Given the recursive formula below, what are the first four terms of the sequence?
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The sum of money that will amount to 5,200 in 6 years at the same rate at which #1706 amounts to #3412 in 20 years is 4000.

The rate of simple interest for changing 1706 to 3412 in 20 years is this:

S.I = PRT/100

Since the principal amount doubled, we can call this a 100% increase.

Thus the rate in 20 years

= 100/20

=5%

Since the rate for the principal amount is 5%, we can apply the same in the second sentence which gives us:

5% × 6

= 30%

5200 = 130%X

X = 520,000/130

= 4,000

So, the sum of money that will amount to #5200 in 6 years at the same rate of interest (simple) as the initial figures is 4000.

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A quadrilateral is a parallelogram if its adjacent angles are supplementary.

We are expected to demonstrate that a quadrilateral is a parallelogram if its adjacent angles are supplementary. Writing down what is given and needs to be supported will be our first step.

1) An ABCD quadrilateral is a given.

2) ∡A supplements ∡B, ∡B supplements ∡C, ∡C supplements ∡D and ∡D supplements ∡A.

To demonstrate: Parallelogram ABCD is a quadrilateral.

Consider AC and BD as evidence. The intersection of AC and BD is AB.

Two angles on the same side of the transversal AB are ∡A and ∡B.

A property states that two lines are parallel if a transversal cuts them and the interior angles on the same side of the transversal are additional.

Here, it is given that ∡A supplements ∡B.

⇒∡A+∡B=180∘

The lines AC and BD are therefore parallel to one another.

Now think about AB and CD. The intersection of AB and CD is AC.

Two angles on the same side of the transversal AB are ∡A and ∡D .

A property states that two lines are parallel if a transversal cuts them and the interior angles on the same side of the transversal are additional.

Here, it is given that ∡D supplements ∡A.

⇒∡A+∡D=180∘

The lines AB and CD are therefore parallel to one another.

Now, since both the pairs of opposite sides are parallel, ABCD is a parallelogram.

Hence proved.

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The required share of John in the profit is given as $8000. Option B is correct.

Given that,
John, Sally, and Jane form a partnership. They agree to distribute profits by paying Sally a $50,000 salary and distributing the balance using a 2:1:2 ratio respectively. Profits for the year are $70,000.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

here,
total profit = 70000
Sally is salary = 50000
remaining profit  = 70000 - 50000 = $20000
Now,
total share as of the proportions is 2 + 1 + 2 = 5

Jhon proportion for the share of the profit = 2 / 5
Now,
John share = 2 / 5 [20000] = $8000

Thus, the required share of John in the profit is given as $8000. Option B is correct.

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Answer:

Step-by-step explanation: you have to use the variables

Triangle ABD and Triangle CBD both are congruent by SAS relation when B is the midpoint of AC.

Given that,

B is the midpoint of AC.

What of the following best sums up the connection between triangles ABD and CBD.

We know that,

B is the midpoint of AC, so, AB=BC.

Here in Triangle ABD and Triangle CBD, we get,

1) AB=BC

2) BD common

3) Angle ABD= Angle DBC=90°(BD is perpendicular on AC on B point),

Therefore, Triangle ABD and Triangle CBD both are congruent by SAS relation when B is the midpoint of AC.

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The value of Warren Ford annuity due is $80,878.21

Define Future Value of an Annuity.

The future value of an annuity is the value of a group of recurring payments at a certain date in the future, assuming a particular rate of return, or discount rate. The higher the discount rate, the greater the annuity's future value.

Given,

Payment fund semiannually is = $1,700

Rate = 6% or 0.06

Time = 15 years

The future value is,

FVₙ =PMT( (1+i/m)ⁿ - 1 ) / (i/m) )

Where,

PMT = $1,700

i = 0.06

m = 2

n = 15 * 2 = 30 periods

Now, plug in the values

FV₃₀ =  PMT ( (1 + 0.06/2)³⁰ - 1 ) / (0.06/2) )

       = $1,700( (1.03)³⁰ - 1 ) / (0.03) )

       ≈ $80,878.2067 or $80,878.21

Hence, the value of Warren Ford annuity due is $80,878.21

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the minimum or lowest point for a curve or namely the U-turn, it'd be the same as saying the maximum and equally its U-turn, which is another name for its vertex.

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=z(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"z"~is~negative}{op ens~\cap}\qquad \stackrel{"z"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=7\\ k=-4 \end{cases} \implies y=z(x-7)^2 -4\implies y=z(x+\stackrel{\textit{\LARGE a}}{(-7)})^2 \underset{\textit{\LARGE b}}{-4}[/tex]

Answer:01:44 PM

Step-by-step explanation: Hope this helps!

Answer:

40

Step-by-step explanation:

let x = # of Qs on the test

0.85x = 34

x = 34/0.85 = 40

Answer:

y = [tex]\frac{-3}{2}[/tex] x + 2

Step-by-step explanation:

I can see the slight tracings of the slope triangle.  I can see that you went down 3 and right 2.  That would be a slope of [tex]\frac{-3}{2}[/tex] and the y intercept is 2.  That is where the line is crossing the y axis.

The required number of degrees is 86° Fahrenheit corresponds to 30° Celsius.

The formula is given in the question following as:

F = (9/5)C + 32 ....(i)

It can be used to convert between degrees Celsius (C) and degrees Fahrenheit (F).

We have to number of degrees Fahrenheit corresponds to 30° Celsius

As per the given question, we have

F = (9/5)C + 32

Substitute the value of C = 30 in the given formula, and solve for F

F = (9/5)(30) + 32

F = (270)/(5) + 32

F = 54 + 32

F = 86

Thus, the required number of degrees is 86° Fahrenheit corresponds to 30° Celsius.

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Answer: the answer is 86

Step-by-step explanation: I have my ways ;>

The account balance in her account will be $9675.30 after 12 years.

What is compound interest?

The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.

The formula of semi annual compound interest is

A = P [ 1 + r/n]^{nt}

P = principal

n =  number of period

t = time

r =  Rate of interest.

Given that Sandra open a bank account with $3000.

The semi annually compound interest is 10%.

She deposits it for 12 years.

Here P = 3000, n = 2, t = 12, r = 10% = 0.1

A = 3000 [ 1 + 0.1/2]^{24}

A = 9675.30

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Answer: Parallelogram

Step-by-step explanation: [Parallelogram definition]: A parallelogram is a quadrilateral with 2 pairs of parallel sides. In these figures, sides of the same color are parallel to each other. A shape with four sides of equal length.

To see a shape that is a parallelogram, look at the attachment down below:

Answer:

[tex]x = -1[/tex]

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Addition

Subtraction

~

First, subtract 12 from both sides of the equation:

[tex]10x + 12 = 2\\10x + 12 (-12) = 2 (-12)\\10x = 2 - 12\\10x = -10[/tex]

Next, divide 10 from both sides of the equation:

[tex]10x = -10\\\frac{(10x)}{10} = -\frac{(10)}{10}\\ x = -\frac{10}{10} = -1\\ x = -1[/tex]

[tex]\textbf {x = -1}[/tex] is your answer.

~

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X (the number that reach a live person) have a binomial distribution.

In this question we have been given when an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. You watch the random dialing machine make 15 calls, X is the number that reach a live person.

We need to state whether X have a binomial distribution.

20% of the calls reach a live person.

So, the probability that any individual call reaches a live person is 0.2

The sample size (n) = 15 calls

X represent the number of calls that actually reach a live person.

So there are 15 attempts, 15 calls that will attempt to reach a live person.

The probability that any one of those individual calls actually reaches a live person is 0.20 and X will represent the number out of those 15 calls that are placed actual represent the number of those calls that actually reached a live person.

Therefore, the X is a binomial random variable.

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the flow through a sphere of radius 3 that is centered at the origin and facing outward of the vector field F(x, Y, Z) = 2i - 4k.Flux = (4πr3)F = (4π3^3)(2*i - 4*k) = 216πi - 864πk

the flux of the vector field F(x, y, z) = 2i - 4k through the square of side 8 in the plane, centered on the -axis, with sides parallel to the and axes, both of which are pointed in the right direction.

Flux = Area*F = (8^2)*(2*i - 4*k) = 128i - 256k

To calculate the flux of the vector field F(x, y, z) = 2i - 4k through a square of side 8 in the plane, centered on the -axis, with sides parallel to the and axes, and oriented in the positive -direction, we will use the formula for flux:

Flux = Area*F

Where F is the vector field, and area is the area of the square, which is 8^2. As a result, the flux can be determined as follows:

Flux = (8^2)*(2*i - 4*k) = 128i - 256k

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6/11 is the probability that a randomly selected student speaks French, given that the student is male

It is a branch of mathematics that deals with the occurrence of a random event.

There are 11 members who speak french and 5 are females in 11 members

5/11

p(a given b) = p(a and b) / p(b).

6 of the people in the group are men that speak french, then the probability of (a and b) becomes 6/40

probability that a person speaks french is 11/40

p(a given b)=6/40/11/40

=6/40×40/11=6/11

Hence, 6/11 is the probability that a randomly selected student speaks French, given that the student is male.

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Answer:27,299

Step-by-step explanation:

The inequality represents all possible combinations of x roses and y carnations is 3x+2y≤30.

Different types of inequalities can be represented by a number of different notations. A relationship between two expressions or values that is not equal in mathematics is referred to as an inequality. To correct an inequality, take the following actions: Prior to subtracting any fractions, multiply each phrase by the sum of the least common denominators of all the fractions. Step 2: To make the inequality simpler, combine related terms on both sides. Step 3: To calculate the value of the unknown, subtract or add the amounts from the numbers on either side.

The cost of each rose flower is $3

The cost of each carnation is $2

The cost for x roses will be 3x$

The cost for y carnations will be 2y$

The overall cost must be less than or equal to $30

Therefore, 3x+2y≤30.

Hence, the inequality represents all possible combinations of x roses and y carnations is 3x+2y≤30.

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308.265 is the distance from the point A to point B.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

From point A, the boat's crew measures the angle of elevation to the beacon, 13°.

The height of the lighthouse is given as: h = 140

The distance between point A and the base of the lighthouse is calculated using the following tangent ratio

A=140/tan13=608.695

The distance between point B and the base of the lighthouse is calculated using the following tangent ratio

tan (25)= 140/B

B=140/tan25

=300.43

The distance AB, is then calculated as:

AB=A-B

=608.695-300.43

=308.265

Hence, the distance from point A to point B is 308.265 feet.

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The Median age for the Chess Club members is 14 and  the Median age for the Chess Club members is 12.

Option A. The Median age for the Chess Club members is less than the Median age for the Checkers Club members is the correct option of the given figure.

The value that, when a dataset is arranged, lies exactly in the middle is the median. The difference between the lowest 50% and highest 50% of data is a measure of central tendency. Depending on whether you have an odd or an even number of data points, there are several procedures to find the median.

Identifying the median The data points should be arranged from smallest to largest. The median is the middle data point in the list if the number of data points is odd. The median is the average of the two middle data points in the list if the number of data points is even.

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It's True because zero cannot divided by any number it is undefined.

In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as a/0, where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number that, when multiplied by 0, gives a (assuming a ≠ 0); thus, division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 is also undefined; when it is the form of a limit, it is an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a/0 is contained in Anglo-Irish philosopher George Berkeley's criticism of infinitesimal calculus in 1734 in The Analyst

It's True because zero cannot divided by any number it is undefined.

let us consider

x = 3

and y =0

x/y = 3/0 = undefined

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Answer:

---------------------------------------

Given inequality:

Divide both sides by -25:

the inequality of the number line will be -6<x<2.

What is number line?

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

In this number line the max point its marked is 2

and the minimum point is -6

So the value of unknown x should lie in between

-6<x<2

So, the inequality of the number line will be -6<x<2.

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0.6 gives the value of green cars 120 that is not possible in the problem,  0.6 can not be the probability of selected green car.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

total cars= 200

white cars= 100

red cars = 30

silver cars = 20

occupied space = 50+30+20 = 100

remaining space= 200- 100= 100

let number of green car in parking lot is 'x'

check every given probability of selecting a green car with x

according to question x <=(less than or equals to)100

p(prob. of green car) = x/200

a) 0.2

p=0.2

x/200= 0.2

x=0.2*200 = 40

b) 0

p=0

x/200=0

x= 0*200= 0

c) 0.1

p= 0.1

x/200 = 0.1

x= 0.1*200 = 20

d) 0.6

p = 0.6

x/200 = 0.6

x =0.6 * 200 =120

e) 0.5

p  = 0.5

x/200 = 0.5

x= 0.5*200 = 100

Hence,  0.6 gives the value of green cars 120 that is not possible in the problem,  0.6 can not be the probability of selected green car.

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Using De Moivre’s theorem, the complex number (1+i)¹⁸ simplifies to 512√2

For a complex number of the form z = a + ib, its polar form is written as:

z = r(cosθ + isinθ)

Where, r = √(a²+b²) and θ = tan⁻¹(b/a)

De Moivre’s theorem => (cos x + i sinx)ⁿ = rⁿ cos(nx) + i sin(nx)

Given: (1+i)¹⁸

To simplify (1+i)¹⁸, first needs to convert it into its polar form

z = 1 + i

r = √(1²+1²) = √2 and θ = tan⁻¹(1/1) = π/4

polar form:

z = √2 (cos(π/4) + isin(π/4))

Thus, (1+i)¹⁸ = [√2 (cos(π/4) + isin(π/4))]¹⁸

Using DeMoivre’s theorem, (cos x + i sinx)ⁿ = rⁿ cos(nx) + i sin(nx):

[√2 (cos(π/4) + isin(π/4))]¹⁸ = (√2)¹⁸ (cos(π/4) + isin(π/4))

                                            = 512 (cos(π/4) + isin(π/4))

                                            = 512 ((√2)/2 + (√2)/2)

                                            = 512(√2)

Therefore, (1+i)¹⁸ = 512√2

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Answer:

116

Step-by-step explanation:

42/100 (that's the percent) = 84/200

200-84=116

From the following obeservation done by Kate, the hypothesis that the population proportions is equal for all four locations is not true. Also, the population of male fish are not equal in all four locations and the p-value is greater than 0.10

A chi square ( χ2) test is performed in order to find a co relation between two unrelated variables. The main objective of the test is to prove whether the relationship holds true or is just a product of mere chance. For example, if we are conducting a survey of two different paramters, first being the population of people who are married and the other about their educational qualififcation, we will get two distinct table of values without any significant corelation. But now if we wnt to establish a relationship, lets say that married people have less educational qualifications, we need to prove our statement by performing a chi square test. The final value can either be a null hypothesis which states that their is no convinving relationship betwwen the two paramters or can be a alternate hypothesis with significant corelation.

For this problem lets focus on the male fish population alone and perform the test:

                                                       Population (Observed)

                              A                      B                    C                 D           TOT

Male fish                49                   44                   49               39           181

Female fish            41                    46                   36               44           167

                              90                   90                   85               83           348

                                                        Population(Expected)

Male fish                 46.81              46.81               44.20           43.16

Female fish              43.18             43.18               40.79           39.83

χ2 = ∑[tex]\frac{(Obsereved-Expected)^2}{Expected}[/tex];

=[tex]\frac{4.79}{46.81} +\frac{7.89}{46.81} +\frac{23.04}{44.20} +\frac{17.30}{43.16}[/tex]

= 0.10+0.16+0.52+0.40 = 1.18

Now to calculate degree of freedom= (coulmn-1)(row-1)= 3×1= 3.

Looking at the reference table at 0.05 significance level, the value shows 7.815

Thus as our value of 1.18 is less than the given value, null hypothesis cannot be rejected.

Hence the population proportions are not equal at all four locations. Whether this conclusive difference in gender proportions is due to varied contaminants cant be answered with this single observation and further tests are needed to be performed to construct a well found connection.

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Answer:

multiplying numerator by denominator, as in number times number equals = A = answer

Step-by-step explanation: