Suppose a certain amount of money is deposited into an account paying 4%, compounded annually. For each non-negative integer n, let S(n)= the total amount in the account after n years, and let S(0) be the initial amount deposited. (a) Find a recurrence relation for S(0),S(1),S(2),⋯ assuming no additional deposits or withdrawals for n years; provide your answer as a recurrence formula with base case. (b) If S0​=$5000, find the amount of money on deposit at the end of 4 years.

Answer:60

Step-by-step explanation:

An inequality that represents all possible values of x, the number of adoptions from the animal rescue group during the first week is x ≤ 10.

In order to write an inequality that represents all possible values of x, we would assign a variable to the number of adoptions, and then translate the word problem into algebraic equation as follows:

Let the variable x represent the number of adoptions.

Therefore, translating the word problem into an algebraic equation, we have the following;

For the first week, the number of adoptions is x while the number of adoptions during the second week was 10 more than number of adoptions in the first week (x + 10), with twice as many adoptions for the third week (2x), and a total of at least (≥) 50 adoptions during the three weeks.

Combining the expressions together, we have:

x + (x + 10) + (2x) ≤ 50

x + x + 10 + 2x ≤ 50

4x + 10 ≤ 50

4x ≤ 50 - 10

4x ≤ 40

x ≤ 40/4

x ≤ 10.

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Number of kids ticket is 40

What do you mean by system of linear equation?

A set of two linear equations with two variables is a system of linear equations. There are infinitely many possible solutions to a linear equation with two variables. There can be a single solution to a system of two linear equations with two variables that satisfies both solutions. It is necessary to combine two equations with two variables into one equation with one variable while solving a system of equations.

Total number of tickets = 60

Cost of 1 kid ticket = $3

Cost of 1 adult ticket = $5

Total profit = $220

Let number of kid tickets = x

number of adult tickets = y

According to question:

x + y = 60 ......(1)

3x + 5y = 220 ........(2)

Substitute the value of x from eq(1) to eq(2)

3(60 - y) + 5y = 220

180 - 3y + 5y = 220

180 + 2y = 220

2y = 220 - 180

2y = 40

y = 40/2

y = 20

Substitute this value of y in eq(1)

x + 20 = 60

x = 60 - 20

x = 40

Therefore, number of kids ticket is 40

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t approaches infinity then salt is:

[tex]Q(\infty) = 18lb[/tex]

What is volume?

Volume is a mathematical term used to describe how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. Volume is sometimes referred to as capacity.

The amount of salt in the barrel at time t is given by

where Q(t) is in pounds and time t is in minutes.

(a) Salt after 5 minutes i.e. t=5

[tex]Q(5) = 18(1 - e^{-0.08(5)} ) = 18(1 - e^{-0.4})\\\\Q(5) = 18(1 - 0.6703) = 5.93 \\\\Q(5) = 5.93lb[/tex]

(b) Salt after 10 minutes i.e. t=10

[tex]Q(10) = 18(1 - e^{-0.08(10)} ) = 18(1 - e^{-0.8} )\\\\Q(10) = 18(1 - 0.4493 ) = 9.91\\\\Q(10) = 9.91lb[/tex]

(d) When t becomes large, let say when t approaches infinity then salt is

[tex]Q(\infty) = 18(1 - e^{-0.08(\infty)} ) = 18(1- e^{-\infty})\\\\Q(\infty) = 18(1 - 0) = 18\\\\Q(\infty) = 18lb[/tex]

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Angle of the ladder with the floor is 74.5°.

We have given that,

base of the ladder from the wall, x₀ = 2.70 m

top of the ladder above the floor y = 5.13 m

speed of the spaceship = 0.85 c

and we have to find the angle ladder makes with the floor, θ.

From the given information we will construct a diagram.

From the diagram,

tanθ = y/x₀

tanθ = y / x₀√(1- V^2 / c^2)

we will substitute all the values,

tanθ = 5.13 / 2.70√(1-((0.85c)^2 / c^2))

        = 5.13 / 2.70√(1-(0.85^2))

        = 5.13 / 2.70√(1 - 0.7225)

        = 5.13 / 2.70√0.2775

        = 5.13 / 1.4223

tanθ = 3.606

    θ = tan⁻¹(3.606)

    θ = 74.5°

Therefore angle the ladder makes with the floor is 74.5°.

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Answer:

x^2+16x+64

Step-by-step explanation:

(x+8)^2 is (x+8)(x+8)

This equals x^2+8x+8x+64=x^2+16x+64

The smallest number is 27 and the greater number is 39 when  the smaller number is 15 more than the larger number twice.

Given that,

The smaller number is 15 more than the larger number twice.

We have to find what are the two numbers whose sum is 66.

We know that,

Let x = big number

Let y = small number

x + y = 66---->equation(1)

2y = x + 15---->equation(2)

We have to dins the x and y values

x+(x+15)/2=66

2x+x+15=66×2

3x+15=132

3x=132-15

3x=117

x=117/3

x=39

We take equation 2 and substitute x as 39

2y=x+15

2y=39+15

2y=54

y=54/2

y=27

Therefore, The smallest number is 27 and the greater number is 39 when  the smaller number is 15 more than the larger number twice.

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The least possible area is 0 meter² and the greatest possible area is 49.5metre².

With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object.

A rectangle has equal and parallel opposing sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's length is its longer side, while its width is its shorter side.

A little information

1) Parallelograms are all squares, yet squares are all not parallelograms

2) A rectangle is divided into four triangles by its diagonals.

3) While not all rectangles are squares, all squares are rectangles.

How to solve?

Area of rectangle is given by = length × breadth.

For minimum area, we have one digit whole number.

In whole number smallest digit is 0

so, least possible area =0×breadth=0 metres²,

Now talking about maximum possible area, the greatest one digit whole number is 9.

width of rectangular region is 5.5 meters.

The greatest possible area is =9×5.5=49.5meters².

Hence, the answers are 0 and 49.5 meters².

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(Complete question) is:

A landscaper digs a rectangular region for a garden. The length is a one digit whole number of meters and width is 5.5 meters. What is the least possible area? What is the greatest possible area?

Answer:

x less than or equal to $75 + $8

Step-by-step explanation:

itll look like this

x <= 75   + 8

x is the price of the hoodie

u can pay for a hoodie that will be under $75 including shipping

Answer:125

Step-by-step explanation:

Consta8of proportionality is 1/9

The median will be greater than 10 and less than 15.

Given,

The mean of the skewed distribution = 15

The mode of the skewed distribution = 10

We have to find the potential range of the median for a positively skewed distribution;

Here,

The empirical relationship between mean, median, and mode for a frequency distribution that is positively skewed is mean > median > mode. Based on this, the range of the median is 15 > median > 10 if the mean is 15 and the mode is 10.

Therefore,

The median will  be higher than 10 and lower than 15.

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The quadratic function which models the motion of the penny is

h(t) = -4.9t² -0.327761 t + 52.6  

and the maximum height reached is 57.43

h(t) = - 0.5gt² + vt + h

g = 9.8 m/s²

h = 52.6 m

v = ?

For v,

h(t) = -0.5gt² + vt + 52.6

h(t) = - 4.9t² + vt + 52.6

Time when penny hits the ground ; t = 3.31

h(3.31) = 0

0 = -4.9(3.31)² + v(3.31) + 52.6

0 = -53.68489 + 3.31v +52.6

3.31v = -1.08489

v = -1.08489/3.31

v = -0.327761 m/s

Therefore,

h(t) = -4.9t² -0.327761 t + 52.6

2.) Maximum height of the penny above the ground

t = 0.85 seconds

h(0.85) = -4.9(0.85^2)-0.327761 (0.85) + 52.6

Maximum height reached =  57.43 meters

Therefore, the maximum height reached is 57.43 meters.

An object changing its position with regard to time is referred to as motion. Motion is mathematically characterised in terms of displacement, distance, velocity, acceleration, and speed as well as the observer's frame of reference and the measurement of the change in the body's position with respect to that frame over time. Kinematics is the area of physics that studies how motion is affected by forces, whereas dynamics is the area that studies how motion is affected by forces.

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The response variable in this study is

Yield of crop.

"Information available from the question"

In the question:

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil.

Now, According to the question:

Let's know:

What is called fertilizer?

A fertiliser is a natural or artificial substance containing chemical elements (such as Nitrogen (N), Phosphorus (P) and Potassium (K)) that improve growth and productiveness of plants. Some synonyms include the terms "enrichment" or "plant nutrient".

The answer is:

Yield of crop.

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The complete question is this:

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. The response variable in this study is

Answer:

Step-by-step explanation:

You want the acute angles in a right triangle in which the larger is 8 times the smaller.

The ratio of the acute angles in the triangle is 1 : 8, so the smaller one is 1/(1+8) = 1/9 of the sum of the two angles.

The sum of the acute angles in a right triangle is 90°, so the smaller one is ...

  (1/9)(90°) = 10°

The larger is 8 times that:

  8 × 10° = 80°

The smaller angle is 10°; the larger angle is 80°.

