Answer:
The function that represents a vertical stretch of the function ƒ (x) = e^x is option c) g(x) = 5e^x.
To see why, we can compare the graphs of the two functions. The graph of ƒ(x) = e^x is an exponential function that starts at the point (0,1) and increases rapidly as x increases. The graph of g(x) = 5e^x is also an exponential function, but it starts at the point (0,5), which is five times higher than the starting point of ƒ(x). This means that g(x) is a vertical stretch of ƒ(x) by a factor of 5.
Option a) g(x) = e^x + 7 is a vertical shift of ƒ(x) by 7 units, but it does not represent a vertical stretch.
Option b) g(x) = 1/3e^x is a vertical compression of ƒ(x) by a factor of 1/3, rather than a vertical stretch.
Option d) g(x) = e^4x represents a horizontal stretch of ƒ(x) by a factor of 1/4, but it does not represent a vertical stretch.
A number cube is rolled
twice. What is the probability
of getting a 6 on the first roll,
then a number less than 5
on the second roll?
A) 1/9
B) 2/3
C) 5/36
D 5/12
E) 1/36
Therefore , the solution of the given problem of probability comes out to be the response is A 1/9.
What is probability exactly?The primary goal of the systems inside a procedure known as criteria is to determine the average possibility that a statement is true or that a specific occurrence will occur. Any value from 0 to 1, when 0 is frequently utilized to denote that something is likely and 1 is typically used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.
Here,
If a 6 is rolled on the first roll, the probability of spinning a number less than 5 on the second roll is 2/3,
since there are the four possible outcomes on the third roll that are less than 5 (rolling a 1, 2, 3, or 4) out of an overall of six possible outcomes (rolling any plenty from 1 to 6),
so the probability of a favorable outcome is 4/6, which simplifies to 2/3.
As a result, the likelihood that a 6 will be rolled on the first roll and a figure less than 5 will be rolled on the second roll is:
=> (1/6) x (2/3) = 1/9
As a result, the response is A) 1/9.
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Mai's water bottle had 24 ounces in it. After she drank x ounces of water, there were 10 ounces left. Select ALL the equations that represent this situation. * (a) 24 ÷ 10 = x (b) 24 + 10 = x (c) 24 − 10 = x (d) x + 10 = 24 (e) 10x = 24
Answer:
1 4/5
Step-by-step explanation:
true or false: if event a is tina is the first woman to finish the 2020 boston marathon and event b is tina is the first woman to finish the 2021 new york marathon, event a and event b are independent.
It is true that the events a and b, relating to Tina being the first woman to finish the 2020 Boston Marathon and the 2021 New York Marathon, are independent.
What are independent events?Independent events are events where the occurrence or non-occurrence of one event does not affect the probability of the occurrence or non-occurrence of the other event. In other words, the outcome of one event has no impact on the outcome of the other event.
In the context of this problem, the outcome of one marathon has no bearing on the outcome of another marathon, hence it is true that the events a and b are independent.
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Order the angles from greatest to least.
Answer:
∠D, ∠C, ∠E
Step-by-step explanation:
"The angle opposite to the shortest side is the smallest angle and the side opposite to the longest side is the largest angle."
GIVING BRAINLIEST FOR RIGHT ANSWER (provide proof please i need to know how you got the answer)
Answer:
x > 3
Step-by-step explanation:
This is an open circle, meaning there will be no equal sign.
The line is going to the right of 3, meaning x > 3
So, our inequality is x > 3
assuming that the population from which you select your sample is not normal, which of the statements about m are true? check all that apply.
1. m may be higher or lower than the population mean.
2. The value of m is not necessarily representative of the population mean.
3. The sampling distribution of m is not necessarily normal.
4. The mean, median, and mode of the sample may all be different.
Assuming that the population from which you select your sample is not normal, the following statements about m (the mean of the sample) are true:
1. m may be higher or lower than the population mean.
2. The value of m is not necessarily representative of the population mean.
3. The sampling distribution of m is not necessarily normal.
4. The mean, median, and mode of the sample may all be different.
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When a population is not normal, it means that the distribution of the data is not symmetric and has non-uniform spread.
