Answer:
8 classmates
Step-by-step explanation:
[tex]9/1\frac{1}{8}=\\9/\frac{9}{8}=\\9*\frac{8}{9}=\\\frac{72}{9}=\\8[/tex]
A company manufacturing oil seals wants to establish X and R control charts on the process. There are 25 preliminary samples of size 5 on the internal diameter of the seal. The summary data (in mm) are as follows:
sigma^25_i = 1 X_t = 1, 253.75, sigma^25_i = 1 R_i = 14.08
(a) Find the control limits that should be used on the X and R control charts. For n = 5, A2 = 0.577, D4 = 2.114, D3 = 0
(b) Assume that the 25 preliminary samples plot in control on both charts. Estimate the process mean and standard deviation.
Answer:
A ) i) X control chart : upper limit = 50.475, lower limit = 49.825
ii) R control chart : upper limit = 1.191, lower limit = 0
Step-by-step explanation:
A) Finding the control limits
grand sample mean = 1253.75 / 25 = 50.15
mean range = 14.08 / 25 = 0.5632
Based on X control CHART
The upper control limit ( UCL ) =
grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475
The lower control limit (LCL)=
grand sample mean - A2 * mean range = 50.15 - 0.577(0.5632) = 49.825
Based on R control charts
The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191
The lower control limit = D3 * mean range = 0 * 0.5632 = 0
B) estimate the process mean and standard deviation
estimated process mean = 50.15 = grand sample mean
standard deviation = mean range / d2 = 0.5632 / 2.326 = 0.2421
note d2 is obtained from control table
8,5,15,18,3,what's next
13 since i think it's when a single didget number has a 1 at the beginning. i might be wrong thoough
The graph for the equation y = 2 x + 4 is shown below. On a coordinate plane, a line goes through (negative 2, 0) and (0, 4). If another equation is graphed so that the system has one solution, which equation could that be?
Answer: x = 1
Step-by-step explanation:
x = 1 provides one solution for any linear equation, as it is a straight vertical line.
Hope it helps <3
Answer:
x=2
Step-by-step explanation:
Our equation is y=2x+4
the line goes through (2,0) and (0,4)
(2,0) is the x-axis intercept wich is given by y=0(0,4) is the y-intercept wich by y= 2*0+4This equation has one solution for y=0
there are millions of similar equations that has one solution like:
x = 2
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = zeyi + x cos(y)j + xz sin(y)k, S is the hemisphere x2 + y2 + z2 = 16, y ≥ 0, oriented in the direction of the positive y-axis.
Stokes' theorem equates the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation
[tex]x^2+z^2=16[/tex]
Parameterize this circle by
[tex]\mathbf r(t)=4\cos t\,\mathbf i+4\sin t\,\mathbf k[/tex]
with [tex]0\le t\le2\pi[/tex].
The surface is oriented such that its normal vector points in the positive y direction, which corresponds to the curve having counterclockwise orientation. The parameterization we're using here already takes this into account.
