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3 years ago

√(2x-5)=1+√(x-3)

Mathematics

1 answer:

Ostrovityanka [42]3 years ago

4 0

Answer:

x = 3 only

Step-by-step explanation:

$\sqrt{2x-5} =1+\sqrt{x-3}$

$\implies 2x-5=(1+\sqrt{x-3})^2\\\\ \implies 2x-5=x+2\sqrt{x-3} -2$

$\implies x-3=2\sqrt{x-3}$

$\implies (x-3)^2=(2\sqrt{x-3})^2$

$\implies x^2-6x+9=4x-12$

$\implies x^2-10x+21=0$

$\implies (x-3)(x-7)=0$

$\implies x=3, x=7$

Check by substituting found values of x into original equation:

$x=3 \implies \sqrt{2(3)-5} =1+\sqrt{3-3} \implies 1 = 1 \ \ \ \checkmark$

$x=7 \implies \sqrt{2(7)-5} =1+\sqrt{7-3} \implies 3\neq 2 \ \ \ \ incorrect$

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The one I’m pointing to

sveticcg [70]

Answer: hope that helps

Step-by-step explanation: 128 divided by 640 x 100 = 20%

4 0

4 years ago

Find an exponential function that fits the information (hint: putting them in a table may help you see).

Vilka [71]

Answer:

f(x)=8*(3.5)^x

Step-by-step explanation:

2=98

3= 98r

4= 98r^2

5= 98r^3

6= 98r^4

98r^4/98, 98 crosses out and its just r^4. r^4= 14706.125/98

r=3.5

So you plug that in and you get f(x)=8*(3.5)^x

I hope this helped. XD

7 0

3 years ago

In a recent Super Bowl, a TV network predicted that 50 % of the audience would express an interest in seeing one of its forthcom

coldgirl [10]

Answer:

z= -0.968

We can conclude that we fail to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they would watch one of the television shows not differs from 0.5 or 50% .

Step-by-step explanation:

1) Data given and notation n

n=106 represent the random sample taken

X=48 represent the people who says that they would watch one of the television shows.

$\hat p=\frac{48}{106}=0.453$ estimated proportion of people who says that they would watch one of the television shows.

$p_o=0.5$ is the value that we want to test

$\alpha$ 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 50% of people who says that they would watch one of the television shows.:

Null hypothesis: $p=0.5$

Alternative hypothesis: $p \neq 0.5$

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:

$z=\frac{0.453 -0.5}{\sqrt{\frac{0.5(1-0.5)}{106}}}=-0.968$

4) Statistical decision

P value method or p value approach . "This method consists on 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 is not provided, but we can assume $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z$

So based on the p value obtained and using the significance level assumed $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they would watch one of the television shows not differs from 0.5 or 50% .