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1 year ago

PLEASE HURRYYYY

Mathematics

2 answers:

kirill [66]1 year ago

5 0

The endpoint F's coordinates should be given by the formula

x = 2×35 - 15 and y = 2×(- 3) - 26.

<h3>What is the procedure to find the other endpoint?</h3>

In order to solve this problem, we need to derive expressions for the coordinates of the endpoint F using the midpoint formula.

We know the coordinates of the endpoint E and the midpoint M of the line segment EF.

M(x, y) = 0.5×E(x, y) + 0.5×F(x, y).

2×M(x, y) = E(x, y) + F(x, y).

F(x, y) = 2×M(x, y) - E(x, y).

Given that M(x, y) = (35, -3) and E(x, y) = (15, 26), the endpoint F's coordinates are,

F(x, y) = 2×(35, - 3) - (15, 26).

F(x, y) = (70, - 6) + (- 15, - 26).

F(x, y) = (55, - 32).

The equations should be x = 2×35 - 15 and y = 2×(- 3) - 26.

learn more about midpoint here :

brainly.com/question/28224145

#SPJ1

MariettaO [177]1 year ago

3 0

The equations for the coordinates of the endpoint F should be x = 2 · 35 - 15 and y = 2 · (- 3) - 26.

<h3>How to derive the equations for the missing endpoint of a line segment</h3>

In this problem we know the coordinates of the endpoint E and the midpoint M of the line segment EF and we need to derive expressions of the coordinates of the endpoint F by the midpoint formula:

M(x, y) = 0.5 · E(x, y) + 0.5 · F(x, y)

2 · M(x, y) = E(x, y) + F(x, y)

F(x, y) = 2 · M(x, y) - E(x, y)

If we know that M(x, y) = (35, - 3) and E(x, y) = (15, 26), then the coordinates of the endpoint F are:

F(x, y) = 2 · (35, - 3) - (15, 26)

F(x, y) = (70, - 6) + (- 15, - 26)

F(x, y) = (55, - 32)

The equations should be x = 2 · 35 - 15 and y = 2 · (- 3) - 26.

To learn more on midpoints: brainly.com/question/8943202

#SPJ1

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kirza4 [7]

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6 0

3 years ago

Read 2 more answers

Two cables support a 800-lb weight, as shown. Find the tension in each cable.

jeka94

Answer:

892 lb (right)
653 lb (left)

Step-by-step explanation:

The weight is in equilibrium, so the net force on it is zero. If R and L represent the tensions in the Right and Left cables, respectively ...

Rcos(45°) +Lcos(75°) = 800

Rsin(45°) -Lsin(75°) = 0

Solving these equations by Cramer's Rule, we get ...

R = 800sin(75°)/(cos(75°)sin(45°) +cos(45°)sin(75°))

= 800sin(75°)/sin(120°) ≈ 892 . . . pounds

L = 800sin(45°)/sin(120°) ≈ 653 . . . pounds

The tension in the right cable is about 892 pounds; about 653 pounds in the left cable.

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This suggests a really simple generic solution. For angle α on the right and β on the left and weight w, the tensions (right, left) are ...

(right, left) = w/sin(α+β)×(sin(β), sin(α))

5 0

3 years ago

A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and standard deviation equal to 16. (G

dezoksy [38]

Answer:

a) The mean of a sampling distribution of $\\ \overline{x}$ is $\\ \mu_{\overline{x}} = \mu = 20$ . The standard deviation is $\\ \frac{\sigma}{\sqrt{n}} = \frac{16}{\sqrt{64}}=2$ .

b) The standard normal z-score corresponding to a value of $\\ \overline{x} = 16$ is $\\ Z = -2$ .

c) The standard normal z-score corresponding to a value of $\\ \overline{x} = 23$ is $\\ Z = 1.5$ .

d) The probability $\\ P(\overline{x}$ .

e) The probability $\\ P(\overline{x}>23) = 1 - P(Z$ .

f) $\\ P(16 < \overline{x} < 23) = P(-2 < Z < 1.5) = P(Z$ .

Step-by-step explanation:

We are dealing here with the concept of a sampling distribution, that is, the distribution of the sample means $\\ \overline{x}$ .

We know that for this kind of distribution we need, at least, that the sample size must be $\\ n \geq 30$ observations, to establish that:

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

In words, the distribution of the sample means follows, approximately, a normal distribution with mean, $\mu$ , and standard deviation (called standard error), $\\ \frac{\sigma}{\sqrt{n}}$ .

The number of observations is n = 64.

We need also to remember that the random variable Z follows a standard normal distribution with $\\ \mu = 0$ and $\\ \sigma = 1$ .

$\\ Z \sim N(0, 1)$

The variable Z is

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [1]

With all this information, we can solve the questions.

Part a

The mean of a sampling distribution of $\\ \overline{x}$ is the population mean $\\ \mu = 20$ or $\\ \mu_{\overline{x}} = \mu = 20$ .

