Given that every tenth person in line will get a coupon for a free box of popcorn at the movies what is the probability that you don't get a coupon when your in line
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Given that every tenth person in line will get a coupon for a free box of popcorn at the movies.
We are meant to find the probability that you don't get a coupon when you are in the line.
Step 2:
We can see that the probability that the person was in the line and got a coupon is:
[tex]\frac{1}{10}[/tex]Then, the probability that the person did not get a coupon when he was in the line is:
[tex](\text{ 1 -}\frac{1}{10})\text{ = }\frac{9}{10}[/tex]Related Questions
-4x-5-2x+3 simplify
Answers
Starting with the expression:
[tex]-4x-5-2x+3[/tex]Use the commutative property to bring like terms together:
[tex]-4x-5-2x+3=-4x-2x-5+3[/tex]Add like terms:
[tex]-4x-2x-5+3=-6x-2[/tex]Therefore:
[tex]-4x-5-2x+3=-6x-2[/tex]Which definition best describes a perpendicular bisector?Required to answer. Single choice. A line segment from a vertex of the triangles to the opposite side that divides an angle into two congruent adjacent angles. A line segment from a vertex of the triangles to the midpoint of the opposite side.A line segment from any vertex perpendicular to the line containing the opposite side of a triangle.A line that is perpendicular to a side of the triangle and also bisects that side of the triangle (it goes through the midpoint).
Answers
Answer:
A line that is perpendicular to a side of the triangle and also bisects that side of the triangle (it goes through the midpoint)
Step-by-step explanation:
A perpendicular bisector is a line segment perpendicular to and passing through the midpoint, dividing it into two equal segments and creating right angles.
Use graph to find the slope and y-intercept of the line. Compare the values to the equation y= -x+5
Answers
As given by the question
There are given that the graph of the line.
Now,
To find the slope and y-intercept of the line, first select two intersect point from the graph.
Then,
The points are:
[tex](0,\text{ 5) and (5, 0)}[/tex]Then,
First find the slope,
So,
From the formula of slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=0,y_1=5,x_2=5,y_2=0[/tex]Then,
Put all the value into the given formula.
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0_{}-5_{}}{5_{}-0_{}} \\ m=-\frac{5}{5} \\ m=-1 \end{gathered}[/tex]Now,
From the standard form of the line,
[tex]y=mx+b[/tex]Then,
Put y is 5, x is 0 and m is -5 into the above equation to find the y-intercept
So,
[tex]\begin{gathered} y=mx+b \\ 5=-1(0)+b \\ b=5 \end{gathered}[/tex]Hence, the value of the y-intercept is 5.
Now,
The line equation is shown below:
[tex]\begin{gathered} y=mx+b \\ y=-1x+b \\ y=-x+5 \end{gathered}[/tex]Hence, the slope of the line is -1, y-intercept of the line is 5 and the equation of line is y = -x + 5.
9. Leyla has 18 50-cent and 20-cent coins altogether. She has a total of $6.90. How many 20-cent coins does she have?
Answers
According to the information given in the exercise:
- Leyla has 18 coins of 50 cents and 20 cents.
. She has a total of $6.90.
Let be "f" the number 50-cent coins and "t" the number 20-cent coins.
Since 1 dollar is equal to 100 cents, you know that:
[tex]6.90dollars=690cents[/tex]Then, knowing the above, you can set up the following System of Equations:
[tex]\begin{cases}f+t=18 \\ \\ 50f+20t=690\end{cases}[/tex]To find the value of "t", you can apply the Substitution Method:
1. Take the first equation and solve for "f":
[tex]f=18-t[/tex]2. Substitute this equation into the second equation and solve for "t":
[tex]\begin{gathered} 50f+20t=690 \\ \\ 50(18-t)+20t=690 \end{gathered}[/tex][tex]\begin{gathered} 50(18-t)+20t=690 \\ \\ 900-50t+20t=690 \end{gathered}[/tex][tex]\begin{gathered} 900-30t=690 \\ \\ -30t=690-900 \\ \\ -30t=-210 \end{gathered}[/tex][tex]\begin{gathered} t=\frac{-210}{-30} \\ \\ t=7 \end{gathered}[/tex]Therefore, the answer is: She has 7 coins of 20 cents.
Solve the following equation for x. Please show all your solution steps. 2x - 5 + 3x = x - 41
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Two more than the cube root of a number
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We have
[tex]undefined[/tex]Diane opened a savings account 3 years ago the account earns 9% interest compounded monthly if the current balance is 100.00 how much did she despoit initially
Answers
Answer:
The amount she deposited initially is $76.41.
[tex]\text{ \$76.41}[/tex]Explanation:
We want to find the amount of Principal she deposited initially.
