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____ [38]
3 years ago
8

Rachel is drawing a square. She draws a circle with a compass setting of r units. Which of the following is the next thing Rache

l should do?
A. Draw a diameter of the circle.

B. Draw a perpendicular bisector of the circle.

C. Draw arcs on the circle with the compass set at r units.

D. Draw arcs on the circle with the compass set at r units.
Mathematics
1 answer:
natka813 [3]3 years ago
6 0

Answer:

<em><u /></em>

  • <em><u>A. Draw a diameter of the circle. </u></em>

Explanation:

To<em> draw a square</em> you can <em>draw a circle</em> with a <em>compass</em> and then construct the inscribed square.

You can construct an inscribed square with a compass and a straightedge.

The <u>first step</u> is to draw the circle.

The <u>next</u> step is to <em>draw a diameter</em> (any line that passes through the center of the circle, which you marked when drew the circle). Hence, this is the correct answer to the queston, and it is described by the choice A.

After that, you will be able to draw the perpendicular bisector of the diameter. The two diameters drawn will mark four equidistant points on the circle which will be the four vertices of your square.

Finally, you just must join the adjacent vertices with the straightedge.

You might be interested in
8) through: (-3, -2), perp. to y = x – 1<br> A) y=-5x – 1 B) y=-4x – 5<br> C) y=-x – 5 D) y=-5x – 4
nexus9112 [7]

<u>Answer:</u>

The equation through (-3, -2) and perpendicular to y = x – 1 is y = -x -5 and option c is correct.

<u>Solution:</u>

Given, line equation is y = x – 1 ⇒ x – y – 1 = 0. And a point is (-3, -2)

We have to find the line equation which is perpendicular to above given line and passing through the given point.

Now, let us find the slope of the given line equation.

\text { Slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-1}{-1}=1

We know that, <em>product of slopes of perpendicular lines is -1. </em>

So, 1 \times slope of perpendicular line =  -1

slope of perpendicular line = -1

Now let us write point slope form for our required line.

\mathrm{y}-\mathrm{y}_{1}=\mathrm{m}\left(\mathrm{x}-\mathrm{x}_{1}\right)

y – (-2) = -1(x – (-3))

y + 2 = -1(x + 3)

y + 2 = -x – 3

x + y + 2 + 3 = 0

x + y + 5 = 0

y = -x -5

Hence the equation through (-3, -2) and perpendicular to y = x – 1 is y = -x -5 and option c is correct.

8 0
3 years ago
Find four rational numbers between<br> −6/7 and 9/14
Digiron [165]

Answer:-5/7,-4/7,-3/7,-2/7

Step-by-step explanation:

4 0
2 years ago
The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the Quality of Management and
natali 33 [55]

Answer:

a)\chi^2 = \frac{(40-35)^2}{35}+\frac{(35-40)^2}{40}+\frac{(25-25)^2}{25}+\frac{(25-24.5)^2}{24.5}+\frac{(35-28)^2}{28}+\frac{(25-17.5)^2}{17.5}+\frac{(5-10.5)^2}{10.5}+\frac{(10-12)^2}{12}+\frac{(15-7.5)^2}{7.5} =17.03

p_v = P(\chi^2_{4} >17.03)=0.0019

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(17.03,4,TRUE)"

Since the p value is lower than the significance level we can reject the null hypothesis at 5% of significance, and we can conclude that we have association or dependence between the two variables.

b)

P(E|Ex)= P(EΛEx )/ P(Ex) = (40/215)/ (70/215)= 40/70=0.5714

P(E|Gx)= P(EΛGx )/ P(Gx) = (35/215)/ (80/215)= 35/80=0.4375

P(E|Fx)= P(EΛFx )/ P(Fx) = (25/215)/ (50/215)= 25/50=0.5

P(G|Ex)= P(GΛEx )/ P(Ex) = (25/215)/ (70/215)= 25/70=0.357

P(G|Gx)= P(GΛGx )/ P(Gx) = (35/215)/ (80/215)= 35/80=0.4375

P(G|Fx)= P(GΛFx )/ P(Fx) = (10/215)/ (50/215)= 10/50=0.2

P(F|Ex)= P(FΛEx )/ P(Ex) = (5/215)/ (70/215)= 5/70=0.0714

P(F|Gx)= P(FΛGx )/ P(Gx) = (10/215)/ (80/215)= 10/80=0.125

P(F|Fx)= P(FΛFx )/ P(Fx) = (15/215)/ (50/215)= 15/50=0.3

And that's what we see here almost all the conditional probabilities are higher than 0.2 so then the conclusion of dependence between the two variables makes sense.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

Quality management        Excellent      Good     Fair    Total

Excellent                                40                35         25       100

Good                                      25                35         10         70

Fair                                         5                   10          15        30

Total                                       70                 80         50       200

Part a

We need to conduct a chi square test in order to check the following hypothesis:

H0: There is independence between the two categorical variables

H1: There is association between the two categorical variables

The level of significance assumed for this case is \alpha=0.05

The statistic to check the hypothesis is given by:

\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}

The table given represent the observed values, we just need to calculate the expected values with the following formula E_i = \frac{total col * total row}{grand total}

And the calculations are given by:

E_{1} =\frac{70*100}{200}=35

E_{2} =\frac{80*100}{200}=40

E_{3} =\frac{50*100}{200}=25

E_{4} =\frac{70*70}{200}=24.5

E_{5} =\frac{80*70}{200}=28

E_{6} =\frac{50*70}{200}=17.5

E_{7} =\frac{70*30}{200}=10.5

E_{8} =\frac{80*30}{200}=12

E_{9} =\frac{50*30}{200}=7.5

And the expected values are given by:

Quality management        Excellent      Good     Fair       Total

Excellent                                35              40          25         100

Good                                      24.5           28          17.5        85

Fair                                         10.5            12           7.5         30

Total                                       70                 80         65        215

And now we can calculate the statistic:

\chi^2 = \frac{(40-35)^2}{35}+\frac{(35-40)^2}{40}+\frac{(25-25)^2}{25}+\frac{(25-24.5)^2}{24.5}+\frac{(35-28)^2}{28}+\frac{(25-17.5)^2}{17.5}+\frac{(5-10.5)^2}{10.5}+\frac{(10-12)^2}{12}+\frac{(15-7.5)^2}{7.5} =17.03

Now we can calculate the degrees of freedom for the statistic given by:

df=(rows-1)(cols-1)=(3-1)(3-1)=4

And we can calculate the p value given by:

p_v = P(\chi^2_{4} >17.03)=0.0019

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(17.03,4,TRUE)"

Since the p value is lower than the significance level we can reject the null hypothesis at 5% of significance, and we can conclude that we have association or dependence between the two variables.

Part b

We can find the probabilities that Quality of Management and the Reputation of the Company would be the same like this:

Let's define some notation first.

E= Quality Management excellent     Ex=Reputation of company excellent

G= Quality Management good     Gx=Reputation of company good

F= Quality Management fait     Ex=Reputation of company fair

P(EΛ Ex) =40/215=0.186

P(GΛ Gx) =35/215=0.163

P(FΛ Fx) =15/215=0.0697

If we have dependence then the conditional probabilities would be higher values.

P(E|Ex)= P(EΛEx )/ P(Ex) = (40/215)/ (70/215)= 40/70=0.5714

P(E|Gx)= P(EΛGx )/ P(Gx) = (35/215)/ (80/215)= 35/80=0.4375

P(E|Fx)= P(EΛFx )/ P(Fx) = (25/215)/ (50/215)= 25/50=0.5

P(G|Ex)= P(GΛEx )/ P(Ex) = (25/215)/ (70/215)= 25/70=0.357

P(G|Gx)= P(GΛGx )/ P(Gx) = (35/215)/ (80/215)= 35/80=0.4375

P(G|Fx)= P(GΛFx )/ P(Fx) = (10/215)/ (50/215)= 10/50=0.2

P(F|Ex)= P(FΛEx )/ P(Ex) = (5/215)/ (70/215)= 5/70=0.0714

P(F|Gx)= P(FΛGx )/ P(Gx) = (10/215)/ (80/215)= 10/80=0.125

P(F|Fx)= P(FΛFx )/ P(Fx) = (15/215)/ (50/215)= 15/50=0.3

And that's what we see here almost all the conditional probabilities are higher than 0.2 so then the conclusion of dependence between the two variables makes sense.

7 0
3 years ago
The person swims at 4 kilometers per hour and runs at 20 kilometers per hour. For what distance x is the total time for swimming
gtnhenbr [62]

Answer:

Amm ask to your teacher not to this apps ok

Step-by-step explanation:

THANK you

4 0
3 years ago
Find m<br> A. 38<br> B. 76<br> C. 142<br> D. 71
baherus [9]
I think the answer is a. because all sides are the same.

1 side = 38

side m = probably 38

Hope this helped☺☺
8 0
3 years ago
Read 2 more answers
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