This is not a fair game since P + Q is greater than 1. To make game fair, we can modify conditions for scoring points. One possible modification is to give Pietro a point if all three toss results match (HHH or TTT).
This gives Pietro an additional outcome to score a point, which makes the game fair. Another modification is to give Eva a point if any two toss results match (H-T-H, T-H-T, T-T-H, H-T-T, HHT, TTH, THT, HTT). This also makes the game fair since both players have 3 possible outcomes to score a point.
There are 2³ = 8 possible outcomes when a coin is tossed three times. We can list them as follows:
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
Let E be the event that no two consecutive toss results match and let P(E) be the probability of event E. We can count the number of outcomes that satisfy E as follows:
HTH
HTT
THT
TTH
THT
TTT
Therefore, there are 6 outcomes that satisfy E and P(E) = 6/8 = 0.75.
Let P be the probability that Pietro scores a point and let Q be the probability that Eva scores a point. We can count the number of outcomes that satisfy each player's condition as follows:
Pietro: HHT, HTH, THH (3 outcomes)
Eva: H-T-H, T-H-T, T-T-H, H-T-T (4 outcomes)
Therefore, P = 3/8 and Q = 4/8 = 1/2.
The game is not fair since P+Q is greater than 1. This means that the players have a greater than 50% chance of scoring a point on each turn, so the first player to reach 10 points will have an advantage.
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Robin was given a $40 monthly allowance. She wants to go to the movies as many times as possible and have at least $12.50 left at the end
of the month to go to a concert. A movie ticket costs $5. Write and solve an inequality to determine how many times Robin can go to the
movies this month. Then interpret the solution.
PLEASE WRITE THE INEQUALITY WITH THE ANSWER AND A SUMMARY OF HOW TO SOLVE IT
Answer:
If Robin was given a $40 monthly allowance. She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert. A movie ticket costs $5. Then she can go six times to the movies.
Step-by-step explanation:
Two or more expressions with an Equal sign is called as Equation.
Given,
Robin was given a $40 monthly allowance.
She wants to go to the movies as many times as possible and have at least $12.50 left at the end of the month to go to a concert.
The amount spent on movies
40-12.5
$27.5
A movie ticket costs $5.
We need to find how many times can she go to the movies.
To find this we need to divide $27.5 by 5
$27.5/5=5.5
Robin can go 6 times to the movies.
In a triangle ABC angle A is twice as large as angle B and B is 20 more than angle c. what are the measure of each angles
Answer:
Step-by-step explanation:
catss
please help.
a helicopter hovers 1400 feet above a small island. the figure shows that the angle of the depression from the to the point P is 30 degrees. how far off the coast, to the nearest foot, is the island?
Step-by-step explanation:
this (outside) angle of depression is equal to the inner angle at P.
because the line of sight from the helicopter to P is like the diagonal in a rectangle spring the rectangle into 2 equal right-angled triangles (one of just rotated by 180° of the other).
so, the angle at P is 30°.
1400 ft = sin(30)×radius
radius being the line of sight from the helicopter to P.
we need to calculate the radius, because we need it for d :
d = cos(30)×radius
radius = 1400/sin(30) = 2800 ft
d = cos(30)×2800 = 2,424.871131... ft ≈ 2,425 ft
THE PIC IS ATTACHED NOW PLS ANSWEE
Answer: C
Step-by-step explanation:
A farmer sells 6.7 kilograms of pears and apples at the farmer's market. 2 5 of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?
By performing subtraction we know that the farmer sold 4.2 kilograms of apples in the market.
What is subtraction?One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction.
Removal of items from a collection is represented by the operation of subtraction.
For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.
Subtraction in mathematics is the process of subtracting one integer from another. In other words, the result of subtracting two from five is three. After addition, subtraction is usually the second operation you learn in math class.
So, to find the weight of apples, perform subtraction as follows:
= 6.7 - 2.5
= 4.2 kilograms
Therefore, by performing subtraction we know that the farmer sold 4.2 kilograms of apples in the market.
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Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of
cubic feet, HCF). When graphed, the function gives a line with a slope of 1.65. See the figure below.
If the monthly cost for 21 HCF is $49.58, what is the monthly cost for 24 HCF?
