Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object.

scZoUnD [109]

Roll dice and flip coin:
Probability of rolling a cube and getting a 3 = 1/6 .
Probability of flipping a coin and getting HEADS = 1/2 .

Probability of both = (1/6) x (1/2) .
You do the multiplication.

4 blue, 2 green, 6 red
Probability of a blue on the first draw = 4 out of 12 marbles = 1/3 .
Without putting the blue back in ...
Probability of a red on the next draw = 6 out of 11 marbles = 6/11 .

Probability of both = (1/3) x (6/11) .
You do the multiplication.

8 0

3 years ago

Can someone please help me with 2 and explain the steps to 3 thanks!

Gelneren [198K]

Answer:

#2 is a ratio so you gotta add.

#3 it’s just adding it for example 2p + 5a = 7pa

7 0

3 years ago

Please help! I'm not real good with Algebra....

____ [38]

2xy, -xy, and 1/2xy because they contain the same variables

8 0

3 years ago

There are 4 empty seats and 76 occupied seats in a train. What percentage of the seats on the train are empty?

Norma-Jean [14]

Answer:

5%

Step-by-step explanation:

fraction empty = empty / total

= 4/ (76+4)

= 4/80

=1/20

Changing to a percent

1/2 *5/5 = 5/100 = 5%

5 0

3 years ago

The bacterial strain Acinetobacter has been tested for its adhesion properties. A sample of five measurements gave read- ings of

oksian1 [2.3K]

Answer:

Part a

We need to conduct a one tailed test

We need to conduct a hypothesis in order to check if the mean is higher than 2.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.5$

Alternative hypothesis: $\mu > 2.5$

Part b: Calculate the statistic

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

$z=\frac{3.372-2.5}{\frac{0.66}{\sqrt{5}}}=2.954$

Part c :P-value

Since is a one sided test the p value would be:

$p_v =P(z>2.954)=0.0016$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, we can conclude that the true mean is higher than 2.5 at 1% of signficance.

Step-by-step explanation:

a. Should the alternative hypothesis be one-sided or two-sided?

b. Test the hypothesis that the mean adhesion is 2.5 dyne-cm².

c. What is the P-value of the test statistic?

Data given and notation

Data: 2.69, 5.76, 2.67, 1.62 ,4.12

We can calculate the sample mean with this formula:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$\bar X=3.372$ represent the sample mean

$\sigma=0.66$ represent the population standard deviation

$n=5$ sample size

$\mu_o =2.5$ represent the value that we want to test

$\alpha=0.01$ 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: State the null and alternative hypotheses.

We need to conduct a one tailed test

We need to conduct a hypothesis in order to check if the mean is higher than 2.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.5$

Alternative hypothesis: $\mu > 2.5$

If we analyze the size for the sample is < 30 but we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Part b: Calculate the statistic

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

$z=\frac{3.372-2.5}{\frac{0.66}{\sqrt{5}}}=2.954$

Part c :P-value

Since is a one sided test the p value would be:

$p_v =P(z>2.954)=0.0016$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, we can conclude that the true mean is higher than 2.5 at 1% of signficance.

8 0

3 years ago