Answer:
No. By definition, mutually exclusive events cannot occur together.
Step-by-step explanation:
If two events are mutually exclusive, can they not occur concurrently because by definition, mutually exclusive events cannot occur together or at the same time. This ultimately implies that the events or outcome of the sampling is disjointed.
Mathematically, if two events A and B are mutually exclusive;
[tex]P(AnB) = 0[/tex]
From the above expression, we can deduce that the probability of the two (2) events occurring or having an intersection is zero (0).
[tex]P(A or B) = P(A) + P(B)[/tex]
From the above expression, we can deduce that the probability of either of the two (2) events occuring is the sum of the probability of each occurrence.
For example, when a fair die is tossed once, the outcomes are mutually exclusive.
P(d) = 1, 2, 3, 4, 5 and 6.
Other examples include;
1. Tossing a coin once, you'll either get a head or a tail but not a head and a tail at the same time.
2. In cards, both a king and an ace or a king and a queen are mutually exclusive because you can't have both occurring at the same time.
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:
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!
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]
a sample of 25 workers with employer provided health insurance paid an average premium of $6600 eith a sample standard deviation of $800. Construct a 95% confidence interval for the mean premium amount paid by all workers who have employer provided health insurance g
Answer:
$6284.4≤μ≤$6313.6
Step-by-step explanation:
Using the formula for calculating confidence interval as shown:
CI = xbar ± Z×S/√n
xbar is the average premium
Z is the z-score at 95% confidence
S is the standard deviation
n is the sample size
Given parameters
xbar = $6600
Z score at 95% CI = 1.96
S = $800
n = 25
Substituting this parameters in the formula we have;
CI = 6600±1.96×800/√25
CI = 6600±(1.96×800/5)
CI = 6600±(1.96×160)
CI = 6600±313.6
CI = (6600-313.6, 6600+313.6)
CI = (6284.4, 6913.6)
Hence the 95% confidence interval for the mean premium amount paid by all workers who have employer provided health insurance is $6284.4≤μ≤$6313.6
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:
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:
In the figure above, ABCD is a parallelogram
with AB = BE = EC. If the area of right triangle
BEC is 8, what is the perimeter of polygon
ABECD?
The perimeter is 21.66
The figure is something like the one that is in the image below:
We want to find the total perimeter of the polygon ABECD
This will be:
AB + BE + EC + CD + DA
Remember that for a triangle rectangle of catheti A and B, the area is given by:
A*B/2
We know that the sides of the triangle rectangle are:
BE, EC, BC.
Because BE = EC, these can not be the hypotenuse of the triangle, then the catheti are BE and EC
Knowing that the area of the triangle rectangle is 8, we can write:
EC*BE/2 = 8
and EC = BE = x
x^2/2 = 8
x^2 = 8*2 = 16
x = √16 = 4
Then the two catheti of the triangle rectangle are 4 units long.
EC = 4
BE = 4
and we know that:
AB = BE = EC
then:
AB = 4
and because this is a rectangle, we also have:
DC = AB = 4
now we want to find the last side of the figure, AD,
Which we already know is equal to the hypotenuse of the triangle.
Remember the Pythagorean's theorem, which says that the sum of the squares of the catheti is equal to the square of the hypotenuse.
Both catethus are equal to 4, then we have:
H^2 = 4^2 + 4^2 = 32
H = √32 = 5.66
then:
DA = 5.66
Now we have:
AB = BE = EC = DC = 4
DA = 5.66
Then the perimeter is:
AB + BE + EC + CD + DA
4 + 4 + 4 + 4+ 5.66 = 21.66
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Will give brainliest. A farmer is painting a new barn. He will need to calculate the surface area of the barn to purchase the correct amount of paint. In which of the following units can the farmer expect to calculate the surface area? yd2 yd m3 m
Answer:
yd^2
Step-by-step explanation:
I took the test :)
The farmer calculate surface area in unit of [tex]yd^{2}[/tex]
Surface area :The surface area of any given object is the area or region occupied by the surface of the object.
Volume is the amount of space available in an object. Each shape has its surface area as well as volume.Surface area is the total area of the faces of a three-dimensional shape. Surface area is measured in square units.Thus , The farmer calculate surface area in unit of [tex]yd^{2}[/tex]
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A television screen has a length to width ratio of 8 to 5 and a perimeter of 117 inches. What is the diagonal measure of the screen (to the nearest tenth of an inch)?