Monthly cost 49.58
(in dollars)
21
Water usage
(in HCF)
$0
X
5
INIC
The monthly cost for an HCF of 24 will be $39.13.
What is an expression?In mathematics, an expression is a combination of symbols and/or numbers that represents a quantity or a mathematical relationship between quantities. An expression can consist of variables, constants, and operators such as addition, subtraction, multiplication, and division.
Since the monthly water bill is a linear function of the amount of water used, we can use the point-slope form of a linear equation to write an equation for the line. Let y be the monthly cost (in dollars) and x be the amount of water used (in HCF). Then the equation of the line is:
y - 49.58 = 1.65(x - 21)
Simplifying this equation, we get:
y = 1.65x - 13.57
This means that the monthly cost (y) is equal to 1.65 times the amount of water used (x) minus a constant term of $13.57.
To find the monthly cost for 24 HCF, we simply substitute x = 24 into the equation we just found:
y = 1.65(24) - 13.57
y = 39.13
Therefore, the monthly cost for 24 HCF is $39.13.
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Dividing integers. Dan's scores for speed this season are -1, -3, 1, -1, -2, 0. What is his average speed score for the season? (The average is the sum of the points divided by the number of scores)
Dan's average speed score for the season is -1.
What is the arithmetic operations?
Arithmetic operations are mathematical operations that involve manipulating numbers to perform calculations. The four basic arithmetic operations are addition, subtraction, multiplication, and division.
To find Dan's average speed score for the season, we need to add up all his scores and divide by the total number of scores. We can do this as follows:
-1 + (-3) + 1 + (-1) + (-2) + 0 = -6
Dan's total score for the season is -6. To find his average score, we need to divide this total by the number of scores, which is 6 in this case:
-6 / 6 = -1
Hence, Dan's average speed score for the season is -1.
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Given the polynomial 9x^2y^6 - 25x^4y^8 rewrite as a product of polynomials
Answer:
The given polynomial already has two terms that can be factored out:
9x^2y^6 - 25x^4y^8 = (3xy^3)^2 - (5x^2y^4)^2
Now we have a difference of squares:
= (3xy^3 - 5x^2y^4)(3xy^3 + 5x^2y^4)
Therefore, 9x^2y^6 - 25x^4y^8 can be rewritten as the product of (3xy^3 - 5x^2y^4) and (3xy^3 + 5x^2y^4).
Answer: The answer would be (3xy^3-5x^2y^4)(3xy^3+5^2y^4)
(C)
Step-by-step explanation: Cant explain how to but for a quick answer it is C, and you can check the image for proof.
what is the surface area of the cone?
What is the total surface area of the prism?
82 sq. cm
12 sq. cm
94 sq. cm
HEPLP WLL MAR BRANLEST
Answer:
12 as. cm that's the answer
4.
Which problem situation matches this equation?
74.80 = 8 x
Karen got $8.00 per hour for babysitting. Find x, the amount she was paid for 8 hours of babysitting.
The cost of a video game is $74.80. Find x, the amount Josh needs to buy the game if he had $8.00.
Eight friends spent $74.80 each to pay for a camping trip. Find x, the total amount they paid.
Charlene got a paycheck for $74.80 for 8 hours of work. Find x, the amount she was paid per hour.
Answer:
Karen got $8.00 per hour for babysitting. Find x, the amount she was paid for 8 hours of babysitting.
Step-by-step explanation:
how many terms 20 - (4 to the second power divided by 2) has
The number of terms in the expression is 2
How to determine the number of terms in the expressionFrom the question, we have the following:
20 - (4 to the second power divided by 2)
Express properly
so, we have the following representation
20 - (4^2/2)
A term is a mathematical expression that can be added or subtracted to form a larger expression.
For example, in the expression 3x + 2y - 5, each of the three parts (3x, 2y, and -5) is a term.
Using the above definition, we have the terms to be
20 and (4^2/2) i.e. 2 terms
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O is the center of the regular octagon below. Find its area. Round to the nearest tenth if necessary.
The answer of the given question based on regular octagon ,the area of the regular octagon with center O is approximately 232.98 square units.
What is Area?Area is measure of amount of space inside 2-dimensional figure or shape, usually measured in square units like square centimeters or square meters. It is calculated by multiplying length and width of the figure or a shape.