The standard deviation is the population standard deviation $\\ \sigma = 16$ divided by the root square of n, that is, the number of observations of the sample. Thus, $\\ \frac{\sigma}{\sqrt{n}} = \frac{16}{\sqrt{64}}=2$ .

Part b

We are dealing here with a random sample. The z-score for the sampling distribution of $\\ \overline{x}$ is given by [1]. Then

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

$\\ Z = \frac{16 - 20}{\frac{16}{\sqrt{64}}}$

$\\ Z = \frac{-4}{\frac{16}{8}}$

$\\ Z = \frac{-4}{2}$

$\\ Z = -2$

Then, the standard normal z-score corresponding to a value of $\\ \overline{x} = 16$ is $\\ Z = -2$ .

Part c

We can follow the same procedure as before. Then

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

$\\ Z = \frac{23 - 20}{\frac{16}{\sqrt{64}}}$

$\\ Z = \frac{3}{\frac{16}{8}}$

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

$\\ Z = 1.5$

As a result, the standard normal z-score corresponding to a value of $\\ \overline{x} = 23$ is $\\ Z = 1.5$ .

Part d

Since we know from [1] that the random variable follows a standard normal distribution, we can consult the cumulative standard normal table for the corresponding $\\ \overline{x}$ already calculated. This table is available in Statistics textbooks and on the Internet. We can also use statistical packages and even spreadsheets or calculators to find this probability.

The corresponding value is Z = -2, that is, it is two standard units below the mean (because of the negative value). Then, consulting the mentioned table, the corresponding cumulative probability for Z = -2 is $\\ P(Z$ .

Therefore, the probability $\\ P(\overline{x}$ .

Part e

We can follow a similar way than the previous step.

$\\ P(\overline{x} > 23) = P(Z > 1.5)$

For $\\ P(Z > 1.5)$ using the cumulative standard normal table, we can find this probability knowing that

$\\ P(Z1.5) = 1$

$\\ P(Z>1.5) = 1 - P(Z$

Thus

$\\ P(Z>1.5) = 1 - 0.9332$

$\\ P(Z>1.5) = 0.0668$

Therefore, the probability $\\ P(\overline{x}>23) = 1 - P(Z$ .

Part f

This probability is $\\ P(\overline{x} > 16)$ and $\\ P(\overline{x} < 23)$ .

For finding this, we need to subtract the cumulative probabilities for $\\ P(\overline{x} < 16)$ and $\\ P(\overline{x} < 23)$

Using the previous standardized values for them, we have from Part d:

$\\ P(\overline{x}$

We know from Part e that

$\\ P(\overline{x} > 23) = P(Z>1.5) = 1 - P(Z$

$\\ P(\overline{x} < 23) = P(Z1.5)$

$\\ P(\overline{x} < 23) = P(Z$

Therefore, $\\ P(16 < \overline{x} < 23) = P(-2 < Z < 1.5) = P(Z$ .

5 0

3 years ago

Line segment AB has a length of 15 and angle a=35degrees . A segment with a length of 12 will form the third side of the triangl

PtichkaEL [24]

Answer:

C = 45.8 or C = 117.69

Step-by-step explanation:

Remark

Only SSA gives the possibility of 2 answers. This one does not give that opportunity. There is one unique answer. We'll discuss 2 and zero after finding 1 answer. On looking at it again, the question might be ambiguous. We'll check that out as well.

Given

AB = 15

<A = 35

point C opposite line AB such that CB = 12 These givens give a unique answer.

Solution

Sin(35) / 12 = Sin(C) / 15 Multiply both sides by 15

15*Sin(35) / 12 = Sin(C) Find 15/12

1.25*sin(35) = Sin(C) Write Sin(35)

1.25*0.5736 = Sin(C) Multiply the left

0.71697 = Sin(C) Take the inverse Sin

C = 45.805 degrees This is the angle opposite AB

Angle B = 180 - 35 - 45.805 = 99.2

Ambiguous Case

If AC = 12 we have another answer entirely. This is SAS which will give just 1 set of answers for the triangle. The reason the case is ambiguous is because we don't exactly know where that 12 unit line is. It could be AC or BC.

I will set up the Sin law for you, and let you solve it

Sin(B) / 12 = Sin(35)/15

When you solve for Sin(B) as done above you, get 0.45886 from which B = 27.31 degrees

C = 180 - 35 - 27.31 = 117.69

So that's two values that C could have. I think that's all given these conditions.

Two Cases or None

<A = 35 degrees

AC = 15

CB = 12

This should give you two possible cases or none. You can check which by finding the height of the triangle from C down to AB (which has no distinct length. The h is 15 * Sin35 = 8.6. If CB < 8.6, there are no solutions. If CB < AC then if CB > that 8.6, there are 2 solutions.

7 0

3 years ago

Help! Please!

Lemur [1.5K]

Answer:

1) 130°

2) 130°

Step-by-step explanation:

Assuming SR, TU, and PQ are parallel, they would both be 130. (180-50)

7 0

3 years ago