An analyst surveyed the movie preferences of moviegoers of different ages. Here are the results about movie preference, collected from a random sample of 400 moviegoers.
A 4-column table with 4 rows. The columns are labeled age bracket and the rows are labeled type of movie. Column 1 has entries cartoon, action, horror, comedy. Column 2 is labeled children with entries 50, 22, 2, 24. Column 3 is labeled teens with entries 10, 45, 40, 64. Column 4 is labeled adults with entries 2, 48, 19, 74.
Suppose we randomly select one of these survey participants. Let C be the event that the participant is an adult. Let D be the event that the participant prefers comedies.
Complete the statements.
P(C ∩ D) =
P(C ∪ D) =
The probability that a randomly selected participant is an adult prefers comedies is symbolized by P(C ∩ D).
Answers
Using it's concept, it is found that the probabilities are given as follows:
P(C ∩ D) = 0.185.P(C ∪ D) = 0.5775.What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there is a total of 400 moviegoers.
From the table, 74 are adults who prefer comedies, hence:
P(C ∩ D) = 74/400 = 0.185.
2 + 48 + 19 + 74 = 143 are adults, while 24 + 64 = 88 are not adults but prefer comedies, hence the "or probability" is given by:
P(C ∪ D) = (143 + 88)/400 = 0.5775.
More can be learned about probabilities at https://brainly.com/question/14398287
Answer:
0.3575
0.405
Step-by-step explanation:
Related Questions
One smartphone plan costs $52 per month for talk and messaging and $8 per gigabyte of data used each month. A second smartphone plan costs $82 per month for talk and messaging and $3 per gigabyte of data used each month. Let c represent the total cost in dollars and d represent the amount of data used in gigabytes.
The system of equations
c=52+8d
c−3d=82
can be used to represent this situation.
How many gigabytes would have to be used for the plans to cost the same? What would that cost be?
Answers
Answer:
Both plans would cost $100 if 6 gigabytes of data are used.
Explanation:
From the question, the system of equation are correctly represented by using small letter c to represent the total cost in dollars for both equations as already assumed in the question as follows:
c = 52 + 8d ........................... (1)
c = 82 + 3d ........................... (2)
Since c is common to both, equations (1) and (2) can therefore be equated and d solved for as follows:
52 + 8d = 82 + 3d
8d - 3d = 82 - 52
5d = 30
d = 30 / 5
d = 6
Substituting d = 6 into equation (1), we have:
c = 52 + (8 * 6)
c = 52 + 48
c = 100
Since d = 6 and c = 100, it therefore implies that both plans would cost $100 if 6 gigabytes of data are used.
9. Determine whether the parallelogram is a rectangle, square, or rhombus. G(-4,3), D(2,1) F(-5, 0) and E(1, -2)
Answers
Answer:
rectangle
Step-by-step explanation:
Answer:
Rectangle
Step-by-step explanation:
FG's slope is the opposite reciprocal of GD's, so they are perpendicular. The same with the other sides.
The opposite sides have the same length.
Leo solved the equation b = 12 a−1−−−−−√3 for a, but made an error. His work is shown. Complete the sentences that follow.
Answers
The value of a in terms of b is given as [tex]a = 8b^3[/tex]
Given the equation solved by Leo expressed as [tex]b=\frac{1}{2}\sqrt[3]{a-1}[/tex]
We are to solve the equation for the variable "a"
Given;
[tex]b=\frac{1}{2}\sqrt[3]{a-1}[/tex]
Cross multiply
[tex]2b=\sqrt[3]{a-1}[/tex]
Cube both sides of the equation:
[tex](2b)^3=(\sqrt[3]{a-1})^3 \\8b^3=a-1[/tex]
Add 1 to both sides of the equation:
[tex]8b^3+1=a-1+1\\8b^3=a\\Swap\\a=8b^3[/tex]
Hence the value of a in terms of b is given as [tex]a = 8b^3[/tex]
Learn more on subject of formula here: https://brainly.com/question/657646
Find 34−13.95 . Express your answer in decimal form.
Answers
Answer:
34-13.95 = 20.05
Step-by-step explanation:
Answer:
20.05
Step-by-step explanation:
34 - 13.95 = 20.05
5+2x=2x+6
do anyone know the answer
Answers
Answer:
no solutions
Step-by-step explanation:
5+2x = 2x+6
Subtract 2x from each side
5+2x-2x = 2x+6-2x
5 = 6
This is not a true statement so there are no solutions
Cube root -125 over 216
Answers
Hope this helps
Select all the functions whose output is 4 when the input is 16.
A.
y = 2x
B. y=x?
2
= x
C.
y = x + 12
D.
y = x - 12
E. y = 1
x
Answers
Answer:
Please check your post. I did the best I could.
Step-by-step explanation:
A. y = 2x 4 = 2*(16)? Nope
B. y=x? I don't understand the equation: y = x? 2 = x?????
C. y = x + 12 4 = 16 + 12? Nope
D. y = x - 12 Same???
E. y = 1 x 4 = 16? Nope
Which inequality represents this statement?
A number is no more than 5.
n<5
n≥5
n>5
n≤5
Answers
Answer: the last one!! [tex]n\leq 5[/tex]
Step-by-step explanation:
When there is a line under it means no more than!
2(2c+12)=68
Using the opposite steps, inverse operations, solve for the value of the variable
Answers
[tex]\huge\boxed{Good\:evening!:)}[/tex]
2(2c+12)=68
4c+24=68
4c=68-24
4c=44
Divide both sides by 4:
c=11
[tex]\huge\boxed{Hence,\:the\:answer\:is\:11.:)}[/tex]
[tex]\huge\underline{Hope\:it\:helps!}[/tex]
[tex]\huge\sf{Good\:luck.}[/tex]
[tex]\boxed{DreamyTeenager\:here\:to\:help}[/tex]
help me answer please
Answers
Answer:
Sorry
Step-by-step explanation:
I need help with this question
Answers
Answer:
2√14m
Step-by-step explanation:
Hypothenus = 9m
Second side = x
third side = 5m
Using Pythagoras theorem
9² = x² + 5²
81 = x² + 25
x² = 81 - 25
x² = 56
x = √56
= √4 × √ 14
= 2√14m
Let $F,$ $G,$ and $H$ be collinear points on the Cartesian plane such that $\frac{FG}{GH} = 1.$ If $F = (a, b)$ and $H = (7a, c)$, then what is the $x$-coordinate of $G$?
Answers
F, G, and H all lie on the same line. If FG/GH = 1, then FG = GH, which is to say the distance between F and G is equal to the distance between G and H. This means either F and H are the same point, or G is the midpoint of F and H.
They're not the same point, because the x-coordinate of H is 7 times that of F. So G must be halfway between F and H.
Then the x-coordinate of G is
(a + 7a)/2 = 8a/2 = 4a
Given the figure below, which statement correctly completes the following? ABE and HCD are what type of angles
Answers
Angles are classified based on their measures.
Classification of angles
The following are the classification of angles
Acute AnglesRight AnglesObtuse AnglesStraight linesReflex AnglesThe smallest angle is 0 degrees and the largest is 360 degrees.
When the measure of an angle is less than 90 degrees, such angle is an acute angle
When the measure of an angle is exactly 90 degrees, such angle is a right angle
Angles greater than 90 degrees, but less than 180 degree are obtuse angles, while angles that measure exactly 180 degrees are straight lines.
The last type of angle is the reflex angle, and it has a measure between 180 degrees and 360 degrees (exclusive)
The question is incomplete, so I gave a general explanation
Read more about angles at:
https://brainly.com/question/17972372
II. Solve the problems involving variations. Show your complete solution. (3 points each) 1. If y varies directly as the square of x, and y = 32 when x = 2, find y when x = 5. 2. The force of attraction (F) between two opposite electrical charges varies inversely as the square of the distance (d) between them. If F = 18 when d = 10, find F when d = 15. 3. If y varies jointly as x and z, find y if x = 3, k = 6 and z = 9
Answers
Answer:
see explanation
Step-by-step explanation:
(1)
y varies directly as x² then the equation relating them is
y = kx² ← k is the constant of variation
To find k use the condition y = 32 when x = 2
32 = k × 2² = 4k ( divide both sides by 4 )
8 = k
y = 8x² ← equation of variation
When x = 5 , then
y = 8 × 5² = 8 × 25 = 200
(2)
Given F varies inversely as d² then the equation relating them is
F = [tex]\frac{k}{d^2}[/tex] ← k is the constant of variation
To find k use the condition F = 18 when d = 10
18 = [tex]\frac{k}{10^2}[/tex] = [tex]\frac{k}{100}[/tex] ( multiply both sides by 100 )
1800 = k
F = [tex]\frac{1800}{d^2}[/tex] ← equation of variation
When d = 15 , then
F = [tex]\frac{1800}{15^2}[/tex] = [tex]\frac{1800}{225}[/tex] = 8
(3)
y varies jointly as x and z then the equation relating them is
y = kxz ← k is the constant of variation
when x = 3, y = 6, z = 9 ,then
y = 6 × 3 × 9 = 162
Am I right? Should I've to add more info?(only about Rectangle and Square)
Answers
Answer:
Yh its right.
Step-by-step explanation:
Have a great day!
Answer:
yeah it is correct
Step-by-step explanation:
and well hruu
Sonja has a bank account balance of $1400. Each week, her balance changes by-$85.25. She wants to keep the balance above $377. How many weeks will Sonja's balance remain above $377? Select from the drop-down menu to correctly complete the statement. Sonja's balance will remain above $377 Choose... v weeks.
Answers
Answer:
12 Weeks
Step-by-step explanation:
$1400 - $377 = $1023
1023 / 85.25 = 12 Weeks
Answer:
Its will take Sonja 12 weeks
Step-by-step explanation:
The relationship between y and x is 9/3 which table represents this relationship and why?
Answers
Answer:
First one
Step-by-step explanation:
For every 1 in x the y goes up by 3
given a isotope with a 3 charge, a mass number of 28, and an atomic number of 13, what are:
Answers
Answer: The element described is aluminum.
Can someone answer number 9 for and tell me if the others are correct i have a 64% in geometry trying to raise grade up to alteast 70%
Answers
Answer:
5, 6, 7, 8: correct
9: the Hi.nge theorem does not apply
Step-by-step explanation:
The Hi.nge theorem says that the side opposite the angle between two pairs of congruent sides is longer if the angle is larger. This theorem is applicable to problems 5-8, and your application is correct.
__
9) The Hi.nge theorem does not apply. The marked angles are not between the congruent sides. There is no necessary relation between the marked angles and the angles that are between the congruent sides, so no conclusion can be drawn regarding the relative lengths of AB and CD.
solve similar triangles (advanced)
Answers
Answer:
12 =x
Step-by-step explanation:
We can use proportions to solve
6 x
---- = -------
10 10+10
Using cross products
6 ( 10+10) = x*10
6*20 = 10x
120 = 10x
Divide by 10
120/10 = x
12 =x
Answer:
x = 12
Step-by-step explanation:
ABC ~ ADE
AB/AD = BC/DE
10/20 = 6/x
x = 20 x 6 ÷ 10
x = 12
Help please
Simplify the difference quotient (f(x + h) − f(x) )/h if h ≠ 0.
f(x) = x2 + 38
Answers
Answer:
2x + h
Step-by-step explanation:
[tex]\frac{f(x+h)-f(x)}{h}[/tex]
= [tex]\frac{(x+h)^2+38-(x^2+38)}{h}[/tex]
= [tex]\frac{x^2+2hx+h^2+38-x^2-38}{h}[/tex]
= [tex]\frac{2hx+h^2}{h}[/tex]
= [tex]\frac{h(2x+h)}{h}[/tex] ← cancel h on numerator/ denominator
= 2x + h
Two squares are congruent if and only if:
A. any two corresponding angles are
congruent
B. two pairs of corresponding angles are
congruent
C. all four pairs of corresponding angles are
congruent
D. a side of one is congruent to a side of the
other
Answers
D) a side of one is congruent to side of the other
Coz in the question it specified that both the shapes are square so obviously all angles are equal (90°)
Now we only need one side of it congruent .
Write
48
:
132
:
84
in its simplest form.
Answers
Answer:
4:11:7
Step-by-step explanation:
Find the GCF, or greatest common factor of the 3 numbers. In this case it is 12. To simplify, divide each number by 12
Answer:
4:11:7
Step-by-step explanation:
please mark me as brainlest
у — 3x 4
у > 4х +1
Anyone know the answe on how to solve this???
Answers
Answer:
Unbounded, infinite number of solutions
Step-by-step explanation:
1. Graph each inequality separately
2. Choose test point to determine which side of line needs to be shaded
3. The solution will be the the area where the shadings from both inequalities overlap
Since, the overlap almost covers the 2nd and 3rd quadrants there are an infintite number of solutions
WILL GIVE YOU 50 POINT
Find M AFE.
Answers
Answer:
The answer is C
Step-by-step explanation:
25 + 57 + 34 = 116, so at least 116, not 116.
The angle is close to 90+45 = 135
assuming with this, the asnwer is C
Answer:
B. 173
Step-by-step explanation:
just add them all up! for DFE, BFC has the same sign, which i assume means it is the same thing
Graph the line with the equation
y = -1/3x + 4.
Answers
Answer:
Answer in the image
Step-by-step explanation:
i really need your help on this
Answers
Answer:
That is an improper fraction
Step-by-step explanation:
When the numerator (the top) is greater than the denominator (The bottom) then the fraction is improper
Hope this helps!
Answer:
Improper fraction
Step-by-step explanation:
Based on the Rational Zero Test, which of the following is
NOT a possible zero of f(x) given below after the reciprocal
of LCD is factored out?
f(x)=x^3 -5x + (2/5)
(A) 1/2
(B) 1/5
(C) 1
(D) -1
Answers
The rational zero test is also known as the rational root test, and it is used to determine the potential root of a function.
(a) 1/2 is not a possible zero of the function
The function is given as:
[tex]f(x) =x^3 - 5x + \frac 25[/tex]
For a function,
[tex]f(x) = px^n +......q[/tex]
The list of possible roots is:
[tex]Roots = \pm\frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
Multiply both sides of [tex]f(x) =x^3 - 5x + \frac 25[/tex] by 5
[tex]5f(x) = 5x^3 - 25x + 2[/tex]
So, we have:
[tex]p= 5[/tex]
[tex]q = 2[/tex]
The factors are:
[tex]p =\pm 1, \pm 5[/tex]
[tex]q =\pm 1, \pm 2[/tex]
So, the possible roots are:
[tex]Roots = \pm\frac{1,2}{1,5}[/tex]
Split
[tex]Roots = \pm1, \pm \frac 15, \pm 2, \pm \frac 25}[/tex]
Hence, 1/2 is not a possible zero of the function
Read more about rational zero test at:
https://brainly.com/question/12860313
Which expression is equivalent lo the following complex fraction?
Answers
Answer:
[tex] \frac{ - 1}{2} [/tex]
Hope this helps you !!9) Jamar drove 228 miles and used 6 gallons of gas.
a) How many miles/gallon did he get on the trip?
b) On another trip, he used 9 gallons of gas. How far did he travel?
Answers
Answer: 38 miles per gallon ; 342 miles.
Step-by-step explanation:
The miles/gallon that he got on the trip will be:
= 228/6
= 38 miles per gallon.
When he used 9 gallons of gas, the distance travelled will be:
= 38 × 9
= 342 miles
Answer:
Question :
Jamar drove 228 miles and used 6 gallons of gas.
a) How many miles/gallon did he get on the trip?b) On another trip, he used 9 gallons of gas. How far did he travel?Solution :
a) How many miles/gallon did he get on the trip?
[tex]{\implies{\sf{\dfrac{228}{6}}}}[/tex]
[tex]{\implies{\sf{ \cancel{\dfrac{228}{6}}}}}[/tex]
[tex]{\implies{\sf{\underline{\underline{\red{36 \: miles/gallon}}}}}}[/tex]
Hence, he get 38 miles/gallon for his trip.
[tex]\rule{200}2[/tex]
b) On another trip, he used 9 gallons of gas. How far did he travel?
[tex]{\implies{\sf{38 \times 9}}}[/tex]
[tex]{\implies{\sf{\underline{\underline{\red{342 \: miles}}}}}}[/tex]
Hence, he traveled 342 miles by using o gallon og gas.
[tex]\underline{\rule{220pt}{3pt}}[/tex]