Let A, B, and W denote the sets of students apply to Addis Ababa Uni (A), Bahir Dar Uni (B), or Wachemo Uni (W). Let U denote the universal set of all students in the class.
We're given the cardinalities of several sets:
• total number of students: [tex]n(U) = 60[/tex]
• A applicants: [tex]n(A) = 30[/tex]
• B applicants: [tex]n(B) = 25[/tex]
• W applicants: [tex]n(W) = 24[/tex]
• A and B applicants: [tex]n(A\cap B) = 11[/tex]
• A and W applicants: [tex]n(A \cap W) = 6[/tex]
• B and W applicants: [tex]n(B\cap W) = 9[/tex]
• non-applicants: [tex]n(U \setminus (A\cup B\cup W)) = 4[/tex]
The last cardinality tells us [tex]n(A\cup B\cup W) = 60-4 = 56[/tex] students applied anywhere at all.
We want to find [tex]n(A\cap B\cap W)[/tex], the number of students that applied to each of the three universities.
By the inclusion/exclusion principle,
[tex]n(A\cup B\cup W) = n(A) + n(B) + n(W) \\\\~~~~~~~~~~~~~~~~~~~~~~~~ - n(A\cap B) - n(A\cap W) - n(B\cap W)\\ \\~~~~~~~~~~~~~~~~~~~~~~~~ + n(A\cap B\cap W)[/tex]
That is, we count up all the students in the sets A, B, and W, then subtract the number of students in each pairwise intersection to not double-count, then add back the number of students in the intersection of all three sets since it was removed in the previous step.
Now solve.
[tex]56 = 30 + 25 + 24 - 11 - 6 - 9 + n(A\cap B\cap W)[/tex]
[tex]\implies n(A\cap B\cap W) = \boxed{3}[/tex]
If f(x) = 3x + 10x and g(x) = 2x - 4, find (f+ g)(x).
Answer:
25x-4
Step-by-step explanation:
3x+10x
+ 2x. -4
=5x+10x-4
=15x-4
Please help
The mean length of 7 childrens' index finger is 7.8cm.
The mean length of 7 adults' index finger is 17.7cm.
What is the mean length (rounded to 2 DP) of these 14 people's index finger?
The combined mean of the 14 people's index finger is: 12.75 cm.
How to Find the Combined Mean?Combined mean = [(mean of first group × number of data of the first group) + (mean of second group × number of data of the second group)] ÷ (number of data of the first group + number of data of the second group).
Given the following:
Mean of first group = 7.8
Number of data of the first group = 7
Mean of second group = 17.7
Number of data of the second group = 7
Combined mean = [(7.8 × 7) + (17.7 × 7)] / (7 + 7)
Combined mean = 178.5 / 14
Combined mean = 12.75 cm.
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Daisy's Diner offers a side dish of broccoli, apple slices, or pretzels with their kids' meals. Last weekend, they sold 1,038 kids' meals. Twice as many kids chose pretzels as chose broccoli and 3 times as many chose apple slices as chose broccoli.
How many kids chose apple slices?
519 children chose apple slices.
PossibilitiesGiven that Daisy's Diner offers a side dish of broccoli, apple slices, or pretzels with their kids' meals, and last weekend, they sold 1,038 kids' meals, and twice as many kids chose pretzels as chose broccoli and 3 times as many chose apple slices as chose broccoli, to determine how many kids chose apple slices, the following calculation must be performed:
1038 = 2B + B + 3B1038 = 6BB = 1038 / 6B = 173P = 173 x 2 = 346A = 173 x 3 = 519Therefore, 519 children chose apple slices.
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Answer:519 children chose apple slices.
Step-by-step explanation:
Select the correct answer. What is the domain of y = tan (x)?
At 90 degrees, the tangent of x is undefinable.
What does determining the domain mean?The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain. Keep in mind that a fraction's denominator (bottom) cannot be zero when determining the domain. The integer that comes after a square root symbol in this section needs to be positive.The domain of y = tan (x):
y = tan(x)
Except for 90, all sets of positive real numbers fall within the domain of y = tan(x).
At 90 degrees, the tangent of x is undefinable.
Due to the exclusion of 90, all sets of positive real numbers are included in the domain of y = tan(x).
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find each lettered angle
Answer:
a = 103°
b = 103°
c = 97°
d = 83°
e = 154°
what is f(x) in the expression?
[tex]f(x) = 7x {}^{2} - 3x {}^{4} [/tex]
The x-intercept of a line is 2 and the y-intercept is 4. Explain how to use this information to write the equation of the line.
Answer:
y = -2x + 4
Step-by-step explanation:
The x-intercept would be the point (2,0) and the y intercept would have the point (0,4). Once we know two points we can write the equation in the line intercept for of y = mx + b.
We need to find the slope and the y intercept. The slope is the steepness of the line and it is the change in y over the change in x.
The ordered pairs are written in the form of (x, y). From our two points, we will subtract the y's to find the top number of our fraction.
0 - 4 = -4 that is the numerator (top number) of our slope. We do the same with the two x numbers that we have been given.
2 - 0 = 2 This is our numerator (or bottom number of our slope)
Our slope is -4 /2 to simplify, we divide the top and bottom number by 2 to get -2 / or just -2
Now that we have the slope we need to find the y-intercept. We can use either of our original two points and our slope to determine the y-intercept. It does not matter if you use the point (2,0) or (0,4). I will use (2,0) and the slope of -2
y = mx + b
0 = -2(2) + b
0 = -4 + b add 4 to both sides of the equation
4 = b
Now that we have the slope and the y-intercept, we can write the equation
y = mx + b
y = -2x + 4
What is 13 2/3 subtracted from 49 1/3
Answer:
35 2/3
Step-by-step explanation:
49 1/3 - 13 2/3
First convert both into improper fractions, which is
148/3 - 41/3
Then subtract!
107/3
Next simplify the fraction.
35 2/3
Simplify the trigonometric expression (sin^2(x/2)) (1 + cos(x)) using Half-Angle Identities.
Answer:
B
Step-by-step explanation:
1-cos2x=2sin²(x/2)
[tex]sin^2(\frac{x}{2} )=\frac{(1-cos(2x))}{2}\\(sin^2(\frac{x}{2} ))(1+cos(x))= \frac{(1-cos(2x))(1+cos(x))}{2}[/tex]
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 46 ounces and a standard deviation of 11 ounces.
Use the Empirical Rule and a sketch of the normal distribution in order to answer these questions.
a) 68% of the widget weights lie between________and_______
b) What percentage of the widget weights lie between 24 and 57 ounces?
c) What percentage of the widget weights lie below 79
Using the Empirical Rule, it is found that:
a) 68% of the widget weights lie between 35 and 57.
b) The percentage is 81.5%.
c) The percentage is 99.85%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For this problem, we have that:
In item a, 68% of the widgets are within 1 standard deviation of the mean, hence between 35 and 57.In item b, between 2 standard deviations below the mean(95% of 50% due to the symmetry of the normal distribution) and 1 above(68% of 50%), hence the percentage is: P 34% + 47.5% = 81.5%.For item 3, below 3 standard deviations above the mean, hence removes only the top 0.15%, hence 99.85%.More can be learned about the Empirical Rule at https://brainly.com/question/4079902
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A(4,3) B(1/2, 1/5) C( 3/4, 7/4). Which point lies on the circumstance of the unit circle?
None of the three points (A, B, C) lies on the circumference of the unit circle.
What point is in the circumference of an unit circle?
Unit circles are circles centered at the origin and with a radius of 1. A point is on the circumference if and only if the distance of the point respect to the origin is equal to 1. The distance of each point is determine by Pythagorean theorem:
Point A
[tex]d = \sqrt{4^{2}+3^{2}}[/tex]
d = 5
Point B
[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{1}{5}\right)^{2} }[/tex]
d = √29 /10
d ≈ 0.539
Point C
[tex]d = \sqrt{\left(\frac{3}{4} \right)^{2}+\left(\frac{7}{4} \right)^{2}}[/tex]
d = √58 /4
d ≈ 1.904
None of the three points (A, B, C) lies on the circumference of the unit circle.
RemarkThe statement presents a typing mistake, correct form is shown below:
A(x, y) = (4, 3), B(x, y) = (1/2, 1/5), C(x, y) = (3/4, 7/4). Which point lies on the circumference of the unit circle?
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find the slope of this line
Answer:
0
Step-by-step explanation:
On a graph, any line that is horizontal has a slope of zero. Try any points and and plug them into the slope formula equation
(Y2-Y1/X2-X1).
The answer will always be zero.
The arrival times of geese to a gaggle were recorded (in seconds) and given in the stemplot below.
Stem&Leaf
What is the 12th fastest time a goose took to join the gaggle? Make sure to use labels and avoid the use of abbreviations.
The 12th fastest time a goose took to join the gaggle is 49 seconds.
What is the 12th fastest time a goose took to join the gaggle?
A Stem and Leaf Plot is a type of graph where the data is divided into a stem (the first digit or digits) and a leaf (usually the last digit).
The data in the stem plot arranged from the first fastest time it takes a goose to join the gaggle is: 13, 14, 15, 19, 19, 21, 27, 27, 28, 32, 45, 49, 49, 62, 62.
The 12th fastest time is 49
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a using the strategy to determine the area of the large rectangle
b explain how this strategy relates to the binomial multiplication
c focused on multiplying two binomials, explain a strategy that can be used to multiply any two polynomials
The area of the large rectangle by using the strategy is; 168cm².
What is the area of tge large rectangle?The area of the rectangle can be determined by multiplying the length and width of the rectangle as follows;
Area = Length × width
Area = (10cm + 4cm) × (10cm × 2cm)
Area = (100+20+40+8)cm²
Area = 168 cm².
The strategy used above entails that the two binomials used to represent the length and width of the rectangle are multiplied according to binomial multiplication.
The strategy is that each term of the first binomials is used to multiply the terms in the second polynomial and the aggregate result of the multiplications is determined.
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Need stats help! Answer all questions with equations
The two kinds of formula are used in the excel . One from the data analysis the t test assuming equal variances as nothing was mentioned. But if the t test for the means is used there might be slight variation in the values.
The other formula was of descriptive statistics.
The data was
No of feedback (sec) Feedback (sec) Difference
45 54 9
33 50 17
59 58 -1
32 38 6
30 42 12
27 35 8
29 38 9
59 66 7
64 65 1
38 55 17
The null hypothesis is accepted because t stat= -1.322 is less than t critical which is t critical= ±2.119 and lies in the acceptance region.
The p- value is 2.04 which is greater than alpha= 0.05
The t stat for 0.01= 4.561578674 and t Critical two-tail 3.249835541
The t stat is greater than t critical at alpha 0.01 so it is rejected.
The difference t test gives
Count=N 9 9
Mean 41.2 49.67
Mean Difference 8.4
Standard Deviation 14.967 11.97
Variance 223.944 143.25
Standard Error 2.0824
t = -1.322
df = 16
t Critical two-tail 2.119905285
Confidence Level(95.0%) 4.802039614
Lower CI (95.0%) = 3.6
Upper CI(95.0%)= 13.2
t stat for 0.01= 4.561578674
t Critical two-tail 3.249835541
Confidence Level(99.0%) 6.055710988
Lower CI (99.0%) = 2.345
Upper CI(99.0%)= 14.457
For values between 3.6 and 13.2 we are 95% confident that there is no difference between the means of two given data values.
The null hypothesis is accepted because t stat= -1.322 is less than t critical which is t critical= ±2.119 and lies in the acceptance region.
The p- value is 2.04 which is greater than alpha= 0.05
The t stat for 0.01= 4.561578674 and t Critical two-tail 3.249835541
The t stat is greater than t critical at alpha 0.01 so it is rejected.
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Determine the interval(s) on which the given function is decreasing?
Answer:
[tex](-\infty, -1) \cup (0, \infty)[/tex]
Step-by-step explanation:
The function is decreasing if, as x increases, the value of the function (y) gets smaller. This means as you read the graph from left-to-right, the function is decreasing if the graph is falling.
From -infinity to -1, the graph is falling, then the graph rises (f is increasing) until x =0, then the graph falls again from x = 0 to infinity.
Rectangle MNPQ is rotated using the origin as the center of rotation, resulting in rectangle M’N’P’Q’, as shown below.
On a coordinate plane, rectangle M N P Q has points (negative 2, 6), (0, 4), (negative 3, 1), (negative 5, 3). Rectangle M prime N prime P prime Q prime has points (6, 2), (4, 0), (1, 3), (3, 5).
Which rotation may have occurred?
a 45° rotation clockwise
a 45° rotation counterclockwise
a 90° rotation clockwise
a 90° rotation counterclockwise
Answer:
45° rotation clockwise
Step-by-step explanation:
When you plot these on the graph, the non prime ones are on quadrant 2 and when you plot the prime ones, it is on quadrant 1. This means that it is 45° to the right(clockwise)
⬇️red is prime blue is regular ⬇️
Find the arc length of the partial circle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
The arc length of the partial circle is 7.5π
Calculating arc lengthFrom the question, we are to determine the arc length of the partial circle
The length of an arc can be calculated by using the formula
[tex]l = \frac{\theta}{360^\circ} \times 2\pi r[/tex]
Where [tex]l[/tex] is the length of the arc
[tex]\theta[/tex] is the angle subtended
and r is the radius
From the diagram,
θ = 270°
r = 5
Putting the values into the equation, we get
[tex]l = \frac{270 ^\circ}{360^\circ} \times 2\pi \times 5[/tex]
[tex]l = \frac{3}{4} \times 2\pi \times 5[/tex]
[tex]l = \frac{30\pi}{4}[/tex]
[tex]l = \frac{15}{2}\pi[/tex] OR 7.5π
Hence, the arc length of the partial circle is 7.5π
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How much money is borrowed if the interest rate is 9.25% simple interest and the loan is made for 3.5 years and has 904.88 interest
The amount borrowed is 2795
What is Principal?Principal is the amount loaned or invested in a bank or a financial institution that gives a certain interest on a specific rate over a period of time.
Analysis:
P = principal = unknown
R = rate = 9.25%
T = time = 3.5 years
I = interest = 904.88
simple interest(I) = PRT/100
P = 100I/RT
P = 100 x 904.88/3.5 x 9.25 = 2795
In conclusion, the amount borrowed is 2795.
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What numbers are the arrows pointing to?
a)
b)
c)
60
∞
2.5
70
3.5
Using proportions, the numbers that the arrows are pointing to are:
a) 62.
b) 8.8.
c) 2.8.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In item a, the arrow is 2/10 of the way from 60 to 70, hence the number is:
60 + 0.2(70 - 60) = 60 + 2 = 62.
In item b, the arrow is 8/10 of the way from 8 to 9, hence the number is:
8 + 0.8(9 - 8) = 8.8.
In item c, the arrow is 3/10 of the way from 2.5 to 3.5, hence the number is:
2.5 + 0.3(3.5 - 2.5) = 2.8.
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Pakistan scored 270 runs and fell short of India's score by 10%. How much did
India score?
Answer:
India score 290 more than pakistan
Step-by-step explanation:
India score 20 more
Did you ever purchase a bag of M&M Peanut candies and wonder about the distribution of
the colors? A recent article reported that 30 percent of the candies are brown, 20 percent yellow,
20 percent red, 20 percent green, and 10 percent orange. A one-pound bag of M&M peanut
candies was purchased at Wal-Mart here in Lubbock. A total of 188 candies were in the bag,
with 67 brown, 22 yellow, 51 red, 24 green, and 24 orange.
Fill in the following chart on the frequency of the colors.
Color Brown Yellow Red Orange Blue Green
Observed
Frequency
Expected
Frequency
Using the information from our sample bag, determine if our bag’s distribution matches the
advertised distribution. Use an alpha = 0.05.
1. What is the null hypothesis?
2. What is the alternative hypothesis?
3. What distribution are you using?
4. What test are you running?
5. What is the critical value?
6. What is your test value?
7. What is your conclusion?
The null hypothesis is that the proportions are 0.30, 0.20, 0.20, 0.20, 0.10 and the alternative hypothesis is that the proportions are not as given above.
How to illustrate the information?It should be noted that the null hypothesis is the theory that states that there is no statistical relationship between the variables.
In this case, the Chi square test can be run to get the desired information. Therefore, X² was gotten as 19.597. The degree of freedom is 4 and the p value is 0.0006 from the distribution table.
In this case, the critical value of 0.006 is less than the 0.05. Therefore, we need to reject the null hypothesis.
This implies that there's evidence that the distribution doesn't correlate with what we've.
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Calculate the area of a rectangular field with perimeter 88 cm and length 18 cm
The area of the rectangular field is 468cm².
Step-by-step explanation:
If, length is 18cm; width is unknown( let x represent width). Then,
Perimeter of a rectangle= Length + Width+ Length + Width
88= 18 + x + 18 + x
88= 36 + 2x
88-36 =2x
52= 2x
52/2=2x/2
26=x
•x=26cm
The width of the rectangle is 26cm.
Area of a rectangle= Length × Width
=18cm×26cm
= 468cm².
Find the missing coordinate.
x=t+2
y = 1 + 3/t
(-1,[?])
Answer:
0
Step-by-step explanation:
Since the x coordinate is -1, 2+t = -1, and thus t = -3.
So, y = 1+(3/(-3)) = 0.
40.Find the difference
41&42. Find the product
Answer:
40. 398nine
41: 432six
42: 14714eight
Step-by-step explanation:
765-367=398
The 'nine' is probably confusing you
3x144=432
The 'six' is there to confuse you.
2x7357=14714
The 'eight' is again here to confuse you.
Ignore the 'six' and 'eight' and 'nine' they are making it harder for no reason
select all the statements that are true
Answer:
C & D
Step-by-step explanation:
A. 4 is greater than 0, so use the third equation to find f(x). 4*4 - 1 = 15, so A is wrong.
B. -2 is less than 0, so use the first equation to find f(x). -(-2) + 1 = 3, so B is also wrong.
C. -1 is less than 0, so use the first equation to find f(x). -(-1) + 1 = 2, so C is correct.
D. 1 is greater than 0, so use the third equation to find f(x). 1*1 - 1 = 0, so D is also correct.
A bank charges 12% simple interest p.a. on a cash loans for R10 000,must repay the loan over 4 years.
Calculate the interest which is gonna be paid to the loan?
Answer:
$4800
Step-by-step explanation:
Let's use the simple interest formula, P(1+rt), to find the final amount of the loan
10000(1+.12*4) = 14800, the final amount
14800 - 10000 = 4800 total in interest
find x and y
can someone pls solve
First, we need to understand that these two triangles are
similar.
we know this because their lines (the arrows) prove they are the same direction. A similar triangle does
NOT mean they are proportional,
they are just similar by ratio.
Lets call the triangle on the left ABC and the triangle on the right A'B'C'.
I will attach an image of the labels.
Because they are similar triangles, angle A is the same as angle A'. Angle B is the same as angle B', angle C is the same as angle C'.
Based on that information, we know xº is = 65º. We know that the interior angles add up to 180º. So for triangle A'B'C', we can do 180º-40º-65º which is 70º. This means angle C' is 70º.
Now the important part is getting yº. A line is 180º. That means that 180º-70º=yº which is 110º.
If you do not understand anything, please let me know and I will try to teach you.
Which is the graph of the function f(x) = 1/2x2 + 2x - 6?
Answer:i would need to see the graph but here is what i think you are talking about and it shows how to it popular- problems /Algebra/ 262080
Step-by-step explanation:
Answer: man i wish i knew
Step-by-step explanation:
Find the value of variable X.
16
41
10
17.5
Using secant rule, the value of variable x in the diagram is 10.
What is a secant?A secant is a line that intersect a circle in two points.
Therefore, the following rule guides a secant.
(x + 32)32 = (20 + 28)28
Hence,
32x + 1024 = (48)28
32x + 1024 = 1344
32x = 1344 - 1024
32x = 320
divide both sides by 32
32x / 32 = 320 / 32
x = 10
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