Given that:
- A fair die is rolled three times.
- A 1 is considered "success".
- All other outcomes are "failures".
You know that a die has 6 faces numbered from 1 to 6. In this case, these outcomes are considered "failures":
\(\begin{gathered} 2 \\ 3 \\ 4 \\ 5 \\ 6 \end{gathered}\)That is a total of 5 numbers considered "failures".
Since the events are independent, you can determine that the probability of 0 successes is:
\(P=\frac{5}{6}\cdot\frac{5}{6}\cdot\frac{5}{6}\)Solving the Multiplications, you get:
\(P=\frac{5\cdot5\cdot5}{6\cdot6\cdot6}\)\(P=\frac{125}{216}\)Hence, the answer is:
\(P=\frac{125}{216}\)How much did the population change between 1970 and 1980? population change between 1990 and 1995? What was the average annual change for that period?
Hint: Calculate the changes, then calculate the mean, or average, by dividing by the number of years. State the units clearly. The units are listed on the chart.
The population change for each period is given as follows:
1970 to 1980: 0.748 billion.1990 to 1995: 0.407 billion.Hence the average annual change for the period between 1970 and 1995 is given as follows:
7,932,000 people a year.
How to obtain the population change?The population change over a period is given by the subtraction of the population at the end of the period by the population at the beginning of the period.
The population data for each year is given by the table on the image presented at the end of the answer.
Hence the changes are obtained as follows:
1970 to 1980: 4.456 - 3.708 = 0.748 billion.1990 to 1995: 5.691 - 5.284 = 0.407 billion.The change between 1970 and 1995 is of:
5.691 - 3.708 = 1.983 billion.
This period is composed by 25 years, hence the average annual change is of:
1.983/25 = 0.07932 billion people a year = 7,932,000 people a year.
Missing InformationThe chart is given by the image presented at the end of the answer.
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List the key features of the quadratic function y = x2 – 16
The general parabola equation
\(ax^{2} +bx+c=0\)
in this equation
\(y=x^{2} -16\) you have
a=1 b=0 and c=-16
\(xv=\frac{b}{2a} =-\frac{0}{2} =0\)
\(yv=(0)^{2} -16=-16\)
the vertex is (0,-16)
graph{y=x^2-16 [-26.2, 25.1, -19.67, 6]}
Answer:
Step-by-step explanation:
in this equation
you have
a=1 b=0 and c=-16
the vertex is (0,-16)
graph{y=x^2-16 [-26.2, 25.1, -19.67, 6]}
Given f(x) = 1/2 (3 - x) ^ 2, what is the value of f(15)?
If Given f(x) = 1/2 (3 - x) ^ 2 , the value of f(15) is 72.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.
The given function is:
f(x) = 1/2 (3 - x)²
To find the value of f(15), we need to substitute 15 for x in the function:
f(15) = 1/2 (3 - 15)²
Here, we subtract 15 from 3 to get -12 in the parentheses, and then we square it to get 144. We can simplify the expression further by multiplying 144 by 1/2, which gives us 72:
f(15) = 1/2 (144)
f(15) = 72
Therefore, the value of f(15) is 72.
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You are training to compete in a 10-kilometer race, and you know the circular running trail at
your park is one mile long. How many times will you need to run this trail in order to run 10
kilometers? (round to the nearest whole number) 1 Kilometer=0.62
.
Answer:
6.2 rounds
Step-by-step explanation:
since 1 kilometer is 0.62 miles
10 kilometers is 6.2 miles
so about 6 and 1/5 rounds
Find the area of the figure. Type your answer as just a number, without units.
After considering all the given data we conclude that the area of the given figure is 80, under the condition that the given figure is a rhombus.
Let us name the rhombus as ABCD, now looking at the figure we can detect that there are two diagonals crossing each other making a point E, this allows the two diagonals to split in four smaller lines that are congruent in value
Then
Line AE = 5ft and Line ED = 5ft (because of congruency)
Line CE = 8ft and Line EB = 8ft(because of congruency)
Therefore,
Now we know that the diagonals
AD = 10ft
CB = 18 ft
The area of a rhombus can be evaluated applying the formula
Area = (d1 × d2) / 2,
Here,
d1 and d2 = lengths of the diagonals.
For this case, the diagonals are 10 ft and 16 ft.
