Considering the Set A and B given, Applying inclusion - exclusion principle the number of elements common to both Sets is 10
What is inclusion - exclusion principle?This is a counting techniques that ensures that elements are not counted twice
It is achieved by the formula:
(A ∪ B) = n(A) + n(B) - n(A ∩ B)
Finding the elements Sets A and B have in commonThe information from the question include the following
Set A contains 48 elements
Set B contains 16 elements
The total number elements in either Set A or Set B is 54
Applying inclusion - exclusion principle gives the formula
Set A + Set B - ( Set A ∩ Set B ) = Set A ∪ Set B
substituting the values gives
48 + 16 - ( Set A ∩ Set B ) = 54
48 + 16 - 54 = ( Set A ∩ Set B )
10 = ( Set A ∩ Set B )
( Set A ∩ Set B ) = elements Sets A and B have in common
Therefore the number of the elements common to Sets A and B is 10
Learn more on Sets here; https://brainly.com/question/13458417
#SPJ1
How many different arrangements of 5 be formed if the first must Work (of allowed?
ANSWER
There are 913,952 different 5-letter combinations that can be formed.
EXPLANATION
Recall that there are 26 letters in the English Alphabet.
From the question, we are to find the arrangement of 5 letters with the first letter being either W or K, and repetition of letters is allowed.
The possibilities for the 1st letter is 2 since the 1st letter can be either W or K;
More so, the possibilities for the 2nd letter is 26;
The possibilities for the 3rd letter is 26;
The possibilities for the 4th letter is 26, and
The possibilities for the 5th letter is 26;
The possibilities of arranging 5 letters = 2 x 26 x 26 x 26 x 26 = 913,952.
Hence, a total of 913,952 different 5-letter combinations can be formed.
How many different lineups can Coach Lay create using 10 girls to fill 5 spots on the basketball court. Positions do not matter.
This is the formula for combinations
In this case, n = 10 and k = 5
C = 10!/(10-5)!(5)! = 3628800/(120)(120) = 3628800/14400 = 252
Answer:
252 different line u
74. Noam wants to put a fence around his rectangular garden. His garden measures 35 feet by 50 feet. Thegarden has a path around it that is 3 feet wide. How much fencing material does Noam need to enclose thegarden and path?A. 97 ftB. 194 ftC. 182 ftD. 146 ft
Given:
The length of the rectangular garden, l=50 feet.
The breadth of the rectangular garden, b=35 feet.
The width of the path around the garden, w=3 feet.
The figure can be drawn as,
So, the length of the fence, L=l+2w.
The breadth of the fence, B=b+2w
The perimeter of the fence can be calculated as,
[tex]\begin{gathered} P=2(L+B) \\ =2(l+2w+b+2w) \\ =2(l+b+4w) \\ =2(50+35+4\times3) \\ =2(50+35+12) \\ =2\times97 \\ =194\text{ ft} \end{gathered}[/tex]Therefore, the perimeter of the fence is 194 ft.
Option B is correct.
Triangle XYZ is rotated 90° counterclockwise about the origin.The result is Triangle X'Y'Z', as shown below.
A shortcut for a 90° counterclockwise rotation:
• If the point (h, k) is rotated 90° counterclockwise rotation, then the final point will be (-k, h).
Answer:
Therefore the coordinates would be:
• X,(-5, 3) → ,X',(-3, -5)
,• Y,(-1, 1) → ,Y',(-1, -1)
,• Z,(-8, -4) → ,Z',(4, -8)
Then, the rule is (x, y) → (-y, x).
A boat travels 82 km on a 160 degree course. Find the distances it travel south and east, respectively
A boat travels 82 km on a 160-degree course. Find the distances it travels south and east, respectively
see the attached figure to better understand the problem
step 1
Find out the East's distance (dx)
we have that
cos(20)=dx/82
dx=82*cos(20)
dx=77.05 Kmstep 2
Find out the South's distance (dy)
sin(20)=dy/82
dy=82*sin(20)
dy=28.05 KmThor is at the lowest point of Asgard whichis 280 feet below sea level (-280 ft.). He flies tothe highest point 520 feet above sea level(520 ft.). How far did he fly? Answer in acomplete sentence.
We have that:
We want to find how far did he fly. This means, we want to find the distance between -280 ft and 520 ft. (Which is 520 ft + 280 ft = 800 ft)
In order to find it out we substract them (we substract the first measure from the second):
520 - (-280)
Since - (-280) = +280, then
520 - (-280) = 520 + 280
= 800
Answer: he flied 800 ft
Solve for x
4x = -5
Put the answer in its simplest form.
Answer:
[tex] \sf x=-1.25 [/tex]
[tex]\sf--------------------------------------------------------------------- [/tex]
Step-by-step explanation:
4x = -5
Divide both sides by 4 to single out the variable
4x/4 = -5/4
x = -1.25
What does the y-intercept mean? What does the x-intercept mean? Explain what each intercept means and then Identify the x-intercept and y-intercept from each equation.A. y=7/2x -2B. x=-3
x intercept = where the function crosses the x axis (x,0)
y intercept = where the function crosses the y-axis (0,y)
A. y=7/2x-2
x intercept , replace y by 0 and solve for x:
0 =7/2x-2
2= 7/2 x
2 / (7/2) = x
x= 4/7
y-intercept, replace x by 0 and solve for y
y= 7/2x-2
y= 7/2 (0) -2
y=-2
B.
x-intercept:
x=-3
y-intercept
0=-3
It doesn't have a y-intercept.
Use the functions f(x) = 8x + 11 and g(x) = 4x² + 7x - 2 to evaluate the following:a. f(8) =b. f(-8)=c. g(6) =d. g(-7)=e. g(a) =
Given:
f(x) = 8x + 11
g(x) = 4x² + 7x - 2
We are asked to evaluate using the following:
(a) f(8)
f(8) = 8(8) + 11
f(8) = 64 + 11
f(8) = 75
(b) f(-8)
f(-8) = 8(-8) + 11
f(-8) = -64 + 11
f(-8) = -53
(c) g(6)
g(6) = 4(6)² + 7(6) - 2
g(6) = 4(36) + 42 - 2
g(6) = 144 + 42 - 2
g(6) = 184
(d) g(-7)
g(-7) = 4(-7)² + 7(-7) - 2
g(-7) = 4(49) - 49 - 2
g(-7) = 196 - 49 - 2
g(-7) = 145
(e) g(a)
g(a) = 4(a)² + 7(a) - 2
g(a) = 4a² + 7a - 2
Finding Angles with JustificationIn the diagram below BC = EC and m
Answer:
Angle Reason
m∠ECD = 140 Given
m∠ECB = 40 Supplementary angles
m∠EBC = 70 Isosceles triangle
m∠ABE = 110 Supplementary angles
Explanation:
Angle ECB and CED are supplementary because they form a straight line and their sum is 180 degrees. So, we can calculate the measure of ∠ECB as
m∠ECB = 180 - 140
m∠ECB = 40
Then, the interior sum of the angles of a triangle is equal to 180 degrees, so
m∠ECB + m∠EBC + m∠BEC = 180
40 + m∠EBC + m∠BEC = 180
However, m∠EBC = m∠BEC because triangle ABC is an isosceles triangle where 2 sides have the same length BC and EC. So, we can find m∠EBC as follows
40 + m∠EBC + m∠EBC = 180
40 + 2m∠EBC = 180
40 + 2m∠EBC - 40 = 180 - 40
2m∠EBC = 140
m∠EBC = 140/2
m∠EBC = 70
Then, the measure of ∠ABE is equal to
∠ABE = 180 - m∠EBC
∠ABE = 180 - 70
∠ABE = 110
Therefore, we can answer it as follows
Angle Reason
m∠ECD = 140 Given
m∠ECB = 40 Supplementary angles
m∠EBC = 70 Isosceles triangle
m∠ABE = 110 Supplementary angles
How many modes does the following dataset have? 9,29,13,4,2,16,10,14,27
Given:
[tex]9,29,13,4,2,16,10,14,27[/tex]To find- the mode of the given dataset.
Explanation-
We know that the mode is the most occuring frequency of the dataset. Let us arrange the data in ascending order first, and we get
[tex]2,4,9,10,13,14,16,27,29[/tex]Since there is no repeated frequency, we can say that there is no mode for the given data set.
The answer is 0.
The length of the diagonal of a Rectangle is 14cm,and it forms a 30 degree angle in one corner of the rectangle.What is the area of the rectangle.(A=LxW)
We can find W and L using the sine and the cosine functions:
[tex]\begin{gathered} \sin (30)=\frac{W}{14} \\ so\colon \\ W=14\cdot\sin (30) \\ --------- \\ \cos (30)=\frac{L}{14} \\ so\colon \\ L=14\cdot\cos (30) \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} A=L\cdot W \\ A=14\cdot\cos (30)\cdot14\cdot\sin (30) \\ A=49\sqrt[]{3} \\ A\approx84.87cm^2 \end{gathered}[/tex]Answer:
84.87 cm²
Kayla wants to have new doors installed in herhome. A door company charges a one-time fee of$125 plus $ per window installed. Write anexpression that represents the total cost to installnew windows in terms of the number of windows(w) installed.
Kayla wants to have new doors installed.
The door company charges $125 as a one time fee.
They also charge $50 per window installed.
If the number of new windows installed is w, then it means that to install w new windows, they will charge an additional:
w * 50 = $50w
This will be in addition to the one time fee.
Let T be the total cost of installation.
Therefore, the total cost for installing w new windows (in dollars) is:
T = 125 + 50w
use the formula Sn to find the sum of the first five terms of the geometric sequence.
First, find the common ratio r:
-4/9 : 4/3 = -1/3
4/3 : -4 = -1/3
-4:12 = -1/3
r= -1/3
[tex]Sn=\frac{a(r^n-1)}{r-1}[/tex]Where:
a= first term = 12
n= number of terms = 5
Replacing:
[tex]Sn=\frac{12(-\frac{1^{}}{3}^5-1)}{-\frac{1}{3}-1}[/tex]Sn= 244/27 = 9 1/27
9.State the slope and y-value of the y-intercept of the equation, y = 6x + 9Slopey-intercept
The slope is 6 and the y-intercept is 9
Explanation:The given equation is:
y = 6x + 9
The general form of the equation of a line is
y = mx + c
where m is the slope and c is the y-intercept.
Comparing these equations, we see that
m = 6 and c = 9
Therefore, the slope is 6 and the y-intercept is 9
which graph represents the solution to -1/2m>7/11
The graph of the inequality:
(-1/2)*m > 7/11
Can be seen in the image at the end.
Which graph represents the solution for the inequality?Here we have the following inequality:
(-1/2)*m > 7/11
First, let's solve this for m, this means that we need to isolate the variable in one side of the inequality.
If we multiply both sides by -2, we get:
-2*(-1/2)*m < -2*(7/11)
Where the direction of the symbol changes because we are multiplying by a negative number.
m < -14/11
The graph of this will be an open circle at -14/11 and an arrow that goes to the left, like the one below.
Learn more about inequalities:
https://brainly.com/question/24372553
#SPJ1
Painter charges $20 every hour that he paints let H represent the number of hours he paints & E represent his earnings select all statements that are trueA. The equation H equals 20 E shows the correct relationship between the earnings and hours worked B. With this hourly rate the painter must work more than 12 hours to earn 500C. With this hourly rate the painter earns 20h dollars for each hour worked.D. With this hourly rate if the painter works 10 hours he earns 20.E. Is the painter raises his hourly rate by two dollars the new equation is e=22h
Answer:
No.
Yes.
Yes.
No.
Yes...
differentiate t^4 In(8cost)
⇒It is way more appropriate if I use the product rule. That states that:
⇒f(x)g(x)=f'(x)g(x)+f(x)g'(x)
[tex]t^{4} In(8cos(t))\\=4t^{3}In(8cos(t))+t^{4} \frac{1}{8cos(t)} *(0cos(t)+8*(-sin(t))*1)\\=4t^{3}In(8cos(t))+\frac{t^{4}-8sin(t)}{8cos(t)}[/tex]
Note:
Given F(x)=In(x)
⇒[tex]F'(x)=\frac{1}{x}[/tex]
Goodluck
Answer:
t^3 (4 ln(cos8t) - t tant)
Step-by-step explanation:
Using the Product Rule:
dy/dt = t^4 * d(ln(8cost) / dt + ln(8cost) * d(t^4)/dt
= t^4 * 1/ (8cost) * (-8sint) + 4t^3 ln(8cost)
= -8t^4 sint / 8 cost + 4t^3 ln(8cost)
= -t^4 tan t + 4t^3 ln(8cost)
= t^3 (4 ln(cos8t) - t tant)
Evaluate the expression shown below and write your answer as a fraction in
simplest form.
-3/8+(-9/10)
Answer:
-1 11/40
Step-by-step explanation:
-51/40 this is simplest form.
Step-by-step explanation:
Hello am just trying to see if I did this right
Answer
Variable
c = Cost of one bag of chips
Equation
2.50 + 3c = 5.05
Solution
c = Cost of one bag of chips = 0.85 dollars
Explanation
Cost of one juice pouch = 1.25 dollars
Cost of 2 juice pouches = 2(1.25) = 2.50 dollars
Cost of a bag of chips = c dollars
Cost of 3 bags of chips = (3)(c) = (3c) dollars
(Cost of two juice pouches) + (Cost of three bags of chips) = Total Cost
2(1.25) + 3c = 5.05
2.50 + 3c = 5.05
Subtract 2.50 from both sides
2.50 + 3c - 2.50 = 5.05 - 2.50
3c = 2.55
Divide both sides by 3
(3c/3) = (2.55/3)
c = 0.85 dollars
Hope this Helps!!!
you own a pet store that sells fish tank you brought a fish tank for $35 and are going to mark it up 20% what is the selling price going to be on the fish tank
If you're marking the fish tank up by 20%, it means you're looking to sell it at 120% of its original value.
Now, let's use a rule of three to calculate such percentage:
Thereby,
[tex]x=\frac{120\cdot35}{100}\rightarrow x=42[/tex]The selling price would be $42
The table below shows the average annual cost of health insurance for a single individual, from 1999 to 2019, according to the Kaiser Family Foundation.YearCost1999$2,1962000$2,4712001$2,6892002$3,0832003$3,3832004$3,6952005$4,0242006$4,2422007$4,4792008$4,7042009$4,8242010$5,0492011 $5,4292012$5,6152013$5,8842014$6,0252015$6,2512016$6,1962017$6,4352017$6,8962019$7,186(a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).Pt = (b) Using this linear model, predict the cost of insurance in 2030.$ (c) = According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020)..
The given data plot will look thus:
a) Building a model using just the 1999 and 2019 years:
[tex]\begin{gathered} 1999\rightarrow0\rightarrow2196 \\ 2019\rightarrow20\rightarrow7186 \\ \text{Havng} \\ x_1=0,y_1=2196 \\ x_2=20,y_2=7186 \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}_{} \\ \text{The model will be:} \\ P_t=249.5t+2196 \end{gathered}[/tex]b) The cost of insurance in 2030
[tex]\begin{gathered} P_t=249.5t+2196 \\ t=2030-1999=31 \\ \text{The cost of insurance in 2030 therefore will be:} \\ =249.5(31)+2196 \\ =7734.5+2196 \\ =\text{ \$9930.5} \end{gathered}[/tex]c) When do we expect the cost to reach $12,000
[tex]\begin{gathered} P_t=249.5t+2196 \\ 12,000=249.5t+2196 \\ 12000-2196=249.5t \\ 9804=249.5t \\ \frac{9804}{249.5}=\frac{249.5t}{249.5} \\ 39.2946=t \\ Since\text{ t = year -1999} \\ 39.2946+1999=\text{year} \\ 2038.2946=\text{year} \\ Since\text{ we are to give our answer as an exact year} \\ \text{The year will be }2039. \end{gathered}[/tex]it's Hamilton path and Hamilton circuitweighted graph / graph theoryyou have to add each angle up and find the answer for each row 12 grade math
What you need to do in order to solve this is add the values that are defined by the begining and end points declared in there:
[tex]A\text{ B D E C A}[/tex]that means the distance defined by AB, BD, DE, EC & CA:
[tex]4+8+11+10+8\text{ = 41}[/tex]And in the same manner all of the other series of distances.
4x + x + 4 = 8x -3x + 4
x can take any real value
Explanation
[tex]4x+x+4=8x-3x+4[/tex]
Step 1
add similar terms in both sides
[tex]\begin{gathered} 4x+x+4=8x-3x+4 \\ 5x+4=5x+4 \end{gathered}[/tex]Step 2
subtract 5x+4 in both sides
[tex]\begin{gathered} 5x+4=5x+4 \\ 5x+4-(5x+4)=5x+4-(5x+4) \\ 0=0 \end{gathered}[/tex]0=00 means that as an equation, its solution is that x can take any real value .
I hope this helps you
I just need to know the answer quick because I have to go somewhere
From the given graph, it is seen that f(x) is not defined for x<-4. The function g(x) is not defined for x>2
But the function p(x) represents a straight line which is defined for all real x.
Hence, the function p(x) has all real numbers as its domain.
Thus, the correct option is (D)
The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt. Find the probability of wearing a seat belt, given that the driver did not survive a car accident. Part 1: The probability as a decimal is _ (Round to 3 decimal places as needed.) Part 2: The probability as a fraction is _
Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
The table shows the outcome of car accidents by whether or not the driver wearing a seat belt.
Let's call:
A = The event of the driver wearing a seat belt in a car accident.
B = The event of the driver dying in a car accident
The conditional probability is calculated as follows:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]The conditional probability stated in the formula is that for the driver wearing a seat belt knowing he did not survive the car accident.
The numerator of the formula is the probability of both events occurring, i.e., the driver wore a seat belt and died. The denominator is the simple probability that the driver died in a car accident.
From the table, we can intersect the first column and the second row to find the number of outcomes where both events occurred. The probability of A ∩ B is:
[tex]P(A\cap B)=\frac{511}{583,470}[/tex]The probability of B is:
[tex]P(B)=\frac{2217}{583,470}[/tex]The required probability is:
[tex]P(A|B)=\frac{\frac{511}{583,470}}{\frac{2217}{583,470}}[/tex]Simplifying the common denominators:
[tex]P(A|B)=\frac{511}{2217}=0.230[/tex]Hello I need help with this question as fast as possible please , I am on my last few questions and I have been studying all day for my final exam for math tomorrow. It is past my bed time and I am exhausted . Thank you so much for understanding:))
Notice that:
[tex]665.6=10.4\times64.[/tex]Therefore, if we divide the resulting equation of step 3 by 10.4 we get:
[tex]\begin{gathered} \frac{10.4x}{10.4}=\frac{665.6}{10.4}, \\ x=64. \end{gathered}[/tex]Then the missing step is:
Divide both sides of the equation by 10.4.
Answer: Last option.
Instructions: Factor 2x2 + 252 + 50. Rewrite the trinomial with the c-term expanded, using the two factors. Answer: 24 50
Given the polynomial:
[tex]undefined[/tex]Two cars are driving on the same road, in the same
direction. They start driving from the same place and are
traveling at a constant speed. The second car started
driving 1.5 hours after the first car started driving. If the
second car drives 60 miles per hour and the first drives 40
miles per hour, how many miles will each car have
traveled when the second car catches up to the first?
Answer:
180 miles
Step-by-step explanation:
distance = rate x time
t = time
1st car:
distance = 40t
2nd car:
distance = 60(t - 1,5)
When the car catch up to each other the distances will be the same, so set the equation equal to each other. Calculate the time and then put the time back into either equation and solve for the distance.
40t = 60(t-1.5) Distribute the 60
40t = 60t -(60)1.5
40t = 60t - 90 Subtract 60t from both sides of the equation
-20t = -90 Divide both sides by -20
t = 4.5
Now that we know the time, substitue that back into either equaiton and solve for the time
distance = 40 (4.5)
180 miles
Solve any quality express your answer in interval notation you decimal forms for numerical values
Solution
[tex]\begin{gathered} 5z-11<-6.6+3z \\ Subtract\text{ 3z from both side} \\ 5z-3z-11<-6.6+3z-3z \\ 2z-11<-6.6 \\ Add\text{ 11 to both sides } \\ 2z-11+11<-6.6+11 \\ 2z<4.4 \\ \end{gathered}[/tex][tex]\begin{gathered} Divide\text{ both sides by 2} \\ \frac{2z}{2}<\frac{4.4}{2} \\ z<2.2 \\ z<2.2 \end{gathered}[/tex]In interval notation, we have
[tex]\left(-\infty \:,\:2.2\right)[/tex]The answer is
[tex]\left(-\infty \:,\:2.2\right)[/tex]