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3 years ago

What are the coordinates of the circumcenter of a triangle with vertices A(4,10), B(10, 10) , and C(10, 2) ?

Mathematics

1 answer:

const2013 [10]3 years ago

4 0

Answer:

(7,6)

Step-by-step explanation:

Triangle ABC with vertices at points A(4,10), B(10, 10) , and C(10, 2) is a right triangle with the hypotenuse AC.

The circumcenter of the right triangle is the midpoint of the hypotenuse.

Find the coordinates of the midpoint O of the hypotenuse AC:

$x_O=\dfrac{4+10}{2}=7\\ \\y_O=\dfrac{10+2}{2}=6$

So, O(7,6)

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Veronica’s velocity was measured as 4.3 m/s. She displaced 20 meters in 4.7 seconds. Which piece of information is missing for t

telo118 [61]

We are given displacement = 20 meters.

Time given = 4.7 seconds.

Velocity = 4.3 m/s.

Please note : Velocity is a vector quantity. A vector quantity depends on magnitude and direction as well.

We are given magnitude of displacement = 20 meter and time 4.7 seconds but the direction is missing there.

If it would be in forward direction it would be positive and if it would be in backward direction, it would be of negative.

Therefore, <u>"B)the direction"</u> is correct option.

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3 years ago

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3 years ago

You can spend at most $60 on beads. A bag containing red beads costs $2 per bag. A bag containing blue beads costs $3 per bag. Y

nexus9112 [7]

For this case, the first thing we must do is define variables.
We have then:
x: number of blue beads
y: number of red beads
We now write the inequations system:
$3x + 2y \leq 60

x\ \textgreater \ y$
Answer:
a system of linear inequations that represents the situation is:
$3x + 2y \leq 60 x\ \textgreater \ y$

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3 years ago

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A sample of 200 observations from the first population indicated that x1 is 170. A sample of 150 observations from the second po

igor_vitrenko [27]

Answer:

a) For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b) Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c) $z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d) Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

Step-by-step explanation:

Data given and notation

$X_{1}=170$ represent the number of people with the characteristic 1

$X_{2}=110$ represent the number of people with the characteristic 2

$n_{1}=200$ sample 1 selected

$n_{2}=150$ sample 2 selected

$p_{1}=\frac{170}{200}=0.85$ represent the proportion estimated for the sample 1

$p_{2}=\frac{110}{150}=0.733$ represent the proportion estimated for the sample 2

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

a.State the decision rule.

For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b. Compute the pooled proportion.

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c. Compute the value of the test statistic.

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d. What is your decision regarding the null hypothesis?

Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

5 0

3 years ago

(07.07 lc) a cheetah runs at a speed of 49 miles for every hour. if the distance traveled, in miles, is d and time, in hours, is

alexgriva [62]

The relationship between d and t.

d = 49t

The correct equation is C.

<h3>What is Distance, speed and Time ?</h3>

How quickly something or someone is moving is determined by their speed. If you know how far an object has traveled and how long it has taken, you can calculate its average speed. Speed equals distance times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.

<h3>Given data:</h3>

speed = 49 miles/hour

Distance

Time

as we know :

Speed = Distance / Time .

Then:

49 = Distance/Time

Distance = 49*Time .

the relationship between d and t ( d = 49t).

To know more about Distance , speed and Time visit :

brainly.com/question/28035975

#SPJ4

I understand that the question you are looking for is :

A cheetah runs at a speed of 49 miles for every hour. If the distance traveled, in miles, is d and time, in hours, is t, which equation shows the relationship between d and t?

A. d = 49 + t

B. t = 49 + d

C. d = 49t

D. t = 49d

8 0

2 years ago