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3 years ago

What are the solutions?

1 answer:

5 0

In order to answer this, we must factor x3-8x2-x+8=0

We can make 2 pairs of 2 terms in order to make the factoring easier,

(x3-8x2)+(-x+8)=0

Now we can begin to factor each pair of terms one at a time,

x2(x-8)-(x-8)=0

We can see that we have 2 (x-8)s so that is our common and we have x2-1 (we can't see the 1 because anything times 1 equals itself so we don't need to put it there).

(x2-1)(x-8)=0

Expand,

(x+1)(x-1)(x-8)=0

In order for 0=0, we must find values of x that will make 0=0

When x=1

(1+1)(1-1)(1-8)=0
2 x 0 x -7=0
0=0

When x=8

(8+1)(8-1)(8-8)=0
9 x 7 x 0=0
0=0

When x=-1

(-1+1)(-1-1)(-1-8)=0
0 x -2 x -9=0
0=0

Therefore, the answer is x=8,1,-1 or (8,1,-1)

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Help????????????????

valentina_108 [34]

Area of the base=
5×12=60 square inches.
Area of two triangles=
4.3×5=21.5 square inches
Area of the other two sides=
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60+21.5+120=201.5 square inches is your final answer. Hope it help!

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4 years ago

Kaden is making loaves of banana bread. He makes 4 loaves of banana bread, and he uses 9 cups of flour in all. How much flour do

Andreas93 [3]

2.25 per loaf divide 9 by 4

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3 years ago

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Monica [59]

Answer:

15.9

Step-by-step explanation:

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3 years ago

The highest and lowest temperatures of Town X were 4°C and -18°C respectively. Find the difference between these two temperature

prisoha [69]

Answer:

Difference: 4-(-18)=22

=22 degrees celcius

Lowest temperature: 12 degrees higher that -18 degrees

= 12+(-18)

= -6 degrees celcius.

Step-by-step explanation:

4 0

3 years ago

Suppose the method of tree ring dating gave the following dates A.D. for an archaeological excavation site. Please show your wor

natita [175]

Answer:

a) $\bar X=\frac{1245+1245+1321+1191+1295+1330+1239+1250+1228}{9}= 1260.444$

b) $s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And if we replace we got:

$s = 45.580$

c) For this case since the sampel size is n=9 <30 we can use the t distribution in order to find the confidence interval.

d) $1260.444-2.306 \frac{45.580}{\sqrt{9}}= 1225.408$

$1260.444+2.306 \frac{45.580}{\sqrt{9}}= 1295.480$

Step-by-step explanation:

For this case we ave the following data:

1245 1245 1321 1191 1295 1330 1239 1250 1228

Part a

We can calculate the sample mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And if we replace we got:

$\bar X= \frac{1245+1245+1321+1191+1295+1330+1239+1250+1228}{9}= 1260.444$

Part b

For this case we can use the following formula in order to find the sample standard deviation:

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And if we replace we got:

$s = 45.580$

Part c

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".

For this case since the sampel size is n=9 <30 we can use the t distribution in order to find the confidence interval.

Part d

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

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

We need to find the degrees of freedom given by:

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

Since the Confidence is 0.95 or 95%, the value of $\alpha=1-0.95=0.05$ 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(0.025,8)".And we see that $t_{\alpha/2}=2.306$

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

$1260.444-2.306 \frac{45.580}{\sqrt{9}}= 1225.408$

$1260.444+2.306 \frac{45.580}{\sqrt{9}}= 1295.480$

8 0

4 years ago