The Amount from contributions = R * n
Define the term future value?The future value refers to the value of an asset or investment at a specified time in the future, based on a specific interest rate or rate of return.
Without knowing the specific values of R, interest rate, and number of years, we cannot calculate the amounts from contributions and interest. However, we can provide the general formula for calculating the future value of an ordinary annuity:
FV = R * [(1 + i)ⁿ - 1] / i
where FV is the future value of the annuity, R is the periodic payment, i is the interest rate per period, and n is the number of periods.
To calculate the amount from contributions, we can multiply the periodic payment R by the number of periods n.
Amount from contributions = R * n
To calculate the amount from interest, we can subtract the amount from contributions from the future value of the annuity.
Amount from interest = FV - R * n
Once the specific values for R, interest rate, and number of years are provided, we can use these formulas to calculate the amounts from contributions and interest.
To know more about future value, visit:
https://brainly.com/question/30741148
#SPJ1
An 8 foot long ladder is leaning against a wall. The top of the ladder is sliding down the wall at the rate of 2 feet per second. How fast is the bottom of the ladder moving along the ground at the point in time when the bottom of the ladder is 4 feet from the wall.
"The rate at which the bottom of the ladder moving along the ground at the point in time when the bottom of the ladder is 4 feet from the wall is calculated to be 3.464 ft/s."
At a pace of 2 feet per second, the lower end of the ladder is being pulled away from the wall.
At a specific moment, when the lower end of the ladder is 4 feet from the wall, we should determine the rate at which the bottom of the ladder is lowering.
From the point t, the bottom of the ladder is x m, the top of the ladder is y m from the wall.
x² + y² = 64
Differentiating the given relationship with regard to t,
2x dx/dt + 2y dy/dt = 0
x dx/dt + y dy/dt = 0
We need to find out dx/dt at x = 4.
dy/dt = -2
At x = 4, we have,
x² + y² = 64
16 + y² = 64
y² = 48
y = 4√3
Put in the known values to find out dx/dt,
x dx/dt + y dy/dt = 0
4 dx/dt + 4√3 (-2) = 0
4 dx/dt = 8√3
dx/dt = 2√3 = 3.464
Thus, the bottom of the ladder is calculated to be moving at the rate 3.464 ft/s.
The figure can be drawn as shown in the attachment.
To know more about speed:
https://brainly.com/question/13548149
#SPJ4
3. Factor 72x³ +72x² +18x.
The expression's fully factored form is:[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]
Factored value is what?Factored Value, also known as "trended value," is the base annual value plus a yearly inflation factor based on a variation in the cost if live that is not to exceed 2% and is set by the State Agency of Equalization.
What is a factored expression example?Rewriting an expression as the sum of factors is referred to as factor expressions or factoring. For instance, 3x + 12y may be expressed as 3 (x + 4y), which is a straightforward equation. The computations get simpler in this method. Three or (x + 4y) were examples of factors.
We can factor out [tex]18x[/tex] from each term to simplify the expression:
[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{3} + 4x^{2} + 1)[/tex]
An expression enclosed in parentheses can now be calculated by grouping or factoring.
[tex]4x^{3} + 4x^{2} + 1 = (4x^{2} + 1)(x + 1)[/tex]
The expression's properly factored version has the following result,
[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]
To know more about factored visit:
https://brainly.com/question/20168177
#SPJ1
What is the limit of (n!)^(1/n) as n approaches infinity?
Note: n! means n factorial, which is the product of all positive integers up to n.
Answer:
Step-by-step explanation:
To find the limit of (n!)^(1/n) as n approaches infinity, we can use the Stirling's approximation for n!, which is:
n! ≈ (n/e)^n √(2πn)
where e is the mathematical constant e ≈ 2.71828, and π is the mathematical constant pi ≈ 3.14159.
Using this approximation, we can rewrite (n!)^(1/n) as:
(n!)^(1/n) = [(n/e)^n √(2πn)]^(1/n) = (n/e)^(n/n) [√(2πn)]^(1/n)
Taking the limit as n approaches infinity, we have:
lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n)
Using the fact that lim a^(1/n) = 1 as n approaches infinity for any constant a > 0, we can simplify the second term as:
lim [√(2πn)]^(1/n) = 1
For the first term, we can rewrite (n/e)^(n/n) as [1/(e^(1/n))]^n and use the fact that lim a^n = 1 as n approaches infinity for any constant 0 < a < 1. Thus, we have:
lim (n/e)^(n/n) = lim [1/(e^(1/n))]^n = 1
Therefore, combining the two terms, we have:
lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n) = 1 x 1 = 1
Hence, the limit of (n!)^(1/n) as n approaches infinity is 1.
Answer:1
Step-by-step explanation:
I will mark you brainiest!
Determine the MOST PRECISE name for the quadrilateral below.
A) rhombus
B) parallelogram
C) square
D) trapezoid
E) kite
The answer is A, rhombus.
A teacher has a large yellow bulletin board in her classroom. She decides to use purple paper to frame a smaller rectangle inside the original board. The paper will create a border that is x inches wide. The teacher's bulletin board plan and dimensions are shown below.
Look at the picture then choose the answer from the options below:
Select the true statement about the expression.
A.
The factor (96 − 2x) represents the length, in inches, of the uncovered portion of the bulletin board.
B.
The term 4x2 represents the area, in square inches, of the entire bulletin board.
C.
The factor (48 − 2x) represents the height, in inches, of the bulletin board including the decorative border.
D.
The term -288x represents the area, in square inches, of the decorative border.
Option A: The factor (96 − 2x) represents the length, in inches, of the uncovered portion of the bulletin board.
How to obtain the area of a rectangle?To obtain the area of a rectangle, you need to multiply the dimensions of the rectangle, which are the length and the width.
Hence the formula for the area of the rectangle is given as follows:
Area = Length x Width.
The area of the uncovered region is given by the total area subtracted by the area of the covered region.
Then the dimensions for the uncovered region are given as follows:
96 - 2x.48 - 2x.The area of the covered region is given as follows:
4x².
The area of the entire region is given as follows:
4x² - 288x + 4608.
Hence the correct statement is given by option A.
More can be learned about the area of a rectangle at brainly.com/question/25292087
#SPJ1
A company reported the following:
$275,270
Preferred dividends
$20,390
Shares of common stock outstanding
36,000
Market price per share of common stock
$118.87
Calculate the company's price-earnings ratio. Round your answer to two decimal places.
Net income
The company's price-earnings ratio for a company that reported net income of $275,270 with $20,390 for preferred dividends and 36,000 shares of common stock, is 16.79.
What is the price-earnings ratio?The price-earnings ratio represents the per-dollar amount that an investor can expect to invest in a company in order to receive $1 of that company's net earnings.
The price-earnings (P/E) ratio is also referred to as the price multiple.
The price-earnings (P/E) ratio compares the market price with the earnings per share.
Net income = $275,270
Preferred Dividends = $20,390
Net income available to Common Stockholders = $254,880 ($275,270 - $20,390)
Number of common stock outstanding = 36,000 shares
Market price per share of common stock = $118.87
Earnings per share (Common Stock) = $7.08 ($254,880/36,000)
Price-earnings ratio = Market price per share/Earnings per share
= 16.79 ($118.87/$7.08).
Learn more about the price-earnings ratio at https://brainly.com/question/18484440.
#SPJ1
The pens in a box are repackaged equally into 9 packs. Each pack has more than 15 pens.
1. Find an inequality to represent n, the possible number of pens in the box.
2. Explain why you chose this inequality.
Therefore, the possible number of pens in the box is p, where p is greater than 135.
What is inequality?Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.
Inequalities are mathematical expressions that compare two values using the symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). To solve an inequality, you need to isolate the variable (the unknown quantity) on one side of the inequality symbol and determine the range of values for which the inequality holds true.
