Answer:
L = 13.3649
Step-by-step explanation:
We are given;
x = t − 2 sin(t)
dx/dt = 1 - 2 cos(t)
Also, y = 1 − 2 cos(t)
dy/dt = 2 sin(t)
0 ≤ t ≤ 2π
The arc length formula is;
L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt
Where α and β are the boundary points. Thus, applying this to our question, we have;
L = (0,2π)∫√((1 - 2 cos(t))² + (2 sin(t))²)dt
L = (0,2π)∫√(1 - 4cos(t) + 4cos²(t) + 4sin²(t))dt
L = (0,2π)∫√(1 - 4cos(t) + 4(cos²(t) + sin²(t)))dt
From trigonometry, we know that;
cos²t + sin²t = 1.
Thus;
L = (0,2π)∫√(1 - 4cos(t) + 4)dt
L = (0,2π)∫√(5 - 4cos(t))dt
Using online integral calculator, we have;
L = 13.3649
Which of the following is equivalent to –2i(6 – 7i)?
Answer:
[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
A
Step-by-step explanation:
Answer = A
helppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
Brainliest!
Step-by-step explanation:
36x^-4y^2/5x^2y^-3z^-2
36y^5z^2/5x^6
make everything positive
An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind. What is the speed of the plane in still air and what is the wind speed?
Answer:
Speed of plane in still air is 270 mph
Wind speed is 30 mph
Step-by-step explanation:
Check the picture.
The speed of the plane in still air is 270 mph and the speed of the wind will be 30 mph.
What is the distance formula?The distance traveled by an object is the product of the speed of an object and the time taken.
Distance = speed x time
An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind.
Let the speed of the plane be x
The speed of wind be y
Distance covered with the wind = (x + y)t
1200 = (x + y)4
(x + y) = 1200/4
(x + y)= 300 .....(a)
Distance covered against the wind = (x - y)t
1200 = (x - y)5
(x - y) = 1200/5
(x - y) = 240 .......(b)
By solving both the equation
(x + y)= 300
(x - y) = 240
Therefore the values will be x= 270mph and y = 30 mph
Learn more about the distance formula:
https://brainly.com/question/15172156
will rate you brainliest need help
Answer:
x = 0.09
Step-by-step explanation:
[tex] {3}^{x + 2} = {2}^{3} [/tex]
Taking Logarith both sides, we get :
Using the properties of Logarithms:
[tex](x + 2) log(3) = 3 log(2) [/tex]
[tex](x + 2) = 1.91[/tex]
(taking log2= 0.3 and log3= 0.47)
x = 0.09
STUCK Basic geometry A for senior year school
Answer:
(C) A reflection across a horizontal line and a horizontal translation
Step-by-step explanation:
We can see that, near the x-axis, these shapes are 3 y values away from the x-axis, meaning that if we reflect one over the x-axis we will be at the same y values as the other shape.
Reflecting these points shows that we’ve got the same shape, just skewed the one side. We can then translate this shape horizontally to get it to where we want it.
Hope this helped!
Answer this will give 10 points
Answer:
maximum --> 62
median --> 46.5
upper quartile --> 60
lower quartile --> 37
minimum --> 32
Step-by-step explanation:
Forgive me on the explanation as I'm a bit rusty on these types of problems.
First, we need to put the set of numbers in order -->
from: 34, 37, 39, 32, 48, 45, 53, 62, 58, 61, 60, 41 -->
to: 32, 34, 37, 39, 41, 45, 48, 53, 58, 60, 61, 62
maximum = biggest number => thus, 62
median = middle number in a sense => (45+48)/2 => thus, 46.5
upper quartile = median over the median => thus, 60
lower quartile = median under the median => thus, 37
minimum = lowest number => thus, 32
And there we have our 5 answers.
Hope this helps!
Given m = - 1/4 & the point (4, 5)which of the following is the point slope form of the equation?
Answer:
y - 5 = -1/4(x - 4)
Step-by-step explanation:
Point slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
To find the point slope form, plug in the point given and the slope.
y - y1 = m(x - x1)
y - 5 = -1/4(x - 4)
Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100100100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 20 \text{ cm}20 cm20, start text, space, c, m, end text. How far did Chubby run? Round your answer to the nearest \text{cm}cmstart text, c, m, end text.
Answer:
63 cm
Step-by-step explanation:
If Chubby ran his wheel, which has a diameter of 20cm, we want to find its circumference - this will tell us how far Chubby has ran one one full rotation of the wheel.
The formula for the circumference of a circle is [tex]2\pi r[/tex], where r is the radius. We know the diameter is 20, which is double the radius, so the radius is [tex]20\div2=10[/tex] cm.
