To find the probability of rolling six standard, six-sided dice and getting six distinct numbers, we need to calculate the total number of possible outcomes and the number of outcomes that satisfy the given condition.
Total Number of Outcomes:
The total number of possible outcomes when rolling six dice is 6^6, which is 46,656. Each die has six possible outcomes (1, 2, 3, 4, 5, or 6), and there are six dice being rolled.
Number of Outcomes with Six Distinct Numbers:
To get six distinct numbers when rolling six dice, each number must be different from the others. We can choose any six numbers from 1 to 6, and there are 6! (6 factorial) ways to arrange them on the six dice.
This is because there are six choices for the first die, five choices for the second die (since we can't repeat the number on the first die), four choices for the third die, and so on, down to one choice for the sixth die. Therefore, the number of outcomes with six distinct numbers is:6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Probability of Getting Six Distinct Numbers:
To find the probability of rolling six standard, six-sided dice and getting six distinct numbers, we divide the number of outcomes with six distinct numbers by the total number of possible outcomes:
P(six distinct numbers) = number of outcomes with six distinct numbers / total number of outcomes
P(six distinct numbers) = 720 / 46,656
P(six distinct numbers) = 5 / 324
Therefore, the value of the probability is 5/324 or approximately 0.0154.
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HELP** complete the problem by creating two binomials that represent that sides of the shape . Then multiply to get a quadratic equation . Draw a picture to help set up the problem . 6. Albert installs swimming pools . While the pools can come in different sizes, Albert only offers rectangular pools that are always twice as wide as they are long. He also puts a deck around the entire pool, and the deck is always 4ft wide on each side. Write an equation to represent the total area of the pool and deck.
Let's denote the width and length of the pool by “w” and “l” respectively. Then, the width of the pool and deck combined would be:So the equation that represents the total area of the pool and deck as binomials is [tex]: A = 2(L + 8)(2L + 8)[/tex]
What binomials that represent that sides of the shape?Let's start by drawing a diagram of the rectangular pool and the surrounding deck:
___________ Pool Length (L)
| |
| |
| |
| |
W|___________|
| Deck Width|
| = 4ft |
|___________|
We know that the width of the pool (W) is twice its length (L), so we can write:
[tex]W = 2L[/tex]
We also know that the deck is 4ft wide on each side, so the total width of the pool and deck is:
[tex]W_total = W + 8 = 2L + 8[/tex]
And the total length of the pool and deck is:
[tex]L_total = L + 8[/tex]
The total area of the pool and deck can be found by multiplying the total width by the total length:
[tex]A = W_total \times L_total[/tex]
Substituting our expressions for W_total and L_total, we get:
[tex]A = (2L + 8) * (L + 8)[/tex]
Expanding the brackets, we get:
[tex]A = 2L^2 + 24L + 64[/tex]
So the equation that represents the total area of the pool and deck is:
2L^2 + 24L + 64
To represent the sides of the shape as binomials, we can factor out a common factor of 2 from the quadratic expression:
[tex]A = 2(L^2 + 12L + 32)[/tex]
Then we can write the sides of the shape as:
[tex]L + 8[/tex] and [tex]2L + 8[/tex]
Therefore, So the equation that represents the total area of the pool and deck as binomials is: [tex]A = 2(L + 8)(2L + 8)[/tex]
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please help i’m going insane 15 points
The inverse variation for each of these relation is [tex]x*y = 72[/tex].
How do we write direct or inverse variation equation for each relation?To determine if the relation between x and y is a direct or inverse variation, we can check if their ratio is constant for all values of x and y.
x y x/y
3 24 8
4 18 4.5
8 9 1.125
Since x/y is not constant for all values of x and y, we conclude that the relation between x and y is not a direct variation.
We can also check if it's an inverse variation by checking if x*y is constant.
x y x*y
3 24 72
4 18 72
8 9 72
Since x*y is constant for all values of x and y, we conclude that the relation between x and y is an inverse variation.
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Suppose a basketball team had a season of games with the following characteristics:
60% of all the games were at-home games. Denote this by H (the remaining were away games).
25% of all games were wins. Denote this by W (the remaining were losses).
20% of all games were at-home wins.
Of the at-home games, we are interested in finding what proportion were wins. In order to figure this out, we need to find:
A P(H)
B P(W)
C P(H and W)
D P(H | W)
E P(W | H)
In summary, understanding the probability of a basketball team's performance in a season can be done by examining conditional probabilities such as P(H) and P(W|H). This analysis can provide insights into the team's performance and help identify areas for improvement.
Based on the given information, it seems you are referring to the probability of a basketball team's performance in a season with specific characteristics, namely the probability of a home game (P(H)) and the probability of a win given a home game (P(W|H)).
In order to analyze these probabilities, we can use the concept of conditional probability. Conditional probability helps us understand the likelihood of an event occurring given that another event has occurred.
In this case, P(H) represents the probability of the team playing a home game, and P(W|H) represents the probability of the team winning given that they are playing a home game. Knowing these probabilities can help us understand the team's overall performance and the advantage of playing at home.
To calculate the overall probability of a win, we can use the following formula:
[tex]P(W) = P(W|H) * P(H) + P(W|A) * P(A)[/tex]
Here, P(W|A) represents the probability of a win given an away game and P(A) represents the probability of an away game. By calculating P(W), we can determine the team's overall chances of winning a game, taking into account both home and away games.
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Write a recursive formula for the sequence: 25, 5, 1,...
O a (1)=25 and a (n) = a(n − 1)
O a (1)=25 and a (n) = 5 a(n-1)
O a (1)=25 and a (n) = a(n-1) +5
O a (1) = 25 and a (n) = a(n-1) - 20
Answer: B)
The recursive formula for the sequence 25, 5, 1,… is a(1) = 25 and a(n) = 5 * a(n-1) for n > 1.
Step-by-step explanation:
This is because each term is 1/5 of the previous term. So, the sequence is a(1) = 25, a(2) = 5, a(3) = 1, a(4) = 1/5, a(5) = 1/25, and so on. Does that help?
-8 6/7 - 5/6 simply your answer if needed to
Answer:
-407/42
Step-by-step explanation:
-8 6/7 - 5/6
-8 6/7 = -62/7
-62/7 - 5/6
= -372/42 - 35/42
= -407/42
Michelle has $80 to buy a new outfit. She found a skirt for $20, a blouse for $25, and a belt for $8. How much does she have left to buy shoes?
i need help with homework
The mean of the data set of the people at a birthday party would be 11. The mean absolute deviation would be 5.25
The mean absolute deviation might not be good to use for variation here because there is an outlier of 32.
How to find the mean and mean absolute difference ?To find the mean and the mean absolute deviation (MAD) for this data set, we first need to find the mean age.
Mean = (Sum of ages) / (Number of people)
Mean = (7 + 7 + 7 + 8 + 8 + 9 + 10 + 32) / 8
Mean = 88 / 8 = 11
The MAD is the average of the absolute differences between each data point and the mean.
Find the sum of the absolute differences:
4 + 4 + 4 + 3 + 3 + 2 + 1 + 21 = 42
Divide the sum of the absolute differences by the number of data points (8) to get the MAD:
MAD = 42 / 8 = 5.25
The MAD might not be a good measure of the variation in this data set because there is an outlier (32) in the data. The presence of an outlier can significantly impact the MAD, making it seem like there is more variation in the data than there actually is.
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an actuary has discovered that policyholders are three times as likely to file two claims as to file four claims. if the number of claims filed has a poisson distribution, what is the standard deviation of the number of claims filed?
The standard deviation of the number of claims filed, in this case, is equal to 1.732. This is an important metric for the actuary, as it provides an indication of how much variation there is in the number of claims filed.
The standard deviation of the number of claims filed is equal to the square root of the mean. In this case, the mean is equal to three. Thus, the standard deviation of the number of claims filed is equal to the square root of three, which is equal to 1.732.
To explain further, the Poisson distribution is a discrete probability distribution that is used to calculate the probability of a certain number of events occurring within a given time interval. It is based on the assumption that these events occur independently and at a constant rate. In this case, the rate is equal to the mean, which is equal to three. Thus, the standard deviation is equal to the square root of the mean.
The standard deviation of the number of claims filed is an important metric for the actuary, as it provides an indication of how much variation there is in the number of claims filed. The larger the standard deviation, the greater the amount of variation, and vice versa. In this case, the standard deviation is relatively low, which suggests that the number of claims filed is relatively consistent.
In conclusion, the standard deviation of the number of claims filed, in this case, is equal to 1.732. This is an important metric for the actuary, as it provides an indication of how much variation there is in the number of claims filed.
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Show by completing the survey slip on the answer sheet , how Samantha, a 14 year old girl who feels a lot of pressure to achieve at school, would complete the survey form
Samantha would fill in the following information on the survey sheet based on the data provided:
Sex: Female
Age: 13-14
How much pressure do you feel to achieve at school? c. A lot
Samantha, a 14-year-old girl, would complete the survey slip by selecting "Female" under "Sex," "13-14" under "Age," and "A lot" under "How much pressure do you feel to achieve at school?"
This indicates that Samantha is feeling a significant amount of pressure to succeed academically. It's common for high school students to feel pressure to perform well in school, and this can be due to various factors such as parental expectations, college aspirations, or personal goals.
As a school counselor, it's essential to understand the level of pressure students are experiencing to provide appropriate support and guidance. Identifying and addressing the sources of pressure can help students like Samantha better manage stress and achieve academic success.
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The question is -
A school counselor conducted a survey among a group of high school students using the following survey slip:
Survey (please tick the correct boxes)
Sex: Male Female
Age: 13-14 15 -16 17–18
How much pressure do you feel to achieve at school?
a. None b. A little c. A lot And d. the unbearable amount
Show, by completing the survey slip on the answer sheet, how Samantha – a 14-year-old girl who feels a lot of pressure to achieve at school – would complete the survey
Noah was at home. He got on his bike and rode to his friends
Answer:
what's your exact question
Answer:
can u pls type the full question
A child earns $2 per completed household chore and an additional $12 per month if the child completes all the chores on the chore list. If the child completed the entire chore list last month and earned a total of $44, which statement is true?
Hence, C) The child performed every task on the list last month is the right answer.
what is unitary method ?Mathematicians utilize the unitary approach as a tool for solving proportionality-related problems. Given certain known values, it entails applying ratios and proportions to find unknown quantities. According to the unitary technique, if two quantities are connected to one another in a particular way, we can determine the value of one quantity by knowing the value of the other. This is accomplished by first determining the unit value of the given quantity, which is then multiplied or divided to yield the desired value.
given
Let's name the quantity of housework the youngster performed "x".
The total earnings can be expressed by the equation below, where the child earns an additional $12 if they finish all the chores on the chore list:
Total income = 2x plus 12
We are informed that the child accomplished all of the chores on the list for the previous month and earned $44. We may set this equal to 44 and find x by using the equation above:
2x + 12 = 44
2x = 32
x = 16
The kid finished 16 housework tasks last month.
Now that we know which of the following is true:
A) The youngster finished ten domestic duties.
This is untrue, since we determined that the child accomplished 16 domestic duties.
A) The youngster received $4 for finishing all the tasks on the list.
This is untrue because the child receives $12 for finishing the chores on the list.
B) Last month, the youngster finished all of the chores on the list.
This is accurate because we were told the child accomplished every task on the list and discovered that there were 16 in all.
Hence, C) The child performed every task on the list last month is the right answer.
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Please help i really need help due tomorrow
The area of the composite figure is 80ft².
Define area of composite figure?Composite shapes may have overlaps between their perimeter and area.
Although we frequently define any shape's area through its perimeter, these two ideas are distinct. The area determines how much room the shape can store, while the perimeter merely draws the object's exterior border. Hence, the space that a shape encloses within its perimeter or boundary is its area.
Calculating the areas of various fundamental shapes is necessary to determine the area of a composite shape.
Breaking the form down is the easiest method:
Separate the composite shape into its constituent parts.
Each fundamental shape's area should be determined separately.
Add these areas together to determine the composite shape's area.
Here, first the area of the triangle:
1/2 × b × h
=1/2 ×(18-7-7) × 4
= 1/2 × 4 × 4
= 8ft².
Now, area of the rectangle:
b × l
= 4× 18
= 74ft².
Area of the whole figure = 8 + 72 = 80ft².
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A sheet of cardboard 10 inches by 12 inches will be made into a box by cut into equal sided squares from each corner and folding up the edges. write a polynomial expression that represents the area of the base according to the specified dimensions
Find the value of x.
a) Complete the table of values for y = 3/x
b) which is true correct curve for y= 3/x?
A , B, or C??
Answer:
A is correct
Step-by-step explanation:
find the perimeter
side A: x+10y units
side B:7x^2-x+9y units
Answer:
14x^2 + 2y
Step-by-step explanation:
We are given two expressions as the side lengths of a rectangle we must find the perimeter.
The formula for perimeter of a rectangle is [tex]P=l+l+w+w[/tex]. Judging by this, we will have add up all the sides of the rectangle. Lets start by adding the two length expressions first.
[tex](x+10y)+(x+10y)[/tex]
Add x terms
[tex]2x[/tex]
Add y terms
[tex]2x+20y[/tex].
Now lets add the width terms
[tex](7x^2 - x - 9y) + (7x^2 - x - 9y)[/tex]
Add x squared terms
[tex]14x^2[/tex]
Add x terms
[tex]14x^2-2x[/tex]
Add y terms
[tex]14x^2-2x-18y[/tex]
Now we need to add both of the two expressions together
[tex](14x^2-2x-18y)+(2x+20y)[/tex]
We can bring down our x squared term since we have no like terms
[tex]14x^2[/tex]
Add x terms, which cancel.
[tex]14x^2+0[/tex]
Add y terms
[tex]14x^2 +2y[/tex]
The perimeter of the rectangle is 14x^2 + 2y
Please help anyone!!
|x-3|\ge11 ∣x−3∣≥11 please anwser quickly
The given inequality is [tex]|x-3|/11 \geq 1[/tex]and the solution to the inequality is [tex]x \leq -8[/tex] or [tex]x \geq 14.[/tex]
We want to solve for [tex]x[/tex], which means we want to find all possible values of [tex]x[/tex] that satisfy the inequality.
To start, we multiply both sides of the inequality by 11, which gives us:
[tex]| x - 3 | \geq 11[/tex]
Now we have an inequality without any fractions. The absolute value sign means that we need to consider two cases: one where [tex]x-3[/tex] is positive, and one where [tex]x-3[/tex] is negative.
Case 1: [tex]x-3[/tex] is positive
If [tex]x-3[/tex] is positive, then [tex]| x - 3 |[/tex] is equal to [tex]x-3[/tex]. So we can rewrite the inequality as:
[tex]x - 3 \geq 11[/tex]
Adding 3 to both sides, we get:
[tex]x \geq 14[/tex]
This means that if [tex]x[/tex] is greater than or equal to 14, then the inequality is satisfied.
Case 2: [tex]x-3[/tex] is negative
If [tex]x-3[/tex] is negative, then [tex]| x - 3 |[/tex] is equal to [tex]-(x - 3)[/tex]. So we can rewrite the inequality as:
[tex]-(x - 3) \geq 11[/tex]
Multiplying both sides by -1, we get:
[tex]x - 3 \leq -11[/tex]
Adding 3 to both sides, we get:
[tex]x \leq -8[/tex]
This means that if [tex]x[/tex] is less than or equal to -8, then the inequality is satisfied.
Putting these two cases together, we get:
[tex]x \leq -8[/tex] or [tex]x \geq 14[/tex]
These are all the possible values of [tex]x[/tex] that satisfy the inequality.
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The complete question is:
Solve the equation: | x - 3 | / 11 ≥ 11 and determine the type of solution.
please help me solve this i’ll mark brainliest
Answer:
measure of angle MPQ is 125
Step-by-step explanation:
1) Corresponding angles are congruent
5x=3x+50
2x=50
x=25
2) Substitute back into the equation
3(25)+50 = 125
Can someone tell me the answer to this question is please?
Each student should receive 1/2 kg of soil.
How to distribute same amount of soil?To find out how much soil each student will have, we need to first add up the total amount of soil collected and then divide it equally among the 10 students.
Let's start by converting all the amounts of soil to a common unit, such as kilograms:
3 students brought 1/4 kg each, so they brought a total of 3/4 kg.
4 students brought 1/2 kg each, so they brought a total of 2 kg.
3 students brought 3/4 kg each, so they brought a total of 2 1/4 kg.
Adding up these amounts, we get:
3/4 + 2 + 2 1/4 = 5 kg
So the total amount of soil collected is 5 kg.
To redistribute this soil equally among the 10 students, we need to divide it by 10:
5 kg ÷ 10 = 1/2 kg per student
Therefore, each student should receive 1/2 kg of soil.
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COFFEE A national coffee chain makes and serves 4 billion cups of coffee in a year. If the average cup of coffee costs $3.15, how much money does the coffee chain make in a year? Write your answer in scientific notation.
Answer: 1.26 × 10 to the 10th power
Step-by-step explanation:
a bag contains marbles, marbles, and marbles. if a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a marble and then a marble?
To find the probability of drawing a marble and then another marble from the bag, we need to multiply the probabilities of the individual events. This is because the two events are independent, and the outcome of the first event does not affect the outcome of the second event.
Let P(R) denote the probability of drawing a red marble, and P(B) denote the probability of drawing a blue marble. We are given that the bag contains red, blue, and green marbles, but we do not know the exact numbers of each color.
Since we replace the marble after each draw, the probability of drawing a red marble and then a blue marble can be found as:
P(RB) = P(R) x P(B)
To find P(R), we need to divide the number of red marbles in the bag by the total number of marbles. Similarly, to find P(B), we need to divide the number of blue marbles in the bag by the total number of marbles. However, since we do not know the exact numbers of each color, we cannot compute these probabilities exactly.
Therefore, we can only say that the probability of drawing a marble and then another marble is equal to the product of the probabilities of drawing each marble separately. In other words, the probability of drawing a red marble and then a blue marble is:
P(RB) = P(R) x P(B)
where P(R) and P(B) are the probabilities of drawing a red marble and a blue marble, respectively, which we cannot determine without more information about the contents of the bag.
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There are 19 animals in the field. Some are cows and some are ducks. There are 60 legs in all. How many of each animal are in the field?
Answer:
There are 11 cows and 8 ducks
Step-by-step explanation:
x will represent number of cows and (19-x) will represent ducks
[tex]4x+2(19-x)=60[/tex]
multiply 2 with (19-x)
[tex]4x+38-2x=60[/tex]
add your x's
[tex]2x+38=60[/tex]
subtract 38 on both sides
[tex]2x=22[/tex]
then divided 2 on both sides
[tex]x=11[/tex] cows
now to find ducks subtract
[tex]19-11[/tex]
your answer will be 8
So there are 11 cows and 8 ducks
to double check do this
[tex]11*4 + 8*16\\=44+16\\=60[/tex]
Find the slope of the line that passes through (2,1) and (0,-2) with explanation please
Answer: 3/2
Step-by-step explanation:
To find the slope of the line that passes through the points (2, 1) and (0, -2), we can use the formula:
m = (y2 - y1) / (x2 - x1)
where:
m = slope of the line
(x1, y1) = coordinates of the first point
(x2, y2) = coordinates of the second point
Plugging in the values we have, we get:
m = (-2 - 1) / (0 - 2)
m = -3 / -2
m = 3/2
Therefore, the slope of the line that passes through the points (2, 1) and (0, -2) is 3/2.
what is one million, five hundred fifty-three thousand, five hundred fifty-five in standard form
help me pls!
Answer: 1,553,555
Step-by-step explanation:
1,000,000
553,000
550
1,553,555
Answer:
1553,555 that's the answer for that question
Can some one. Give me an explanation and answer please thank you
Answer: b
Step-by-step explanation:
u just add them together
what is -4x+20≥28 i need to fast though
Answer:
[tex]x\leq -2[/tex]
Step-by-step explanation:
Solve for x:
[tex]-4x+20\geq 28[/tex]
Subtract 20 on both sides
[tex]-4x\geq 8[/tex]
Flip the sign and multiply both sides by -4
[tex]16x\leq -32[/tex]
Divide by 16
[tex]x\leq -2[/tex]
Function "p" is in the form y = ax2 + c. If the values of "a" and "c" are both less than 0, which graph could represent "p"?
Question 6 options:
Graph D
Graph A
Graph C
Graph B
The correct option is - Graph B, represent quadratic function "p", when values of "a" and "c" are both less than 0.
Explain about the quadratic function?f(x) = ax² + bx + c, in which a, b, and c are numbers and an is not equal to zero, is a quadratic function.
A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.You are aware that a line is defined by two points. This implies that there is only one line that incorporates both points if you are provided any two points in the plane.Standard form refers to the quadratic function f(x) = a(x - h)² + k, where an is not equal to zero. The graph opens either upward or downward depending on the value of a. The vertex is the point, while the line of symmetry is really the vertical line x = h. (h,k).The given function :
y = ax² + c.
a < 0 and c <0.
Thus, Graph B, represent function "p", when values of "a" and "c" are both less than 0, and the graph will open downward with c less than 0.
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a studeny of road rage asked random samples of 596 men and 523 women about their behavior while driving based on their answers each person was assigned a road rage score on a scale of
In this study on road rage, a random sample of 596 men and 523 women were surveyed about their driving behavior.
Based on their responses, each individual was assigned a road rage score on a scale of .
The road rage score scale should be selected according to the researcher's preference, and it should be explained.The researcher should clarify how the data was collected in order to improve the study's transparency and reliability.
ll of these aspects should be explained to make the research findings more reliable.The study's results should be presented in tabular or graphical format to better comprehend the data.
The researcher can use bar charts, pie charts, or histograms, among other things. The researcher should also utilize statistical tools such as mean, median, and mode to present the data's central tendency.
Based on the road rage score results, the study's conclusions and implications should be drawn.
The researcher should emphasize the gender-based findings of the study and discuss whether there is a difference between male and female road rage. Furthermore, the study should propose measures to reduce road rage among motorists.
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Kira has $2.20 in dimes and quarters. If the number of dimes
is the number of quarters, how many dimes does she have?
Answer:
There are 2 dimes in the purse that contains $2.20
What is an equation?
An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Let quarters be = x
The dimes be = 1/4 * x
25x+10x/4 = 220
(100x + 10x) /4 = 220
110x/4 = 220
110x = 220*4
110x = 880
x = 880/110
x = 8
The dimes be = 1/4 * x
The dimes be = 1/4 * 8
The dimes be = 2
Step-by-step explanation:
Pls ad brainliest!!!