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hoa [83]
3 years ago
12

Please Help! 20 Points!

Mathematics
1 answer:
iVinArrow [24]3 years ago
6 0
\text {x - coordinate = }  \bigg( 5\dfrac{1}{2}  +  3\dfrac{3}{4} \bigg) \div 2

\text {x - coordinate = }  \bigg( 5\dfrac{2}{4}  +  3\dfrac{3}{4} \bigg) \div 2

\text {x - coordinate = } 8\dfrac{5}{4}   \div 2

\text {x - coordinate = }\dfrac{37}{4}   \times  \dfrac{1}{2}

\text {x - coordinate = }\dfrac{37}{8}

\text {x - coordinate = } 4\dfrac{5}{8}



\text {y - coordinate = } \bigg( -4\dfrac{1}{4} - 1\dfrac{1}{4} \bigg) \div 2

\text {y - coordinate = } -5\dfrac{2}{4} \div 2

\text {y - coordinate = } -\dfrac{22}{4} \times  \dfrac{1}{2}

\text {y - coordinate = } -\dfrac{11}{4}}

\text {y - coordinate = } -2\dfrac{3}{4}}



\text {The coordinate is }\bigg( 4\dfrac{5}{8}, -2\dfrac{3}{4}} \bigg)

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Help me Please....................
MakcuM [25]

9514 1404 393

Answer:

  1.3363

Step-by-step explanation:

The basic idea here is to find an expression for the direction vector between a point on L1 and a point on L2. Then, solve for the points on L1 and L2 that make that vector perpendicular to both lines L1 and L2. (The dot product of direction vectors is zero.) The distance between the points found is the shortest distance between the lines.

__

Let P be a point on L1. Then the parametric equation for P is ...

  P = (6t, 0, -t) . . . . . . origin + t × direction vector

Let Q be a point on L2. The direction vector for L2 is given by the difference between the given points. It is (4-1, 1-(-1), 6-1) = (3, 2, 5). Then the parametric equation for Q is ...

  Q = (3s+1, 2s-1, 5s+1) . . . . (1, -1, 1) + s × direction vector

The direction vector for PQ is ...

  Q -P = (3s+1-6t, 2s-1, 5s+1+t)

The dot product of this and the two lines' direction vectors will be zero:

  (3s+1-6t, 2s-1, 5s+1+t)·(6, 0, -1) = 0 = 13s -37t +5 . . . perpendicular to L1

  (3s+1-6t, 2s-1, 5s+1+t)·(3, 2, 5) = 0 = 38s -13t +6 . . . perpendicular to L2

The solution to these equations is ...

  s = -157/1237

  t = 112/1237

Then (Q-P) becomes (94, -1551, 564)/1237, and its length is ...

  |PQ| = √(94² +1551² +564²)/1237 ≈ 1.3363

The distance between the two lines is about 1.3363 units.

8 0
3 years ago
The claim that 40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable j
Bad White [126]

Answer:

The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.

Step-by-step explanation:

Test if the proportion is less than 40%:

At the null hypothesis, we test if the proportion is of at least 0.4, that is:

H_0: p \geq 0.4

At the alternative hypothesis, we test if the proportion is of less than 0.4, that is:

H_1: p < 0.4

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that \mu = 0.4, \sigma = \sqrt{0.4*0.6}

74 out of the 200 workers sampled said they would return to work

This means that n = 200, X = \frac{74}{200} = 0.37

Value of the test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.37 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}

z = -0.87

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.37, which is the p-value of z = -0.87.

Looking at the z-table, z = -0.87 has a p-value of 0.1922.

The p-value of the test is of 0.1922 > 0.02, which means that there is not significant evidence to reject the null hypothesis, that is, there is not significant evidence to conclude that the proportion is of less than 40%.

7 0
2 years ago
Can someone please tell me if these are correct?
iragen [17]
Number one is correct and so is two
3 0
3 years ago
Read 2 more answers
Marquise has 200200200 meters of fencing to build a rectangular garden.
Lera25 [3.4K]

Answer:

2500 Square meters

Step-by-step explanation:

Given the garden area (as a function of its width) as:

A(w)=-w^2+100w

The maximum possible area occurs when we maximize the area. To do this, we take the derivative, set it equal to zero and solve for w.

A'(w)=-2w+100

-2w+100=0

-2w=-100

w=50 meters

Since Marquise has 200 meters of fencing to build a rectangular garden,

Perimeter of the proposed garden=200 meters

Perimeter=2(l+w)

2(l+50)=200

2l+100=200

2l=200-100=100

l=50 meters

The dimensions that will yield the maximum area are therefore:

Length =50 meters

Width=50 meters

Maximum Area Possible =50 X 50 =<u>2500 square meters.</u>

3 0
3 years ago
a tire on a toy car has a diameter of 8 cm. if the toy car travels 12560 cm, approximately how many times does the Tire rotate
Zina [86]
The answer is 1,570 cm
Hope it helps
4 0
3 years ago
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