We can know substitute inside the formula:
[tex]2\cdot \pi \cdot10\\\\2\cdot 3.14 \cdot10\\\\ 6.28\cdot10\\\\62.8[/tex]
62.8 rounded to the nearest cm is 63.
Hope this helped!
Answer:
6280
Step-by-step explanation:
Let s1 = k and define sn+1 = √4sn − 1 for n ≥ 1. Determine for what values of k the sequence (sn) will be monotone increasing and for what values of k it will be monotone decreasing.
Answer:
The answer is "[tex]\bold{\frac{1}{4}<k\leq 2+\sqrt{3}}[/tex]"
Step-by-step explanation:
Given:
[tex]\ S_1 = k \\\\ S_{n+1} = \sqrt{4S_n -1}[/tex] [tex]_{where} \ \ n \geq 1[/tex]
In the above-given value, [tex]S_n[/tex] is required for the monotone decreasing so, [tex]S_2 :[/tex]
[tex]\to \sqrt{4k-1} \leq \ k=S_1\\\\[/tex]
square the above value:
[tex]\to k^2-4k+1 \leq 0\\\\\to k \leq 2+\sqrt{3} \ \ \ \ \ and \ \ 4k+1 >0\\\\[/tex]
[tex]\bold{\boxed{\frac{1}{4}<k\leq 2+\sqrt{3}}}[/tex]
Lila is camping with her family. She wants to hike to the lake, go fishing, and hike back before 6:05 P.M. It will take 1 hour and 10 minutes to hike to the lake and 1 hour and 50 minutes to hike back. Lila wants to fish for 3 hours and 10 minutes. What is the latest time Lila can start the hike to the lake?
Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 p.m (6: 04 p.m.)
Explanation:
To solve this question, the first step is to calculate how much time does hiking to the lake, go fishing, and go back takes in total. This can be calculated by adding the time of the three activities. This means 1 hour 10 minutes + 3 hours 10 minutes + 1 hour 50 minutes which is equal to 6 hours 10 minutes. The detailed process is shown below.
Add the hours: 1 + 3 + 1 = 5
Add the minutes: 10+50 +10 = 70
Also, because the total of minutes is above 60 (each hour has 60 minutes) it is necessary to subtract 60 minutes and add 1 hour.
5 hours + 1 hour and 70 minutes - 60 minutes = 6 hours and 10 minutes
Now, to solve the question subtract the time of the activities to the time Lila needs to complete all the activities.
6: 05 p.m. - 6 hours and 10 minutes = 11: 55 a.m
You can get this result by substracting first the hours and then the minutes
6: 05 p.m. - 6 hours = 12: 05 p.m.
12: 05 - 10 minutes = 11: 55 a.m.
According to this, Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 a.m because if she starts at 11: 54 a.m. she will be back at 6:04, which is a minute before 6:05 p.m.
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement
Answer:
Step-by-step explanation:
Following the cardinal points as regards location of points, the sketch of Musah's movement can be as what is attached to this answer.
Beer shelf life is a problem for brewers and distributors because when beer is stored at room temperature, its flavor deteriorates. When the average furfuryl ether content reaches 6 μg per liter, a typical consumer begins to taste an unpleasant chemical flavor. At α = .05, would the following sample of 12 randomly chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold? 8.92 6.99 5.54 5.73 6.38 5.51 6.45 7.50 8.48 5.56 6.90 6.46
Answer:
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
Step-by-step explanation:
We formulate our null and alternative hypotheses as
H0 u≤ 6 ug Ha : u > 6 ug
The significance level ∝ = 0.05
The test statistic used is
t = X` - u / s/ √n
which if H0 is true, has the students' t test with n-1 = 11 degrees of freedom.
The critical region t > t (0.05,11) = 1.796
We compute the t value from the data
Xi Xi²
8.92 79.5664
6.99 48.8601
5.54 30.6916
5.73 32.8329
6.38 40.7044
5.51 30.3601
6.45 41.6025
7.50 56.25
8.48 71.9104
5.56 30.9136
6.90 47.61
6.46 41.7316
80.42 553.0336
Now x` = ∑x/ n = 80.42/12 = 6.70
S²= 1/n-1 ( ∑(xi- x`)²= 1/11 ( 553.034 - (80.42)²/12)
= 1/11 (553.034-538.948) = 1.2805
s= 1.1316
Putting the values in the test statistics
t = X` - u / s/ √n = 6.70- 6 / 1.1316 / √12
= 2.1698
The critical region t > t (0.05,11) = 1.796
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
Multiply the following complex numbers:
(7+2i)(2+3i)
Please don’t guess
Answer:
14 + 25l + 6l^2
Step-by-step explanation:
(7 + 2i) (2 + 3i)
=> 14 + 4l + 21l + 6l^2
=> 14 + 25l + 6l^2
This is the correct answer
Kim is earning money for a trip. She has saved and she earns per hour babysitting. The total amount of money earned (y) after (x) number of hours worked is given by the equation . How many hours will she need to work in order to earn for her trip?
Answer:
what is the amount of money Kim earn per hour of babysitting? Also I need to know how much trip cost to find out how many hours she need to work.
Step-by-step explanation:
what is 76.32 divided by 24.98 using compatible numbers to estimate each quotient?
Answer:
Approximately 3.05
Step-by-step explanation:
Using "compatible numbers" we can simply round these numbers to integer values. Let's make 76.32 => 76 and 24.98 => 25
So from here let's do 76/25 to get 3 R 1/25
1/25 as a decimal is .04
So far, we have 3.04. Going back to Look at our decimals, .32 and .98, there is a larger difference in our down rounding with the .32 than the up rounding from our .98. So we should consider an extra value in our decimal.
Considering our whole number of 3.0, we can assume that our rounding will have an increase of about .01 or .015 in error.
Thus our number will be 3.04 + .01.
Making our quotient approximately 3.05.
Cheers.
Find a8 of the sequence 10,9.75,9.5,9.25,….
Answer:
10,9.75,9.5,9.25,9, 8.75 , 8.5, 8.25, 8...
Step-by-step explanation:
Subtract 0.25 from each to find the next number
Answer:
8.25
Step-by-step explanation:
If you substract .25 from each number until you get to a8 you will get 8.25
What is the value of 20 + 3 (7 + 4) + 5 + 2 (7 + 9)?
Answer:
90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
Here is the equation
[tex]20+3\times(7+4)+5+2\times(7+9)[/tex]
In the order of operations parentheses go first so we get
[tex]20+3\times11+5+2\times16[/tex]
Next we do the multiplication
[tex]20+33+5+32\\[/tex]
And finally we add them all up
[tex]20+33+5+32=90\\[/tex]
Thus, 90 is the answer of [tex]20+3\times(7+4)+5+2\times(7+9)[/tex] or [tex]20+3(7+4)+5+2(7+9)[/tex]
In a school, there are 25% fewer 11th graders than 10th graders, and 20% more 11th graders than 12th graders. The total number of students in 10th, 11th, and 12th grades in the school is 190. How many 10th graders are there at the school?
Answer:
There are 80 10th graders in the school
Step-by-step explanation:
Let the number of 10th graders be x
There are 25% fewer 11th graders
That mean x - 25% of x
x -0.25x = 0.75x
There are 20% more 11th graders than 12th graders
So if number of 12th graders = y, then
0.75x = y + 20/100 * y = y + 0.2y = 1.2y
Since ;
0.75x = 1.2y
then y = 0.75x/1.2 = 0.625x
So let’s add all to give 190
x + 0.75x + 0.625x = 190
2.375x = 190
x = 190/2.375
x = 80
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want % confidence that the sample mean is within points of the population mean, and the population standard deviation is .
Answer: hello below is the complete question
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number
answer : 737 adults
Step-by-step explanation:
confidence interval = 90% = 0.9
( E ) = 4
standard deviation = 66
first we have to calculate the value of a
a = 1 - confidence interval
= 1 - 0.9 = 0.10 hence a / 2 = 0.05
next find the value of Z a/2 from table
Z[tex]_{0.05}[/tex] = 1.645
The number of Adults selected can be determined using this relation
N = [tex](Z_{a/2} * (s/E))^2[/tex]
= [tex](Z_{0.05} * ( 66/4))^2[/tex]
= 737
Suppose the radius of a circle is 5 units. What is its circumference?
Answer:
C≈31.42
Step-by-step explanation:
C=2πr
C=2xπx5
C≈31.42
pls mark as brainliest
In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is
Complete Question
In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:
A -1.645
B -2.066
C -2.000
D-1.960
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The population mean is [tex]p = 0.50[/tex]
The sample size is [tex]n = 64[/tex]
The number that met the standard is [tex]k = 24[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{24}{64}[/tex]
[tex]\r p =0.375[/tex]
Generally the standard error is mathematically evaluated as
[tex]SE = \sqrt{ \frac{p(1- p )}{n} }[/tex]
=> [tex]SE = \sqrt{ \frac{0.5 (1- 0.5 )}{64} }[/tex]
=> [tex]SE = 0.06525[/tex]
The test statistics is evaluated as
[tex]t = \frac{ \r p - p }{SE}[/tex]
[tex]t = \frac{ 0.375 - 0.5 }{0.0625}[/tex]
[tex]t = -2[/tex]
What is the scale factor of this dilation?
Answer:
5/3
Step-by-step explanation:
on both sides we can see that the orginal length of 3 increased to five
therfore if we multiply 3 by 3/5 we get five which means the scale factor is 5/3
In Triangle A B C, what is the value of x? Triangle A B C. Angle A is (10 x minus 10) degrees, angle B is (8 x) degrees, angle C is (10 x + 8) degrees.
Answer:
6.5
Step-by-step explanation:
The sum of all angles in a triangle are 180 degrees.
=> 10x -10 + 8x + 10x + 8 = 180
=> 28x -2 = 180
=> 28x = 182
=> x = 6.5
So, Angle A = 10 x 6.5 -10 = 65 - 10 = 55 degrees
Angle B = 8 x 6.5 = 52 degrees
Angle C = 10 x 6.5 + 8 = 65 + 8 = 73 degrees.
55 + 52 + 73 = 55 + 125 = 180 degrees
Determine the equation of the exponantial function with a common ratio of 2, a horizontal asymptote at y=4 and passin through the point (2,10).
Answer:
Step-by-step explanation:
The time between consecutive uses of a vending machine is exponential with an average of 15 minutes. a)Given that the machine has not been used in the previous 5 minutes, what is the probability that the machine will not be used during the next 10 minutes
Answer5
Step-by-step explanation:
In a simple regression analysis with age as the only explanatory variable, the effects of other factors, such as faminc, are
Answer:
In the error term.
Step-by-step explanation:
A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).
Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.
A study was conducted to assess the effects that occur when children are exposed to cocaine before birth. Children were tested at age 4 for object assembly skill, which was described as a task requiring visual spatial skills related to mathematical competence. The 190 children born to cocaine users had a mean of 7.3 and a standard deviation of 3.0 The 186 children not exposed to cocaine had a mean score of 8.2 with a standard deviation of 3.0 Use a 0.05 significance level to test the claim that prenatal cocaine exposure is associated with lower scores of four year old children on the test of object assembly.
What are null and alternative hypothesis? What is test statistics?
Answer:
We conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.
Step-by-step explanation:
We are given that the 190 children born to cocaine users had a mean of 7.3 and a standard deviation of 3.0 The 186 children not exposed to cocaine had a mean score of 8.2 with a standard deviation of 3.0.
Let [tex]\mu_1[/tex] = population mean score for children born to cocaine users.
[tex]\mu_2[/tex] = population mean score for children not exposed to cocaine.
So, Null Hypothesis, : = 490 {means that the prenatal cocaine exposure is not associated with lower scores of four-year-old children on the test of object assembly}
Alternate Hypothesis, : 490 {means that the prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly}
The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean score of children born to cocaine users = 7.3
[tex]\bar X_2[/tex] = sample mean score of children not exposed to cocaine = 8.2
[tex]s_1[/tex] = sample standard deviation for children born to cocaine users = 3
[tex]s_2[/tex] = sample standard deviation for children not exposed to cocaine = 3
[tex]n_1[/tex] = sample of children born to cocaine users = 190
[tex]n_2[/tex] = sample of children not exposed to cocaine = 186
Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(190-1)\times 3^{2}+(186-1)\times 3^{2} }{190+186-2} }[/tex] = 3
So, the test statistics = ~
= -2.908
The value of t-test statistics is -2.908.
Now, at a 0.05 level of significance, the t table gives a critical value of -1.645 at 374 degrees of freedom for the left-tailed test.
Since the value of our test statistics is less than the critical value of t as -2.908 < -1.645, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.
Therefore, we conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.
