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patriot [66]
1 year ago
7

7 of 9

Mathematics
1 answer:
aleksklad [387]1 year ago
8 0

Using proportions, it is found that the total volume of the glass is of 216 cm³.

<h3>What is the missing information?</h3>

The problem is incomplete, but researching it on a search engine, it is found that:

  • Initially, the glass is 1/3 full.
  • After adding 63 cm³ of orange of juice, the glass is 5/8 full.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Considering the volume of the glass as x, and the information given in the problem, the following equation can be built:

\frac{x}{3} + 63 = \frac{5x}{8}

We solve for x to find the volume of the glass as follows:

\frac{5x}{8} - \frac{x}{3} = 63

\frac{15x - 8x}{24} = 63

Then, applying cross multiplication:

7x = 24 x 63

Simplifying by 7:

x = 24 x 9

x = 216 cm³.

The total volume of the glass is of 216 cm³.

More can be learned about proportions at brainly.com/question/24372153

#SPJ1

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Answer:

Not a native English speaker, but ig this is what u want:

Step-by-step explanation:

6(3x+4)=15x+24

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Answer:

Null hypothesis:p \leq 0.5  

Alternative hypothesis:p > 0.5  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

p_v =P(Z>7.36)=9.19x10^{-14}  

Since the p value obtained was a very low value and using the significance level given \alpha=0.01 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of adults prefer window seats when they fly is significantly higher than 0.5 .  

Step-by-step explanation:

1) Data given and notation

n=778 represent the random sample taken

X=492 represent the people that chose a window seat.

\hat p=\frac{492}{778}=0.632 estimated proportion of people that chose a window seat.

p_o=0.5 is the value that we want to test

\alpha=0.01 represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the majority of adults prefer window seats when they fly:  

Null hypothesis:p \leq 0.5  

Alternative hypothesis:p > 0.5  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.632 -0.5}{\sqrt{\frac{0.5(1-0.5)}{778}}}=7.36  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.01. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

p_v =P(Z>7.36)=9.19x10^{-14}  

5) Conclusion

Since the p value obtained was a very low value and using the significance level given \alpha=0.01 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of adults prefer window seats when they fly is significantly higher than 0.5 .  

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Quadratics formula 4x^2+3x-1=0
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Now divide 4 from both sides

like this 4x/4=1/4

now cancel out two 4's so the answer will be x=1/4

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