When the members of a family discussed where their annual reunion should take place, they found that out of all the family members, 10 would not go to a park, 9 would not go to a beach, 11 would not go to the family cottage, 3 would go to neither a park nor a beach, 4 would go to neither a beach nor the family cottage, 6 would go to neither a park nor the family cottage, 1 would not go to apark or a beach or to the family cottage,and 2 would go to all three places. What is the total number of family members?
Answers
Answer:
20
Explanation:
Let:
• NP = The non-park goers.
,• NB = The non-beach goers.
,• NC = The non-cottage goers.
The Venn diagram below is used to represent the given information:
Given:
• There are 10 non-park goers: a+b+c+g=10
,• There are 9 non-beach goers: b+d+e+g=9
,• There are 11 non-cottages goers: c+e+f+g=11
,• There are 3 non-park and non-beach goers: b+g=3
,• There are 4 non-beach and non-cottage goers: e+g = 4
,• There are 6 non-park and non-cottage goers: c+g=6
,• There is 1 non-park, non-beach, and non-cottage goer: g=1
,• There are 2 who are neither a non-park, non-beach, or non-cottage goer: h=2
So, the total number of family members will be:
[tex]Total=a+b+c+d+e+f+g+h[/tex]Since g=1:
[tex]\begin{gathered} b+g=3\implies b+1=3\implies b=2 \\ c+g=6\operatorname{\implies}c+1=6\operatorname{\implies}c=5 \\ e+g=4\operatorname{\implies}e+1=4\operatorname{\implies}e=3 \end{gathered}[/tex]Next:
[tex]\begin{gathered} c+e+f+g=11 \\ 5+3+f+1=11 \\ f+9=11 \\ f=11-9 \\ f=2 \end{gathered}[/tex]Next:
[tex]\begin{gathered} b+d+e+g=9 \\ 2+d+3+1=9 \\ d+6=9 \\ d=9-6 \\ d=3 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} Total=(a+b+c+g)+d+e+f+h \\ =10+3+3+2+2 \\ =20 \end{gathered}[/tex]The total number of family members is 20.
Related Questions
Consider the scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5800. By 2012 the population had dropped to 4,600. Assume the trend continues predict the population in 2016.
Answers
Given:
In 2010 the population was 5800.
2012 the population had dropped to 4,600.
Let 't=0' be the year 2010.
P(t) represents the year population of the town t years after 2010.
Slope of a function P(t) is
[tex]\begin{gathered} m=\frac{4600-5800}{2012-2010} \\ m=-600 \end{gathered}[/tex]Population of town t years after 2010.
[tex]P(t)=-600(t)+5800[/tex]Population in the year 2016 that is t=6
[tex]\begin{gathered} P(6)=-600(6)+5800 \\ =2200 \end{gathered}[/tex]Population in the year 2016 is 2200
Josslyn has nickels and dimes in her pocket. The number of nickels is three more than seven times the number of dimes let d represent the number of dimes. Write the expression for the number of nickels
Answers
to solve this we need to translate into math terms, so
Step 1
a) let d represents the number of dimes
let n represents the number of nickles
so
re write the expressions
[tex]\begin{gathered} number\text{ of dimes=d} \\ seven\text{ times the number of dimes = 7d} \\ \end{gathered}[/tex]The number of nickels is three more than seven times the number of dimes in other words you have to add 7 to seven times the number of dimes to obtain the number of nickles
hence
[tex]n=7d+3[/tex]therefore , the expression for the number of nickles is
[tex]7d+3[/tex]I hope this helps you
Perform the indicated operation -27÷-9
Answers
-27/9 = -3
answer is -3
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 6z
Answers
Answer:
(-1, 7, - 4)(1, -1, 4)=====================
Given systemx² + z² = 174x + y = 3y + z = 3Rearrange the last two equation4x = 3 - yz = 3 - yThis gives us:
z = 4xSubstitute the value of z into fist equationx² + (4x)² = 17x² + 16x² = 1717x² = 17x² = 1x = 1 and x = - 1Find values of z and yx = 1 ⇒ z = 4*1 = 4 ⇒ y = 3 - 4 = - 1 x = - 1 ⇒ z = 4*(-1) = - 4 ⇒ y = 3 - (-4) = 7Answer:
[tex](x,y,z)=\left(\; \boxed{-1,7,-4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y,z)=\left(\; \boxed{1,-1,4} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}x^2+z^2=17\\\;4x+y=3\\\;\;\;y+z=3\end{cases}[/tex]
To solve by the method of substitution, first rearrange the third equation to make y the subject:
[tex]\implies y=3-z[/tex]
Substitute this into the second equation and solve for z:
[tex]\begin{aligned}\implies 4x+(3-z)&=3\\3-z&=3-4x\\-z&=-4x\\z&=4x\end{aligned}[/tex]
Substitute the found expression for z into the first equation and solve for x:
[tex]\begin{aligned}\implies x^2+(4x)^2&=17\\x^2+16x^2&=17\\17x^2&=17\\x^2&=1\\x&=\pm1\end{aligned}[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}\implies x=-1 \implies 4(-1)+y&=3\\-4+y&=3\\y&=7\end{aligned}[/tex]
[tex]\begin{aligned}\implies x=1 \implies 4(1)+y&=3\\4+y&=3\\y&=-1\end{aligned}[/tex]
Substitute the found values of x into the derived expression for z and solve for z:
[tex]\begin{aligned}\implies x=-1 \implies z&=4(-1)\\z&=-4\end{aligned}[/tex]
[tex]\begin{aligned}\implies x=1 \implies z&=4(1)\\z&=4\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y,z)=\left(\; \boxed{-1,7,-4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y,z)=\left(\; \boxed{1,-1,4} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Algebraically determine whether each of the following functions is even, odd or neither. then graph it B. y = x^3 – 3 C. y = 2x^3 - x
Answers
According to the even and odd function rules, we found out that the function [tex]y=x^{3}-3[/tex] is neither even nor odd and the function [tex]y=2x^{3}-x[/tex] is an odd function.
It is given to us that the functions are -
B. [tex]y=x^{3}-3[/tex]
C. [tex]y=2x^{3}-x[/tex]
We want to determine each of the following functions is even, odd or neither.
To see if the function is even, we have to check if [tex]f(-x)=f(x)[/tex]
To see if the function is odd, we have to check if [tex]f(-x)=-f(x)[/tex]
B. Here, we have
[tex]y=x^{3}-3\\= > f(x)=x^{3}-3\\= > f(-x)=(-x)^{3}-3\\= > f(-x)=-x^{3}-3[/tex]
We see that [tex]f(-x)\neq f(x)[/tex]. This implies that the function is not even.
Also, [tex]f(-x)\neq -f(x)[/tex]. This implies that the function is not odd.
Therefore, this function is neither even nor odd.
C. Here, we have
[tex]y=2x^{3}-x\\= > f(x)=2x^{3}-x\\= > f(-x)=2(-x)^{3}-(-x)\\= > f(-x)=-2x^{3}+x[/tex]
We see that [tex]f(-x)\neq f(x)[/tex]. This implies that the function is not even.
However,
[tex]f(-x)=-2x^{3}+x\\= > f(-x)= -(2x^{3}-x)\\ = > f(-x)=-f(x)[/tex]
This implies that the function is odd.
Therefore, this function is odd.
Thus, the function [tex]y=x^{3}-3[/tex] is neither even nor odd and the function [tex]y=2x^{3}-x[/tex] is an odd function.
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Hi!A particle moves along a straight line, so its speed is () = ^2 − + 6, where t is the time measured in seconds and the speed is measured in meters timessecond.a) Calculate the distance traveled between the seconds t=1 and t=3
Answers
In this problem
the distance traveled between the seconds t=1 and t=3 is given by
[tex]\int_1^3(t^2-t+6)dt=\frac{50}{3}\text{ m}[/tex]The answer is
50/3 metersor 16.67 metersExplanation of integrals
In this problem we have
[tex]\int_1^3(t^2-t+6)dt=\int_1^3t^2dt-\int_1^3tdt+\int_1^36dt[/tex][tex]\begin{gathered} \int_1^3t^2dt=\frac{t^3}{3} \\ Evaluate\text{ at 3 and 1} \\ \frac{(3)^3}{3}-\frac{1^3}{3}=\frac{27}{3}-\frac{1}{3}=\frac{26}{3} \end{gathered}[/tex][tex]\begin{gathered} -\int_1^3tdt=-\frac{t^2}{2} \\ evaluate\text{ at 3 and 1} \\ -\frac{3^2}{2}+\frac{1^2}{2}=-\frac{9}{2}+\frac{1}{2}=-4 \end{gathered}[/tex][tex]\begin{gathered} \int_1^36dt=6t \\ evaluate\text{ at 3 and 1} \\ 6(3)-6(1)=12 \end{gathered}[/tex]substitute
[tex]\int_1^3t^2dt-\int_1^3tdt+\int_1^36dt=\frac{26}{3}-4+12=\frac{50}{3}[/tex]Simplify. Assume that all variables result in nonzero denominators.
2n^3 y−8n^2 y/3y^4 * 12/n-4
Answers
The simplified form of given expression 2n^3 y−8n^2 y/3y^4 * 12/n-4 is 8n^2/y^3
In this question, we have been given an expression.
2n^3 y−8n^2 y/3y^4 * 12/n-4
We need to simplify given expression.
2n^3 y − 8n^2 y/3y^4 * 12/n-4
= [2n^2y (n - 4)] / 3y^4 * 12/(n - 4)
= 4 * (2n^2y)/y^4
= 8n^2/y^3
Therefore, the simplified form of given expression 2n^3 y−8n^2 y/3y^4 * 12/n-4 is 8n^2/y^3
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The graph of f(x) = x² is translated to formg(x) = (x-2)2-3.--5-4-3-2-1-2+Which graph represents g(x)?#
Answers
Step 1
Plot the graph of f(x)
[tex]f(x)=x^2[/tex]Step 2
The function of g(x) suggests that f(x);
[tex]\begin{gathered} 1)\text{ it was moved 2 units towards the right} \\ 2)\text{ It was then moved 3 units down} \end{gathered}[/tex]Thus, the graph of g(x) will look like this;
Answer;
What is the equation for the linear model in the scatterplot obtained by choosing the two points closest to the line
Answers
consider two points closest to the line. say ,
[tex]\begin{gathered} (x_1,y_1)=(6,0) \\ (x_2_{}_{}_{},y_2)=(8,1) \end{gathered}[/tex]let us find the slope, m by the formula
[tex]m=\frac{y_2-y_1}{x_2_{}_{}-x_1}[/tex]subsitute the points in the formula,
[tex]\begin{gathered} m=\frac{1-0}{8-6} \\ m=\frac{1}{2} \end{gathered}[/tex]let us find the y - intercept.
[tex]y=mx+b\ldots(1)[/tex]subsitute the one of the point (6,0) in the above equation.
[tex]\begin{gathered} 0=\frac{1}{2}\times6+b \\ 0=3+b \\ b=-3 \end{gathered}[/tex]thus,
subsitute m= 1/2 and b = - 3 in the equation (1),
[tex]y=\frac{1}{2}x-3[/tex]I need help with triangles
Answers
what digit is in the
Answers
Rounding each number to the nearest ten:
• 96 = 100
,• 63 = 60
,• 27 = 30
,• 76 = 80
Sum with rounded numbers:
[tex]100\text{ + 60+30+80=270}[/tex]Answer = 270
find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores. z= 1 and z= 1.9
Answers
The area, to the nearest thousandth, of the standard normal distribution between the z-scores z= 1 and z= 1.9 is 0.130
Hello I need help with this I’m in a rush thanks
Answers
Recall that:
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)},[/tex]and that the domain of a rational function consists of all real numbers such that the denominator is different from zero.
If f(x)=5x+3 and g(x)=4x-5 we get that:
[tex]\frac{f}{g}(x)=\frac{5x+3}{4x-5}\text{.}[/tex]The domain of the above rational function is:
[tex]\begin{gathered} \mleft\lbrace x|g(x)\ne0\mright\rbrace=\lbrace x|4x-5\ne0\rbrace \\ =\lbrace x|4x\ne5\rbrace=\lbrace x|x\ne\frac{5}{4}\rbrace\text{.} \end{gathered}[/tex]Answer: Last option.
I tested positive for covid yesterday so i have no motivation to do this problem. Please don’t be slow when answering, I am every tired.