Here are some general steps to solve an inequality:
Simplify both sides of the inequality as much as possible. This may involve combining like terms, distributing terms, or factoring.Get all the variable terms on one side of the inequality symbol and all the constant terms on the other side. Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality symbol.Solve for the variable by isolating it on one side of the inequality symbol. If the variable has a coefficient, divide both sides of the inequality by that coefficient.Write down the solution as an inequality. If you have solved for x, the solution will be in the form of x < a or x > b, where a and b are numbers.Check your solution by testing a value in the original inequality that is within the range of the solution. If the inequality holds true for that value, then the solution is correct. If not, then you may need to recheck your work or adjust your solutionby the question.
Let's say there are 'p' pens in the box. Each pack has more than 15 pens, so we can write the inequality:
p/9 > 15
Multiplying both sides by 9, we get:
p > 135
To learn more about inequality:
https://brainly.com/question/30231190
#SPJ1
What are inequalities?
Answer:
In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.
There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:
Greater than: x > y (read as "x is greater than y")
Less than: x < y (read as "x is less than y")
Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")
Less than or equal to: x ≤ y (read as "x is less than or equal to y")
Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.
Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.
Step-by-step explanation:
Question 15 (2 points)
A standard deck of cards contains 4 suits of the same 13 cards. The contents of a
standard deck are shown below:
Standard deck of 52 cards
4 suits (CLUBS SPADES, HEARTS, DIAMONDS)
13 CLUBS
13 SPADES
13 HEARTS
DIAMONDS
If a card is drawn at random from the deck, what is the probability it is a jack or ten?
0
4/52- 1/13
8/52 = 2/13
48/52- 12/13
Answer: 2/13
Step-by-step explanation:
There are four jacks and four tens in a standard deck of 52 cards. However, the jack of spades and the ten of spades are counted twice since they are both a jack and a ten. Therefore, there are 8 cards that are either a jack or a ten, and the probability of drawing one of these cards at random is:
P(Jack or Ten) = 8/52 = 2/13
So the answer is 2/13.
Step-by-step explanation:
a probability is airways the ratio
desired cases / totally possible cases
in each of the 4 suits there is one Jack and one 10.
that means in the whole deck of cards we have
4×2 = 8 desired cases.
the totally possible cases are the whole deck = 52.
so, the probability to draw a Jack or a Ten is
8/52 = 2/13
How do I solve? I don’t understand
Step-by-step explanation:
Use the 110 to find the 70 degree angle (they form a straight line = 180°)
then 70 + 64 + R angle = 180° ( sum of angles of a triangle)
then : R angle = 46°
then the R angle + 2x-10 = 90° ( because the two lines are perpendicular)
(2x -10)° + 46 ° = 90 °
x = 27
In the diagram below, MN is parallel to JK. If MN=10,LK=7.2, JL=13.2, and LN=6.find the length of JK. Figures are not necessarily drawn to scale.
The length of JK is 18.333.
Since MN is parallel to JK, the angles formed by JLN and MLK are equal. Therefore, we can use the Triangle Proportionality Theorem, which states that if a line parallel to one side of a triangle divides the other two sides proportionally, then the triangles are similar.
Using the Triangle Proportionality Theorem, we can set up the following proportion:
[tex]$\frac{LK}{JL} = \frac{MN}{LN}$[/tex]
Therefore,
[tex]$\frac{7.2}{13.2} = \frac{10}{6}$[/tex]
We can cross-multiply to solve for JK:
[tex]$7.2 \cdot 6 = 13.2 \cdot 10$\\$43.2 = 132$\\$JK = \frac{132}{7.2} = 18.333$[/tex]
Therefore, the length of JK is 18.333.
Learn more about Triangle Proportionality Theorem here:
https://brainly.com/question/11807262
#SPJ1
Use the power of a power property to simplify the numeric expression.
(91/4)^7/2
Using the power property to simplify the expression (9¹⁺⁴)⁷⁺², we have 9^7/8
Given the expression
(9¹⁺⁴)⁷⁺²
To simplify this expression using the power of a power property, we need to multiply the exponents:
(9¹⁺⁴)⁷⁺² = 9(¹⁺⁴ ˣ ⁷⁺²)
Simplifying the exponents in the parentheses:
(9¹⁺⁴)⁷⁺² = 9⁷⁺⁸ or 9^7/8
Therefore, (9¹⁺⁴)⁷⁺² simplifies to 9^(7/8).
