9x^3+27x (factor it completely, PLEASE

The sum of two numbers is 18. Twice the first number (x) minus the second number (y) is 6. Find the two numbers

ki77a [65]

Answer:

8 and 10

Step-by-step explanation:

Set the first number as x, the second as y

x+y=18

2x-y=6

This is an binary system of first order equations

3x=24

x=8

y=10

8 0

3 years ago

Theo fills a large box with boxes of staples. The volume of each box of staples is 120 cu cm. Estimate the volume of the large b

riadik2000 [5.3K]

I saw the image. The large box is filled with 6 columns of staples which has 5 box of staple each.

6colums * 5boxes/column = 30 boxes of staples.

30 boxes * 120 cu cm/box= 3,600 cu cm.

The estimated volume of the large box is 3,600 cu cm.

8 0

3 years ago

Please help me with this i don’t understand much

Alexus [3.1K]

Answer:

See below

Step-by-step explanation:

Three lengths will be a triangle only if the sum of two sides is greater than the third side.

$19+11 > 17$

This is a triangle.

$23+28> 52\\51>52\\51 \ngtr 52$

This is not a triangle.

$9+25> 34\\34>34\\34\ngtr 34$

This is not a triangle.

$13+14> 22\\27>22$

This is a triangle.

8 0

2 years ago

Health insurance benefits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sa

xxMikexx [17]

Answer:

$\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.221)=0.000067$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

Since the p values is higher than a significance level for example $\alpha=0.05$ , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.

Step-by-step explanation:

Previous concepts

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Solution to the problem

Assume the following dataset:

Size Company/ Heal. Ins. Yes No Total

Small 32 18 50

Medium 68 7 75

Large 89 11 100

_____________________________________

Total 189 36 225

We need to conduct a chi square test in order to check the following hypothesis:

H0: independence between heath insurance coverage and size of the company

H1: NO independence between heath insurance coverage and size of the company

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{50*189}{225}=42$

$E_{2} =\frac{50*36}{225}=8$

$E_{3} =\frac{75*189}{225}=63$

$E_{4} =\frac{75*36}{225}=12$

$E_{5} =\frac{100*189}{225}=84$

$E_{6} =\frac{100*36}{225}=16$

And the expected values are given by:

Size Company/ Heal. Ins. Yes No Total

Small 42 8 50

Medium 63 12 75

Large 84 16 100

_____________________________________

Total 189 36 225

And now we can calculate the statistic:

$\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.221)=0.000067$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

Since the p values is higher than a significance level for example $\alpha=0.05$ , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.

3 0

3 years ago

Find the surface area of the prism. 4 cm 3 cm 5 cm 9 cm

iren [92.7K]

Answer:

540cm^3

Step-by-step explanation:

4*3*5*9=12*5*9=60*9=540

8 0

3 years ago

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