}{ccc}2\\7\\13\end{array}\right]\\\\\rightarrow X=A^{-1}B\\\\\rightarrow X=\frac{Adj.A}{|A|}\times B\\\\a_{11}=-1,a_{12}=1,a_{13}=1,a_{21}=-2,a_{22}=3,a_{23}=1,a_{31}=1,a_{32}=-2,a_{33}=-1\\\\|A|=1\times(0-1)-1\times(1-2)-1\times(1-0)\\\\=-1+1-1\\\\|A|=-1\\\\Adj.A=\left[\begin{array}{ccc}-1&-2&1\\1&3&-2\\1&1&-1\end{array}\right]$

$\frac{Adj.A}{|A|}=\left[\begin{array}{ccc}1&2&-1\\-1&-3&2\\-1&-1&1\end{array}\right]\\\\X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}1&2&-1\\-1&-3&2\\-1&-1&1\end{array}\right]\times\left[\begin{array}{ccc}2\\7\\13\end{array}\right]\\\\x=3,y=3,z=4$

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3 years ago

48a2 + 32a2 + 16a by 4a?

lbvjy [14]

(48a^3 + 32a^2 + 16a) / 4a = ?

48a^3 / 4a = 12a^2

32a^2 / 4a = 8a

16a / 4a = 4

(48a^3 + 32a^2 + 16a) / 4a = 12a^2 + 8a + 4

Answer is D. 12a^2 + 8a + 4

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3 years ago

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A cabinet door is 13 inches wide and has an area of 260 inches. Use the formula A=lw. How tall is the cabinet door?

klio [65]

Answer:

Step-by-step explanation:

260/13=20

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3 years ago

A random sample of 864 births in a state included 426 boys. Construct a 95% confidence interval estimate of the proportion of bo

oksian1 [2.3K]

Using the z-distribution, it is found that the 95% confidence interval is (0.46, 0.526), and it does not provide strong evidence against that belief.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

We have that a random sample of 864 births in a state included 426 boys, hence the parameters are given by:

$n = 864, \pi = \frac{426}{864} = 0.493$

Then, the bounds of the interval are given by:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.493 - 1.96\sqrt{\frac{0.493(0.507)}{864}} = 0.46$

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.493 + 1.96\sqrt{\frac{0.493(0.507)}{864}} = 0.526$

The 95% confidence interval estimate of the proportion of boys in all births is (0.46, 0.526). Since the interval contains 0.506, it does not provide strong evidence against that belief.

More can be learned about the z-distribution at brainly.com/question/25890103

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2 years ago

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Oxana [17]

Answer:

B.x>4is a required interval.

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3 years ago