Answers
In this problem, the random variable is X, the amount of winnings.
From the statement, we know that:
• the theatre group sells 100 tickets for $5 each,
,• you purchase 4 tickets,
,• the prize worth is $150.
Part (d)
• The net amount of profit is X (profit) = -5 * $4 + $150 = -$20 + $150 = $130.
,• The net amount of losing is X (loss) = -5 * $4 = -$20.
,• The probability of profit is:
[tex]P(profit)=\text{ }\frac{\#\text{ of tickets bought}}{#\text{ of tickets }}=\frac{4}{100}=0.04.[/tex]• The probability of losing is:
[tex]P\left(loss\right)=1-P\left(profit\right)=1-0.04=0.96.[/tex]• The mean value of profit is:
[tex]x(profit)\times P(x=profit)=\text{ \$130}\times0.04=\text{ \$5.2.}[/tex]The mean value of the loss is:
[tex]x(loss)\times P(x=loss)=\text{ -\$20}\times0.96=-\text{ \$19.2.}[/tex]Using these data, we complete the table:
Part (e)
If this event is repeated often and you repeat the strategy, the expected average winnings per raffle will be:
[tex]\text{ Average = }x(profit)\times P(x=profit)+x(loss)\times P(x=loss)=\text{ 5.2 + \lparen-19.2\rparen = -14.}[/tex]AnswerPart (d)
Part (e):
-14
Related Questions
Convert 291 dg to kg.
Answers
Answer:
Question:
Convert 291 dg to kg
Concept:
Using the conversion rate, we will have
[tex]1kg=10^4dg[/tex]By applying the conversion rate above, we will have that
[tex]\begin{gathered} 1kg=10^4dg \\ xkg=291dg \\ cross\text{ multiply, we will have} \\ 1\times291=x\times10^4 \\ 291=10000x \\ divide\text{ both sides by 10000} \\ \frac{10000x}{10000}=\frac{291}{10000} \\ x=0.0291kg \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow0.0291kg[/tex]if RT is extended to contain a point W so that UW =8, What is SW?
Answers
We know form the image that SR and SU are congruent therefore SW and UW must be congruent.
Therefore if UW=8 SW=8
ANSWER
SW=8
the manager counted orders for a total of 24 dozen shamrock-shaped cookies, horseshoe-shaped cookies, and mint chocolate chip cupcakes. They sold four times as many cupcakes as shamrock cookies and three times as many horseshoe cookies as shamrock cookies. How many mint chocolate chip cupcakes did they sell?
Answers
Let's begin by identifying key information given to us:
Number of cookies = 24 dozens = 24 x 12 = 288 cookies
Let the shamrock cookies be s.
Let the horseshoe cookies be h.
Let the chip cupcakes be c.
They sold four times cupcakes as shamrock cookies & three times as many horseshoe cookies as shamrock cookies
[tex]\begin{gathered} c=4s,h=3s \\ s+h+c=288 \\ s+4s+3s=288 \\ 8s=288 \\ s=\frac{288}{8}=36 \\ But, \\ c=4s \\ c=4(36)=144 \\ c=144 \\ \\ h=3s \\ h=3(36)=108 \\ h=108 \end{gathered}[/tex]They sold 144 mint chocolate chip cupcakes
Scott invested a total of $5400 at two separate banks. One bank pays simple interest of 10% per year while the other pays simple interest at a rate of 8% per year. If Scott eamed $492.00 in interest during asingle year, how much did he have on deposit in each bank?
Answers
Given:
Total principal = $5400
Interest rate of bank A = 10% = 0.10
Interest rate of bank B = 8% = 0.08
Total interest = $492
Let's find how much he deposited in each bank.
Equation for total principal:
A + B = 5400
Equation for total interest:
0.10A + 0.08B = 492
Hence, we have the system of equations:
A + B = 5400
0.10A + 0.08B = 492
Where A and B represents the amount deposited in each bank.
Let's solve the system simultaneously using substitution method:.
