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3 years ago

-x+y+z=1, x-y+z=2, x+y-z=1

Mathematics

1 answer:

Virty [35]3 years ago

6 0

Answer:

Step-by-step explanation:

Given the simultaneous equation

-x+y+z=1... 1

x-y+z=2 ... 2

x+y-z=1 .... 3

Add equation 1 and 2;

-x+x + y - y + z + z = 1+2

0 + 0 + 2z = 3

2z = 3

z = 3/2

Add equation 2 and 3

x+x = 2 + 1

2x = 3

x = 3/2

Substitute x = 3/2 and z = 3/2 into 3

From 3;

x+y-z = 1

3/2 + y - 3/2 = 1

y + 0 = 1

y = 1

<em>Hence the solution (x, y, z) is (3/2, 1, 3/2)</em>

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(4.7 x 10^5) + (2.8 x 10^3)

EleoNora [17]

Answer:

472800 or 4.728x10^5

Step-by-step explanation:

first you would slove (4.7x10^5) and (2.8x 10^3). Which would be 470000 and 2800. Then add the two together to get 472800. And if they want you to put it back into scientific notation then it would be 4.728x10^5

3 0

3 years ago

Read 2 more answers

Suppose that the researchers wanted to estimate the mean reaction time to within 6 msec with 95% confidence. Using the sample st

Lisa [10]

Answer:

a) The 95% confidence interval would be given by (509.592;550.308)

b) n=523 rounded up to the nearest integer

Step-by-step explanation:

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".

$\bar X=530$ represent the sample mean for the sample

$\mu$ population mean

s=70 represent the sample standard deviation

n=48 represent the sample size (variable of interest)

Confidence =95% or 0.995

Part a

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

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

The degrees of freedom are df=n-1=48-1=47

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 table to find the critical value. The excel command would be: "=-T.INV(0.025,47)".And we see that $z_{\alpha/2}=2.01$

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

$530-2.01\frac{70}{\sqrt{48}}=509.692$

$530+2.01\frac{70}{\sqrt{48}}=550.308$

So on this case the 95% confidence interval would be given by (509.592;550.308)

Part b

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

Assuming that $\hat \sigma =s$

And on this case we have that ME =6msec, and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval is provided, $z_{\alpha/2}=1.96$ , replacing into formula (b) we got:

$n=(\frac{1.96(70)}{6})^2 =522.88 \approx 523$

So the answer for this case would be n=523 rounded up to the nearest integer

3 0

3 years ago

What’s the square root of 64

Luba_88 [7]

Answer:

The square root of 64 is 8

Step-by-step explanation:

7 0

3 years ago

I've done the y = equations but I don't know how to do this one.

Tems11 [23]

Consider the equation

$-10x-y=-20$

1) First row of the table

Set x=0 and solve as follows:

$\begin{gathered} -10(0)-y=-20 \\ \Rightarrow-y=-20 \\ \Rightarrow y=20 \end{gathered}$

The answer is y=20 and the pair x-y is (0,20)

2) Second row

Set x=1 and solve, as follows:

$\begin{gathered} -10(1)-y=-20 \\ \Rightarrow-10-y=-20 \\ \Rightarrow-y=-10 \\ \Rightarrow y=10 \end{gathered}$

The answers are y=10 and (1,10)

3) Third row.

Set y=0 and solve as follows:

$\begin{gathered} -10x-(0)=-20 \\ \Rightarrow-10x=-20 \\ \Rightarrow x=\frac{20}{10}=2 \\ \Rightarrow x=2 \end{gathered}$

The answers are x=2 and (2,0)

6 0

1 year ago

Help! what is the surface area of the prism? 128in^2, 768in^2, 384in^2, or 480in^2

Nimfa-mama [501]

Option C: $384 \ in^2$ is the surface area of the prism

Explanation:

Given figure is a triangular prism.

We need to determine the surface area of the triangular prism.

The formula to find the surface area of the triangular prism is given by

$S A=b h+(s 1+s 2+s 3) H$

where b is the base of the triangle,

h is the height of the triangle,

$s1,s2,s3$ are the three sides of the triangle and

H is the height of the prism.

Let us substitute the values $b=16$ , $h=6$ , $s1=16$ , $s2=10$ , $s3=10$ and $H=8$ in the formula, we get,

$SA=16(6)+(16+10+10)(8)$

Simplifying, we get,

$SA=96+(36)(8)$

Multiplying the term, we get,

$SA=96+288$

Adding the terms, we have,

$SA=384 \ in^2$

Thus, the surface area of the prism is $384 \ in^2$

Hence, Option C is the correct answer.

6 0

3 years ago