In the null hypothesis, a test always forecasts no effect, while the alternate theory states the research expectation impact, and calculation as follows:
Null and alternative hypothesis:Calculating the pooled estimator of [tex]\sigma^2[/tex], denoted by [tex]S^2_p[/tex], is defined by
[tex]\to \bold{S^2_p= \frac{(n_1 - 1) S^2_1+ (n_2 - 1)S^2_2}{n_1 + n_2 - 2}}[/tex]
Null hypothesis:
[tex]\to H_0 : \mu_1 - \mu_2 = \Delta_0\\[/tex]
Test statistic:
[tex]\to T_0=\frac{\bar{X_1}- \bar{X_2} -\Delta_0}{S_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \\\\[/tex]
Alternative Hypothesis:
[tex]H_1 : \mu_1 -\mu_2 \neq \Delta_0\\\\ H_1 : \mu_1 -\mu_2 > \Delta_0\\\\H_1 : \mu_1 -\mu_2 < \Delta_0\\\\[/tex]
Rejection Criterion
[tex]t_0 > t_{\frac{\alpha}{2} , n_1+n_2 -2}\ \ \ or\ \ \ t_0 < - t_{\frac{\alpha}{2} , n_1+n_2 -2} \\\\t_o > t_{\alpha , n_1+n_2 -2} \\\\t_o > -t_{\alpha , n_1+n_2 -2}[/tex]
Given value:
[tex]\to S_p=9\\\\\to \Delta_0=0\\\\\to t_0=-\frac{0.9}{3(\sqrt{(\frac{1}{190}+\frac{1}{186})})}=-2.9\\\\\to t_{0.05,374}=1.645\\\\[/tex]
here
[tex]\to t_0 < -t_{0.05,374}[/tex]
hence rejecting the [tex]H_0[/tex]
Since there should be enough evidence that prenatal cocaine exposure is linked to inferior item assembly scores in 4-year-olds.
Find out more about the alternative hypothesis here:
brainly.com/question/18831983
Draw a Venn diagram and use the given information to fill in the number of elements in each region.
Answer: Check out the diagram below for the filled in boxes
14 goes in the first box (inside A, but outside B)
7 goes in the overlapping circle regions
5 goes in the third box (inside B, outside A)
3 goes in the box outside of the circles
==============================================================
Explanation:
[tex]n(A \cup B) = 26[/tex] means there are 26 items that are in A, B or both.
n(A) = 21 means there are 21 items in A
n(B) = 12 means there are 12 items in B
We don't know the value of [tex]n(A \cap B)[/tex] which is the number of items in both A and B at the same time. This is the intersecting or overlapping regions of the two circles. Let [tex]x = n(A \cap B)[/tex]
It turns out that adding n(A) to n(B), then subtracting off the stuff they have in common, leads to n(A u B) as shown below.
--------
[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)\\\\26 = 21+12 - x\\\\26 = 33 - x\\\\x+26 = 33\\\\x = 33-26\\\\x = 7\\\\n(A \cap B) = 7\\\\[/tex]
So there are 7 items in both regions.
This means there are [tex]n(A) - n(A \cap B) = 21 - 7 = 14[/tex] items that are in set A only. In other words, 14 items are in circle A, but not in circle B.
Notice how the values 14 and 7 add back up to 14+7 = 21, which represents everything in set A.
Similarly, there are [tex]n(B) - n(A \cap B) = 12 - 7 = 5[/tex] items that are in circle B, but not in circle A. The values 5 and 7 in circle B add to 5+7 = 12, matching with n(B) = 12.
The notation n(A') means the number of items that are not in set A. We're given n(A') = 8. We already know that 5 is outside circle A. So if 5+y = 8, then y = 3 must be the missing value for the box that is outside both circles.
Again the diagram is posted below with the filled in values.
A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
The filled Venn diagram is given below.
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
n(A) = 21
This is the total of all the items included in Circle A.
n(B) = 12
This is the total of all the items included in Circle A.
n(A') = 8
The items that are not in circle A.
n(A U B ) = 26
The items that are in both circle A and circle B.
Now,
n (A U B) = n(A) + n(B) - n(A ∩ B)
26 = 21 + 12 - n(A ∩ B)
n(A ∩ B) = 33 - 26
n(A ∩ B) = 7
Thus,
The filled Venn diagram is given below.
Learn more about the Venn diagram here:
https://brainly.com/question/1605100
#SPJ2
What is the circumference of the following circle?
Answer:
The answer is 157 inStep-by-step explanation:
Circumference of a circle = 2πr
where
r is the radius
From the above question
radius = 25 in.
Substitute this value into the above formula
That's
Circumference = 2(25)π
= 50π
= 157.079
We have the final answer as
Circumference = 157 inHope this helps you
A poker hand consisting of 7 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactly 3 face cards. Leave your answer as a reduced fraction.
Answer:
The probability is 2,010,580/13,378,456
Step-by-step explanation:
Here is a combination problem.
We want to 7 cards from a total of 52.
The number of ways to do this is 52C7 ways.
Also, we know there are 12 face cards in a standard deck of cards.
So we are selecting 3 face cards from this total of 12.
So also the number of cards which are not face cards are 52-12 = 40 cards
Out of all these 40, we shall be selecting exactly 4. The number of ways to do this 40C4
Thus, the required probability will be;
(40C4 * 12C3)/52C7 = (91,390 * 220)/133,784,560
= 20,105,800/133,784,560 = 2,010,580/13,378,456
