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2 years ago

Simplify each of the following ratios.e) 2/3 : 3/2 : 5/8

Mathematics

2 answers:

kotegsom [21]2 years ago

7 0

Answer:

32/45

Step-by-step explanation:

2/3 : 3/2 : 5/8.

Remember, a ration and a fraction are both division. Therefore you can rewrite the problem like so:

2/3 ÷ 3/2 ÷ 5/8

Dividing fractions is the same as multiplying them by the reciprocal.

2/3 * 2/3 * 8/5

Now simplify:

32/45

32 and 45 have no common factor, hence the final answer is 32/45

May I have brainliest please? :)

Snezhnost [94]2 years ago

6 0

Answer:

32/45

Step-by-step explanation:

2/3 : 3/2 : 5/8

Remember, a ratio and a fraction are both division. Therefore you can rewrite the problem like so:

2/3 ÷ 3/2 ÷ 5/8

Dividing fractions is the same as multiplying them by the reciprocal.

2/3 * 2/3 * 8/5

Now simplify:

32/45

32 and 45 have no common factor, hence the final answer is 32/45

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A survey was conducted in the United Kingdom, where respondents were asked if they had a university degree. One question asked,

katovenus [111]

Answer:

$z=\frac{0.121-0.0892}{\sqrt{0.101(1-0.101)(\frac{1}{373}+\frac{1}{639})}}=1.620$

$p_v =2*P(Z>1.620)=0.105$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the two proportions are not statistically different at 5% of significance

Step-by-step explanation:

Data given and notation

$X_{1}=45$ represent the number of correct answers for university degree holders

$X_{2}=57$ represent the number of correct answers for university non-degree holders

$n_{1}=373$ sample 1 selected

$n_{2}=639$ sample 2 selected

$p_{1}=\frac{45}{373}=0.121$ represent the proportion of correct answers for university degree holders

$p_{2}=\frac{57}{639}=0.0892$ represent the proportion of correct answers for university non-degree holders

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportions are different between the two groups, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{45+57}{373+639}=0.101$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.121-0.0892}{\sqrt{0.101(1-0.101)(\frac{1}{373}+\frac{1}{639})}}=1.620$

Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

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

$p_v =2*P(Z>1.620)=0.105$

7 0

3 years ago

Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+11x+21=0

IgorLugansk [536]

We must graph y=x^3-9x^2+11x+21. Please, see the attached file.
Then we see were the graph cuts the x-axis, and these values of x are the real solutions of the given equation:

The real solutions of the given equation are:x = -1, 3, and 7