Rewrite the first equation for A:
A = 5400 - B
Substitute (5400 - B) for A in equation 2:
[tex]\begin{gathered} 0.10(5400-B)+0.08B=492 \\ \\ 540-0.1B+0.08B=492 \\ \\ -0.1B+0.08B=492-540 \\ \\ -0.02B=-48 \end{gathered}[/tex]Divide both sides by -0.02:
[tex]\begin{gathered} \frac{-0.02B}{-0.02}=\frac{-48}{-0.02} \\ \\ B=2400 \end{gathered}[/tex]Now, substitute 2400 for B in either of the equations:
[tex]\begin{gathered} A=5400-B \\ \\ A=5400-2400 \\ \\ A=3000 \end{gathered}[/tex]Therefore, we have the following:
Amount deposited in the bank that pays 10% interest = $3000
Amount deposited in the bank that pays 8% interest = $2400
• ANSWER:
Amount deposited in the bank that pays 10% interest = $3000
Amount deposited in the bank that pays 8% interest = $2400
One of the lines has a positive slope, one has a negative slope. Which one do you think has a Negative Slope?
Answers
The line thas has a negative slope is the blue one.
Remember that the slope gives the change rate between y and x, that is, the slope is defined by
[tex]m=\frac{\Delta y}{\Delta x}[/tex]
This means that for every
[tex]\Delta x[/tex]we move to the right, then we move the ammount
[tex]\Delta y[/tex]in the y direction. Therefore the sign of the slope tell us if we move down (if the slope is negative) or up (if the slope is postive) while we move to the right.
Mrs. Mazzucco dumps out her change purse and finds that
she has 15 coins, all dimes and quarters, for a total of $2.70.
How many quarters does she have?
Answers
Answer: 10 quarters and 2 dimes.
Step-by-step explanation:
4 quarters = 1 dollar
1 quarter = 25 cents
1 dime = 10 cents
If 4 quarters are 1 dollar then 2 dollars would be 8 quarters.
8 quarters + 2 quarters (50 cents) would be 2.50
You cant add another quarter or that would be 2.75.
Instead you do: 10 quarters + 2 dimes = 2.70
So to sum it all up there are 10 quarters and 2 dimes.
0 2 20) 5x - (x + 2) >-5(1 + x) + 3 섥놈 SXX2=55*3 x>0 4.x.-25-5x-2 Darsx-23-2 985-272 vhose 22) Name one particular solution to question #20.
Answers
5x - (x + 2) > -5(1 + x) + 3
Removing parentheses and distributing
5x - x - 2 > -5*1 + (-5)*x + 3
4x - 2 > -5 - 5x + 3
4x - 2 > -2 - 5x
5x is subtracting on the right, then it will add on the left
4x -2 + 5x > -2
9x - 2 > -2
2 is subtracting on the left, then it will add on the right
9x > -2 + 2
9x > 0
9 is multiplying on the left, then it will divide on the right
x > 0/9
x > 0
Every x greater than zero is a solution, like for example 1, 2, 10, etc.
Jessica gave 6 people candy. She split 7/8 pounds among them. What is the unit rate in pounds per person
Answers
Number of people: 6
Number of pounds: 7/8
The unit rate in pounds per person can be calculated using the formula:
[tex]\text{ unit rate }=\frac{\text{ number of pounds}}{\text{ number of people}}[/tex]Then, using the values from the beginning:
[tex]\begin{gathered} \text{ unit rate }=\frac{7/8}{6}=\frac{7}{8\cdot6} \\ \\ \therefore\text{ unit rate }=\frac{7}{48}\text{ pounds per person} \end{gathered}[/tex]“ using the figure below, state 4 different angles that are congruent to EFC using 4 different conjectures. State the congruent angles and the appropriate conjecture” this is confusing if someone could help that would be appreciated
Answers
From the given figure
Since AC intersects EH at point F, then
Since AC // BD, and EH is the transversal
express the following as a function of a positive acute angle show work
Answers
We have the following:
There is a property that allows us to remove the negative sign from inside the angle parenthesis and put it outside, just as follows
[tex]\tan (-60\text{\degree)}=-\tan (60\text{\degree)}[/tex]Dominick borrowed $6,000 from a credit union at 9% simple interest for 30 months. What is the total amount of interest Dominick will pay throughout the life of the loan?$1350$1325$1300$1250None of these choices are correct.
Answers
$1350
Explanation
the simple interest formula is given by:
[tex]\begin{gathered} I=\text{P}\cdot\text{R}\cdot\text{T} \\ \text{where} \\ I\text{ is the interest} \\ P\text{ is the principal amount } \\ r\text{ is the interest rate} \\ \text{and t is the time ( in years)} \end{gathered}[/tex]Step 1
convet the time from months to years
use:
[tex]1\text{ year}\rightarrow12\text{ months}[/tex]so
[tex]30\text{ months(}\frac{1\text{ year}}{12\text{ months}}\text{)=2.5 years}[/tex]Step 2
Let
time=2.5 years
Interest= I
interest rate(r)=9%=0.09
Principal(p)=6000
Now, replace.
[tex]\begin{gathered} I=\text{P}\cdot\text{R}\cdot\text{T} \\ I=\text{\$ 6000 }\cdot0.09\cdot2.5 \\ I=1350 \end{gathered}[/tex]therefore the answer is $1350
I hope this helps you
I need help finding 5 points. 2 to the left of the vertex, the vertex, and 2 to the right of the vertex. the graph only goes up to 14
Answers
In order to graph the parabola, first let's identify the x-coordinate of the vertex.
To do so, we can use the formula below, after identifying the parameters a, b and c from the standard form of the equation:
[tex]\begin{gathered} x_v=\frac{-b}{2a} \\ \\ y=ax^2+bx+c \\ a=-3,b=0,c=3 \\ \\ x_v=\frac{-0}{2\cdot(-3)}=0 \end{gathered}[/tex]Now, let's calculate the points using x = -2, x = -1, x = 0, x = 1 and x = 2:
[tex]\begin{gathered} x=-2\colon \\ y=-3(-2)^2+3=-3\cdot4+3=-12+3=-9 \\ x=-1\colon \\ y=-3(-1)^2+3=-3\cdot1+3=0 \\ x=0\colon \\ y=-3\cdot0^2+3=0+3=3 \\ x=1\colon \\ y=-3\cdot1^2+3=0 \\ x=2\colon \\ y=-3\cdot2^2+3=-12+3=-9 \end{gathered}[/tex]Graphing these points and the corresponding parabola, we have:
draw a model to support your solution 3/5 thought of juice is poured equally into 6 glasses how much juice is in each glass.
Answers
We have to divide 3/5 by 6. The picture above represents 3/5.
Drawing 5 vertical lines, we divide the whole block into 6 equal parts.
Now we have a total of 5*6 = 30 little squares. Dividing 3/5 into 6 equal parts we shade 3 out of 30 little squares. Then, 3/5 ÷ 6 = 3/30 = 1/10 (simplifying)
The graph of a cosine function shows a reflection over the x-axis, an amplitude of 5, a period of 6, and a phase shift of 0.25 to the right.Which is the equation of the function described?a. f(x)=−5cos(πx/3−1/4)b. f(x)=−5cos(πx/3 − π/12)c. f(x)=−5cos(3πx − 1/4)d. f(x)=−5cos(πx/3 − 4π/3)
Answers
Answer:
Given that:
The graph of a cosine function shows a reflection over the x-axis, an amplitude of 5, a period of 6, and a phase shift of 0.25 to the right.
To find the equation of the function described.
Explanation:
we have that,
General formula of cosine function is,
[tex]f(x)=a\cos(b(x+c))+k[/tex]where a is amplitude, b is period factor, c is shift (left/right) and k is shift (up/down)
From given,
a=5
b=2pi/6=pi/3
c=0.25
we get,
[tex]f(x)=-5\cos\frac{\pi}{3}(x-0.25)[/tex][tex]f(x)=-5\cos\frac{\pi}{3}(x-\frac{1}{4})[/tex][tex]f(x)=-5\cos(\frac{\pi}{3}x-\frac{\pi}{12})[/tex]Answer is: option:b
[tex]f(x)=-5\cos(\frac{\pi}{3}x-\frac{\pi}{12})[/tex]Put these points into an equation IN STANDARD FORM!!!!!!
(3,0) and (0,-7)
Answers
⇒The standard form of a straight line equation is given by y= mx+c
where m is the gradient and (x, y) are the given points and c is the y intercept.
⇒We can the gradient of the line using the formula
⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\ m=\frac{-7-0}{0-3} \\m=\frac{-7}{-3}\\m=\frac{7}{3}[/tex]
⇒To find the value of c we can plug in any point in the equation y=mx+c ,you will get the same value.
⇒I will use the point (3,0)
[tex]0=\frac{7}{3}(3)+c\\ 0=7+c\\c=-7[/tex]
This simply means that the equation of the straight line is
[tex]y=\frac{7}{3} x-7[/tex]
GoodLuck!!
The equation in standard form for the line that passes through the given points (3,0) and (0, -7) will be 2x + 3y = 12.
Linear equation: It is defined as the relation between two variables, if we plot the graph of the linear equation, we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that the line that passes through the given points (3,0) and (0, -7) is
The slope m of the line is,
m = (y₂-y₁) / (x₂ - x₁)
m =3 - 0 / 0 -7
m = 3 / -7
The standard equation of the line is,
y - y₁ = m(x - x₁)
y - 0 = -2/3 (x + 7)
y = -2/3x + 4
y+2/3x =4
Multiply by 3 in the whole equation,
3(2/3x + y = 4)
2x + 3y = 12
Thus, the equation in standard form for the line that passes through the given points (3,0) and (0, -7) will be 2x + 3y = 12.
Learn more about the linear equation at:
brainly.com/question/11897796
The tree diagram shows the sample space of two-digit numbers that can be created using the digits 9,2 1, and 8. What is the probability of choosing a number from the sample space that contains both 2 and 8?
Answers
Help! Identify the binomial that is a factor of the polynomial.
Answers
The binomial that is a factor of the polynomial is (x-2).
STEP - BY - STEP EXPLANATION
What to find?
The binomial that is a factor of the polynomial.
Given:
P(x) =3x³ - 11x² -2x + 24
The factor can be determine by simply finding the zeros of the polynomial.
The zeros of a polynomial when substituted into the polynomial makes it zero.
From the given option, we shall test to see which makes the polynomial zero.
Substitute x=2 into the given polynomial and simplify.
That is;
p(3) = 3(2)³ - 11(2)² -2(2)+ 24
=3(8) - 11(4) - 2(2) + 24
=24 - 44 - 4 + 24
=0
Hence, p(x) = 0 when x=2.
This implies x-2 is a factor of the polynomial.
Since x=2 is the only digit among the option that makes p(x) =0, then (x-2) is the only binomial that is a factor among the options given.
Use this model to calculate6Ο Α.1618ОВ.1324
Answers
Answer:
To find the value of,
[tex]\frac{3}{8}\times\frac{2}{6}[/tex]by using the given model
Since the denominators are 8 and 6, construct the model with 6 rows and 8 columns
For 3/8 shade 3 columns and for 2/6 shade 2 rows
From
40. Assume the lines that appear to be tangent are tangent. O is the center of the circle. Findthe value of xmZP-12c. 102d. 24a. 78b. 39
Answers
Answer
a. 78
Step-by-step explanation
Given that side PQ is tangent to circle O, then angle Q measures 90 degrees.
