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3 years ago

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Alanah is picking up two friends to go to a concert. She drives from her house to pick up Mia, then she drives to pick up Teresa

, and then they go to the arena to see the concert. Answer the questions to find the total distance of Alanah's trip to the arena. When necessary, round answers to the nearest tenth.

2 answers:

gladu [14]3 years ago

8 0

Answer:

1. Find the distance from Alanah's house to Mia's house. Show your work.

Alanah (2,8) Mia (8,16) √( (8 - 2)² + (16 - 8)² ) = 10 Distance from Alanah to Mia is 10 units

2. What is the distance from Mia's house to Teresa's house? Explain how you found this distance. Write your answer in the space below. √( (8 - 8)² + (2 - 16)² ) = 14 distance from Mia to Teresa is 14 units

3. Find the distance from Teresa's house to the arena. Show your work.

Write your answer in the space below. √( (14 - 8)² + (4 - 2)² ) = 6.3 ≈ 6

4. What is the total distance of Alanah's trip to the arena?

Write your answer in the space below. 10 + 14 + 6 = 30 30 units is the total distance of the trip

Step-by-step explanation:

Ksivusya [100]3 years ago

3 0

Answer:

Total distance = 30.3 units

Step-by-step explanation:

Coordinates for the location of Alanah, Mia, Teresa and Arena are,

Alanah → (2, 8)

Mia → (8, 16)

Teresa → (8, 2)

Arena → (14, 4)

Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula,

d = $\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Distance between Alanah and Mia = $\sqrt{(16-8)^2+(8-2)^2}$

= $\sqrt{100}$

= 10 units

Distance between Mia and Teresa = $\sqrt{(16-2)^2+(8-8)^2}$

= 14 units

Distance between Teresa and Arena = $\sqrt{(4-2)^2+(14-8)^2}$

= $\sqrt{40}$

= 6.3 units

Total distance of Alanah's trip to Arena = 10 + 14 + 6.3

= 30.3 units

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aev [14]

Answer:

x/2 > 5

Step-by-step explanation:

Quotient means division

x/2

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x/2 > 5

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MrMuchimi

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Read 2 more answers

In tests of a computer component, it is found that the mean time between failures is 937 hours. A modification is made which is

VladimirAG [237]

Answer:

Null hypothesis is $\mathbf {H_o: \mu > 937}$

Alternative hypothesis is $\mathbf {H_a: \mu < 937}$

Test Statistics z = 2.65

CONCLUSION:

Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

P- value = 0.004025

Step-by-step explanation:

Given that:

Mean $\overline x$ = 960 hours

Sample size n = 36

Mean population $\mu =$ 937

Standard deviation $\sigma$ = 52

Given that the mean time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours

Null hypothesis is $\mathbf {H_o: \mu > 937}$

Alternative hypothesis is $\mathbf {H_a: \mu < 937}$

Degree of freedom = n-1

Degree of freedom = 36-1

Degree of freedom = 35

The level of significance ∝ = 0.01

SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;

from t-table t(0.99,35), the critical value = 2.438

The test statistics is :

$Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}$

$Z = \dfrac{960-937 }{\dfrac{52}{\sqrt{36}}}$

$Z = \dfrac{23}{8.66}$

Z = 2.65

The decision rule is to reject null hypothesis if test statistics is greater than critical value.

CONCLUSION:

Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

The P-value can be calculated as follows:

find P(z < - 2.65) from normal distribution tables

= 1 - P (z ≤ 2.65)

= 1 - 0.995975 (using the Excel Function: =NORMDIST(z))

= 0.004025

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Akimi4 [234]

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sergiy2304 [10]

Answer:

1: Reflect M across the x-axis

2: Dilate about the center by 3/2

Step-by-step explanation:

Given

See attachment for M and N

Required

Which maps M to N

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$M = (5,5)$

$N = (5,-5)$

And the radius of circles are:

$r_M=2$

$r_N=3$

The first transformation from M to M' is:

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The rule is:

$(x,y) \to (x,-y)$

$M(5,5) \to M'(5,-5)$

<em>At this point, M' and N now have the same center but different radius.</em>

The second transformation from M' to N is:

- Dilate about the center by dividing the radius of N by the radius of M

i.e.

$k =\frac{r_N}{r_M}$

$k =\frac{3}{2}$

<em>At this point, M has been completely mapped to N.</em>

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