To find the area of a regular octagon, we need to use the following formula:
A = 2(1 + √2) × s²
Since O is the center of the octagon, we can draw lines from O to each vertex of the octagon. This will divide the octagon into 8 congruent isosceles triangles.
Let's call the length of each side of the octagon "s". Then the base of each triangle will also be "s". We can use the Pythagorean theorem to find the length of the other sides of the triangle:
s²+ s² = (2s)²/2
2s² = 4s² - 4s²/2
2s² = 2s²/2
s² = s²/2
s = √2s/2
Now we can substitute this value of s into the formula for the area of the octagon:
A = 2(1 + √2) × s²
A = 2(1 + √2) × (√2s/2)²
A = 2(1 + √2) × 2s²/4
A = (1 + √2) × s²/2
A = (1 + √2) × (17/2)²/2
A ≈ 232.98 square units
Therefore, the area of the regular octagon with centre O is approximately 232.98 square units.
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How many terms are in this expression? 7p + 6 + r
pls show work i’m struggling
Answer:
Step-by-step explanation:
The Pythagorean Theorem states that: a^2+b^2=c^2.
Therefore 6^2+8^2= c^2
36+64= 100^2
Then square root that. The square root of 100 is 10.
The length of XY is 6. The length of XZ is 10. The difference is 4 units
Jason will receive a series of payments at the beginning of each year for 20 years. The first payment is 100. The subsequent 9 payments increase by 10% from the previous payment. After the 10th payment, each payment decreases by 10% from the previous payment. At an annual effective interest rate of 4%, calculate the present value of these payments at the time of the first payment.
A) 2,078.99
B) 2,118.01
C) 2,164.98
D) 2,193.24
E) 2,516.16
Answer:
2,118.01
Step-by-step explanation:
A meteorologist reports that the chance of snow is less than 30%. The correct inequality to represent this comparison is s < 30. The variable s represents the likelihood of snow.
Which numbers are solutions of the inequality?
Choose all that apply.
20%
35%
17%
30%
29 and one-half percent%
1.5%
The solutions to the inequality s < 30 are 20%, 17%, 29 and one-half percent (which is equivalent to 29.5%), and 1.5%.
The disparity that best illustrates the phrase "the possibility of snow is less than 30%" is:
s < 30
This implies that the inequality can be solved for any value of s that is less than 30.
We must compare the numbers to 30 and see if they are less than it in order to identify which ones are the answers to the inequality.
The answer is yes because 20% = 0.2 is less than 30%.
It is not a solution because 35% = 0.35 is not less than 30%.
The answer is yes because 17% = 0.17 is less than 30%.
It is not a solution because 30% = 0.3 is not less than 30%.
That is a solution since 29 and a half percent = 0.295 is less than 30%.
The answer is yes because 1.5% = 0.015 is less than 30%.
As a result, the answers to the inequality s 30 are 20%, 17%, 29 and a half percent (or 29.5%), and 1.5 percent.
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Are -1/3(-3m+6-12+15m) and 2(1-2m) equivalent expression?
Answer:
Yes, -1/3(-3m+6-12+15m) and 2(1-2m) are equivalent expressions. When simplified, both expressions can be written as -5m+4. This can be verified by substituting different values for m in both expressions and then simplifying the expressions. By doing so, the same result of -5m+4 will be obtained for both expressions indicating that they are equivalent
Step-by-step explanation:
Answer: -2and^2*(2m-1)^2
Step-by-step explanation: Step by Step Solution
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "d2" was replaced by "d^2".
