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Elina [12.6K]
3 years ago
10

Identify an equation in point-slope form for the line perpendicular to

Mathematics
1 answer:
LenaWriter [7]3 years ago
3 0

Answer:

A. y - 7 = -4(x + 2)

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, <em>y</em><em> </em><em>-</em><em> </em><em>y</em><em>₁</em><em> </em><em>=</em><em> </em><em>m</em><em>(</em><em>x</em><em> </em><em>-</em><em> </em><em>x</em><em>₁</em><em>)</em><em>,</em><em> </em>all the negative symbols give the OPPOSITE term of what they really are.

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A manufacturer of a new medication on the market for Alzheimer's disease makes a claim that the medication is effective in 65% o
NeX [460]

Answer:

z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309  

p_v =P(z  

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65

Step-by-step explanation:

Data given and notation

n=180 represent the random sample taken

X=115 represent the adults with the medication was effective

\hat p=\frac{115}{180}=0.639 estimated proportion of adults with the medication was effective

p_o=0.65 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that true proportion is less than 0.65.:  

Null hypothesis:p \geq 0.65  

Alternative hypothesis:p < 0.65  

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.

Calculate the statistic  

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

z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309  

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=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 given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65

3 0
3 years ago
Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (4, 0), (4, 14); endpoints of th
saul85 [17]

Answer:

The standard form of the ellipse is \frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1.

Step-by-step explanation:

The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:

(h, k) =\frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2} (x,y) (1)

If we know that V_{1} (x,y) = (4,0) and V_{2}(x,y) = (4, 14), then the coordinates of the center are, respectively:

(h,k) = \frac{1}{2}\cdot (4, 0) + \frac{1}{2}\cdot (4,14)

(h,k) = (2,0) + (2, 7)

(h, k) = (4, 7)

The length of each semiaxis is, respectively:

a = \sqrt{(1 - 4)^{2}+(7-7)^{2}}

a = 3

b = \sqrt{(4-4)^{2}+(0-7)^{2}}

b = 7

The standard equation of the ellipse is described by the following formula:

\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} = 1

Where:

h, k - Coordinates of the center of the ellipse.

a, b - Length of the orthogonal semiaxes.

If we know that h = 4, k = 7, a = 3 and b = 7, then the standard form of the ellipse is:

\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1

4 0
3 years ago
On a coordinate plane, a triangle has points A prime (1, 2), B prime (3, negative 3), C prime (negative 1, negative 3). Triangle
Volgvan

Answer:

A'(5.5, -4.2), B'(7.5, -9.2), C'(3.5, -3.2)

Step-by-step explanation:

I really do hope I understood you correctly. I figured that the rule would have to be added to each point. If those are wrong, try subtracting the rule.

Again, I'm not trying to take your points and leave you with a wrong answer. I really did give it my best.

4 0
3 years ago
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Round 2481.65 to the neartheast 10 tenth
gregori [183]

2481.7

         ^ is the tenth place.

The 5 would either round it up or down by one-tenth. Since we like big numbers... we'll round it to 7 from 6.

5 0
2 years ago
Read 2 more answers
The total surface area of a cube is 294 cm ² work out the volume of the cube
mihalych1998 [28]

\text{ Total Surface Area of cube, with Side $a$ is } 6a^2 \\ \text{ (six times the area of each face)} \\ 6a^2=294 \ m^2 \\ a^2= \frac{294}{6} \\ a^2=\frac{49\times6}{6} \\ a^2=49 \\ a=\sqrt{49} \\ a=7 \ m \\ \text{Volume of cube with Side $a$ is } a^3 \\ V= 7^3=49\times7 \\ \text{volume of the cube is } 343 \ m^3

6 0
3 years ago
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