Answer:
200 lbs.
Step-by-step explanation:
Divide mass value by 16 to convert oz to lbs.
3,200/16=200
the figure below shows the change of a population over time. which statement best describes the mode of selection depicted in the figure?
The statement that best describes the mode of selection depicted in the figure is (b) Directional Selection, changing the average color of population over time.
The Directional selection is a type of natural selection that occurs when individuals with a certain trait or phenotype are more likely to survive and reproduce than individuals with other traits or phenotypes.
In the directional selection of evolution, the mean shifts that means average shifts to one extreme and supports one trait and leads to eventually removal of the other trait.
In this case, one end of the extreme-phenotypes which means that the dark-brown rats are being selected for. So, over the time, the average color of the rat population will change.
Therefore, the correct option is (b).
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The given question is incomplete, the complete question is
The figure below shows the change of a population over time. which statement best describes the mode of selection depicted in the figure?
(a) Disruptive Official, favoring the average individual
(b) Directional Selection, changing the average color of population over time
(c) Directional selection, favoring the average individual
(d) Stabilizing Selection, changing the average color of population over time
for a given sample size, when we increase the probability of a type i error, the probability of a type ii error
Increasing the probability of a type I error generally leads to a decrease in the probability of a type II error, and vice versa.
What is type 1 and type II error?If your data have statistical significance, this suggests that even if the null hypothesis is correct, they are extremely improbable to occur. You would then reject your null hypothesis in this situation. Yet occasionally, this may be a Type I mistake.
If your results are not statistically significant, the null hypothesis is likely to be correct and they have a high probability of occurring. As a result, your null hypothesis is not rejected. Yet occasionally, this may be a Type II mistake.
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Find the mean of 8,2,2 graphically.
The mean of the numbers 8, 2 and 2 when solved graphically is 4
How to determine the mean of numbersThe numbers in the dataset are given as
8, 2 and 2
The mean is also known as the average and is calculated by adding up all the values in a dataset and then dividing the sum by the total number of values.
To find the mean of 8, 2, and 2 graphically, we can use a number line.
First, we mark the three numbers on the number line:Next, we find the midpoint of the three numbers on the number line, which represents the mean:The midpoint between 2 and 8 is 5, and the midpoint between 2 and 2 is also 2.
Therefore, the mean of 8, 2, and 2 is the average of the midpoints
Mean = (8 + 2 + 2)/3
Mean = 4
Hence, the mean is 4
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Please see attached picture.
Need help answering.
In the given graph, the x-intercepts are (2,0) and (6,0).
The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.
The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).
The sign of the leading coefficient is positive, since it is 1/2.
To find the equation of the quadratic function, we start by using the vertex form:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the vertex. Plugging in the given vertex (4,-2), we get:
[tex]y = a(x - 4)^2 - 2[/tex]
Next, we use the other two points to find two additional equations:
[tex]6 = a(8 - 4)^2 - 2 (plugging in (8,6))\\0 = a(2 - 4)^2 - 2 (plugging in (2,0))[/tex]
Simplifying these equations, we get:
[tex]6 = 16a - 2\\8a = 4 -- > a = 1/2 \\0 = 4a - 2 \\4a = 2 -- > a = 1/2 \\[/tex]
So the equation of the quadratic function is:
[tex]y = (1/2)(x - 4)^2 - 2[/tex]
Now, we can answer the questions:
The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0 in the equation:
[tex]y = (1/2)(0 - 4)^2 - 2 = 6[/tex]
So the y-intercept is (0,6).
To find the x-intercepts, we set y = 0 in the equation:
[tex]0 = (1/2)(x - 4)^2 - 2[/tex]
Simplifying, we get:
[tex](x - 4)^2 = 4\\ - 4 = \pm 2 \\= 2, 6[/tex]
So the x-intercepts are (2,0) and (6,0).
The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.
The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).
The sign of the leading coefficient is positive, since it is 1/2.
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Jacobil and her friends are making a large homemade circular pizza. Jacobi cut her piece of pizza and it formed a sector with a radius of 9 Inches and a central angle measuring 75°. If the other 5 friends
equally share the remaining portion of the pizza, what is the approximate area of pizza each person receives? Use 3.14 for and round your answer to the nearest hundredth.
Jacobi get area of pizza is 52.987 in²
5 friends getting equally share each one area of pizza is 40.27 in²
Area of sectorAny point in a plane that is a certain distance away from another point forms a circle. The fixed point is known as the center of the circle and the fixed distance is known as the radius of the circle.
The formula for calculating a circle's sector's area is (∅/360°) ×π×r²
Jacobi get area of pizza =(75/360°) × π×9²=52.987in²
5 friends getting pizza with each central angle measuring=360°-75°/5
=57°
5 friends getting each one area of pizza = (57/360°) × π×9²
40.27in².
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Which is not a good way to protect yourself from fraud? O A. Keeping your personal information private B. Shredding or locking up your important documents OC. Using encrypted websites when entering bank account information D. Sharing your passwords with others
Question is on the picture
By answering the presented question, we may conclude that She spends equation 40% of her time at work and 15% of her time on other hobbies. She spends 20% of her time napping.
What is equation?In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion [tex]"2x + 3 = 9"[/tex] states that the word [tex]"2x + 3"[/tex] Corresponds to the number "9".
The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components.
For example, in the equations [tex]"x2 + 2x - 3 = 0[/tex] ," the variable x is lifted to the powercell. Lines are utilized in many areas of mathematics, include algebra, arithmetic, and geometry.
Abby, according to the picture, spent:
She spends 25% of her time in school.
She spends 40% of her time at work and 15% of her time on other hobbies.
Therefore, Furthermore, she spends [tex]20[/tex] of her time napping.
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find the probability of not spinning red on either spin. (not red on the first spin and not red on the second spin.)
The probability of not spinning red on either spin (not red on the first spin and not red on the second spin) is 1/12
The probability of an event is a number that indicates how likely the event is to do. It's expressed as a number in the range from 0 and 1, or, using chance memorandum, in the range from 0 to 100. The more likely it's that the event will do, the advanced its probability. The probability of an insolvable event is 0; that of an event that's certain to do is 1.
It is know to us that Probability (Red) = 3/6 = 1/2
also Probability (Blue) = 2/6 = 1/3
and Probability (CYAN) = 1/6, therefore,
a) Probability ( CYAN then red) = 1/6 x 1/2 = 1/12
b) Probability ( CYAN then Blue) = 1/6 x 1/3 = 1/18
c) Probability ( no Cyan on 2 spins) = (1/2+1/3) x (1/2+1/3) = 5/6 x 5/6 = 25/36
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Complete question:
The spinner below is spun twice. If the spinner lands on a border, that spin does not count and spin again. It is equally likely that the spinner will land in each of the six sectors.
REDREDREDBLUEBLUECYAN
For each question below, enter your response as a reduced fraction.
a) Find the probability of spinning cyan on the first spin and red on the second spin.
b) Find the probability of spinning cyan on the first spin and blue on the second spin.
c) Find the probability of NOT spinning cyan on either spin. (Not cyan on the first spin and not cyan on the second spin.)
PLS HELP FAST + BRAINLIEST!!
When a tuba is played, the player makes a buzzing sound and blows into one end of a tube that has an effective length of 3.50 m. The other end of the tube is open. If the speed of sound in air is 343 m/s, what is the lowest frequency the tuba can produce?Please show all work and formulas to receive credit for best answer
The lowest frequency the tuba can produce is approximately 49 Hz.
The lowest frequency produced by the tuba is called its fundamental frequency, which corresponds to the longest wavelength that can fit in the tube. The wavelength of a sound wave is related to its frequency and the speed of sound by the equation
wavelength = speed of sound / frequency
In this case, the effective length of the tube is equal to half of the wavelength of the fundamental frequency (because the tube is open at one end and closed at the other), so we can write
wavelength = 2 × effective length = 7.00 m
Solving for the frequency using the above equation, we get
frequency = speed of sound / wavelength = 343 m/s / 7.00 m ≈ 49 Hz
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One 12 ounce can of soda has 150 calories. If Josiah drinks the big 24 ounce size from the local mini-mart, how many calories does he get?
Answer:
Step-by-step explanation:
12 ounces = 150 calories, so
12 x 2 ounces = 150 x 2 calories,
24 ounces = 300 calories
5) A research study gives a 95% confidence interval for the proportion of subjects helped by a new anti- inflammatory drug is (0.56, 0.65). (a) Interpret this interval in the context of the problem. dolo hoone (b) What is the TRUE meaning of "95%" confidence interval as stated in the problem?
(a) This 95% confidence interval indicates that there is a 95% chance that between 56% and 65% of subjects will be helped by the new anti-inflammatory drug.
(b) There is a 95% confidence level that the percentage of participants who benefit from a new anti-inflammatory medication falls between (0.56, 0.65).
(a) According to this 95% confidence interval, there is a 95% likelihood that the new anti-inflammatory medication will be beneficial to between 56% and 65% of participants.
(b) There is a 95% confidence interval for the percentage of subjects who were benefitted by a new anti-inflammatory medicine (0.56, 0.65).
The percentage of participants who contributed to the development of a new anti-inflammatory medicine has a 5% probability of falling outside the range above.
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In the year 1985, a house was valued at $108,000. By the year 2005, the value had appreciated to $148,000. What was the annual growth rate percentage between 1985 and 2005? Assume that the value continued
to grow by the same percentage. What was the value of the house in the year 2010?
Answer:
To find the annual growth rate percentage, we can use the formula:
annual growth rate = [(final value / initial value)^(1/number of years)] - 1
where "final value" is the value in the ending year, "initial value" is the value in the starting year, and "number of years" is the total number of years between the starting and ending years.
Using the given values, we have:
annual growth rate = [(148,000 / 108,000)^(1/20)] - 1
= 0.0226 or 2.26%
So the house appreciated at an annual growth rate of 2.26%.
To find the value of the house in 2010, we can use the same growth rate to project the value from 2005 to 2010:
value in 2010 = 148,000 * (1 + 0.0226)^5
= $175,465.11 (rounded to the nearest cent)
Therefore, the value of the house in the year 2010 was $175,465.11.
Graph the equation y = 3/2x -2
Graph these twο pοints (0, -2) & (4/3, 0) and yοu have yοur slοpe graphed fοr the equatiοn y = 3/2x -2.
What is an equatiοn?
An equatiοn is a mathematical statement containing two algebraic expressiοns flanked by equal signs (=) on either side.
It shows that the relationship between the left and right printed expressiοns is equal.
All fοrmulas have LHS = RHS (left side = right side).
Yοu can sοlve equatiοns tο determine the values οf unknοwn variables that represent unknοwn quantities.
If a statement does not have an equals sign, it is not an equatiοn. A mathematical statement called an equatiοn cοntains the symbοl "equal tο" between twο expressiοns οf equal value.
Tο find the x-intercept, substitute y = 0 and sοlve fοr x. Tο find the y-intercept, substitute x = 0 and sοlve fοr y.
y = 3/2(0) -2
y = -2
⇒ (0, -2)
And for x
0 = 3/2x -2
2 = 3/2x
x = 4/3
(4/3, 0)
Now graph these two points and you have your slope graphed
Hence, The graph of the equation is given below.
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If A B C are three matric such that AB=AC such that A=C then A is
Answer:
invertible
Step-by-step explanation:
If A is invertible then ∣A∣ =0
Pls help There is a 20% chance that a customer walking into a store will make a purchase. A computer was used to generate 5 sets of random numbers from 0 to 9, where the numbers 0 and 1 represent a customer who walks in and makes a purchase.
A two column table with title Customer Purchases is shown. The first column is labeled Trial and the second column is labeled Numbers Generated.
What is the experimental probability that at least one of the first three customers that walks into the store will make a purchase?
A) 60%
B) 13%
C) 40%
D) 22%
The experimental probability that at least one of the first three customers that walks into the store will make a purchase is 60%.
What is experimental probability?It is determined by counting the number of times an event occurs in a given experiment and dividing the total number of trials by the number of successful outcomes.
The experimental probability that at least one of the first three customers that walks into the store will make a purchase is calculated by dividing the total number of customers who make a purchase by the total number of customers who enter the store.
In this case, there are 3 trials and 2 customers who make a purchase.
The experimental probability is 3 by 5 which is the total number of trials.
Thus, the experimental probability
=3/5
= 60%.
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1) Pendant la période des soldes, tous les manteaux d'un magasin sont soldés à 15%.
a. Marjorie a repéré un manteau qui coûtait initialement 78€.
Quel est son prix après réduction ?
b. Mélanie veut acheter un manteau dont le prix après réduction est de 55,25€.
Quel était son prix initial ?
2) Manu affirme que sur les étiquettes suivantes, le pourcentage de réduction appliqué au prix
de la montre est supérieur à celui appliqué aux lunettes. A-t-il raison ?
45€→ 35,55€
Réduction
de 20%
Answer: Zemāk
Step-by-step explanation:
1)
a. Le prix du manteau après la réduction de 15% est:
78€ - (15/100)*78€ = 66,30€
Le prix du manteau après la réduction est de 66,30€.
b. Soit x le prix initial du manteau.
Le prix du manteau après la réduction de 15% est:
x - (15/100)*x = 55,25€
Simplifions cette équation:
0,85x = 55,25€
x = 65€
Le prix initial du manteau était de 65€.
2)
Pour les lunettes, le prix initial est de 45€ et la réduction appliquée est de 20%:
45€ - (20/100)*45€ = 36€
Pour la montre, le prix initial est de 35,55€ et la réduction appliquée est également de 20%:
35,55€ - (20/100)*35,55€ = 28,44€
On constate que le pourcentage de réduction est le même pour les deux articles, donc Manu a tort.
How does f(t) = 7 change over the interval from t = -4 to t = -3?
f(t) decreases by 7
f(t) increases by 600%
f(t) decreases by 7%
f(t) increases by 700%
Answer:
None of the options provided in the question accurately describe the behavior of f(t) = 7 over the interval from t = -4 to t = -3.
Step-by-step explanation:
he function f(t) = 7 is a constant function that does not depend on the value of t. Therefore, f(t) = 7 remains the same over the interval from t = -4 to t = -3. In other words, there is no change in the value of f(t) over this interval.
Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long would you have to wait for 1/7 of it to disappear?
You would have to wait ___ years for 1/7 of the radium to disappear.
Accοrding tο the half-life fοrmula, we wοuld have tο wait apprοximately 4975 years fοr 1/7 οf the radium tο decay.
What is Expοnential Decay ?Expοnential decay is a mathematical prοcess in which a quantity decreases οver time in a manner prοpοrtiοnal tο its current value. This means that the rate οf decay is prοpοrtiοnal tο the amοunt οf the substance remaining, and as the amοunt οf the substance decreases, the rate οf decay alsο decreases. The fοrmula fοr expοnential decay is οften written as:
N(t) = N₀ *[tex]e^{(-kt)[/tex]
where N(t) is the amοunt οf substance remaining at time t, N₀ is the initial amοunt οf the substance, k is the decay cοnstant, and e is the base οf the natural lοgarithm.
The half-life οf radium is apprοximately 1590 years, which means that after 1590 years, half οf the οriginal radium will have decayed. Therefοre, we can use the half-life fοrmula tο find the amοunt οf time it wοuld take fοr 1/7 οf the radium tο decay:
N = N₀[tex]* (1/2)^{(t/t1/2)[/tex]
where N is the final amοunt (1/7 οf the οriginal amοunt), N0 is the initial amοunt, t is the time elapsed, and t1/2 is the half-life.
We can rearrange this fοrmula tο sοlve fοr t:
t = t1/2 * lοg2(N₀/N)
t = 1590 years * lοg2(7)
t ≈ 4975 years
Therefοre, we wοuld have tο wait apprοximately 4975 years fοr 1/7 οf the radium tο decay.
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The measure of HI based on the given diagram is 70 units.
What is a triangle mid segment?A triangle mid segment is the line joining the midpoint of any two sides of the triangle which is parallel to the third side and is also half of the length of the third side.
HI = 3x + 5
EF = -3x + 55
So,
HI = 1/2(EF)
3x + 5 = 1/2(-3x + 55)
3x + 5 = (-3x + 55) / 2
cross product
2(3x + 5) = -3x + 55
open parenthesis
6x + 10 = - 3x + 55
6x + 3x = 55 - 10
9x = 45
divide both sides by 9
x = 45/9
x = 5
Therefore, the measure of HI and EF are;
HI = 3x + 5
= 3(5) + 55
= 15 + 55
= 70
EF = -3x + 55
= -3(5) + 55
= -15 + 55
= 40
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The triangle shown has an area of 46 square centimeters. Find the measure of the base (segment AB ). Triangle A B C. A line goes from point C to point D on side A B. Side A C is 11 centimeters, C B is 9 centimeters, and A B is question mark.
By answering the presented question, we may conclude that Therefore, triangle the length of the base AB is approximately 20.88 centimeters.
What precisely is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
the length of the base AB,
Area = (1/2) * base * height
[tex]CB^2 = CD^2 + BD^2\\9^2 = x^2 + (AB - x)^2\\81 = x^2 + (AB^2 - 2ABx + x^2)\\AB^2 - 2ABx + 2x^2 = 81\\[/tex]
We also know that the area of the triangle is:
[tex]46 = (1/2) * AB * CB\\46 = (1/2) * AB * \sqrt(x^2 + 81)\\Now we can solve for AB in terms of x:AB = (2 * 46) / \sqrt(x^2 + 81)\\AB = 92 / \sqrt(x^2 + 81)\\(92 / \sqrt(x^2 + 81))^2 - 2(92 / \sqrt(x^2 + 81))x + 2x^2 = 81\\[/tex]
[tex]8464 / (x^2 + 81) - (184x) /sqrt(x^2 + 81) + 2x^2 = 81\\8464 - 184x(x^2 + 81) + 2x^2(x^2 + 81) * sqrt(x^2 + 81) = 81(x^2 + 81)\\2x^4 - 181x^2 + 7743 = 0\\x^2 = (181 + \sqrt(181^2 - 427743)) / (2*2)\\x^2 = (181 + sqrt(129961)) / 4\\x^2 = (181 + 361) / 4\\x^2 = 90^2 / 4\\x = 45\sqrt(2) / 2\\[/tex]
[tex]AB = 92 / \sqrt(x^2 + 81)\\AB = 92 / \sqrt((45sqrt(2) / 2)^2 + 81)\\AB = 92 / \sqrt(4050)\\AB ≈ 20.88 cm\\[/tex]
Therefore, the length of the base AB is approximately 20.88 centimeters.
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Solve the polynomial equation by factoring and then using the zero-product principle.
4x = 864x
Rewrite the equation in factored form.
(Blank)= 0
What is the solution pair?
In response to the stated question, we may state that As a result, the equation's answer is x = 0.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
4x = 864x is the provided equation.
This equation may be simplified by deleting 4x from both sides:
[tex]860x = 0[/tex]
This equation may now be rewritten in factored form:
[tex]860x = 0 \sx(860) = 0[/tex]
We know from the zero-product principle that if the product of two elements is zero, then at least one of them must be zero. As a result, we may set each component to zero and solve for x:
x = 0 or 860 = 0 (which is impossible) (which is impossible)
As a result, the equation's answer is x = 0.
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Let
X 1
,…,X n
be i.i.d. random variables with the inverse Gaussian distribution whose pdf is given by
f(x∣μ,λ)=( 2πx 3
λ
) 1/2
exp[− 2μ 2
x
λ(x−μ) 2
],0
Find a sufficient statistic for
(μ,λ)
A sufficient statistic for the parameters (μ, λ) is T(X) = (T1(X), T2(X)) where T1(X) = Σ Xi^(-1) and T2(X) = Π Xi.
To find a sufficient statistic for (μ,λ), we can use the factorization theorem which states that a statistic T(X) is sufficient for a parameter θ if and only if the joint probability distribution of X can be factorized as follows
f(x∣θ) = g[T(x)∣θ]h(x)
where g and h are non-negative functions that do not depend on θ.
Using the given probability density function, we have
f(x∣μ,λ) = (λ/2πx^3)^(1/2)exp[−λ(x-μ)^2/(2μ^2 x) ]
= [(λ/2π)^(1/2)/x^(3/2)] exp[−λ(x-μ)^2/(2μ^2 x)]
= [(λ/2π)^(1/2)/x^(3/2)] exp[−(λ/2μ^2) x + (λμ/μ^2) x^(-1)]
= [exp(λμ/μ^2)/(2πλ)^(1/2)] [x^(-3/2) exp(−λ/2μ^2 x)]
Let's define two functions as follows
T1(X) = Σ Xi^(-1)
T2(X) = Π Xi
Then, we can write the joint pdf of X as follows
f(x1, x2, ..., xn | μ, λ) = [exp(λμ/μ^2)/(2πλ)^(1/2)] [Π xi^(-3/2) exp(−λ/2μ^2 xi)]
= [exp(λμ/μ^2)/(2πλ)^(1/2)] [Π xi^(-3/2)] [exp(−λ/2μ^2 Σ xi)]
Notice that the term [Π xi^(-3/2)] does not depend on (μ, λ), and can be factored out. Therefore, the joint pdf can be rewritten as
f(x1, x2, ..., xn | μ, λ) = [Π xi^(-3/2)] [exp(λμ/μ^2)/(2πλ)^(1/2)] [exp(−λ/2μ^2 Σ xi)]
= g(T1(X), T2(X) | μ, λ) h(X)
where g(T1(X), T2(X) | μ, λ) = [exp(λμ/μ^2)/(2πλ)^(1/2)] [exp(−λ/2μ^2 Σ xi)] and h(X) = [Π xi^(-3/2)].
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The given question is incomplete, the complete question is:
Let X1,…,Xn be i.i.d. random variables with the inverse Gaussian distribution having pdf is given by f(x∣μ,λ)= (λ/2πx^3)^(1/2)exp[−λ(x-μ)^2/(2μ^2 x) ] 0 <x <∞, Find a sufficient statistic for
(μ,λ)
A sports car accelerates from a stopped position (0 m/s) to 27.7 m/s in 2.4 seconds. What is the acceleration of the car?
Using simple division we know that the acceleration per second is 11.54 m/s.
What is division?Multiplication is the opposite of division.
If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
The division is a mathematical process that includes dividing a sum into groups of equal size.
For instance, "12 divided by 4" translates to "12 shared into 4 equal groups," which would be 3 in our example.
So, to find the acceleration per second:
We need to perform division as follows:
= 27.7/2.4
= 11.54
Therefore, using simple division we know that the acceleration per second is 11.54 m/s.
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Directions: Find the prime factors of the polynomials.
1. 2a2 - 2b2
2. 6x2 - 6y2
3. 4x2 - 4
4. ax2 - ay2
5. cm2 - cn2
6. st2 - s
7. 2x2 - 18
8. 2x2 - 32
9. 3x2 - 27y2
10. 18m2 - 8
11. 12a2 - 27b2
12. 63c2 - 7
13. x3 - 4x
14. y3 - 25y
15. z3 - z
16. 4c3 - 49c
17. 9db2 - d
18. 4a3 - ab2
19. 4a2 - 36
20. x4 - 1
21. 3x2+ 6x
22. 4r2 - 4r - 48
23. x3 - 7x2 + 10x
24. 4x2 -6 x - 8
25. 16x2 - x2 v 4
The prime factors of the given polynomial are 1. 2(a + b)(a - b), 2. 6(x + y)(x - y).
What is factoring?A mathematical equation is factored when it is divided into smaller parts, or factors, that may be multiplied together to create the original expression. Mathematicians can benefit from factoring for a variety of reasons. It can aid in the simplification of complicated phrases, making them simpler to use and comprehend. By dividing an expression into its component parts and making each factor equal to zero, it may also be used to solve equations. In algebra, factoring is crucial for solving quadratic equations, locating polynomial roots, and factoring huge integers.
The given expressions is 2a² - 2b².
Factor out 2 and using the difference of squares identity we have:
2(a² - b²) = 2(a + b)(a - b)
2. 6x² - 6y²
6(x² - y²) = 6(x + y)(x - y)
Hence, the prime factors of the given polynomial are 1. 2(a + b)(a - b), 2. 6(x + y)(x - y).
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Consider the initial value problem y⃗ ′=[33????23????4]y⃗ +????⃗ (????),y⃗ (1)=[20]. Suppose we know that y⃗ (????)=[−2????+????2????2+????] is the unique solution to this initial value problem. Find ????⃗ (????) and the constants ???? and ????.
The unique solution to the initial value problem of differential equation is y(t) = -t^2 + 2t + 3sin(3t) - 1 with e(t) = -t^2 + 2t + 3sin(3t) - 9, a = 2, and B = -21.
To find the solution to the initial value problem, we first need to solve the differential equation.
Taking the derivative of y(t), we get:
y'(t) = -2t + a
Taking the derivative again, we get:
y''(t) = -2
Substituting y''(t) into the differential equation, we get:
y''(t) + 2y'(t) + 10y(t) = 20sin(3t)
Substituting y'(t) and y(t) into the equation, we get:
-2 + 2a + 10(-2t + a) = 20sin(3t)
Simplifying, we get:
8a - 20t = 20sin(3t) + 2
Using the initial condition y(0) = 2, we get:
y(0) = -2(0) + a = 2
Solving for a, we get:
a = 2
Using the other initial condition y'(0) = 21, we get:
y'(0) = -2(0) + 2(21) + B = 21
Solving for B, we get:
B = -21
Therefore, the solution to the initial value problem is:
y(t) = -t^2 + 2t + 3sin(3t) - 1
Thus, we have e(t) = y(t) - 8, so
e(t) = -t^2 + 2t + 3sin(3t) - 9
and a = 2, B = -21.
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_____The given question is incomplete, the complete question is given below:
Consider the initial value problem >= [22. 2.1]+20). 361) = [2] Suppose we know that (t) = -2t + a 21? + is the unique solution to this initial value problem. Find e(t) and the constants and B. a = B= 8(t) =
Mr. wings class collected empty soda, cans for recycling project. each of the 20 students had to collect 40 cans. Each can has a mass of 15 grams. How many kilograms of cans did the class collect to recycle?
A 0.6 kg.
B 12 kg
C 12,000 kg
D 12,000,000 kg
Step-by-step explanation:
40 cans/student X 20 students X 15 gram/can = 12 000 gm = 12 kg
Suppose a student takes mathematics and economics as subjects. He obtains the following marks on his tests 82% for maths and 89% for economics. Using the available information determine how the student performed relative to the rest of the class in each subject. Describe this in terms of where his z-scores lie on the normal distribution curve. In which subject did he perform better?
Information
Mathematics
Mean 68
Standard deviation 8
Economics
Mean 80
Standard deviation 6
Answer:
The student's z-score for mathematics is 0.75, which means that his score is 0.75 standard deviations above the mean. This puts him in the upper quartile of the class, indicating that he performed better than 75% of the class.
The student's z-score for economics is 1.5, which means that his score is 1.5 standard deviations above the mean. This puts him in the upper quintile of the class, indicating that he performed better than 80% of the class.
The student performed better in economics than in mathematics.
which of the following represents the percentage of students who have disabilities in both reading and math?
The percentage of students who have disabilities in both reading and math is 20%.
The percentage of students who have disabilities in both reading and math refers to the proportion of students who are identified as having a disability in both reading and math. This means that these students require additional support and accommodations to help them succeed academically. Among the total number of students, 20% of them have disabilities in both reading and math.
Students with disabilities in reading and math may struggle with comprehension, fluency, or other aspects of these subjects. They may require specialized instruction, such as one-on-one tutoring, assistive technology, or modifications to classroom materials or assessments, in order to fully participate in the curriculum.
It is important for schools and educators to identify students who have disabilities in both reading and math early on and provide them with the necessary support and accommodations to help them succeed. This can help to ensure that these students are able to access high-quality education and achieve their full potential, despite their disabilities.
The complete question is
Which of the following represents the percentage of students who have disabilities in both reading and math?
80%30%20%50%To know more about the Disabilities, here
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Thomas bought 120 whistles, 168 yo-yos and 192 tops . He packed an equal amount of items in each bag.
a) What is the maximum number of bag that he can get?
Answer:
To find the maximum number of bags that Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192.
Prime factorizing the three numbers:
120 = 2^3 x 3 x 5
168 = 2^3 x 3 x 7
192 = 2^6 x 3
The GCD is the product of the common prime factors with the lowest exponents, which is 2^3 x 3 = 24.
So, Thomas can pack the items into 24 bags, each containing an equal number of whistles, yo-yos, and tops.
Answer:
Step-by-step explanation:
To find the maximum number of bags that Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192.
We can start by finding the prime factorization of each number:
120 = 2^3 × 3 × 5
168 = 2^3 × 3 × 7
192 = 2^6 × 3
Then we can find the GCD by taking the product of the smallest power of each common prime factor:
GCD = 2^3 × 3 = 24
Therefore, Thomas can pack a maximum of 24 bags.