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svet-max [94.6K]
3 years ago
14

Which system of equations is represented by the graph?

Mathematics
1 answer:
o-na [289]3 years ago
5 0
The answer is the third option, which is:
<span> y = x^2 + 5x + 3 
 6x + y = −27
 The explanation is shown below:
 1. When you solve this problem you have the following solution:
 x=-6
 y=9

 x=-5
 y=3

 2. As you can see the solution corresponds with the graph shown above.
 3. You can give value to the variable x of the first equation and values to the x of the second equation, and plot each point obtain. You will see that the parabola and the line, touch each other at the points (-5,3) and (-6,9)</span>
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Solve for x and find m∠FGH
mel-nik [20]

Answer:

x° = 11°

<em>Z </em><em>FGI </em><em>=</em><em> </em><em> </em><em>6</em><em>0</em><em>°</em>

Step-by-step explanation:

<em>I</em><em>f</em><em> </em><em>GH</em><em> </em><em>bisects</em><em> </em><em>Z </em><em>FGI</em>

<em>then</em><em> </em><em>Z </em><em>FGH </em><em>=</em><em> </em><em>Z </em><em>H</em><em>GI</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>or,</em><em> </em><em>(</em><em>3</em><em>x</em><em> </em><em>-</em><em> </em><em>3</em><em>)</em><em>°</em><em> </em><em>=</em><em> </em><em>(</em><em>4</em><em>x</em><em> </em><em>-</em><em> </em><em>1</em><em>4</em><em>)</em><em>°</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>or,</em><em> </em><em>3</em><em>x</em><em>°</em><em> </em><em>-</em><em> </em><em> </em><em>4</em><em>x</em><em>°</em><em> </em><em>=</em><em> </em><em>-</em><em> </em><em>1</em><em>4</em><em>°</em><em> </em><em>+</em><em> </em><em>3</em><em>°</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>or,</em><em> </em><em>x°</em><em> </em><em>=</em><em> </em><em>1</em><em>1</em><em>°</em>

<em>Z </em><em>FGI </em><em>=</em><em> </em><em>3</em><em>3</em><em>°</em><em> </em><em>-</em><em> </em><em>3</em><em>°</em><em> </em><em>+</em><em> </em><em>4</em><em>4</em><em>°</em><em> </em><em>-</em><em> </em><em>1</em><em>4</em><em>°</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>=</em><em> </em><em> </em><em>6</em><em>0</em><em>°</em>

3 0
3 years ago
A horizontal line passes through (5,-2). Which other point is also on that line?
xenn [34]
Another point on the line is (6,-1)
4 0
3 years ago
The following data lists the ages of a random selection of actresses when they won an award in the category of Best​ Actress, al
Valentin [98]

Answer:

a) p_v =P(t_{(9)}

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best​ Actors at 1% of significance.

b) The 99% confidence interval would be given by (-21.469;2.069)

c) We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two

Step-by-step explanation:

Part a

Let put some notation  

x=actor's age , y = actress's age

x: 58 41 36 36 34 33 48 37 37 43

y: 26 27 34 26 35 29 23 42 30 34

The system of hypothesis for this case are:

Null hypothesis: \mu_y- \mu_x \geq 0

Alternative hypothesis: \mu_y -\mu_x

The first step is calculate the difference d_i=y_i-x_i and we obtain this:

d: -32, -14, -2, -10, 1, -4, -25, 5, -7, -9

The second step is calculate the mean difference  

\bar d= \frac{\sum_{i=1}^n d_i}{n}= -9.7

The third step would be calculate the standard deviation for the differences, and we got:

s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =11.451

The 4 step is calculate the statistic given by :

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-9.7 -0}{\frac{11.451}{\sqrt{10}}}=-2.679

The next step is calculate the degrees of freedom given by:

df=n-1=10-1=9

Now we can calculate the p value, since we have a left tailed test the p value is given by:

p_v =P(t_{(9)}

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best​ Actors at 1% of significance.

Part b

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The confidence interval for the mean is given by the following formula:  

\bar d \pm t_{\alpha/2}\frac{s}{\sqrt{n}} (1)  

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that t_{\alpha/2}=3.25  

Now we have everything in order to replace into formula (1):  

-9.7-3.25\frac{11.451}{\sqrt{10}}=-21.469  

-9.7+3.25\frac{11.451}{\sqrt{10}}=2.069  

So on this case the 99% confidence interval would be given by (-21.469;2.069)

Part c

We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two means is 0.

8 0
3 years ago
Which of these is a common characteristic of cnidarians?
Sergio039 [100]
Hello there,

<span>Which of these is a common characteristic of cnidarians?

</span>All Cnidarians<span> have tentacles with stinging cells in their tips which are used to capture and subdue prey.
</span>
Therefore, your answer would be
<span>They have tentacles with stinging cells. (OptionB)

</span>
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Answer:

3%%%%+<+<&+788>,,jjajahjahajiijbbsnsjiaja

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