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Reptile [31]
3 years ago
5

Subtract 5 from 1/3 of 23

Mathematics
1 answer:
Lilit [14]3 years ago
4 0
2.6
I got this because to get 1 over 3 you have to divide by three. so I did 23 divided by three then took away 5
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A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain sca
saul85 [17]

Answer:

The 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between -1.776 \leq \mu_d \leq 0.376. Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Let put some notation  

x=test value before , y = test value after

x: 6.4 2.6 7.7 10.5 11.7 5.8 4.3 2.8

y: 6.7 2.4 7.4 8.1 8.6 6.4 3.9 2.7

The differences defined as d_i = y_i -x_i and we got:

d: 0.3, -0.2, -0.3, -2.4, -3.1, 0.6, -0.4, -0.1

We can calculate the mean and the deviation for the sample with the following formulas:

\bar d=\frac{\sum_{i=1}^n d_i}{n}

s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}

\bar d=-0.7 represent the sample mean for the difference

\mu_d population mean (variable of interest)

s_d=1.32 represent the sample standard deviation

n=8 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

\bar d \pm t_{\alpha/2} *\frac{s_d}{\sqrt{n}}  (1)

In order to calculate the critical value t we need to find first the degrees of freedom, given by:

df=n-1=8-1=7

Since the Confidence is 0.95 or 95%, the value of alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that t_(\alpha/2)=2.306

Now we have everything in order to replace into formula (1):

-0.7-2.306\frac{1.32}{\sqrt{8}}=-1.776    

-0.7+2.306\frac{1.32}{\sqrt{8}}=0.376    

So on this case the 95% confidence interval for the difference would be given by (-1.776;0.376)

We are 95% confidence that the true mean difference is between -1.776 \leq \mu_d \leq 0.376. Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.

6 0
3 years ago
A hiker starting at point P on a straight road wants to reach a forest cabin that is 2 km from a point Q, 3 km down the road fro
pantera1 [17]

Answer:

2.19 km

Step-by-step explanation:

If x is the distance she walks down the road before turning, then the total time is:

t = x/8 + √((3 − x)² + 2²) / 3

t = x/8 + √(9 − 6x + x² + 4) / 3

24t = 3x + 8√(13 − 6x + x²)

24t = 3x + 8(13 − 6x + x²)^½

Take derivative of both sides with respect to x.

24 dt/dx = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

When t is a minimum, dt/dx = 0.

0 = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

-3 = 4(13 − 6x + x²)^-½ (-6 + 2x)

3 / (6 − 2x) = 4(13 − 6x + x²)^-½

3 / (24 − 8x) = (13 − 6x + x²)^-½

(24 − 8x) / 3 = (13 − 6x + x²)^½

(24 − 8x)² / 9 = 13 − 6x + x²

576 − 384x + 64x² = 117 − 54x + 9x²

459 − 330x + 55x² = 0

Solve with quadratic formula.

x = [ 330 ± √((-330)² − 4(55)(459)) ] / 2(55)

x = (330 ± √7920) / 110

x = 2.19 or 3.81

Since 0 < x < 3, x = 2.19.

7 0
3 years ago
Corbin made a scale model of the San Jacinto Monument. The monument has an actual height of 604 feet. Corbin's model used a scal
photoshop1234 [79]

<u>Answer: </u><u>6.04 inches</u>

<u>Step-by-step explanation:</u>

The actual height of the monument = 604 feet

The scale used by Corbins is 1 inch = 100 feet

The height of the Corbins model in inches= \frac{604}{100} = 6.04 inches

the height of the Corbins model = 6.04 inches

8 0
2 years ago
You and a friend are doing a science project together The whole project should take 7 hours to complete if you share the project
DerKrebs [107]
3.5 hours each.... 7hrs if work/2 people = 3.5 hrs of work each
4 0
3 years ago
The height of the average wave, in feet, over thours at Sandy Beach is modeled by the equation below.
Naddika [18.5K]

Answer:

Check below

Step-by-step explanation:

With the information given, let's consider some aspects of Sandy Beach behavior.

1. Sandy Beach

Let's calculate the period of this function

t=4sin(s)+5

T=\frac{2\pi}{b} \:b=1 \:in \:this \:case

T=\frac{2\pi}{1}  \therefore T= 2\pi

The Period of sin function is 2\pi

2. Verifying the Range, in this case the lapse of time.

A <em>sin</em> function varies from -1 to 1, i.e.

-1\leq sin(s) \leq1 \therefore-4\leq 4sin(s)\leq4 \\ adding \:the\:5\\-4+5\leq 4sin(s)\leq4+5\\\\\1\leq4sin+5\leq9 \therefore t=[1,9]\\

So, within an interval form 1 to 9 hours the waves at Sandy Beach come and go.

3. Check the graph below.

7 0
3 years ago
Read 2 more answers
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