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Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after

At a standard deviation of $15,000, the probability that the condominium will sell at a price below $200,000 is 0.2525 and above $240,000 is 0.02. At a standard deviation of $20,000, the probability that the condominium will sell at a price below $200,000 is 0.3085 and above $240,000 is 0.0668.

From the given question;

Let the average sale price(μ)=210,000

Standard Deviation(σ)=$15,000

(a) We have to find the probability that the condominium will sell at a price.

(i) below $200,000, i.e. P(x<200,000)

Z=(x−μ)/σ

Z=(200,000−210,000)/15,000

Z= −10,000/15000

Z= −0.67

Now finding P(x<200,000) is same as finding P(Z<−0.67) using the standard table of z.

P(Z<−0.67) = 0.2525

(ii) above $240,000, i.e. P(x>240,000)

Z=(x−μ)/σ

Z=(240,000−210,000)/15,000

Z= 30,000/15000

Z= 2

Now finding P(x>240,000) is same as finding P(Z>2) using the standard table of z.

P(Z>240,000)=P(Z>2)

P(Z>240,000)=1−P(Z<2)

P(z>240,000)=1−0.98

P(z>240,000)=0.02

(b) Now the average sale price(μ)=210,000

Standard Deviation(σ)=$20,000

We have to find the probability that the condominium will sell at a price.

(i) below $200,000, i.e. P(x<200,000)

Z=(x−μ)/σ

Z=(200,000−210,000)/20,000

Z= −10,000/20000

Z= −0.5

Now finding P(x<200,000) is same as finding P(Z<−0.5) using the standard table of z.

P(Z<−0.5) = 0.2085

(ii) above $240,000, i.e. P(x>240,000)

Z=(x−μ)/σ

Z=(240,000−210,000)/20,000

Z= 30,000/20000

Z= 1.5

Now finding P(x>240,000) is same as finding P(Z>1.5) using the standard table of z.

P(Z>240,000)=P(Z>1.5)

P(Z>240,000)=1−P(Z<1.5)

P(z>240,000)=1−0.93319

P(z>240,000)=0.0668

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The probabilty that the first card is 7 and the second card is 6 numbered would be 0.0059.

What is probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

It is given that there is a deck of 52 cards.

So sample space (n) = 52.

Now in the first draw, 7 numbered card should be drawn

and there are four 7 numbered cards in a deck of 52 cards

so probability of drawing a 7 numbered card will be = 4/52 = 2/26

Now in the second draw, 6 numbered cards should be drawn

and there are four 6 numbered cards in a deck of 52 cards but already one card is drawn so there will be 51 cards remaining in the deck.

so probability of drawing a 6 numbered card will be = 4/51

Hence the probability that the first card is 7 and the second card is 6 numbered will be = 2/26 * 4/51

                             = 0.076 * 0.078

                             = 0.0059

Hence, the probabilty that the first card is 7 and the second card is 6 numbered would be 0.0059.

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Answer:

Step-by-step explanation:

12 root 6 is the answer because the 3 root 8 can be simplified to 6 root 2, so you when you multiply 2 root 3 with 3 root 8, you get 12 root 6.

Answer:

[tex]12\sqrt{6}[/tex]

Step-by-step explanation:

Given expression:

[tex]2 \sqrt{3} \cdot 3 \sqrt{8}[/tex]

Multiply the numbers 2 and 3:

[tex]\implies 6\sqrt{3}\sqrt{8}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]

[tex]\implies 6\sqrt{3 \cdot 8}[/tex]

Simplify:

[tex]\implies 6\sqrt{24}[/tex]

Rewrite 24 as 4 · 6:

[tex]\implies 6\sqrt{4 \cdot 6}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 6\sqrt{4}\sqrt{6}[/tex]

Rewrite 4 as 2²:

[tex]\implies 6\sqrt{2^2}\sqrt{6}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies 6 \cdot 2 \sqrt{6}[/tex]

Multiply the numbers 6 and 2:

[tex]\implies 12 \sqrt{6}[/tex]

Answer:

Step-by-step explanation:

Answer= use 2 eggs per 1 cup of flour to make 1 serving.

Answer:

Step-by-step explanation:

i don't think so

The minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738

A company's unit cost is the cost of producing, storing, and selling one unit of a specific product. Unit costs encompass all fixed and variable production costs. A cost unit is a quantity measuring unit for a product or service.

A unit cost is the overall cost incurred by a business to manufacture, store, and sell one unit of a specific product or service. Unit costs are the same as cost of goods sold (COGS). This accounting metric incorporates all fixed and variable expenses related with the manufacture of a good or service.

Given,

C(x)=1.2x²-600x+82,738

Minimum value [tex]C_{min}[/tex]=c-(b²/4a)

Where a=1.2, b=-600, c=82738

[tex]C(x)_{min}[/tex]=82738-((-600)²/4(1.2))

=82738-(360000/4.8)

=7738

Therefore, the minimum unit cost is 7738.

Hence, the minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738

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The area of the part of the plane 2x+y+2z=4 in the first octant is S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\frac{3}{2}dydx[/tex].

In the given question we have to check which of the following integrals represents the area of the part of the plane in the first octant.

The given plane is 2x+y+2z=4 that lies in the first octant.

In the first octant the all variables are positive.

First we need to find the equation of hypotenuse in the linethat intersects xy plane means z=0. So:

2x+y=4

y=4-2x

Now find the surface area. We need the function in the form of z=f(x,y). So:

2x+y+2z=4

2z=4-2x-y

z=(4-2x-y)/2

On taking the partial derivative we get

f(x) = -1 and f(y) = -1/2

Now the defining the limits will be;

0≤x≤2 and 0≤y≤ (-2x+4)

So the area will be;

S= [tex]\int \int _{D}\sqrt{f(x)^{2}+f(y)^{2}+1}dydx[/tex]

S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\sqrt{(-1)^{2}+(-1/2)^{2}+1}dydx[/tex]

S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\sqrt{1+1/4+1}dydx[/tex]

S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\sqrt{(4+1+4)/4}dydx[/tex]

S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\sqrt{9/4}dydx[/tex]

S= [tex]\int_{0}^{2}\int_{0}^{-2x+4}\frac{3}{2}dydx[/tex]

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Answer:

x^2 + 10

Step-by-step explanation:

From the given Venn diagram, the value of  M∩N={4,7}.

A Venn diagram is a prominent diagram type that depicts the logical relationship between sets. It was popularized in the 1880s by John Venn (1834-1923). The diagrams are used to teach elementary set theory and to show simple set relationships in probability, logic, statistics, linguistics, and computer science. To depict sets, a Venn diagram uses basic closed curves drawn on a plane. These curves are almost often circles or ellipses.

Before Venn, similar concepts had been presented. Similar ideas were proposed by Christian Weise in 1712 and Leonhard Euler (Letters to a German Princess) in 1768. Venn popularized the concept in Symbolic Logic, Chapter V "Diagrammatic Representation," 1881.

The intersection of two sets is the set of all the elements that are shared by both.

M={4,7,9,3}

N={4,7,6}

Because M and N share the numbers 4 and 7, M∩N={4,7}.

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Answer:

attached in the file

The sampling technique used in the given scenario is Systematic sampling technique.

Systematic sampling technique

Systematic sampling is a probability sampling technique in which researchers randomly choose individuals of a population at regular intervals. The sampling interval, or fixed periodic interval, is calculated by dividing the population size by the required sample size.

Types of Systematic sampling technique

A systematic sample can be generated in three ways:

Systematic random sampling: The most common type of systematic sampling in which the subject is chosen at a predefined interval.

Linear systematic sampling: Instead of picking the sample interval at random, a skip pattern is constructed by following a linear path.

Circular systematic sampling: It occurs when a sample begins from the same spot where it ends.

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The equation that can be used to describe g(x) in terms of f(x), considering the transformations, is given as follows:

A. g(x)=-f(x+2)+1.

From the image given at the end of the answer, the function f(x) is given as follows:

f(x) = x².

The transformations to obtain function g(x) are given as follows:

Meaning that option A gives the correct option to describe the function g(x) as a function of the function f(x).

The functions are given by the image presented at the end of the answer.

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The solution of the equations 3x - 5y = 15 and x - 4y = 12 will be (0, -3).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of equations is given below.

3x - 5y = 15         ...1

x - 4y = 12          ...2

From equation 2, then we have

x = 4y + 12  

Put in equation 1, then we have

3(4y + 12) - 5y = 15

12y + 36 - 5y = 15

7y = -21

y = - 3

Then the value of the variable 'x' is calculated as,

x = 4(-3) + 12

x = - 12 + 12

x = 0

The solution of the equations 3x - 5y = 15 and x - 4y = 12 will be (0, -3).

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V = 4/3 r3, where V is the volume and r is the radius, is the formula for a sphere's volume. A sphere's radius is equal to half of its diameter.

Given data :

radius = 3x²

volume of sphere =  V = 4/3 π r³

v = 4 x π x (3x²)[tex]{3}[/tex] / 3

= 4π.[tex]x^{5}[/tex]

volume of cube = side3

= (x²)[tex]^{3}[/tex]

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