The probability that the last person to board sits in the assigned seat is always 1/2, regardless of the number of people n in the line.
The issue can be tackled utilizing numerical enlistment.
Base Case:
At the point when n = 2, there are two travelers and two seats. The principal traveler takes an irregular seat, and the subsequent traveler will sit in his doled out seat with likelihood 1/2 or take the other seat with likelihood 1/2. Consequently, p2 = 1/2.
Inductive Speculation:
Accept that for some certain number k, pk = 1/2.
Inductive Step:
Think about n = k+1 travelers. The principal traveler takes an irregular seat. There are two cases to consider:
Case 1: The primary traveler sits down relegated to the k+1-th traveler. For this situation, the last traveler will be ensured to sit in his doled out seat, and the leftover k travelers can be considered as a subproblem with similar circumstances. By the inductive speculation, the likelihood that the last traveler in the subproblem sits in his alloted seat is 1/2. Thusly, the likelihood that the last traveler in the first issue sits in his doled out seat for this situation is 1/(k+1) + (k/(k+1)) * 1/2 = (k+2)/(2(k+1)).
Case 2: The primary traveler sits down other than the one doled out to the k+1-th traveler. For this situation, the issue lessens to the case with k travelers, and the likelihood that the last traveler in the decreased issue sits in his doled out seat is pk = 1/2 (by the inductive speculation). Thusly, the likelihood that the last traveler in the first issue sits in his doled out seat for this situation is (k/(k+1)) * 1/2 = k/(2(k+1)).
Joining the two cases, we have:
pk+1 = (k+2)/(2(k+1)) + k/(2(k+1)) = (k+1)/(2(k+1)) = 1/2.
Consequently, by numerical acceptance, the likelihood that the last individual to board sits in the appointed seat is dependably 1/2, no matter what the quantity of individuals n in the line.
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Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of several mice takes with a noise as stimulus. What are the null hypothesis H0 and alternative hypothesis Ha?
The null hypothesis H0 to for mice to complete the maze is equal to 18 seconds and alternative hypothesis Ha for mice to complete the maze is less than 18 seconds.
The null hypothesis is the default assumption that there is no effect of the noise stimulus on the time it takes for mice to complete the maze. The alternative hypothesis is the hypothesis that the noise stimulus does have an effect and causes the mice to complete the maze faster. The researcher will conduct a statistical test to determine if there is sufficient evidence to reject the null hypothesis and support the alternative hypothesis.
The researcher is hypothesizing that the true population mean time taken by mice to complete the maze with a loud noise stimulus is less than 18 seconds, Ha< 18seconds. The mean time for mice to complete the maze with the noise stimulus is equal to 18 seconds. Ha: 18 seconds
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in a ballroom dance competition, each couple is identified by a number worn on the leader's back. at a recent competition, forty couples competed. their numbers are listed below:
The average value of the competition is 193.525.
To find the average value of the competition, we need to add up all the assigned numbers and divide by the total number of couples. In other words, we need to find the arithmetic mean of the data set.
In a ballroom dance competition, each couple is assigned a number for identification purposes. In this particular competition, forty couples competed, and we are interested in finding the average value of their assigned numbers.
First, we add up all the numbers:
=> 103 + 105 + 112 + 116 + 117 + 122 + 126 + 130 + 139 + 147 + 154 + 159 + 165 + 170 + 176 + 178 + 182 + 184 + 187 + 193 + 196 + 199 + 206 + 207 + 211 + 216 + 224 + 227 + 230 + 237 + 242 + 246 + 249 + 252 + 258 + 264 + 267 + 270 + 275 + 281 = 7741
Next, we divide by the total number of couples, which is 40:
7741 ÷ 40 = 193.525
It is important to note that the average is not necessarily a value that is present in the data set. In this case, none of the couples were assigned the exact number 193.525.
Instead, the average represents a central tendency of the data set, which can be useful in comparing and analyzing different competitions.
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Complete Question:
In a ballroom dance competition, each couple is identified by a number worn on the leader's back. At a recent competition, forty couples competed. Their numbers are listed below: 103 105 112 116 117 122 126 130 139 147 154 159 165 170 176 178 182 184 187193 196 199 206 207 211 216 224 227 230 237 242 246 249 252 258 264 267 270 275 281
Find the average value of the competition
9. What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale
A.)22
B.) √22
C.)√105
D.)105
The length of the altitude drawn to the hypotenuse is √105 units
How to determine the length of the altitude drawn to the hypotenuse?From the question, we have the following parameters that can be used in our computation:
The triangle
Represent the required length
so, we have the following representation
x/7 = 15/x
Cross multiply the equation
x^2 = 7 * 15
So, we have
x^2 = 105
Take the square roots
x = √105
Hence, the length is √105 units
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Which graphs represent functions?
HELPPPPPPPPP
A . c and d
B. d only
C. b and d
D. a only
Answer:
A
Step-by-step explanation:
There probably is a good explanation but I don't have it.
HELP ASAP!!
The sum of two integers is three the sum of the squares 185 find the integers.
Answer:
the two integers are 11 and -8
Step-by-step explanation:
Let's call the two integers we're trying to find "x" and "y".
From the problem statement, we know two things:
x + y = 3 (the sum of the two integers is three)
x^2 + y^2 = 185 (the sum of the squares is 185)
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for "y" in terms of "x" by subtracting "x" from both sides:
y = 3 - x
Now we can substitute this expression for "y" into the second equation:
x^2 + (3 - x)^2 = 185
Expanding the square on the left-hand side, we get:
x^2 + 9 - 6x + x^2 = 185
Combining like terms, we get:
2x^2 - 6x - 176 = 0
We can simplify this equation by dividing both sides by 2:
x^2 - 3x - 88 = 0
Now we can solve for "x" using the quadratic formula:
x = (3 ± sqrt(3^2 - 4(1)(-88))) / 2(1)
Simplifying, we get:
x = (3 ± sqrt(361)) / 2
We can ignore the negative root, since it would give us a negative value for "y". So, taking the positive root, we get:
x = (3 + 19) / 2 = 11
Now we can use the first equation to solve for "y":
y = 3 - x = 3 - 11 = -8
Just solve number 2 please. Thanks
The probability of digits 0 to 9 represent the medicine being not effective.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
As the digit 9 is not effective
So the number of not effective is 2+1+2+2+1+3
=11
The probability=effective numbers/all numbers
=30-11/30
=19/30
Hence, the probability of digits 0 to 9 represent the medicine being not effective.
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Any help would be great
Answer:
50+6.3= 56.3
Step-by-step explanation:
Discuss the pros and cons of different times in a person's life when taxes can be withheld.
Early tax withholding offers predictability and facilitates effective financial planning but restricts financial flexibility and investment potential. Meanwhile, late tax withholding fosters short-term financial flexibility and investment opportunities but carries the risk of miscalculations, underestimations, and potential penalties.
Explanation:The timing of tax withholding can have different pros and cons depending on an individual's current financial status, revenue predictions, and personal preferences.
A primary advantage of early tax withholding is increased predictability. By setting aside funds for taxes in advance, an individual can have a clearer picture of their net income and employ effective financial planning strategies. However, this approach does have a notable drawback. Specifically, the individual may miss potential investment opportunities as a result of having their money tied up in tax withholdings.
On the other hand, late tax withholding allows greater short-term financial flexibility, providing the opportunity to use funds for immediate personal or business needs. It can also enable investment in lucrative opportunities. However, the main downside is the potential for miscalculation and underestimation of the tax liability, which can lead to financial strain or penalties.
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These tables represent the relationships between x and y for two different sets of data. Which statements correctly describe the relationships between x and y for each table? Responses Table A represents an additive relationship because y is 1.5 more than x, and Table B represents a multiplicative relationship because y is 3 times x. Table A represents an additive relationship because , y, is 1.5 more than , x, , and Table B represents a multiplicative relationship because , y, is 3 times , x, . Table A represents a multiplicative relationship because y is 2.5 times x, and Table B represents an additive relationship because y is 2 more than x. Table A represents a multiplicative relationship because , y, is 2.5 times , x, , and Table B represents an additive relationship because , y, is 2 more than , x, . Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times x. Both data sets represent multiplicative relationships. In Table A, , y, is 2.5 times , x, , and in Table B, , y, is 3 times , x, . Both tables represent additive relationships. In Table A, y is 1.5 more than x, and in Table B, y is 2 more than x. Both tables represent additive relationships. In Table A, , y, is 1.5 more than , x, , and in Table B, , y, is 2 more than , x, . Table A x 1 2 3 4 y 2.5 5.0 7.5 10.0 Table B x 1 2 3 4 y 3 6 9 12
Correct expression is,
Table A represents an additive relationship because y is 5.5 more than x.
