The probability that all of them get the same number is 1/36.
Given :
Three people are asked to throw a fair die.
Probability :
Probability is a branch of mathematics that deals with the occurrence of a random event.
In one dice probable outcomes 1, 2, 3, 4, 5 and 6
Total out comes in three dice = ( 6 * 6 * 6 = 216 )
Probability of getting 1 = 1/216
Similarly for 2, 3, 4, 5 and 6
Probability of getting same number = 6 * 1/6 * 1/6 * 1/6
= 6*1/6 * 1 * 1 / 6 * 6
= 6/6 * 1/36
= 1 * 1/36
= 1/36
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A laptop computer i purchaed for. Each year, it value i $1500 of it value 75% the year before. After how many year will the laptop computer be worth $200 or le
After 7 years the laptop computer will be worth $200 or less.
In this question, we have been given a laptop computer is purchased for $1500 . Each year, its value is 75% of its value the year before.
We need to find the number of years when laptop computer be worth $200 or less.
We can see that given situation represents exponential decay function with initial value 1500, decay rate = 0.75 and the final value = 200
We need to find period t.
For given situation we get an exponential function as,
1500 * (0.75)^t ≤ 200
(0.75)^t ≤ 2/15
t * ln(0.75) ≤ ln(2/15)
t * (-0.2877) ≤ -2.0149
t ≥ (-2.0149)/(-0.2877)
t ≥ 7
Therefore, the laptop computer will be worth $200 or less after 7 years.
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Find the 3 smallest positive x-intercepts of the graph of
y = cos(12x) + cos(16x) and list them in increasing order.
Submit your answer as a list of x-coordinates from least to greatest.
To find the 3 smallest positive x-intercepts of the graph of y = cos(12x) + cos(16x), you can use the following steps:
Set y equal to 0 and solve for x to find the x-intercepts of the graph.
Since the graph of y = cos(12x) + cos(16x) is periodic with period 2π/12 = π/6 and 2π/16 = π/8, respectively, you only need to consider x-intercepts in the interval [0,π/6).
Use the identity cos(a+b) = cos(a)cos(b) - sin(a)sin(b) to rewrite the equation y = cos(12x) + cos(16x) as:
y = 2cos(4x)cos(8x) - sin(4x)sin(8x)
Set y equal to 0 and solve for x to find the x-intercepts. This will give you the x-coordinates of all the x-intercepts of the graph.
Sort the x-coordinates in increasing order and take the first three smallest positive values to find the 3 smallest positive x-intercepts.
For example, if you set y equal to 0 and solve for x, you get:
0 = 2cos(4x)cos(8x) - sin(4x)sin(8x)
This equation can be rewritten as:
cos(4x)cos(8x) = sin(4x)sin(8x)
Using the identity cos(a) = sin(π/2 - a) and substituting this into the equation above, we get:
sin(4x)sin(8x) = sin(4x + π/2)sin(8x)
This equation simplifies to:
sin(4x)sin(8x) = sin(4x)cos(8x)
Dividing both sides by sin(4x) and rearranging, we get:
sin(8x) = cos(8x)
This equation holds for all values of x that satisfy sin(8x) = cos(8x), so we can find the x-intercepts by setting these two functions equal to each other and solving for x:
sin(8x) = cos(8x)
sin^2(8x) = cos^2(8x)
sin^2(8x) - cos^2(8x) = 0
1 - cos(16x) = 0
cos(16x) = 1
Thus, the x-intercepts of the graph are at x = 0, x = π/16, x = π/8, x = 3π/16, and so on. Since we are only interested in the 3 smallest positive x-intercepts, we can take the first three values in this list: x = 0, x = π/16, and x = π/8.
Therefore, the 3 smallest positive x-intercepts of the graph of y = cos(12x) + cos(16x) are [0, π/16, π/8].
A line has a slope of –20/11 and passes through the point (0, –2) What is its equation in slope intercept form?
It takes one machine 25 minutes to pick a bale of cotton, and another machine takes 30 minutes to compete the same job. If both machines are used, how long will it take them to pick a bale of cotton?
Answer:
Hi i'm wondering how to find the answer the answer is 3 over 2 (2k-8) > 1 over 3(k-9)
Reduce -15/-3 to the standard form
Answer:
5 x 10⁰
Step-by-step explanation:
-15 / -3 = 5
5 in standard form is 5 x 10⁰
Answer: 5
Step-by-step explanation:
-15/-3
negative signs cancel out each other to make positive
⇒15/3
⇒5/1
⇒5 answer.
hope that helps...
Find each percentage of 75. Explain your reasoning.
1. What is 10% of 75?
2. What is 1% of 75?
3. What is 0.1% of 75?
4. What is 0.5% of 75?
Answer:
1. 7.5
2. 0.75
3. 0.075
4. 0.375
Step-by-step explanation:
Yw, and have a good day to everyone who reads this <3 :)
for fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.
As per the concept of margin of error, the standard deviation increases as the margin of error increases.
The term margin of error is referred as the estimate of a small sample drawn from a relatively large population data.
Here the margin of error is usually governed by parameters such as standard deviation of population, sample size and desired confidence level.
Here we have given that for fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.
And we need to find the missing term in the statement.
Here let us consider that the following values are represented the given situation,
=> σ = Standard deviation for population
=> m = Margin of error
=> Z = Empirical value of Z-score at a given confidence level
Then the minimum sample size for a given confidence level is written as
=> (Z x σ)²/m²
Here from the above given formula it can be inferred that the minimum sample size is directly related to the population standard deviation. Therefore, the minimum sample size required would increase with the increase in population standard deviation.
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Sam had 1 whole 1/2 m 5/8 m used it for a project. how much rope does San have left.
Sam has 7/8 m of rope left.
What is fraction ?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
To derive a solution, you have to subtract the meter of rope that Sam has from the meter of rope he cut for a project.
Therefore,
1½ - 5/8,
Since the meter of rope Sam had is represent with a mixed fraction, we have to convert it to an improper fraction, and therefore 1½ can also be written as 3/2
Therefore, we have
3/2 – 5/8
To solve this fraction, you need to find the smallest number that can divide the denominator (2 and 8), which is 8.
Now divide the denominators with 8 and multiply the answers you get by the numerators.
Therefore, we have
3/2 -5/8
= 12/8 – 5/8
= 7/8 m.
Therefore, Sam has 7/8 m of rope left.
The smallest number used to divide the denominators is also known as the lowest common denominator (LCD).
A fraction has 2 parts, which are numerator and denominator. The numerator is the number at the top in a fraction while the denominator is the number below in a fraction.
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im kinda confused of a question right now, i have to find the median and there are 2 numbers in the middle, and i think you add the 2 numbers in the middle and turn it into a fraction right? but do you always put the denominator as 2?
Answer:
Yes, you take the average value of the two numbers in the middle.
Step-by-step explanation:
Since there are TWO middle values, you always put 2 as a denominator.
x+10=y, then 45 is equal to
Sarah pent 30 minute practicing her pelling word. She pent 3 time a much time reading. How many minute did Sarah pend reading?
Sarah completed reading for x = 18 minutes.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question
The number of pages Sarah will read in an hour is x. (this is "pages per hour" rate).
(10 minutes) / (3 pages) = (x pages) / (60 minutes)
cross-multiply:
10x = 3*60
x = 18
Hence, Sarah completed reading for x = 18 minutes.
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a pianist plans to play 3 pieces at a recital from her repertoire of 23 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. how many different recital programs are possible?
Answer:
10626 different recital programs possible
Step-by-step explanation:
Since there is no repetition we can tackle this problem in the following manner.
Out of the 23 pieces, the pianist can choose the first one in 23 ways
Out of the remaining 22 pieces she can choose the second one in 22 different ways
Out of the remaining 21 pieces she can choose the third one in 21 different ways
So total number of ways in which 3 pieces can be played without repetition is 23 x 22 x 21 = 10,626 ways
There is a formula for this kind of situation
If there are a total of n items and you want to choose r items from this, the number of possible ways to do this without repetition is given by the formula
[tex]_{n}P_{r} = \dfrac{n!}{(n-r)!}[/tex]
In this case, n = 23, r = 3 so we get
[tex]_{23}P_{3} = \dfrac{23!}{(23-3)!} = \dfrac{23!}{20!} = 23 \times 22 \times 21 = 10626[/tex]
Same as the above
for both anorexia and bulimia, the rate of occurrence in females compared to in males is about: group of answer choices equal 10 to 1 5 to 1 2 to 1
Both Anorexia and Bulimia the rate of occurrence is high in females as compare to males so the choice is female to male ratio is 12 to 1.
Eating disorder of Anorexia nervosa and Bulimia nervosa is more common in women as compare to men due to dieting habits.Patient suffering from Bulimia nervosa eat in such a way that it implies to lose weight and prevent him ' her from weight gain.Anorexia nervosa patients used to follow restrictive diets and apply lots of restrictions in consumption of their food. Males are more into muscles making so they consume food in good quantity very less percent of males are into diet restriction .Rate of occurrence in both the case anorexia and bulimia in females sufferer is more compare to males.Correct option is ratio female to male is 12 to 1.Therefore, the rate of occurrence in females is much more than the males. Correct option is 12 to 1.
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Five times a number decreased by 2 is 4, find the number.
