Answer:
[tex]2\sqrt{2}[/tex]
Step-by-step explanation:
Think of it in terms of a and b if its too difficult to understand what it is in its current state.
[tex]\sqrt{3} = a & \sqrt{2} = b\\(\sqrt{3} + \sqrt{2}) - (\sqrt{3} - \sqrt{2})\\(a + b) - (a - b)\\a + b - a + b\\2b \\2\sqrt{2}[/tex]
A student drives home from college on break. She travels 412 miles in 8 hours. What was the student’s speed in mph? Round to 1 decimal place. If the student wants to return to school in 6 hours, what should her average speed be? Round to 1 decimal place. Her father tells her not to travel back at over 60 mph. If 60 mph is her average speed, how long will it take her to get back to school? Round to 1 decimal place.
Answer:
Average peed from college to home in 8 hours = 51.5 mphAverage peed from home to college in 6 hours = 68.7 mphTime taken to reach college at 60mph = 6 hours 52 minutes
Step-by-step explanation:
Student's speed from college to home
Distance from college to home = 412 milesTime taken to travel this distance = 8 hoursAverage Speed = Distance/Time = 412/8 = 51.5 mphStudent's speed from home to college
The distance from home to college is assumed to be the same as from college to homeDistance from home to college = 412 milesTime taken for travel = 6 hoursAverage speed = 412/6 = 68.7 mphTime take to travel from home to college at 60 mph
Distance = 412 milesAverage speed = 60 mphTime taken = Distance/speed = 412/60 = 6.8666 hoursConverting to fraction, 412/60 = 6 13/15 hours13/15 hour = 13/15 x 60 minutes = 52 minutesSo time taken to reach school at 60 mph average speed = 6 hours 52 minutesEddy's plum weighs 3.042 ounces. Desta's plum weighs 3.24 ounces. Whose plum weighs more? How can you tell?
Desta's plum weigh more because the tenth value of the weight is greater than that of Eddy.
Whose plum weigh more?A decimal is a number that is made up of integers and non-integers. The whole numbers are separated from numbers that are not whole number by a decimal point.
Here is the place value of the weight of Eddy's plum:
3.042
3 = unit
0 = tenth
4 = hundredth
2 = thousandth
Here is the place value of the weight ofDesta's plum:
3.24
3 = unit
2 = tenth
4 = hundredth
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What is the sum of the sequence 1+(a+b)+(a^2+ab+b^2)+(a^3+a^2b+ab^2),up to n terms?
The sum can be rewritten like this:
∑k=0n−1∑l=0kalbk−l.
If a=b=1
then the sum is that of the first n
integers, n(n+1)2
.Assume now that (a,b)≠(1,1)
. If b=1
then the somme becomes geometric so,
∑k=0n−1∑l=0kal=∑k=0n−11−ak+11−a=11−a(n−a1−an1−a).Likewise if a=1
. Assume now that a,b≠1
.If a=b
then the sum becomes
∑k=0n−1(k+1)ak.
Multiplying it by 1−a
gives
(1−a)∑k=0n−1(k+1)ak=∑k=0n−1(k+1)ak−∑k=0n−1(k+1)ak+1=∑k=0n−1(k+1)ak−∑k =1nkak=∑k=0n−1ak−nan=1−an1−a−nan.
So, ∑k=0n−1(k+1)ak=11−a(1−an1−a−nan).
Assume now that a≠b
.Note that for all k∈{0,...,n−1} , so
(a−b)∑l=0kalbk−l=∑l=0kal+1bk−l−∑l=0kalbk−l+1=∑l=1k+1albk−l+1−∑l=0kalbk−l+1=ak+1−bk+1.
So we have two geometric sums, hence
∑k=0n−1∑l=0kalbk−l=1a−b(∑k=0n−1ak+1−∑k=0n−1bk+1)
=1a−b(a1−an1−a−b1−bn1−b).
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Identify the three triangle theorems explain what the theorem states
The three triangle theorems include the following:
The Pythagorean TheoremThe Law of CosinesThe Law of Sines What do the triangular theorems state?The positions of the theorems are as follows:
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse). This can be written as a^2 + b^2 = c^2, where c is the length of the hypotenuse and a and b are the lengths of the legs.
The Law of Cosines states that in any triangle, the square of the length of a side is equal to the sum of the squares of the lengths of the other two sides, minus twice the product of the length of one side times the cosine of the angle between the other two sides. This can be written as c^2 = a^2 + b^2 - 2ab * cos(C)
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. This can be written as a/sin(A) = b/sin(B) = c/sin(C)
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You are given the following information about N, the annual number of claims for a randomly selected insured:
P(N=0) = 1/2
P(N=1) = 1/3
P(N>1) = 1/6
Let S denote the total annual claim amount for an insured. When N=1, S is exponentially distributed with mean 5. When N>1, S is exponentially distributed with mean 8. Determine P(4
When N=1, P(S=4) = 1 - exp^(-4/5). When N>1, P(S=4) = 1 - exp^(-4/8). Therefore, P(S=4) = 1/2 * (1 - exp^(-4/5)) + 1/6 * (1 - exp^(-4/8)). S denote the total amount for an insured.
When N=1, the total annual claim amount for an insured, S, is exponentially distributed with mean 5. This means that the probability of S being equal to 4 is 1 - exp^(-4/5). When N>1, the probability of S being equal to 4 is 1 - exp^(-4/8). Since P(N=0) = 1/2 and P(N=1) = 1/3, the total probability of S being equal to 4 is the sum of the probabilities for N=1 and N>1. This is equal to 1/2 * (1 - exp^(-4/5)) + 1/6 * (1 - exp^(-4/8)).
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By the age of 21, the best violinists and pianists will have practiced at least 10,000 hours. If you practice an instrument 45 minutes, 0.75 hour, a day for 365.25 days, the length of a year, how many hours will you have practiced?
Answer:
Step-by-step explanation:
if you practice an instrument for 45 minutes or 0.75 hrs per day
The violinist's Age is 21 years
The total number of hours practiced per year is 0.75 hours /day * 365days/year
If you want to reach 10,000 hours by the age of 21, you would need to practice for approximately:
10000 hours / 21 years = 476 hours per year
So, you would need to practice for approximately 476 hours/year for 21 years to reach 10,000 hours of practice.
show that after choosing a basis the vector space of linear functions l(v,w) from v to w is isomorphic to m mn where m
A linear transformation L: V→W is called an isomorphism if it is a bijection. Two vector spaces are called isomorphic if there is an isomorphism mapping one of the spaces onto the other.
Often two vector spaces can consist of quite different types of vectors but, on closer examination, turn out to be the same underlying space displayed in different symbols. For example, consider the spaces
R² = {(a, b) | a, b ∈ R} and P₁= {a+bx|a,b ∈ R}
Compare the addition and scalar multiplication in these spaces:
(a,b) + (a₁,b₁) = (a+a₁, b+b₁) (a+bx) + (a₁+b₁x) = (a+a₁) + (b+b₁)x
r(a,b) = (ra,rb) r(a+bx)=(ra)+(rb)x
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An engineering construction firm is currently working on power plants at three different sites. Let Ai denote the event that the plant at site i is completed by the contract date. Use the operations of union, intersection, and complementation to describe each of the following events in terms of A1, A2, and A3, draw a Venn diagram, and shade the region corresponding to each one.
a. At least one plant is completed by the contract date.
b. All plants are completed by the contract date.
c. Only the plant at site 1 is completed by the contract date.
d. Exactly one plant is completed by the contract date.
e. Either the plant at site 1 or both of the other two plants are completed by the contract date.
By using Venn Diagram,
A: A1 U A2 U A3
B: A1 n A2 n A3
C: A1 n A2' n A3'
D: (A1 n A2' n A3') U (A1' n A2 n A3') U (A1' n A2' n A3')
E: A1 U (A2 n A3).
Given,
A set is a group of items with specific qualities. A series of events Ai can be used to describe how a contract is fulfilled.
The set that contains all of the items that belong to A1, A2, and A3 is referred to as the union of a set, or simply U.
The set that contains or is shared by each of the occurrences A1, A2, or A3 is the set we refer to as the intersection of sets, n.
All elements in the universal set that are not also found in A1, A2, or A3 are referred to as complement of a set (').
Consequently, to answer the question using Venn Diagram;
A: A1 U A2 U A3
B: A1 n A2 n A3
C: A1 n A2' n A3'
D: (A1 n A2' n A3') U (A1' n A2 n A3') U (A1' n A2' n A3')
E: A1 U (A2 n A3).
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What is the result when 2.5(3x + 8) is subtracting from 1.5(2x - 5)
The resulting expression when 2.5(3x + 8) is subtracting from 1.5(2x - 5) is; 4.5x + 27.5.
Which expression results from subtracting 2.5(3x + 8) from 1.5(2x - 5)?Since the given expressions whose difference is to be determined are; 2.5(3x + 8) and 1.5(2x - 5).
On this note, the difference in the two expressions can be determined as follows;
2.5 ( 3x + 8 ) - 1.5 ( 2x - 5 )
= 7.5x + 20 - 3x + 7.5
= 4.5x + 27.5
Ultimately, the result of the subtraction is; 4.5x + 27.5.
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Each of 7 students reported the number of movies they sa
18, 12, 6, 7, 11, 20, 15
Send data to calculator
Find the mean number of movies that the students saw.
If necessary, round your answer to the nearest tenth?
Explanation:
Add the values to get 18+12+6+7+11+20+15 = 89
Then divide by 7, since there are 7 values.
89/7 = 12.7143 approximately which rounds to 12.7
Data will be collected on the following variables. Which variable in most likely to be approximated by a normal model? A. The distribution of the number of books read last week by middle school students, where the right tal of the distribution is longer than the left b. The distribution of life spar, in minutes, for batteries of a certain size, where most life spans cluster around the center of the distribution but with some very low and some very high Me sans с. The distribution of uger, in years, of the students at a certain college, where most students are between 18 and 22 years old, but ages greater than 22 will probably be more spread out than ages less than 18 d. The distribution of the number of birthdays per month for the employees at a certain company, where the number of birthdays in each month is approximately equat e. The distribution of the length of a stay, in days, in a hospital after surpery, where many patients have very short hospital stays, but some stays are quite lengthy and considered high outliers.
The variable most likely to be approximated by a normal model is c. The distribution of age, in years, of the students at a certain college, where most students are between 18 and 22 years old, but ages greater than 22 will probably be more spread out than ages less than 18.
A normal model is used to describe data that has a symmetrical distribution and where most values cluster around the center of the distribution. Of the variables listed, c. The distribution of age, in years, of the students at a certain college, where most students are between 18 and 22 years old, but ages greater than 22 will variable probably be more spread out than ages less than 18 is the most likely to be approximated by a normal model as it does have a symmetrical distribution and most values will cluster around the center.
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5.5b≤10.89 solve for b
[tex]5.5b\leq 10.89[/tex]
Divide both sides by 5.5:
[tex]\dfrac{5.5b}{5.5} \leq \dfrac{10.89}{5.5}[/tex]
Answer:
[tex]b\leq 1.98[/tex]
Answer:
b ≤ 1.98
Step-by-step explanation:
Given equation,
→ 5.5b ≤ 10.89
Now the value of b will be,
→ 5.5b ≤ 10.89
→ b ≤ 10.89 ÷ 5.5
→ [ b ≤ 1.98 ]
Hence, value of b is 1.98.
Write an algebraic expression as indicated.
Rachel needs a mixture of 58 pounds (lb) of nuts consisting of peanuts and cashews. Let p represent the number of pounds of peanuts in the mixture. Write an
algebraic expression for the number of pounds of cashews that she needs to add.
Algebraic expression for the number of pounds of cashews that she needs to add is c = 58 - p
What is an algebraic expression?An algebraic expression can be described as an expression that is mostly composed or consists of variables, coefficients, terms, factors and constants.
Algebraic expressions are mathematically expressions and thus are made up of arithmetic operations, such as;
SubtractionMultiplicationFloor divisionBracketParenthesesDivisionAdditionFrom the information given, we have that;
58 pounds of nuts is a mixture of peanuts and cashewsThe variable, p represented the number of cashews in the mixtureTo determine the number of pounds of cashew, we have;
p + c = 58
Make 'c' the subject
c = 58 - p
Hence, the expression is c = 58 - p
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Which of the following is a possible event?
A) Pulling a blue sock from a drawer with 5 red socks and 4 pink socks.
B) Pulling a blue sock from a drawer with 1 blue sock and 8 pink socks.
C) Pulling a blue sock from a drawer of 9 red socks.
D) Pulling 2 blue socks from a drawer with 1 blue sock and 4 pink socks.
A possibility to event pulling a blue sock from a drawer with 1 blue sock and 8 pink socks.
What is an event in probability?Events in probability are the results of an experiment. An event's probability is a gauge of its likelihood to transpire as a result of an experiment.
In this question
A) Pulling a blue sock from a drawer with 5 red socks and 4 pink socks. - This is a possible event. There is one blue sock in the drawer, so it is possible to pull it out.
B) Pulling a blue sock from a drawer with 1 blue sock and 8 pink socks. - This is a possible event. There is one blue sock in the drawer, so it is possible to pull it out.
C) Pulling a blue sock from a drawer of 9 red socks. - This is not a possible event. There are no blue socks in the drawer, so it is not possible to pull one out.
D) Pulling 2 blue socks from a drawer with 1 blue sock and 4 pink socks. - This is not a possible event. There is only one blue sock in the drawer, so it is not possible to pull two out.
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Tracy is receiving lanoxin every 8.0 hours. She weighs 61 kg. The
dose range for this drug is 0.030 to 0.060 mg/kg every day. What is
the maximum safe dose (in mg) you could deliver every 8.0 hours?
The maximum safe dosage that can be delivered every 8 hours is 1.22 mg.
What is maximum value?A point in mathematics where the value of a function is greatest. It is an absolute maximum if the value is greater than or equal to all other function values.The smallest value in a given data set will be the minimum. The maximum is the most significant value in the data set.Here given that,
Tracy receives the drug lanoxin every 8.0 hours.
Her weight = 61 kg
The minimum dosage range = 0.03 mg/kg
The maximum dosage range = 0.060 mg/kg
To find,
Drug requirement for Tracy is :
0.060 x 61
= 3.66 mg per day
The maximum safe dose for each 8.0 hours is :
3.66 / 3 = 1.22mg
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Square ABCD and equilateral triangle AED are coplanar and share AD, as shown. what is the measure, in degrees, of angle BAE?
The measure of angle BAE is equal to the sum of the measures of angles ABC and ACD, or 120°.
Since ABCD and AED are both plane figures and share AD, the measure of angle BAE must be equal to the measure of angle BCD. Angle BCD is the exterior angle of triangle ABC, so the measure of angle BCD is equal to the sum of the measures of angles ABC and ACD. Therefore, the measure of angle BAE can be calculated using the formula:
m∠BAE=m∠ABC+m∠ACD
Since triangle AED is equilateral, all three angles are equal to 60°. Therefore, the measure of angles ABC and ACD are both equal to 60°. Therefore, the measure of angle BAE is equal to the sum of the measures of angles ABC and ACD, or 120°.
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25. At a cost of $1.41 per foot, what does 8 feet of air duct hose cost?
(Round the answer to the nearest cent)
Zachary purchased a computer for $1,400 on a payment plan. Five months afyer he purchased the computer, his balance was $625. seven months after he purchased the computer, his balance was $315. what is the equationt that models the balance y after x months?
hi id torjwh3 tenthjge r t
What is a name for the marked angle?
in a triangle with heigh 10 and base 6 a square is inscribed with a side along the base of the triangle as show. the length of a side of the square is:
In a triangle with heigh 10 and base 6 a square is inscribed with a side along the base of the triangle as show. the length of a side of the square is: 3
The length of a side of the square is the same as the length of the base of the triangle, which is 6. Therefore, the length of the side of the square is 6.
The triangle has a height of 10 and a base of 6, and a square is inscribed with a side along the base of the triangle. The side of the square must be equal to the length of the base of the triangle, which is 6. Therefore, the length of the side of the square is 6. This is because the side of the square must be equal to the length of the base of the triangle in order for the square to fit perfectly within the triangle. It is impossible for the side of the square to be any other length than 6, as this would cause the square to not fit within the triangle. Therefore, the answer to the question is that the length of the side of the square is 6.
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Which is the simplified form of the expression (6-2•65)-3?
0 630
0 0 о
O
% -1% % -12
O 6⁰
613
What is the value of x in the equation 3/4(1/4x+7)-(1:2x+2)=3/8(4-x)-1/4x?
The value of x in the given equation is 6.4. The solution is obtained by solving the linear equation.
What is a linear equation?
A linear equation is the equation which has the highest degree as 1. This shows that a linear equation with an exponent greater than one has no variables. On the graph, such an equation results in a straight line.
We are given [tex]\frac{3}{4} (\frac{x}{4} +8) - (\frac{x}{2} +2)=\frac{3}{8} (4-x) - \frac{x}{4}[/tex]
Now, let's simplify the linear equation
⇒[tex]\frac{3x}{16} + 6 - \frac{x}{2} -2= 6 - \frac{3x}{8} - \frac{x}{4}[/tex]
Now, on combining the like terms, we get
⇒[tex]\frac{3x}{16} - \frac{x}{2} +\frac{3x}{8} + \frac{x}{4} = 2[/tex]
⇒[tex]\frac{3x-8x+6x+4x}{16} = 2[/tex]
⇒[tex]\frac{5x}{16} = 2[/tex]
⇒ 5x = 32
⇒ x = 6.4
Hence, the value of x in the given equation is 6.4.
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hello i need help with 20983x3
Answer: 62,949
Step-by-step explanation: Information attached below…
For example, you can select the coordinates of the black point (plus symbol) you placed on the graph previously to see that the intersection of the curves occurs at the point representing a quantity of ________ boxes.
The black point (plus symbol) selected on the graph has coordinates of (4, 0.4).
This point represents the intersection of the two curves on the graph. To calculate the quantity of boxes represented by this point, we can use the equation y=mx+b, where m is the slope of the line, x is the x-coordinate, and b is the y-intercept.
In this case, the slope of the line is -2, the x-coordinate is 4, and the y-intercept is 0.4. We can substitute these values into the equation to solve for the quantity of boxes, which would be: y=-2x+0.4. Plugging in the x-coordinate of 4, we would get: 0.4=-2(4)+0.4, which simplifies to 0.4=-8. Solving for y, we would get 8 boxes. Therefore, the point (4, 0.4) on the graph represents a quantity of 8 boxes.
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show that each vertex of g can be assigned an integer in {1, 2, . . . , d 1} so that no two adjacent vertices are assigned the same integer. hint: use induction on the number of vertices.
Every vertex of a graph can be assigned an integer in {1, 2, ..., d1} so that no two adjacent vertices are assigned the same integer.
We can use induction to show that every vertex of a graph can be assigned an integer in {1, 2, ..., d1} so that no two adjacent vertices are assigned the same integer. Let G be a graph with d vertices, and assume that the result is true for all graphs with fewer than d vertices. Consider any vertex v in G and let N(v) be the set of neighbours of v. Since |N(v)| < d, by our induction hypothesis, there is an assignment of the integers 1,2, ..., d−1 to the vertices in N(v) so that no two adjacent vertices are assigned the same integer. Now assign the dth integer, i.e., d, to v and we are done. By our induction hypothesis, this assignment works for all graphs with d vertices. Thus, by induction, every vertex of a graph can be assigned an integer in {1, 2, ..., d1} so that no two adjacent vertices are assigned the same integer.
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For the following code, the summation that represents the worst-case runtime in terms of n is: the primitive operation costs 1 unit, for example: int x=0 ; takes 1 unit time int x = 0; for (int i=0; i for (int j=0; j
The code provided contains two nested for loops. This means that the complexity of the code is O(n^2). This means that the worst-case runtime in terms of n can be expressed by a summation of O(n^2).
O(n^2)
As we can see from the code, there are two nested for loops which means that the complexity of the code is O(n^2). The two for loops will execute n*n times which means the summation for the worst-case runtime in terms of n is O(n^2).
The code provided contains two nested for loops. This means that the complexity of the code is O(n^2). This means that the worst-case runtime in terms of n can be expressed by a summation of O(n^2). This means that the code will execute n*n times, meaning that the time taken for the code to run will increase in proportion to the square of n. As n increases, the time taken for the code to run will increase exponentially. In other words, the time taken for the code to run will increase significantly as n increases, making the code less efficient.
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Simplify 5/8x+1/2(1/4x+10)
The simplification 5/8(x )+ 1/2 ( 1/4( x) +10) is 3/4(x) + 5
What is simplification of fractions?The word simplify means to make something easier to do or understand. So, reducing or simplifying fractions means we make the fraction as simple as possible. We do this by dividing the numerator and the denominator by the largest number that can divide into both numbers exactly.
For example 25/100 can be simplified by cutting down 25 and 100 by their common factor which is 25.
25/100 = 1/4
⅝(x) + 1/8(x) + 5
= 6/8(x) +5
= 3/4(x) + 5
therefore the simplification of 5/8(x )+ 1/2 ( 1/4( x) +10) is 3/4(x) + 5
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which has the benefit of being cheaper and easier to conduct than conducting a study of an entire population. however, this method leaves room for possible error because you're not observing every member of the student body (the population). ultimately, the goal of inferential statistics is to use sample statistics to make inferences about population parameters.
This method uses a sample of the population mean to make generalizations about the whole, but can introduce error due to not observing the whole population.
The goal of inferential statistics is to use sample statistics to make inferences about population parameters. This is done by taking a sample of the population, usually a relatively small one, and using it to draw conclusions about the entire population. This method has the benefit of being much cheaper and easier to conduct than studying an entire population, however, it leaves room for error because it does not observe every member of the population. If the sample is not representative of the population, it can lead to faulty conclusions about the population as a whole. Additionally, if the sample size is too small, it may not be able to accurately represent the population. Therefore, it is important to carefully consider the sample size, as well as the representativeness of the sample, in order to draw reliable conclusions from inferential statistics.
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Abby rode her bike 1 1/2 miles from her home to school. On her way back from school she took a different route, and rode 1 3/8 of a mile. How many miles did Abby ride in total?
Answer:
11/2 + 13/8
add together
44+13/8
57/8
7.125
I need help with this question that I’m suck on
The value of x which is base of the given right angle triangle is, 30.724
What is Pythagoras theorem?It is the most important theorem of mathematics, which tells us the relationship between sides of the right angle triangle, which are known as Base(A), Height(B), Hypotenuse(H).
Pythagoras theorem,
H² = A² + B²
Given that,
A right angle triangle,
Sides are respectively, 63, x, ?
One segment on hypotenuse having length 55
As it can seen that segment has equal length of height of the perpendicular
So, A = 55 unit
H = 63 unit
x = ?
H² = A² + B²
63² = 55² + x²
x² = 63² - 55²
x = 30.724
Hence, the length of base is 30.724
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