Recall that the formula for calculating the Principal of a compound interest is;
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Where;
P = Principal / initial amount
A = Future/ final amount
r = Interest rate (decimal)
n = number of times the interest is compounded per year.
t = Time in years
From the question, we were given the following;
A = $100.00
r = 9% = 0.09
n = monthly (12 months in a year) = 12 times
t = 3 years
Substituting the given values into the formula, we have;
[tex]\begin{gathered} P=\frac{100.00}{(1+\frac{0.09}{12})^{12(3)}} \\ P=\frac{100.00}{(1+0.0075)^{36}} \\ P=\frac{100.00}{(1.0075)^{36}} \\ P=76.41 \\ P=\text{ \$76.41} \end{gathered}[/tex]Therefore, the amount she deposited initially is $76.41.
[tex]\text{ \$76.41}[/tex]What is the equation of the line that passes through the point (5, 3)and has a slope of -4/5
Answers
Given:
The slope of the line
[tex]m=-\frac{4}{5}[/tex]The line passes through from the point (5,3).
Required:
Find the equation of the line.
Explanation:
The equation of the line that passes through from the point and has slope m is given by the formula as:
[tex]y-y_1=m(x-x_1)[/tex]Consider
[tex](x_1,y_1)=(5,3)[/tex]Now the equation of the line:
[tex]\begin{gathered} y-3=\frac{-4}{5}(x-5) \\ 5(y-3)=-4(x-5) \\ 5y-15=-4x+20 \\ 4x+5y=35 \end{gathered}[/tex]Final Answer:
The equation of the line passes through from point (5,3) and has a slope -4/5 is 4x + 5y = 35
guess this i am less than 10 i am not a multiple of 2 i am a composite number
Answers
Composite numbers have a smaller divisor, other than 1 and itself. Hence, the required number is 9.
What is composite number?Any positive integer that may be created by multiplying two other positive integers is referred to as a composite number. It is, in other words, a positive integer that has at least one divisor besides itself and the number 1.
Numbers with more than two elements are known as composite numbers in mathematics. Composite numbers are non-prime numbers that can be divided by more than two other numbers.
Composite numbers below 10 :
4, 6, 8, 9
From the composite numbers given, the value which is not a multiple of 2 is 9.
The values 4, 6, and 8 are multiples of 2.
Hence, the required is 9.
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If the population of a small town satisfies the exponential model A = Aoe^0.015t, where is measured in years, how long will it take for the town's population to increasefrom 5,450 to 10,355? Round your answer to two decimal placesAnswer
Answers
ANSWER :
The answer is 42.79 years
EXPLANATION :
From the problem, we have the function :
[tex]A=A_oe^{0.015t}[/tex]Solve for the value of t when A = 10,355 and Ao = 5,450
That will be :
[tex]\begin{gathered} 10355=5450e^{0.015t} \\ \frac{10355}{5450}=e^{0.015t} \\ 1.9=e^{0.015t} \\ \text{ Take the ln of both sides :} \\ \ln(1.9)=\ln(e^{0.015t}) \\ \ln(1.9)=0.015t \\ t=\frac{\ln(1.9)}{0.15} \\ t=42.79 \end{gathered}[/tex]Traci needs to change $300 US Dollars into Euros. the exchange rate is 1 euro for 1.25 dollars. how many euros does Traci get for her dollars?
Answers
Let's begin by identifying key information given to us:
Amount = $300
Amount (after changing) = ?
Exchange rate: €1 = $1.25
We will calculate how much Euros Traci gets for her dollar using simple proportion:
[tex]\begin{gathered} x=\text{\$}300 \\ \euro1=\text{\$}1.25 \\ \text{Cross multiply, we have:} \\ 1.25(x)=300\cdot1 \\ x=\frac{300}{1.25}=240 \\ x=\euro240 \end{gathered}[/tex]Therefore, Traci gets €240 for her dollars
5. The shadow of a tree extends 25 feet from the top of the tree to the ground. Sarah measures thatthe distance from the base of the tree to the tip of its shadow is 15 feet. How tall is the tree?A. 20 feetB. 25 feetC. 29.2 feetD. 40 feetO
Answers
Given :
The shadow of the tree = 25 feet from the top of the tree to the ground
the distance from the base of the tree to tip of its shadow is 15 feet
Let the height of the tree = x
So, 25 , 15 and x are forming a right angle triangle
25 is the hypotenuse of the triangle ,
x and 15 are the legs of the triangle
WE will find x using Pythagorean theorem
So,
[tex]\begin{gathered} x^2+15^2=25^2 \\ x^2=25^2-15^2=625-225=400 \\ x=\sqrt[]{400}=20 \end{gathered}[/tex]So, the height of the tree = 20 feet
The answer is option A. 20 feet
On January 1, 2012 Hector put his life savings of $17,229 into a savings account at Barclays, which was pain 0.9 interest at the time. Over the next year, the inflation rate averaged 1.7%. Now consider the following propositions
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Answer:
what propositions?
Step-by-step explanation:
Five students, Stella, Victoria, Alexander, Eva, and Hunter, line up one behind theother. How many different ways can they stand in line?
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Permutations formula
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]where n things are chosen r at a time.
In this case, we need to find the number of permutations of n = 5 students chosen r = 5 at a time. That is,
[tex]\begin{gathered} _5P_5=\frac{5!}{(5-5)!} \\ _5P_5=\frac{5!}{0!} \\ _5P_5=\frac{5\cdot4\cdot3\cdot2\cdot1}{1} \\ _5P_5=120 \end{gathered}[/tex]They can stand in line in 120 different ways
what is 9/7 ÷ 2/3 ?
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we have the expression
[tex]\frac{9}{7}\div\frac{2}{3}=\frac{9*3}{2*7}=\frac{27}{14}[/tex]The answer is 27/14Andy, Bobby, and Cathy each went for a walk yesterday afternoon. Andy walked 1 3/4 mi at a constant speed of 1 1/4 mi/h. Bobby walked 2 3/4 mi at a constant speed of 2 1/2 mi/h. Cathy walked for 1 h and 22 min at a constant speed of 1 1/4 mi/h. List the three people in order of the times they spent walking from least time to greatest time.
Answers
Answer:
In order of the times they spent walking from the least to the greatest time, we have:
Cathy
Andy
Bobby
Explanation:
Given the following:
Andy walked 1 3/4 min at a constant speed of 1 1/4 mi/h
Bobby walked 2 3/4 mi at a constant speed of 2 1/2 mi/h
Cathy walked for 1 h and 22 min at a constant speed of 1 1/4 mi/h
We are required to list the three people in order of the times they spent walking from least to the greatest time,
This is the same thing as listing the following numbers:
1 3/4, 2 3/4, and 1h 22min from least to greatest.
Andy: 1 3/4 = 7/4 = 1.75 = 2 hours, 15 minutes
Bobby: 2 3/4 = 11/4 = 2.75 = 3 hours, 15 minutes
Therefore, from the least to the greatest time, we have:
Cathy
Andy
Bobby
The left and the right page of numbers of an open book are two consecutive integers whose sum is 381 . Whats are the page numbers
Answers
In order to determine the number of page numbers, let x the number of one page and x + 1 the number of the other page.
The sum of both numbers is 381, then:
x + (x + 1) = 381
Solve the previous equation for x, as follow:
x + x + 1 = 381 simplify like terms
2x + 1 = 381 subtract 1 both sides
2x = 381 - 1
2x = 380 divide by 2 both sides
x = 380/2
x = 190
Then, the numbers are 190 + 191
Name the rotation that maps the black triangle onto the red triangle. Explain how you know(See picture below)
Answers
We would compare the coordinates of corresponding vertices on the red and black triangles. The vertex at the top of the black triangle and the vertex at the bottom of the red triangle correspond to each other. We would compare them.
For black triangle, coordinate is (1, - 3)
For red triangle, coordinate is (- 1, 3)
If a vertex with coordinate, (x, y) is rotated 180 degrees counterclockwise about the origin, the new coordinate is (- x, - y). By rotating (1, - 3) 180 degrees counterclockwise, it becomes (- 1, - - 3) = (- 1, 3). This corresponds to the coordinate of the corresponding vertex of the red triangle. Thus, the rotation that maps the black triangle onto the red triangle is 180 degrees counterclockwise rotation about the origin
Lily has 30 Marvel Funko Pops. The number of Marvel Funky Pops in her collection is only 60% of hes total Funko Pops. How many total Funko Pops are in her collection?
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Lily has 30 Marvel Pops, they are 60% of the total Pops
How many in total ?
We can say that the realation between 30 an the total is the same relation between 60% and 100%, so we can write:
30/x = 60/100
[tex]\frac{30}{x}=\frac{60}{100}[/tex]Where x is the total number of Pops
Solving this for x:
x = 30(100)/60 = 3000/60 = 50
[tex]x\text{ = }\frac{\text{30(100)}}{60}=\frac{3000}{60}=50[/tex]Answer:
Number of total Funlo Pops in her collection: 50
[tex] \frac{1}{5} [/tex]convert into a prercentage
Answers
Answer:
20%
Explanation:
To convert a fraction into a percentage, multiply the fraction by 100.
Thus, the fraction 1/5 as a percentage is:
[tex]\begin{gathered} =\frac{1}{5}\times100 \\ =\frac{100}{5} \\ =20\% \end{gathered}[/tex]The percentage equivalent of 1/5 is 20%.
Find the Value of X, round your answer to the nearest 10th
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The value of x is 13.31 units.
What is trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.
Given a right angle with perpendicular = 8 units and base = x units and one acute angle = 59°
tangent of an angle = perpendicular/base
Therefore,
tan59° = x/8
x = tan59°*8
x = 13.31
Hence, the value of x is 13.31 units.
For more references on trigonometric ratios, click;
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AT&T is having a sale on all cell phones. They will give you a loan to pay for the phone. Your phone costs $899 How much will you pay for the phone if they charge you 4.5% interest, and it will take you 24 months to pay it off.
-How do you do this equation?
Answers
Answer:
Its a scam AT&T has no such sale going on right now.
Step-by-step explanation:
I need help with my practice questions. I don’t know where i’m supposed to plot the points on the graph and I need an explanation please.
Answers
Step by step
When rotating a point 270 degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means, you change the sign on your x value first and then switch positions of x and y.
X = (2, -1) ➡️ X’ = (-1, -2)
Y = (-4, -3) ➡️ Y’ = (-3, 4)
Z = (3, 2) ➡️ Z’ = (2, -3)
Now to graph, start with your pre image points. (x, y)
From (0, 0) center /origin, move your cursor (left negative or right positive) for x, (down negative or up positive) for y.
Then plot your image points to see how the figure has transformed.
I graphed them for you in the attachment
how do I find the length of x and y?
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PLEASE HELP ME.Match the shape with its area formula Column A Column B 1: Triangle a. A= LW2: Parallegram. b: A=(TTr^2)/23: Semi- circle. c:(bh)/2 or 1/2(bh)4:Trapizoid. D. A= (b1+b2)(h)2
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1. Triangle: the area of the triangle is C. (bh)/2
2:Parallegram: the area is a. LW
3. Semi-circle: the area is b. (pi r^2)/2
4. Trapezoid: the area will be D. (b1+b2)(h)2
Use the following two points to answer parts a - c. (2, 9), (4, - 7) a . Find the slope of the line passing through the two points. b . Write an equation of a line passing through the two points in point-slope form. c Rewrite the equation of the line in slope-intercept form.
Answers
slope= m =y2-y1/x2-x1, then
[tex]\begin{gathered} m=\frac{-7-9}{4-2} \\ m=-\frac{16}{2} \\ m=-8 \end{gathered}[/tex]a. slope = -8
Trey made $2000 in taxable income last year. suppose the income tax rate is 10% for the first $9500 plus 14% for the amount over $9500. How much must trey pay in income tax for last year?
Answers
SInce he made $2000 , and this is less than the limit for the first bracket, Trey will need to pay just 10% on his gain:
10% of $2000 = 0.1 * 2000 = $200.
His tax is $200.
graph the function f(x)=3-(x)
Answers
The given function is
[tex]f(x)=3-x[/tex]To graph this linear function we have to complete a table of values. We replace each x-value in the function to get each y-values to form coordinated pairs.
x f(x)
-2 5
-1 4
0 3
1 2
Let's do the calculations for each f(x) value.
[tex]\begin{gathered} f(-2)=3-(-2)=3+2=5 \\ f(-1)=3-(-1)=3+1=4 \\ f(0)=3-0=3 \\ f(1)=3-1=2 \end{gathered}[/tex]At last, we have to graph each point and draw a straight line. The graph below shows the graph for the function.
Solve the system of equations x + 2y = 0 Solve the equation for x.
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Given the equation :
[tex]x+2y=0[/tex]Solve the equation for x:
[tex]x=-2y[/tex]Final Answer:
x = -2yIn-depth explanation:
Hi! The question is asking us to solve the equation x + 2y = 0 for x.
________________________
To Solve
Rearrange the equation for x.
________________________
All we need to do is subtract '2y' from both sides.
[tex]\implies\sf{x+2y=0}[/tex]
[tex]\implies\sf{x=0-2y}[/tex]
[tex]\implies\sf{x=-2y}[/tex]
∴ Equation: x = -2y
_______________________
Unit 4 What is the rate of return when 20 shares of Stock A, purchased for $20/share, are sold for $490? The commission on the sale is $6. Rate of Return = [?] % Give your answer as a percent rounded to the nearest tenth.
Answers
Answer:
21%
Step-by-step explanation:
You want the rate of return on 20 shares of stock bought for $20 per share and sold for $490 with a commission on the sale of $6.
Rate of returnThe rate of return is the percentage change between the sale proceeds and the cost of the stock.
rate of return = (proceeds/cost -1) × 100%
= ((490 -6)/(20·20) -1) × 100% = 21%
The rate of return is 21%.
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