Answer:
3600
Step-by-step explanation:
Given that there are 8 people to be seated around a circular table.
As per formula:
Number of ways that they n people can sit around a circular table = [tex](n-1)![/tex]
We know that 2 people of out of these 8 are not allowed to sit together.
If we subtract the number of ways of these 2 people sitting together from the total number of ways of sitting of 8 people, we will get the number of ways that these 2 people do not sit together.
Number of ways of 2 people not sitting together = Total number of ways of 8 people sitting - Number of ways these 2 people sitting together.
Using formula:
Total number of ways = [tex](8-1 )! = 7! = 5040[/tex]
Let these two people always sit together, so these 2 can be thought as one pair.
So, 6 people and 1 pair,
Total number of ways the 2 people sitting together = [tex](7-1)! \times 2 = 6! \times 2 = 720 \times 2 =1440[/tex]
Total number of ways that the two do not sit together =
[tex]5040 - 1440\\\Rightarrow 3600[/tex]
The valve was tested on 270 engines and the mean pressure was 6.6 lbs/square inch. Assume the variance is known to be 0.49. If the valve was designed to produce a mean pressure of 6.5 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications
Answer:
[tex]z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347[/tex]
The p value for this case would be given by"
[tex]p_v =2*P(z>2.347)=0.0189[/tex]
For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications
Step-by-step explanation:
Information given
[tex]\bar X=6.6[/tex] represent the sample mean
[tex]s=\sqrt{0.49}= 0.7[/tex] represent the population deviation
[tex]n=270[/tex] sample size
[tex]\mu_o =6.5[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value for the test
Hypothesis to verify
We want to verify if the true mean for this case is equal to 6.5 lbs/square inch or not , the system of hypothesis would be:
Null hypothesis:[tex]\mu= 6.5[/tex]
Alternative hypothesis:[tex]\mu \neq 6.5[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347[/tex]
The p value for this case would be given by"
[tex]p_v =2*P(z>2.347)=0.0189[/tex]
For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications
A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 5% margin of error at a 99% confidence level, what size of sample is needed
Answer:
A sample size of 664 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
If the candidate only wants a 5% margin of error at a 99% confidence level, what size of sample is needed
A sample size of n is needed.
n is found when M = 0.05.
We have no estimate, so we use [tex]\pi = 0.05[/tex]. Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.05\sqrt{n} = 2.575*0.5[/tex]
[tex]\sqrt{n} = \frac{2.575*0.5}{0.05}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.575*0.5}{0.05})^{2}[/tex]
[tex]n = 663.1[/tex]
Rounding up
A sample size of 664 is needed.
what is the quotient of (x^3-3x^2+5x-3) divided by (x-1)
Answer:
x² -2x + 3
Step-by-step explanation:
You can use, long division, synthetic division, or simply factor out the equation.
Given that
[tex] sec( \alpha) - tan( \alpha ) = \frac{1}{4} \: find \: \sec( \alpha ) + \tan( \alpha ) [/tex]
Answer:
4.
Step-by-step explanation:
(sec α - tan α)(sec α + tan α) = sec^2 α - tan^2α
But sec^2 α = 1 + tan^2 α so
sec^2 α - tan^2α = 1 + tan^2 α - tan^2α
= 1
so 1 = (sec α - tan α)(sec α + tan α) = 1/4 * x where x is sec α + tan α
1/4 * x = 1
x = 4.
math hw graded on accuracy pls help!!
Answer:
see below
Step-by-step explanation:
Putting n=1 into the formulas eliminates the first two choices, since they evaluate to 3.57 and 0.85, respectively, not 4.2.
Putting n=2 into the formula eliminates the third choice, because you know that 4.2(0.15) < 3.57 without even using a calculator.
The only viable choice (and the correct choice) is the last one.
Given that P(A)=0.8 and P(A and B)=0.6, if A and B are independent events, what is the probability of event B?
Answer:
0.2 I think
Step-by-step explanation:
A plane flies 240 miles due north, then 320 miles due west. How
many miles must it fly to return to its starting point by the shortest
route? (Enter your answer without units.)
