A = {u + 2v, -3} is the basis for subspace U given that the set A is now linearly independent and that U = span(A).
Since U = span(S), and the set S is linearly independent, let S = {u, v} be the basis of the subspace U.
Now determine whether or not the set A = {u + 2v, -3v} is linearly independent.
A set of vectors must all have linear combinations that add up to zero in order for them to be considered linearly independent. Let a and b represent any scalars so that,
a(u + 2v) + b(-3v) = 0
Simplify the obtained equation.
au + 2av - 3bv = 0
au + v(2a - 3b) = 0
Make 2a - 3b = A.
Rewrite the equation that was found using this.
Now because u and v are linearly independent, a and A must be zero, and as a result, the constant b is also zero.
Set A is hence linearly independent.
Also, au + Av ∈ U, so, U = span(A).
Considering that the set A is now linearly independent and that U = span(A), the basis for subspace U is A = {u + 2v, -3}.
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The complete question is:
If {u, v} is a basis for the subspace U, show that {u + 2v, −3v} is also a basis for U.
Which graph represents the function on the interval [-3,3]?
f(x)=[x]-4
Answer:
in this problem, it wants us to graph this piecewise function and then determine which answer choice matches. And I'm not sure if you gave me all the answer choices, but let's go ahead and try and graph this. So first we have a vertical line at negative three from negative 22 negative one. So here is -2. It's going to be open circled at negative two, two, which is going to have a closed circle since it's less than or equal to. And it would just connect right in there. Then we would have an open circle at negative one at negative two And then closed at zero And then an open circle at zero and -1 closed at one. So that would be a graph of this function. It doesn't look like I have all the answer choices, which you want to look for, the one that starts at -3. And it's open circle.
Step-by-step explanation:
hope its help
thank you
What is tangent and how do you calculate it from the unit circle?
Answer:
The unit circle has many different angles that each have a corresponding point on the circle. The coordinates of each point give us a way to find the tangent of each angle. The tangent of an angle is equal to the y-coordinate divided by the x-coordinate.
Which graph matches the function given:
f(x)=((sqrt)x+5) if x<-2
|x+1| if -2 ≤ x ≤ 2
(x-2)^2 if x>2
The correct graph that matches the given function is option (C).
What does graphing function rules entail?To graph a function, select x-values and input them into the equation. Once those values have been put into the equation, you will get a y-value. The x and y values together make up a single point's coordinates.
Option is the appropriate graph for the specified function (C).
For x -2, the function is f(x) = (x+5), which is a half-parabola that starts at (5, 0) and travels through (2, 3) before opening towards the positive y-axis. Both (A) and (B) are incompatible with this aspect of the function.
The function is f(x) = |x+1| for -2 x 2, which is a V-shaped graph with an upward opening and a vertex at (1, 0). This portion of the function is covered by Option (C).
When x is greater than 2, the function is f(x) = (x2)2, which is a parabola with an upward opening and a vertex at (2, 0). This portion of the function is covered by Option (D).
No portion of the function matches option (E).
Thus, option is the appropriate graph that matches the specified function (C).
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What is the value of x ? Will give brainiest .
Answer:
x = 14√2 or 19.8 units---------------------------------
Given is the special right triangle.
It is a 45° isosceles right triangle. It has a property that the hypotenuse is √2 times the leg.
We have a hypotenuse of 28 units, so the leg is:
x = 28/√2 =28√2/2 = 14√2 or 19.8 unitsAnswer:
14√2
Step-by-step explanation:
Here we need to find out the value of "x" in the given right angled triangle, here we can make use of trigonometric ratios to find out the value of x .
In a right angled triangle, sine is defined as the ratio of perpendicular and hypotenuse . With respect to angle 45° , x is the perpendicular and 28 is hypotenuse (side opposite to 90° ) .
So we have;
sin45° = x/28
value of sin45° is 1/√21/√2 = x/28
x = 28*1/√2
x = 14 * (√2)² / √2
x = 14√2
Hence the value of x is 14√2 .
Annual Premium per $100 of coverage
Brick
Steel
Mixed
Wood
Area Building Contents Building Contents Building Contents Building Contents
rating
City 0.39 0.43
Suburb 0.45 0.52
Rural 06
0.69
0.5
0.56
0.71 0.8
0.54
063
0.55
0.72
0.89
0.65
0.74
091
0.66
0.83
1
0.76
0.85
1.02
Ashley owns a brick house in the country worth $85,000, and the contents of the
house are valued at $18,000. She wants to know her property insurance premium.
1.
What is Ashley's annual
premium on her house?
2.
What is Ashley's annual
premium on the contents of her
house?
Therefore, Ashley's annual premium on the contents of her house is $127.80.
What is percent?Percent is a term used to express a fraction or a ratio as a portion of 100. It is denoted by the symbol % (per cent or percent). Percentages are commonly used in many different contexts, such as finance, statistics, science, and everyday life. They are used to express changes, comparisons, rates, probabilities, and many other types of information. To calculate a percentage, we usually divide the part by the whole and multiply the result by 100.
Here,
Based on the provided table, we can calculate Ashley's annual premium on her house and the contents of her house as follows:
Annual premium on Ashley's house:
Since Ashley's house is made of brick and located in a rural area, we can use the values from the "Brick" and "Rural" columns of the table. The premium per $100 of coverage for a brick house in a rural area is $0.60 for the building and $0.69 for the contents.
To calculate the annual premium for the house, we first need to determine the coverage amount. The coverage amount is the value of the house divided by 100, so in this case, it is $85,000 / 100 = $850.
The annual premium for the house is then calculated by multiplying the coverage amount by the premium per $100 of coverage:
Annual premium on house = coverage amount * premium per $100 of coverage for brick house in rural area
= $850 * $0.60
= $510
Therefore, Ashley's annual premium on her house is $510.
Annual premium on Ashley's contents:
To calculate the annual premium for the contents of Ashley's house, we use the same method as above. The coverage amount is the value of the contents divided by 100, so in this case, it is $18,000 / 100 = $180.
The annual premium for the contents is then calculated by multiplying the coverage amount by the premium per $100 of coverage:
Annual premium on contents = coverage amount * premium per $100 of coverage for contents in rural area
= $180 * $0.71
= $127.80
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TRUE/FALSE.For a Binomial experiment, the second moment about mu is given by the second derivative of (p+qeAt) with respect to t evaluated at t-0.
False. The second moment about mu for a binomial experiment is not given by the second derivative of [tex](p+qeAt)[/tex]with respect to t evaluated at t=0.
The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success. The probability of success in each trial is denoted by p, and the probability of failure is denoted by q=1-p.
The second moment about mu is a measure of the variability of the binomial distribution, and is given by the formula[tex]E[(X-mu)^2][/tex] , where X is the random variable, mu is the mean, and E is the expected value operator.
To calculate the second moment about mu for a binomial distribution with parameters n and p, we can use the formula npq, where np is the mean and q=1-p. This formula can also be derived using the properties of variance, which state that [tex]Var(X)=E[X^2] - (E[X])^2.[/tex]
Therefore, the statement that the second moment about mu for a binomial experiment is given by the second derivative of [tex](p+qeAt)[/tex]with respect to t evaluated at t=0 is false. This statement does not relate to the binomial distribution or its properties, and is not a relevant formula for measuring the variability of a binomial experiment.
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What is 0.35+0.4 show your work
Answer:
0.75
Step-by-step explanation:
0.4 = 0.40
Add 0.40 + 0.35 = 0.75
here are the factors of sixteen and twenty. click the factors that are common to both numbers. (choose 3)
The common factors of sixteen and twenty are 1, 2, and 4.
The factors of sixteen are 1, 2, 4, 8, and 16. The factors of twenty are 1, 2, 4, 5, 10, and 20. The factors that are common to both numbers are 1, 2, and 4.
To calculate the factors of sixteen, we can start by dividing sixteen by two until we cannot divide any further. We can start with sixteen divided by two, which equals eight. Eight divided by two equals four. Four divided by two equals two. Two divided by two equals one. As we can see, the factors of sixteen are 1, 2, 4, 8, and 16
To calculate the factors of twenty, we can start by dividing twenty by two until we cannot divide any further. We can start with twenty divided by two, which equals ten. Ten divided by two equals five. Five divided by two equals two. Two divided by two equals one. As we can see, the factors of twenty are 1, 2, 4, 5, 10, and 20.The common factors of sixteen and twenty are 1, 2, and 4. This can be determined by comparing the two lists of factors. As we can see, 1, 2, and 4 are present in both lists.
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Complete question
What are the common factors of sixteen and twenty ?
put the following steps in order to produce the algorithm for multiplying two n-bit (binary) integers a
Steps in order to produce the algorithm is multiplies two n-bit binary integers a and b using only bitwise operations (shift and AND) and addition.
Set the product P to 0.
Repeat n times we get,
If the least significant bit of a is 1, add the value of b to P.
Shift b one bit to the left.
Shift a one bit to the right.
The final value of P is the product of a and b.
This algorithm is known as the binary multiplication algorithm
And it multiplies two n-bit binary integers a and b using only bitwise operations (shift and AND) and addition.
The algorithm works by iteratively adding shifted copies of b to the product P.
Depending on whether the corresponding bit in a is 1 or 0.
At the end of the iteration, P contains the product of a and b.
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please assist with this question...
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
(a)
the experimental probability is just using the actual experience to predict any future results.
the total number of cases was 20, and the number of desired cases (yellow) was 12.
so, the experimental probability of landing on yellow is
12/20 = 3/5 = 0.600
(b)
the theoretical probability of a totally fair spinner landing on yellow is 2 out of 5 possibilities, so
2/5 = 0.4000
(c)
the correct statement is the first one.
with a more or less balanced (fair) spinner the experimental numbers should get closer and closer to the theoretical numbers, the more spins we make.
A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Answer:
A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Step-by-step explanation:
The total surface area of the pyramid can be calculated using the formula for the lateral surface area of a pyramid:
Lateral surface area = (1/2) × perimeter of base × slant height
Since the base is an equilateral triangle, the perimeter is 3 times the length of one side:
Perimeter of base = 3 × 40 feet = 120 feet
Lateral surface area = (1/2) × 120 feet × 50 feet = 3000 square feet
To paint 75% of the pyramid, the painter needs to paint:
0.75 × 3000 square feet = 2250 square feet
Since the painter can paint 100 square feet in 18 minutes, the time required to paint 2250 square feet can be calculated as:
2250 square feet ÷ 100 square feet per 18 minutes = 225 ÷ 10 × 18 minutes = 405 minutes
Therefore, the painter would need 405 minutes or 6 hours and 45 minutes to paint 75% of the pyramid.
Jenny took the car, the bus, and the train to get home in time.
What form of punctuation is missing?
O A. No punctuation is missing.
OB.
A period
OC.
A comma
OD. A semicolon
Last three times I have tried to take a picture of my question. Nothing comes up that resembles any of it. I don’t know what’s wrong with this app but it’s not helping.
According to the question. A. No punctuation is missing.
What is punctuation ?Punctuation is the use of symbols to indicate the structure and organization of written language. It is used to help make the meaning of sentences clearer and to make them easier to read and understand. Punctuation marks can also be used to indicate pauses in speech, to create emphasis, and to indicate the speaker’s attitude. There are many different types of punctuation marks, each with its own purpose. The most commonly used punctuation marks are the period, comma, question mark, exclamation mark, quotation marks, and the apostrophe.
Quotation marks are used to enclose quoted material, while the apostrophe is used to indicate possession or to replace missing letters in a word or phrase. By using punctuation correctly, writers can ensure that their messages are correctly understood by their readers.
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Question 7
On June 22, 1947, in Holt, Missouri, 12 inches of rain fell in just 42 minutes. What was the average
rainfall per minute rounded to the nearest hundredth of an inch?
A
1 p
Question 8
1 pts
The average rainfall per minute is 0.29 inches.
What is Average?
The average of a set, also called the mean, is a measure of central tendency that represents the typical value of the set. It is found by adding up all the values in the set and then dividing by the total number of values in the set.
To find the average rainfall per minute, we need to divide the total rainfall by the number of minutes:
Average rainfall per minute = Total rainfall / Number of minutes
In this case, the total rainfall is 12 inches and the number of minutes is 42, so:
Average rainfall per minute = 12 / 42
Using a calculator or performing the division manually, we get:
Average rainfall per minute = 0.2857142857
Rounding this to the nearest hundredth of an inch, we get:
Average rainfall per minute ≈ 0.29 inches
Therefore, the average rainfall per minute during that 42-minute period was approximately 0.29 inches.
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A large drug company must determine how many sales representatives to assign to each of four sales districts. The cost of having ???? (???? > 0) representatives in a district is 88,000 + 80,000???? dollars per year, and you only pay 88,000 fixed cost if there is at least one sales representative at that district. If a sales rep is based in a given district, the time it takes to complete a call on a doctor (i.e., the sales rep travels to the doctor’s office) in each of the actual sales call district is given in the following table, where times are in hours: Actual Sales Call District Rep’s Base District 1 2 3 4 1 1 4 5 7 2 4 1 3 5 3 5 3 1 2 4 7 5 2 1 Each sales rep can work up to 160 hours per month. Each month a certain number of calls, given in the following table, must be made in each district (i.e., this is the total number of calls to be completed by all of the sales reps). Number of calls District 1 50 District 2 80 District 3 100 District 4 60 A fractional number of representatives in a district is not permissible. Determine how many representatives should be assigned to each district.
Answer:
Dont understand. Repeat question?
Step-by-step explanation:
Need help please!
Thank you so much!!
The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]
What is an interactive widget in graphs:An interactive widget in a graph is a tοοl that allοws the user tο manipulate different elements οf the graph using their mοuse οr tοuch screen.
Interactive widgets can be used tο explοre the behaviοr οf a functiοn οr dataset in a mοre dynamic and engaging way than a static graph.
Sοme cοmmοn examples οf interactive widgets in graphs include sliders, buttοns, checkbοxes, and drοpdοwn menus.
Here we have
y = -5 cοs (π/16 x) - 4
Represents a periοdic functiοn with a cοsine wave shape that is shifted dοwnwards by 4 units.
The cοsine functiοn οscillates between -1 and 1, sο multiplying it by -5 stretches the wave vertically by a factοr οf 5 and reflects it acrοss the x-axis.
The cοefficient οf x, π/16, cοntrοls the periοd οf the functiοn, which is the distance between twο cοnsecutive peaks οr trοughs οf the wave.
Specifically, the periοd οf this functiοn is 32 units, since the cοsine functiοn has a periοd οf 2π and 2π/(π/16) = 32.
Therefοre,
The graph repeats itself every 32 units hοrizοntally. [ The graph is attached belοw ]
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2 PART QUESTION PLS HELP Harris has a spinner that is divided into three equal sections numbered 1 to 3, and a second spinner that is divided into five equal sections numbered 4 to 8. He spins each spinner and records the sum of the spins. Harris repeats this experiment 500 times.
Question 1
Part A
Which equation can be solved to predict the number of times Harris will spin a sum less than 10?
A) 3/500 = x/15
B) 12/500 = x/15
C) 12/15 = x/500
D) 3/15 = x/500
QUESTION 2
Part B
How many times should Harris expect to spin a sum that is 10
or greater?
_______
Answer:
Step-by-step explanation:
Question 1
Part A:
To predict the number of times Harris will spin a sum less than 10, we need to find the probability of getting a sum less than 10 and multiply it by the total number of spins, which is 500.
The possible outcomes of the first spinner are 1, 2, and 3, and the possible outcomes of the second spinner are 4, 5, 6, 7, and 8. The minimum sum we can get is 1+4=5, and the maximum sum we can get is 3+8=11.
To get a sum less than 10, we can get:
1+4=5
1+5=6
1+6=7
1+7=8
1+8=9
2+4=6
2+5=7
2+6=8
2+7=9
3+4=7
3+5=8
3+6=9
There are 12 possible outcomes that result in a sum less than 10. So the probability of getting a sum less than 10 is 12/15, or 4/5.
To find the number of times Harris will spin a sum less than 10, we can use the equation:
probability of getting a sum less than 10 × total number of spins = x
So the equation that can be solved to predict the number of times Harris will spin a sum less than 10 is:
C) 12/15 = x/500
Part B:
To find the number of times Harris should expect to spin a sum that is 10 or greater, we can subtract the number of times he will spin a sum less than 10 from the total number of spins:
total number of spins - number of times he will spin a sum less than 10 = number of times he should expect to spin a sum that is 10 or greater
Substituting the values, we get:
500 - (12/15 × 500) = 500 - 400 = 100
So Harris should expect to spin a sum that is 10 or greater 100 times.
Proofs help ASAP…….$;$3$3
What is 11 1/2 minus 6 2/3
The answer is 4 5/6
Step-by-step explanation:
Let $a \equiv 1 \pmod{4}$. Find the value of $6a + 5 \pmod{4}$Express your answer as a residue between 0 and the modulus.
The value of [tex]$6a + 5 \pmod{4}$[/tex] is given by 3 or -1 (mod4) using the proper expression.
In mathematics, modular arithmetic is a method of integer arithmetic in which numbers "wrap around" after they reach a predetermined value known as the modulus. Carl Friedrich Gauss created the contemporary method to modular arithmetic in his 1801 work Disquisitiones Arithmeticae.
We have [tex]$a \equiv 1 \pmod{4}$[/tex]
to find the value of [tex]$6a + 5 \pmod{4}$[/tex]
putting the value of a≡1
6a + 5 (mod 4)
=(6*1 + 5) (mod 4)
=11 (mod4)
11/4=2R3 or 3R-1
= 3 or -1 (mod4)
A congruence relation is an equivalence relation that is consistent with addition, subtraction, and multiplication. Congruence modulo n is one such connection.
[tex]{\displaystyle a\equiv b{\pmod {n}}.}[/tex]
Display Style: A Equivalent B Modified N.
Because of the parenthesis, the full equation—rather than just the right-hand side—is covered by the (mod n) formula (here, b). This notation should not be confused with the modulo operation's notation, b mod n (without parenthesis).
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Solve the Linear Programming Problem.
Maximize z = 5x+5y
subject to 10x +6y ≥ 150
13x - 13y ≥ - 13
x + y ≤ 45
x ≥ 0
y ≥ 0
What is the maximum value of z? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. z = ___
B. There is no maximum value of z.
At what corner point(s) does the maximum value of z occur? Select the correct choice below and, if necessary, fill in the answer box to complete your choice
A. The maximum value of z occurs only at the point(s) ___
(Type an ordered pair. Use a comma to separate answers as needed.)
B. The maximum value of z occurs at the points ___
(Type an ordered pair. Use a comma to separate answers as needed.)
C. There is no maximum value of z.
Answer:
A. z = 225
B. The maximum value of z occurs at the points (22, 23) and (45, 0).
Step-by-step explanation:
To solve the linear programming problem using graphical methods, we need to graph the inequalities and find the feasible region. Then, we can identify the corner points of the feasible region and evaluate the objective function at each of these points to determine the maximum value of z.
Objective function: z = 5x + 5y
Constraints:
10x + 6y ≥ 15013x - 13y ≥ -13x + y ≤ 45x ≥ 0y ≥ 0Graph each of these inequalities by first plotting the corresponding boundary line, and then shading in the appropriate region.
Rearrange the first three inequalities to isolate y:
[tex]\boxed{\begin{aligned}10x +6y &\geq 150\\6y &\geq-10x+ 150\\y &\geq -\dfrac{5}{3}x+25\\\end{aligned}}[/tex] [tex]\boxed{\begin{aligned}13x - 13y &\geq - 13\\x -y &\geq -1\\ x +1 &\geq y\\ y &\leq x+1\end{aligned}}[/tex] [tex]\boxed{\begin{aligned}x + y &\leq 45\\y&\leq-x+45\\\phantom{w}\\\phantom{w}\end{aligned}}[/tex]
Graph the inequalities.
If the inequality sign is ≥, draw a solid line and shade above the line.If the inequality sign is ≤, draw a solid line and shade below the line.The feasible region is the region that is shaded by all of the inequalities.
Please see the attached graph.
A bounded feasible region may be enclosed in a circle and will have both a maximum value and a minimum value for the objective function. Therefore, as the feasible region for the given constraints is bounded, there is a maximum value of z.
The feasible region is bounded by the corner points:
(9, 10)(22, 23)(45, 0)(15, 0)
Evaluate the objective function z = 5x + 5y at each of these corner points:
Point (9, 10): z = 5(9) + 5(10) = 95
Point (22, 23): z = 5(22) + 5(23) =225
Point (45, 0): z = 5(45) + 5(0) = 225
Point (15, 0): z = 5(15) + 5(0) = 75
Therefore, the maximum value of z is 225, which occurs at the corner points (22, 23) and (45, 0).
Please indicate which is the best answer to complete the figure below.
Answer:
E
Step-by-step explanation:
Answer has to have a star, the object (star) needs to be on the right side, and the two colors cannot be the same as any of the rest in the set. So E?
solve for X
Five stars and like, I suck at geometry
The value of x is 30° as per below diagram.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
We know that,
All the angles in a triangle sum → 180°An isosceles triangle: two equal angles → two equal sides.Draw a line segment BG is with CBG equal to 20° on line CE.
So that, (40 + x) = 70, so that means x = 30°
Therefore, The value of x is 30°
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Triangle: According to the question the value of x is 30° as per below diagram.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
We know that,
All the angles in a triangle sum → 180°
An isosceles triangle: two equal angles → two equal sides.
Draw a line segment BG is with CBG equal to 20° on line CE.
So that, (40 + x) = 70, so that means x = 30°
Therefore, The value of x is 30°
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Complete question:
Using the Distributive Property as a good first step to solving the equation, you could simplify to get which of these choices?7(5x + 2) = -4(6 - 5x)35x + 14 = -24 - 20x35x + 14 = -24 + 20x5x + 14 = 6 + 20x35x + 2 = -24 - 5x35x + 2 = 24 - 20x
In equation 7(5x + 2) = -4(6 - 5x), Using the Distributive Property, we get 35x + 14 = -24 + 20x. So, the correct option is D).
To solve the equation 7(5x + 2) = -4(6 - 5x), a good first step is to use the Distributive Property to simplify both sides of the equation. Distributing the 7 and -4 on the left and right sides, respectively, we get
35x + 14 = -24 - 20x.
Next, we can combine like terms by adding 20x to both sides to get 55x + 14 = -24. Then, subtracting 14 from both sides, we get 55x = -38. Finally, we can solve for x by dividing both sides by 55, giving us x = -38/55. Therefore, the solution to the equation is x = -38/55.
The evaluation process involves performing arithmetic operations in a logical order to simplify the equation step-by-step until a solution is reached. So, the correct answer is D).
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Suppose the time it takes Jack to eat an apple is uniformly distributed between 5 and 11 minutes.
Let X = the time, in minutes, it takes Jack to eat an apple. Round answers to at least 4 decimal places.
a. What is the probability that it takes Jack more than 12 minutes to finish the next apple?
b. Enter an integer or decimal number [more.Js Jack less than 5.8 minutes to finish the next apple?
c. What is the probability that it takes Jack between 5.3 minutes and 6.5 minutes to finish the
next apple?
d. What is the probability that it takes Jack fewer than 5.3 minutes or more than 6.5 minutes to
finish the next apple?
The probability that it takes Jack between 5.3 minutes and 6.5 minutes to finish the next apple is 0.24.
What is the probability?a. Since Jack takes between 5 and 11 minutes to finish an apple, there is no way he can take more than 11 minutes to finish one. The probability that it takes Jack more than 12 minutes to finish the next apple is 0.
b. To find the probability that Jack takes less than 5.8 minutes to finish the next apple, we need to calculate the probability of X being less than or equal to 5.8.
Since X is uniformly distributed between 5 and 11, we can find this probability by calculating the proportion of the interval [5, 11] that is less than or equal to 5.8:
[tex]P(X < = 5.8) = (5.8 - 5) / (11 - 5) = 0.8[/tex]
the probability that Jack takes less than 5.8 minutes to finish the next apple is [tex]0.8[/tex] .
c. To find the probability that it takes Jack between 5.3 minutes and 6.5 minutes to finish the next apple, we need to calculate the proportion of the interval [5, 11] that falls within this range:
[tex]P(5.3 < = X < = 6.5) = (6.5 - 5.3) / (11 - 5) = 0.24[/tex]
d. To find the probability that it takes Jack fewer than 5.3 minutes or more than 6.5 minutes to finish the next apple. we can find the probability of the complement event, which is the probability that Jack takes between 5.3 minutes and 6.5 minutes to finish the apple:
[tex]P(X < 5.3 or X > 6.5) = 1 - P(5.3 < = X < = 6.5) = 1 - 0.24 = 0.76[/tex]
Therefore, the probability that it takes Jack fewer than 5.3 minutes or more than 6.5 minutes to finish the next apple is [tex]0.76[/tex] .
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In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.
What is the expected mean for a sample of 150 women?
What is the standard deviation of the mean for a sample of 150 women?
What is the probability of 150 women having a sample mean below 160 pounds?
What is the probability of 150 women having a sample mean above 175 pounds?
What is the probability of 200 women having a sample mean below 160 pounds? Notice the change in sample size.
What is the probability of 200 women having a sample mean above 175 pounds?
Answer:
Notice the change in sample size.
Answer:
1. The expected mean for a sample of 150 women is 168.5 pounds.
2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.
3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.
4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.
5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.
6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.
The solution is given below. Notice the change in sample size.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.
so. we get,
1. The expected mean for a sample of 150 women is 168.5 pounds.
2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.
3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.
4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.
5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.
6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.
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how many one-to-one functions are there from a set with five elements to sets with the following number of ele- ments? a) 4 b) 5 c) 6 d) 7
a) Number of one-to-one functions are equal to the zero, because n< m.
b) Number of one-to-one functions are equal to the ⁵P₅ = 120.
c) Number of one-to-one functions are equal to the ⁶P₅ = 720.
c) Number of one-to-one functions are equal to the ⁷P₅ = 2250.
One to one function is a special form of function that defined from one set to another and maps every element of the range to exactly one element of its domain unique output. As we know a set A has m elements and set B has n elements, then
Number of one-to-one functions from set A to Set B = P(n,m) or ⁿPₘ , n≥ m and number of one-to-one functions from set A to Set B = 0 , n< m.Now, we have a domain set with five elements, m = 5
a) Here, another set (co-domain) has 4 elements, n = 4. So, Number of one-to-one functions = 0 , n<m.
b) number of elements in another set,n= 5
So, Number of one-to-one functions = ⁵P₅ = 5!/(5 - 5 )! ( permutation formula)
= 5!/0! = 120
c) Number of elements in another set, n= 6
So, Number of one-to-one functions= ⁶P₅
= 6!/(6 - 5)!
= 6!/1! = 720
d) Number of elements in another set, n
= 7
So, Number of one-to-one functions
= ⁷P₅ = 7!(7 - 5)!
= 7!/2! = 2250
Hence, required value is 2250.
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13) Raymond and Kevin want to purchase a house. They offer $235,000 with 30% down payment. They are pre-qualified for a 30-year loan at 3.8%. Calculate their anticipated monthly payments.
Answer:
Step-by-step explanation:
The down payment is 30% of $235,000, which is $70,500. This means they are financing the remaining amount of $164,500.
Using the loan amount, interest rate, and loan term, we can calculate the monthly payment using the formula for a fixed-rate mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
where:
M = monthly payment
P = loan amount
i = monthly interest rate (annual rate divided by 12)
n = total number of payments (loan term in years multiplied by 12)
Plugging in the numbers, we get:
M = 164500 [ 0.038/12 (1 + 0.038/12)^360 ] / [ (1 + 0.038/12)^360 – 1]
Simplifying this expression, we get:
M = $765.84
Therefore, their anticipated monthly payments would be $765.84.
The table below shows the number of painted pebbles of Claire and Laura. If Greg chooses a pebble at random from the box 75 times, replacing the pebble each time, how many times should he expect to choose a yellow pebble??
A) 11
B) 33
C) 32
D) 22
The number οf times that Greg chοοses a yellοw pebble is 22 times.
Thus, option D is correct.
Finding the number οf chοices:Tο find the number οf pοssible chοices, calculate the number οf chances in the tοtal number οf οutcοmes.
Since we need tο find the number οf chοices that are expecting a yellοw pebble, find the tοtal number οf yellοw pebbles in the number οf pebbles in bοth Claire and Laura's cases and find the tοtal number οf yellοw pebbles.
Here we have
A table belοw shοws the number οf painted pebbles by Claire and Laura
Frοm the table,
Number οf pebbles that Laura painted = 8 yellοw, 7 green, 10 blue
Number οf pebbles that Claire painted = 14 yellοw, 5 green, 6 blue
Tοtal number οf yellοw pebbles = 8 + 14 = 22
Given that
Greg chοοses a pebble at randοm frοm the bοx 75 times, and each time replaces the pebble
Hence, the number οf time that Greg get yellοw pebble = number οf yellοw pebbles
Therefοre, The number οf times that Greg chοοses a yellοw pebble is 22 times.
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a plumber can do a job in 5 hours, and his apprentice can do the same job in 8 hours. What part of the job is left if they start the job and work together for 2 hours.
The total amount of charge in coulombs that has entered a wire at time is given by the expression Q = 6 t + 2 t^2, where t is in seconds and t greaterthanorequalto 0. Find an expression for the current in the wire at time t.
The rate at which electric charge flows through a circuit is used to quantify electrical current: I (t) equals dQ (t) / dt. The derivative of the electric charge by time yields the momentary current. I (t) is the amps of the transient current I at time t. (A).
The temporary electric charge, measured in coulombs, is Q(t) (C).
The time in seconds is t. (s).
I =ΔQ / Δt
ΔQ is the amount of electric current flowing at time Δt, measured in coulombs (C).
The time length in seconds is t. (s).
We know that I = dQ/dt by definition; thus, if Q = f(t), then I = f' (t). By stating this, we obtain the current's expression as follows:
I (t) = (d/dt) (Q(t)) = (d/dt) (6t + 2t2) = 6 + 4t: I(t) = 4t + 6; t >= 0
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