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4 years ago

What does a graph with no trend show about the variables

1 answer:

4 0

A graph with no trend shows that the variables are unchanging. For instance if they were changing they would be either "trending upwards" or "trending downwards". But if there is no change there is no trend.

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Please help me i need the answer right now. The lesson is Rational Root Theorem.

Debora [2.8K]

Step-by-step explanation:

1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the

x+4.(3x+1)(x)
The volume is 720.
Volume of Rectangular prism is LxWXH. So the volume is equal to the terms all multiplied. which is

$(3x + 1)(x + 4)$

$(3 {x}^{2} + 13x + 4)x = 720$

Multiply it by x.

$3 {x}^{3} + 13 {x}^{2} + 4x = 720$

$3{x}^{3} + 13 {x}^{2} + 4 x - 720$

The possible roots

The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be

$x = 5$

2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.

Let check via synethic division to see which are roots.

Let try 1 and -1 first. If we plug 1 into the equation, we get

$1 - 2 - 5 + 6 = 0$

So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in

${x}^{2} - x - 6$

We can then factor this into

$(x - 3)(x + 2)$

So our roots or factors is

$(x - 1)(x - 3)(x + 2)$

6 0

3 years ago

An article reported that for a sample of 52 kitchens with gas cooking appliances monitored during a one-week period, the sample

kolbaska11 [484]

Answer:

a) $654.16-2.01\frac{164.55}{\sqrt{52}}=608.29$

$654.16+2.01\frac{164.55}{\sqrt{52}}=700.03$

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

b) $n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189$

Step-by-step explanation:

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)

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

$df=n-1=52-1=51$

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(0.025,51)".And we see that $t_{\alpha/2}=2.01$

Replacing we got:

$654.16-2.01\frac{164.55}{\sqrt{52}}=608.29$

$654.16+2.01\frac{164.55}{\sqrt{52}}=700.03$

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

Part b

The margin of error is given by :

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

The desired margin of error is ME =50/2=25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

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

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , and we use an estimator of the population variance the value of 175 replacing into formula (b) we got: