As a result, the simplified expressiοn is (1/4)m(-3)p. by subtracting the apprοpriate expοnents frοm 3 and then dividing it by 12.
What is variables ?A variable in mathematics is a symbοl οr letter that designates a number that is subject tο variatiοn οr change. Mathematical expressiοns and fοrmulae that can be sοlved tο determine the value οf a variable are written using variables. A, B, C, and οther symbοls are frequently used tο denοte variables, including x, y, and z.
Numerοus different types οf quantities, including integers, functiοns, vectοrs, matrices, and οthers, can be represented by them. X and Y are factοrs in the equatiοn y = 2x + 1, fοr instance. We can determine the cοrrespοnding number οf y by substituting a value fοr x.
given
By dividing 3 by 12 and taking away the cοrrespοnding expοnents οf r and p, we can first simplify the numeratοr οf the expressiοn.
[tex](3m^{(-3)}r^{(4)}p^{(2)})/(12r^{(4)}) = (1/4)m^{(-3)}r^{(4-4)}p^{(2)}[/tex]
Even mοre simply put, we have:
[tex](1/4)m^{(-3){p^{(2)}[/tex]
As a result, the simplified expressiοn is (1/4)m(-3)p. by subtracting the apprοpriate expοnents frοm 3 and then dividing it by 12.
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Question 2
1 pts
At a community event, a vendor lets attendees spin their prize wheel. The wheel consists of 5
colored sections that the vendor claims to be equally likely. One of the sections is labeled "winner!"
A diligent observer records the outcomes of 75 spins. Let X = the number of spins that resulted in a
win.
Use this normal distribution to calculate the probability that AT MOST 10 of the spins result in a
win. Use up to 4 decimal places for the final answer. Use Table A for this one. Stapplet will give a
different value.
Next ▸
A bookstore sells 7 books for $89.25. Which table represents the relationship between number of books and the total price?
Answer: C is our answer.
The first thing that we can do is divide the known number of books into the price that they sold for.
Our equation would be 89.25 divided by 7, which is 12.75. This means that one single book is 12.75. We can look at the charts and point out where one book is 12.75, that is both A and D. While Chart B and C have 7 books for 89.25 which we know is correct.
Lets look at chart D.The next part we can solve is the price of 2 books. 12.75 x 2 is 25.50, so we can mark question B incorrect since two books are 25.50 not 13.75.Chart B is incorrect because 14 books is double 7, so it should be twice as much as 89.25, which we should know 90 dollars is not two times as much 80. Chart A is incorrect because 11 x 12.75 is 140.25, while the chart reads as 22.75.
Now lets look at chart C. Next we can solve the price of 8 books. 8 x 12.75 is 102. Then we solve for 9 books. 12.75 x 9 is 114.75, which means that C is correct.
I hope this helped & Good Luck <3!!
1.Let X 1 ,X 2 ,…,X 10 y Y 1 ,Y 2 ,…,Y 11 be two independent random samples from N(μ X ,4) y N(μ Y ,4) , respectively, that is, they have a common variance σ 2 =4 . Determine the Probability P(S p 2 <6.9157)
Probability 0.919
The probability that the pooled sample variance, S2p, is less than 6.9157 is given by:
P(S2p < 6.9157) = P(S2p - S20 < 6.9157 - S20)
where S20 = ((n1-1)S21 + (n2-1)S22)/(n1+n2-2)
Here, n1 = 10 and n2 = 11. The individual sample variances S21 and S22 are both equal to 4, since both X and Y are samples from N(μ, 4).
Therefore, S20 = ((10-1)4 + (11-1)4)/(10+11-2) = 4.
Hence, P(S2p < 6.9157) = P(S2p - 4 < 6.9157 - 4) = P(S2p - 4 < 2.9157)
The probability can be computed using a chi-square cumulative distribution table. We obtain:
P(S2p - 4 < 2.9157) = 0.919.
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The Probability P(Sp² <6.9157) is 0.6672.
To solve this problem, we need to first recognize that the statistic Sp² follows a chi-squared distribution with 10+11-2 = 19 degrees of freedom, where:
Sp² = [(nX-1)*SX² + (nY-1)*SY²]/(nX+nY-2)
Here, nX = 10, nY = 11, SX² is the sample variance of X and SY² is the sample variance of Y.
Since X and Y are both normally distributed, we know that the sample variances SX² and SY² follow chi-squared distributions with 9 and 10 degrees of freedom, respectively, and scaled by the common variance sigma² = 4.
So we have:
SX² ~ chi-squared(9)*4 = chi-squared(36)
SY² ~ chi-squared(10)*4 = chi-squared(40)
Now we can use the fact that the sum of two independent chi-squared random variables with k1 and k2 degrees of freedom follows a chi-squared distribution with k1+k2 degrees of freedom.
Therefore, Sp² = [(nX-1)*SX² + (nY-1)*SY²]/(nX+nY-2) follows a chi-squared distribution with 9+10 = 19 degrees of freedom and scale parameter 4/(nX+nY-2) = 4/19.
To find P(Sp² < 6.9157), we can use a chi-squared distribution table or calculator. Using a chi-squared calculator, we find:
P(Sp² < 6.9157) = 0.6672
Therefore, the probability that Sp² is less than 6.9157 is 0.6672.
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which expression has a negative value
A. x + y
B. x - y
C. x*y
D. x/y
Answer:
It depends on the values of x and y. If x is positive and y is negative, then option A (x + y) would have a negative value. If y is greater than x, then option B (x - y) would have a negative value. If either x or y (or both) is negative, then option C (x*y) could have a negative value. Option D (x/y) could also have a negative value if x is negative and y is positive, or if both x and y are negative.
Answer:
Step-by-step explanation:
B because it has subtraction
An object is dropped from a small plane. As the object falls, its distance, d, above the ground after t seconds, is
given by the formula d = -16² +1,000. Which inequality can be used to find the interval of time taken by the object
to reach the height greater than 300 feet above the ground?
-16² +1,000 <300
-16² +1,000 ≤300
-16² +1,000 ≥ 300
-16f²+1,000 > 300
Answer:
-16²+1,000 > 300 [After an edit in the original expression, as noted below).
Step-by-step explanation:
The equation d = -16² +1,000 tells us the height above ground, d, of the object after t seconds. When t = 0 seconds, the ball has not been dropped yet, but the equation tells us that d = 1,000 at t = 0. That means the object starts at 1,000 feet above ground.
We want the time it takes for the object to reach any height greater than 300 feet above ground. This is a tad (metric for just a tiny bit) unexpected, since even at time of 0 the object is greater than 1,000 feet.
Looking at the answer options, note that the left side of the inequalities is -16^2+100. I will assume the 4th option has a typo: the f^2. It should read the same as the others.
-16^2+100 is the distance, d. So to help us think this through, let's rephrase the answer options in terms of distance, d:
1) d<300
2) d≤300
3) d≥300
4) d>300
The question asks "We want the time it takes for the object to reach any height greater than 300 feet above ground."
Option 4 says d>300, or height greater than 300. That is the inequality that matches the question. [Note: It did not say greater than or equal to (option 3).]
A traditional western pack of playing cards consists of four suits. Each suit has 13cards. Find the fraction of the playing cards are:
a)red. B)diamonds
c)face cards. D)black and face cards
a) 1/2, b) 1/4, c) 3/13, d) 7/26 (fraction of black and face cards) in a traditional Western pack of playing cards.
A traditional Western pack of playing cards consists of four suits: Hearts (colored red), Diamonds (colored red), Spades (colored black), and Clubs (colored black). Each suit has 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.
a) To find the fraction of the playing cards that are red, we need to add up the number of red cards and divide by the total number of cards in the deck. There are two red suits, Hearts and Diamonds, and each has 13 cards. So there are 26 red cards in total. Since there are 52 cards in a deck, the fraction of red cards is 26/52 or 1/2.
b) To find the fraction of cards that are Diamonds, we simply divide the number of Diamonds (13) by the total number of cards (52). This gives us a fraction of 13/52 or 1/4.
c) To find the fraction of face cards, we need to add up the number of face cards and divide by the total number of cards in the deck. In each suit, there are three face cards: King, Queen, and Jack. So there are 12 face cards in each deck (4 suits x 3 face cards per suit). Therefore, there are 12/52 or 3/13 face cards in the deck.
d) To find the fraction of black and face cards, we need to count the number of black cards and the number of face cards that are also black. There are two black suits, Spades and Clubs, and each has 13 cards. So there are total 26 black cards. Of these 26 cards, there are 12 face cards (King, Queen, and Jack) which are not black, leaving 14 black cards which are face cards. Therefore, the fraction of black and face cards is 14/52 or 7/26.
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Calculate the following using the Long Division Method. Do not use a calculator. 8328÷24
Answer:347
Step-by-step explanation:=
347 ⇔ 347 R 0
8328 divided by 24
=
347 with a remainder of 0
In an elementary chemical reaction, single molecules of two reactants A and B form a molecule of the product C: A+B - C. The law of mass action states that the rate of reaction is proportional to the product of the concentrations of A and B: dc dt = k[A]B] (See Example 3.7.4.) Thus, if the initial concentrations are [A] = a moles/Land (B] = b moles/L and we write r = (C), then we have do dt ka - x)( - ) a. Assuming that a b, find as a function of t. Use the fact that the initial concentration of C is o. b. Find (t) assuming that a = b. How does this expression for a(t) simplify if it is known that 1 [C] - a after 20 seconds?
For the given elementary chemical reaction, the solution to the question is: C = a^2 * (1-t^2/400(1-a))
The question asks about calculating the concentration of C in a chemical reaction. Given that the reaction equation is as follows: A + B → C The rate of reaction can be expressed as: dc/dt = k[A][B] Where, k is the rate constant[A] is the concentration of reactant A in moles/L[B] is the concentration of reactant B in moles/L, c is the concentration of product C in moles/L
The initial concentration of A and B is [A] = a moles/L, [B] = b moles/L Let r be the rate of reaction, i.e. r = dc/dt Thus, using the equation r = k[A][B], we get r = k(a)(b)Now, we can write a differential equation for the concentration of C as follows: dc/dt = r, with initial concentration of C as 0 moles/L∴ dc/dt = kab
Substituting r = k(a)(b) in the equation, we get dc/dt = kabdc/db = kab*dt Differentiating both sides, we get, ln(C) = kab*t + C where C is a constant, ln(C) = ln(a^2) = 2ln(a) = C When a = b, the concentration of C will be maximum at t = (1/k)(ln(a)).
Thus the concentration of C as a function of time (when a = b) is given by C = a^2 * (1-t^2/2)If [C] = a after 20 seconds, then using the equation, we get a = a^2 * (1 - 20^2 * k^2/2)Therefore, 1 = a * (1 - 200k^2) Solving this equation for k, we get, k = ± sqrt[(1-a)/200a^2] For the positive value of k, the concentration of C as a function of time is given by C = a^2 * (1-t^2/400(1-a)).
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Which two sequences of transformations could be used to prove figure 1 and figure 2 are congruent?
In some circumstances, it might also be essential to demonstrate congruence using various transformations.
what is transformations ?In mathematics, transformations are modifications done to a geometric figure in a coordinate plane, such as a shape, point, or line. Applying various operations or functions on the coordinates of the points that make up the figure will result in these changes. Four fundamental types of transformations exist: Translation: A figure is moved horizontally, vertically, or both while maintaining its size, form, and orientation.
Translation, rotation, and reflection are the three fundamental transformations that can be employed to demonstrate the congruence of two figures.
To demonstrate that Figures 1 and 2 are congruent with one another, the following two transformational sequences could be used:
Figure 1 should be translated to overlap with Figure 2, then rotated.
b. Rotate Figure 1 about a point until it aligns with Figure 2's orientation.
c. Evaluate the two figures side by side to ensure that all related sides and angles match.
Rotation after reflection:
a. Create a mirror image of Figure 1 by reflecting it across a line.
b. Rotate the reflected Figure 1 about a certain point until it aligns with Figure 2's orientation.
c. Evaluate the two figures side by side to ensure that all related sides and angles match.
To ensure that the two figures are congruent, the transformations must be used in a precise order.
In some circumstances, it might also be essential to demonstrate congruence using various transformations.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
plot the point at 1
Step-by-step explanation:
An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $4500 and her stock in Company B was worth $3900. The stock in Company A has increased 5% since last year and the stock in Company B has increased 11%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
The total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.
To calculate the total percentage increase in the investor's stock account, we first need to calculate the new values of the stocks in Company A and Company B after the increase.
The new value of the stock in Company A is:
[tex]4500 + (5 \times 4500) = $4725[/tex]
The new value of the stock in Company B is:
[tex]3900 + (11 \times 3900) = 4339[/tex]
The total value of the investor's stock account after the increase is:
$4725 + $4339 = $9064
To calculate the percentage increase in the investor's stock account, we need to find the difference between the new total value and the original total value, and then divide that difference by the original total value:
($9064 - $8400) / $8400 = 0.0795
We then multiply this decimal by 100 to get the percentage increase:
0.0795 x 100 = 7.95%
Therefore, the total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).
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PLEASE HELP WITH THIS PROBLEM ASAP
16. The base side y = 10.565 and altitude x = 22.657
17. The hypotenuse c = 49.70 and base y = 46.70.
18. The value of AB = 30√3 and AC = 45
19. The value of AB = 36√3 and BC = 18√3.
What is a hypotenuse?In geοmetry, a hypοtenuse is the lοngest side οf a right-angled triangle, the side οppοsite the right angle. The length οf the hypοtenuse can be fοund using the Pythagοrean theοrem, which states that the square οf the length οf the hypοtenuse equals the sum οf the squares οf the lengths οf the οther twο sides.
16. Given hypotenuse = 25
θ = 25°
Sin θ = opposite/hypotenuse
Sin 25° = y/25
y = Sin 25° × 25
y = 10.565
Given hypotenuse = 25
θ = 25°
Cos θ = adjacent/hypotenuse
Cos 25° = x/25
x = Cos 25° × 25
x = 22.657
17. Given Side = 17
θ = 20°
Sin 20° = 17/c
c = 17/Sin 20°
c = 49.70
Cos θ = adjacent/hypotenuse
Cos 20° = y/49.70
y = Cos 20° × 49.70
y = 46.70
18. Given BC = 15√3
In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3√ times the length of the shorter leg.
Thus, BC = 15√3
AB = 2(15√3)
= 30√3
and
AC = √3(15√3)
= 15 × 3
= 45
Thus, when BC = 15√3, then AB = 30√3 and AC = 45
19. Given AC = 54
In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3√ times the length of the shorter leg.
Thus, BC = x and AC = x√3
54 = x√3
54 = x√3
x = 54/√3
x = 18√3
BC = 18√3
AB = 2x = 2(BC) = 2(18√3)
= 36(√3)
Thus, when AC = 54, then AB = 36√3 and BC = 18√3.
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When asked to draw a quadrilateral with all four sides measuring 5 cm, Jada drew a square.
5 cm
15 cm
5 cm
1. Do you agree with Jada's answer?
2. Is there a different shape Jada could have drawn that would answer the question? Explain your
reasoning
Absolutely, Jada's response is right. A square is a quadrilateral with four equal-length sides. A quadrilateral is a square if all four sides measure 5 cm.
Unfortunately, there is no alternative form Jada could have drawn that meets the requirement of all four sides measuring 5 cm. Every other quadrilateral with four equal-length sides is likewise a square. If Jada had drawn a quadrilateral with one or more sides of varying lengths, the specified criterion would not have been met. As a result, the only design Jada could have sketched that meets the requirement of having all four sides measure 5 cm is a square. It is worthwhile to investigate the properties of quadrilaterals and how they connect to the conditions presented in the problem. A quadrilateral is a four-sided polygon. Quadrilaterals come in a variety of shapes, including squares, rectangles, parallelograms, trapezoids, and kites. Certain quadrilaterals have unique qualities, such as opposing sides that are parallel or all angles that are right angles. The criterion in the provided problem is that all four sides of the quadrilateral measure 5 cm.
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Determine whether enough information is given to prove that the triangle PQR and triangle STU are congruent. Explain your answer.
Step-by-step explanation:
I do not believe you are given enough info to prove they are congruent....you only have ONE angle and one side that are equal ....you need another side or another angle to prove congruency....
I've added an illustration to show how the two triangles would not be congruent without changing the info given in the pic
.
Draw a line representing the "rise" and a line
representing the "run" of the line. State the
slope of the line in simplest form.
Click twice to plot each segment.
Click a segment to delete it.
-10 -9 -8 -7 -6 -5 -4 -3
-2
-1
y
10
9
8
7
6
5
4
3
2
1
-1
-2
ỗ có có ý ới ơi Á có nó
4
-5
-6
-8
-9
-10
1
2
3
45
6
78
9
10
·x
Answer:
Step-by-step explanation:
rise is up and run is over.
The first number would be y and the second number would be x
and x is run
y is rise.
Select the graph that would represent the best presentation of the solution set for |x| < 5.
Based on the principle of Inequality, Attached image is a graph of the inequality for |x| < 5. The red region is the solution set.
What is the graph equation?A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, subtraction, multiplication, division, exponents, and so forth.
Therefore, An expression that demonstrates a non-equal comparison of numbers and variables is called an inequality. So, the graph that best represents this solution set is a number line with open circles at x = -5 and x = 5 and a shaded region in between, indicating that all values of x within this range satisfy the inequality.
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Calculate the following without using a calculator -5×(-3+7)+20÷(-4)
Answer:
-25
Step-by-step explanation:
simplification using BODMAS
[tex]-5 * 4 + -5[/tex]
-20 - 5
= -25
what is the result of substituting for y in the bottom equation?
Answer:
A. y=(x-3)^2+2(x-3)-4
B. x-3=x^2+2x-4
C. y=x^2+2x-4-(x-3)
D. (x-3)=x^2
Optiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 =x² + 2x - 4.
What is the equivalent expression?Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.
Tο substitute fοr y in the secοnd equatiοn, we can replace y with its equivalent expressiοn in terms οf x frοm the first equatiοn, which gives us:
x - 3 = x² + 2x - 4
This is option B.
Optiοn A is incοrrect because it substitutes y fοr its expressiοn in terms οf x in the wrοng equatiοn.
Optiοn C is incοrrect because it subtracts (x-3) instead οf adding it tο the secοnd equatiοn.
Optiοn D is incοrrect because it sets the expressiοn fοr y in the first equatiοn equal tο x² instead οf the expressiοn fοr y in the secοnd equatiοn.
Hence, οptiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 = x² + 2x - 4.
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Complete question:
What is result of substituting for y in the bottom equation?
y = x – 3,
y = x² + 2x – 4
A. y=(x-3)²+2(x-3)-4
B. x-3=x²+2x-4
C. y=x²+2x-4-(x-3)
D. (x-3)=x²
An iPhone costs £800 in London, €880 in Paris and $850 in New York. Using £1 = €1.16 and £1 = $1.41, state the lowest price of the iPhone in £. Give your answer to 2 dp.
Answer:
£602.84 in New York
Step-by-step explanation:
London Cost:
Converting pound to dollars:
£800 * 1.41 = $1128
Paris cost:
Converting euro to pounds:
€880/1.16 = £759
Converting pound to dollars again:
£759 * 1.41 = $1070
New york cost:
$850
The lowest price is in new york which is:
$850/1.41 = £602.84
Feel free to mark this as brainliest (I'm one brainliest off 50 so please help out
What is the equation of the graph below?
On a coordinate plane, a curve crosses the y-axis at (0, negative 1). It has a minimum of negative 1 and a maximum of 1. It goes through 1 cycle at 2 pi.
y = cosine (x + StartFraction pi Over 2 EndFraction)
y = cosine (x + 2 pi)
y = cosine (x + StartFraction pi Over 3 EndFraction)
y = cosine (x + pi)
The equation of the given graph is: y = cosine (x + pi)
Equation of cosine graphsBy convention, the cosine function like most other trigonometric functions has a period of 2π.
Since, the parental function is y = cos x, which has y-intercept at y = 1, and x-intercept at π/2.
From observation, the function showed in the graph attached has y-intercept at y = -1 and x-intercept at π/2.
This can be interpreted to mean that the function has been translated leftwards π units.
Ultimately, the function that belongs to this graph is; y = cosine (x + pi)
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Answer: D. y = cosine (x + pi)
Step-by-step explanation:
A catapult launches a pumpkin from the base of a hill. The hill follows an incline with the
height in meters, y, in terms of horizontal distance in meters, x, given by the equation
y=0. 9x. The height of the pumpkin, as it is launched uphill, is given by the function
y = -0. 1x² +4. 9x
What is the height, in meters, where the pumpkin lands on the hill?
The height, in meters, where the pumpkin lands on the hill is 4.9 meters.The equation for the height of the hill is y = 0.9x.
This equation can be rearranged to solve for x, giving x = y/0.9. The equation for the height of the pumpkin is y = -0.1x² + 4.9x. Substituting the x value from the previous equation into the equation for the height of the pumpkin gives y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying this equation gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill.
The equation for the height of the hill is y = 0.9x, which describes the incline of the hill. This equation can be rearranged to solve for x, giving x = y/0.9. This equation can then be used to substitute into the equation for the height of the pumpkin, which is y = -0.1x² + 4.9x. When the x value from the previous equation is substituted into the equation for the height of the pumpkin, the equation simplifies to y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying further gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill. This can be verified by substituting 4.9 for y in the equation for the height of the hill, which gives x = 4.9/0.9 = 5.4. This value can be substituted into the equation for the height of the pumpkin, which gives y = -0.1(5.4)² + 4.9(5.4) = 4.9, verifying the result.
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A population has a standard deviation of sigma = 24. a. On average, how much difference should exist between the population mean and the sample mean for n = 4 scores randomly selected from the population? b. On average, how much difference should exist for a sample of n = 9 scores? c. On average, how much difference should exist for a sample of n = 16 scores?
Therefore , the solution of the given problem of standard deviation comes out to be he average difference between the population mean and the sample mean is 6.
What is standard deviation?Variance is a measure of variation used in statistics. The average difference between the gathering and the mean is calculated using the photo of that figure. By comparing each number to the mean, it incorporates those data points into the calculations on their own, in contrast to many other legitimate measures of variable. Variations could result from deliberate errors, unrealistic expectations, or changing economic or commercial circumstances.
Here,
For a group of n = 4, the standard error of the mean (SEM) is as follows:
=> SEM = α/√(n)
=> 24/√(4) = 12
Therefore, for n = 4 scores drawn at random from the population, the average difference between the population mean and the sample mean is 12.
b. The SEM for a group of n = 9 is:
=> α/√(n) = 24/√(9)
=> 8; SEM = α
Therefore, for n = 9 scores drawn at random from the population, the average difference between the population mean and the sample mean is 8.
c. The SEM for a sample of 16 is as follows:
=> α / √(n) = 24 / √(16) = 6;
=> SEM =α
Therefore, for n = 16 scores drawn at random from the population, the average difference between the population mean and the sample mean is 6.
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Use a system of equations to find the cubic function f(x)=ax3+bx2+cx+d that satisfies the equations. Solve the system using matrices. f(−2)=−7; f(−1)=2; f(1)=−4; f(2)=−7
The solution of the system is a = -1, b = 1, c = 0, and d = -3.
To find the cubic function f(x) = ax³ + bx² + cx + d that satisfies the given equations by using a system of equations and solving the system using matrices, we proceed as follows:Equations for the given cubic function:f(-2) = a(-2)³ + b(-2)² + c(-2) + d = -7 ...(1)f(-1) = a(-1)³ + b(-1)² + c(-1) + d = 2 ...(2)f(1) = a(1)³ + b(1)² + c(1) + d = -4 ...(3)f(2) = a(2)³ + b(2)² + c(2) + d = -7 ...(4)The matrix form of the system of equations is given by AX = B, whereA = [(-2)³ (-2)² -2 1; (-1)³ (-1)² -1 1; (1)³ (1)² 1 1; (2)³ (2)² 2 1],X = [a; b; c; d], andB = [-7; 2; -4; -7].The augmented matrix form of the system of equations is given by [A|B] = [(-2)³ (-2)² -2 1 -7; (-1)³ (-1)² -1 1 2; (1)³ (1)² 1 1 -4; (2)³ (2)² 2 1 -7].Performing the row operations, we get the row echelon form of the augmented matrix as follows:[A|B] = [1 0 0 0 -1; 0 1 0 0 1; 0 0 1 0 0; 0 0 0 1 -3].Therefore, the solution of the system is a = -1, b = 1, c = 0, and d = -3.Hence, the cubic function f(x) = ax³ + bx² + cx + d that satisfies the given equations is given by f(x) = -x³ + x² - 3.
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Given the expression
Choose all the equivalent expressions as your answer.
The equivalent expressions of [tex]x^3[/tex] are[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]and [tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex], the expressions [tex]\frac{(x^{30}) }{(x^{10})}[/tex] and [tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] are not equivalent to [tex]x^3[/tex].
What are equivalent expressions?
Equivalent expressions are different algebraic expressions that have the same value when evaluated for a particular set of variables.