Table B represents a multiplicative relationship because , y, is 4.5 times x.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
These tables represent the relationships between x and y for two different sets of data.
Hence, The equation for table A is,
Two points from the table A are, (1, 6.5) and (2, 7.5)..
Thus, The equation fop table is,
y - 6.5 = (7.5 - 6.5) / (2 - 1) (x - 1)
y - 6.5 = 1 (x - 1)
y - 6.5 = x - 1
y = x - 1 + 6.5
y = x + 5.5
Thus, Table A represents an additive relationship because y is 5.5 more than x.
Hence, The equation for table B is,
Two points from the table A are, (1, 4.5) and (2, 9)..
Thus, The equation fop table is,
y - 4.5 = (9 - 4.5) / (2 - 1) (x - 1)
y - 4.5 = 4.5 (x - 1)
y - 4.5 = 4.5x - 4.5
y = 4.5x
Thus, Table B represents a multiplicative relationship because , y, is 4.5 times , x,.
Therefore, We get;
Correct expression is,
Table A represents an additive relationship because y is 5.5 more than x.
Table B represents a multiplicative relationship because , y, is 4.5 times x.
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Another customer calls you wanting to know how much fence they should install around the circumference of their circular garden if they bought 210 feet of topsoil. assume the customer created a circle out of the soil and calculate the circumference in linear feet.
The circumference of a circular garden is 51.5 feet.
What is area of a circle?The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.
Given that, the area of a circular garden is 210 square feet.
Here, 210=3.14×r²
r²=210/3.14
r²=66.87
r=8.2 feet
Now, circumference =2πr
= 2×3.14×8.2
= 51.5 feet
Therefore, the circumference of a circular garden is 51.5 feet.
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A floor plan was drawn using the following scale:
1 inch: 2 1/2 feet
One wall of the house was represented by a line 6 1/2
inches long on the floor plan. Which proportion could be used to find the length of the actual wall, in feet? pls help me hurry than k u
a. 2/5=13/2x
b. 2/5=13x/2
c. 5/2=13/2x
d. 5/2=13x/2
The proportion that could be used is (a) 2/5=13/2x
How to determine the proportion that could be usedFrom the question, we have the following parameters that can be used in our computation:
Scale = 1 inch: 2 1/2 feet
The proportion that can be used is:
actual length / length on the floor plan = scale factor
So, we can set up the proportion as follows:
actual length / 6 1/2 inches = 2 1/2 feet / 1 inch
Solving for actual length (x), we get:
x/(13/2) = 5/2
So, we have
2x/13 = 5/2
Rewrite as
13/2x = 2/5
Hence, the proporton is (a) 2/5=13/2x
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Mrs. Taylor, the librarian, has the following puzzle on a shelf: 3 puzzle with 1,000 pieces 8 puzzle with 500 4 puzzle with 100 pieces 3 puzzle with 50 pieces. Lola will randomly choose 1 puzzle to put together. What is the probability that lola will choose a puzzle with 1,000 pieces?
Answer:
Step-by-step explanation:
how does the phase of matter affect its properties
The process by which the various phase of matter affect its properties is mentioned below.
What is a state of matter?In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life : solid, liquid, gas, and plasma.Given is to find how does the phase of matter affect its properties.
A solid holds its shape and the volume of a solid is fixed by the shape of the solid. In the liquid phase the molecular forces are weaker than in a solid. A liquid will take the shape of its container with a free surface in a gravitational field. In microgravity, a liquid forms a ball inside a free surface.Matter in the gaseous state has both variable volume and shape, adapting both to fit its container. Its particles are neither close together nor fixed in place.Therefore, the process by which the various phase of matter affect its properties is mentioned above.
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a football is thrown horizontally at 56ft/s parallel to the sideline. a tv camera is 92ft/s from the path of the football. find theta/dt the rate at whicht the camera must turn to foloow the ball when theta
The camera must turn at a rate of about 53.67 degrees/s to follow the ball at an angle of 15 degrees.
In this issue, we are given the underlying speed of the football and the distance of the television camera from the way of the football. We really want to find the rate at which the camera should go to follow the ball at a specific point theta=15 degrees. We can utilize geometry to take care of this issue. The point between the way of the ball and the line associating the camera and the ball is given by 90 - 15 = 75 degrees. Utilizing the cosine capability, we can find the part of the speed of the football opposite to the camera, which is 56*cos(15) = 53.17 ft/s. Presently, utilizing the digression capability, we can find the rate at which the camera should go to follow the ball, which is (53.17/92)*tan(75) = 0.937 radians/s or roughly 53.67 degrees/s. In this manner, the camera should turn at a pace of around 53.67 degrees/s to follow the ball at a point of 15 degrees.
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The complete question is:
A football is thrown horizontally (very little arc) at 56 ft./s parallel to the sideline. A TV camera is 92 ft. from the path of the football. Find de/dt, the rate at which the camera must turn to follow the ball when θ = 15°. football TV camerao 92 ft.
Andrew's bank account started off with a deposit of $750, and after 4 years he earned $165 in interest. The interest is simple interest, calculated on the basis of the initial deposit. What is the interest rate that Andrew's bank provides? Give your answer as a percentage to the nearest tenth of a percent.
The solution is, 5.5% is the interest rate that Andrew's bank provides.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
here, we have,
Andrew's bank account started off with a deposit of $750,
and after 4 years he earned $165 in interest.
we know,
formula: I = Prt.
let, the interest rate that Andrew's bank provides = r%
so, solving we get,
r = 5.5%
Hence, The solution is, 5.5% is the interest rate that Andrew's bank provides.
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identify the numerator and the denominator of the fraction and identify the fraction as proper or improper. 4/7
The numerator is 4 and the denominator is 7. It is a proper fraction.
What is fraction?A fraction represents the part of a set of objects. It has two parts separated by a dividing line, generally written
a/b
Where
a is numeratorb is denominatorThere are 3 types of fraction. They are
1. Proper fraction
A proper fraction is a fraction whose numerator is less than the denominator. It makes the value is less than 1.
Example: 3/4, 2/5.
2. Improper fraction
An improper fraction is a fraction whose numerator is more than the denominator. The value is more than 1.
Example: 9/8, 7/5.
3. Mixed fraction
A mixed fraction is a combination of a whole number and a proper fraction. It is the quotient and the remainder of improper fraction.
Example:
9/5 = 1 4/511/2 = 5 1/2From the explanation above, the fraction of 4/7 has the numerator of 4 and the denominator of 7. The numerator 4 is less than the denominator 7, so the fraction is a proper fraction.
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The cafeteria manager took a poll of 150 students to find the most popular lunch. The circle graph below displays the data
How many more students chose spaghetti and pizza than corn dogs , tacos, and cheeseburgers, as their favorite lunch
There are 60 students who chose spaghetti and pizza over corn dogs, tacos, and cheeseburgers, as their favorite lunch.
What is a circular graph?
A circular graph is also known as a pie chart. It is used to display a set of data. The data can be in percentages or degrees or radians.
The given data are as follows:
Pizza: 45%
Corn dogs: 10%
Cheeseburger: 8%
Tacos: 12%
Spaghetti: 25%
The total number of students is 150.
The total percentage of students who eat spaghetti and pizza is (25%+45%), that is, 70%.
The total percentage of students who eat corn dogs, tacos, and cheeseburgers is (10%+12%+8%), that is, 30%.
The percentage difference is (70%-30%), that is, 40%.
Now, calculate 40% of the total students, that is, 150.
150×40% = 150×40/100
= 60
Therefore, the obtained answer is 60.
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The complete question is given in the following chart.
find the measure of such angle whose supplementary angle is 35 degree more than twice of its complementary angle
The required angle is 35 degrees whose supplementary angle is 35 degrees more than twice its complementary angle.
What is the supplementary angle?The definition of a supplementary angle is that it adds up to 180 degrees.
Let's represent the required angle as "x".
We know that the supplementary angle to "x" is 180 - "x".
Similarly, the definition of a complementary angle is that it adds up to 90 degrees, so we know that the complementary angle to "x" is 90 - "x".
Given that the supplementary angle to "x" is 35 degrees more than twice its complementary angle, so we can write this as an equation:
180 - x = 2(90 - x) + 35
Simplifying this equation, we get:
180 - x = 180 - 2x + 35
Adding x to both sides, we get:
x = 35
Therefore, the required angle is 35 degrees.
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jack and diane are designing a trellis for some special plants they are planning to put in their backyard garden. use the values provided on the sketch of the trellis to find the missing values for and . (round your answers to the nearest hundredth.)
Using the values provided on the sketch of the triangular trellis, the values for x, y, and z are 13.33 ft, 6.75 ft, and 17.37 ft, respectively.
From the provided sketch of the trellis, we can use the similar triangles and similar trapezoids to solve the values of x, y, and z.
Consider similar trapezoids at the bottom of the trellis.
10/(10 + 6) = x/(8 + x)
80 + 10x = 16x
6x = 80
x = 40/3 = 13.33
Consider the similar triangles at the top of the trellis.
9/(9 + x) = 7/z
9/(9 + 40/3) = 7/z
z = 469/27 = 17.37
y/(y + 10) = 9/(9 + x)
y/(y + 10) = 9/(9 + 40/3)
(67/3)y = 9y + 90
(40/3)y = 90
y = 27/4 = 6.75
Hence, the length of x, y, and z is 13.33 ft, 6.75 ft, and 17.37 ft, respectively.
The problem seems incomplete, it must have been...
"Jack and Diane are designing a trellis for some special plants they are planning to put in their backyard garden. Use the values provided on the sketch of the trellis to find the missing values for x, y, and z. (Round your answers to the nearest hundredth.)
See attached copy of the complete question."
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find the value of x. SIMPLEST RADICAL FORM
For given triangle, x is 4√5 using Pythagorean theorem.
What is Pythagorean Theorem?
Pythagoras Theorem (also known as Pythagorean Theorem) is a mathematical concept that explains the relationship between the sides of a right-angled triangle. The sides of a right triangle are also referred to as Pythagorean triples. This theorem's formula and proof are discussed with examples here.
The Pythagorean theorem is used to calculate the length of an unknown side and the angle of a triangle. We can deduce the base, perpendicular, and hypotenuse formulae from this theorem.
The Pythagoras Theorem formula is presented in the definition as:
Perpendicular² + Base² = Hypotenuse²
c² = a² + b²
Now,
Given that perpendicular =19
Hypotenuse=21
then Base²=21²-19² using Pythagoras theorem
Base=√441-361
=√80
=4√5
Hence,
x is 4√5
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if one person from this study is randomly selected, find the probability, rounded to four decimal places, that their class / academic rank is that of a junior and they usually drink bottled water.
The probability of selecting a junior who usually drinks bottled water is 0.0156. This is calculated by finding the probability of each separate event (being a junior and drinking bottled water) and multiplying them together.
To find the probability of selecting a junior who usually drinks bottled water, first calculate the probability of being a junior. There are 12 juniors out of a total of 30 students, so the probability of being a junior is 0.4. Then, calculate the probability of usually drinking bottled water. There are 10 students who usually drink bottled water out of a total of 30, so the probability of usually drinking bottled water is 0.3333. Finally, multiply the probabilities together to get the overall probability of 0.0156. This can be rounded to four decimal places to get the final answer of 0.0156.
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On many cell phones with GPS, an approximate location can be given before the GPS signal is received. This is done by a process called triangulation, which works by using the distance from two known points. Suppose there are two cell phone towers within range of you, located 3000 feet apart along a straight highway that runs east to west, and you know you are north of the highway. Based on the signal delay, it can be determined you are 2050 feet from the first tower, and 1420 feet from the second. Determine the angle, , between your line of sight to the first tower and the highway to the nearest tenth of a degree. (A calculator is needed for this question)
STEVE HAS A BUDGET OF 45.00 TO SPEND ON DECORATION FOR A PARTY HE BOUGHT 5 PACKAGES OF STREAMERS FOR 1.59 EACH HE ALSO WANTS TO BUY BALLOONS THAT COST 3.29 PER PACKAGE WRITE AN INEQULITY TO MODEL THE STIUATION USE THE VARIABLE N TO REPRESENT PACKAGES OF BALLOONS THEN SOLVE
Step-by-step explanation:
Inequality: 1.59(5) + 3.29n ≤ 45.00
Explanation: 1.59(5) represents the total cost of the streamers, and 3.29n represents the total cost of the balloons (since we don't know how many packages of balloons Steve will buy, we use the variable n to represent this unknown quantity). The sum of these costs must be less than or equal to Steve's budget of $45.00.
To solve for n:
1.59(5) + 3.29n ≤ 45.00
7.95 + 3.29n ≤ 45.00
3.29n ≤ 37.05
n ≤ 11.27 (rounded to two decimal places)
So Steve can buy a maximum of 11 packages of balloons within his budget.
Theorem: The difference between any odd integer and any even integer is odd. In an attempted proof of this statement a student wrote the following lines: Suppose n is any odd integer, and m is any even integer. By definition of odd, n = 2k + 1 where k is an integer. By definition of even, m = 2k where k is an integer. Then n m = (2k + 1) – 2k = 1 and 1 is odd. Therefore, the difference between any odd integer and any even integer is odd. Which one of the following best describes the reason the proof is not correct? a. The proof assumes m and n are consecutive integers.
b. It does not prove that 1 is odd. c. The proof violates the parity property. d. The proof violates the zero product property.
The best describes reason the proof is not correct is c. The proof violates the parity property.
The reason the attempted proof of the statement "The difference between any odd integer and any even integer is odd" is not correct is "The proof violates the parity property."
The student incorrectly subtracted an even integer from an odd integer and concluded that the result is odd. However, the difference between an odd integer and an even integer is always odd, which can be proven directly as follows:
Let n be any odd integer and m be any even integer. Then, by definition, n = 2k + 1 and m = 2j for some integers k and j. The difference between n and m is:
n - m = (2k + 1) - 2j
= 2k - 2j + 1
= 2(k - j) + 1
Since k and j are integers, k - j is also an integer. Therefore, the difference between any odd integer and any even integer is of the form 2x + 1, where x is an integer, which is an odd integer.
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65 mi/hr = ? meters per min
Answer:
1743.46[tex]\frac{meters}{min}[/tex]
Step-by-step explanation:
Two unit multipliers will be used here:
1 mile (mi) = 1,609.344 meters
1 hour (hr) = 60 minutes (min)
65 [tex]\frac{mi}{hr}[/tex] = (65[tex]\frac{mil}{hr}[/tex])×([tex]\frac{1609.344 meters}{1 mile}[/tex])×([tex]\frac{1 hour}{60 minutes}[/tex])
The miles unit in the numerator and denominator will cannel each other out completely. In addition, the hour unit in the numerator and denominator will also cancel each other out completely:
= 1743.46 [tex]\frac{meters}{min}[/tex]
Simplify (6x4y2 − 3xy3 − 4xy) + (4x4y2 − xy3 + 4xy).
10x4y2 − 2xy3
10x4y2 − 4xy3
10x4y2 − 4xy3 − xy
10x4y2 − 4xy3 + 2xy
An equation is a part of every formula. A formula is not always an equation. In order to be solved for a variable, equations must be given. Evaluation of formulas
What is meant by equation?An equation is a mathematical statement made up of two expressions connected together by the equal sign. An example of an equation is 3x - 5 = 16. By resolving this equation, we can establish that the variable x has a value of 7.In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. Take a look at the formula 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the word "equal."A mathematical expression called an equation has two equal sides and an equal sign in the middle. For example, 4 + 6 = 10 is an equation.Given,
[tex]$\left(6 x^4 y^2-3 x y^3-4 x y\right)+\left(4 x^4 y^2-x y^3+4 x y\right)[/tex]
[tex]$=6 x^4 y^2-3 x y^3-4 x y+4 x^4 y^2-x y^3+4 x y[/tex]
Group like terms
[tex]$=6 x^4 y^2+4 x^4 y^2-3 x y^3-x y^3-4 x y+4 x y[/tex]
Simplifying the above equation,
[tex]$=10 x^4 y^2-3 x y^3-x y^3-4 x y+4 x y[/tex]
Simplify,
[tex]$=10 x^4 y^2-4 x y^3-4 x y+4 x y[/tex]
Then we get,
[tex]$=10 x^4 y^2-4 x y^3[/tex]
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Suppose the speeds that people drive down the Pat Bay Highway are normally distributed with a mean of 90 km/hr and a standard deviation of 7 km/hr. Answer each of the following.
(a) What proportion of drivers are travelling between 80 and 120 km/hr? To answer this question, convert the probability question that is being asked to a probability question regarding Z
How do you get 2.57 for Z2
Answer:
92.3%
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
Mean μ = 90Standard deviation σ = 7Therefore, if the speeds that people drive down the Pat Bay Highway are normally distributed:
[tex]\boxed{X \sim\text{N}(90,7^2)}[/tex]
where X is the speed in km/h.
f we want to find what proportion of drivers travel between 80 and 120 km/h, we need to find P(80 ≤ X ≤ 120).
[tex]\implies \sf P(80 \leq X \leq 120)=P(X \leq 120)-P(X \leq 80)[/tex]
Converting to the Z distribution:
[tex]\boxed{\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \dfrac{X-\mu}{\sigma}=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)}[/tex]
Transform X to Z:
[tex]\sf P(X \leq 120)=P\left(Z \leq \dfrac{120-90}{7}\right)=P\left(Z \leq \dfrac{30}{7}\right)[/tex]
[tex]\sf P(X \leq 80)=P\left(Z \leq \dfrac{80-90}{7}\right)=P\left(Z \leq -\dfrac{10}{7}\right)[/tex]
Therefore:
[tex]\begin{aligned}\implies \sf P(80 \leq X \leq 120)&=\sf P\left( -\dfrac{10}{7} \leq Z \leq \dfrac{30}{7}\right)\\\\&=\sf P\left(Z \leq \dfrac{30}{7}\right)-P\left(Z \leq -\dfrac{10}{7}\right)\\\\&=\sf 0.999990892...-0.0765637255...\\\\&= \sf 0.9234271...\\\\&=\sf 92.34271...\%\end{aligned}[/tex]
Therefore, the proportion of drivers travelling between 80 and 120 km/h is 92.3% (nearest tenth).
Find the result if 24,312 is increased by 22,211.
Answer:
Step-by-step explanation:
To find the result of increasing 24,312 by 22,211, you would simply add the two numbers:
24,312 + 22,211 = 46,523
So, the result of increasing 24,312 by 22,211 is 46,523.
Answer: 46,523
Step-by-step explanation:
Line up the two numbers by their number places (making sure to put the larger number on top). The add the digits that are on top of each other until you get your answer.
An oil tank is to be drained for cleaning. There are V(t) gallons of oil left in the tank t minutes after the draining began, where V(t)= 45(60-t)^2.
a) Find the average rate at which oil drains during the first 15 minutes.
b) Find the average rate at which oil drains during the time interval [10, 15].
c) Find the rte at which oil is flowing out of the tank 15 minutesafter the draining began.
a - The average rate at which oil drains during first 15 minutes is -4725 gallons/min
b - The average rate at which oil drains during time interval [10 , 15] is -4275 gallons/min
c - The rate of oil flowing out 15 min after the drain began is -4050 gallon/min
We have ,
V(t) = 45(60 - t)²
The average rate at which oil drains during first 15 minutes can be given as:
V(0,15)=[tex]\frac{V(15)-V(0)}{t2-t1}[/tex]
= (45(60-15)²-45(60-0)²)/15
= -70875/15
= -4725 gallons/min
Similarly , the average rate for time interval [10 , 15] is
V(10 , 15) = [tex]\frac{V(15)-V(10)}{t2-t1}[/tex]
= (45(60-15)²-45(60-10)²)/(15-10)
= -21375/5
= -4275 gallons/min
Now , to find rate of oil flowing out 15 min after the drain began
For that we will differentiate the given equation with respect to t
V(t) = 45(60 - t)²
= 45(3600 - 120t + t²)
= 16200 - 5400t + 45t²
Differentiating with respect to t we have
V'(t) = -5400 + 90t
V'(t) = -5400 + 90(15)
= -4050 gallon/min
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If 2x+1/3x=4, then find the value of 27x³+1/8x³
Answer: We can find the value of x by solving the equation 2x + 1/3x = 4.
Combining the terms on the left side, we get:
(6/3)x = 4
Dividing both sides by 6/3, we get:
x = 2
Substituting the value of x back into the expression 27x³ + 1/8x³, we get:
27 * 2³ + 1/8 * 2³ = 27 * 8 + 1/8 * 8 = 216 + 1 = 217
So the value of the expression 27x³ + 1/8x³ is 217.
Step-by-step explanation: