6.

Ludmilka [50]

Remark

All you need is 2 points to get the line of the equation. One is itself (B and B') is the same in both triangles. Now we need to find one more point. Since this is a reflection, the midpoint between C and C' is the second point. That choice of C and C' is completely arbitrary.

Step One

y intercept of the line. That point is B which is (0,1)

Step Two

Find the midpoint between C and C'

C is (-4,-2) and C' is ( 0 , - 4) The midpoint is

C" = (x2 + x1)/2 , (y2 + y1)/2

C" = (-4 + 0 )/2 , (-2 + - 4) / 2

C" = (-4)/2 , - 6/2

C" = (-2, - 3) C" is the midpoint between C and C'

Step 3

Find the equation of the line.

y = ax + b We are trying to find A

y = ax + 1

-3 = a(-2) + 1

-3 - 1 = a(-2)

- 4 = a(-2) Divide by -2

-4/-2 = a

a = 2

The slope of the line is 2

Answer

y = 2x + 1

6 0

3 years ago

journee ate 9 grapes . grandma gave her more grapes . journee ate 15 grapes in all . how many grapes did grandma give her ?

Law Incorporation [45]

Answer:

6 grapes.

Step-by-step explanation:

If she already had 9 grapes, subtract 15 and 9 to get 6.

6 0

3 years ago

Read 2 more answers

What is the 7th term of the geometric sequence for 400, 200,100,....

loris [4]

Step-by-step explanation:

400,200,100,50,25,12.5, ...... 0.78125

4 0

3 years ago

2. A scuba diver was exploring a reef 77.5 m below sea level. The diver ascended to the surface at a rate of 12.5 m/min. (a) Wri

Elodia [21]

Answer:

77.5 = 12.5t

6.2 mins.

Step-by-step explanation:

The scuba diver was at the sea bed from where the water surface is at 77.5 m height. The ascending speed of the diver is 12.5 m/minute.

a. If the diver take t minutes to reach the water surface, then the equation that models the situation is

77.5 = 12.5t ......(1)

b. If we consider the sea bed as a reference level i.e. zero height, then the sea surface will be at 77.5 m height.

Therefore, in that case, it is reasonable to write the distance 77.5 m as a positive number.

c. Solving the equation (1), we get, t = 6.2 minutes.

So, the diver will take 6.2 mins to reach the surface. (Answer)

7 0

3 years ago

Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8

Vlad1618 [11]

Answer:

Step-by-step explanation:

From the given information:

the null hypothesis and the alternative hypothesis can be computed as follows:

$\mathbf{H_o:}$ The sample have a distribution that agrees with the distribution of state populations.

$\mathbf{H_1:}$ The sample have a distribution that does not agrees with the distribution of state populations.

The Chi-Square test statistics $\mathbf{X^2 = \dfrac{(Observed \ value - Expected \ value )}{(Expected \ value ) ^2 }}$

Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana.

The observed and the expected value can be computed as follows:

States Observed Expected $X^2 = \dfrac{(O- E)^2}{E}$

Washington 450 0.51 × 1000 = 510

Oregon 340 0.30 × 1000 = 300

Idaho 150 0.11 × 1000 = 110

Montana 60 0.08 × 1000 = 80

Total 1000 1000

For washington :

$X^2 = \dfrac{(O- E)^2}{E}$

$X^2 = \dfrac{(450 -510)^2}{510}$

$X^2 = \dfrac{3600}{510}$

$X^{2}=$ 7.06

For Oregon

$X^2 = \dfrac{(O- E)^2}{E}$

$X^2 = \dfrac{(340- 300)^2}{300}$

$X^2 = \dfrac{1600}{300}$

$X^{2}=$ 5.33

For Idaho

$X^2 = \dfrac{(O- E)^2}{E}$

$X^2 = \dfrac{(150- 110)^2}{110}$

$X^2 = \dfrac{1600}{110}$

$X^2 =14.55$

For Montana

$X^2 = \dfrac{(O- E)^2}{E}$

$X^2 = \dfrac{(60- 80)^2}{80}$

$X^2 = \dfrac{400}{80}$

$X^2 = 5$ .00

The Chi-square test statistics for the observed and the expected value can be computed as follows:

States Observed Expected $X^2 = \dfrac{(O- E)^2}{E}$

Washington 450 0.51 × 1000 = 510 7.06

Oregon 340 0.30 × 1000 = 300 5.33

Idaho 150 0.11 × 1000 = 110 14.55

Montana 60 0.08 × 1000 = 80 5.00

Total 1000 1000 31.94

The Chi-square Statistics Test $\mathbf{X^2 = 31.94}$

Degree of freedom = n - 1

Degree of freedom = 4 - 1

Degree of freedom = 3

At 0.05 level of significance, the critical value of :

$X^2_{(df, \alpha) }=X^2_{(3, 0.05)$ = 7.815

Decision Rule: To reject null hypothesis if the test statistics is greater than the critical value

Conclusion: We reject the null hypothesis since test statistics is greater than critical value, therefore, we conclude that there is sufficient information to say that the sample has a distribution that does not agrees with the distribution of state populations.

7 0

3 years ago