Two hens can lay 2 eggs in 2 minlutes if that is the maximum speed how many hens can lay 500 eggs in 500 minutes

Answer:

Step-by-step explanation:

To find the equation for the nth term in the sequence, we need to determine the pattern or rule that generates the sequence.

From the given information, we can see that the sequence is not arithmetic because the differences between consecutive terms are not constant. Instead, the sequence appears to be quadratic because the second difference between consecutive terms is constant.

Using the given values of a₁, a₃, and a₅, we can find the first few differences:

a₃ - a₁ = 4 - (-6) = 10

a₅ - a₃ = 14 - 4 = 10

So, the first difference is 10, which indicates a linear term in the equation for an. We can now use the given value of a₁ and the first difference to find the constant term in the quadratic equation. Let d be the common difference, then we have:

a₂ = a₁ + d = -6 + 10 = 4

a₄ = a₃ + d = 4 + 10 = 14

a₆ = a₅ + d = 14 + 10 = 24 - 1

a₇ = a₆ + d = 24 - 1 + 10 = 33

Now, we can find the second difference between consecutive terms:

a₄ - 2a₃ + a₂ = 14 - 2(4) + (-6) = 0

a₆ - 2a₅ + a₄ = 19 - 2(14) + 4 = -5

a₇ - 2a₆ + a₅ = 33 - 2(19) + 14 = 9

Since the second difference is constant (-5), this confirms that the sequence has a quadratic term in its equation. Let's assume the equation for the nth term is:

an = an² + bn + c

Substituting the values we know, we get three equations:

a₁ = a₁² + b₁ + c --> -6 = c

a₃ = a₃² + b₃ + c --> 4 = 9a + b + c

a₅ = a₅² + b₅ + c --> 14 = 25a + 5b + c

Solving this system of equations, we get:

a = 1/2, b = 19/2, and c = -6

Therefore, the equation for the nth term in the sequence is:

an = (1/2)n² + (19/2)n - 6.

Answer:

c=(1,9,5,13)

D={5,11,1)

The set that represents the subset of the set U will be {1, 9, 5, 13} and {5, 11, 1}. Then the correct option is C and D.

Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

If every member of set A is also a component of set B, then set B is a superset of set A, and set A is a subset of set B. A and B might be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of some other.

The set is given below.

U = {1, 3, 5, 9, 11, 13}

Let's check all the options, then we have

A = {0}, the set does not have an 0 number. So, it is not a subset.

B = {2, 4}, the set does not have an even number. So, it is not a subset.

C = {1, 9, 5, 13}, the set has an odd number. So, it is a subset.

D = {5, 11, 1}, the set has an odd number. So, it is a subset.

E = {2, 3, 4, 5}, the set does not have an even number. So, it is not a subset.

The set that represents the subset of the set U will be {1, 9, 5, 13} and {5, 11, 1}. Then the correct option is C and D.

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The simplified expression of the radical expression ∛135a¹³ is (135a¹³)¹/³

From the question, we have the following parameters that can be used in our computation:

A radical expression

The radical expression is given as

\sqrt[3]{135^{a13}}

Represent the expression properly

So, we have the following representation

∛135a¹³

Apply the exponent rule of indices

This gives

∛135a¹³ = (135a¹³)¹/³

135 and a¹³ are not perfect cube root expressions

This means that the expression cannot be further simplified

Hence, the solution is (135a¹³)¹/³

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An investment of $6,400 to increase to $14,000 if it is invested at 5% per year compounded continuously is ≈15.6

Define compound interest?

Given that :

P = $ 6,400

Q = $ 14,000

r = 5%

Let P be the initial investment

r be the rate of interest

t be the time

Q be the increase amount

Q = P \(e^{rt} }\)

14,000 = 6,400 (\(e^{0.05t}\))

\(e^{0.05t}\) = \(\frac{14000}{6400}\)

\(e^{0.05t}\)  = 2.187

Taking log on both sides , we get

0.05t = ln (2.187)

0.05t = 0.78

       t = \(\frac{0.78}{0.05}\)

       t ≈ 15.6

An investment of $6,400 to increase to $14,000 if it is invested at 5% per year compounded continuously is ≈ 15.6

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Based on a system of equations, a pound of apples costs $0.89.

A system of equations is two or more equations solved at the same time or concurrently.

A system of equations is also referred to as simultaneous equations.

                    Apples     Pears     Total Cost

Janice              2              3             $3.85

Lisa                  4              2             $4.94

Let the cost of a pound of apples = x

Let the cost of a pound of pears = y

2x + 3y = 3.85 ... Equation 1

4x + 2y = 4.94 ... Equation 2

Multiply Equation 1 by 2:

4x + 6y = 7.7 ... Equation 3

Subtract Equation 2 from Equation 3:

4x + 6y = 7.7

-

4x + 2y = 4.94

4y = 2.76

y = 0.69

Substitute y = 0.69 in Equation 1 or 2:

4x + 2y = 4.94

4x + 2(0.69) = 4.94

4x + 1.38 = 4.94

4x = 3.56

x = 0.89

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The correct statement regarding the inverse function of f(x) = 4x^4 is given as follows:

\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\); f^(-1)(x) is not a function.

The function in this problem is defined as follows:

f(x) = 4x^4.

To obtain the inverse of a function y = f(x), first the variables y and x are exchanged, as follows:

x = 4y^4.

Isolating the variable y, we have that:

y^4 = (x/4).

The inverse operation of the fourth power is the fourth root, hence:

\(y = \pm \sqrt[4]{\frac{x}{4}}\)

\(f^{-1}(x) = \pm \sqrt[4]{\frac{x}{4}}\)

\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\)

The plus/minus symbol means that for each input of x, the inverse function gives two outputs, meaning that there are multiple outputs mapped to each input, and thus the inverse is not a function.

This means that the second statement is correct.

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Answer:

The correct option is A. Parallel line.

Answer: \(x^4-x^3-16x^2+16x\)

Step-by-step explanation:

Factor theorem : If x=a is a zero of a polynomial p(x) then (x-a) is a factor of p(x).

Given: Zeroes of polynomial : -4,0, 1, and 4.

Then Factors = \((x-(-4)), (x-0), (x-1) and (x-4)\)   [By factor theorem ]

\(=(x+4), (x-0), (x-1) and (x-4)\)

Multiplying these factors to get polynomial in standard form.

\((x+4)\times(x-0)\times(x-1)\times(x-4) \\\\= x(x+4)(x-4)(x-1)\\\\= x(x^2-4^2)(x-1)\\\\= x(x^2-16)(x-1)\\\\= x(x^2-16)(x-1)\\\\=x(x^2x+x^2\left(-1\right)+\left(-16\right)x+\left(-16\right)\left(-1\right))\\\\= x(x^3-x^2-16x+16)\\\\=x^4-x^3-16x^2+16x\)

Hence, B is the correct option.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

(5,0)

»»————-　★　————-««  

Here’s why:  

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

From Mark studies of a parallelogram and discovering that the slope of the diagonals are 5/3 and -3/5 the conjecture that can be made is

The diagonals are perpendicular to each other

The two different lines that cross each other at a 90° angle are called perpendicular lines.

If two lines intersect at a 90 degree angle, we say that the two lines are perpendicular.

Perpendicular lines have a feature which relates with the slope of the line as being a negative reciprocal

In the context of the given problem,

diagonal 1 has slope 5/3, the negative reciprocal is -3/5.

Since the two diagonals posses this relationship they are said to be parallel

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the Equation A. r²+ y² = 5 degenerate the circle.

The circumference, which is the distance around the object, the diameter, which is the length of a circle measured from one end to the other and passing through its center, and the radius, which is equal to half of the diameter, are the three key characteristics.

The general coordinate equation of a circle is:

(x-h)² + (y - k)² = r²

Where,

(h, k) is the center of a circle,

"r" is the radius of the circle.

Only option A, r²+ y² = 5

Satisfies the general equation of the line,

thus, From option A the coordinates of the circle on the plane r-y

is (0, 0) and the radius of the circle will be √5.

From option B,  x+y=7

It is the equation of the line.

From option C, x² + y² = -2

The sum of two squares can not be negative so it is not a real equation

From equation D, (x - 5)²+(y - 3)² = 0

The radius of a circle can not be zero otherwise it will become a point.

therefore, the Equation A. r²+ y² = 5 degenerate the circle.

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Complete question:

Which of the following is a degenerate circle?

O A. r²+ y² = 5

O B. x+y=7

O c. x² + y² = -2

O d. (x - 5)²+(y - 3)² = 0

Answer:

80%

Step-by-step explanation:

To write 4/5 as a percent have to remember that 1 equal 100% and that what you need to do is just to multiply the number by 100 and add at the end symbol %. 4/5 * 100 = 0.8 * 100 = 80% And finally we have: 4/5 as a percent equals 80%

Answer:

0.80

Step-by-step explanation:

1/5=0.20

1/5×4=0.80

Answer:

\(x - 3 = 13 \\ \\ x = 13 + 3 \\ \\ x = 16\)

-3 goes to other side and changes into +3

A la sala de cine ingresaron 180 niños y 165 adultos.

De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:

3 · x + 5 · (345 - x) = 1365

Donde x es el número de niños que asistieron a la sala de cine.

Ahora despejamos la variable correspondiente mediante propiedades algebraicas:

3 · x + 1725 - 5 · x = 1365

1725 - 2 · x = 1365

2 · x = 1725 - 1365

2 · x = 360

x = 180

Ahora, el número de adultos es:

y = 345 - 180

y = 165

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The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

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Answer: The probability that both events A and B will occur is 5/18 or 0.28.

Step-by-step explanation:

To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.

Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.

Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.

To find the probability that both events A and B occur, we multiply the probabilities:

Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.

9514 1404 393

Answer:

  58

Step-by-step explanation:

The marked points on the graph show that the number of hot cocoas sold decreases by 6 when the temperature goes up by 6 degrees. That is, the line has a slope of -1. The y-intercept is 100, so the equation of the line can be written as ...

  y = mx +b . . . . . line with slope m and y-intercept b

  y = -x +100

Then for x = 42, the expected value of y is ...

  y = -42 +100 = 58

Mei Mei can expect to sell 58 hot cocoas on a day when the high is 42°F.

Layla needs 1.75 cups of blueberries to make 6 muffins.

The utilization of two or more additional numbers that compares is known as the ratio.

If 24 muffins require 7- cups of blueberries, then the equation we can be given as,

24/7 = 6/x

24/7 = 6/x

24x = 42

x = (42)/24

x = 1.75

Therefore, Layla needs 1.75 cups of blueberries to make 6 muffins.

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Answer:

x = 11/3 or in decimal form x =3.6

Step-by-step explanation:

Based on the given information, we have a square pyramid with points M and N being the midpoints of the edges of one face. and forms a parallelogram. Option D

Since the base of the pyramid is a square, the cross section will consist of a square shape. Additionally, since the slice is made through the midpoints of the edges of the face, the resulting cross section will have parallel sides.

Considering these characteristics, we can conclude that the shape of the resulting cross section is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel. In this case, the opposite sides of the square cross section will be parallel, as the slice passes through the midpoints of the edges.

Therefore, the correct answer is D. parallelogram.

It's important to note that a triangular prism is not the correct answer because a triangular prism is a three-dimensional figure with two triangular bases and three rectangular faces. The cross section resulting from the given slice will not have the characteristics of a triangular prism. Option D.

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Answer:

\(x = 52\)

Step-by-step explanation:

Step 1:  Create an expression

\(2x + 76 = 180\)

Step 2:  Subtract 76 from both sides

\(2x + 76 - 76 = 180 - 76\)

\(2x = 104\)

Step 3:  Divide both sides by 2

\(\frac{2x}{2} = \frac{104}{2}\)

\(x = 52\)

Answer: \(x = 52\)

Answer:

x = 52

Step-by-step explanation:

the 2 inside angles add up to 180 degress since they lie on the same side on the transversal line. so we set the eqaution up:

2x+76=180

2x=104

x=54

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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According to the given data we have the following equation:

11² - 11 = 0​

To factor the expression above we would make the following:

First we would calculate exponents 11^2

Finally we would add and substract from left to right 121-11

So:

Hence, the expression factorized would be the result of 110

Answer:

-9 is less than x, which is less than or equal to 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Domain is where the function exists for x.

The functions domain goes in terms of x goes from -9 to 11 not including -9 and including 11.

Interval notation:

-9 < x ≤ 11

Set notation:

(-9, 11]

With constant of proportionality=2, the direct proportion equation for the given information is m = 2n.

What is a constant of proportionality?

A constant of proportionality is a value that relates two variables that are directly proportional to each other. In a direct proportion, if one variable (say, x) increases by a certain factor, then the other variable (say, y) also increases by the same factor. The constant of proportionality is the ratio of the two variables.

For example, if y varies directly with x, we can write:

y = kx

where k is the constant of proportionality.

Now,

If m varies directly as n, then we can write:

m = k * n

where k is a constant of proportionality. To find the value of k, we can use the given information that m = 14 when n = 7:

14 = k * 7

Solving for k:

k = 14/7

k = 2

Substituting this value of k in the direct proportion equation:

m = 2n

Therefore,

                the direct proportion equation for the given information is m = 2n.

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The following can be determined about the slopes and y-intercepts of the system of equations: A. The slopes are different, and the y-intercepts are different.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we have the following system of equations in standard form:

4x + 2y = −2

x − 3y = 24

By rewriting system of equations in slope-intercept form, we have:

y = -2x - 1  ⇒ m = -2, b = -1

y = x/3 - 8  ⇒ m = 1/3, b = -8

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1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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Answer:

10

Step-by-step explanation:

2x^2-x-5= 2x^2-6x + 5x -15 +10= 2x(x-3) +5(x-3) + 10= (2x+5)(x-3) + 10

(2x^2-x-5)/(x-3)= 2x+5 + 10/(x-3)

So the remainder is 10​

Answer:

30%

Step-by-step explanation:

500 divided by 100=50

50x3=30

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