The nth term of a sequence is n²+20
a) Work out the first three terms of the sequence.?
b) How many terms in the sequence are less than 50 ?

The solution is

a) The amount Connor has to pay for parking if he left his car for y hours is given by the equation A = 8 + 2y where y is the number of hours

b) The amount Connor has to pay for parking if he left his car for t hours is given by the equation B = 8 + 2t where t is the number of hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Let the second equation be represented as B

Now , the value of A is

The automatic fee for parking = $ 8

The additional fee for parking every hour = $ 2

So , for x number of hour , the additional parking fee = 2x

And , the total parking fee including x hours = automatic fee for parking + additional parking fee

Substituting the values in the equation , we get

The total parking fee including x hours = 8 + 2x

Now , when x = y hours

The total parking fee including y hours A = 8 + 2y

And , when x = t hours

The total parking fee including t hours B = 8 + 2t

Hence , the equations are A = 8 + 2y and B = 8 + 2t where y and t are number of hours

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Option 1: An initial investment of $5 that increases by 50% every year

as after 20 years, it amounts to a greater value.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

The given situations can be modeled as a geometric sequence.

Option A :

a₁ = 5, r = 1.5.

We know Sₙ = a₁(rⁿ - 1)/(r -1).

Sₙ = 5(1.5ⁿ - 1)/(1.5 - 1).

Sₙ = 5(1.5ⁿ - 1)/(0.5).

Let us see for n = 20, 20th year.

S₂₀ = 5(1.5²⁰ - 1)/(0.5).

S₂₀ = 5(3324.25)/(0.5).

S₂₀ = 33242.5.

Option B :

a₁ = 0.01 and r = 2.

Sₙ = 0.01(2ⁿ - 1)/(1).

S₂₀ = 0.01(2²⁰ - 1)/(1).

S₂₀ = 10,485.75

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The probability of selecting chocolate such that:

(a) both have cherry centers: 0.1630

(b) one has a cherry center and one does not: 0.507

In this question, we have been given a box of chocolates contains 24 chocolates.

n(S) = 24

Ten of the chocolates with cherry centers.

n(A) = 10

So, the number of chocolates with no cherry centers are:

n(B) = 14

We need to find the probability of selecting chocolate such that

(a) both have cherry centers

P = (10/24)(9/23)

P = 90/552

P = 15/92

P = 0.1630

(b) one has a cherry center and one does not

P = 2*(10/24)(14/23)

P = 0.507

Therefore, the probability of selecting chocolate:

(a) both have cherry centers

P = 0.1630

(b) one has a cherry center and one does not

P = 0.507

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Answer:

13

Step-by-step explanation:

The box plot ends at 13.

Box plots show the average score of the data. It shows the minimum, median and maximum. The line inside the box is the median. The minimum, in this case is 0 and the max is 13.

Answer:

Step-by-step explanation:

P = 4 a

a = √p^2 + q^2 / 2

P = 2√p^2 + q^2 = 2 x √42^2 + 40^2 = 116cm

∴ the perimeter of a rhombus when the diagonals are 42cm and 40cm is 116cm

The expression that represents the amount of money Angel would have savings in w weeks is 30+8w

The total amount of money saved after 5 weeks is $70

Which algebraic expression is required for Angel's total savings?

Total savings=30+8w

Now by substituting 5 , the number of weeks for w, we can determine total savings after 5 weeks

total savings=30+(8*5)

total savings=30+40

Total savings=$70

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The following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.

Given :

the values f ( x ) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1.

Function :

In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Every function has a domain and a co - domain.

x sufficiently close to 1 means x → 1

but x ≠ 1.

so function = [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞

Therefore the following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.

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Answer:

Step-by-step explanation:

A

The minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean is 40.

In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter.

We have that to find our α level, that is the subtraction of 1 by the confidence interval divided by 2.

α = (1 - 0.90)/2 = 0.05.

Now, we have to find z in the Ztable as such z has a p-value of 1 - α.

So it is z with a pvalue of  1 - 0.05 = 0.95 = 1.96.

Now, find the margin of error M as such,

M = z×(sigma/√n).

5 = 1.96×(16/√n).

5√n = 31.36.

n = 39.9.

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Answer: If 30% of the fruits in the box are apples, then 100% - 30% = 70% of the fruits in the box are not apples. Of these non-apple fruits, 25% are pears, so the remaining fruits, 100% - 25% = 75% are oranges. Since 75% of the fruits in the box are oranges, and the total number of fruits in the box is 160, then the number of oranges in the box is 75/100 * 160 = <<75/100*160=120>>120. Answer: \boxed{120}.

a) The values are given as follows:

b) The solution of the equation is of: -0.25410169644.

The equation in this problem is given as follows:

y = (x³ - 1)/4.

The solution is obtained using a iterative solution method, until the difference between previous iterations is less than 10^-6, as the solution is exact to 6 decimal places.

Then the values are given as follows:

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Answer: 4x^2(7x+1)

Step-by-step explanation: Divide by the common divisible of 4x^2 and you will get your answer/.

Answer:4x^2(1+7x)

Step-by-step explanation:

4x^2(1+7x)

Solution

Given series is [tex]$5+11+17+\ldots .+95$.[/tex]

Thus,

[tex]$\mathrm{a}=5, \mathrm{~d}=11-5=6,1=95$$$\begin{aligned}& \mathrm{n}=\frac{1-a}{d}+1 \\& =\frac{95-5}{6}+1 \\& =\frac{90}{6}+1=15+1=16\end{aligned}[/tex]

Therefore, [tex]$\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}(\mathrm{a}+1)$$$\begin{aligned}& =\frac{16}{2}(5+95) \\& =8(100) \\& =800\end{aligned}$$[/tex]

What is arithmetic series?

The total of the terms in an arithmetic sequence with a predetermined number of terms is known as an arithmetic series. Here is a straightforward formula for calculating the sum: Formula 1: If the sum of an arithmetic series of terms is represented by S n, then The first and last terms' values, as well as the total number of terms, are needed for this formula.

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If 25% of Tolla's salary is Birr 135.75, then the full amount of his salary is 4 times this amount, since 25% is one quarter of the total amount.

Therefore, the full amount of Tolla's salary is 4 * Birr 135.75 = Birr 543.

This is the amount of Tolla's full salary.


LOL

By using the distance formula, the length of the interval AC 10.8, After rounding it will be 11 units.

The distance formula is given as:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Give the example of two decimal rounding off.

Here are two examples of rounding off to two decimal places:

12.3456 rounded to two decimal places is 12.35

0.678 rounded to two decimal places is 0.68

Plugging in the coordinates of the two points, we get:

Distance = sqrt((5 - (-1))^2 + (4 - 13)^2)

= sqrt(6^2 + (-9)^2)

= sqrt(36 + 81)

= sqrt(117)

= approximately 10.8

Therefore, the distance between the points (-1,13) and (5,4) is approximately 10.8.

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Answer:

the range of the graph would move down by 4 units.

Step-by-step explanation:

f(x) is the original/basis equation

g(x) is the translation equation

-4 does not have any x's attached to it, so it would affect the range, or the y of the equation

for example:

f(x) = 2x + 8

if you subtracted 4 from that it would be:

f(x) = 2x - 4, so the range would be affected

The value of r(x) approaches as x approaches Infinity is; 0

Limit is defined as the value that a function approaches for the given input value.

We have been given a function;

r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction

We can rewrite this function as;

r(x) = (axᵇ + 8)/(cx^d)

where a, b, c, and d are positive integers and b < d.

We need to find the value of r(x) approach as x approaches Infinity.

This means, we need to find the value of the limit [tex]\lim_{x \to \infty} r(x)[/tex]

Now, we find the value of limit for given function;

[tex]\lim_{x \to \infty} \frac{ax^b + 8 }{cx^d}[/tex]

This simplifies to;

[tex]\lim_{x \to \infty} \frac{8 }{cx^d}[/tex] (since d > b)

Thus;

[tex]\lim_{x \to \infty} r(x) = 0[/tex]

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Answer:

880 is the answer

Step-by-step explanation:

hope this helps

The number of movies rented when the cost for Movies Plus and Movies-To-Go is the same is 10.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Let the no. of movies be 'm' and the total cost is 'C'

Movies Plus charges a one-time fee of $20 plus $5 per movie

which is, C = 5m + 20.

Movies-To-Go charges $7 per movie

which is, C = 7m.

Now,  the number of movies rented when the cost for Movies Plus and Movies-To-Go is the same will be when we equate both equations.

∴ 7m = 5m + 20.

2m = 20.

m = 10.

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Answer:

answer for no.10 is {11,12,13,14}

Step-by-step explanation:

According to question domain and equation is given. At first we have to write equation as f(y)=5x+1 and at the place of y we have to write the given domain respectively then we can get the answers

Area or a circles given by the formula = radius , r

What is area?

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

For the circle or area given by the formula is radius ,r.

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Answer:

44.8

Step-by-step explanation:

Volume = Length * Height * Width

Volume = 10 * 1.5 * 3.2

Volume = 44.8cm

The probability that the total time taken by a random sample of 52 customers is less than 180 minutes is 0.02%.

μ=Population mean=4

σ=Population standard deviation=2

n=Sample size=50

The sampling distribution of the sum S is roughly normal if the sample size is big (30 or more), according to the central limit theorem.

The central limit theorem tells us that the sampling distribution of the sum S is about normal because the sample size of 50 is at least 30.

The sum S's sample distribution has a mean and standard deviation of n and n, respectively.

The z-score is the value decreased by the mean, divided by the standard deviation

z = ( x -μS ) / √σS

= 150 - 50(4) / √ 50(2)

= 3.54

Using the appendix's normal probability table, get the relevant probability,

P(S < 150 ) = P(Z< -3.54)

= 0.0002

=0.02%

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

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The measure of AB in the figure is C. 100 degree

The measure of AB in the figure is the length of arc, this is given by the formula

given angle / 360 * 2πr

However, the measure in degree is equal to the angle given which is 100 degree.

The size or the measure of the angle is same at any point within same lines that formed the angel AB.

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Answer:

150 in^2

Step-by-step explanation:

It is a cube...it has six equal sides

  the surface area of one side is 5 x 5 = 25 in^2

       there are six   ....    so   6 x 25 = 15o in^2

Edited:  should be in^2    not cm^2 as originally posted...wrong units

Answer:

150

Step-by-step explanation:

To find the surface area of a cube, you do 6a^2. That would mean it is 150.

The side lengths of each triangle are given as follows:

D. [tex]DE = \sqrt{13}, PQ = \sqrt{13}, EF = 2\sqrt{5}, QR = \sqrt{26}, DF = \sqrt{29}, PR = \sqrt{13}[/tex]

The side lengths of each triangle are given by the distances between the vertices.

These vertices are in the coordinate plane, hence the distance between them is found using the equation for the distance between two points.

Suppose two points in the coordinate plane with notation given as follows:

[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Then the distance between them is given by the equation presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Thus the side lengths are given as follows:

Meaning that option D is correct.

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Answer: The total amount of overdraft fees that Lewis will pay is {$1149.28}.

Step-by-step explanation:

To find out how much Lewis will pay in overdraft fees, we need to calculate the total amount of his overdrafts. We can do this by subtracting the sum of his checks from his account balance on June 5. This gives us:

overdraft = 932.77 - (791.29 + 340.50 + 208.35 + 428.61 + 113.3)

         = 932.77 - 2082.05

         = -1149.28

Since the bank charges a $31-per-check overdraft protection fee, Lewis will have to pay $31 for each check that he overdraws his account. Since he overdraws his account by $1149.28 in total, he will have to pay $31 * (1149.28 / 31) = $1149.28 in overdraft fees.

Therefore, the total amount of overdraft fees that Lewis will pay is {$1149.28}.

The point of intersection between the function f(x) and g(x) is x = 4 then, g(x)=18 where option E (4,18) is correct answer.

What is a function?

A function is defined as a relation between a set of inputs having one output each.

We have,

f(x) = ( x + 5 ) ( x - 2 )

g(x) = ( 2x + 1 ) ( x - 2 )

To find the points of intersection between the two functions we must equal the function.

f(x) = g(x)

( x + 5 ) ( x - 2 ) = ( 2x + 1 ) ( x - 2 )

( x - 2 ) gets canceled

x + 5 = 2x + 1

5 - 1 = 2x - x

4 = x

x = 4

This means that at x =4 the function f(x) and g(x) intersect.

we can see that at x = 4 both the functions have the same value.

f(x) = ( x + 5 ) ( x - 2 ) = ( 4 + 5 ) ( 4 - 2 ) = 9 x 2

f(x) = 18

g(x) = ( 2x + 1 ) ( x - 2 ) = ( 2 x 4 + 1 ) ( 4 - 2 ) = ( 8 + 1 ) ( 4 - 2 )

     = 9 x 2

g(x) = 18

Thus the point of intersection between the function f(x) and g(x) is x = 4 then, g(x) =18 where option E (4,18) is correct answer.

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The maximum area is 12.25 square feet

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

Perimeter = 14 feet

This means that

P = 2(l + w)

So, we have

2(l + w) = 14

Divide by 2

l + w = 7

Make l the subject

l = 7 - w

The area is calculated as

A = lw

So, we have

A = (7 - w)w

Expand

A = 7w - w²

Differentiate and set to 0

7 - 2w = 0

So, we have

w = 3.5

Substitute w = 3.5 in A = (7 - w)w

A = (7 - 3.5) * 3.5

Evaluate

A = 12.25

Hence, the area is 12.25 square feet

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Complete question

There is 14 feet of fencing available to enclose a rectangular region. For what value of area is the area maximum