Then, the area of the rhombus is
(10 × 16) / 2
= 80
Then, the area of the given figure is 80.
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Choose all the statements about the diagram that are true.
Angles 4 and 3 form a linear pair and are supplementary.
Since angles 4 and 5 are both inside the parallel lines and on the same side of the transversal, they are supplementary.
Angles 4 and 6 are alternate interior angles and are supplementary.
Angles 4 and 8 are corresponding angles and are supplementary.
Answer:
Option A - TrueOption B - TrueOption C - FalseOption D - FalseExplanation:
Option A is true because if we add ∠4 and ∠6 together, we will get a straight line, which is 180°.Option B is true because the angles stated are in the parallel lines and are supplementary.Option C is false because they are not supplementary angles. Instead, they are equal due to alternate interior angles. Option D is false because they are not supplementary angles.Hence, we can conclude that Option A and B are correct.
Hoped this helped.
\(BrainiacUser1357\)
For every 3 boys at a volleyball summer camp, there are 5 girls. If there are 136 boys and girls at the camp altogether, how many boys and girls are there?
Answer:
Let b = number of boys and g = number of girls.
g/b = 5/3, so g = (5/3)b
b + g = 136
b + (5/3)b = 136
(8/3)b = 136, so b = 136(3/8) = 51 boys, and g = 85 girls
There are 51 boys and 85 girls at the volleyball summer camp.
The ratio of boys to girls at the camp is 3 to 5. By applying this ratio to the total number of children at the camp (136), we find that there are 51 boys and 85 girls.
Explanation:The question tells us that for every 3 boys at a camp, there are 5 girls. This means that the ratio of boys to girls is 3:5. This ratio tells us that out of every 8 (3+5) children, 3 are boys and 5 are girls.
Now it's mentioned there are 136 children in total. We divide total children by sum of the ratio to find out the number of boys and girls. 136 divided by 8 equals 17. This means there are 17 sets of 'every 8 children'.
To find the number of boys, multiply 3 (number of boys in one set) by 17 (total sets) and we get 51 boys. Using the same process for the girls, we multiply 5 (number of girls in one set) by 17 (total sets), resulting in 85 girls. Thus, among the 136 children at the camp, there are 51 boys and 85 girls.
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i will mark brainliest please help me on this question!
Mr. Mole left his burrow that lies below the ground and started digging his way at a constant rate deeper into the ground.
Let
y
yy represent Mr. Mole's altitude (in meters) relative to the ground after
x
xx minutes.
Which of the following could be the graph of the relationship?
Choose 1 answer:
Choose 1 answer:
The correct graph of the relationship is shown in Option D.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Mr. Mole left his burrow that lies below the ground and started digging his way at a constant rate deeper into the ground.
Now, Let y represent Mr. Mole's altitude (in meters) relative to the ground after x minutes.
Hence, The graph of line goes down with constant rate.
Thus, The correct graph of the relationship is shown in Option D.
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i need help The first number in a pattern is 84. The pattern follows the rule divide by 2 then add 10. Find the next three terms and then describe the pattern. and i put Divide 84/2=42 Add 42+10=52
Divide 52/2=26 26+10=36. so far giving brainliest\(mathematics\)
The next three terms after the numbers 52 & 36 are 28, 24, 22.
What is division?Division is a mathematical operation, in which we distribute the number in equal parts, the number on the upper side is the total quantity and the number on the bottom side is equal parts of numbers which have to be distributed.
We denote division by '÷' this symbol.
Given that,
The first number in a pattern is 84.
Using the given rule, we can find the next three terms of the pattern:
Divide 84 by 2 and add 10 to get 52.Divide 52 by 2 and add 10 to get 36.Divide 36 by 2 and add 10 to get 28.Divide 28 by 2 and add 10 to get 24.Divide 24 by 2 and add 10 to get 22.So the next three terms of the pattern are 28, 24, and 22.
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HELP ASAP!!! A padlock has a rotary dial of numbers from 0 to 59. The combination is a series of three numbers, each between 0 and 59. If you were to guess random numbers, what is the probability of guessing the combination correctly?
Answer
1/216000
Step-by-step explanation:
1/60 x 1/60 x 1/60
I hope this helps
The probability of guessing the combination correctly is extremely low, approximately 0.00046%.
What is probability?Probability is represented as the likelihood of an occurrence being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
There are 60 possible numbers on the rotary dial of the padlock, from 0 to 59. To calculate the total number of possible combinations, we can use the multiplication principle of counting.
Since the combination has three numbers, each of which may be any of the dial's 60 possible digit numbers, the total number of possible combinations is:
60 x 60 x 60 = 216,000
As a result, the padlock has 216,000 probable combinations.
If you were to predict random numbers, your chances of getting the proper combination are as follows:
1 / 216,000
This is due to the fact that there is only one accurate combination among the total of 216,000 conceivable combinations.
The likelihood of successfully guessing the combination is extremely low, around 0.00046%, implying that a human cannot open the padlock by randomly guessing the combination.
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c(x) = 4x + 2 Find c(2)
c(2) = 8
Step-by-step explanation:Hi there !
c(x) = 4x + 2
replace x = 2
c(2) = 4×2 + 2
= 8 + 2
= 10
Good luck !
Find the value of x.
x=
Answer:
my guess is 135 because there both the same corners
Step-by-step explanation:
Answer:
110
Step-by-step explanation:
900-(105+150+140+135+125+135)= 110
using elimination, solve
-12x + 9y = 7
9x ÷ 12y = 6
Answer:
3x=24y
-12x+9y=7
let me know if this helps :3
Step-by-step explanation:
a group of mapuve CLC MLMS4 STUDENTS were questioned how they got to school.half of the students said they walk, one-third said they take a taxi,and the rest claimed they drive.calculate the number of students delivered by a car using proper fractions
The fraction of those who were delivered by car will be 1/6.
How to calculate the fraction?It should be noted that from the information given, the students were questioned on how they got to schoo and half of the students said they walk, one-third said they take a taxi,and the rest claimed they drive.
Therefore, the fraction of those who were delivered by car will be:
= 1 - (1/2 + 1/3)
= 1/2 - 5/6
= 1/6
In conclusion, the fraction of those who were delivered by car will be 1/6.
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A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in
20.4 days
22.5 days
25.6 days
30.1 days
A thermometer reading 10°C is brought into a room with a constant temperature of 36°C. if the thermometer reads 14°C after 2 minutes, what will it read after beint left in the room for 4 minutes? and for 9 minutes?
Answer:
4 minutes: 17.4 °C9 minutes: 23.7 °CStep-by-step explanation:
You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.
Newton's law of coolingNewton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...
T = 36 -26·(22/26)^(t/2)
At times of t=4 and t=9, the temperature readings will be ...
4 minutes: 36 -26(11/13)^(4/2) ≈ 17.4 °C9 minutes: 36 -26(11/13)^(9/2) ≈ 23.7 °C__
Additional comment
The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.
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Two triangles are cut from a rectangle to form a trapezoid. What is the ratio of the area of the trapezoid to the combined area of the triangles? A 18:54 C 54:18 B 18:72 D 72:18 12 in group of students is painting a background piece
The image showing the trapezoid is missing, so i have attached it.
Answer:
C 54:18
Step-by-step explanation:
Formula for area of trapezoid is;
A_trap = ½(sum of parallel sides) × height = ½(12 + (12 - (3 + 3))) × 6
A_trap = ½(12 + 6) × 6
A_trap = 54 in²
Combined area of triangle:
A_tria = 2 × ½ × 3 × 6 = 18 in²
Thus;
A_trap:A_tria = 54 in²:18 in² = 54:18
The image showing the trapezoid is missing, so i have attached it.
Answer:
C 54:18
Step-by-step explanation:
Formula for area of trapezoid is;
A_trap = ½(sum of parallel sides) × height = ½(12 + (12 - (3 + 3))) × 6
A_trap = ½(12 + 6) × 6
A_trap = 54 in²
Combined area of triangle:
A_tria = 2 × ½ × 3 × 6 = 18 in²
Thus;
A_trap:A_tria = 54 in²:18 in² = 54:18
Prove (a) B(x+1,y)= x+y
x
B(x,y). (b) Γ(2x)= π
2 2x−1
Γ(x)Γ(x+ 2
1
).
The simplified equation is (π2 / 2) * ∫[0, ∞] (x(2x-1) * e(-x) / (Γ(x) * Γ(1 - x)) DX
a. To prove B(x+1, y) = x * B(x, y), proceed as follows.