Answers
The value of sector KL is 52
If JM and KN are two diamters of the circle,
then they intersect at the center
The sector JK and NM are equal
Thus,
The sector JN and KM are also equal
sector KM = sector KL + sector LM
Sector JN = Sector KM
sector JN = sector KL + sector LM
125 = 6x + 4 + 8x + 9
125 = 14x + 13
14x = 125 - 13
14x = 112
x = 8
sector KL = 6x + 4
= 6(8) + 4 = 48 + 4 = 52
Therefore, the sector KL is 52
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Which Venn diagram correctly shows the relationships between the subsets of rational numbers?
Answers
By definition, consider that natural numbers are all numbers from 1 to infinity. Whole numbers are the same natutal numbers plus zero. Integers are all numbers from minus infinity to infinity and rational are all number with finite decimals, and periodic infinite decimals.
Then, based on the previous description, the diagram which correctly shows the subsets of rational numbers is:
diagram F.
If 20 assemblers can complete a certain job in 6 hours, how long will the same job take if the number of assemblers is cut back to 8?
Answers
ANSWER
[tex]15[/tex]EXPLANATION
For 1 assembler, it will take;
[tex]\begin{gathered} 20\times R\times6=1 \\ R=\frac{1}{120} \end{gathered}[/tex]For 8 assemblers;
[tex]8\times R\times T=1[/tex]Substitute R
[tex]\begin{gathered} 8\times R\times T=1 \\ 8\times\frac{1}{120}\times T=1 \\ \frac{8T}{120}=1 \\ 8T=120 \\ T=\frac{120}{8} \\ =15 \end{gathered}[/tex]find x=, if x-3=13 please
Answers
Answer:
[tex]x - 3 = 13 \\ \\ x = 13 + 3 \\ \\ x = 16[/tex]
-3 goes to other side and changes into +3
Question content area topPart 1A medical researcher administers an experimental medical treatment to patients. The patients in the study are categorized by blood types A, B, AB, and O. The researcher observed that the treatment had a favorable outcome for of the patients with blood type A, of the patients with blood type B, of the patients with blood type AB, and none of the patients with blood type O. Use this information to complete parts (a) through (d).
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
total patients = 300
type A:
total patients = 90
favourable patients = 27
type B:
total patients = 124
favourable patients = 31
type AB:
total patients = 6
favourable patients = 6
type O:
total patients = 80
favourable patients = 0
Step 02:
empirical probability:
probability = favourable outcomes / total outcomes
probability (A) = 27/ 90 = 0.3
probability (B) = 31 / 124 = 0.25
probability (AB) = 6 / 6 = 1
probability (O) = 0 / 80 = 0
That is the full solution.
Suppose a binomial trial has a probability of success of 0.3 and 450 trials are performed. What is the standard deviation of the possible outcomes?6.3614.8511.629.72
Answers
The standard deviation of a binomial distribution with n trials and a probability of success of p is given by the formula:
[tex]\sigma=\sqrt[]{n\cdot p\cdot(1-p)}[/tex]From the problem, we identify:
[tex]\begin{gathered} n=450 \\ p=0.3 \end{gathered}[/tex]Then:
[tex]\begin{gathered} \sigma=\sqrt[]{450\cdot0.3\cdot(1-0.3)}=\sqrt[]{450\cdot0.3\cdot0.7} \\ \sigma\approx9.72 \end{gathered}[/tex]Which graph represents the function f(x) = -x + 31?
Answers
Answer:
Step-by-step explanation:
I hope this helps! :) If it does could you please mark me brainliest?
Answer:
Slope : -1
y = intercept : (0,31)
Step-by-step explanation:
which measurement could create more than one triangle measuring 20 cm / 9 cm and 10cm be a triangle with sides measuring 10 cm and 20 cm and included angle measurement 65 C a right angle with acute angles measuring 45 and 45 d a triangle with sides measuring 15 in 20 in and 25 in
Answers
Input data
The triangles created by the measurements of options A, B and D have specific side lengths. Therefore, you cannot create more than one triangle.
However, for a triangle with acute angles measuring 45° and 45°, a countless number of similar triangles (triangles with the same shape but different sizes) can be created.
The correct choice is C.
what is the surface area, in square centimeters, of the pyramid ?
Answers
17. In trapezoid FGJK, what is the value of x? N CO 18.6 L K 23.6 9.3 11.8 ET O 13.6
Answers
Given data:
The given figure is shown.
The expression for the trapezium is,
[tex]\begin{gathered} \frac{x}{18.6}=\frac{18.6}{23.6} \\ 23.6x=18.6^2 \\ x=14.6 \\ =15 \end{gathered}[/tex]Thus, thi
A toy factory makes 5.7 x 10³ toys each day.At this rate, how many toys will be made in 9 days?Express the answer in scientific notation.
Answers
First We will put the number of toys per day in simple form:
[tex]5.7\times10^3=5.7\times1000=5700[/tex]Then, to know how many toys will be made in 9 days, let's multiply the number of toys per day by the given number of days:
[tex]5700\times9=51300[/tex]Now We will put the number in scientific notation:
[tex]5.13\times10^4[/tex]Find the values of x and y in the equation below.a³b4a²b= a*b²X=
Answers
To divide, subtract exponents to same base variables.
[tex](ab^3)^6[/tex]Multiply exponents of exponents
[tex]a^6b^{18}[/tex]x= 6
y= 18
How do I get to the answer of this question?
Answers
Okay, here we have this:
Considering the provided information, and that we must identify which of the provided options allow us to determine that the two triangles are similar, we obtain the following:
As the angle-angle similarity says that if two angles of one triangle are congruent with two angles of another triangle, then the triangles are similar.
Finally, we see that the only option that satisfies this statement is option D, since it indicates that two angles of the triangles are congruent. Therefore the correct option is D.
1. Find the surface area and volume of box where: L = 31.59ft, W = 24.98ft and H = 43.23ft.
Answers
ANSWER
[tex]\begin{gathered} A=6469.28ft^2 \\ V=34113.58ft^3 \end{gathered}[/tex]EXPLANATION
The surface area of the box (rectangular prism) is:
[tex]A=2(LW+WH+LH)[/tex]where L = length; W = width; H= height
Therefore, we have that the surface area of the box is:
[tex]\begin{gathered} A=2\lbrack(31.59\cdot24.98)+(24.98\cdot43.23)+(31.59\cdot43.23)\rbrack \\ A=2\lbrack(789.1182)+(1079.8854)+(1365.6357)\rbrack \\ A=2(3234.6393) \\ A\approx6469.28ft^2 \end{gathered}[/tex]The volume of the box is:
[tex]V=L\cdot W\cdot H[/tex]Therefore, the volume of the box is:
[tex]\begin{gathered} V=31.59\cdot24.98\cdot43.23 \\ V\approx34113.58ft^3 \end{gathered}[/tex]Determine the equation of the graphed circle below!Equation should look like the example below!
Answers
Step 1:
Write the formula for the equation of a circle.
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{Center = ( a , b )} \\ \text{Radius = r} \end{gathered}[/tex]Step 2:
Locate and write the center and radius of the circle.
Step 3:
Write the equation of the circle with center (-7, -2) and radius r = 2
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (x-(-7))^2+(y-(-2))^2=2^2 \\ (x+7)^2+(y+2)^2=\text{ 4} \end{gathered}[/tex]Final answer
[tex](x+7)^2+(y+2)^2=\text{ 4}[/tex]in DEF, K is the centroid. If KH=12 find DH
Answers
the lines that cross the centroid are divided into 2 by this the short line corresponds to 1/3 of the complete line and the long line corresponds to 2/3 of the complete line
so KH is 1/3 of DH
if KH=12, then
[tex]\begin{gathered} DH=3KH \\ DH=3\times12 \\ DH=36 \end{gathered}[/tex]the value of DH is 36
you are selling snacks at the border trade fair. you are selling nachos and lemonade. each nachos costs $2.50 and each lemonade cost $2.25. at the end of the night you made a total of $112.50. you sold a total of 94 nachos and lemonade combined. how many nachos and lemonades were sold?
Answers
In order to determine the number of nachos and lemonade sold, you first write the given situation in an algebraic way.
If x is the number of nachos and y the number of lemonades, then, you have:
2.50x + 2.25y = 112.50 cost of the nachos and lemonade sold
x + y = 94 nachos and lemonade sold
Next, solve the previous system.
Multiply the second equation by 2.50. Next, subtract the equation to the first one:
(x + y = 94)(2.50)
2.50x + 2.50y = 235
2.50x + 2.25y = 112.50
-2.50x - 2.50y = -235
-0.25y = -122.5
solve the previous equation for y:
y = -122.5/(-0.25)
y = 490
Next, replace the previous value of y into the expression x + y = 94 and solve for x:
x + y = 94
x + 490 =