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Alenkasestr [34]
3 years ago
10

A study of 35 golfers showed that their average score on a particular course was 92. The sample standard deviation was 5. We wan

t to construct a 95% confidence interval to estimate the value of the true population mean. What is the t-value that should be used to compute the confidence interval (to the third decimal place)?
Mathematics
1 answer:
svlad2 [7]3 years ago
7 0

Answer:

t_{\alpha/2} = t_{0.05/2} = t_{0.025} = 2.0322

Step-by-step explanation:

We have a sample of size n = 35, \bar{x} = 92 and s = 5. As we want to construct a 95% confidence interval to estimate the value of the true population mean \mu, we should use the pivotal quantity given by T = \frac{\bar{X}-\mu}{S/\sqrt{n}} which comes from the t distribution with n - 1 = 35 - 1 = 34 degrees of freedom. Besides we should use the t-value t_{\alpha/2} = t_{0.05/2} = t_{0.025} = 2.0322, i.e., regarding the t-distribution with 34 degrees of freedom, we have an area of 0.025 above 2.0322 and below the probability density function. The rationale behind this is that P(-2.0322\leq T\leq 2.0322) = 0.95 because of the simmetry of the t distribution.

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Distance between parallel lines y=3x+10 and y=3x-20
Alecsey [184]

1. Take an arbitrary point that lies on the first line y=3x+10. Let x=0, then y=10 and point has coordinates (0,10).


2. Use formula d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}} to find the distance from point (x_0,y_0) to the line Ax+By+C=0.


The second line has equation y=3x-20, that is 3x-y-20=0. By the previous formula the distance from the point (0,10) to the line 3x-y-20=0 is:

d=\dfrac{|3\cdot 0-10-20|}{\sqrt{3^2+(-1)^2}}=\dfrac{30}{\sqrt{10}}=3\sqrt{10}.


3. Since lines y=3x+10 and y=3x-20 are parallel, then the distance between these lines are the same as the distance from an arbitrary point from the first line to the second line.


Answer: d=3\sqrt{10}.

4 0
3 years ago
If a bloodstain has a length of 3.0cm and a width of 1.5cm what is the angle of impact?
zalisa [80]

The angle of impact is 30°

<h3>What is the angle of impact?</h3>

In a bloodstain, the angle of impact can be used to determine the appearance of the resulting bloodstain if the bloodstain has a tail or pattern.

  • Bloodstain pattern analysis is the study of bloodstains at a scene of the crime in an attempt to reconstruct the events that resulted in the bloodshed.

Mathematically;

\mathbf{Angle  \ of \  impact = sin^{-1} (\dfrac{width \ stain}{length \ stain} )}

\mathbf{Angle  \ of \  impact = sin^{-1} (\dfrac{1.5}{3.0} )}

\mathbf{Angle  \ of \  impact = 30 ^0}

Learn more about the angle of impact here:
brainly.com/question/19423063

6 0
2 years ago
Which graph shows the solution to this system of inequalities?<br> y &lt; 2x + 4<br> y &gt; -X -3
Arturiano [62]

Answer:

The answer is Graph X.

  • Always start by isolating the variable \color{red}y on the left side of the inequality.
  • Change the inequality to equality symbol.
  • Graph the boundary line from step 2 in the XY-plane.
  • The last step is to shade one side or region of the boundary line.

Please Mark Brainliest If This Helped!

3 0
2 years ago
PLEASE HELP ASAP !!
ololo11 [35]

Answer:

  MK

Step-by-step explanation:

ML is the short side of right triangle MLK. MJ is the hypotenuse of right triangle MKJ. This gives you a clue that the ratios of interest are the short side to the hypotenuse. All these right triangles are similar, so ...

  ML/MK = MK/MJ . . . . . ratio of short side to hypotenuse is the same

  ML·MJ = MK² . . . . . . . cross multiply

  MK = √(ML·MJ) . . . . . the geometric mean of ML and MJ is MK

7 0
3 years ago
The fourth term of an Arithmetic Sequence is equal to 3 times the first term, and the seventh term exceeds twice the third term
11Alexandr11 [23.1K]

Answer:

The first term is 3. The common difference is 2.

Step-by-step explanation:

The first term is x.

The common difference is d.

The second term is x + d.

3rd term: x + 2d

4th term: x + 3d

7th term: x + 6d

"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"

x + 3d = 3 * x       Eq. 1

"the seventh term exceeds twice the third term by 1"

x + 6d = 2(x + 2d) + 1       Eq. 2

Simplify Eq. 1:

2x = 3d

Simplify Eq. 2:

x + 6d = 2x + 4d + 1

x = 2d - 1

Multiply both sides of the last equation by 2.

2x = 4d - 2

2x = 3d   (simplified Eq. 1)

Since 2x = 2x, then the right sides are equal.

3d = 4d - 2

d = 2

2x = 3d

2x = 3(2)

2x = 6

x = 3

Answer: The first term is 3. The common difference is 2.

8 0
3 years ago
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