Read more about expression at
https://brainly.com/question/4344214
#SPJ1
Subtract 1/9 - 1/14 and give answer as improper fraction if necessary.
Answer:
To subtract 1/9 - 1/14, we need to find a common denominator. The smallest number that both 9 and 14 divide into is 126.
So, we will convert both fractions to have a denominator of 126:
1/9 = 14/126
1/14 = 9/126
Now we can subtract them:
1/9 - 1/14 = 14/126 - 9/126
Simplifying the right-hand side by subtracting the numerators, we get:
5/126
Therefore, 1/9 - 1/14 = 5/126 as an improper fraction.
Answer:
1/9-1/14
=14-9/9*14
=5/126
= 25 1/5
Mason earns $8.10 per hour and worked 40 hours. Noah earns $10.80 per hour. How many hours would Noah need to work to equal Mason’s earnings over 40 hours?
Answer:
Noah would need to work 30 hours to equal Mason's earning for 40 hours
Step-by-step explanation:
Mason;
8.10 x 40 = 324
324 ÷ 10.80 = 30 hours.
Helping in the name of Jesus.
Answer:
30 hours
Step-by-step explanation:
40 times 8.10 is 324 and 324 divided by 10.8 is 30 hours
for a given positive integer n, output all the perfect numbers between 1 and n, one number in each line.
Perfect numbers between 1 and n (where n is a positive integer) are 6, 28, 496, 8128.
A positive integer that is the sum of its appropriate divisors is referred to as a perfect number. The sum of the lowest perfect number, 6, is made up of the digits 1, 2, and 3. The digits 28, 496, and 8,128 are also ideal.
Perfect numbers are whole numbers that are equal to the sum of their positive divisors, excluding the number itself. Examples of perfect numbers include 6 (1 + 2 + 3 = 6), 28 (1 + 2 + 4 + 7 + 14 = 28) and 496 (1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496).
To learn more about Perfect numbers link is here
brainly.com/question/29291022
#SPJ4
The complete question is:
What are all the perfect numbers between 1 and n (where n is a positive integer)?
the position vector r describes the path of an object moving in the xy-plane. position vector point r(t)
a) Velocity vector v(t) = i - 2tj, Speed s(t) = sqrt(1 + 4t²), Acceleration vector a(t) = -2j. b) Velocity vector v(1) = i - 2j, Acceleration vector a(1) = -2j
This problem is about finding the velocity, speed, and acceleration vectors of an object moving in the xy-plane, described by a position vector r(t). We can find the velocity vector by taking the derivative of the position vector, and the speed by taking the magnitude of the velocity vector. The acceleration vector can be found by taking the derivative of the velocity vector. We can then evaluate the velocity and acceleration vectors at a given point by plugging in the coordinates of the point. This problem requires basic vector calculus and understanding of the relationship between position, velocity, speed, and acceleration vectors.
Learn more about graphs here: brainly.com/question/17267403
#SPJ4
Complete question is attached below
-6(4p+5) > 34-8p HELP ASAP
Answer:
p < -4
Step-by-step explanation:
-6(4p+5) > 34 - 8p
-24p - 30 > 34 - 8p
-16p - 30 > 34
-16p > 64
p < -4
i need the answer to this question
The measure of angle BAC is 55°, which is closest to option B (50°).
What is a tangent angle?The ratio of the length of the side directly opposite an acute angle to the side directly adjacent to the angle is known as the tangent in trigonometry. Only triangles with straight angles can have this.
Let's give the angles shown in the diagram the following labels:
Angle ACD = 55°
Angle ABD = 35°
Angle BCD = 90°
To determine the size of angle ABC, we can use the knowledge that a triangle's total angles equal 180°. Because the straight line formed by angles ABD and BCD, we have:
[tex]Angle ABC = 180° - Angles ABD and BCD.[/tex]
[tex]Angle ABC = 180° - 35° - 90°Angle ABC = 55°[/tex]
Given that triangle ABC has two angles, we can use the knowledge that a triangle's total of angles equals 180° to determine the size of angle BAC:
[tex]Angle BAC = 180° - Angle ABC - Angle ACBAngle BAC = 180° - 55° - 70°Angle BAC = 55°[/tex]
To know more about angle visit:-
https://brainly.com/question/28451077
#SPJ1
It is most similar to option B (50°) when the angle BAC is 55°.
What is a tangent angle?
The tangent in trigonometry is the length of the side directly opposite an acute angle divided by the length of the side directly next to the angle.
This property can only be found in triangles with straight angles.
Let's give the angles shown in the diagram the following labels:
Angle ACD = 55°
Angle ABD = 35°
Angle BCD = 90°
We can use the fact that a triangle's total number of angles is 180° to calculate the size of angle ABC. due to the fact that the straight line created by angles ABD and BCD
Triangle ABC has two angles, so we can use the fact that a triangle's sum of angles is 180° to calculate the size of angle BAC.
Therefore, the BAC measurement is 55°, which is closest to option B's 50°.C is 55°, which is closest to option B (50°).
To know more about angle from the given link:-
brainly.com/question/28451077
#SPJ1
determine, without actually computing the z transform, the rocs for the z transform of the following signals:
The ROC of a given signal's Z-transform can be determined without actually computing the Z-transform by identifying the maximum and minimum magnitude of the signal and checking for any poles of the Z-transform within the resulting annular region.
Let's take a signal as an example, suppose x[n] = {1, -2, 3, -4, 5}. In order to determine the ROC of its Z-transform, we are firstly required to first look for any regions in the complex plane where the sum of the absolute values of the Z-transform is found finite. It can be done by looking for the maximum and minimum magnitude of x[n] and denote them as R1 and R2 respectively. Then, the ROC of the Z-transform will be the annular region between R1 and R2, excluding any poles of the Z-transform that lie within this annular region.
In this case, the maximum absolute value of x[n] is 5 and the minimum is found being 1. So, the ROC of the Z-transform will be the annular region between |z| = 1 and |z| = 5. We can denote this as 1 < |z| < 5. We also need to check if there are any poles of the Z-transform within this annular region. Since we haven't actually computed the Z-transform, we cannot determine the exact location of any poles.
However, we can check for any values of z that would make the Z-transform infinite. For example, if x[n] is a causal signal (i.e., x[n] = 0 for n < 0), then the ROC cannot include any values of z for which |z| < 1, since this would make the Z-transform infinite.
So, the ROC of the Z-transform for the given signal x[n] can be written as 1 < |z| < 5, assuming that x[n] is a causal signal.
Learn more about Z-Transform :
https://brainly.com/question/14979001
#SPJ4
The complete question is :
Can you explain how to determine the ROCs (regions of convergence) for the Z-transform of a given signal without actually computing the Z-transform? Please provide an example signal with random data and demonstrate how to find its ROCs using this method.
Marcos had $60 in his savings account in January. He continued to add money to his account and by June, the value of the savings account had increased by 50%. How much money is in Marcos's account in June?
Answer: 90$
Step-by-step explanation: 50% of 60 is 30 so 60+30=90
Type the correct answer in each box. Assume π = 3.14. Round your answer(s) to the nearest tenth. 90° 30° In this circle, the area of sector COD is 50.24 square units. The radius of the circle is units, and m AB is units.
Therefore, the length of segment AB is approximately 7.4 units.
What is area?Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width.
Here,
To find the radius of the circle, we can use the formula for the area of a sector:
Area of sector = (θ/360) x π x r²
where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is approximately 3.14.
We're given that the area of sector COD is 50.24 square units and the central angle of the sector is 90°. So we can plug in these values and solve for r:
50.24 = (90/360) x 3.14 x r²
50.24 = 0.25 x 3.14 x r²
r² = 50.24 / (0.25 x 3.14)
r² = 201.28
r = √201.28
r ≈ 14.2
Therefore, the radius of the circle is approximately 14.2 units.
Next, we need to find the length of segment AB. Since AB is a chord of the circle, we can use the formula:
AB = 2 x r x sin(θ/2)
where θ is the central angle of the sector in degrees, r is the radius of the circle, and sin() is the sine function.
We're given that the central angle of sector COD is 30°. So we can plug in this value and the radius we found earlier to solve for AB:
AB = 2 x 14.2 x sin(30/2)
AB = 2 x 14.2 x sin(15)
AB ≈ 7.4
To know more about area,
https://brainly.com/question/22469440
#SPJ1
The circle graph below represents the favorite fruit of 300 people How many prefer oranges? b. How many prefer pineapples? c. How many prefer blueberries? d. How many prefer apples? e. How many prefer strawberries?
Hey!
A: 50% Of people = 150 people prefer oranges.
B: 10% Of people = 15 people prefer pineapple.
C: 15% Of people = 20 people prefer blueberries.
D: 5% Of people = 5 people prefer apples.
E: 20% Of people = 22 people prefer strawberries
if the sum of a number and eight is doubled, the result is seven less than the number. Find the number.
Answer:
Step-by-step explanation:
Let's call the number we're looking for "x".
The problem tells us that "if the sum of a number and eight is doubled, the result is seven less than the number", which can be translated into an equation:
2(x+8) = x-7
Now let's solve for x:
2x + 16 = x - 7
2x - x = -7 - 16
x = -23
Therefore, the number we're looking for is -23.
Expand and simplify completely
[tex]x(x+(1+x)+2x)-3(x^2-x+2)[/tex]
Answer:
x² + 4x - 6
Step-by-step explanation:
x(x + (1 + x) + 2x) - 3(x² - x + 2) ← simplify parenthesis on left
= x(x + 1 + x + 2x) - 3(x² - x + 2)
= x(4x + 1) - 3(x² - x + 2) ← distribute parenthesis
= 4x² + x - 3x² + 3x- 6 ← collect like terms
= x² + 4x - 6
5/9=
1/14=
12/13=
2/13=
9/11=
9/17=
To round each fraction
Answer:
Step-by-step explanation:
1. Rounded to 0.56
2. Rounded
Let X1, X2, ..., Xn denote n independent and identically distributed Bernoulli random vari- ables s.t. P(X; = 1) = p and P(Xi = 0) = 1 – p. for each i = 1, 2, ..., n. Show that __, Xi is sufficient for p by using the factorization criterion given in Theorem 9.4. THEOREM 9.4 Let U be a statistic based on the random sample Yı, Y2, ..., Yn. Then U is a sufficient statistic for the estimation of a parameter 0 if and only if the likelihood L(0) = L(y1, y2, ..., yn 10) can be factored into two nonnegative functions, L(y1, y2, ..., yn (0) = g(u,0) x h(yı, y2, ..., yn) where g(u,0) is a function only of u and 0 and h(y1, y2, ..., yn) is not a function of o.
The likelihood function can be factored using Theorem 9.4 as L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn), where g(Σⁿᵢ=1Xᵢ, p) = p^Σⁿᵢ=1Xᵢ (1-p)^(n-Σⁿᵢ=1Xᵢ) and h(X₁, X₂, ..., Xn) = 1. This satisfies the factorization criterion, and thus, Σⁿᵢ=1Xᵢ is a sufficient statistic for p.
To show that Σⁿᵢ=1Xᵢ is sufficient for p, we need to show that the likelihood function can be factored using Theorem 9.4 as:
L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn)
where g(Σⁿᵢ=1Xᵢ, p) is a function only of Σⁿᵢ=1Xᵢ and p, and h(X₁, X₂, ..., Xn) is not a function of p.
First, we can write the joint probability mass function of X₁, X₂, ..., Xn as:
P(X₁ = x₁, X₂ = x₂, ..., Xn = x_n) = p^Σⁿᵢ=1xᵢ (1-p)^Σⁿᵢ=1(1-xᵢ)
Taking the product of these probabilities for all i, we get:
L(p) = L(X₁, X₂, ..., Xn | p) = Πⁿᵢ=1P(Xᵢ = xᵢ) = p^Σⁿᵢ=1Xᵢ (1-p)^Σⁿᵢ=1(1-Xᵢ)
Using the factorization criterion given in Theorem 9.4, we need to find functions g(u, p) and h(X₁, X₂, ..., Xn) such that:
L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn)
Let's take g(u, p) = pᵘ(1-p)⁽ⁿ⁻ᵘ⁾, which only depends on u and p. Then:
L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn)
= p^Σⁿᵢ=1Xᵢ (1-p)^Σⁿᵢ=1(1-Xᵢ) * h(X₁, X₂, ..., Xn)
We can see that the term Σⁿᵢ=1Xᵢ appears in the exponent of p, and Σⁿᵢ=1(1-Xᵢ) appears in the exponent of (1-p). Therefore, we can write:
L(p) = L(X₁, X₂, ..., Xn | p) = [p^Σⁿᵢ=1Xᵢ (1-p)^Σⁿᵢ=1(1-Xᵢ)] * [1]
where the second factor is a constant function of p. This satisfies the factorization criterion, with g(u, p) = pᵘ(1-p⁽ⁿ⁻ᵘ⁾ and h(X₁, X₂, ..., Xn) = 1.
Therefore, we have shown that Σⁿᵢ=1Xᵢ is a sufficient statistic for p.
Learn more about probability here: brainly.com/question/30034780
#SPJ4
Complete question is in the image attached below
main Street tea company blends black tea that sells for $3.45 a pound with Earl Gray tea that sells for $2.15 a pound to produce 80 lb of mixture that they sell for $2.75 a pound how much of each kind of tea does the mixture contain rounding to the nearest pound
36.92 lbs. of the $3.45 tea and 43.08 lbs. of the $2.15 tea are needed.
Let x and y be the amount of tea that sells fo 3.45 and 2.15 a pound respectively:
x+y=80....................eq 1
3.45x+2.15y=2.75(80)......eq 2
:
rewrite eq 1 to x=80-y and plug that value into eq 2
:
3.45(80-y) +2.15y=2.75(80)
:
276-3.45y+2.15y=220
:
-1.3y=56
:
y=43.07 pounds of $2.15 tea
:
28x=80-43.07=36.93 pounds of $3.45 tea
Let a= the pounds of the more expensive tea needed
Let b= the pounds of the less expensive tea needed
(1) a+%2B+b+=+80
(2) 345a+%2B+215b+=+80%2A275 (in cents)
--------------------------
In words, (2) says.
(lbs of 'a' tea x price/lb) + (lbs of 'b' tea x price/lb) =
(lbs of mixture x price/lb of mixture)
-------
Multiply both sides of (1) by 215 and then.
subtract from (2)
345a+%2B+215b+=+80%2A275
-215a+-+215b+=+-80%2A215
130a+=+80%2A60
130a+=+4800
a+=+36.92
and, from (1)
(1) a+%2B+b+=+80
36.92+%2B+b+=+80
b+=+80+-+36.92
b+=+43.08
36.92 lbs. of the $3.45 tea and 43.08 lbs. of the $2.15 tea are needed.
Learn more about value
https://brainly.com/question/30145972
#SPJ1
The mixture contains 34 pounds of black tea and 46 pounds of Earl Gray tea.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations.
Let's denote the amount of black tea in pounds by "x" and the amount of Earl Gray tea in pounds by "y".
Since the total amount of mixture is 80 lb, we have:
x + y = 80 ----(1)
We also know that the mixture sells for $2.75 a pound, so the total revenue from selling 80 lb of mixture is:
80 x $2.75 = $220
On the other hand, the cost of the mixture is the sum of the costs of the black tea and the Earl Gray tea, which is:
3.45x + 2.15y
Since the company wants to make a profit, the revenue must be greater than the cost, so we have:
3.45x + 2.15y < $220
We can simplify this inequality by dividing both sides by 0.1:
34.5x + 21.5y < 2200 ----(2)
Now we have two equations with two unknowns (equations (1) and (2)), which we can solve using substitution or elimination.
Substitution method:
From equation (1), we have:
y = 80 - x
Substituting this into equation (2), we get:
34.5x + 21.5(80 - x) < 2200
Simplifying and solving for x, we get:
x < 34.5
Rounding x to the nearest pound, we get x = 34.
Substituting this value into y = 80 - x, we get y = 46.
Therefore, the mixture contains 34 pounds of black tea and 46 pounds of Earl Gray tea.
To learn more about algebraic expression from given link
https://brainly.com/question/19245500
#SPJ1
Question 1: 10 pts
A triangle has a base length of 2ac² and a height 6 centimeters more than the base
length. Find the area of the triangle if a = 4 and c = 2.
608 cm²
224 cm²
1,216 cm²
576 cm²
The area of the triangle with the given base and height where a = 4 and c = 2 is: 608 cm²
What is the Area of a Triangle?Area = 1/2(base)(height).
Given the parameters:
Base length = 2ac² cmHeight = 2ac² + 6 cmIf a = 4 and c = 2, then:
Area = 1/2(base)(height) = 1/2(2ac²)(2ac² + 6)
Area = 1/2(2 × 4 × 2²)(2 × 4 × 2² + 6)
Area = 1/2(32)(38)
Area = 608 cm²
Learn more about the area of a triangle on:
https://brainly.com/question/21735282
Consider the line that passes through the point and is parallel to the given vector. (4, -1, 9) ‹-1, 4, -2› symmetric equations for the line. -(x - 4) = y+1/ 4 = − z−9 /2 . (b) Find the points in which the line intersects the coordinate planes.
The symmetric equations of the line passing through a point and parallel to a vector are -(x - 4) = y + 1/4 = -(z - 9)/2. The line intersects the xy-, xz-, and yz-planes at (5, -9/4, 0), (15/4, 0, 23/2), and (0, -17/4, 11/2), respectively.
To find the symmetric equations of the line, we first need to find the direction vector of the line. Since the line is parallel to the vector <4, -1, 9>, any scalar multiple of this vector will be a direction vector of the line. So, let's choose the parameter t and write the vector equation of the line:
r = <4, -1, 9> + t<-1, 4, -2>
Expanding this vector equation component-wise, we get:
x = 4 - t
y = -1 + 4t
z = 9 - 2t
These equations can be rearranged to get the symmetric equations of the line:
-(x - 4) = y + 1/4 = -(z - 9)/2
To find the points in which the line intersects the coordinate planes, we substitute the corresponding variables with 0 in the equations for the line.
For the xy-plane, we set z = 0 and solve for x and y:
-(x - 4) = y + 1/4 = -(-9)/2
x = 5, y = -9/4
So, the line intersects the xy-plane at the point (5, -9/4, 0).
For the xz-plane, we set y = 0 and solve for x and z:
-(x - 4) = 0 + 1/4 = -(z - 9)/2
x = 15/4, z = 23/2
So, the line intersects the xz-plane at the point (15/4, 0, 23/2).
For the yz-plane, we set x = 0 and solve for y and z:
-(-4) = y + 1/4 = -(z - 9)/2
y = -17/4, z = 11/2
So, the line intersects the yz-plane at the point (0, -17/4, 11/2).
To know more about line intersection:
https://brainly.com/question/21445233
#SPJ4
Drag each tile to its equivalent measure, rounded to the nearest tenth.
Options: 19.8, 10.2, 22.7, 15.4
Measure Equivalent
4 in. _____ Cm
7 kg _____lb
6 gal _____L
65 ft _____ m
The correct matches are: 4 in. → 10.2 cm , 7 kg → 15.4 lb
6 gal → 22.7 L and 65 ft → 19.8 m.
What are conversions?Conversions refer to the process of changing a measurement from one unit to another unit that measures the same quantity.
For example, converting distance from miles to kilometers, or converting weight from pounds to kilograms.
Here are the conversions:
1 inch = 2.54 cm (approx.)
1 kg = 2.205 lb (approx.)
1 gal = 3.785 L (approx.)
1 ft = 0.3048 m (approx.)
Using these conversions, we can find the equivalent measures:
4 in. → 4 × 2.54 = 10.16 ≈ 10.2 cm
7 kg → 7 × 2.205 = 15.435 ≈ 15.4 lb
6 gal → 6 × 3.785 = 22.71 ≈ 22.7 L
65 ft → 65 × 0.3048 = 19.812 ≈ 19.8 m
To know more about equivalent measures visit:
https://brainly.com/question/29156458
#SPJ1
