Solve for x. x/2+1= √3

8. For questions 8-9, determine whether the two figures are similar. If so, give the scale factor of the smaller figure to the l

Vinvika [58]

Question 8:

Your choice is correct: two figures are similar if all correspondant sides are in the same ratio.

In your case, the figure on the right have correspondant sides which are all three times the figure on the left, since

$12 = 4\times 3, 21 = 7\times 3, 54 = 18\times 3$

So, the two figures are similar and their ratio is 1:3.

Question 9:

We follow exactly the same approach: let's see if the radii and the heights are in the same ratio: the radii are in ratio

$\cfrac{3.2}{2} = 1.6 = \cfrac{16}{10} = \cfrac{8}{5}$

While the heights are in ratio

$\cfrac{6.4}{4} = 1.6 = \cfrac{16}{10} = \cfrac{8}{5}$

So, the answer is again yes, they are similar, and the ratio is 1.6.

8 0

3 years ago

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The probabilities that Sani, Kolo and Tato will hit a target are 3/4, 2/3 and 7/3 respectively If all three men shot once what i

Natali [406]

Step-by-step explanation:

get the lcm of the numerals and the denominators then simplify

hope it is correct

7 0

2 years ago

We are conducting a hypothesis test to determine if fewer than 80% of ST 311 Hybrid students complete all modules before class.

Juli2301 [7.4K]

Answer:

$z=\frac{0.881 -0.8}{\sqrt{\frac{0.8(1-0.8)}{110}}}=2.124$

Null hypothesis: $p\geq 0.8$

Alternative hypothesis: $p < 0.8$

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

$p_v =P(Z$

So the p value obtained was a very high value and using the significance level assumed $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Be Careful with the system of hypothesis!

If we conduct the test with the following hypothesis:

Null hypothesis: $p\leq 0.8$

Alternative hypothesis: $p > 0.8$

$p_v =P(Z>2.124)=0.013$

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation

n=110 represent the random sample taken

X=97 represent the students who completed the modules before class

$\hat p=\frac{97}{110}=0.882$ estimated proportion of students who completed the modules before class

$p_o=0.8$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v{/tex} represent the p value (variable of interest) 2) Concepts and formulas to use We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.8 or 80%: Null hypothesis:[tex]p\geq 0.8$

Alternative hypothesis: $p < 0.8$

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 $p_o$ .

3) Calculate the statistic

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

$z=\frac{0.881 -0.8}{\sqrt{\frac{0.8(1-0.8)}{110}}}=2.124$

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 assumed $\alpha=0.05$ . The next step would be calculate the p value for this test.

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

$p_v =P(Z$

So the p value obtained was a very high value and using the significance level assumed $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Be Careful with the system of hypothesis!

If we conduct the test with the following hypothesis:

Null hypothesis: $p\leq 0.8$

Alternative hypothesis: $p > 0.8$

$p_v =P(Z>2.124)=0.013$

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

5 0

4 years ago

What is the y intercept of y=5x+1

finlep [7]

The y intercept is (0, 1)

4 0

3 years ago

Please help me find out what the question marks are

quester [9]

Question a

g(x) times $\sqrt{x-5}=\sqrt{x^2-5}$
divide both sides by √(x-5)
$g(x)=\frac{\sqrt{x^2-5}}{\sqrt{x-5}}$
$g(x)=\frac{(\sqrt{x-5})(\sqrt{x^2-5})}{x-5}$
$g(x)=\frac{\sqrt{x^3-5x^2-5x+25}}{x-5}$

question b
$g(x) \space\ times \space\ 1+\frac{1}{x}=x$
divide both sides by 1+1/x
$g(x)=\frac{x}{1+\frac{1}{x}}$
times by x/x
$g(x)=\frac{x^2}{x+1}$

question c
$\frac{1}{x} \space\ times \space\ f(x)=x$
times both sides by x
$f(x)=x^2$

question d
the (f*g)(x) collumn seems to have a domain of only x is greater than or equal to 0?
so maybe we squared the whole thing, ya
wait
ah, ya
basically
$|x|=(\sqrt{x})^2=(\sqrt{x})(\sqrt{x})$
so f(x)=√x

a. $g(x)=\frac{\sqrt{x^3-5x^2-5x+25}}{x-5}$
b. $g(x)=\frac{x^2}{x+1}$
c. $f(x)=x^2$
d. $f(x)=\sqrt{x}$

3 0

4 years ago

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