The equivalent expressions [tex]x^3[/tex] are:
[tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex]
= [tex]\frac{(x ^ 8)}{(x ^ 2) }[/tex]
=[tex]x^{8-2}[/tex]
= [tex]x^6[/tex]
[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]
= [tex]x^{6-3}[/tex]
=[tex]x^3[/tex]
[tex]\frac{(x^{30}) }{(x^{10})}[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x^{30}) }{(x^{10})}[/tex]
=[tex]x^{30-10}[/tex]
=[tex]x^{20}[/tex]
[tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex] : This expression can be simplified as follows:
=[tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex]
=[tex]x^{-3-(-6)}[/tex]
=[tex]x^{-3+6}[/tex]
=[tex]x^{3}[/tex]
Therefore, the equivalent expressions of [tex]x^3[/tex] are[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]and [tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex] , the expressions [tex]\frac{(x^{30}) }{(x^{10})}[/tex] and [tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] are not equivalent to [tex]x^3[/tex].
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Do the Ratios 6/5 and 4/3 fit a Proportion
Answer:
No
Step-by-step explanation:
[tex]\frac{6}{5}=1.2[/tex]
[tex]\frac{4}{3} =1.33[/tex]
[tex]\frac{6}{5} < \frac{4}{3}[/tex]
Hope this helps.
Answer:
No
Step-by-step explanation:
6/5=4/3
18=20
9≠10
Find the area of the shaded region. The area of the shaded region is____
Answer:
[tex]x^{2}[/tex]
Step-by-step explanation:
x*x=[tex]x^{2}[/tex]
What is the answer to this question?
Answer:
Step-by-step explanation:
The domain is found by setting the denominator equal to 0 and solving for y. This value of y gives you the values that cause the denominator to go to 0, which is a problem. In this rational expression, there are no real numbers that cause the denominator to go to 0, so the domain is all real numbers.
Cumulative distribution function for a continuous random variable x
The cumulative distribution function gives us the probability that the random variable is less than or equal to a given value.
The cumulative distribution function (CDF) of a continuous random variable x is a function which gives the probability that the random variable x is less than or equal to a given value x. Mathematically it is expressed as:
[tex]F(x) = P(X ≤ x)[/tex]
The calculation of the cumulative distribution function is done by integrating the probability density function (PDF) from the lower limit to the given value x. Thus,
[tex]F(x) = ∫-∞ x f(u) du[/tex]
Where f(u) is the probability density function.
For example, if we have a continuous random variable x with probability density function f(x) = x2, then the cumulative distribution function [tex]F(x) = ∫-∞ x x2 du = 1/3x3 + c.[/tex]
Thus, It is a powerful tool for analysing the probability distribution of a continuous random variable.
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Complete question:
What is the cumulative distribution function for a continuous random variable x?
Please help me! A sector has a central angle measure of 90 degrees, and a radius of 8 cm. Which equation shows the correct calculation of the area of the sector?
Therefore , the solution of the given problem of area comes out to be
A = 16 is the equation that accurately depicts how to calculate the sector's area.
What is an area ?Its total size can be determined by figuring out how much space is required to completely cover the outside. The immediate surroundings are taken into consideration when calculating the surface of a trapezoidal shape. The total measurements of something are determined by its surface area. A cuboid's capacity for internal water is determined by the sum of the borders that link all of it's six rectangle edges.
Here,
The formula for calculating a circle's sector's area is:
=> A = (θ/360) x πr²
where A is the sector's area, is its central angle measurement, and r is the circle's radius.
Since the radius is 8 cm and the central angle is 90 degrees in this instance, we can reduce by plugging in these values:
=> A = (90/360) x π(8²)
=> A = (1/4) x π(64)
=> A = π(16)
=> A = 16π
A = 16 is the equation that accurately depicts how to calculate the sector's area.
The answer will be given in radius squared units, in this case, cm2.
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Option D. The correct calculation of the area of the sector is [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]
What is an area of the sector?An area of the sector is the portion of the area of a circle that is enclosed by two radii and an arc. The area of a sector can be found using the formula:
A = (θ/360)πr²
where A is the area of the sector, θ is the central angle of the sector (in degrees), π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Given, the radius is 8 cm and the central angle is 90° in this instance, put all these values:
[tex]A=(\frac{90}{360}) * \pi (8^{2} )[/tex]
or we can write down, [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]
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(Helpppp)Write slope-intercept form of the line which is perpendicular bisector to
a segment with endpoints A(5,9), B(7,13).
Answer:
the slope-intercept form of the line which is perpendicular bisector to the segment with endpoints A(5,9), B(7,13) is y = (-1/2)x + 14