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3 years ago

Select whether the equation has a solution or not.

Mathematics

1 answer:

vredina [299]3 years ago

4 0

Answer: The equation has a solution .

Step-by-step explanation:

Since we have given that

$\sqrt{x+1}=7-2\sqrt{x}$

Squaring on both the sides, we get that,

$x+1=(7-2\sqrt{x})^2\\\\x+1=49+4x-28\sqrt{x}\\\\3x+48-28\sqrt{x}=0$

Let $\sqrt{x}=y\implies x=y^2$

So, our equation becomes,

$3y^2-28y+48=0\\\\y=\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3}\\\\\sqrt{x}=\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3}\\\\x=(\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3})^2$

So, $x=\dfrac{248}{9}\pm \dfrac{56\sqrt{13}}{9}$

Hence, the equation has a solution .

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What are independent and dependent variables?

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I'm pretty sure this doesn't belong in mathematics but this belongs to science. Anyways.. an independent variable is the only variable that is being changed. The dependent variable is what you find out- in other words it is the outcome.

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3 years ago

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strojnjashka [21]

Answer:

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Step-by-step explanation:

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3 years ago

A manufacturer of precision measuring instruments claims that the standarddeviation in the use of the instruments is less than 0

alexdok [17]

Answer:

i) There is insufficient evidence to support the claim that the standard deviation of the instruments is less than 0.00002 millimeters.

ii) $p_v= P(\chi^2_{7}$

Step-by-step explanation:

$s=0.00001$ represent the sample standard deviation

$\alpha =0.01$ represent the significance level for the test

$\sigma_o =0.00002$ represent the value that we want to test

n=8 represent the sample size

A chi-square test can be used to test "if the standard deviation of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test".

Null and alternatve hypothesis

The system of hypothesis on this case would be given by:

Null Hypothesis: $\sigma \geq 0.00002$

Alternative Hypothesis: $\sigma$

The statistic to test this is given by:

$T=(n-1)(\frac{s}{\sigma_0})^2$ (1)

Part i) Calculate the statistic

If we replace into formula (1) we got this:

$T=(8-1)(\frac{0.00001}{0.00002})^2 =1.75$ (1)

The critical region for a for a lower one-tailed alternative is given by

$T< \chi^2_{1-\alpha/2,N-1}$

The degrees of freedom are given by

$df=n-1=8-1=7$

And if we use the Chi Square distribution with 7 degrees of freedom we see that $\chi^2_{1-0.01/2,7}=1.239$

And our critical region would be $T< 1.239$ so on this case we can conclude that we fail to reject the null hypothesis. So it's not enough evidence to conclude that the population standard deviation is less than 0.00002 mm.

Part ii) Calculate the p value

In order to calculate the p value we can do this:

$p_v= P(\chi^2_{7}$

If we compare this value with the significance level (0.01) we see that $p_v>\alpha$

This agrees with the conclusion since when the p values is greater than the significance level we FAIL to reject the null hypothesis, same conclusion as part i).

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3 years ago

The first terms of an infinite geometric sequence, Un are 2, 6, 18, 54... The first terms of a second infinite geometric sequenc

gladu [14]

Answer:

r = 9 and m = 112

Step-by-step explanation:

$\sum_{k=1}^{225}W_{k}=\sum_{k=0}^{m}4r^{k}$

Write W in terms of U and V.

$\sum_{k=1}^{225}(U_{k}+V_{k})=\sum_{k=0}^{m}4r^{k}\\\sum_{k=1}^{225}U_{k}+\sum_{k=1}^{225}V_{k}=\sum_{k=0}^{m}4r^{k}$

Define U and V using geometric series formula.

$\sum_{k=1}^{225}2(3)^{k-1}+\sum_{k=1}^{225}2(-3)^{k-1}=\sum_{k=0}^{m}4r^{k}$

Use sum of geometric series formula.

$2(\frac{1-(3)^{225}}{1-3})+2(\frac{1-(-3)^{225}}{1-(-3)})=4(\frac{1-(r)^{m+1}}{1-r})$

Simplify.

$-1(1-3^{225})+\frac{1+3^{225}}{2}=4(\frac{1-(r)^{m+1}}{1-r})\\-1+3^{225}+\frac{1}{2}+\frac{3^{225}}{2}=4(\frac{1-(r)^{m+1}}{1-r})\\-\frac{1}{2}+\frac{3(3^{225})}{2}=4(\frac{1-(r)^{m+1}}{1-r})\\\frac{-1+3(3^{225})}{2}=4(\frac{1-(r)^{m+1}}{1-r})\\\frac{-1+3^{226}}{2}=4(\frac{1-(r)^{m+1}}{1-r})\\4\frac{-1+3^{226}}{8}=4(\frac{1-(r)^{m+1}}{1-r})\\4\frac{1-3^{226}}{-8}=4(\frac{1-(r)^{m+1}}{1-r})\\4\frac{1-9^{113}}{1-9}=4(\frac{1-(r)^{m+1}}{1-r})$

Therefore, r = 9 and m = 112.

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3 years ago

Toby found a $52 wallet on the clearance rack for 60% off. If sales tax is 6.25%, how much will he pay in total?

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Answer:

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Step-by-step explanation:

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4 years ago

Read 2 more answers