To know whether people can bargain the price down when purchasing a house at a 5% level of significance, we need to put a hypothesis test. The null hypothesis would be that people cannot bargain the price down
To determine whether 3-bedroom houses are cheaper than 4-bedroom houses, we would again give out a hypothesis test. The null hypothesis would be that there is no difference in price between 3-bedroom and 4-bedroom houses.
but the other hypothesis would be that 3-bedroom houses are cheaper than 4-bedroom houses. If the p-value is less than 0.05, we can reject the null hypothesis and say that 3-bedroom houses are more cheaper than 4-bedroom houses.
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Equations with x in the denominator
Can someone please explain to me, step by step, how to answer this question.
Answer:
x=5/6
Step-by-step explanation:
lcm=6x
6xX1/2x+6xX1/3x=6xX1 (divide through)
3x1+2x1=6xX1
3+2=6x
5=6x
5/6=6x/6 (divide through)
x=5/6
Hope it help
Given data on shoulder girth and height of a group of individuals. The mean shoulder girth is 107. 20 cm with a standard deviation of 10. 37 cm. The mean height is 171. 14 cm with a standard deviation of 9. 41 cm. The correlation between height and shoulder girth is 0. 67.
Write the equation of the regression line for predicting height
The equation of the regression line for predicting height based on shoulder girth is:y = 103.82 + 0.607x, which mean that for every one-unit increase in shoulder girth, the predicted height increase by 0.607 units.
Since the equation of the regression line for predicting height based on shoulder girth can be written as: y = a + bx, where y is the predicted height, x is the shoulder girth, a is the y-intercept, and b is the slope of the regression line.
To find the values of a and b, we need to use the following formulas:
b = r(Sy/Sx)
a = ybar - b(xbar), where r is the correlation coefficient between height and shoulder girth, Sy is the standard deviation of height, Sx is the standard deviation of shoulder girth, ybar is the mean height, and x bar is the mean shoulder girth. now substituting the values we get :
b = 0.67(9.41/10.37) ≈ 0.607
a = 171.14 - 0.607(107.20) ≈ 103.82
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Chose the domain for which each function is defined f(x)=x+4/x
The function f(x) = (x+4)/x is defined for all real numbers except x = 0, since division by zero is undefined. Therefore, the domain of the function is all real numbers except x = 0.
In interval notation, we can write the domain of the function as: (-∞, 0) U (0, ∞). This means that the function is defined for all values of x that are less than zero or greater than zero, but it is not defined at x = 0. The domain of a function is the set of all possible input values (also called independent variables) for which the function is defined. In other words, it is the set of values for which the function yields a valid output (also called dependent variable). In the case of the function f(x) = (x+4)/x, the domain is restricted by the fact that division by zero is undefined. Therefore, we cannot include x = 0 in the domain of the function. To find the domain of a function, we need to look for any values of the input variable that would make the function undefined or result in an error. These include situations such as division by zero, taking the square root of a negative number, or taking the logarithm of a non-positive number. In general, the domain of a function can be described using interval notation or set-builder notation, depending on the specific circumstances of the function. It is important to identify the domain.
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what is the value of the expression
3/5(X-8)-y
when x=15 and y=1/10
a 11/10
b 21/10
c 31/10
d 41/10
Answer:
The answer is to this question is D. 41/10
Consider the following experiment: Throw two fair dice sequentially and define a random variable X as the sum of the numbers of the two dice. Please compute the mean and standard deviation of 5x3+8. Mean of 5x3+8 is_1_ standard deviation of 5x3+8 is_2 Enter the correct answer below. (round down to 2 decimal places) 1 N
The mean of 5x3+8 is 23 and the standard deviation of 5x3+8 is 5.65, rounded down to 2 decimal places.
Consider the following experiment: Throw two fair dice sequentially and define a random variable X as the sum of the numbers of the two dice. We are to compute the mean and standard deviation of 5x3+8. Mean of 5x3+8 is 23 and standard deviation of 5x3+8 is 5.65. Thus, option 1 and option 2 are the correct answers.What is the expected value of a discrete random variable?In probability theory and statistics, the expected value of a random variable is the measure of the center of the probability distribution. It represents the long-run mean of occurrences, for example, the average value in a long sequence of trials.The standard deviation of a random variable is the measure of the spread or variability of a probability distribution, similar to variance. It is the square root of variance, denoted as σ.Here, the sum of the numbers of two dice follows a uniform distribution, where each event is equally likely, and the probability of each event is 1/36. Therefore, the random variable X is discrete with probability mass function:f(x) = 1/36, for x = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.Using this distribution, we can find the mean and standard deviation of the random variable X.Mean of 5x3+8=5(3)+8=23σ2=∑(x−μ)2P(X=x)where,μ = E(X) = ∑xf(x) = 7σ = √σ2=√ ∑(x−μ)2P(X=x)= √(2-7)2 (1/36)+ (3-7)2 (2/36)+ (4-7)2 (3/36)+ (5-7)2 (4/36)+ (6-7)2 (5/36)+ (7-7)2 (6/36)+ (8-7)2 (5/36)+ (9-7)2 (4/36)+ (10-7)2 (3/36)+ (11-7)2 (2/36)+ (12-7)2 (1/36)≈ 5.65Therefore, the mean of 5x3+8 is 23 and the standard deviation of 5x3+8 is 5.65, rounded down to 2 decimal places.
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One day, David hands out flyers to 7 people. The next day, each person copies the flyer and hands them out to 7 people. The following day, these people copy their flyer and hand them out to 7 people.
How many people now have flyers?
THE ANSWER IS 343
The total number of people with flyers after 3 days of copying and distributing them is 343, which can be calculated using the formula P = 7^n, where P is the total number of people with flyers and n is the number of times the flyers are copied and distributed.
The formula for this problem is P = 7^n where P is the total number of people with flyers and n is the number of times the flyers are copied and distributed.
In this problem, n = 3 as the flyers were distributed on three separate days.
Therefore, P = 7^3 = 343
The calculation can be shown as follows:
1st day: 7 people receive the flyer
2nd day: 7 x 7 = 49 people receive the flyer
3rd day: 49 x 7 = 343 people receive the flyer
Therefore, the total number of people with flyers after 3 days is 343.
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a) Work out the angle of elevation from R to T in the rectangle below. Give your answer to 1.d.p. b) Which angle fact tells you that the answer to part a) is also the angle of depression from T to R? 340cm 165cm
a) Note that the Angle of Elevation from R to T is 63.4°
b) The angle fact tells you that the answer to part a) is also the angle of depression from T to R is "the Alternate Angle Postulate"
What is the justification for the above response?
The principle used in below is SOH CAH TOA.
a) Tanθ = Opp/Adjacent
Tanθ = 340/165
Tanθ = 2.0606060606
θ = Tan⁻¹ 2.0606060606
θ = 63.4349
θ [tex]\approx[/tex] 63.4
b) The principle of alternate angles is a theorem in geometry that states that when a straight line intersects two other lines, the angles formed on opposite sides of the intersection and on opposite sides of the transversal are equal. This principle is based on the fact that parallel lines cut by a transversal create corresponding angles that are congruent.
Thus the angle fact tells you that the answer to part a) is also the angle of depression from T to R is "the Alternate Angle Postulate"
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Find the missing length of the triangle. 7.2 feet, 9.6 feet, and c
By using pythagorean theorem, the length of the missing side is 12 feet.
What is the Pythagorean theorem?
Pythagoras' theorem is a fundamental principle in geometry that relates to the three sides of a right-angled triangle. It states that:
"In a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides."
In mathematical terms, if a, b, and c are the lengths of the sides of a right-angled triangle, where c is the hypotenuse, then the theorem can be written as:
[tex]c^2 = a^2 + b^2[/tex]
We can use the Pythagorean theorem to determine the length of the missing side if we know that the given sides form a right triangle.
In this case, we have two sides of the triangle given: 7.2 feet and 9.6 feet. Let's assume that c is the length of the hypotenuse.
If the triangle is a right triangle, then we can use the Pythagorean theorem to solve for c:
[tex]c^2 = 7.2^2 + 9.6^2[/tex]
[tex]c^2 = 51.84 + 92.16[/tex]
[tex]c^2 = 144[/tex]
[tex]c = \sqrt{144}[/tex]
c = 12 feet
Therefore, if the triangle is a right triangle, then the length of the missing side is 12 feet.
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the height of a cylindrical pole is 12 feet and its circumference is 2 feet. a rope is attached to a point on the circumference at the bottom of the pole. the rope is then wrapped tightly around the pole four times before it reaches a point on the top directly above the starting point at the bottom. what is the minimum number of feet in the length of the rope? express your answer in simplest radical form.
The minimum number of feet in the length of the rope [tex]8\sqrt{(4\pi^2 + 36)}[/tex] feet.
To find the minimum number of feet in the length of the rope, we need to first calculate the height of the point on the circumference where the rope is attached. We can do this by using the formula for the circumference of a cylinder:
C = 2πr
where C is the circumference, r is the radius of the cylinder, and π is pi. Since we know that the circumference of the pole is 2 feet, we can solve for the radius:
2 = 2πr
r = 1/π
Next, we need to calculate the length of the rope that is wrapped around the pole. We know that the rope is wrapped around the pole four times, so the length of the rope is:
L = 4 × height of the pole
To find the height of the pole, we can use the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
where a is the radius of the pole, b is the height of the point where the rope is attached, and c is the length of the rope wrapped around the pole.
Solving for b, we get:
b = [tex]\sqrt{c^2 - a^2)}[/tex]
Substituting the values we know, we get:
b = [tex]\sqrt{((4\pi^2 + 12^2) - \pi^2)}[/tex]
b = [tex]\sqrt{sqrt(16\pi^2 + 144)}[/tex]
Finally, we can substitute this value into the formula for the length of the rope:
[tex]L = 4 * \sqrt{16\pi^2 + 144)}[/tex]
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A carpenter has a piece of plywood whose area is 20ft2. He cuts out a 0.75ft2 notch and a 3.25ft2 hole in the plywood.
What is the sum?
13.5
15.0
16.0
The tοtal area οf the plywοοd after cutting οut the nοtch and hοle is 16ft²
Define the term area?Area is the measure οf a regiοn's size οn a surface. The area οf a plane regiοn οr plane area refers tο the area οf a shape οr planar lamina, while surface area refers tο the area οf an οpen surface οr the bοundary οf a three-dimensiοnal οbject.
Area can be understοοd as the amοunt οf material with a given thickness that wοuld be necessary tο fashiοn a mοdel οf the shape, οr the amοunt οf paint necessary tο cοver the surface with a single cοat
Area is a measure οf the amοunt οf space inside a 2-dimensiοnal shape οr regiοn, typically expressed in square units such as square inches, square feet, οr square meters.
Tο find the tοtal area οf the plywοοd after cutting οut the nοtch and hοle, we need tο subtract their areas frοm the οriginal area:
Tοtal area = 20ft² - 0.75ft² + 3.25ft²
Tοtal area = 16ft²
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Find the missing length A=50 b=50
The value of sides a and b from the triangle. A = 50 degrees, B = 50 degrees, c = 12 meters is 9.341 metres and angle C is 80 dgree.
How can the angles and the sides be determined?From the Law of Sines states that the follow proportions must be true which is
sin (A)/a = sin (B)/b= sin (C)/c
Where A = 50 degrees
B = 50 degrees
c = 12 meters
Angle C = (180-100=80 ( angle in the triangle is 180 degree)
sin (50)/a = sin (50)/b= sin (80)/12
0.766/a = 0.766/b= 0.985/12
0.766/a = 0.766/b=0.082
0.766/a =0.082
a =0.766/0.082 = 9.341
0.766/b=0.082
b=0.766/0.082= 9.341
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complete questions
Solve the given triangle. A = 50 degrees, B = 50 degrees, c = 12 meters
Round your answers to the nearest integer.
C = ? degrees
b = ? meters
c = ? meters
8lb= __ oz? what is 8lb equal to in oz?
i. How does a person's cycling rate show up in his or her equation?
A person's cycling rate can be expressed mathematically in the equation that describes their cycling motion. Specifically, the cycling rate can be represented by the frequency or number of revolutions per unit time (usually in seconds) that the person completes while cycling.
The equation that describes a person's cycling motion is typically a kinematic equation that relates the person's position, velocity, and acceleration as a function of time. One commonly used equation is:
d = vit + 1/2at^2
where d is the distance traveled by the person, vi is the initial velocity (usually zero), a is the acceleration, and t is the time elapsed.
The cycling rate can be incorporated into this equation by expressing the velocity as a function of the frequency of revolutions (f) and the radius of the wheel (r). This gives:
v = 2πrf
where v is the velocity of the cyclist, r is the radius of the wheel, and π is the mathematical constant pi (approximately 3.14).
Substituting this expression for v into the kinematic equation gives:
d = (2πrf)t + 1/2at^2
This equation shows how the person's cycling rate, represented by the frequency f, affects their distance traveled as a function of time. If the person increases their cycling rate, their velocity increases, and they will travel a greater distance in the same amount of time.
Determine the quadrants in which the points are located: A=(2,-3) B=(-4,1) A is in quadrant IV and B is in quadrant II. A is in quadrant II and B is in quadrant IV. A is in quadrant I and B is in quadrant IV. A is in quadrant IV and B is in quadrant I.
The quadrants in which the points A = (2,-3) B = (-4,1) as required to be determined are fourth and second quadrant respectively.
What quadrants are the given points located?As evident from the task content; the quadrant in which the given points are located are to be determined.
On the Cartesian plane; given a pair of coordinates (x, y).
In the first quadrant; x is positive and y is positive.
In the second quadrant; x is negative and y is positive.
In the third quadrant; x is negative and y is negative.
In the fourth quadrant; x is positive and y is negative.
Ultimately, the point A = (2, -3) is located in the fourth quadrant and the point B = (-4, 1) is located in the second quadrant.
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2.4 m × 0.7 m Find the length volume = 1.512 meters³
The length of the rectangular prism with a volume of 1.512 m³ is equal to 0.9 meters.
How to calculate the volume of a rectangular prism?Mathematically, the volume of a rectangular prism can be calculated by using this formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given parameters into the formula for the volume of a rectangular prism, we have;
Volume of a rectangular prism = L × W × H
1.512 = L × 2.4 × 0.7
Length, L = 1.512/1.68
Length, L = 0.9 meters.
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Complete Question:
Find the length of the rectangular prism shown below with a volume of 1.512 m³, a width of 2.4 m and a height of 0.7 m.
what is the surface area of prism. base=5. height=2. length=3
Answer:
62
Step-by-step explanation:
Surface area of a prism = S = 2(lw + lh + wh)
where l = length
w = width
h = height
Given l = 3, w = 5 and h = 2
S = 2(3 x 5 + 3 x 2 + 5 x 2)
= 2(15 + 6 + 10)
= 2(31)
= 62
I need help working this out, I only need help with question a.
Answer:
-3, -1 and 1
Step-by-step explanation:
substitute what ever the x column says into 2x-3
2×0-3=-3
2×1-3=-1
2×2-3=1
the answers: -3, -1, 1
In Cape Town there is a shortage of water and so water is getting more expensive. Water from the tap costs a flat rate of 15 plus per liter. Water from the store costs 3 per liter. At what number of liters would the cost from the store and the cost from the tap be the same ?
The cost of water from the store and the cost from the tap will be the same when the number of liters
reaches 7.5 liters.
Let's assume that the cost of buying 'x' liters of water from the store is the same as the cost of buying 'x' liters of water from the tap.
For water from the store, the cost per liter is 3, so the cost of buying 'x' liters of water from the store would be 3x.
For water from the tap, there is a flat rate of 15 plus per liter. So, the cost of buying 'x' liters of water from the tap would be 15 + x.
Now we can set up an equation to find the value of 'x' when the costs are equal:
3x = 15 + x
Simplifying this equation, we get:
2x = 15
x = 7.5
Therefore, the cost from the store and the cost from the tap would be the same at 7.5 liters.
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a fair ordinary dice is thrown once
select the probability a 4 or a 5
A/1/6 B/2/6 C 4/6 D/5/6
What function does this graph represent?
We can conclude after answering the provided question that If the data expression points are arranged in a curve, the function could be a quadratic, exponential, or other non-linear equation.
what is expression ?In mathematics, an expression is a grouping of representations, digits, and huge corporations that resemble a clear relationship or regimen. An expression can be a real number, a transitory, or a combination of the two. Addition, subtraction, pervasiveness, division, and exponentiation are examples of mathematical operators. Expressions are common in arithmetic, mathematics, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.
This graph appears to be a scatter plot of data points based on the visual representation you provided. The values of an independent variable are represented by the horizontal axis (x-axis), while the values of a dependent variable are represented by the vertical axis (y-axis).
Without any additional information, determining the specific function represented by this graph is difficult. The shape and pattern of the scatter plot, on the other hand, can provide some insight into the relationship between the two variables. If the data points are arranged in a linear pattern, for example, the function could be a linear equation. If the data points are arranged in a curve, the function could be a quadratic, exponential, or other non-linear equation.
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Using Unit Rates to compare Ratios continued
5 Branden and Pete each play running back. Branden carries the ball 75 times for
550 yards, and Pete has 42 carries for 380 yards. Who runs farther per carry?
Pete did more his outcome was 9. 0 which was bigger the branden do
380 divided by 42 for your answer
Pete runs farther per carry, with a unit rate of 9.05 yards per carry compared to Branden's unit rate of 7.33 yards per carry.
A unit rate is a rate that has a denominator of 1. It is a ratio that compares a quantity to its unit of measurement.
To determine who runs farther per carry, we can use unit rates to compare the distance each player runs per carry.
For Branden:
Distance per carry is
= 550 yards ÷ 75 carries
Divide the numbers
= 7.33 yards per carry
For Pete:
Distance per carry is
= 380 yards ÷ 42 carries
Divide the numbers
= 9.05 yards per carry
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(09.01 LC)
The circle shown below has AB and BC as its tangents:
AB and BC are two tangents to a circle which intersect outside the circle at a point B.
If the measure of arc AC is 140°, what is the measure of angle ABC? (1 point)
The measure of angle ABC is: 20°
How to find the measure of the angle in the circle?Consider quadrilateral ABCO. The sum of all of the measures of all interior angles in the quadrilateral ABCO is equal to 360°.
The Lines given as BA and BC are seen to be tangent to the circle, and then this means that the radii OC and OA are perpendicular to the tangent lines BC and BA. Therefore,
m∠BCO=90°;
m∠BAO=90°.
The measure of the angle AOC is 160° (because the measure of arc AC is 140°). So,
m∠ABC + m∠BCO + m∠BAO + m∠AOC = 360°,
m∠ABC = 360° - (m∠BCO + m∠BAO + m∠AOC)
= 360° - (90° + 90° + 160°)
= 20°
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Weights of adult males.
The weights of adult individuals in a certain country are normally distributed with a population mean of μ=172 pounds and a population standard deviation of σ=29 pounds. Suppose n=36 individuals are sampled.
1)
What is the mean of the sampling distribution of the means?
The sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.
In the context of sampling distribution of the means, the standard deviation represents the degree of spread or variation of sample means around the true population mean.
To compute the standard deviation of the sampling distribution of the means, one typically divides the population standard deviation by the square root of the sample size.
Therefore, the standard deviation of the sampling distribution of the means is 29/√36 = 29/6 = 4.83 pounds.
So, the sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.
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Put the function y=-8x(x+6) in factored form f(x)=
a(x-r)(x-s) and state the values of a,r, and s. Assume
r_
The factored form of the function y = -8x(x + 6) is f(x) = -8(x + 3)(x - 3). The values of a, r, and s are -8, -3, and 3, respectively.
To put the function y = -8x(x + 6) in factored form f(x) = a(x - r)(x - s), the values of a, r, and s have to be identified. The step-by-step explanation is given below.Step 1: The given function is y = -8x(x + 6).Step 2: To write it in the factored form f(x) = a(x - r)(x - s), let us first multiply -8 by 6, which gives -48.Step 3: We now have y = -8x(x + 6) = -8x² - 48x.Step 4: Rearranging it, we get y = -8x² - 48x.Step 5: Factoring out -8 from both the terms, we get y = -8(x² + 6x).Step 6: Next, add (6/2)² = 9 to both the sides to make the expression a perfect square. y + 72 = -8(x² + 6x + 9).Step 7: The right side of the equation is now a perfect square. It can be written as y + 72 = -8(x + 3)². (x + 3)² = x² + 6x + 9Step 8: Simplifying, we get y = -8(x + 3)² - 72.Step 9: The function y in factored form is f(x) = -8(x + 3)² - 72. Here, a = -8 and r = -3. Since the function is in the form f(x) = a(x - r)(x - s), we can find s by dividing -72 by -8 and adding r to the quotient. That is, s = (-72/-8) - 3 = 6 - 3 = 3. Therefore, the factored form of the function y = -8x(x + 6) is f(x) = -8(x + 3)(x - 3). The values of a, r, and s are -8, -3, and 3, respectively.
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6. andrew is flipping over the cards in a standard 52-card deck. he continues until he has revealed an ace. what is the probability that no face card has been revealed? what is the expected number of face cards he has revealed?
The probability that no face card has been revealed is 1/3.
The expected number of face cards he has revealed is 12.
Probability is the branch of mathematics that deals with uncertainty. When a fair die is rolled, there are 6 possible outcomes. A deck of 52 cards has 13 ranks of four suits each. These suits are spades, clubs, hearts, and diamonds. A standard deck of cards contains 26 red cards and 26 black cards.
There are four aces in a deck of 52 cards. The probability of obtaining an ace on the first attempt is
4/52 ⇒ 1/13 ⇒ 0.0769.
The probability of not getting an ace on the first try is
48/52 ⇒ 12/13 ⇒ 0.9231.
The second attempt at drawing an ace is conditional on the first attempt.
If the first attempt results in not getting an ace, the probability of getting an ace on the second attempt are 4/51.
If the first attempt is unsuccessful, the probability of not getting an ace on the second attempt is 47/51.
The probability of getting an ace on the third attempt, after the first two attempts have failed, is 4/50.
The probability of not getting an ace on the third attempt is 46/50. And so on...
The probability of not revealing any face card is 16/48 = 1/3 because there are 16 non-face cards in the deck.
The expected number of face cards he has revealed is 12, and the expected number of non-face cards he has revealed is 40.
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Solve the equation by factoring:
9y^2 - 49=0
Answer:
Step-by-step explanation:
do it yourself
select all statements that are true. assume that is smooth function in a neighborhood around and that all the difference points are contained in that neighborhood. and are the forward and backward finite differences, respectively.
There are several statements that are true when it comes to a smooth function in a neighborhood around a point and the forward and backward finite differences.
The true statements are:
1) The forward finite difference is the difference between the function value at a point and the function value at the next point.
2) The backward finite difference is the difference between the function value at a point and the function value at the previous point.
3) The forward and backward finite differences can be used to approximate the derivative of a function at a point.
4) The forward and backward finite differences are both equal to the slope of the tangent line to the function at the point.
5) The forward and backward finite differences are both equal to the derivative of the function at the point.
Therefore, the true statements are "The forward finite difference is the difference between the function value at a point and the function value at the next point.", "The backward finite difference is the difference between the function value at a point and the function value at the previous point.",
"The forward and backward finite differences can be used to approximate the derivative of a function at a point.", "The forward and backward finite differences are both equal to the slope of the tangent line to the function at the point.", and "The forward and backward finite differences are both equal to the derivative of the function at the point."
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If a1=5 and an=an-1-4 then find the value of a5
A5 has a value of -11. This can also be confirmed by looking at the words in order: 5, 1, -3, -7, and -11.
Using the given formula, we can find the value of the nth term by recursively applying the formula, starting from the first term:
a1 = 5
a2 = a1 - 4 = 1
a3 = a2 - 4 = -3
a4 = a3 - 4 = -7
a5 = a4 - 4 = -11
Therefore, the value of a5 is -11. We can also verify this by checking the sequence of terms: 5, 1, -3, -7, -11.
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An account with an initial balance of $3500 earns interest that is compounded annually. If no other deposits or withdrawals are made, the account will have a balance of $4390.40 after 2 years. Find the annual interest rate.
Therefore, the annual interest rate is approximately 12%.
What factors determine interest rates?How to compute interest is as follows: P x R x T is the formula for calculating interest. Principal Amount is P. (the beginning balance). rates of interest (usually per year, expressed as a decimal). T stands for the value T. (generally one-year time periods).
Let r be the annual interest rate as a decimal. Then the balance after 2 years is given by:
Balance = 3500(1+r)²
Setting this equal to $4390.40 and solving for r, we have:
4390.40 = 3500(1+r)²
Dividing both sides by 3500 and taking the square root, we get:
(1+r)² = 4390.40/3500 = 1.2544
Taking the square root of both sides, we get:
1 + r = √(1.2544) ≈ 1.12
Subtracting 1 from both sides, we get:
r ≈ 0.12 or 12%
Therefore, the annual interest rate is approximately 12%.
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We have seen in lectures how the binomial distribution with n large p small can be approximated by a Poisson distribution with λ=np. We have also seen that a binomial ( n large and p not too small) can be approximated by a normal distribution. This suggests that a Poisson distribution may be able to be approximated by a normal distribution, provided λ is large enough. (a) Consider a Poisson random variable with λ=10. What is probability of at least 9 events? You can use the ppois function in R to calculate this probability. (b) Approximate the answer using a normal approximation to the Poisson. Do remember to apply the continuity correction.
P(Z > -0.475) ≈ 0.68
(a) The probability of having at least 9 events can be calculated as follows:ppois(8, 10, lower.tail = FALSE)This gives the probability of having less than or equal to 8 events, so we subtract it from 1 to get the probability of having at least 9 events. Hence, the probability of having at least 9 events is:1 - ppois(8, 10, lower.tail = FALSE) = 0.3446(b) For a Poisson distribution with λ=10, the mean is μ=10 and the variance is σ²=10. Hence, the standard deviation is σ=√10 ≈ 3.162.To approximate this using a normal distribution, we need to standardize the Poisson random variable. That is,(X-μ)/σ ~ N(0,1)where X is a Poisson random variable with λ=10. We want to find P(X ≥ 9), which can be written as P(X > 8.5) using the continuity correction. Hence,P(X > 8.5) = P(Z > (8.5-10)/3.162) = P(Z > -0.475)Using a standard normal table or calculator, we find that P(Z > -0.475) ≈ 0.68. Therefore, the approximate probability of having at least 9 events is 0.68.
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