Answer: The distance of the shortest route of return is 400
Step-by-step explanation:
The direction of travel of the plane forms a right angle triangle ABC as shown in the attached photo. C represents the starting point of the plane. To determine the distance of the shortest by which the plane can return to its starting point, BC, we would apply the Pythagorean theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
BC² = 320² + 240²
BC² = 160000
BC = √160000
BC = 400
Si lanzas una moneda justa 4 veces, ¿cuál es la probilidad
de que obtengas exactamente 2 soles?
Answer:
The probability of getting exactly 2 soles is 0.375.
Step-by-step explanation:
The question is:
If you toss a fair coin 4 times, what's the probability that you get exactly 2 soles?
Solution:
A fair coin has two parts.
On tossing a coin once there is 50-50 odds of both the sides.
So, the probability of one side is, p = 0.50.
It is provided that a fair coin is tossed n = 4 times.
The event of any of the sides showing up after the toss are independent of each other.
The random variable X defined as soles, follows a Binomial distribution with parameters n = 4 and p = 0.50.
The probability mass function of X is:
[tex]P(X=x)={4\choose x}\ (0.50)^{x}\ (1-0.50)^{4-x};\ x=0,1,2,3,4[/tex]
Compute the probability of getting exactly 2 soles as follows:
[tex]P(X=2)={4\choose 2}\ (0.50)^{2}\ (1-0.50)^{4-2}[/tex]
[tex]=6\times 0.25\times 0.25\\\\=0.375[/tex]
Thus, the probability of getting exactly 2 soles is 0.375.
What is the height of the triangle
Answer:
9.6 inches
Step-by-step explanation:
[tex]A_\text{triangle}=\dfrac{bh}{2} \\\\\\ 227.04=\dfrac{47.3 \cdot h}{2} \\\\\\47.3 \cdot h = 454.08 \\\\\\h=9.6[/tex]
Hope this helps!
Answer:
9.6 inches
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh
227.04 = 1/2 ( 47.3) h
227.04 = 23.65 h
Divide each side by 23.65
227.04/23.65 = h
9.6 = h
Evaluate 5x-\dfrac xy5x−
y
x
5, x, minus, start fraction, x, divided by, y, end fraction when x=4x=4x, equals, 4 and y=2y=2y, equals, 2.
Answer:
5x - (x/y) = 18 when x=4 and y=2
Step-by-step explanation:
5x - (x/y)
When x=4 and y=2
Substitute the value of x=4 and y=2 into the expression
5x - (x/y)
5(4) - (4/2)
Multiply 5 by 4 and divide 4 by 2
=20 - 2
Subtract 2 from 20
=18
5x - (x/y) = 18 when x=4 and y=2
the equation of straight line passing through the point (2,3)&perpendicular to the line 4x-3y=10 is
Answer:
4y = -3x +18
Step-by-step explanation:
Let's get the gradient from this line equation first.
4x-3y=10
4x-10=3y
Y= 4/3x -10/3
The gradient is 4/3.
For a line perpendicular to another line.
M*M'= -1
M= -/(4/3)
M = -3/4
So the gradient to be used is -3/4
Formula for solving is
(Y-y1)/(x-x1)= M
X1= 2
Y1= 3
M = -3/4
(Y-y1)/(x-x1)= M
(Y-3)/(x-2)= -3/4
4(y-3)= -3(x-2)
4y -12 = -3x +6
4y = -3x +18
write 2^((5)/(2)) in surd form
Answer:
[tex]\sqrt{2^5}[/tex]
Step-by-step explanation:
The applicable rule of exponents is ...
[tex]\displaystyle a^{b/c}=\sqrt[c]{a^b}[/tex]
So, ...
[tex]2^{5/2}=\boxed{\sqrt{2^5}}[/tex]
_____
This can be simplified to ...
[tex]\sqrt{32}=4\sqrt{2}[/tex]
Add 2/7 + 2/7 Is 4/7 the correct answer
Answer:
Yes
Step-by-step explanation:
The denominator always stays the same
Good Job!
Hope this helps :)
Answer:
yes 4/7 is the answer
Step-by-step explanation:
2/7+2/7
l.c.m is 7
2+2/7
4/7
what are the solutions to the system of equations graphed below
Answer:
B.
Step-by-step explanation:
Wherever the 2 lines meet and pass through each other will be the area where the points are situated that are the solutions to the graph.
Find the range of the function f(x) = -x 2 + 4x if the domain is {-2, 0, 1}.
Answer:
y≤4
Step-by-step explanation:
y≤4
try to graph it on a parabola and u will find the answer above :D hope this helped
Lena told her mother that the jeans that she bought were on sale for 10 percent off and she had saved $8.25 on them. Lena’s mother wanted to know the price of the jeans before the discount to determine if Lena was shopping for jeans that were too expensive. What was the price of the jeans before the discount?
Answer:
$82.50
Step-by-step explanation:
Set up an equation to find the original price
(0.1)(x) = 8.25
x = 82.5
Answer:
The answer will be C. (82.50)
Step-by-step explanation:
took the test on edg2020
the ratio of men to women in a village is 12: 25. if there are 120men, (a)how many women are there ?, (b) what is the total number of men to women
Answer:
250 women.
370 men and women.
Step-by-step explanation:
The ratio of men to women in a village is 12:25.
120 are men.
120/12 = 10
10*12:10*25
120:250
250 are women.
All together,
120+250=370
Question 6 of 25
2 Points
Which of the following would be a good name for the function that takes the
weight of a box and returns the energy needed to lift it?
A. Box(cost)
B. Weight(energy)
C. Weight(box)
D. Energy(weight)
Answer:
C
Step-by-step explanation:
because you need the energy of the box to lift it, as my old professor used to say " you can only push on somthing as much as it can push you back "
Answer:
D. energy(weight) is the correct answer
hope this helps
What is the slope-intercept form of the equation 6x-3y=18
Answer:
Step-by-step explanation:
Saying "put an equation into slope-intercept form" is another way of saying, "solve this equation for y". Not 6y or -3y...just plain old ordinary positive y. In order to begin that process, we need to first isolate the term that has the y in it. We do that by subtracting 6x from both sides to get
-3y = -6x + 18
Now, again, we are not solving for -3y, just y. We do that by dividing both sides by -3 to get
[tex]y=\frac{-6x}{-3}+\frac{18}{-3}[/tex]
Simplifying that gives us
y = 2x - 6
The number of songs enjoyed by the band Metallica by a sample of six teachers is also below. 2,13,5,11,3,14. What is the mean of this sample? (line over the x) X=? What is the standard deviation of this sample? S=?
Answer:
8
Step-by-step explanation:
2,3,5,11,13,14
Mean= 8
Standard deviation= 4.830
Please help! Thank you!
Answer:
a-bi
Step-by-step explanation:
The complex conjugate root theorem states that
(a+bi) is one root then (a-bi) must also be a root
Please answer this correctly
Answer:
6 books
Step-by-step explanation:
22, 23, 25, 25, 26, 28
6 books contained at least 22 characters but less than 29.
What is the midpoint of the line segment with endpoints (1,-6) and (-3,4)?
O A. (-1,-1)
O B. (-2,-2)
O C. (-1,-2)
OD. (-2,-1)
please help
Answer:
(-1,-1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
(1+-3)/2 = -2/2 = -1
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
(-6+4)/2 = -2/2 = -1
(-1,-1)
Please answer number 7 I give brainliest thank you!
Answer:
q1: 80
q2:85
q3:91.5
Work:
- rearrange the numbers from least to greatest
68,78,82,84,86,89,94,100
q1- add 78 and 82, divide by 2
q2: add 84 and 86, divide by 2
q3- add 89 and 94, divide by 2
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97%, how many citizens should be included in your sample
Question:
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97% , how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 18 years.
Answer:
61.03
Step-by-step explanation:
Given:
Standard deviation = 18
Sample estimate = 5
Confidence level = 97%
Required:
Find sample size, n.
First find the Z value. Using zscore table
Z-value at a confidence level of 97% = 2.17
To find the sample size, use the formula below:
[tex] n = (Z * \frac{\sigma}{E})^2[/tex]
[tex] n = ( 2.17 * \frac{18}{5})^2 [/tex]
[tex] n = (2.17 * 3.6)^2 [/tex]
[tex] n = (7.812)^2 [/tex]
[tex] n = 61.03 [/tex]
Sample size = 61.03
Assume that adults have IQ scores that are normally distributed with a mean of 95.9 and a standard deviation of 16.4. Find the following probabilities. Round your answers to three decimal places; add trailing zeros as needed. The probability that a randomly selected adult has an IQ greater than 122.6 is 0.052 . The probability that a randomly selected adult has an IQ lower than 92.0 is 0.413 . The probability that a randomly selected adult has an IQ between 80.0 and 110.0 is 0.639 .
Answer:
a) The probability that a randomly selected adult has an IQ greater than 122.6 is 0.052.
b) The probability that a randomly selected adult has an IQ lower than 92.0 is 0.405.
c) The probability that a randomly selected adult has an IQ between 80.0 and 110.0 is 0.639.
Step-by-step explanation:
This is a normal distribution problem with
Mean = μ = 95.9
Standard deviation = σ = 16.4
a) The probability that a randomly selected adult has an IQ greater than 122.6
= P(x > 122.6)
We first normalize or standardize 122.6
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (122.6 - 95.9)/16.4 = 1.63
To determine the required probability
P(x > 122.6) = P(z > 1.63)
We'll use data from the normal distribution table for these probabilities
P(x > 122.6) = P(z > 1.63) = 1 - P(z ≤ 1.63)
= 1 - 0.94845
= 0.05155 = 0.052 to 3 d.p
b) The probability that a randomly selected adult has an IQ lower than 92.0 = P(x < 92)
We first normalize or standardize 92.0
z = (x - μ)/σ = (92 - 95.9)/16.4 = - 0.24
To determine the required probability
P(x < 92.0) = P(z < -0.24)
We'll use data from the normal distribution table for these probabilities
P(x < 92.0) = P(z < -0.24) = 0.40517 = 0.405 to 3 d.p
c) The probability that a randomly selected adult has an IQ between 80.0 and 110.0.
P(80 ≤ x ≤ 110)
We first normalize or standardize 80.0 and 110.0
For 80.0
z = (x - μ)/σ = (80 - 95.9)/16.4 = - 0.97
For 110.0
z = (x - μ)/σ = (110 - 95.9)/16.4 = 0.86
The required probability
P(80 ≤ x ≤ 110) = P(-0.97 ≤ z ≤ 0.86)
We'll use data from the normal distribution table for these probabilities
(80 ≤ x ≤ 110) = P(-0.97 ≤ z ≤ 0.86)
= P(z ≤ 0.86) - P(z ≤ -0.97)
= 0.80511 - 0.16602
= 0.63909 = 0.639 to 3 d.p
Hope this Helps!!!
Find the product.
-2x a(-4x b - 2x 3 + 5x)
Answer:
556
Step-by-step explanation:
7+8+8+9
Answer:
-8x^a+b + 4x^a+3 - 10x^a+1
Find the volume of the following solid figure. Use = 3.14.
V = 4/313. A sphere has a radius of 3.5 inches.
Answer:
V = 51.3 in.³
Step-by-step explanation:
Volume of Sphere = [tex]\frac{4}{3} \pi r^3[/tex]
Where r = 3.5
So,
V = [tex]\frac{4}{3} (3.14)(3.5)^3[/tex]
V = [tex]\frac{4}{3} (3.14)(12.25)[/tex]
V = [tex]\frac{153.9}{3}[/tex]
V = 51.3 in.³
Solve for x. 9x-2c=k
11) At a certain company, an HR benefits meeting and shareholders meeting happen at the same time, so it is impossible for an employee to be at both. If the probability that an employee goes to the HR benefits meeting is 0.33, and the probability that an employee goes to the shareholders meeting is 0.66, what is the probability that an employee
Answer:
0.99
Step-by-step explanation:
The computation of the probability for employee goes for shareholder meeting or HR benefits meeting is
= Probability of HR benefits meeting + Probability of shareholder meeting
= 0.33 + 0.66
= 0.99
We simply added the both meeting probability i.e HR benefits and shareholder meeting so that the given probability could come