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Mrs Smith paid 13 450.00 for a couch after a 25% discount. What was the
original price of the couch?
Answer:
The price was originally 16,812.00
Step-by-step explanation:
25% of 13,450 is 3,362.50.
The present shown below is a cube.
Find the surface area of the present.
cm
20
cm
20
Answer:
2400 cm^2
Step-by-step explanation:
we first find the area of a face of the cube, which is a square, with the formula A=L^2, we multiply the result by the number of faces (6) and we have the surface area of the cube
everything is resolved with the expression:
20^2 x 6 = 2400 cm^2
2e - 1 ≤ 18
I need to solve the inequality and I need the work and the answer
Answer:
To solve the inequality 2e - 1 ≤ 18, we can add 1 to both sides of the inequality to isolate the term with e:
2e - 1 + 1 ≤ 18 + 1
Simplifying:
2e ≤ 19
Finally, we can divide both sides of the inequality by 2 to isolate e:
2e/2 ≤ 19/2
Simplifying:
e ≤ 19/2
Therefore, the solution to the inequality is e ≤ 9.5.
A circular cookie cake costs $14.13. if the diameter of the cookie cake is 6 inches, what is the approximate cost per square inch of the cookie cake? use π = 3.14. a. $0.13 b. $0.25 c. $0.50 d. $0.75
The approximate price per square inch of the cookie cake is $0.50
The area of a circle is given through the formulation:
A = πr^2
In which r is the radius of the circle.
for the reason that diameter of the cookie cake is 6 inches, the radius is half of of that, or three inches.
Substituting this into the formulation, we've:
A = π(3^2) = 28.26 square inches (approximate)
The value per square inch is the overall value of the cookie cake divided with the aid of its area:
value per square inch = $14.13 / 28.26 sq.in = $0.50 (approximate)
Therefore, the approximate price per square inch of the cookie cake is $0.50
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there are 204 students at lliswerry high
the teacher put 15 chairs on each roll in the school
how many complete rows of chairs must a teacher put so that all the student can sit and how many empty chairs will remain
the defect levels, as reported by motorola in their six sigma program, were higher than they expected from using a standard normal table for their capability calculations. why was this true? motorola found their processes followed the exponential distribution motorola allowed for failure in one tail only motorola had not allowed for a 1.5 sigma shift in the mean motorola found that six sigma efforts increased process variation
The defect levels reported by Motorola in their Six Sigma program were higher than expected because of the nature of their processes following an exponential distribution.
This means that Motorola only allowed for failure in one tail of the distribution, which increases the likelihood of failure and causes the defect levels to be higher than the standard normal table's capability calculations. Additionally, Motorola had not accounted for a 1.5 sigma shift in the mean, which also contributed to the higher defect levels. Through their Six Sigma efforts, Motorola found that their process variation had increased, which explains why their defect levels were higher than expected.
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suppose you are on the sandy river 20 river miles from mount hood. if a lahar originates on mount hood at 3 pm and travels down the sandy river at a 40 miles an hour when should you expect it to arrive at your location?
We should expect the lahar to arrive at your location at 3:30 pm if we travel down the sandy river at 40 miles an hour.
The given data is as follows:
Length of river = 20 miles
Time = 3 pm
Speed = 40 miles an hour
To calculate the time, we need to use the formula,
Time required = (distance/speed)
It is given that the distance between Mount Hood and your location is 20 river miles, and the speed of the lahar is 40 miles per hour. Therefore, the time it will take for the lahar to arrive is calculated as:
Time required = distance/speed
Time required = 20 miles / 40 miles per hour
Time required = 0.5 hours = 30 min
to determine the expected arrival time at your location,
Total time required = 3.00 + 0.30 = 3.30 pm.
Therefore we can conclude that we should expect the lahar to arrive at your location at 3:30 pm.
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"A box contains 8 crayons: 3 red, 2 blue, 1 black, 1 green, and 1 yellow. Remove one crayon from the box at random and set it apart, then remove a second crayon from the box. Use the conditional probability equation to find P (the second crayon is blue and the first crayon is blue)
The probability that the second crayon drawn is blue and the first crayon drawn is blue is 1/28.