Answer: x= 6/5
Step-by-step explanation:
Let an unknown number be x
5x - 2 = 4
5x = 6
x= 6/5
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what is the distance between -5, -3 and -5, -6
To calculate the distance between the points -5, -3 and -5, -6. We apply the following formula:
(x₁, y₁) and (x₂, y₂) d = √(x₂ - x₁)² + (y₂ - y₁)²
The points are:
(x₁ = -5, y₁ = -3) and (x₂= -5, y₂= -6)
We apply the above formula and solve.
d = √(x₂ - x₁)² + (y₂ - y₁)²d = √ (-5 - (-5))² + (-6 - (-3))²d = √ 02 + (-3)² = √ 0 + 9d = √9 = 3The distance between the points -5, -3 and -5, -6 is 3.
2. (6) The probability distribution below is for the random variable X = number of mice
caught in traps during a single night in small apartment building.
a. Find P(X = 2)
0
X
P(X) 0.12
1
0.20
2
h
3
4
0.14 0.16
b. Describe P(X ≥ 2)in words and find its value.
5
0.07
c. Find μx and ox. Show work. You may use your calculator to check solutions.
The probabilities are P(X = 2) = 0.14 and P(X ≥ 2) = 0.30
The mean and the standard deviation are 0.96 and 0.90
How to determine the probabilitiesP(x = 2)
From the question, we have the following parameters that can be used in our computation:
X 0 1 2 3
P(X) 0.12 0.20 0.14 0.16
From the above table, we have
P(X = 2) = 0.14
P(x ≥ 2)
From the question, we have the following parameters that can be used in our computation:
X 0 1 2 3
P(X) 0.12 0.20 0.14 0.16
From the above table, we have
P(X ≥ 2) = P(2) + P(3)
Substitute the known values in the above equation, so, we have the following representation
P(X ≥ 2) = 0.14 + 0.16
Evaluate the sum
P(X ≥ 2) = 0.30
The mean and the standard deviationThe mean is calculated as
μx = sum of the products of x and P(x)
So, we have
μx = 0 * 0.12 + 1 *0.20 + 2 * 0.14 + 3 * 0.16
Evaluate
μx = 0.96
The standard deviation is calculated as
ox = the square root of sum of the products of x and P(x) * (1 - P(x)
So, we have
ox = √[(0 * 0.12 * 0.88) + (1 * 0.20 * 0.80) + (2 * 0.14 * 0.86) + (3 * 0.16 * 0.84)]
Evaluate
ox = 0.90
Hence, the standard deviation is 0.90
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Help Pleaseee ONLY CORRECT ANSWERSS> I WILL GIVE BRAINIEST.
Answer:
16[tex]\pi[/tex]
Step-by-step explanation:
Area = [tex]\frac{\pi r^{2} }{4}[/tex] It is only 1/4 of a circle so we have to divide by 4
a = [tex]\frac{8^{2}\pi }{4}[/tex]
a = 16[tex]\pi[/tex]
Which statements are not true and true?
statement 1: the sum of two negative integers is positive
Statement 2: the product of two negative integers is positive
Statement 3: the difference of two negative integers is positive
Statement 4: the quotient of two negative integers is positive
For both statements that are not true at all, provide one counter example for each statement that proves the statement can be false.
Answer: Statements 1, 3, and 4 are not true. The sum, difference, and quotient of two negative integers can be positive, negative, or zero, depending on the values of the two integers. For example, the sum of -5 and -7 is -12, which is a negative number. The difference of -5 and -7 is 2, which is a positive number. The quotient of -5 and -7 is -0.7142857142857143, which is a negative number.
Only statement 2 is true. The product of two negative integers is always a positive number. For example, the product of -5 and -7 is 35, which is a positive number. This is because the two negative signs "cancel out" when multiplying two numbers, resulting in a positive product.
Tom has a total of $220 and he spent $35 on a baseball ticket. What percent of his money did he have left
Answer:
He has $185 left
Step-by-step explanation:
Subtract $220 from how much he spent
how do i comeplete this equation using substitution?
The solution to the equations using the substitution method is x = - 2 and y = 0
What are the solutions?The two equations given are known as system of equations. The equations have to be solved simultaneously to determine the required values.
y = 6x + 12 equation 1
y = 4x + 8 equation 2
Equate equation 1 and equation 2 together
6x + 12 = 4x + 8
6x - 4x = 8 - 12
2x = -4
x = -4 / 2
x = -2
Substitute for x in equation 1:
y = 4(-2) + 8
y = -8 + 8
Y = 0
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statistical measures that communicate the most information should be used with scales that contain the most information. true false
True , statistical measures that communicate the most information should be used with scales that contain the most information.
Given :
statistical measures that communicate the most information should be used with scales that contain the most information. true or false .
we know that ,
What is statistical measures ?
The mean, median, mode, percentiles, range, variance, and standard deviation are the most commonly used numerical measures for quantitative data.
So the statistical measures that must communicate the most information should be used with scales that contain the most information for knowing the details of the given data .
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The three (3) statements which are true include the following:
A. The radius of the circle is 3 units.
B. The center of the circle lies on the x-axis.
D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the equation of a circle?Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² ....equation 1.
Where:
h and k represents the coordinates at the center of a circle.
r represents the radius of a circle.
From the information provided, we have the following equation of a circle:
x² + y² – 2x – 8 = 0 ......equation 2.
In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:
x² – 2x + y² = 8 = 0
x² – 2x + (2/2)² + y² = 8 + (2/2)²
x² – 2x + 1 + y² = 8 + 1
(x – 1)² + (y - 0)² = 9 .......equation 3.
Comparing equation 1 and equation 3, we have the following:
Center (h, k) = (1, 0)
Radius, r = 3
Additionally, this line and the circle's center lies on the x-axis because the y-value is equal to zero (0).
(x – 0)² + (y - 0)² = 3²
x² + y² = 9.
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PLEASE HELP ILL GIVE BRAINLIEST use the similar triangles as a guild to find the slope of the line
Answer:
Slope is 1, since we use rise over run which is expressed as 1/1
Cameron has papayas and bananas in a ratio of 6:19. How many bananas does he have if he has 36 papayas?
Answer: 113 bananas
Step-by-step explanation:
The ratio is 6:19, with 6 papayas for every 19 bananas.
We have 36 papayas, which is 6 times, so we just need to get 19 times 6 = 113 bananas
A line passes through (−1, 5) and (1, 3).
Which answer is the equation of the line? PLEASE HELP
help pretty please :)
Answer: B
Step-by-step explanation:
A company has 30 employees 20 female 10 male, the board of directors decides to ask a group of 10 people, half of which are male, about expanding the company. Determine how many possible groups are there?
Answer:
M=960
F=480
Step-by-step explanation:
look at the work I did
The parabola y=x^2 i reflected acro the x-axi and then caled vertically by a factor of 1/8. What i the equation of the new parabola?
The equation of the parabola will be y = -1/8[tex]x^{2}[/tex].
What is parabola?A right circular cone and a plane perpendicular to one of the cone's elements cross to form a parabola, also known as an open curve.
Y = a(x - h)2 + k or x = a(y - k)2 + h is the general equation of a parabola. The vertex is shown here as (h, k).
The parabola's y= value is provided to us.
When we mirror this parabola along the x-axis, we scale the resulting image vertically by a factor of 1/8.
Then we get y = -1/8[tex]x^{2}[/tex]
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Workers install 480 chairs at a constant rate. After 3 days, the workers still have to install 120 chairs. How much time does it take to install the chairs from start to finish?
The 480 chairs were all finished by the employees in 4 days while maintaining a steady pace.
What is time and work?Time and work deals with the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the work done by each of them.
Work Done = Time Taken × Rate of Work.
Rate of Work = 1 / Time Taken.
Time Taken = 1 / Rate of Work.
If a piece of work is done in x number of days, then the work done in one day = 1/x.
Total Work Done = Number of Days × Efficiency.
Here,
Total number of chairs=480
Chairs left to work on=120
It took them 3 days to install 360 chairs which means if they were working at a constant rate they got 120 chairs installed daily.
With 120 chairs left that means in 1 days they will finish.
So overall, it took the workers 4 days to finish.
The workers took 4 days to complete all the 480 chairs from start to finish at a constant rate.
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Tyshawn has a quarters and y dimes, having at most 22 coins worth no less than
$3.40 combined. At most 16 of the coins are quarters and a maximum of 6 of the
coins are dimes. Solve this system of inequalities graphically and determine one
possible solution.
Answer: To solve this system of inequalities graphically, we can plot the two inequalities on the same coordinate plane and find the region where they overlap.
First, let's consider the inequality that states that Tyshawn has at most 22 coins worth no less than $3.40 combined. We can represent this inequality as follows:
Quarters * $0.25 + Dimes * $0.10 ≥ $3.40
Next, we can consider the inequality that states that at most 16 of the coins are quarters. We can represent this inequality as follows:
Quarters ≤ 16
Finally, we can consider the inequality that states that a maximum of 6 of the coins are dimes. We can represent this inequality as follows:
Dimes ≤ 6
To solve the system of inequalities graphically, we can plot the three inequalities on the same coordinate plane and find the region where they overlap. The region where the three inequalities overlap represents all of the possible values of Quarters and Dimes that satisfy all three inequalities.
One possible solution to the system of inequalities is (Quarters = 12, Dimes = 10). This solution satisfies all three inequalities and is represented by a point within the region where the three inequalities overlap on the coordinate plane.