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QveST [7]
3 years ago
7

81, 27, 9 finish the sequence

Mathematics
2 answers:
Anna11 [10]3 years ago
7 0
3,1, 1/3, 1/9, 1/27, 1/81
The sequence is dividing by 3
ololo11 [35]3 years ago
3 0
3, 1, \frac{1}{3}, \frac{1}{9}
You might be interested in
My favorite pizza restaurant advertises that their average delivery time is 20 minutes. It always feels like it takes forever fo
andrezito [222]

Answer:

Population parameter(s): mean μ=20

Sample statistics: M=20.7, s=2.1

Hypotheses:

H_0: \mu=20\\\\H_a:\mu> 20

Test Statistic: t=2.357

p-value: 0.011

Reject H? YES

Conclusion (in context of the problem): There is  enough evidence to support the claim that the advertised delivery time is overly optimistic and it is larger than 20 minutes.  

<em>Is this difference practically significant? </em>No, the difference as the sample mean delivery time is under one minute of difference from the advertised time. Although it is significantly from the statistical point of view, the  difference is under 5% of the advertised delivery time.

The 99% confidence interval for the mean is (19.904, 21.496).

With this level of confidence, the null hypothesis failed to be rejected, as t=20 is a possible value for the true mean (is included in the confidence interval).

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the advertised delivery time is overly optimistic and it is larger than 20 minutes.  

Then, the null and alternative hypothesis are:

H_0: \mu=20\\\\H_a:\mu> 20

The significance level is 0.05.

The sample has a size n=50.

The sample mean is M=20.7.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.1.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2.1}{\sqrt{50}}=0.297

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{20.7-20}{0.297}=\dfrac{0.7}{0.297}=2.357

The degrees of freedom for this sample size are:

df=n-1=50-1=49

This test is a right-tailed test, with 49 degrees of freedom and t=2.357, so the P-value for this test is calculated as (using a t-table):

P-value=P(t>2.357)=0.011

As the P-value (0.011) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is  enough evidence to support the claim that the advertised delivery time is overly optimistic and it is larger than 20 minutes.  

2. We have to calculate a 99% confidence interval for the mean.

The sample mean is M=20.7.

The sample size is N=50.

The t-value for a 99% confidence interval is t=2.68.

The margin of error (MOE) can be calculated as:

MOE=t\cdot s_M=2.68 \cdot 0.297=0.796

Then, the lower and upper bounds of the confidence interval are:

LL=M-t \cdot s_M = 20.7-0.796=19.904\\\\UL=M+t \cdot s_M = 20.7+0.796=21.496

The  99% confidence interval for the mean is (19.904, 21.496).

With this level of confidence, the null hypothesis failed to be rejected, as t=20 is a possible value for the true mean (is included in the confidence interval).

7 0
3 years ago
Bethany can mow her family’s lawn in 4 hours. Her brother Colin can mow the lawn in 3 hours. Which equation can be used to find
maria [59]
In 4 hours Bethany did the whole fraction 1 of the house.

In 1 hour he would do 1/4 of it.

In 3 hours Colin did the whole fraction 1 of the house.

<span>In 1 hour he would do 1/3 of it.
</span>
In 1 hour they would both do (1/4 + 1/3)

If it takes both of them x hours to finish 1 whole fraction of the house.

In 1 hour they will both do   1/x

That means that:

1/x = 1/4 + 1/3

That is the equation.   x can be solved for.
5 0
3 years ago
Read 2 more answers
A pole, 4m high, stands, vertically, on
Lostsunrise [7]

Answer:

Length of the shadow of the pole is 6.93 metres

Step-by-step explanation:

Given:

Height of the pole = 4 m

The angle sun makes with the horizontal = 30 degrees

To Find:

Length of the shadow of the pole = ?

Solution:

The tangent ratio is the value received when the length of the side opposite of angle theta is divided by the length of the side adjacent to angle theta

Let x be the length of the shadow

According to the tangent ratio

tan {\theta} = \frac{opposite}{adjacent}

On substituting the values,

ta( {30^{o}) = \frac{4}{x}

x  = \frac{4}{tan ({30^{o})}}

x =\frac{4}{0.57735027}

x  = 6.93 m

6 0
3 years ago
Two inches is approximately _____. 10 cm 5 cm 500 mm .5 m
k0ka [10]

Answer:

5 cm

Step-by-step explanation:

Since 1 inch is 2.5 cm, you'll haft to double that. Making the answer 5 cm.

5 0
3 years ago
Read 2 more answers
You purchase a car using a $20,000 loan with a 5% simple interest rate.
hammer [34]
Simple interest = Cost Price + (Interest Percentage of Cost Price × number of years or months we are paying off)

a) SI = £20 000 + (5% of £20 000 × 4)
SI = £20 000 + (£1000 × 4)
SI = £20 000 + £4000 = £24 000

b) SI = £20 000 + (5% of £20 000 × 3)
SI = £20 000 + (£1000 × 3)
SI = £20 000 + £3000 = £23 000

£24 000 - £23 000 = £1000 that you saved!
3 0
3 years ago
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