A group of people were asked "What time do you prefer to see a movie? The two way tablebelow represents the results by their age.Morning 4 2 12 25 4316-20 21-25 26-30 Over 30 TotalsAfternoon 8 12 18 32 70EveningTotals28 34 28 11 101Late Night 34 18 21 4 7774 66 79 72 291What the approximate probability that a person will be over 30 given they prefer afternoonmovies?
Answers
From theinformation given,
total number of people = 291
Number of persons over 30 that prefer afternoon movies = 32
Number of persons that prefer afternoon movies = 70
This is a conditional probability.
Recall, Probability of event A given event B = P(A and B)/P(B)
Thus,
Probability that a person will be over 30 given that they prefer afternoon movies = 32/70
By multiplying by 100, it becomes
32/70 x 100
= 46%
Probability that a person will be over 30 given that they prefer afternoon movies = 46%
Related Questions
Solve the system by graphing. (If there is no solution, enter NO SOLUTION.)x + 2y < 6y < x − 5
Answers
From the problem, we have the inequalities :
[tex]\begin{gathered} x+2y<6 \\ yNote that the boundary line is dashed if the symbols are < or >.Let's graph first the first inequality :
[tex]\begin{gathered} x+2y<6 \\ \text{Change the symbol into ''=''} \\ x+2y=6 \\ \text{Solve for the intercepts} \\ \text{when x = 0} \\ 0+2y=6 \\ y=\frac{6}{2}=3 \\ \\ \text{when y = 0} \\ x+2(0)=6 \\ x=6 \end{gathered}[/tex]Plot the points (0, 3) and (6, 0)
The region will pass through the origin if (0, 0) satisfies the inequality.
Test for (0, 0)
[tex]\begin{gathered} x+2y<6\text{ } \\ 0+0<6 \\ 0<6 \\ \text{TRUE!} \end{gathered}[/tex]Since it is true, the region will pass through the origin.
The graph will be :
Next is to graph the second inequality :
[tex]\begin{gathered} yPlot the points (0, -5) and (5, 0)Check again origin (0, 0) to the inequality :
[tex]\begin{gathered} ySince it is false, the region will not pass through the origin.Tha graph will be :
The solution to the system is the overlapping region between the two inequalities.
Simplify this expression. Assume that x is nonzero.– 11.7X<-11.x?(Type exponential notation with positive exponents.)
Answers
If two numbers have the same base ( the number below the exponent) then the multiplication of the two of them is the number with the same base but with the sum of its exponents (rule of exponents)
[tex]x^{-11}\cdot x^7=x^{-11+7}=x^{-4}[/tex]On the other hand, if a number is to the power a negative number, it means that it is the reciprocal elevated to the number, in this case
[tex]x^{-4}=(\frac{1}{x})^4[/tex]Nina deposited $20.59 in her checking account. Later that week, she wrote a checkfor one-third the amount in the account, and then another check for $9.74. If shehad $108.60 left in her account, how much did she have to begin with.
Answers
1) Reading carefully, we can do it step by step.
2) She had deposited $20.59 and wrote a check, since she wrote a check we can understand that as a debit so we can write out the following:
[tex]\begin{gathered} 20.59-\frac{20.59}{3}= \\ 20.59-6.86 \\ 13.7 \end{gathered}[/tex]Note that we rounded off to the nearest hundredth.
2.2) So now, she wrote another check, i.e. -$9.74
[tex]\begin{gathered} \$13.7-\$9.74 \\ \$4 \\ 108.60 \\ 108.60+\mleft(20.59-6.86-9.74\mright)=112.59 \end{gathered}[/tex]The sum of two numbers is 20. The difference between three times the first rumber and twice the second is 40. Find the two numbers.
Answers
Let the first number is x and second number is y.
According to given conditions:
The sum of two numbers is 20.
[tex]x+y=20[/tex]And The difference between three times the first rumber and twice the second is 40.
[tex]3x-2y=40[/tex]Now multiply equation 1 with 2 and add in second eqution;
[tex]\begin{gathered} 2(x+y)+(3x-2y)=2(20)+40 \\ 2x+2y+3x-2y=40+40 \\ 5x=80 \\ x=16 \end{gathered}[/tex]Now put the value of x in equation 1:
[tex]\begin{gathered} 16+y=20 \\ y=4 \end{gathered}[/tex]So the first number is x=16 and second number is y=4.
According to given co
1) P(A) = 0.6 P(B) = 0.45 P(A and B) = ? O 0.35 0.65 O 0.75 O 0.27
Answers
We are given the following probabilities:
[tex]\begin{gathered} P(A)=0.6 \\ P(B)=0.45 \end{gathered}[/tex]We are to find P(A and B), to do that we will use the following relationship:
[tex]P(\text{AandB)=P(A) x P(B)}[/tex]Replacing we get:
[tex]P(AandB)=0.6\times0.45[/tex]Solving the operations:
[tex]P(\text{AandB)}=0.27[/tex]Therefore, the probability of A and B is 0.27.
Millie Gaines 4% by selling her cycle for 6644.80 rupees find a cp for cycle
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
bike price = 644.80 rupees
gain = 4% = 0.04
cp = cost price = ?
Step 02:
cost price = bike price - bike price*gain
= 644.80 rupees - 644.80 rupees * 0.04
= 644.80 rupees - 25.729 rupees
= 619 rupees
The answer is:
The cost price is 619 rupees.
Jake, Becky, and Max are meeting at Charley's Pizza for dinner and then plan to go
pizza place,
each one of them has a different coupbn. They decide to use the coupon that will give them the best deal. movie. When they arrive. the
Jake's coupon is $19.99 for a pizza and pasta meal deal, Becky's
of the menu price; and Max's coupon is for three mediun
coupon is for two large one topping pizas-each at ]
one-topping pizzas - each at -off the menu price. Accordling
to the menu, a medium one-topping pizza is $8.99, and
large one-topping pizza $14.89. They also spend $1.25
for sodas and $5.00 on the tip. At the movie theater. Max has › coupon that's good for ãoff a third movie ticket when
you purchase two other movie tickets at the regular price.
The regular price of each movie ticket is $9.80.
Although Jake, Becky, and Max plan to split the cost of the pizza and movie, they decide that with the coupons, it's just
easier if one of them pays at each place. So, the friends agree that Jake will pay for the pizza and Becky will pay for the
movies. At the end of the night, they'll figure out how much Max owes
both Jake and Becky.
After all costs
split evenly, how much will each person contribute?
between $14 and $15
• between $15 and $16
• between $16 and $17
O between $17 and $18
Answers
Answer:
$16 and $17
Step-by-step explanation:
Match the steps to put them in the correct order of something. You will not use all of the options.
Answers
SOLUTION
[tex]\begin{gathered} Given \\ 2h+9=21 \end{gathered}[/tex][tex]\begin{gathered} Step\text{ 1:} \\ Subtract\text{ 9 from both sides} \\ 2h+9-9=21-9 \\ 2h=12 \end{gathered}[/tex][tex]\begin{gathered} Step\text{ }2: \\ Divide\text{ both sides by 2} \\ \frac{2h}{2}=\frac{12}{2} \\ h=6 \end{gathered}[/tex][tex]\begin{gathered} Final\text{ answer:} \\ h=6 \end{gathered}[/tex]Solve the equation for A: 2*Cos A + 2 = 3.
Answers
Answer:
A=60 degrees
Explanation:
Given the equation:
[tex]2\cos A+2=3[/tex]Subtract 2 from both sides of the equation.
[tex]\begin{gathered} 2\cos A+2-2=3-2 \\ 2\cos A=1 \end{gathered}[/tex]Divide both sides by 2:
[tex]\begin{gathered} \frac{2\cos A}{2}=\frac{1}{2} \\ \cos A=\frac{1}{2} \end{gathered}[/tex]Finally, solve for A.
[tex]\begin{gathered} A=\arccos (\frac{1}{2}) \\ A=60\degree \end{gathered}[/tex]2. Perform cach of the following calculations using a single multiplication. Do not round your final answers.(a) Decrease 160 by 10% (b) Decrease 450 by 6%(c) Decrease 122,000 by 12%(d) Decrease $1,820 by 3%(c) Decrease $12,500 by 15%(f) Decrease $4.50 by 8%
Answers
We have the following:
(a) Decrease 160 by 10%
[tex]160\cdot(\frac{100-10}{100})=144[/tex](b) Decrease 450 by 6%
[tex]450\cdot(\frac{100-6}{100})=423[/tex](c) Decrease 122,000 by 12%
[tex]122000\cdot(\frac{100-12}{100})=107360[/tex](d) Decrease $1,820 by 3%
[tex]\begin{gathered} 1820\cdot(\frac{100-3}{100})=1765.4 \\ \end{gathered}[/tex](e) Decrease $12,500 by 15%
[tex]12500\cdot(\frac{100-15}{100})=10625[/tex](f) Decrease $4.50 by 8%
[tex]4.5\cdot(\frac{100-8}{100})=4.14[/tex]directly as Vi and inversely as y°. If: = 61 when = 36 and y = 9, find a if r = 64 and y = 6. (Round off your answer to the nearest hundredth.)
Answers
Given: z directly varies as √x and inversely varies as y³
when x = 36 and y = 9 then z = 61
To find:
when x = 64 and y = 6 then z = ?
explanation:
z ∝ √x / y³
z = k √x / y³
when x = 36 and y = 9 then z = 61
[tex]z=\text{ }\frac{k\text{ }\sqrt{x}}{y^3}[/tex][tex]\begin{gathered} 61=\frac{k\text{ * }\sqrt{36}}{9^3} \\ 61=\frac{k*6}{729} \\ k=\frac{61*729}{6}=\frac{61*243}{2}=\frac{14823}{2} \end{gathered}[/tex]when x = 64 and y = 6
[tex]z=\text{ }\frac{14823}{2}*\frac{\sqrt{64}}{6^3}=\frac{14823*8}{2*216}=\frac{4941*4}{72}=\frac{4941}{18}=274.5[/tex]the value of z = 274.5
final answer:
z = 274.5 ≈ 300 when rounded off to the nearest hundredth
explain how you solve a quadratic equation. How many answers do you expect to get for a quadratic equation?
Answers
1. There are several ways to solve (Quadratic Formula, Graphing, Newton's Identities, Factoring) the most common is using the Quadratic Formula.
2. We can always expect two roots, either identical or different.
1) There are some ways to solve a quadratic equation. We can solve it using the Quadratic Formula, Graphing it or via Newton's Identities, or even factoring
The most common way is via Quadratic Formula:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}[/tex]Which a, b, and c are the coefficients of a Quadratic Equation, say:
x²+6x+9, a= 1, b=6, and c=9.
[tex]x=\frac{-6\pm\sqrt[]{6^2-4(1)(9)}}{2(1)}=x_1=x_2=-3[/tex]Note that in this case, both roots were equal to -3
2) We can always expect two roots. When the Quadratic Formula yields just one answer then we can call it double root, or 1 root with multiplicity 2, actually there are two roots with the same value.
3) Thus the answer is:
1. There are several ways to solve (Quadratic Formula, Graphing, Newton's Identities, Factoring) the most common is using the Quadratic Formula.
2. We can always expect two roots, either identical or different.
What point is a solution to the linear inequality y > 4x -3?
Answers
Answer:
(0,-3 )and (0.75,0)
Step-by-step explanation:
y=4x_3
What is the value of the expression below when z=7 and w=10
Answers
Given that z = 7 and w = 10 then the expression 7z + 10w
substituting the values of z and w into tye expression
= 7(7) + 10 (10)
= 49 + 100
= 149
Answer question number 18. The question is in the image.
Answers
18.
Given:
[tex]g(x)=3sin2x[/tex]Required:
We need to graph the function and find the transformation from the parent function.
Explanation:
The given equation is of the form.
[tex]g(x)=Asin(Bx+C)[/tex]where A =3, B=2, and C=0.
We know that A is amplitude.
[tex]Amplitude=3[/tex][tex]Period=\frac{2\pi}{|B|}[/tex]Substitute B=2 in the equation,
[tex]Period=\frac{2\pi}{|2|}[/tex][tex]Period=\pi[/tex]Recall that the amplitude of a function is the amount by which the graph of the function travels above and below its midline.
The distance between the maximum point and midline is 3.
The time interval between two waves is known as a Period
The time interval between two waves is pi.
The graph of the function.
[tex]The\text{ parent function is f\lparen x\rparen=sinx.}[/tex]Recall that the amplitude stretches or compresses the graph vertically.
Here we have amplitude =3. it is a positive value.
The parent function stretches vertically by 3 units.
Recall that the period stretches or compresses the graph horizontally.
Here we have the period is pi.
The parent function compresses horizontally by pi.
Final answer:
[tex]Amplitude=3[/tex][tex]Period=\pi[/tex]The transformation is stretched vertically by 3 units and compressed horizontally by pi.
A local health clinic surveys its patients about their water drinking habits it found data is normally distributed the mean amount of water consumed daily is 62 ounces and the standard deviation is 5.2how much water in ounces do approximately 95% of the patients drink each day
Answers
The approximate amount of water consumed by 95% of the patients will be given as a range which can be gotten by
[tex]P=x\pm2S[/tex]Where
P = Amount of water.
x = mean
S = Standard Deviation
Therefore,
The lower limit is
[tex]\begin{gathered} x-2s \\ =62-2(5.2) \\ =62-10.4 \\ =51.6\text{ ounces} \end{gathered}[/tex]The upper limit is
[tex]\begin{gathered} x+2s \\ =62+2(5.2) \\ =62+10.4 \\ =72.4\text{ ounces} \end{gathered}[/tex]Therefore, the amount of water that 95% of the patients drink approximately is 51.6 ounces to 72.4 ounces.
Lisa's rectangular living room is 20 feet wide. If the length is 5 feet less than twice the width, what is the area of her living room?
Answers
1) Let's gather all the data
Width: 20'
Length: 2w-5
2) Now we can plug that into the formula for the are of a rectangle, like this
[tex]\begin{gathered} A=wl \\ A=20\cdot(2(20)-5) \\ A=20\cdot(40-5) \\ A=20\cdot35 \\ A=700ft^2 \end{gathered}[/tex]Notice that we have plugged into that the width w=20. Therefore the area of the living room is 700ft²
60% of the
students take the
bus. If there were
120 students on the
busses, how many
total students are
there?
Answers
Answer:
168
Step-by-step explanation:
60%=120
40% of 120
10%12
10%12
10%12
10%12
12×4=48
120+48=168
Enter in the coordinates for each point in the graph below.Quezon 2Not yetansweredPoints out of16.00H.c.5FlagquestionE.5-1990GD
Answers
ANSWER:
A. (-7,2)
B (-5, -2)
C (-3, 5)
D (-2, -7)
E (2, 3)
F (3,3)
G (5,-6)
H (6, 6)
Find the inverse of the function. g(x)= -5x – 20/7
Answers
Given the function:
[tex]g(x)=\frac{-5x-20}{7}[/tex]To find the inverse function, let us first write it as:
[tex]y=\frac{-5x-20}{7}[/tex]Make x the subject of the equation
[tex]\begin{gathered} -5x-20=7y \\ -5x=7y+20 \\ x=\frac{-7y-20}{5} \end{gathered}[/tex]Replace x by y, and y by x to obtain the inverse function
[tex]y=\frac{-7x-20}{5}[/tex]Where
[tex]y=g^{-1}(x)[/tex]What is the greatest common factor of 48x^2?and 32x^3?A. 16x^2B. 96x^3C. 8x^2D. 16x
Answers
greatest common factor (GCF) of 2 algebraic terms is the largest monomial that evenly divides the two expressions.
We have
[tex]\begin{gathered} 48x^2 \\ \text{and} \\ 32x^3 \end{gathered}[/tex]There are two parts, the numbers and variables.
From the numbers, the largest number we can divide 48 and 32 by is:
16
From the variables, the largest factor is x^2
Putting them together, we can say the GCF is:
[tex]16x^2[/tex]Correct Answer: A
from this part ,find the estimated y-intercept .Round your answer to the three decimal places.
Answers
y - incercept = 371.4
X= 7 4. Find the equation of a line passing through (5, -6) perpendicular (b) 3x + 5y = (d) 7x - 12y (f) x = 7 (a) 2x + y = 12 (c) x + 3y = 8 (e) 2y = 5 Find the equation of the line connecting the points of intersect (a) S x + y = 4 S 3x - y = 12 (b) Sy= and 2x=6 = -6 X=
Answers
Given data:
The first set of equations are x+y=4, and x=6.
The second set of equations are 3x-y=12 and y=-6.
The point of intersection of first set of te equations is,
6+y=4
y=-2
The first point is (6, -2).
The point of intersection of second set of te equations is,
3x-(-6)=12
3x+6=12
3x=6
x=2
The second point is (2, -6).
The equation of the line passing through (6, -2) and (2, -6) is,
[tex]\begin{gathered} y-(-2)=\frac{-6-(-2)}{2-6}(x-6) \\ y+2=\frac{-6+2}{-4}(x-6) \\ y+2=x-6 \\ y=x-8 \end{gathered}[/tex]Thus, the required equation of the line is y=x-8.
Which expression is equivalent to 1-51 +131? —8 ООО O2 o 8
Answers
Theg given expression : |-5|+|3|
Since modulus is express as |-a|=a and |a|=a
[tex]undefined[/tex]Use substitution to solve each system of equations.y + 1/2x = 34y + 2x = 6
Answers
Answer:
No solution
Explanation:Given the system of eqations:
[tex]\begin{gathered} y+\frac{1}{2}x=3 \\ 4y+2x=6 \end{gathered}[/tex]From the second equation, find x.
[tex]\begin{gathered} 2x=6-4y \\ x=\frac{6-4y}{2} \\ =3-2y \end{gathered}[/tex]Substitute the obtained value of x into the first equation.
[tex]\begin{gathered} y+\frac{1}{2}(3-2y)=3 \\ y+\frac{3}{2}-y=3 \\ \frac{3}{2}=3 \end{gathered}[/tex]which isnotpossible. So, no solution exists.
Write an Equation: Gary worked for 20 hours tutoring students at the library. He uses $35 to pay for gas on his way home. If he has $60 left after paying for gas, how much money, x, in dollars, was Gary paid per hour?
Answers
Answer:4.75 in us dollars it will be 5.31
Step-by-step explanation:
first you divide 95 by 20 witch will give you 4.75 and if you want to check that answer you do 4.75 times 20 and it will give 95
a jacket at Rick's clothing store originally costs $27 the store is having a 45% off sale on all of its merchandise what is the sale price of the jacket
Answers
Let:
Op = Original price
Sp = Sale price
r = Discount
Express the discount percentage as a decimal:
45% = 45/100 = 0.45
The sale price will be given by:
[tex]\begin{gathered} Sp=Op-0.45Op \\ where \\ Op=27 \\ so\colon \\ Sp=27-12.5 \\ Sp=14.85 \end{gathered}[/tex]$14.85
Use the properties of exponents to simplify. Express all answers using positive exponents.each)35x10 over 5x^5
Answers
Consider the given expression,
[tex]\frac{35x^{10}}{5x^5}[/tex]Consider the property,
[tex]\frac{x^m}{x^n}=x^{m-n}[/tex]Then the given expression can be simplified as follows,
[tex]\begin{gathered} \frac{35x^{10}}{5x^5} \\ =\frac{35}{5}\times\frac{x^{10}}{x^5} \\ =7\times x^{10-5} \\ =7\times x^5 \\ =7x^5 \end{gathered}[/tex]Thus, the given expression is simplified as,
[tex]\frac{35x^{10}}{5x^5}=7x^5[/tex]What is the minimum? Where is the function increasing? Where is the function decreasing?
Answers
As given by the question
There are given that the graph.
Now,
The minimum value of the given graph is shown below:
[tex](2,\text{ -1)}[/tex]evaluate 2x + y when x = 15 and y = 4
Answers
Given the following expressions:
[tex]\text{ 2x + y}[/tex]With x = 15 and y = 4, let's evaluate by substituting the values to the respective variables.
We get,
[tex]\text{ 2x + y}[/tex][tex]\text{ 2(15) + (4)}[/tex][tex]\text{ 30 + 4}[/tex][tex]\text{ = 34}[/tex]Therefore, 2x + y when x = 15 and y = 4 is 34.