Start with B(x+1, y) = [(x+1)! * y!] / ((x+y+2)!) (using the definition of B(x, y)).
Rewrite 1 / (x+1) to (x+y+2 - (y+1)) / (x+y+2) .
Using the formula above, express B(x+1, y) as (x+y+2) / (x+y+2) * [(x+1)! to rewrite. * y!] / ((x+y+2)!) - (y+1) / (x+y+2) * [(x+1)! * y!] / ((x+y+2) !).
Simplify the formula to (x+y+2) / (x+y+2) * B(x, y) - (y+1) / (x+y+2) * B(x, y) increase.
Simplify further to B(x, y) - (y+1) / (x+y+2) * B(x, y).
Note that B(x, y) can be expressed as (x / (x+y+1)) * B(x, y) .
Substitute this formula in the previous step to get,
x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y).
x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y)
= x * B(x, y)
You have now proved B(x+1, y) = x * B(x, y).
b. We wish to prove the identity Γ(2x) = ((2sin(πx))) * Γ(x) * Γ(x + 1/2).
Integrate ∫[0, ∞] (x(2x-1) * Start with dx.
Evaluating this integral using the permutation u = du is obtained.
Simplify the integral to (1/2) * Γ(x + 1/2).
Express sin(πx) as π / (Γ(x) * Γ(1 - x)).
Let the original integral be π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) * e(-x) * (1/sin( πx) Rewrite.)) DX.
Substituting the equations,
The integral, π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) *
We get * (π / (Γ(x) * Γ(1 - x)))) dx.
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A pair of parallel lines is cut by a transversal:
A pair of parallel lines is cut by a transversal. The interior angle made on the left by the intersection of the upper parallel line and the transversal is divided into 2 parts by a slanting line. One part of this angle is labeled as x, and the other part is labeled as 25 degrees. The interior angle made on the right by the intersection of the lower parallel line and the transversal is labeled as 60 degrees.
What is the measure of angle x?
30 degrees
35 degrees
65 degrees
85 degrees
Answer:
I think 30 degrees
Step-by-step explanation:
Answer:
65
Step-by-step explanation:
translate and simplify subtract 18 from -11 .enter only the simplified results
Problem
translate and simplify subtract 18 from -11 .enter only the simplified results
Solution
For this case we can do the following:
-11- 18= -29
Final answer: -29
entre dos números positivos es _______el que tiene mayor valor absoluto
Answer:
entre dos número positivos es "mayor" el que tiene mayor valor absoluto.
F(x)=3x-1 and g(x)=x+2 find (f+g)
Answer:
(f+g)(x) = 4x + 1
Step-by-step explanation:
(f+g)(x) = f(x) + g(x) = 3x -1 + x + 2
Combining the like terms:
3x + x - 1 + 2
= 4x + 1
Hence,
(f+g)(x) = 4x + 1
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A model rocket is launched with an initial upward velocity of 195 ft/S the Rockets height H (in feet) after T seconds is given by the following. H= 195T -16 T^2 find all values for t for which the Rockets height is 87 feet. Round your answer to the nearest hundredth
The height, H (in ft), is related to time, T (in seconds), by the next equation:
\(H=-16T^2+195T\)Substituting with H = 85 ft we get:
\(\begin{gathered} 85=-16T^2+195T \\ 0=-16T^2+195T-85 \end{gathered}\)Applying the quadratic formula:
\(\begin{gathered} T_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ T_{1,2}=\frac{-195\pm\sqrt[]{195^2-4\cdot(-16)\cdot(-85)}}{2\cdot(-16)} \\ T_{1,2}=\frac{-195\pm\sqrt[]{32585}}{-32} \\ T_1\approx\frac{-195+180.5}{-32}\approx0.45\text{ seconds} \\ T_2\approx\frac{-195-180.5}{-32}\approx11.73\text{ seconds} \end{gathered}\)A bank manager wants to encourage new customers to open accounts with principals of at least $. He decides to make a poster advertising a simple interest rate of %. What must the principal be if the bank manager also wants to advertise that one can earn $ the first month? Can the poster correctly say, "Open an account of $ and earn at least $ interest in 1 month!"? Can the poster correctly say, "Open an account of $ and earn at least $ interest in !"?
The principal must have a value of $2,500. if the bank manager also wants to advertise that one can earn $10 the first month.
Hence, with a principal of $3,350, it is possible for the poster to correctly say the statement, as the needed principal is less than $3,350.
How to obtain the necessary principal?As the problem states, simple interest is used, meaning that there is a single compounding per period.
The equation that gives the interest accrued after t years is given as follows:
I(t) = Prt.
The parameters of the interest equation are given as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.The values of the measures in this problem are given as follows:
I(1/12) = 10.t = 1/12.r = 0.048.Hence the principal is obtained solving the equation as follows:
10 = P x 1/12 x 0.048
0.004P = 10
P = 10/0.004
P = $2,500.
Missing InformationThe problem is of:
"A bank manager wants to encourage new customers to open accounts with principals of at least $3,500. He decides to make a poster advertising a simple interest rate of 4.8%. What must the principal be if the bank manager also wants to advertise that one can earn $10 the first month? Can the poster correctly say, "Open an account of $3,500 and earn at least $10 interest in 1 month!"?"
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which point is on the line 4y-2x=0
Answer:
(2,1)
Step-by-step explanation:
The line 4y - 2x = 0 can be written in slope-intercept form as y = 1/2x.
So any point that satisfies this equation will lie on the line. For example, the point (2,1) satisfies the equation:
4(1) - 2(2) = 0
So the point (2,1) is on the line.
Let a, b, c, d, e, f be integers selected from the set {1, 2, . . . , 100}, uniformly and at random with
replacement. Set
M = a + 2b + 4c + 8d + 16e + 32f.
What is the expected value of the remainder when M is divided by 64?
So the expected value of the remainder when M is divided by 64 is approximately 0.2080.
To find the expected value of the remainder when M is divided by 64, we can find the probability that M is congruent to each possible remainder modulo 64 and then sum these probabilities multiplied by the corresponding remainders.
For a positive integer n, let P(n) denote the probability that a positive integer chosen from the set {1, 2, . . . , 100} is congruent to n modulo 64. Then
P(0) = P(64) = P(128) = ... = 1/100
P(1) = P(65) = P(129) = ... = 1/100
P(63) = P(127) = P(191) = ... = 1/100
Since the integers a, b, c, d, e, and f are chosen independently and uniformly at random from the set {1, 2, . . . , 100}, the probability that M is congruent to n modulo 64 is P(n)^6.
Therefore, the expected value of the remainder when M is divided by 64 is
E = 0 * P(0)^6 + 1 * P(1)^6 + 2 * P(2)^6 + ... + 63 * P(63)^6
= (0^6 + 1^6 + 2^6 + ... + 63^6) * P(0)^6
= (0 + 1 + 2 + ... + 63) * P(0)^6
= 2080 * (1/100)^6
= 0.2080
So the expected value of the remainder when M is divided by 64 is approximately 0.2080.
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For a positive integer n, let P(n) denote the probability that a positive integer chosen from the set {1, 2, . . . , 100} is congruent to n modulo 64. Then
P(0) = P(64) = P(128) = ... = 1/100
P(1) = P(65) = P(129) = ... = 1/100
P(63) = P(127) = P(191) = ... = 1/100
Since the integers a, b, c, d, e, and f are chosen independently and uniformly at random from the set {1, 2, . . . , 100}, the probability that M is congruent to n modulo 64 is P(n)^6.
Therefore, the expected value of the remainder when M is divided by 64 is
E = 0 * P(0)^6 + 1 * P(1)^6 + 2 * P(2)^6 + ... + 63 * P(63)^6
= (0^6 + 1^6 + 2^6 + ... + 63^6) * P(0)^6
= (0 + 1 + 2 + ... + 63) * P(0)^6
= 2080 * (1/100)^6
= 0.2080
which ones describe this polygon please help i got one shot at this.
Answer:
All the choices except Trapezoid are correct.
Hiked 3 5/6 miles and 2 1/2 miles on Saturday. Hiked 1 1/3 miles on Sunday. How many more miles to hike for a 10 mile hike
Answer:
I dont really know
Step-by-step explanation:
What is the approximate length of minor arc LM? Round to
the nearest tenth of a centimeter.
12.4 centimeters
15.7 centimeters
31.4 centimeters
36.7 centimeters
Answer:its 15.7
Step-by-step explanation:
Answer:
15.7
Step-by-step explanation: