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3 years ago

2x+2y=10 solve for x

Mathematics

1 answer:

irakobra [83]3 years ago

7 0

Isolate the x. Note the equal sign. What you do to one side you do to the other.

Subtract 2y from both sides

2x + 2y (-2y) = 10 (-2y)

2x = 10 - 2y

Isolate the x, divide 2 from both sides and from all terms.

(2x)/2 = (10 - 2y)/2

x = 5 - y

Place the variable in the front

x = -y + 5

x = -y + 5 is your answer

hope this helps

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The students in your class are going on a field trip. The ratio of teachers to students must be 1 to 7.

andrew-mc [135]

Answer:

4 teachers for 28 students

Step-by-step explanation:

28/7 = 4

8 0

3 years ago

A random sample of the correct choice on 400 multiple-choice questions on a variety of AP exams1 shows that B was the most commo

maks197457 [2]

Answer:

a) Null hypothesis: $p\leq 0.2$

Alternative hypothesis: $p > 0.2$

b) $z=\frac{0.225 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=1.25$

$p_v =P(Z>1.25)=0.106$

Step-by-step explanation:

1) Data given and notation

n=400 represent the random sample taken

X=90 represent the number of questions with B as the correct answer

$\hat p=\frac{90}{400}=0.225$ estimated proportion of arrests that were not prosecuted

$p_o=0.2$ is the value that we want to test, since we assume that each question present 5 options and just one is correct, 1/5 =0.2 if all five options were equally likely

$\alpha$ represent the significance level

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 higher than 0.2.:

Null hypothesis: $p\leq 0.2$

Alternative hypothesis: $p > 0.2$

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:

$z=\frac{0.225 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=1.25$

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 $\alpha$ . The next step would be calculate the p value for this test.

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

$p_v =P(Z>1.25)=0.106$

If we compare the p value obtained and the significance level assumed $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 5% of significance the proportion of B correct answers is not significantly higher than 0.2.

8 0

4 years ago

5. (5 points) You have a jar full of jelly beans. You will randomly pick 2 jelly beans without replacement.The probability that

Degger [83]

Answer:

7/19

Step-by-step explanation:

In order to find the probability that two events happen in a sequence you simply have to multiply the probability of each individual event together. Since the probability of the sequence is given to us as well as the probability of drawing the first green jelly bean, this means we need to divide the first probability by the probability of the sequence to get the probability of the second event. Basically, reversing the process. Dividing two fractions, we simply divide the numerators by each other and then the denominators by one another.

$\frac{14 / 2}{95 / 5} = \frac{7}{19}$