The addition of the three interior angles of a triangle is equal to 180 degrees. Applying this to triangle PQO, we get:
[tex]\begin{gathered} m\angle P+m\angle Q+m\angle O=180\degree \\ 12\degree+90\degree+x=180\operatorname{\degree} \\ x=180\operatorname{\degree}-12\degree-90\degree \\ x=78\operatorname{\degree} \end{gathered}[/tex]what point can we use to create the graph of y- 7 =3(x+5)
Answers
ANSWER:
[tex](-5,7)[/tex]STEP-BY-STEP EXPLANATION:
The correct point would be that when the value of x is replaced, the value of y is the corresponding value, we try with each option like this
[tex]\begin{gathered} (7,3)\rightarrow y-7=3\mleft(7+5\mright)\rightarrow y=36+7\rightarrow y=43\rightarrow(7,43)\rightarrow incorrect \\ (3,-5)\rightarrow y-7=3(3+5)\rightarrow y=24+7\rightarrow y=31\rightarrow(3,31)\rightarrow incorrect \\ (7,-5)\rightarrow y-7=3(7+5)\rightarrow y=36+7\rightarrow y=43\rightarrow(7,43)\rightarrow incorrect \\ (-5,7)\rightarrow y-7=3(-5+5)\rightarrow y=0+7\rightarrow y=7\rightarrow(-5,7)\rightarrow correct \end{gathered}[/tex]Find the savings plan after 9 months with an APR of 7% and monthly payments if $250
Answers
ANSWER:
$ 2303.22
STEP-BY-STEP EXPLANATION:
We can calculate the balance using the following formula:
[tex]\text{FVA = }\frac{\text{PMT}\cdot((1+r)^n-1)}{r}[/tex]Given:
n = 9 months
r = 7%/12 = 0.07/12
PMT = 250
Plug in the numbers and solve for FVA
[tex]\begin{gathered} \text{FVA = }\frac{250\cdot((1+\frac{0.07}{12})^9-1)}{\frac{0.07}{12}} \\ \text{FVA =}2303.22 \end{gathered}[/tex]The balance is $ 2303.22
Number of ways to arrange the letters ELEVATED if T and D must not be next to one another.
Answers
Given: A collection of letters- ELEVATED.
Required: To determine the number of ways to arrange the letters ELEVATED such that T and D must not be next to one another.
Explanation: The permutation determines the number of arrangements of the given letter. Then we can exclude the arrangements of TD and DT to get the required answer.
The total number of arrangements of given letters is-
[tex]\begin{gathered} 8!=8\times7\times6\times5\times4\times3\times2\times1 \\ =40320 \end{gathered}[/tex]Now the total arrangements in which T and D are next to each other is-
[tex]\begin{gathered} ^8P_2=\frac{8!}{(8-2)!} \\ =\frac{8\times7\times6!}{6!} \\ =56 \end{gathered}[/tex]Now there can be arrangements like TD and DT. Hence we need to exclude the arrangements from the total number of arrangements as follows-
[tex]40320-56-56=40208[/tex]Final Answer: The number of ways to arrange the letters ELEVATED if T and D are not next to each other is 40208.
Directions: If each quadrilateral below is a parallelogram find the missing measures.
Answers
Given that CDEF is a parallelogram
So, every two opposite sides are equal in length
And the diagonals bisect each other
So, CD = FE , CF = DE , CG = EG and FG = DG
so,
[tex]\begin{gathered} CF=DE=10 \\ \\ FE=CD=15 \\ \\ CE=2\cdot CG=2\cdot7=14 \\ \\ GD=\frac{1}{2}FD=\frac{1}{2}\cdot22=11 \end{gathered}[/tex]
POSSIBLE POINTS: 16.67Chloe is an avid gymnast. An annual membership at the local gymnasium costs $3,500. She canborrow the money from her bank at 1.25% interest for 3 years. By the end of the loan, how muchmoney will Chloe end up paying the bank for the gym membership?
Answers
SOLUTION
Chloe borrowed $3,500 at 1.25% interest rate for 3 years. Let's first find the interest on the money she borrowed. This becomes
[tex]\begin{gathered} \text{Simple interest I = }\frac{P\times R\times T}{100} \\ \text{Where P = the principal which is the money borrowed = \$3,500} \\ R\text{ = interest rate = 1.25\%} \\ T\text{ = time = 3 years } \\ I\text{ = }\frac{P\times R\times T}{100} \\ \\ I\text{ = }\frac{3500\times1.25\times3}{100} \\ \\ I\text{ = }\frac{13125}{100} \\ \\ I\text{ = \$131.25} \end{gathered}[/tex]The interest = $ 131.25. She will pay back an amount of = P + I
Amount = 3500 + 131.25 = $3,631.25
Evaluate the expression.3 - 5(11 + 4) = 52 = 0
Answers
Evaluate the value of expression.