To solve this problem, we can use the conditional probability formula:
P(A and B) = P(B|A) * P(A)
where:
P(A and B) is the probability that both events A and B occur
P(B|A) is the probability of event B given that event A has already occurred
P(A) is the probability of event A occurring
In this case, we want to find the probability of selecting a blue crayon on the second draw given that the first crayon selected was blue. So we have:
P(the second crayon is blue and the first crayon is blue) = P(blue on the second draw | blue on the first draw) * P(blue on the first draw)
To find each of these probabilities, we can start by calculating the total number of possible outcomes:
Total number of outcomes = 8 crayons in the box
Next, we need to find the probability of selecting a blue crayon on the first draw:
P(blue on the first draw) = 2/8 = 1/4
After the first blue crayon has been set aside, there are only 7 crayons left in the box, so the probability of selecting a blue crayon on the second draw given that the first crayon was blue is:
P(blue on the second draw | blue on the first draw) = 1/7
Putting it all together:
P(the second crayon is blue and the first crayon is blue) = P(blue on the second draw | blue on the first draw) * P(blue on the first draw)
= (1/7) * (1/4)
= 1/28
Therefore, the probability that the second crayon drawn is blue and the first crayon drawn is blue is 1/28.
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a jar contains 21 brown and 19 blue marbles. a marble is drawn at random. what is the theoretical probability of drawing a blue marble?
The theoretical probability of drawing a blue marble from a jar containing 21 brown and 19 blue marbles is 19/40, or 0.475.
To calculate this, divide the number of blue marbles by the total number of marbles in the jar. 19 divided by 40 equals 0.475, or 19/40. This means that there is a 47.5% chance of drawing a blue marble from the jar.
The probability of drawing a specific marble from the jar can be expressed using the formula P(A) = n(A)/n(T).
In this example, the probability P(A) is the chance of drawing a blue marble, n(A) is the number of blue marbles (19) and n(T) is the total number of marbles in the jar (40). Therefore, P(A) = 19/40 = 0.475.
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Which of the following are prime factorizations of the number 100? Check all
that apply.
A. 5, 2, 2,5
B. 2, 5, 10
C. 5, 10, 2
D. 5, 2, 5, 2
Answer:
Step-by-step explanation:
A. 5, 2, 2, 5 is a prime factorization of 100 since 5 and 2 are prime factors of 100 and multiplying them gives 100.
B. 2, 5, 10 is not a prime factorization of 100 since 10 is not a prime factor of 100.
C. 5, 10, 2 is not a prime factorization of 100 since 10 is not a prime factor of 100.
D. 5, 2, 5, 2 is not a prime factorization of 100 since it can be simplified as 5x2x5x2 = 100, but it is not a unique prime factorization.
Therefore, the correct answer is A. 5, 2, 2, 5.
write the equation of a circle with center at (-1/2,1/4) and r= [3]
The equation of the circle is 16 x^2 + 16x +16 y^2- 4y -45 =0
Here the center of circle is at (1/2, 1/4 ) and radius is √ 3
The equation of a circle with center (h , k) and radius r is given by
(x - h)^2 + ( y - k)^2 = r^2
Here it is given that the center of circle (-1/2 , 1/4) = (h, k) and radius r= √ 3
Therefore the equation of required circle is
(x - (-1/2) )^2 + (y-1/4)^2= √ 3^2
=> x^2 + 1/4 + x + y^2 +1/16 - 4y= 3
=> 16x^2 + 4 +16x+ 16 y^2 -4y +1= 48
=>16 x^2 + 16x +16 y^2- 4y -45 =0
therefore the required equation of circle is
16 x^2 + 16x +16 y^2- 4y -45 =0
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How do you solve this
The value of side x in the box is 8cm.
Definition of a cuboidA cuboid defined as a solid or figure in three dimensions with six rectangular sides known as faces. A cuboid contains six faces, each of which is a rectangle with all four corners at 90 degrees. It has 12 edges and 8 vertices. A cuboid's opposing faces are always equal. It indicates that the cuboid's opposing surfaces are in the same dimension.
Surface area of box=152cm²
Given:
l=6cm
b=2cm
h=x cm
Surface area of box=2(lb+bh+lh)
152=2(6×2+2×x+x×6)
152=2(12+8x)
12+8x=76
8x=64
x=8
Hence, The value of side x of the box is8cm.
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i thought of a number. 4 times my number increased by 30 equals 70 decreased by the number. what is my number
The 4 is the number the student thought about.
To solve this problem, we will use algebraic expressions. First, let us define the unknown number, x. The problem states that "4 times my number increased by 30 equals 70 decreased by the number." This can be translated into the following equation:
4x + 30 = 70 - x
To solve for x, we need to isolate it on one side of the equation. Let's start by moving all the terms with x to the left side and all the constant terms to the right side.
4x + x = 70 - 30x + 4x + x = 40
Simplifying, we get:
10x = 40
Dividing both sides by 10:
x = 4
Therefore, the number that the student thought of is 4.
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8 x 10^6 is how many times as large as 4 x 10^4
Answer:
200 times as large.
Step-by-step explanation:
To find out how many times 8 x 10^6 is as large as 4 x 10^4, we need to divide 8 x 10^6 by 4 x 10^4:
(8 x 10^6)/(4 x 10^4) = (8/4) x (10^6/10^4) = 2 x 10^2
Therefore, 8 x 10^6 is 200 times as large as 4 x 10^4.
Answer:
3x as large
Step-by-step explanation:
8 x 10^6 = 4800
4 x 10^4 = 1600
4800/3 = 1600
. If your savings account has a %4.50 APR and you have $100 saved, what is the How
much money will earn by the end of the year? What is the equation you will use to figure
this out?
The required amount of money earned on the savings account by the end of the year is $4.50.
How to find the interest amount?To calculate the amount of money earned on a savings account with a given Annual Percentage Rate (APR), we can use the formula:
Interest = Principal x Rate x Time
where:
Principal is the initial amount of money in the account
Rate is the annual interest rate (as a decimal)
Time is the length of time the money is invested (in years)
In this case, the principal is $100, the rate is 4.50% per year (or 0.045 as a decimal), and the time is one year. Therefore, the interest earned can be calculated as:
Interest = $100 x 0.045 x 1
Interest = $4.50
So, the amount of money earned on the savings account by the end of the year is $4.50.
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in a large population, 71% of the people have been vaccinated. if 5 people are randomly selected, what is the probability that at least one of them has been vaccinated? round your answer to three decimal places.
In a large population, 71% of the people have been vaccinated. if 5 people are randomly selected, 0.997 is the probability that at least one of them has been vaccinated.
To compute the probability that at least one of five people selected at random from a large population has been vaccinated if 71% of the population has been vaccinated.
We need to use the Complement Rule.
This rule tells us that the probability of event A not happening is equal to one minus the probability of event A happening.
P (A) + P (A') = 1
where P(A) is the probability of A happening and P(A') is the probability of A not happening.
We need to compute the probability that none of the five people selected at random have been vaccinated.
Then, we will use the Complement Rule to compute the probability that at least one of them has been vaccinated.
The probability that the first person selected has not been vaccinated is:
P(first person not vaccinated) = 1 - 0.71 = 0.29
The probability that the second person selected has not been vaccinated is:
P(second person not vaccinated) = 1 - 0.71 = 0.29
The probability that the third person selected has not been vaccinated is:
P(third person not vaccinated) = 1 - 0.71 = 0.29
The probability that the fourth person selected has not been vaccinated is:
P(fourth person not vaccinated) = 1 - 0.71 = 0.29
The probability that the fifth person selected has not been vaccinated is:
P(fifth person not vaccinated) = 1 - 0.71 = 0.29
We assume that the selections are made randomly and independently of one another.
Thus, we can multiply the probabilities to get the probability that none of the five people selected have been vaccinated:
P(none vaccinated) = 0.29 × 0.29 × 0.29 × 0.29 × 0.29 = 0.0028
We can use the Complement Rule to compute the probability that at least one of the five people selected has been vaccinated:
P(at least one vaccinated) = 1 - P(none vaccinated)P(at least one vaccinated)
= 1 - 0.0028P(at least one vaccinated)
= 0.9972
Thus, the probability that at least one of five people selected at random from a large population has been vaccinated is approximately 0.997 when rounded to three decimal places.
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Which formula would you use to calculate the total enclosed space of firm’s 3 structure?
To calculate the total enclosed space of a firm's 3 structures, you would need to measure the interior space of each structure and then add the three values together.
Why it is?
Assuming that each structure is a simple rectangular prism, the formula to calculate the volume (enclosed space) of a rectangular prism is:
Volume = Length x Width x Height
Therefore, to calculate the total enclosed space of the three structures, you would use the following formula:
Total Enclosed Space = Volume of Structure 1 + Volume of Structure 2 + Volume of Structure 3
where the volume of each structure would be calculated using the formula:
Volume of Structure = Length x Width x Height
Make sure to use the same unit of measurement for all three dimensions (length, width, and height) for each structure to ensure accurate calculations.
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Complete Question:
What formula would you use to calculate the total enclosed space of a firm's three structures? Please provide the necessary information such as the dimensions or measurements of each structure and the units used, if available, to accurately calculate the total enclosed space.
How does the value of a in the function affect its graph when compared to the graph of the quadratic parent function? g(x)=6x^2
Changing the value of "a" in the quadratic function affects the vertical stretch or compression and the direction of the opening of the parabola, compared to the graph of the quadratic parent function.
What is function?
A relationship or expression involving one or more variables
The function g(x) = 6x^2 is a quadratic parent function, which means it is the simplest form of a quadratic function.
When we change the value of "a" in the general form of a quadratic function:
f(x) = ax^2 + bx + c
we change the shape of the graph of the function. Specifically, changing the value of "a" stretches or compresses the graph vertically, and changes the direction of the opening of the parabola.
If "a" is positive, the parabola opens upwards, and if "a" is negative, the parabola opens downwards. The larger the absolute value of "a", the more stretched or compressed the parabola becomes.
In the case of g(x) = 6x^2, "a" is positive and equal to 6, which means the graph is stretched vertically by a factor of 6 compared to the parent function. The parabola opens upwards and is narrower than the parent function.
If we were to change the value of "a" to a different positive value, for example "a" = 3, the graph would still open upwards but would be less stretched than g(x) = 6x^2. On the other hand, if we were to make "a" negative, for example "a" = -6, the graph would open downwards, and be a reflection of the graph of g(x) = 6x^2 about the x-axis.
In summary, changing the value of "a" in the quadratic function affects the vertical stretch or compression and the direction of the opening of the parabola, compared to the graph of the quadratic parent function.
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Determine if the given functions are even, odd or neither f(x)=x^2-7
The function f(x) = x² - 7 is an example of a function that is neither even nor odd, as it does not exhibit either type of symmetry.
To determine whether a function is even, odd, or neither, we need to examine its algebraic form and look for a particular type of symmetry.
Let's apply this concept to the given function, f(x) = x² - 7. To determine whether f(x) is even or odd, we need to evaluate f(-x) and compare it to f(x).
f(-x) = (-x)² - 7 // substitute -x for x
= x² - 7 // simplify
Comparing f(-x) to f(x), we can see that they are not equal:
f(-x) = x² - 7
f(x) = x² - 7
Since f(-x) is not equal to f(x), the function is not even. To determine whether it is odd, we need to evaluate f(-x) + f(x) and see if the result is zero.
f(-x) + f(x) = (x² - 7) + (x² - 7) // substitute -x for x in the second term
= 2x² - 14
Since f(-x) + f(x) is not equal to zero for all values of x, the function is not odd either.
Therefore, we can conclude that the given function, f(x) = x² - 7, is neither even nor odd.
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A rectangle has opposite sides that are parallel and congruent. What is the measure of each interior angle in a rectangle? Each angle measures blankdegrees.
Answer:
90°
Step-by-step explanation:
Each angle measures 90°
how many five-card hands from a normal deck of cards contain exactly two aces and have exactly two red cards.
There are 816 possible five-card hands from a normal deck of cards containing exactly two aces and having exactly two red cards.
There are 80 possible five-card hands from a standard deck of 52 cards that contain exactly two aces and have exactly two red cards.
To calculate this, first count the total number of combinations of two aces from the four aces in the deck. This can be done using the combination formula C(n, r) where n is the number of items (4 aces) and r is the number of items to choose (2 aces). Therefore, the number of combinations of two aces is C(4,2) = 6.
Next, count the number of combinations of two red cards. There are 26 red cards in a deck, which can be divided into the two suits of spades and hearts. For each of these suits, calculate the number of combinations of two cards using the same formula as before, C(n, r). Therefore, the number of combinations of two red cards is C(13,2) * 2 = 156.
Finally, multiply the two values together to get the total number of possible five-card hands with exactly two aces and two red cards. This equals 6 * 156 = 960. This value must be reduced by the number of hands that contain more than two aces and/or more than two red cards. This value can be calculated using the same formula. For instance, the number of hands with three aces is C(4,3) * C(13,2) * 2 = 144. This value must be subtracted from 960, leaving a total of 960 - 144 = 816.
Therefore, there are 816 possible five-card hands from a normal deck of cards containing exactly two aces and having exactly two red cards.
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the probability of margaret receiving a promotion is 0.70. the probability of katia receiving a promotion is 0.60. if the two promotions are independent, what is the probability of both margaret and katia receiving a promotion?
The probability of both Margaret and Katia receiving a promotion is 0.42 (0.70 * 0.60).
When dealing with independent events, the probability of both events occurring is equal to the product of the individual probabilities.
In this case, the probability of Margaret receiving a promotion is 0.70 and the probability of Katia receiving a promotion is 0.60. When these probabilities are multiplied, the result is 0.42, which is the probability of both Margaret and Katia receiving a promotion.
This is due to the fact that the probability of both independent events occurring is the product of the individual probabilities.
For example, if the probability of Event A is 0.5 and the probability of Event B is 0.4, then the probability of both Event A and Event B occurring is 0.20 (0.5 * 0.4). This is true for all independent events.
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if a fair die is rolled 5 times, what is the probability, rounded to the nearest thousandth, of getting at least 2 fours?
So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.
What is the simple definition of probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
According to the given information:The probability of getting at least 2 fours is the sum of the probabilities of getting exactly 2, 3, 4, or 5 fours:
P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5)
Using the binomial formula, we can calculate each of these probabilities:
P(X=k) = (n choose k) p^k (1-p)^(n-k)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n distinct items.
P(X=2) = (5 choose 2) (1/6)² (5/6)³ = 0.1608
P(X=3) = (5 choose 3) (1/6)³ (5/6)² = 0.0322
P(X=4) = (5 choose 4) (1/6)⁴ (5/6)¹ = 0.0013
P(X=5) = (5 choose 5) (1/6)⁵ (5/6)⁰ = 0.00003
Therefore,
P(X ≥ 2) = 0.1608 + 0.0322 + 0.0013 + 0.00003 = 0.1943
So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.
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caden is 208 miles away from rahquez. they are traveling towards each other. if rahquez travels 6 mph faster than caden and they meet after 8 hours, how fast was each traveling?
Caden's speed is 10 mph and Rahquez's speed is 16 mph faster, which is 16+6 = 32 mph
Let's use the formula: distance = rate x time
Since Caden and Rahquez are traveling towards each other, their combined distance will be 208 miles. Let's call Caden's speed "x" and Rahquez's speed "x+6", since Rahquez is traveling 6 mph faster than Caden.
Using the formula above, we can set up the equation:
208 = (x + x + 6) * 8
Simplifying, we get:
208 = (2x + 6) * 8
208 = 16x + 48
160 = 16x
x = 10
Therefore, Caden's speed is 10 mph and Rahquez's speed is 32 mph.
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