Now compute the line integral of F along C :
[tex]\displaystyle\iint_S\mathrm{curl}\mathbf F(x,y,z)\cdot\mathrm d\mathbf S=\int_C\mathbf F(x,y,z)\cdot\mathrm d\mathbf r[/tex]
[tex]=\displaystyle\int_0^{2\pi}\mathbf F(4\cos t,0,4\sin t)\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}(4\sin t\,\mathbf i+4\cos t\,\mathbf j)\cdot(-4\sin t\,\mathbf i+4\cos t\,\mathbf k)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}-16\sin^2t\,\mathrm dt[/tex]
[tex]=-8\displaystyle\int_0^{2\pi}(1-\cos(2t))\,\mathrm dt=\boxed{-16\pi}[/tex]
Line integral of F along C is,
[tex]\rm \int \int_S curl F(x,y,z) dS = -16\pi[/tex]
Step-by-step explanation:
Given :
Hemisphere - [tex]x^2 +y^2+z^2=16[/tex]
Calculation :
Accordind to Stoke's theorem the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation
[tex]x^2+z^2=16[/tex]
then parameterize the circle,
[tex]\rm r(t) = 4 cos(t) \;\hat{i} + 4 sin(t)\;(\hat{k})[/tex]
with , [tex]0\leq t\leq 2\pi[/tex]
Line integral of F along C is,
[tex]\rm \int \int_S curl F(x,y,z) dS = \int_{C}^{} F(x,y,z) \;dr[/tex]
[tex]= \int_{0}^{2\pi} F(4cos(t),0,4sin(t)) \;\dfrac{dr}{dt}.dt[/tex]
[tex]= \int_{0}^{2\pi}(4sin(t)i+4cos(t) j).(-4sin(t)i+4cos(t)k) \;dt[/tex]
[tex]= \int_{0}^{2\pi} -16sin^2tdt[/tex]
[tex]=-8 \int_{0}^{2\pi} (1-cos(2t))dt[/tex]
[tex]= -16\pi[/tex]
For more information, refer the link given below
https://brainly.com/question/8130922?referrer=searchResults
Multiply (x2 + 3x + 4)(3x2 - 2x + 1).
Answer:
The answer is
3x⁴ + 7x³ + 7x² - 5x + 4Step-by-step explanation:
(x² + 3x + 4)(3x² - 2x + 1)
Expand the terms
We have
3x⁴ - 2x³ + x² + 9x³ - 6x² + 3x + 12x² - 8x + 4
Group like terms
That's
3x⁴ - 2x³ + 9x³ + x² - 6x² + 12x² + 3x - 8x + 4
Simplify
We have the final answer as
3x⁴ + 7x³ + 7x² - 5x + 4Hope this helps you
A poll of 61 students found that 22% were in favor of raising tution to pave new parking lots. The standard deviation of this poll is 6%. What would be the standard deviation if the sample size were increased from 61 to 290?
Answer:
The standard Deviation would increase
Step-by-step explanation:
Is this advantages?
Salaries of 43 college graduates who took a statistics course in college have a mean,66,000 , of . Assuming a standard deviation, 18908 , of $, construct a %99 confidence interval for estimating the population mean .
Answer:
$[58543.42; 73456.58]
Step-by-step explanation:
Hello!
For the variable
X: salary of a college graduate that took a statistics course
Out of n= 43 students, the calculated mean is [tex]\frac{}{X}[/tex]= $66000
The population standard deviation is δ= $18908
There is no information about the variable distribution, but since the sample size is big enough (n≥30), you can apply the CLT and approximate the distribution of the sample mean to normal [tex]\frac{}{X}[/tex]≈N(μ;σ²/n)
Then you can apply the approximation of the standard normal distribution to calculate the 99% CI
[tex]\frac{}{X}[/tex] ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{Singma}{\sqrt{n} }[/tex]
[tex]Z_{1-\alpha /2}= Z_{0.995}= 2.586[/tex]
[tex]\frac{Singma}{\sqrt{n} }= \frac{18908}{\sqrt{43} }= 2883.44[/tex]
[66000±2.586*2883.44]
$[58543.42; 73456.58]
With a 99% confidence level you'd expect that the interval $[58543.42; 73456.58] will include the average salary of college graduates that took a course of statistics.
I hope this helps!
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)
Answer:
b. [tex]g(x)=f(x)-5[/tex]
Step-by-step explanation:
You have that the function f(x) has its y-intercept for y=3.
Furthermore, you have that g(x) is a transformation of f(x) with y-intercept for y=-2.
In this case you have that f(x) has been translated vertically downward.
The general way to translate a function vertically in the coordinate system is:
[tex]g(x)=f(x)+a[/tex] (1)
being a positive or negative.
if g(x) has its y-intercept for y=-2, and the y-intercept of f(x) is for y=3, then the value of a in the equation (1) must be a = -5, which is the difference between both y-intercepts, in fact:
a = -2 -3 = -5
Then, the answer is:
b. [tex]g(x)=f(x)-5[/tex]
Answer: g(x) = f(x) - 5
Step-by-step explanation:
just took this
The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and the slips are placed into a hat. If the slips are drawn randomly without replacement, what is the probability that "E" is drawn first and "B" is drawn second?
Answer:
1/30
Step-by-step explanation:
The probability of getting ”E” is 1/6.
There is only 1 “E” out of 6 letters.
There is no replacement.
There are now 5 letters without “E”.
”A”, “B”, “C”, “D”, “F”
The probability of getting ”B” is 1/5.
There is only 1 “B” out of 5 letters.
⇒ 1/6 × 1/5
⇒ 1/30
The circular clock face in the clock tower on campus has a radius of about 4 meters. What is the area of the clock to the nearest square meter? Use 3.14 as an approximation for pi
Answer:
50 meters
Step-by-step explanation:
The area of a circle is [tex]\pi r^2[/tex], so assuming that [tex]\pi[/tex] is 3.14, we can make the equation [tex]3.14 \cdot r^2[/tex].
Assuming the radius is r, which is 4, we can substitute the values into the equation.
[tex]3.14 \cdot 4^2\\3.14\cdot16\\50.24[/tex]
This question is asking for the area to the nearest square meter so rounding 50.24 to the nearest square meter results in 50.
Hope this helped!
A tool rental store charges a flat fee of $10.00 to rent a chain saw, and $4.25 for each day, including the first. Write an equation that expresses the cost y of renting this saw if it is rented for x days.
Answer:
y= 4.25x + $10
Step-by-step explanation:
A tool rental shop charges a flat fee of $10.00 to rent out their chain saw
An amount of $4.25 is charged for each of the days
Let x represent the amount that is charged for each day
Let y represent the total cost of the chain saw
Since the rental fee for each day is given as $4.25 and the flat fee is given as $10 then, the equation can be expressed as
y= $4.25x + $10
Hence the equation that expresses the cost y of renting this saw if it is rented for x days is y= $4.25x + $10
What is the inverse of the function below?
f(x) = x-5
A. f^-1(x) = x + 5
B. f^-1(X) = x-5
C. f^-1(x) = -x + 5
D. f^-1(x) = -x-5
Answer:
f^-1(x) = x + 5
Step-by-step explanation:
f(x) = x-5
y = x-5
Exchange x and y
x = y-5
Solve for y
x+5 = y-5+5
x+5 =y
The inverse is x+5
Which of the following is best described as sets of three whole numbers (a, b, and c) that satisfy the equation ?
A.
The Pythagorean theorem
B.
Prime numbers
C.
Pythagorean triples
D.
Perfect squares
Answer:
Option C
Step-by-step explanation:
The whole numbers a,b and c such that [tex]a^2+b^2 = c^2[/tex] are Pythagorean triples satisfying the Pythagorean theorem.
Answer:
C
Step-by-step explanation:
a, b, and c are side lengths of the triangle.
The three side lengths that make up a right triangle are most commonly known as Pythagorean triples.
Solve the quadratic equation x2 + 2x – 20 = 0 by completing the square.
Answer:
x^2 + 2x - 20 = 0
x^2 + 2x - 20 + 20 = 0 + 20 ( add 20 to both sides)
x^2 + 2x = 20
x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)
( x + 1 )^2 = 21
x = [tex]\sqrt{21}-1[/tex]
x = [tex]-\sqrt{21}-1[/tex]
Answer:
A) x = –1 ± square root 21
is the answer:)
You were recently hired by a company and will recieve a starting salary of $45,000 per year. You will receive a $2,500 raise each year you are with the company. What will your salary be in your 6th year with the company?
Answer:
$60,000
Step-by-step explanation:
$2500*6=15000
45000+15000=60000
The 2010 General Social Survey reported a sample where about 48% of US residents thought marijuana should be made legal. If we wanted to limit the margin of error of a 95% confidence interval to 4%, about how many Americans would we need to survey
Answer:
The sample size is [tex]n = 600[/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.48[/tex]
The margin of error is [tex]MOE = 0.04[/tex]
Given that the confidence level is 95% the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error
Generally the margin of error is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p(1- \r p )}{n} }[/tex]
substituting values
[tex]0.04= 1.96* \sqrt{ \frac{0.48(1- 0.48 )}{n} }[/tex]
[tex]0.02041 = \sqrt{ \frac{0.48(52 )}{n} }[/tex]
[tex]0.02041 = \sqrt{ \frac{ 0.2496}{n} }[/tex]
[tex]0.02041^2 = \frac{ 0.2496}{n}[/tex]
[tex]0.0004166 = \frac{ 0.2496}{n}[/tex]
=> [tex]n = 600[/tex]
Solve the equation below for x.
-1
2(3x - 4) = 11
Find magnetic azimuth from stream 89 degrees magnetic azimuth from pond 14degrees
Answer:
The Azimuths are 81 degrees, 6 degrees for Grid Azimuths and 269 degrees, 194 degrees for back Azimuths
Step-by-step explanation:
Stream = 89 degrees and Pond = 14 degrees
To Convert to grid Azimuth
G-M Azimuth of 89-8=81 degrees
G-M Azimuth of 14-8=6 degrees
To obtain the back Azimuth for the stream
89+180=269 degrees
To obtain the back Azimuth for the pond
14+180=194 degrees
Blue ribbon taxis offers shuttle service to the nearest airport. You loop up online reviews for blue ribbon taxis and find that there are 17 reviews, six of which report that the taxi never showed up.
Is this a biased sampling method for obtaining customer opinion on the taxi service?
If so, what is the likely direction of bias?
explain your reasoning carefully.
Answer:
In order for a sample to be considered biased, some members of the total population must have either a larger or lower chance of being included in the sample. In this case, your sample contained 17 reviews. It is biased because it was completely voluntary and customers who have a bad experience with a product or service generally tend to express more their dissatisfaction than satisfied customers show their satisfaction.
In marketing, there is a saying that unsatisfied clients talk bad about our product or service 4 times more than satisfied clients. I'm not sure if this saying is exact or not, but all marketing research point in the same direction.
This means that clients that did not get a good service or got no service at all, are more likely to post a review about the company than clients who got a good service. This is what makes the sample biased.
The more error we allow, the less precise our estimate.Therefore, as the confidence level increases, the precision of our estimate increases stays roughly the same ___________.
Answer:
Increase
Step-by-step explanation:
Precision describes the closeness of estimates from different samples, it refers to the width of the confidence interval and can aso be described as the margin of error. While the confidence level describes the accuracy.
Going for a higher confidence level will bring about a wider confidence interval, and thus lead to a less precise estimate.
If A divided by B = 10 remainder of 6 what is b
Answer:
B = (A - 6) / 10
Step-by-step explanation:
This problem has 2 variables and 1 equation so it is not trivial to solve with confidence the value of B; however, we can solve for B in terms of A. With that being said, let's start.
If A divided by B = 10:
A/B = 10
10 remainder of 6
Could also be written as 10 & 6/B since B is the divisor. Rewrite this, you can get the equation:
A/B = (10B + 6) / B
A = 10B + 6
A - 6 = 10B
B = (A - 6) / 10
Thus, you have solve B in terms of A.
Cheers.
ABC has been translated 5 units to the right, as shown in the diagram. What is the length of ?
A.
15
B.
6
C.
31
D.
10
Answer:
(A) 15 centimeters
Step-by-step explanation:
A midsegment of a triangle is always 2 things:
Half the size of the bottom of the triangle (in this case AC)
Parallel to the bottom of the triangle.
Since ABC is an equilateral triangle, we know that EVERY side is 30cm, including AC.
So the midsegment of ABC, LM, must be 15 cm.
Hope this helped!
It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 55 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode?
Answer:
Null hypothesis :
[tex]H_o:p_1-p_2 = 0[/tex]
Alternative hypothesis:
[tex]H_1:p_1-p_2 \neq 0[/tex]
Decision Rule:
To reject the null hypothesis if z < -1.65 and z > 1.65
Conclusion:
Failed to reject null hypothesis if z > -1.65 or z < 1.65
z -value = 0.33022
P-value = 0.7414
Decision Rule:
Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1
Conclusion: we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode
Step-by-step explanation:
From the summary of the given statistical data sets.
Let consider to [tex]p_1[/tex] represent percentage of the first group ; &
[tex]p_2[/tex] represent percentage of the second group
The null and the alternative hypothesis can be stated s follows:
Null hypothesis :
[tex]H_o:p_1-p_2 = 0[/tex]
Alternative hypothesis:
[tex]H_1:p_1-p_2 \neq 0[/tex]
At the level of significance ∝ = 0.1; the two tailed critical value from the z-table
[tex]z_{\alpha/2} = 1.65[/tex]
Decision Rule:
To reject the null hypothesis if z < -1.65 and z > 1.65
Conclusion:
Failed to reject null hypothesis if z > -1.65 or z < 1.65
However; from the question:
There are 55 people in the first group and this group will be administered the new drug.
There are 45 people in the second group and this group will be administered a placebo.
After one year, 11% of the first group has a second episode and 9% of the second group has a second episode.
The test statistic for the for the first group who suffered from the second episode can be denoted as :
[tex]\hat p_1 = \dfrac{\overline x_1}{n_1}=0.11[/tex]
The test statistic for the for the second group who suffered from the second episode can be denoted as :
[tex]\hat p_2 = \dfrac{\overline x_2}{n_2}=0.09[/tex]
where;
[tex]n_1[/tex] = sample size of group 1 = 55
[tex]n_2[/tex] = sample size of group 2 = 45
The total probability of both group is :
[tex]\hat p = \dfrac{n_1 \hat p_1 + n_2 \hat p_2}{n_1 + n_2}[/tex]
[tex]\hat p = \dfrac{55*0.11+ 45 * 0.09}{55+45}[/tex]
[tex]\hat p = \dfrac{6.05+ 4.05}{100}[/tex]
[tex]\hat p = \dfrac{10.1}{100}[/tex]
[tex]\hat p = 0.101[/tex]
The standard error of the statistic [tex]\hat p_1 - \hat p_2[/tex] an be computed as follows:
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{ p_1 (1 - \hat p)( \dfrac{1}{n_1}+\dfrac{1}{n_2})}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101 (1 - 0.101)( \dfrac{1}{55}+\dfrac{1}{45})}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101(0.899)(0.0404)}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.0036682796}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)=0.060566[/tex]
Now; The test statistics is determined to be :
[tex]z = \dfrac{(\hat p_1 - \hat p_2 ) - (p_1-p_2)}{SE(\hat p_1 - \hat p_2)}[/tex]
[tex]z = \dfrac{(0.11-0.09) - 0}{0.060566}[/tex]
z = 0.33022
Hence; the value for the test statistics = 0.33022
the value for the test statistics = 0.33
From the z value; The P-value for the test statistics can be computed as:
P-value = 2P(Z ≥ |z|)
P-value = 2P(Z ≥ 0.33022)
P-value = 2 × P (Z ≤ - 0.33022)
From the z table Z ≤ - 0.33022 = 0.3707
P-value = 2 × 0.3707
P-value = 0.7414
Decision Rule:
Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1
Conclusion: we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode
Find the next two !!!
It's adding 3 and subtracting 2 every time.
This means the next two terms would be +3 and -2 since the last one was -2.
The next term = 4+3=7
The next next term = 7-2=5
Answer:
Answer : 7 , 5Please see the attached picture.
Hope it helps...
Best regards!!
What is the converse and the truth value of the converse of the following conditional? If an angle is a right angle, then it’s measure is 90
Answer:
"If an angle has measure 90°, then it is a right angle" , True
Step-by-step explanation:
We have the following:
"If an angle is a right angle, then it’s measure is 90"
The idea is to write the opposite of the previous conditional statement.
We know that if the statement is "If p, then q", then its inverse will be "If q, then p".
So the opposite of our given statement will be :
"If an angle has measure 90°, then it is a right angle"
And this statement is true since every angle that measures 90 ° is considered a right angle.
The valve was tested on 240240 engines and the mean pressure was 7.57.5 pounds/square inch (psi). Assume the population standard deviation is 1.01.0. The engineer designed the valve such that it would produce a mean pressure of 7.67.6 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.10.1 will be used. Find the P-value of the test statistic. Round your answer to four decimal places.
Answer:
z = 1.55
Step-by-step explanation:
The answer is attached.
given that (-9,-3) is on a graph of f(x), find the corresponding point for the function f(x+1)
Answer:
(-10, -3)
Step-by-step explanation:
Replacing x with x+1 in a function moves its graph 1 unit to the left. The point that is 1 unit to the left of (-9, -3) is (-10, -3).
the sum of place value of 5 in 15954
Answer:
5050
Step-by-step explanation:
Place value of a digit is the value of digit based on its position the given number.
to determine the place value of a digit
we multiply the digit by number of 10's which is equal to number of digits in its right.
example
for a number 1234687
the place value of 3 is
we take 3 and
multiply it by number of 10' in its right
number of 10's in the right is 4
thus place value of 3 = 3*10*10*10*10 = 30000
________________________________________________
15954
place value of 5 at thousandth position = 5*10*10*10 = 5000
place value of 5 at tens position = 5*10 = 50
Thus, sum of place value of 5 in 15954 = 5000+50 = 5050
g There are 60 mountain climbers in a club. 10 of these have climbed Mt. Everest. 15 have climbed Mt. Rainier. 8 have climbed both. How many have not climbed either mountain?
Answer:
43 mountain climbers have not climbed either mountain.
Step-by-step explanation:
Total number of mountain climbers, i.e. n(U) = 60
Number of mountain climbers who have climbed Mt. Everest, n(E) = 10
Number of mountain climbers who have climbed Mt. Rainier, n(R) = 15
Number of mountain climbers who have climbed both, n(E [tex]\cap[/tex] R) = 15
Using the formula to find number of climbers who have climbed either of the mountains:
[tex]n(A \cup B) = n(A)+n(B)-n(A\cup B )[/tex]
[tex]\therefore n(E \cup R) = n(E)+n(R)-n(E\cup R )\\\Rightarrow n(E \cup R) = 10+15-8 = 17[/tex]
To find, who have not climbed either mountain:
[tex]n(E\cup B)'=n(U) - n(E\cap B)\\\Rightarrow n(E\cup B)'=60 - 17 = \bold{43}[/tex]
So, the answer is:
43 mountain climbers have not climbed either mountain.
A soup company puts 12 ounces of soup in each can. The company has determined that 97% of cans have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled?
a. n=36, p=0.97, x=1
b. n=12, p=0.36, x=97
c. n=12, p=0.97, x=0
d. n=36, p=0.97, x=36
Answer:
Option d: n = 36, p = 0.97, x = 36.
Step-by-step explanation:
We are given that a soup company puts 12 ounces of soup in each can. The company has determined that 97% of can have the correct amount.
We have to describe a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled.
Let X = Number of cans that are properly filled
The above situation can be represented through binomial distribution;
[tex]P(X = x) = \binom{n}{x} \times p^{x} \times (1-p)^{n-x} ; x = 0,1,2,........[/tex]
where, n = number of trials (samples) taken = 36 cans
x = number of success = all cans are properly filled = 36
p = probabilitiy of success which in our question is probability that
can have the correct amount, i.e. p = 97%
So, X ~ Binom (n = 36, p = 0.97)
Hence, from the options given the correct option which describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled is n = 36, p = 0.97, x = 36.