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2 years ago

Solve each system of equations by substitution. 4y=3x+6 2y=x+8

Mathematics

1 answer:

SSSSS [86.1K]2 years ago

5 0

Answer:

Step-by-step explanation:x=2y-8

4y=3.(2y-8)+6

4y=6y-24+6

4y-6y=-24+6

-2y=-18

Y=9

X=2Y-8

x=2.9-8=10

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Semenov [28]

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3 years ago

Translate the word phrase into a math expression. nine more than five times a number

levacccp [35]

The number is 'n'.

Five times the number is 5n .

Nine more than that is 5n + 9 .

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3 years ago

The following data comparing wait times at two rides at Disney are listed below: Position Pirates Splash Mountain Sample Size 32

myrzilka [38]

Answer:

a) $(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

b) $t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

Step-by-step explanation:

Data given and notation

$\bar X_{A}=14.68$ represent the mean for Pirates

$\bar X_{B}=18.77$ represent the mean for Splash Mountain

$s_{A}=11.87$ represent the sample standard deviation for the sample Pirates

$s_{B}=16.79$ represent the sample standard deviation for the sample Slpash Mountain

$n_{A}=32$ sample size selected for Pirates

$n_{B}=30$ sample size selected for Splash Mountain

$\alpha=0.02$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Part a

The confidence interval would be given by:

$(\bar X_A -\bar X_B) \pm t_{\alpha/2} \sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}$

The degrees of freedom are given by:

$df = n_A +n_B -2 = 32+30-2 = 60$

Since we want 98% of confidence the significance level is $\alpha =1-0.98 =0.02$ and $\alpha/2 =0.01$ , we can find in the t distribution with df =60 a critical value that accumulates 0.01 of the area on each tail and we got:

$t_{\alpha/2}= 2.39$

And replacing we got for the confidence interval:

$(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

Part b

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the means are equal, the system of hypothesis would be:

Null hypothesis: $\mu_{A} = \mu_{B}$

Alternative hypothesis: $\mu_{A} \neq \mu_{B}$

the statistic is given by:

$t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

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2 years ago

The radius of a circle is 7cm. Find the circumference of the circle. Use 22/7 for pi

finlep [7]

Answer:

Hi I'm learning the same thing and I just got it I think it's C=43.98cm

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2 years ago

List all the ways to select two members from S with repetition. The order in which the members are selected is not important. Fo

Taya2010 [7]

9514 1404 393

Answer:

KK KL KM KN KP LL LM LN LP MM MN MP NN NP PP

Step-by-step explanation:

Instead of starting with adjacent letters in the list, we start with the same letter. There are 15 possible pairs.

KK KL KM KN KP LL LM LN LP MM MN MP NN NP PP

<em>Additional comment</em>

We leave out pairs with letters previous, because you've said KL is the same as LK, and KL has already been listed. The problem with this list is that it misstates the probabilities of randomly obtaining a given pair. It is not 1/15, but is 2/25 for all but letter duplicates. For duplicates (KK), the probability is 1/25, not 1/15.

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3 years ago