[tex]\begin{gathered} \frac{3-5(11+4)}{5^2}=\frac{3-5\cdot15}{25} \\ =\frac{3-75}{25} \\ =-\frac{72}{25} \\ =-2.88 \end{gathered}[/tex]So answer is -2.88.
You want to buy a car. The loan amount will be $35,000. The company is offering a 5% interest rate for 36 months (3years). What will your monthly payments be?
Answers
Given that:
[tex]\begin{gathered} \text{Loan amount, P}_0=35000 \\ \text{Annual interst rate, r = }5\%=0.05 \\ \text{Number of compounding periods in one year, k =12} \\ L\text{ength of loan(in years), N = 3} \end{gathered}[/tex]Find the monthly payment, d.
The formula to find the monthly payment is
[tex]P_0=\frac{d(1-(1+\frac{r}{k})^{-Nk})}{(\frac{r}{k})}[/tex]Plug the given values into the formula.
[tex]\begin{gathered} 35000=\frac{d(1-(1+\frac{0.05}{12})^{-3\cdot12})}{(\frac{0.05}{12})} \\ =33.3657d \\ d=\frac{35000}{33.3657} \\ =1048.98 \end{gathered}[/tex]The monthly payment is $1049 approximately.
A rectangle is placed around a semicircle as shown below. The width of the rectangle is 9 yd. Find the area of the shaded region.Use the value 3.14 r*pi and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Given:
The width of the rectangle is 9 yd.
Required:
To find the area of the shaded region.
Explanation:
From the given figure,
Width of the rectangle is 9 yd.
Therefore, the radius of the semicircle is 9yd.
And the length of the rectangle is diameter of the semicircle.
[tex]\begin{gathered} =2\times9 \\ =18yd \end{gathered}[/tex]Now, the area of the rectangle is,
[tex]\begin{gathered} A=L\times W \\ =9\times18 \\ =162yd^2 \end{gathered}[/tex]Now the area of the semicircle is,
[tex]\begin{gathered} A=\frac{\pi r^2}{2} \\ =\frac{3.14\times9^2}{2} \\ =\frac{254.34}{2} \\ =127.17yd^2 \end{gathered}[/tex]Now the area of the shaded region = Area of the rectangle - Area of the semicircle.
[tex]\begin{gathered} =162-127.17 \\ =34.83\text{ yd}^2 \end{gathered}[/tex]Final Answer:
The area of the shaded region is 34.83 yd square.
A rectangle is placed around a semi circle as shown below the length of the rectangle is 12mm. Find The area of the shaded region. Use the value 3.14 for pi, and do not round your answer be sure to include the correct unit in your answer.
Answers
Explanation
We are given a rectangle placed around a semi-circle as shw in the image below:
We are required to determine the area of the shaded portion.
This is achieved thus:
The area of the shaded portion is given as:
[tex]\begin{gathered} Area=Area\text{ }of\text{ }rectangle-Area\text{ }of\text{ }semicircle \\ Area=A_r-A_s \end{gathered}[/tex]The dimension of the rectangle is given as:
[tex]\begin{gathered} Length=Diameter\text{ }of\text{ }the\text{ }semicircle=12mm \\ Width=Radius\text{ }of\text{ }the\text{ }semicircle=\frac{12}{2}=6mm \end{gathered}[/tex]Therefore, the area of the shaded portion is:
[tex]\begin{gathered} Area=A_r-A_s \\ Area=(l\times w)-(\frac{\pi r^2}{2}) \\ Area=(12\times6)-(\frac{3.14\times6^2}{2}) \\ Area=(72)-(56.52) \\ Area=15.48mm^2 \end{gathered}[/tex]Hence, the answer is:
[tex]Area=15.48mm^{2}[/tex]Solve the inequalities|x| < 8
Answers
Given the following inequality:
[tex]|x|<8[/tex]According to the rules of the absolute values, the given inequality will be written as follows:
[tex]-8So, the answer will be:[tex]x=(-8,8)[/tex]The solution on the number line will be as follows:
-4+w+ 17-2/3 W = 16