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Tomtit [17]
2 years ago
13

A train leaves at 10.12 and arrives at its destination at 11.18.

Mathematics
1 answer:
nadezda [96]2 years ago
6 0

Answer:

67.3km/h

Step-by-step explanation:

Find the amount of time it took from 10:12 to 11:18.

Which is 66 minutes.

Find the average speed.

Formula of average speed =

Total distance/time

Which is,

74/66 = 1.121 (recurring decimal)

1.121 x 60 = 67.26km/h

= 67.3km/h (Estimated to 1 dp)

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Find the 9th term of the geometric sequence 5, -25, 125, ...
arlik [135]

Answer:

Step-by-step explanation:

a = 5

r = -5

n = 9

t_9 = a r^(n - 1)

t_9 = (-1)^n*5 (-5) ^ 8

t_9 = (-1)^9 *  5 *  (-5) ^8

t_9 = -1 ( 1953125)

t_9 = - 1953125

6 0
3 years ago
In March 2015, the Public Policy Institute of California (PPIC) surveyed 7525 likely voters living in California. This is the 14
lbvjy [14]

Answer:

We are confident at 99% that the difference between the two proportions is between 0.380 \leq p_{Republicans} -p_{Democrats} \leq 0.420

Step-by-step explanation:

Part a

Data given and notation  

X_{D}=3266 represent the number people registered as Democrats

X_{R}=2137 represent the number of people registered as Republicans

n=7525 sampleselcted

\hat p_{D}=\frac{3266}{7525}=0.434 represent the proportion of people registered as Democrats

\hat p_{R}=\frac{2137}{7525}=0.284 represent the proportion of people registered as Republicans

The standard error is given by this formula:

SE=\sqrt{\frac{\hat p_D (1-\hat p_D)}{n_{D}}+\frac{\hat p_R (1-\hat p_R)}{n_{R}}}

And the standard error estimated given by the problem is 0.008

Part b

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".  

p_A represent the real population proportion of Democrats that approve of the way the California Legislature is handling its job  

\hat p_A =\frac{1894}{3266}=0.580 represent the estimated proportion of Democrats that approve of the way the California Legislature is handling its job  

n_A=3266 is the sample size for Democrats

p_B represent the real population proportion of Republicans that approve of the way the California Legislature is handling its job  

\hat p_B =\frac{385}{2137}=0.180 represent the estimated proportion of Republicans that approve of the way the California Legislature is handling its job

n_B=2137 is the sample for Republicans

z represent the critical value for the margin of error  

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})  

The confidence interval for the difference of two proportions would be given by this formula  

(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}  

For the 90% confidence interval the value of \alpha=1-0.90=0.1 and \alpha/2=0.05, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=1.64  

And replacing into the confidence interval formula we got:  

(0.580-0.180) - 1.64 \sqrt{\frac{0.580(1-0.580)}{3266} +\frac{0.180(1-0.180)}{2137}}=0.380  

(0.580-0.180) + 1.64 \sqrt{\frac{0.580(1-0.580)}{3266} +\frac{0.180(1-0.180)}{2137}}=0.420  

And the 99% confidence interval would be given (0.380;0.420).  

We are confident at 99% that the difference between the two proportions is between 0.380 \leq p_{Republicans} -p_{Democrats} \leq 0.420

5 0
3 years ago
Which box plot represents the data? 43, 48, 52, 61, 74, 81, 40, 42, 56, 77, 81, 43?
frutty [35]
The box plot for the set of data 
<span>43, 48, 52, 61, 74, 81, 40, 42, 56, 77, 81, 43
</span>will be found by rewriting the data in ascending data, then plotting it. This will give us the box plot in the attached figure. 

6 0
3 years ago
Read 2 more answers
Https://d2y2khognlqryx.cloudfront.net/calms_media/media/8376000_8376500/8376375/2/ce6e095ec744ebed7bcb9c367552674e67dc8b1e/MTH_A
lana [24]

Answer:

qwertyuio

Step-by-step explanation:

7 0
2 years ago
Please give me the answer :)
NISA [10]
The answer is -19,683
3 0
1 year ago
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