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Kruka [31]
2 years ago
10

Given the sum s20= 910 of an arithmetic sequence and A20 = 95, Find A1​

Mathematics
1 answer:
Inessa05 [86]2 years ago
5 0

Step-by-step explanation:

Sn=n/2(2a+(n-1)d)

910=n/2{2a+(n-1)d}

1820=n{2a+(n-1)d}

1820=20{2a+(20-1)d}

1820=20{2a+19d}

91=2a+19d

An=a+(n-1)d

95=a+(20-1)d

95=a+19d

91=2a+19d

---------------

4=-a

a=-4

91=2a+19d

91=2(-4)+19d

91=-8+19d

91+8=19d

99=19d

d=99/19

A=-4

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Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yi
aalyn [17]

Answer:

a) t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222  

df=12+15-2=25  

p_v =P(t_{25}>6.222) =8.26x10^{-7}

So with the p value obtained and using the significance level given \alpha=0.01 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis.

b) (91-85) -2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =3.309

(91-85) +2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =8.691

Step-by-step explanation:

Notation and hypothesis

When we have two independent samples from two normal distributions with equal variances we are assuming that  

\sigma^2_1 =\sigma^2_2 =\sigma^2  

And the statistic is given by this formula:  

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}}+\frac{1}{n_2}}  

Where t follows a t distribution with n_1+n_2 -2 degrees of freedom and the pooled variance S^2_p is given by this formula:  

\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}  

This last one is an unbiased estimator of the common variance \sigma^2  

Part a

The system of hypothesis on this case are:  

Null hypothesis: \mu_2 \leq \mu_1  

Alternative hypothesis: \mu_2 > \mu_1  

Or equivalently:  

Null hypothesis: \mu_2 - \mu_1 \leq 0  

Alternative hypothesis: \mu_2 -\mu_1 > 0  

Our notation on this case :  

n_1 =12 represent the sample size for group 1  

n_2 =15 represent the sample size for group 2  

\bar X_1 =85 represent the sample mean for the group 1  

\bar X_2 =91 represent the sample mean for the group 2  

s_1=3 represent the sample standard deviation for group 1  

s_2=2 represent the sample standard deviation for group 2  

First we can begin finding the pooled variance:  

\S^2_p =\frac{(12-1)(3)^2 +(15 -1)(2)^2}{12 +15 -2}=6.2  

And the deviation would be just the square root of the variance:  

S_p=2.490  

Calculate the statistic

And now we can calculate the statistic:  

t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222  

Now we can calculate the degrees of freedom given by:  

df=12+15-2=25  

Calculate the p value

And now we can calculate the p value using the altenative hypothesis:  

p_v =P(t_{25}>6.222) =8.26x10^{-7}

Conclusion

So with the p value obtained and using the significance level given \alpha=0.01 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis.

Part b

For this case the confidence interval is given by:

(\bar X_1 -\bar X_2) \pm t_{\alpha/2} S_p \sqrt{\frac{1}{n_1} +\frac{1}{n_2}}

For the 99% of confidence we have \alpha=1-0.99 = 0.01 and \alpha/2 =0.005 and the critical value with 25 degrees of freedom on the t distribution is t_{\alpha/2}= 2.79

And replacing we got:

(91-85) -2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =3.309

(91-85) +2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =8.691

7 0
3 years ago
Which of the following best describes interval C on the graph shown?
Slav-nsk [51]

Note: <em>The missing graph is attached below. </em>

Answer:

'linear decreasing' best describes interval C on the graph shown.

Step-by-step explanation:

Note: <em>The missing graph is attached below. </em>

From the attached graph, it is easy to figure out that the interval C on the graph shown is showing a straight line. So the graph of the function would be linear.

Also on the interval C, the value of y is decreasing as the value of x increase. So, the slope of the straight line would be negative.

So the interval C indicates that the function is decreasing there.

Therefore, 'linear decreasing' best describes interval C on the graph shown.

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3 years ago
Rewrite the equation in standard form y - 3 = 4(x - 3)
kumpel [21]

Answer:

y=4x-9

Step-by-step explanation:

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Jobisdone [24]

Answer:

8/14

Step-by-step explanation:

there are 5 odd numbers and 3 numbers are coloured red

7 0
2 years ago
One hiking club charges $16 to become a member and $3 to participate on each hike. Another club charges no membership fee, but c
yawa3891 [41]

Answer:

x < 8

Step-by-step explanation:

x= # of hikes

3x +16 =5x

-3x. -3x

16=2x

16/2= 8

2x/2= x

8=x

x=8

check:

3(8) +16 =5(8)

24 +16 =40

40=40 ✓

there for at 8 hikes with either deal it would be the same but if you went up a number of hikes for the first option it would only be $43.00 spent in total. but with the second option it would be $45.00.

7 0
3 years ago
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