STEP
1
:
1
Simplify —
3
Equation at the end of step
1
:
1
((((—•(12m-6))•a)•n)•d2)•(1-2m)
3
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
12m - 6 = 6 • (2m - 1)
Equation at the end of step
3
:
(((2•(2m-1)•a)•n)•d2)•(1-2m)
STEP
4
:
Equation at the end of step 4
((2a • (2m - 1) • n) • d2) • (1 - 2m)
STEP
5
:
Equation at the end of step 5
(2an • (2m - 1) • d2) • (1 - 2m)
STEP
6
:
Equation at the end of step 6
2and2 • (2m - 1) • (1 - 2m)
STEP
7
:
7.1 Rewrite (1-2m) as (-1) • (2m-1)
Multiplying Exponential Expressions:
7.2 Multiply (2m-1) by (2m-1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (2m-1) and the exponents are :
1 , as (2m-1) is the same number as (2m-1)1
and 1 , as (2m-1) is the same number as (2m-1)1
The product is therefore, (2m-1)(1+1) = (2m-1)2
Final result :
-2and2 • (2m - 1)2
find the axis of symmetry for f(x)=x^{2}+12x+31
so since the squared variable is the "x", we're looking at a vertical parabola, and its axis of symmetry will be at the x-coordinate for its vertex, let's find its vertex then
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+31} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 12}{2(1)}~~~~ ,~~~~ 31-\cfrac{ (12)^2}{4(1)}\right) \implies \left( - \cfrac{ 12 }{ 2 }~~,~~31 - \cfrac{ 144 }{ 4 } \right) \\\\\\ \left( -6 ~~~~ ,~~~~ 31 -36 \right)\implies (\stackrel{ x }{-6}~~,~-5)\hspace{5em}\stackrel{ \textit{axis of symmetry} }{x=-6}[/tex]
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The diameter of a circle is 10 3/4 inches.
What is the radius, r, of the circle?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer: The radius of the circle is 5 3/8 inches.
Step-by-step explanation:
The radius of the circle is half of the diameter. We can start by converting the mixed number diameter to an improper fraction:
10 3/4 = (10 × 4 + 3)/4 = 43/4
So, the diameter of the circle is 43/4 inches. The radius is half of this, which we can find by dividing by 2:
r = (43/4) ÷ 2 = 43/8
To simplify the fraction, we can divide the numerator and denominator by their greatest common factor (GCF), which is 1:
r = 43/8 = 5 3/8
Therefore, the radius of the circle is 5 3/8 inches.
Answer:5 3/4
Step-by-step explanation:
10 3/4 * 1/2
1/2 * 43/4 = 43/8
8/43=5 3/4
Find the volume of a right circular cone that has a height of 15.2 m and a base with a radius of 16.2 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
[tex]\boxed{\mathrm \quad {4177.4 \: cm^3}\quad }[/tex]
Step-by-step explanation:
Volume of a right circular cone with radius r and height =is given by the formula
[tex]V = \dfrac{1}{3} \pi r^2 h\\\\\text {We are given}\\\\r = 16.2 \;cm\\h = 15.2\;cm\\\\V = \dfrac{1}{3} \times \pi \times (16.2)^2 \times 15.2\\\\= \dfrac{1}{3} \times \pi \times 262.44 \times 15.2\\\\= 1329.696 \pi cm^3\\\\= 4177.36318 \;cm^3\\\\= 4177.4 \;cm^3 \text{ when rounded to the nearest tenth}[/tex]
You have a portfolio consisting solely of Stock A and Stock B. The portfolio has an expected return of 10.2 percent. Stock A has an expected return of 11.7 percent while Stock B is expected to return 8.3 percent. What is the portfolio weight of Stock A?
The portfolio weight of Stock A is 0.625 for the given situation.
What use do portfolio weights serve?The percentage of a portfolio's investments that are assigned to each asset or security is shown by the portfolio weights. Investors can meet their chosen risk and return objectives by varying the weights of various assets in their portfolios. Portfolio weights are a key component of asset allocation and portfolio optimization methodologies since they are used to determine the expected return and risk of a portfolio.
Let w be the weight (proportion) of Stock A in the portfolio.
The weight of Stock B would be (1-w).
Given that, the portfolio has an expected return of 10.2 percent.
0.102 = w(0.117) + (1-w)(0.083)
w = (0.102 - 0.083)/(0.117 - 0.083) ≈ 0.625
Hence, the portfolio weight of Stock A is 0.625 for the given situation.
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Which of the following sets of numbers could represent the three sides of a right triangle? O {9, 24, 26} O {37, 77,85} O {65, 72, 97} O {32, 56, 65}
From the given data, the only set of numbers that could represent the sides of a right triangle is {9, 24, 26}.
The set of numbers that could represent the three sides of a right triangle is {9, 24, 26}.
To determine if a set of numbers could represent the sides of a right triangle, we can use the Pythagorean theorem, which states that for a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. That is,
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
For the set {9, 24, 26}, we have:
26² = 9² + 24²
676 = 81 + 576
Therefore, the set {9, 24, 26} could represent the three sides of a right triangle.
