Considering the expression of a line, the slope of the line that passes through the points (2,4) and (9,12) is 8/7.
What is Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line is calculated as:
m= (y₂ - y₁)÷ (x₂ - x₁)
Slope of the line in this caseIn this case, being (x₁, y₁)= (2,4) and (x₂, y₂)= (9,12), the slope m can be calculated as:
m= (12 -4)÷ (9 -2)
Solving:
m= 8÷ 7= 8/7
Finally, the slope of the line is 8/7.
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researchers randomly assign study participants to one of two groups: the experimental group receives the and the control group receives the .
This is Single-Blinded Randomized Controlled trial type of study because the recipient is unaware that they are receiving a treatment, only the researchers are aware of who is receiving which treatment. So the option d is correct.
One of the most rigorous research designs is experimental research, which is frequently referred to as the "gold standard" in research designs.
This design involves the researcher manipulating one or more independent variables (as treatments), randomly assigning individuals to various treatment levels (random assignment), and observing the effects of the treatments on outcomes (dependent variables).
Experimental research has a distinct advantage in that it may link cause and effect through treatment manipulation while controlling for the erroneous effect of unrelated variables, which is known as internal validity (causality).
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The complete question is:
A team of researchers randomly separates their study's participants into two groups, giving one group a placebo and the other a new treatment to be tested. As the treatment is somewhat experimental, participants do not know whether they receive the placebo but researchers do know whether a specific participant receives the placebo. What type of study is this?
a. Standard Deviation Study
b. Type 1 Study
c. Case-Control Study
d. Non-Blinded Randomized Controlled Trial
e. Single-Blinded Randomized Controlled trial
find the midpoint of the line segment joining the points R(4,3) and S(-1,6). the midpoint is??
The coordinates of the midpoint M of the line segment RS is (3/2, 9/2).
What is the midpoint line segment?The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given that;
Point R( 4, 3 )
x₁ = 4y₁ = 3Point S( -1,6 )
x₂ = -1y₂ = 6To determine the midpoint, plug the given points into the formula above and simplify.
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
M = ( (4 + (-1) )/2, ( 3 + 6)/2 )
M = ( (4 - 1 )/2, ( 3 + 6)/2 )
M = ( (3 )/2, ( 9)/2 )
M = (3/2, 9/2)
Therefore, the midpoint is (3/2, 9/2).
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given the fact that both roots can easily be represented with a float, why do you get a couple percent error for one of the roots?
There are several reasons why a couple percent error may occur when calculating roots, even if both roots can easily be represented with a float.
These reasons can include rounding errors, numerical instability, algorithm limitations, machine precision, and incorrect input data or model. To minimize the error, it is important to use a stable and accurate algorithm, and to ensure that the input data and model are correct.
The error in the calculation of one of the roots can be due to several reasons, such as:
Rounding errors: In many cases, when performing calculations with floating-point numbers, intermediate results are rounded to a certain number of decimal places. This can result in a small error that accumulates throughout the calculation and leads to an incorrect answer.
Numerical instability: Some mathematical operations, such as division and square roots, can lead to loss of precision or numerical instability. This can result in an incorrect answer, even if the input numbers can be represented as floating-point numbers.
Algorithm limitations: The algorithm used to calculate the roots may have limitations that result in an error, even if the input numbers can be represented as floating-point numbers. For example, some algorithms may not converge to the correct root, or they may converge very slowly.
Machine precision: The precision of the computer used to perform the calculation can also play a role in the error. For example, if the computer uses single-precision floating-point numbers instead of double-precision floating-point numbers, the error will be larger.
Model or input data error: The error could also be due to incorrect input data or an incorrect model. For example, if the mathematical model used to calculate the roots is not an accurate representation of the underlying system, the error will be larger.
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Calculate the rand value of a camera that costs 6 840,45 yuan in China. The exchange rate on the day of the sale was R1 = 0,73 yuan.
Answer: 1000 thats the anwer
The rand value of a camera that costs 6 840,45 yuan is R9,370.47.
What is Exchange rate?A currency's relative value expressed in terms of another currency is called an exchange rate (or group of currencies). The exchange rate is a significant economic variable for nations with active international trade, like Australia.
Given:
The camera that costs 6 840,45 yuan in China.
As, the exchange rate is R1 = 0.73 yuan.
so, the Rand value of Camera
= 6840.45 / 0.73
= R9,370.47
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how much time do students spend on the internet? we collect data from the 32 members of our ap statistics class and calculate the mean amount of time that each student spent on the internet yesterday.
It would be appropriate to construct a t-interval to estimate the population mean.
To determine whether it is appropriate to construct a t interval to estimate the population means, we need to consider if the sample size is large enough and if the population standard deviation is known.
If the sample size is less than 30 and the population standard deviation is not known, then it would be appropriate to use a t-interval.In this case, the sample size is 32, which is large enough to assume that the sample mean is an accurate representation of the population mean.
However, the population standard deviation is not known, so it would be appropriate to use a t interval. The t interval can be calculated using the sample mean, sample standard deviation, and degrees of freedom, which is the sample size minus 1.
The t interval will provide a range of values that we can be confident the population mean falls within, given the sample mean and variability.
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How much time do students spend on the internet? We collect data from the 32 members of our AP Statistics class and calculate the mean amount of time that each student spent on the Internet yesterday. Discuss whether it would be appropriate to construct a t interval to estimate the population mean.
Given: ABCD is a parallelogram
Diagonals AC, BD intersect at E
Prove AE≅CE, and BE≅DE
The two column proof that shows that AE ≅ CE, and BE ≅ DE is as shown below.
How to use two column proof in geometry?A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.
Statement 1: ABCD is a parallelogram
Reason 1: Given
Statement 2: AB ≅ CD
Reason 2: Parallelogram Side Theorem
Statement 3: ∠ABE and ∠CDE are alt. interior angles
Reason 3: Def. of alt. interior angles
Statement 4: ∠BAE and ∠DCE are alt. interior angles
Reason 4: Def. of alt. interior angles
Statement 5: AB ║ CD
Reason 5: Def. of Parallelogram
Statement 6: ∠BAE ≅ ∠DCE
Reason 6: alt. interior angles theorem
Statement 7: ∠ABE ≅ ∠CDE
Reason 7: alt. interior angles theorem
Statement 8: ΔBAE ≅ ΔDCE
Reason 8: ASA
Statement 9: AE ≅ CE
Reason 9: CPCTC
Statement 10: BE ≅ DE
Reason 10: CPCTC
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help plsssssssssssssssssss
Answer:
The slope equals the rise divided by the run: Slope =riserun Slope = rise run .
Rise/ run
Answer
1/2
Khadija buys 17 bottles of cranberry juice at the corner store for a total cost of $7.65. If each bottle costs the same amount, how much is each bottle of juice?
Answer:$2.22
Step-by-step explanation:
divide 17 by 7.65
Answer:
9
20
Step-by-step explanation:
Based on the given conditions ,formulate:
7.65
17
Calculate
7.65
17
Simplify
765
1700
you get 9
20
Calculator
What is mZHLG?
Enter your answer in the box.
(25m 22)
(9)
Answer:
[tex]\angle HLG=18 \textdegree[/tex]
Step-by-step explanation:
The sum of the angles in the top quadrant must add up to 90º.
We are given
[tex]25m+22[/tex] and [tex]9m[/tex]
The sum of those must equal 90.
Therefore we can write
[tex](25m+22)+(9m)=90[/tex]
Rearrange and remove the parenthesis.
[tex]9m+25m+22=90[/tex]
Add [tex]9m[/tex] and [tex]25m[/tex].
[tex]34m+22=90[/tex]
Subtract 22 form both sides of the equation.
[tex]34m=68[/tex]
Divide both sides of the equation by 34.
[tex]m=2[/tex]
Now we can evaluate [tex]\angle HLG[/tex].
[tex]\angle HLG=9m\\m=2\\\angle HLG=9*2\\\angle HLG=18 \textdegree[/tex]
what is From 13 friends to 14 friends
Scott picked x pound of blueberries from a local farm , he gave 3 pounds of his pick to his brother , dean . he shared the remaining blueberries equally with his sister Georgia he now has 5 pounds of blueberries
Scott picked x pounds of blueberries from a local farm and if Scott picked x pounds of blueberries, he now has 5 pounds, so x = 5(2) = 10 pounds.
What is pounds ?Pounds is a unit of mass or weight used in the imperial and United States customary systems of measurement. It is equal to 16 ounces or 0.45 kilograms. In the United Kingdom and the other countries that use the imperial system of measurement, it is the standard unit used to measure the weight of people, animals and other objects. In the United States, the pound is often referred to as the avoirdupois pound to differentiate it from other units of measure.
He gave 3 pounds of his pick to his brother, Dean. This leaves x-3 pounds of blueberries. He then shared the remaining blueberries equally with his sister Georgia, so each of them got (x-3)/2 pounds of blueberries. This means that Scott has (x-3)/2 + 3 = (x+3)/2 pounds of blueberries. Therefore, if Scott picked x pounds of blueberries, he now has 5 pounds, so x = 5(2) = 10 pounds.
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How many pivot columns must A have if its columns span R5? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The matrix must have pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. B. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R5" are logically equivalent. C. The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. D. The columns of a 5x7 matrix cannot span R5 because having more columns than rows makes the columns of the matrix dependent.
The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.
A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.
The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.
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factorise this equation x² - 33²
(x+33)(x-33)
Step-by-step explanation:
a²+b²=(a+b)(a-b) difference of two squares
x²-33²= (x+33)(x-33)
Answer: (x + 33)(x - 33)
What does factorise mean?
In maths, to factorise an expression means to put it in brackets in the max possible multiplication form. It is basically finding what to multiply to get an expression.
If you don't know what expression means: a collection of symbols such as numbers, variables and arithmetic operators that jointly express a quantity.
NOTE: There must be no equal sign in expressions. Equal sign in an expression makes it an equation.
Basic Factorization Formulas: (for your info, " ^ " means, to the power of)
a^2 – b^2 = (a – b)(a + b)(a + b)^2 = a^2 + 2ab + b^2(a – b) 2 = a^2 – 2ab + b^2a^3 – b^3 = (a – b)(a^2 + ab + b^2 )a^3 + b^3 = (a + b)(a^2 – ab + b^2 )(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca(a – b – c)^2 = a^2 + b^2 + c^2 – 2ab + 2bc – 2caNow if you see the formulas; the very first formula seems to match with the expression. If your wondering how,
a^2 - b^2 where , "a" can be replaced by x and, "b" can be replaced by 33 As a result, x^2 - 33^2 can be written in multiplication form as (x - 33)(x + 33)
Hope it helped! If you are still not clear, please get help from a tutor or videos on factorization. Thank you.
Solve for x on the diagram below
The value of x in the diagram is 100 degrees
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
The figure
On the figure, we can see that:
The angle x and 100 degrees are alternate angles
Alternate angles have equal values
So, we have
x = 100
Hence, the value is 100 degree
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what is the value of x
Answer:
x=43
Step-by-step explanation:
since we know already two values (90 which is the right angle and 47)
we can do 90+47 =137
180(angles in a triangle)- 137= 43
HELP pls will mark you the brainliest. Please show your work too.
what is the slope of the line containing the midpoint of the segment with endpoints at $(2, 4)$ and $(0, -2)$ and the midpoint of the segment with endpoints at $(5, 1)$ and $(1, 5)?$ express your answer in simplest form.
The slope of the line is [tex]$\frac{3}{2}$[/tex] containing the midpoint of the segment with certain given endpoints.
The slope is a measure of the steepness of a line, calculated as the ratio of the vertical change to the horizontal change between any two points on the line. It represents the rate of change in the y-coordinate with respect to the x-coordinate.
The midpoint of the first segment is[tex]$\left(\frac{2+0}{2}, \frac{4+(-2)}{2}\right)[/tex]= (1,1) and the midpoint of the second segment is [tex]$\left(\frac{5+1}{2}, \frac{1+5}{2}\right)[/tex] = (3, 3). To find the slope of the line between these two points, we use the formula for the slope of a line: [tex]$\frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex] = [tex]\frac{3 - 1}{3 - 1}[/tex] =[tex]\frac{3}{2}[/tex]. So, the slope of the line is [tex]$\frac{3}{2}$[/tex].
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PLSSS HELPP I SILL DO ANYTHZING
Answer:
well i don't know but i wish you the best of luck sorry always remember YOUR SMART ♥️♥️♥️♥️♥️
Step-by-step explanation:
in how many ways can n identical balls be distributed into r bins such that each bin contains at least two balls
Ways can n identical balls be distributed into r bins such that each bin contains at least two balls are 20 ways.
1 ball in each of 3 boxes: 4 ways
3 balls in one box: 4 ways
2 balls in one box and 1 ball in another box: 3*4=12 ways
There are 20 ways to arrange the balls .
In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.
The combination can also be represented as: –nCr, nCr, C(n,r), Crn
Proof:
nPr = nCr.r!
= [n!/r!(n-r)!].r!
= n!/(n-r)!
Hence the theorem states true.
A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
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in ms. q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1,2, 3, 4, 5 6, and 7). among all the cards of each color, there is exactly one card labeled with each number. the cards in ms. q's deck are shown below. professor grok draws two cards from ms. q's deck at random without replacement. what is the probability that the first card grok draws has an even number, and the second card grok draws has an odd number?
The probability of drawing 5 cards from Ms Q's deck such that three cards have the same number is 876 / 98 = approximately 0.089.
There are a total of 28 possible combinations of 5 cards from Ms Q's deck since there are 4 colours and 7 numbers.
To have three cards with the same number, Yunseol must choose 3 cards with the same number and 2 cards with different numbers. There are 7 possible choices for the number of the three cards, and 4 choices for the colour of each card, so there are 7 × 4³ = 196 ways to choose the 3 cards.
For the other 2 cards, Yunseol must choose 2 different numbers and 2 different colours, so there are 7 choose 2 (or 21) ways to choose the numbers and 4 choose 2 (or 6) ways to choose the colours. Therefore, there are 21 × 6 = 126 ways to choose the other 2 cards.
So, the total number of ways to have 3 cards with the same number is 196 × 126 = 24536.
The probability of having three cards with the same number is 24536 / 28 = 876 / 98.
Therefore, the probability of drawing 5 cards from Ms Q's deck such that three cards have the same number is 876 / 98 = approximately 0.089.
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If working on stairs, which articulated ladder configuration should be used?
An articulated ladder should be utilized in a stepladder design for working on stairs. This structure is especially built for stairway safety and stability, with movable legs that can be placed to different heights to suit uneven stairs and give a level area for standing.
What is area?The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area of a planar figure is the space contained by its border. The number of unit squares that cover the surface of a closed form is the figure's area. The area is the region defined by an object's form.
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six friends all throw their coats on the bed in the spare room when they show up for teesha's birthday party. at the end of the party they all enter the dark room and randomly grab a coat and put it on without knowing if it is actually their coat. what is the probability that exactly three of the friends got the right coat? express your answer as a common fraction.
Answer:%33
Step-by-step explanation:
Complete the table for the function and it’s inverse
1. f(x) = 3x + 2
The complete table for the linear function is:
x = -1, -2/3, -1/3, 1/3
f(x) = -1, 0, 1, 3
And the inverse is:
g(x) = (x - 2)/3
How to complete the table?Here we want to complete the table for the linear function:
f(x) = 3x + 2
To do so, we just need to evaluate the function in the given x-values on the table.
f(-1) = 3*-1 + 2 = -1
f(-2/3) = 3*(-2/3) + 2 = 0
f(-1/3) = 3*(-1/3) + 2 = 1
f(1/3) = 3*(1/3) + 2 = 3
Then the complete table is:
x = -1, -2/3, -1/3, 1/3
f(x) = -1, 0, 1, 3
And i assume that we also want to find the inverse g(x), then we need to solve:
f(g(x)) = x
3*g(x) + 2 = x
g(x) = (x - 2)/3
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if the data show that 63% of respondents favor capital punishment (63.2% favor capital punishment; gss, 2018), what will be your best estimate of the percentage(s) of adult americans who feel this way?
It is difficult to estimate the exact percentage of adult Americans who feel this way without further information, however 63% is a good indication that the majority of adult Americans favor capital punishment.
Based on the data provided, it is reasonable to assume that the majority of adult Americans favor capital punishment. This is supported by the survey results which show that 63% of respondents favor capital punishment (63.2% favor capital punishment; gss, 2018). However, without further information such as the survey sample size and what demographics were surveyed, it is difficult to estimate the exact percentage of adult Americans who feel this way. Nonetheless, the survey results indicate that the majority of adult Americans are in favor of capital punishment.
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a box contains seven 40-w bulbs, five 60-w bulbs, and six 75-w bulbs. if bulbs are selected one by one in random order, what is the probability that at least two bulbs must be selected to obtain one that is rated 75 w?
The probability that at least two bulbs must be selected to obtain one that is rated 75W is 2/3.
Number of 40W bulbs = 7
Number of 60W bulbs = 5
Number of 75W bulbs = 6
We are to find the probability that at least two bulbs must be selected to obtain one that is rated 75 w
Let's say the x is the event in which at least 2 bulbs must be selected to obtain one that is rated 75W and y is the event in which just one bulb was selected which is rated 75 W
So, P(x) = 1 - P(y)
P(x) = 1 - 6/(7 + 5 + 6)
P(x) = 1 - 6/18
P(x) = 1 - 1/3
P(x) = 2/3
Hence, the probability that at least two bulbs must be selected to obtain one that is rated 75W is 2/3.
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two hummingbirds just finished drinking some nectar from a clump of flowers. the first bird flies away east at 8 miles per hour. the second flies north at 6 miles per hour. how many minutes will it take for the birds to be 25 miles apart?
Let's call the time it takes for the birds to be 25 miles apart t, in hours. In this time, the first bird will fly a distance of 8t miles to the east, and the second bird will fly a distance of 6t miles to the north.
To determine t, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the distance between the birds) is equal to the sum of the squares of the other two sides.
So, for the two birds to be 25 miles apart, we have:
25^2 = (8t)^2 + (6t)^2
25^2 = 64t^2 + 36t^2
25^2 = 100t^2
t^2 = 25^2 / 100
t^2 = 0.25
t = √0.25
t = 0.5
So, it will take the birds 0.5 hours, or 30 minutes, to be 25 miles apart.
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The first garden is 4 feet long. Deja is using small bricks, which are 1/3 of a foot long. How many small bricks are neede
Answer: 12
Step-by-step explanation: Divide 4 by 1/3
Answer:
12 bricks
Step-by-step explanation:
This is a division problem.
4 ÷ 1/3 = 4/1 × 3/1 = 12/1 = 12
Answer: 12 bricks
g two statistics students at ucla conducted an energy efficiency survey of graduate student apartments. there were seven university apartment buildings, and the students randomly selected three to be included in the study. in each building, they randomly chose 25 apartments. what is the largest group of students that the study results represent? all ucla graduate student apartments. all ucla graduate student apartments in this group of seven buildings. all ucla graduate student apartments in the three sampled buildings. all ucla graduate student apartments that were sampled in the three buildings.
The largest group of students that the study results represent is "all UCLA graduate student apartments in the three sampled buildings".
The number of graduate student apartments in the three sampled buildings can be represented mathematically as:
N = 25 * 3
Where N is the number of apartments sampled and 25 is the number of apartments randomly selected in each of the three buildings.
This expression represents the total number of apartments in the largest group that the study results represent, which is "all UCLA graduate student apartments in the three sampled buildings."
This is because the survey only included data from 25 apartments in each of the three randomly selected buildings. The results of the study cannot be generalized to represent all UCLA graduate student apartments or even all apartments in the group of seven buildings as the sample size is limited to only three buildings. The results only provide information about the energy efficiency of the apartments in the three sampled buildings.
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Amanda and Hannah like water sports. Amanda is kayaking down the river from a dock in
Fulton County at 9 kilometers per hour. Hannah is jet skiing up the river from the same dock,
going 42 kilometers per hour. How long will it be before the two of them are 16 kilometers
apart on the river?
If necessary, round your answer to the nearest minute.
hours and
minutes
Answer:
Rounding to the nearest minute, the time it will take for Amanda and Hannah to be 16 kilometers apart on the river is 53 minutes.
Step-by-step explanation:
Let's call the time it takes for Amanda and Hannah to be 16 kilometers apart "t" (in hours). During this time, Amanda will have kayaked down the river a distance of 9t kilometers, and Hannah will have jet-skied up the river a distance of 42t kilometers. So, their total separation will be 9t + 42t = 51t kilometers. Setting this equal to 16, we get:
51t = 16
t = 16 / 51
To convert this to hours and minutes, we can multiply by 60 to convert the fraction to minutes:
t = 16 / 51 * 60 = approximately 53.33 minutes
what is the probability that rolling 3 eightsided dice on by one results in 3 strictly incredasing numbers
The probability of rolling a specific sequence of numbers on three eight-sided dice is 1/8 x 1/8 x 1/8, or 1/512. To calculate the probability of rolling three strictly increasing numbers, we need to consider all possible combinations of numbers that meet this condition.
For the first die, any number from 1 to 6 can appear, for the second die, any number from 2 to 6 can appear, and for the third die, any number from 3 to 6 can appear.
Therefore, the number of possible combinations is 6 x 5 x 4 = 120.
The probability of rolling three strictly increasing numbers is 120/512 = approximately 0.234 or 23.4%.
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