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3 years ago

Shortest distance to the origin y=1/2x^2 -4

1 answer:

6 0

X=0 y=-2
y=0 x=4

The shortest distance has to be the perp bisector from origin to the midpoint of the line.
midpoint =(2,-1) and distance from the (0,0) origin is sqrt(5) hence, sqrt(5).

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Assume that you plan to use a significance level of alpha α equals =0.05 to test the claim that p 1 p1 equals = p 2 p2. Use the

stiks02 [169]

Answer:

z=3.536

$\hat p=0.204$

$p_v =2*P(Z>3.54)\approx 0.0004$

Step-by-step explanation:

1) Data given and notation

$X_{1}=172$ represent the number of people with the characteristic 1

$X_{2}=356$ represent the number of people with the characteristic 2

$n_{1}=677$ sample 1 selected

$n_{2}=3377$ sample 2 selected

$p_{1}=\frac{172}{677}=0.254$ represent the proportion estimated for the sample 1

$p_{2}=\frac{654}{3377}=0.194$ represent the proportion estimated for the sample 2

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{172+654}{677+3377}=0.204$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.254-0.194}{\sqrt{0.204(1-0.204)(\frac{1}{677}+\frac{1}{3377})}}=3.536$

4) Statistical decision

Since is a two side test the p value would be:

$p_v =2*P(Z>3.54)\approx 0.0004$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups.

6 0

4 years ago

I don't understand how sine, cosine, and tangent have ANYTHING to do with solving these??

UNO [17]

Sin of an angle=opposite side/hypotenuese
cos of an angle=adjacent side/ hypotenuese
tan of an angle=opposite side / adjacent side
11. sine M=7/25 12. do the same but using the number of this triangle
cos M=24/25
tan M=7/24

14. They give you the angle 35 degrees. So that will be what you start with. Look at the lengths of the sides given. Where are they located in respect to the angle 35. 20 is the hypoteneuse, and x is opposite of 35. So the equation that uses hypoteneuse and opposite is sin.
sin 35=35/x, punch in sin 35 into the calculator. then you would get .57=35/x. The cross multiply .57x=35=61.40.

Now you can repeat for the rest of the problems. I hope this is helpful.

6 0

3 years ago

The figures are similar. Find the area.

TEA [102]

Answer:

108

Step-by-step explanation:

cross multiply fractions:

12/72 = 18/x

x = 108

3 0

3 years ago

In the standard (x,y) coordinate plane, what is the area of the circle x^2 + y^2 =169?

schepotkina [342]

Answer:

169π

Step-by-step explanation:

circle eq: (x-a)²+(y-b)²=r², where (a,b) is center and r is radius

r²=169

r = ±13

since a radius length must be positive, r = +13, not -13

A of circle: πr²

r = 13

169π

given that the circle eq has r², you could've noticed that you can take the constant in the circle eq and multiply that by π to get the same answer

6 0

4 years ago

How do you find the circumference, radius, and diameter?

igor_vitrenko [27]

Check the picture below.

$\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2.9 \end{cases}\implies C=2\pi (2.9)\implies C=5.8\pi \implies C\approx 18.22 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{C\div r}{18.22\div 2.9 \approx 6.28}\qquad \stackrel{C\div d}{18.22\div 5.8 \approx 3.14}~\hfill$

4 0

4 years ago