For the other sets:
{37, 77, 85}: 85² ≠ 37² + 77², so this set does not represent the sides of a right triangle.
{65, 72, 97}: 97² ≠ 65² + 72², so this set does not represent the sides of a right triangle.
{32, 56, 65}: 65² ≠ 32² + 56², so this set does not represent the sides of a right triangle.
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Review
Directions: Identify the type of each of the following triangles based on the sides.
Answer:
• Triangle A: Side lengths of 5, 3, and 4. This is an acute triangle, as all three angle measurements are less than 90°.
• Triangle B: Side lengths of 12, 7, and 15. This is an obtuse triangle, as one angle measurement is greater than 90°.
• Triangle C: Side lengths of 8, 8, and 8. This is an equilateral triangle, as all three sides and all three angle measurements are equal
Step-by-step explanation:
three plus thee equals. what number
Answer:6
Step-by-step explanation:
Answer:
3+3=6
Step-by-step explanation:
Use the tables of values of f and g to answer the problem.
(g ∘ f)(2)
Answer:
giacsybsc
Step-by-step explanation:
vdgsivetshdvx
You pick a card at random
What is P(less than 3)?
Write your answer as a percentage.
Answer:
30% i think
Step-by-step explanation:
Suppose you have 3 jars with the following contents. Jar 1 has 1 white ball and 1 black ball. Jar 2 has 2 white balls and 1 black ball. Jar 3 has 1 white ball and 1 black ball. One jar is to be selected, and then 1 ball is to be drawn from the selected jar. The probabilities of selecting the first, second, and third jars are 1/2, 1/3, and 1/6 respectively. Find the probability the ball was drawn from Jar 3, given that the ball is white.
Given that the ball is white, the probability that it was taken from Jar 3 is 1/5, or 0.2. Given that the ball is white, there is a 20% likelihood that it was selected from Jar 3.
How is probability determined?We must apply Bayes' theorem in order to determine the likelihood that the ball was taken from Jar 3 given that it is white. Let J stand for the scenario in which Jar 3 is chosen, and W for the scenario in which a white ball is drawn. Next, we have:
P(W | J) * P(J) / P = P(J | W) (W)
where P(J) is the prior probability of choosing Jar 3 (1/6), P(W) is the probability of drawing a white ball, and P(W | J) is the probability of drawing a white ball provided that Jar 3 is chosen.
We must apply the law of total probability to determine P(W):
P(W) is equal to P(W | J1) * P(J1), P(W | J2) * P(J2), and P(W | J3) * P. (J3)
where P(W | J1) represents the likelihood that a white ball will be drawn if Jar 1 is chosen (which is 1/2), P(W | J2) represents the likelihood that a white ball will be drawn if Jar 2 is chosen (which is 2/3), and P(W | J3) represents the likelihood that a white ball will be drawn if Jar 3 is chosen (which is 1/2).
Now that the values have been inputted, we can calculate:
P(W) = (1/2 * 1/2) + (2/3 * 1/3) + (1/2 * 1/6) = 5/12
P(J | W) = (1/2 * 1/6) / (5/12) = 1/5
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Apply It 1LFAC is a straight angle and/BAD is a right angle. Find m/FAE Show your work. A B E D (2x + 10) 3x C
Answer:
20x + 6x + 2xc
Step-by-step explanation: the only thing you need to do is simply just use the distribute the 2x t every number
Find the number of arrangements that can be made by taking 4 letters from the letters of the word addressee.
Answer: The word "addressee" has 8 letters. To find the number of arrangements that can be made by taking 4 letters from these 8 letters, we can use the formula for combinations, which is:
n C r = n! / (r! * (n-r)!)
where n is the total number of items, r is the number of items to be selected, and ! represents the factorial function.
In this case, we want to select 4 letters from the 8 letters in "addressee", so n = 8 and r = 4. Substituting these values into the formula, we get:
8 C 4 = 8! / (4! * (8-4)!)
= (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(4 * 3 * 2 * 1) * (4 * 3 * 2 * 1)]
= 70
Therefore, there are 70 different arrangements that can be made by taking 4 letters from the letters of the word "addressee".
Step-by-step explanation: