The expected value of purchasing a raffle ticket is -0.647.
What is the Expected Value of a Probability & Statistical Analysis?The expected value is derived in probability analysis by the multiplication of each of the potential possibilities by the likelihood that each result will occur and then adding all of those values together.
Using the formula below, we can calculate the expected value as follows:
[tex]\mathbf{ E(X)= \sum^{n}_{i=1}X_i P(X_i)}[/tex]
However, the probability (Pr) of each event can be categorized as follows:
Pr (to win a flower arrangement ) [tex]\mathbf{=\dfrac{20}{5500}}[/tex]Pr (to gift a certificate) [tex]\mathbf{=\dfrac{20}{5500}}[/tex]Pr (no win) ) [tex]\mathbf{=\dfrac{5500 - 20 - 20}{5500}=\dfrac{5460}{5500}}[/tex]Thus;
[tex]\mathbf{E(X) = 70(\dfrac{20}{5500} \times 25 ((\dfrac{20}{5500} )- 1(\dfrac{5460}{5500} )}[/tex]
[tex]\mathbf{E(X) =-0.647}[/tex]
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What is the sum of 4 radical 12 and 2 radical 27 in simplest form
Answer:
14√3
Step-by-step explanation:
4√12 + 2√27
First, simplify both terms:
4√3√4 + 2√9√3
4 * 2√3 + 2 * 3√3
8√3 + 6√3
Now, combine the terms:
14√3
To find the sum of 4 radical 12 and 2 radical 27 in simplest form, we simplify each radical expression individually and then add the simplified expressions together, resulting in 5 times the square root of 3.
Explanation:To find the sum of 4 radical 12 and 2 radical 27 in simplest form, we first need to simplify each radical expression individually. The square root of 12 can be simplified as the square root of 4 times the square root of 3, which is 2 times the square root of 3. Similarly, the square root of 27 can be simplified as 3 times the square root of 3.
Now, we can add these simplified radical expressions. 4 radical 12 plus 2 radical 27 equals (2 times the square root of 3) plus (3 times the square root of 3). This can be simplified as 5 times the square root of 3.
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You and your friend each collect rocks and fossils. Your friend collects three times as many rocks and half as many fossils as you. You collect 25 objects. Your friend collects 15 objects. How many rocks and how many fossils do each collect
Answer:
Number of rocks and fossils collected by you is 1 and 24 respectively
Number of rocks and fossils collected by your friend is 3 and 12 respectively
Step-by-step explanation:
Let the number of Rocks you collect be x
Let the number of Fossils you collect be y
Then the total number pf objects you collected will be
x + y = 25
x = 25 - y------------------------------(1)
Your friend collects three times as many rocks and half as many fossils as you.
This can be written as
[tex]3x + y(\frac{1}{2}) = 15[/tex]
[tex]3x + (\frac{y}{2}) = 15[/tex]-------------------(2)
Substituting (1) in (2)
[tex]3(25 -y) + (\frac{y}{2}) = 15[/tex]
[tex] 75 - 3y + (\frac{y}{2}) = 15[/tex]
Grouping the like terms we get,
[tex] 75 - 15 = 3y - (\frac{y}{2})[/tex]
[tex] 60= \frac{6y-y}{2})[/tex]
[tex] 60 \times 2= 6y-y[/tex]
[tex] 120= 5y[/tex]
[tex] y = \frac{120}{5}[/tex]
y= 24
Substituting y value in equation(1) we get
x = 25 - 24
x= 1
Friends collects 3 times rock
so collects 3x =3(1) = 3rocks
Also he collects half as many fossils
That is
[tex]\frac{y}{2} = \frac{24}{2} =12 fossils[/tex]
You collect 1 rock and 24 fossils, while your friend collects 3 rocks and 12 fossils.
Explanation:Let's assign variables to represent the number of rocks and fossils that you and your friend collect.
Let x represent the number of rocks you collect.
Since your friend collects three times as many rocks as you, we can represent the number of rocks your friend collects as 3x.
Let y represent the number of fossils you collect.
Since your friend collects half as many fossils as you, we can represent the number of fossils your friend collects as y/2.
From the information given, we know that you collect 25 objects, so we have the equation:
x + y = 25
We also know that your friend collects 15 objects, so we have the equation:
3x + y/2 = 15
Simplifying the second equation by multiplying both sides by 2, we get:
6x + y = 30
We now have a system of equations:
x + y = 25
6x + y = 30
Solving this system of equations, we can subtract the first equation from the second equation to eliminate y:
(6x + y) - (x + y) = 30 - 25
5x = 5
x = 1
Substituting the value of x into the first equation, we find:
1 + y = 25
y = 24
Therefore, you collect 1 rock and 24 fossils, while your friend collects 3 rocks and 12 fossils.
FInd the value of x
X-(-300)=400
Answer:
X=100
Step-by-step explanation:
X-(-300)=400
X+300=400
X=400-300
X=100
Answer:
x=100
Step-by-step explanation:
2 negatives make a positive
in a 45-45-90 right triangle if the length of the legs is 2 units the length of the hypotenuse will be
Answer:
[tex]2\sqrt{2}\ units[/tex]
Step-by-step explanation:
we know that
In a 45-45-90 right triangle, the length of the two legs are equal
so
Applying the Pythagorean Theorem
[tex]c^2=a^2+b^2[/tex]
where
c is the hypotenuse
a and b are the legs
we have
[tex]a=2\ units\\b=2\ units[/tex]
substitute
[tex]c^2=2^2+2^2[/tex]
[tex]c^2=4+4[/tex]
[tex]c^2=8[/tex]
[tex]c=\sqrt{8}\ units[/tex]
simplify
[tex]c=2\sqrt{2}\ units[/tex]
ANSWER ASAP PLS <3
Write the point-slope form of the equation of the line with a slope of -2 and an x-intercept of -1.
Answer:
y = -2(x + 1)
Step-by-step explanation:
x-intercept of -1 means y=0 when x=-1, so you have your (x₁, y₁) value of (-1, 0).
Slope is -2 so m=-2.
Plug into point-slope formula:
y = m(x - x₁) + y₁
y = (-2)(x - (-1)) + (0)
y = -2(x + 1)
9.
The surface area of the right square pyramid shown is 129.5 cm. The base is 4.5 cm. Determine the slant height, s, of this
pyramid, rounded to the nearest tenth
Answer:
Slant height (s)= 12.1 cm
Step-by-step explanation:
Given: Base= 4.5 cm.
Surface area of right square pyramid= 129.5 cm.
First, calculating slant height (s) of right square pyramid.
Surface area of square pyramid= [tex](a^{2} +2\times a\times s)[/tex]
a= side of square base.
s= slant height
∴ [tex]129.5= (4.5^{2} + 2\times 4.5\times s)[/tex]
⇒ [tex]129.5= (20.25+2\times 4.5\times s)[/tex]
⇒ [tex]129.5= (20.25+9\times s)[/tex]
Now, opening the parenthesis and subtracting both side by 20.25.
⇒ [tex]109.25=9\times s[/tex]
cross multiplying both side
∴ Slant height (s)= 12.1
Final answer:
To find the slant height of the right square pyramid, subtract the base area from the total surface area, divide by four to find the area of one triangular side, and then solve for the slant height using the triangle area formula. The calculated slant height is = 12.1 cm
Explanation:
The student is asking how to find the slant height of a right square pyramid when given the surface area and the base length. To solve this, we need to take into account the formula for the total surface area of a right square pyramid, which is the sum of the base area and the area of the four triangles forming the sides. We know the total surface area is 129.5 cm2 and the base length is 4.5 cm. The area of the base is simply the square of the base length since it's a square base.
Base area = base length2 = (4.5 cm)2 = 20.25 cm2
Total area of four triangular sides = 129.5 cm2 (total surface area) - 20.25 cm2 (base area) = 109.25 cm2
Area of one triangular side = 109.25 cm2 / 4 = 27.3125 cm2
Now, using the formula for the area of a triangle, A = 1/2 × base × height, we can substitute the area of one triangular side and the base length to solve for the slant height:
27.3125 cm2 = 1/2 × 4.5 cm × slant height (s)
Slant height (s) = (2 × 27.3125 cm2) / 4.5 cm = 12.139 cm
Rounded slant height = 12.1 cm
Math Question Time! Grade:6
A teacher asked her students to create an algebraic expression with only subtraction by only getting the answer. The answer given was 3. What is one algebraic expression that it can be?
Rewards for completing problem correctly: 15 points (maybe even Brainliest!)
Explanation has to be provided! Good luck!
Answer:
lol
Step-by-step explanation:
four times a number decreased by 6 is less than -2. Define a variable, write an inequality, and solve for the number
Final answer:
The variable x represents the unknown number, and the inequality is 4x - 6 < -2. Solving it step-by-step, we find that x < 1, which means any number less than 1 satisfies the inequality.
Explanation:
To solve the inequality 'four times a number decreased by 6 is less than -2', let's define a variable x as the number. Expressing the given condition as an inequality, we get 4x - 6 < -2. To solve for x, follow these steps:
Add 6 to both sides of the inequality to isolate the term with the variable: 4x - 6 + 6 < -2 + 6, which simplifies to 4x < 4.
Divide both sides of the inequality by 4 to solve for x: 4x/4 < 4/4, which gives us x < 1.
Check the answer to ensure it is reasonable. Since multiplying a number by four and subtracting six should result in a number less than -2, a number less than 1 seems reasonable.
Therefore, any number less than 1 satisfies the inequality.
i shall brainliest you. Use the distributive property to expand the following expression.
-4(3.2x + 5y - 2.1)
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Multiply everything inside the brackets by -4
-4(3.2x) = -12.8x
-4(5y) = -20y
-4(-2.1) = 8.4
Put it together:
-12.8x - 20y + 8.4
Have A Nice Day ❤
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Provide the reason for Step 4 in the following proof.
A) Additive Inverse Property
B) Commutative Property of Addition
C)Definition of Subtraction
D)Identity Property of Addition
Prove :
Answer:
The Correct option is
A) Additive Inverse Property .
Step-by-step explanation:
Identity Property of Addition :
In math, an identity is a number, n, that when added to other numbers, gives the same number, n.
The additive identity is always zero.
This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.
Statement Reasons
1. -(a+b)+a = -a+(-b)+a 1.Distributive Property
= -a+a+(-b) 2.Commutative Property of Addition
= 0+(-b) 3. Additive Inverse Property
= -b 4. Identity Property of Addition
The drama club spent $35 on decorations and $8.50 per person on food for a cast party. The total cost of the food
and decorations was $264.50. How many people were at the cast party?
A)1,951 people
B)238 people
C)27 people
D)221 people
Answer:
Option C) 27 people
Step-by-step explanation:
Let
x ----> the number of people
we know that
The cost of decorations ($35) plus the number of people (x) multiplied by the cost per person on food ($8.50) must be equal to $264.50
so
The linear equation that represent this situation is
[tex]35+8.50x=264.50[/tex]
solve for x
Subtract 35 both sides
[tex]8.50x=264.50-35[/tex]
[tex]8.50x=229.50[/tex]
Divide by 8.50 both sides
[tex]x=229.50/8.50[/tex]
[tex]x=27\ people[/tex]
A line passes through the point (0,2) and has a slope of -1/2 what is the equation of the line
Answer:
y = -1/2x + 2
Step-by-step explanation:
A line in slope-intercept form in y = mx + b
"m" is the slope
"b" is the y-intercept
x and y represent points on the graph
To write an equation, you need "m" and "b".
We already know m = -1/2
The point (0, 2) is the y-intercept. The y-intercept occurs when x = 0.
Points are in the form (x , y), so x = 0 and y = 2.
Therefore b = 2.
Substitute m = -1/2 and b = 2 into the equation:
y = mx + b
y = -1/2x + 2
Solve q = {(s+t) for t.
-
You randomly choose one of the tiles. Without replacing the first tile, you
choose a second tile. Find the probability of the dependent event(s) both
occurring.
1/2/3/4/5/6/7
-
Choosing a 6 and then a prime number
Choosing two odd numbers
Answer:
Choosing a 6 and then a prime number: 2/21
Choosing two odd numbers: 2/7
Step-by-step explanation:
Choosing a 6 and then a prime number:
The probability of choosing 6 out of 1, 2, 3, 4, 5, 6 and 7 is one event divided by number of total events (which is equal to 7). That results in 1/7. Once 6 is chosen, the probability of choosing a prime number (prime number is a number that can only be divided by 1 and itself) out of 1, 2, 3, 4, 5 and 7 is 4/6 (prime numbers are 2, 3, 5, 7 in total there are 4 number and total number of events are 6). Finally, the probability of choosing a 6 and then a prime number is (1/7)*(4/6)=2/21.
Choosing two odd numbers:
The probability of choosing 1st odd number is 4/7 (number of odd numbers is 4 which includes 1, 3, 5, 7 and the number of total events is 7). Once 1st odd number is chosen, the probability of choosing 2nd odd number is 3/6 (number of odd numbers is 3 - because 1 odd number is already chosen and the number of total events is 6). Finally, the probability of choosing two odd numbers in a sequence is (4/7)*(3/6)=2/7.
Madhu's age is 3 times Sanku's age and difference between their ages is 14. Then find their ages?
Answer:
Madhu's age= 21 and Sanku's age=7
Step-by-step explanation:
let the age of Madhu be x and age of Sanku be y.
now,
x=3y-equation (i)
then,
x-y=14
or,3y-y=14
or,2y=14
or,y=14/2
:. y=7
at last,putting value of y in equation(i)
x=3y
or,x=3x7
or,x=21
Therefore, Madhu's age is 21 and Sanku's age is 7
It is a rectangle and I need to get x and the top is -1+4x and the bottom is 3x+3 I’m in 8th grade geometry
The value of x is 4.
Step-by-step explanation:
Consider a Rectangle ABCD
AB as Top
CD as Bottom
AB = -1 + 4x
CD = 3x + 3
To Find:
x = ?
Solution:
In a Rectangle ABCD
Opposite sides of rectangle congruent,
AB = CD
Top = Bottom
on substituting we get
[tex]-1+4x=3x+3\\\\4x-3x=3+1\\\\x=4\\\therefore x =4[/tex]
The value of x is 4.
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is
the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation
x+y=24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
The test contains 4 three-point questions and 20 five-point questions
The test contains 10 three-point questions and 14 five-point questions
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.
Answer: 10 three points questions and 14 five points questions
Step-by-step explanation: Please see attachment for explanation.
B is the midpoint of AC. AB=7x-4 and BC=4x+5. Find AC.
A) 51
B) 68
C) 17
D) 34
Answer:
D) 34
Step-by-step explanation:
Since B is the midpoint, AB = BC
Plug the two in:
7x - 4 = 4x + 5
Solve for x:
3x = 9, x = 3
Find AB + BC
since BC = AB
AC = 4x + 5 + 4x + 5
AC = 8x + 10
AC = 8(3) + 10
AC = 24 + 10
AC = 34
The calculated length of the segment AC is () 34
How to determine the length of the segment ACFrom the question, we have the following parameters that can be used in our computation:
AB = 7x - 4
BC = 4x + 5
B is the midpoint of AC
So, we have
7x - 4 = 4x + 5
Evaluate
3x = 9
So, we have
x = 3
This means that
AC = 2 * (7 * 3 - 4)
Evaluate
AC = 34
HEnce, the length of the segment AC is () 34
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a clothing distributor sold an $80 coat at a selling price of $73 what was the percentage of discount for the coat
Answer:
91 1/4%
Step-by-step explanation:
To find the percentage of the discount, just divide the new selling price cost from the previous selling price over 100
73/80*100 = 91 1/4%
The rules concerning the age a of a soccer player in a recreational league mandate that a player be 17 years of age or older. Which inequality BEST represents this situation?
A. a > 17
B. a ≤ 17
C. a ≥ 17
D. a < 17
Answer:
It can be represented by a ≥ 17.
Step-by-step explanation:
The rules concerning the age of a soccer player in a recreational league mandate that a player is 17 years of age or older.
Therefore, if the age of a player is a years, then the condition for a soccer player to participate in the league is that a must be equal to 17 or more than 17 years old.
Hence, mathematically it can be represented by a ≥ 17. (Answer)
Determine the length across the river, x to the nearest hundred
Answer:
[tex]x=20.67\ ft[/tex]
Step-by-step explanation:
we know that
The Midpoint Theorem says that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side
so
in this problem
Applying the midpoint theorem
[tex]x=\frac{124}{3}:2=\frac{124}{6}=\frac{62}{3}=20.67\ ft[/tex]
Financial Math question....
What is the monthly payment for a $4,000 3 year loan with an APR of 7.50%
Answer:
$124.42
Step-by-step explanation:
look at the attachment for the formula I used
What is the value of X
4(x - 3) = -8
Solving for x...
4(x-3)=-8
Divide by 4.
x-3=-2
Add 3.
x=1
Answer: x = +1
Step-by-step explanation: To solve for x in this equation, our first step is to simplify the left side by distributing the 4 through both terms inside the parentheses.
When we do that, we get 4 times x which is 4x and 4 times -3 which is -12. So we have 4x - 12 = -8. Our next step is to isolate the x-term by adding 12 to both sides of the equation. On the left, -12 + 12 cancels and we are left with 4x. On the right, -8 + 12 simplifies to 4.
Now we have the equation 4x = 4.
To get x by itself, we divide both sides by 4 and x = +1.
help me pleaseeee!!!!!
Because she needs 3 blankets and it takes 15 day per blanket(rate is given), she needs 3x15 or 45 days. She has 60 days so she can volunteer at most 15 days.
answer: s≤15
A trader bought 3 dozens of milk for #1,008.00.He sold each at #35.00.calculate his profit.
1 piece=3*12
=36
sp=36*35
=1260
profit=s.p-c.p
=1260-1008
=rs.252
2(7-2) also represents the number of tickets Malia has left after she has gone on x
rides. How can each of the following numbers and expressions be interpreted in terms
of tickets and rides?
Answer:
2(7-2)=2(5)=10
Step-by-step explanation:
please help me thanks if you do :') it would also be awesome if you could explain but its ok if you can't i guess. Find x
Answer:
[tex]x=4\sqrt{2}\ units[/tex]
Step-by-step explanation:
Theorem: In the right triangle the leg is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.
Based on the theorem above,
[tex]x^2=2\cdot (2+6)\\ \\x^2=4\cdot 8\\ \\x^2=32\\ \\x=\sqrt{32}\ units\\ \\x=4\sqrt{2}\ units[/tex]
A circle with radius of 1 cm sits inside a 3 cm x 4 cm rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
3 cm
The area of shaded-region is 8.86 cm^2
Step-by-step explanation:
We can see that there is a circle and a triangle in the given figure
In order too find the area of shaded region, we have to find the area of rectangle and circle first. The area of the shaded region will be obtained by subtracting the area of circle from the area of rectangle.
So,
Area of circle:
Radius = r = 1 cm
So,
[tex]A_c = \pi r^2\\= 3.14 * (1)^2\\= 3.14*1\\= 3.14\ cm^2[/tex]
Area of rectangle:
Length of rectangle = l = 4 cm
Width of rectangle = w = 3 cm
So,
[tex]A_r = l*w\\= 4 *3\\=12 cm^2[/tex]
Now,
[tex]Area\ of\ shaded-region = A_r - A_c\\= 12 - 3.14\\=8.86\ cm^2[/tex]
The area of shaded-region is 8.86 cm^2
Keywords: Area, shaded regions
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Explain how to find the number of comic books you could buy with $25.00
Answer:
$25 - c(p)
Step-by-step explanation:
C = amount of comic books
P = price of comic books
$25 - c(p)
Hope this helps :)
Answer:
depends on the price of each book
Step-by-step explanation:
For instance if you have ...
one book sold for $5
you divide the total ($25) by the cost for each book ($5) and you will get the number of comic books (25/5 = 5 comic books)
If the point (1,5) lies on a circle whose center is at the origin, what is the equation of the circle?
Answer:
x^2 + y^2 = 26.
Step-by-step explanation:
The center is at (0, 0) and the radius is sqrt (1^2 + 5^2) = sqrt 26
The general form is
x^2 + y^2 = r^2 so here it is:
x^2 + y^2 = 26.
Final answer:
The equation of the circle whose center is at the origin and passes through the point (1,5) is x² + y² = 25 since the radius of the circle is the distance from the origin to the point, calculated as 5.
Explanation:
If the point (1,5) lies on a circle whose center is at the origin, the equation of the circle can be found using the distance formula which is derived from the Pythagorean theorem. Since the distance from the center (0,0) to the point (1,5) is the radius of the circle, we calculate the radius as follows:
√((x-0)² + (y-0)²) = √((1-0)² + (5-0)²) = √(1 + 25) = √26 = 5.
Therefore, the radius of the circle is 5. The equation of the circle with a radius of 5, centered at the origin, is:
x² + y² = r²
x² + y² = 5²
x² + y² = 25