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sertanlavr [38]
3 years ago
13

-8 -8x + 10 + 6x = 19

Mathematics
1 answer:
hram777 [196]3 years ago
4 0

Answer:

x = -8.5

Step-by-step explanation:

Let's rearrange the question to find x :)

-8x + 6x + 10 - 8 = 19

-2x + 2 = 19

-2             -2

-2x = 17

/-2      /-2

x = -8.5

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s = hours it takes the small pipe on its own.


L = hours it takes the large pipe on its own.


we know the small pipe can do it in 11 hours total, so s = 11, so, how much of the whole job has the small done in 1 hour only?


well, if it takes 11 hours to do the whole thing, in 1 hour it has done only 1/11 of the whole job.


we know both pipes working together can do it in 6 hours flat. So in 1 hour only, both of them have done only 1/6 of the whole thing.


in that 1 hour, how much has the large one done? well, it has only done 1/L of the job.


\bf \stackrel{\textit{how much has it been done by both in 1 hour}}{\stackrel{\stackrel{small}{rate}}{\cfrac{1}{s}}+\stackrel{\stackrel{large}{rate}}{\cfrac{1}{L}}~~=~~\stackrel{job}{\cfrac{1}{6}}} \\\\\\ \cfrac{1}{11}+\cfrac{1}{L}=\cfrac{1}{6}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{66L}}{6L+66=11L}\implies 66=5L \\\\\\ \cfrac{66}{5}=L\implies 13\frac{1}{5}=L\impliedby \textit{13 hours and 12 minutes}


and you can round that up as needed.

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3 years ago
A new dental bondlng agent. When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive(called "Smartbon
Gemiola [76]

Answer:

(a) <em>H</em>₀: <em>μ ≥ 5.70 </em><em>vs. </em><em>Hₐ</em>:<em>μ < 5.70</em>

(b) The rejection region is (<em>t₀.₀₁,₉</em> <em>≤ -2.821</em>).

(c) The value of the test statistic is -4.33.

(d) The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

Step-by-step explanation:

A hypothesis test should be conducted to determine that the if the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

(a)

The hypothesis is:

<em>H</em>₀: The true mean breaking strength of the new bonding adhesive is not less than 5.70 Mpa, i.e. <em>μ ≥ 5.70</em><em>.</em>

<em>Hₐ</em>: The true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, i.e. <em>μ < 5.70</em><em>.</em>

(b)

The alternate hypothesis indicates that the hypothesis test is left-tailed.

The rejection region for the left tailed test will be towards the lower tail of the t<em>-</em>distribution curve.

The significance level of the test is: <em>α</em> = 0.01.

The critical value is:

t_{\alpha ,(n-1)}=t_{0.01,(10-1)}=t_{0.01,9}

Use the <em>t-</em>table for the critical value.

t_{\alpha ,(n-1)}=t_{0.01,9}=-2.821

Since rejection region is in the lower tail the critical value will be negative.

Thus, the rejection region is (<em>t₀.₀₁,₉</em> <em>≤ -2.821</em>).

(c)

The test statistic value is:

t=\frac{\bar x-\mu}{s/\sqrt{n}}

Given:

\bar x=5.07\\s=0.46\\n=10\\\mu=5.70

Compute the value of the <em>t</em>-statistic as follows:

t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{5.07-5.70}{0.46/\sqrt{10}} =-4.33

The value of the test statistic is -4.33.

(d)

The value of the test is less than the critical value.

t=-4.33

This implies that the test statistic lies in the rejection region.

Hence the null hypothesis will be rejected at 1% significance level.

<u>Conclusion:</u>

As the null hypothesis is rejected it can be concluded that the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa.

(e)

The conditions required for the <em>t-</em>test for single mean to be valid is:

  • The data should be continuous.
  • The parent population should be normally distributed.
  • The sample should be randomly selected.

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