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iren [92.7K]
3 years ago
6

If 8x−4y=20 and 4x−8y=4, what is the value of x−y

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
6 0

Answer:

x-y=3-1=2

Step-by-step explanation:

8x-4y=20                            4x-8y=4

8x=20+4y                            4(\frac{20+4y}{8})-8y=4

 x=\frac{20+4y}{8}                                               \frac{80+16y}{8} -8y=4

 x=\frac{20+4}{8}                                                10+2y-8y=4

x=\frac{24}{8}                                                 10-6y=4

x=3                                                  -6y=4-10

                                                   -6y=-6

                                                    y=1<u></u>

so x-y=3-1=2

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Experimental probability of spinning a 3
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Answer:

Depends on what it is.

Step-by-step explanation:

Calculating probability requires following a simple formula and using multiplication and division to evaluate possible outcomes of events like launching new products, marketing to larger audiences or developing a new lead generation strategy. You can use the following steps to calculate probability, and this can work for many applications that fall under a probability format:

1. Determine a single event with a single outcome

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6 0
3 years ago
Read 2 more answers
Test the hypothesis using the P value approach. Be sure the verify the requirements of the test.
Andreas93 [3]

Answer:

p_v =2*P(z  

If we compare the p value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.  

Step-by-step explanation:

1) Data given and notation

n=500 represent the random sample taken

X=380 represent the number of people with some characteristic

\hat p=\frac{380}{500}=0.76 estimated proportion of adults that said that it is morally wrong to not report all income on tax returns

p_o=0.76 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

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 true proportion is 0.7 .:  

Null hypothesis:p=0.77  

Alternative hypothesis:p \neq 0.77  

When we conduct a proportion test we need to use the z statistic, 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.

<em>Check for the assumptions that he sample must satisfy in order to apply the test </em>

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np_o =500*0.77=385>10

n(1-p_o)=384*(1-0.77)=115>10

3) Calculate the statistic  

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

z=\frac{0.76-0.77}{\sqrt{\frac{0.77(1-0.77)}{500}}}=-0.531  

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=0.05. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

p_v =2*P(z  

If we compare the p value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.  

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What is the volume of a sphere with a radius of 4 cm? Use 3. 14 for pi. Round to the nearest hundredth. 50. 24 cm³ 66. 99 cm³ 20
Nimfa-mama [501]

The volume of the sphere is 267. 95 cm³.

<h2>Given </h2>

The radius of the sphere is 4cm.

<h3>What is the volume of sphere?</h3>

The volume of a sphere is the three-dimensional space occupied by a sphere.

The volume of the sphere is determined by the following formula;

\rm Volume = \dfrac{4}{3} \pi r^3

Where r is the radius of the sphere.

Substitute all the values in the formula;

\rm Volume = \dfrac{4}{3} \pi r^3\\\\\rm Volume = \dfrac{4}{3} \times (3.14) \times 4^3\\\\Volume = 4 \times 1.04 \times 64\\\\Volume = 267.95\ cm ^3

Hence, the volume of the sphere is 267. 95 cm³.

To know more about Volume of Sphere click the link given below.

brainly.com/question/369459

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