Answer:
[tex]D = 42.5\ inch[/tex]
Step-by-step explanation:
Given
[tex]L = Length[/tex] and [tex]W = Width[/tex]
[tex]L:W = 8: 5[/tex]
[tex]Perimeter = 117[/tex]
Required
Determine the Diagonal
First, the dimension of the screen has to be calculated;
Recall that; [tex]L:W = 8: 5[/tex]
Convert to division
[tex]\frac{L}{W} = \frac{8}{5}[/tex]
Multiply both sides by W
[tex]W * \frac{L}{W} = \frac{8}{5} * W[/tex]
[tex]L = \frac{8W}{5}[/tex]
The perimeter of a rectangle:
[tex]Perimeter = 2(L+W)[/tex]
Substitute [tex]L = \frac{8W}{5}[/tex]
[tex]Perimeter = 2(\frac{8W}{5}+W)[/tex]
Take LCM
[tex]Perimeter = 2(\frac{8W + 5W}{5})[/tex]
[tex]Perimeter = 2(\frac{13W}{5})[/tex]
Substitute 117 for Perimeter
[tex]117 = 2(\frac{13W}{5})[/tex]
[tex]117 = \frac{26W}{5}[/tex]
Multiply both sides by [tex]\frac{5}{26}[/tex]
[tex]\frac{5}{26} * 117 = \frac{26W}{5} * \frac{5}{26}[/tex]
[tex]\frac{5 * 117}{26} = W[/tex]
[tex]\frac{585}{26} = W[/tex]
[tex]22.5 = W[/tex]
[tex]W = 22.5[/tex]
Recall that
[tex]L = \frac{8W}{5}[/tex]
[tex]L = \frac{8 * 22.5}{5}[/tex]
[tex]L = \frac{180}{5}[/tex]
[tex]L = 36[/tex]
The diagonal of a rectangle is calculated using Pythagoras theorem as thus;
[tex]D = \sqrt{L^2 + W^2}[/tex]
Substitute values for L and W
[tex]D = \sqrt{36^2 + 22.5^2}[/tex]
[tex]D = \sqrt{1296 + 506.25}[/tex]
[tex]D = \sqrt{1802.25}[/tex]
[tex]D = \sqrt{1802.25}[/tex]
[tex]D = 42.4529150943[/tex]
[tex]D = 42.5\ inch[/tex] (Approximated)
Find the length of FT¯¯¯¯¯¯¯ A. 77.71 B. 72.47 C. 56.84 D. 49.42
Answer:
D, 49.42
Step-by-step explanation:
ΔVFT=180-90-43=47
formula
a/sin A = b/sin B/ = c/sin C
So,
FV/sin90=53/sin47
FV=72.4684
FT=√(72.4684)^2-(53)^2
FT=49.4234
Ans:D
The length FT in the given right-angle triangle is 49.42.
So option D is the correct answer.
We are given a right-angle triangle and to find the length of any side we can use Pythagoras theorem or trigonometric identities.
In the triangle, we see that TV = 53 and ∠ FVT = 43°
We will find the length FT by using Pythagoras theorem or trigonometric identities.
What are trigonometric functions?
There are some commonly used trigonometric identities:
SinФ = Perpendicular / hypotenuse
Cos Ф = Base / hypotenuse
Tan Ф = Perpendicular / Base
We will use Tan Ф = Perpendicular / Base to find the length FT.
Because we need to use trigonometric identities that have TV and FT.
Tan Ф = FT / TV
Tan 43° = FT / 53
FT = Tan 43° x 53
FT = 0.932515 X 53
FT = 49.42
Thus we got FT = 49.42 using the tan function.
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2. (1 pt) The following statement is true or false;
When we know the population standard deviation, o, we use a standard normal
distribution (z-score) to calculate the error bound EBM and construct the
confidence interval and when the population standard deviation, o, is unknown,
we use a Student's t distribution (t-score) to calculate the error bound EBM and
construct the confidence interval.
a. true
b. false
If you know the population standard deviation (sigma), then you use the Z distribution. If sigma is not known, then you use the T distribution.
Side note: Even if sigma is not known, you could use the Z distribution if the sample size n is greater than 30. If n > 30, then the T distribution is approximately about the same as the Z distribution.
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
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.
5. When looking at a map, a student realizes that Birmingham is nearly due west of Atlanta, and Nashville is nearly due north of Birmingham. If the distance from Atlanta to Birmingham is roughly 150 mi, and the distance from Birmingham to Nashville is roughly 200 mi, what is the estimated distance from Atlanta to Nashville?
Answer: 250 mi
Step-by-step explanation:
Here we can think in a triangle rectangle:
The distance from Birmingham to Atlanta is roughly 150 mi, and this is one of the cathetus.
And the distance from Birmingham to Nashville is roughly 200 mi, this is the other cathetus of the triangle.
Now, the distance from Atlanta to Nashville will be the hypotenuse of this triangle rectangle.
Now we can apply the Pythagorean's theorem:
A^2 + B^2 = H^2
Where A and B are the cathetus, and H is the hypotenuse:
Then:
H = √(A^2 + B^2)
H = √(150^2 + 200^2) mi = √(62,500) mi = 250 mi
Then the estimated distance from Atlanta to Nashville is 250 mi
X-6 greater then equal to 15 + 8x
Answer:x ≤ 3
Step-by-step explanation:
Answer:
x ≥ -3
Step-by-step explanation:
x - 6 ≥ 15 + 8x
x - 8x ≥ 15 + 6
-7x ≥ 21
x ≥ 21/-7
x ≥ -3
x greater than equal to -3
check:
-3 - 6 ≥ 15 + 8*-3
-9 ≥ 15 - 24
If you rent a car for one day and drive it for 100 miles the cost is 40 dollars if you drive it 220 miles the cost is 46 dollars what is the linear equation for this
Answer:
[tex] y = \dfrac{1}{20}x + 35 [/tex]
Step-by-step explanation:
Let y = cost.
Let x = number of miles.
We have two (x, y) points: (100, 40) and (220, 46).
Now we find the equation of the line that passes through those two points using the two-point form of the equation of a line.
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
[tex] y - 40 = \dfrac{46 - 40}{220 - 100}(x - 100) [/tex]
[tex] y - 40 = \dfrac{6}{120}(x - 100) [/tex]
[tex] y - 40 = \dfrac{1}{20}(x - 100) [/tex]
[tex] y - 40 = \dfrac{1}{20}x - 5 [/tex]
[tex] y = \dfrac{1}{20}x + 35 [/tex]
URGENT, PLEASE HELP! (3/5) -50 POINTS- !please no wrong answers for the points.! A) [tex]y = \frac{9}{2} x + \frac{1}{2}[/tex] B) [tex]y = - \frac{1}{2} x + \frac{7}{2}[/tex] C) [tex]y = -4x + 9[/tex] D) [tex]y = 4x + 15[/tex]
Answer:
B y = -1/2x + 7/2
Step-by-step explanation:
We know that it has a negative slope since the points go from the top left to the bottom right
We can eliminate A and D
The y intercept is where it crosses the y axis
It should cross somewhere between 2 and 4
C has a y intercept of 9 which is too big
Lets verify with a point
x = -4
y = -4(-4)+9 = 16+9 = 25 (-4,25) not even close to being near the points on the graph
checking B
y = -1/2 (-4) +7/2
= 2 + 7/2 = 11/2 = 5.5 it seems reasonable
Answer:
[tex]\Large \boxed{y=-\frac{1}{2} x+\frac{7}{2} }[/tex]
Step-by-step explanation:
Using a graph,
we can see that the line y = -1/2x + 7/2 best fits for the data.
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.
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The ball bearing have volumes of 1.6cm cube and 5.4cm cube . Find the ratio of their surface area.
Answer:
64 : 729
Step-by-step explanation:
Ratio of surface area
= (ratio of linear dimensions) ^2
= 1.6^2 : 5.4^2
= 256 : 2916
= 64 : 729
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
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
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.
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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)
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
C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 4 ± .003 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 4.001 inches with a standard deviation of .002 inch. Calculate the Cpk for this machine.
Answer:
0.3333
Step-by-step explanation:
Given the following :
Sample mean(m) = 4.001 inch
Standard deviation(sd) = 0.002 inch
Key specification : = 4 ± .003 inches
Upper specification LIMIT ( USL) : (4 + 0.003) = 4.003 inches
Lower specification limit (LSL) : (4 - 0.003) = 3.997 inches
Cpk is found using the relation:
min[(USL - mean) / (3 * sd), (mean-LSL) / (3*sd)]
min[(4.003 - 4.001)/(3*0.002), (4.001 - 3.997)/(3*0.002)]
min[(0.002 / 0.006), (0.004 / 0.006)]
min[(0.33333, 0.66667)
Therefore Cpk = 0.3333
Because 0.33333<0.66667
find the product 538 x 100=
Answer:
Answer=53,800
Step-by-step explanation:
just add the two zero behind the number
Please help soon as possible! This is urgent! Match each expression with the correct description.
Answer:
Hey there!
q is 1, and n=-2.
q-n=1-(-2), which is 3.
n-q=-2=1, which is -3.
q is 1.
Thus, the least value is n-q, and the greatest value is q-n. Closest to zero would be q.
Let me know if this helps :)
Answer:
Least: n-q
Greatest: q-n
Closest to zero: q
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]
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
