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3 years ago

360 words in 1/12 hour. Second try 360 words in 1/15 hour. Was he faster or slower second attempt

Mathematics

1 answer:

xxTIMURxx [149]3 years ago

8 0

Answer:

Second Attempt is faster.

Step-by-step explanation:

He reads 360 words in $\frac{1}{12}$ hour in the first attempt and in the second attempt he reads the same number of words in $\frac{1}{15}$ hour.

Since, $\frac{1}{15} < \frac{1}{12}$ he takes less time in the second time. Less time means the work is done faster.

Therefore, second attempt is faster.

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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

2 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used

gladu [14]

Answer:

Part 1) $2x^{2}-32=0----> (-4,4)$

Part 2) $4x^{2}-100=0----> (-5,5)$

Part 3) $x^{2}-55=9----> (-8,8)$

Part 4) $x^{2}-140=-19----> (-11,11)$

Part 5) $2x^{2}-18=0----> (-3,3)$

see the attached figure

Step-by-step explanation:

Solve each quadratic equation

Part 1) we have

$2x^{2}-32=0$

Adds 32 both sides

$2x^{2}=32$

Divide by 2 both sides

$x^{2}=16$

take square root both sides

$x=\pm4$

therefore

The solutions are (-4,4)

Part 2) we have

$4x^{2}-100=0$

Adds 100 both sides

$4x^{2}=100$

Divide by 4 both sides

$x^{2}=25$

take square root both sides

$x=\pm5$

therefore

The solutions are (-5,5)

Part 3) we have

$x^{2}-55=9$

Adds 55 both sides

$x^{2}=9+55$

$x^{2}=64$

take square root both sides

$x=\pm8$

therefore

The solutions are (-8,8)

Part 4) we have

$x^{2}-140=-19$

Adds 140 both sides

$x^{2}=-19+140$

$x^{2}=121$

take square root both sides

$x=\pm11$

therefore

The solutions are (-11,11)

Part 5) we have

$2x^{2}-18=0$

Adds 18 both sides

$2x^{2}=18$

Divide by 2 both sides

$x^{2}=9$

take square root both sides

$x=\pm3$

therefore

The solutions are (-3,3)

7 0

3 years ago

The number of players in a tennis tournament is reduced by half (50%) after every round. In round 1 there are 256 player, in rou

Aleks04 [339]

Answer:

$a_{n} = a_{1} (\frac{1}{2} )^{n - 1}$ where $a_{1} = 256$ .

The number of players compete in round 7 will be 4.

Step-by-step explanation:

The number of players in a tennis tournament is reduced by half (50%) after every round. In round 1 there are 256 players, in round 2 there are 128 players, and so on.

So, the number of players is multiplied by $\frac{1}{2}$ gives the number of players in the next round.

Therefore, the explicit function of number of players in nth round is given by

$a_{n} = a_{1} (\frac{1}{2} )^{n - 1}$ where $a_{1} = 256$ .

Therefore, the number of players compete in round 7 will be $a_{7} = 256 \times (\frac{1}{2} )^{(7 - 1)} = 4$ . (Answer)

8 0

3 years ago

Question 9 of 10 Which of the following is most likely the next step in the series? OA. O B. O C. O D.

uranmaximum [27]

Answer:

Step-by-step explanation:

Vertical line is removed then horizontal. Its goes blue, red, blue. A vertical line is to be removed and the colour is red. That leaves B as the answer.

3 0

2 years ago

Read 2 more answers

I need help on this problem please help me.

a_sh-v [17]

Answer:

150 mL

Step-by-step explanation:

Let x represent the quantity of 75% solution needed. The total amount of alcohol in the 60% mixture will be ...

75%·x + 10%·45 = 60%·(x+45) . . . . . there will be x+45 mL of solution in the end

0.15x = 22.5 . . . . . . . . . . . . . . . . . . . . simplify, subtract .60x+4.5

22.5/0.15 = x = 150 . . . . . . . . . . . . . . mL of 75% solution needed

You will need 150 mL of the 75% solution.

3 0

3 years ago