4. Each year a certain amount of money is deposited in an account which pays an
annual interest rate of r so that at the end of each year the balance in the account is
multiplied by a growth factor of x = 1+r. $1,000 is deposited at the start of the first
year, an additional $300 is deposited at the start of the next year, and $500 at the
start of the following year.
a. Write an expression for the value of the account at the end of three years in
terms of the growth factor x.
b. Determine (to the nearest cent) the amount in the account at the end of three
years if the interest rate is 4%.

The perimeter "P" is equal to the length of the base of one triangle multiplied by the "n" number of triangles in the figure plus two times the length of another side. The equation for the perimeter is P = 5n + 14.

We are given triangles. The triangles are arranged in a certain pattern. The length of the base of each triangle is equal to 5 units. The length of the other two sides is 7 units each. We conclude that all the triangles are isosceles. We need to find the relationship between the number of triangles and the perimeter of the figure. Let the perimeter of the figure having "n" number of triangles be represented by the variable "P".

P(1) = 14 + 5(1)

P(2) = 14 + 5(2)

P(3) = 14 + 5(3)

We can see and continue the pattern. The relationship between the perimeter and the number of triangles is given below.

P(n) = 14 + 5n

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Answer:

Step-by-step explanation:

14

The equation of the line with slope -1/7 is (y-3) = -1/7(x-3).

According to the question,

We have the following information:

Slope of the line = -1/7

Points through which line is passing = (3,3)

We know that the following formula is used to find the equation of the line:

(y-y') = m(x-x') where m is the slope of the line

In this case, we have x' = 3 and y' = 3.

(y-3) = -1/7(x-3)

This expression can be solved further by multiplying -1/7 into the bracket and then by moving 3 from the left hand side to the right hand side. Then this equation will be in slope-intercept form.

Hence, the correct option is B.

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Answer:

Domain: {-1,0,1,4}

Range: {3,5,35}

Step-by-step explanation:

The domain is the set of x values while range is the set of y values

Here, the set of x values would be -1 , 0 , 1 and 4

And the y values would be 5, 3, 5, and 35

When writing the domain and range, you put the values into brackets "{}" and put them in order from least to greatest. Also if there are repeated values you do not repeat them, you only put them once.

This means that the domain would be {-1,0,1,4}

And the range would be {3,5,35}

Ren will have to wait for approximately 31 years for the money compounded annually and a rate of 2.3% to double it's original investment.

Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.

The formula of compound interest is given as

A = P(1 + r/n)^nt

Substituting the values into the equation;

It will take approximately 31 years to double the investment.

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A function assigns the value of each element of one set to the other specific element of another set. The zeroes of the functions are -2, 1, and 3.

A function assigns the value of each element of one set to the other specific element of another set.

The zeros of a function are defined as the values of the variable of the function such that the function equals 0. Graphically, the zeros of a function are the points on the x-axis where the graph cuts the x-axis. In other words, we can say that the zeros of a function are the x-intercepts of its graph.

Now, According t the question:

Given that, f(x) = (x - 1)(x + 2)(x − 3)

Therefore, the zeroes of the functions are -2, 1, and 3. The end behavior of the function is that if x approaches ∞ then f(x) approaches ∞, while if x approaches -∞ then f(x) approaches -∞, as can be observed from the given graph.

Hence, the zeroes of the functions are -2, 1, and 3.

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From the data in the table relating time and depth, we have that:

a) The scatter plot is graphed at the end of the answer.

b) The scatter plot has negative correlation.

c) The estimate for the depth at a time of 15 seconds is of 50.37 cm.

The scatter plot is built inserting all the points of the table in a graph, which are in the following format:

(Time in seconds, Depth in cm).

Hence the scatter plot will be composed by a set of points, without an image, as is shown at the end of the answer.

The points from the table are listed as follows:

(2, 47), (4, 41), (6, 38), (8, 37), (10, 32), (12, 24), (14, 20), (16, 19).

As the input variable time increases, the output variable depth decreases, meaning that the points in the scatter plot also follow the format of a decreasing line, hence there is negative correlation in the scatter plot.

These points are also inserted into a linear regression calculator to built the line of best fit, which is defined as follows:

y = -2.07x + 50.89.

At 15 seconds, the estimate is obtained replacing the lone instance of x in the equation by 15, hence:

y = -2.07 x 0.25 + 50.89 = 50.37 cm.

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Answer: x= 1

Step-by-step explanation:

it represents a distance between observed and predicted values

What is residual?

A residual in statistics is the discrepancy between an observed value and a value that was predicted.

Typically, the anticipated value is based on a model, like a linear regression model. The prediction error is represented by a residual, which can be either positive or negative. A positive residual indicates a difference between the observed and expected values, whereas a negative residual indicates the opposite. Specifically, the residual's absolute value is the distance between the observed value and the predicted value.

For evaluating a model's correctness, residuals are crucial. The residuals should be randomly distributed in the vicinity of zero if the model is valid. The residuals will be biased either in favor of or against the null hypothesis if the model is not accurate. A model's goodness of fit can also be evaluated using the residual. Relatively small residuals characterize a model with a high goodness of fit. Remainders that are far from zero will be present in a model with a low goodness of fit.

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As per given data of living children under 18 years of age , percent of children whose age is under 18 years lived with their mother only is equal to 39.3%.

As given in the question,

Let us consider 100% be the total percent representing the living status of children under 18 years of age

Given:

Percent of children living with both the parents = 49.2%

Percent of children living with only father = 8%

Percent of children living with neither of the parents = 3.5%

Let us consider percent of children living with only mother = x%

Required equation is:

( x + 49.2 + 8 + 3.5 )% = 100%

⇒ x + 60.7% = 100%

⇒ x = 100 - 60.7

⇒ x = 39.3%

Therefore, for the given data of living children under 18 years of age , percent of children whose age is under 18 years lived with their mother only is equal to 39.3%.

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If Lines J and k are perpendicular. The slope of line k is 3, the slope of line j is -1/3

When two lines are perpendicular to each other, the product of their slope results in -1

slope of line j x slope of line k = -1

slope of line j x 3 = -1

slope of line j  is 1/3

Therefore, if Lines J and k are perpendicular. The slope of line k is 3, the slope of line j is -1/3

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Answer:

Step-by-step explanation:

(4-3)/(2-1= 1/1 = slope = 1

y =(1)x + b,  plug in either point to solve for b

3 = 1 +b

b = 2

34 students red is their favorite color

2 out of 7 of the pupils in year 9 say their favourite colour is red

Fraction of pupil that say red is their favorite colour is 7/9

There are 119 pupils in year 9

We need to calculate the number of students out of 119 that would say that their favourite colour is red

To find that,

we multiply the fraction of students that like red with the total number of students

2/7 * 119

= 34

Therefore, if 2 out of 7 of the pupils in year 9 say their favourite colour is red. Then 34 out of 119 pupil will say that their favourite colour is red.

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Answer:

Step-by-step explanation:

Hi Strawberry  :D   so three ways to spend $120

T= tshirts

S=socks

20T +5S= 120

20(5)+5(4) =120      one

20(4) +5(8) =120     two

20(3) +5(12) = 120  three

20x +5y =120

Answer: x∈(-3,-1)

Step-by-step explanation:

13<-5x+8<23

13-8<-5x+8-8<23-8

5<-5x<15

Divide the double inequality by 5:

1<-x<3

Multiply the double inequality by -1:

-1>x>-3

Thus, x∈(-3,-1)

Answer:

Angle CEB

Step-by-step explanation:

They are vertical angles

:]

[tex]{ \boxed{ \orange{ \sf{421.875 \: {cm}^{3}}}}} [/tex]

Step-by-step explanation:-

[tex]{ \red{ \sf{Volume \: of \: the \: cube }}} = { \green{ \sf{ {a}^{3}}}} [/tex]

[tex]{ \red{ \sf{Volume \: of \: the \: cube } = }} \: \: { \green{ \sf{7.5 \times 7.5 \times 7.5}}}[/tex]

[tex]{ \red{ \sf{Volume \: of \: the \: cube = { \green{ \sf{56.25 \times 7.5}}}}}}[/tex]

[tex]{ \boxed{ \sf{Volume \: of \: the \: cube = 421.875 {cm}^{3}}}} [/tex]

The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.5278

The uniform distributed between a and b minutes.

The probability of finding a value above x is:

P(X > x) = [tex]\frac{b-x}{b-a}[/tex]

The time is evenly distributed between 0 and 9 minutes.

This implies that a=0 , b=9

Determine the likelihood that a randomly selected passenger will have to wait longer than 4.25 minutes.

p(X > 4.25) = [tex]\frac{9-4.25}{9-0}[/tex]

                 = 0.5278

There is a 52.78% chance that a randomly selected passenger will have to wait longer than 4.25 minutes.

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Answer:

Multiples of 2 = 2, 4, 6, 8, 10, 12

Multiples of 3 = 3, 6, 9, 12, 15,18

The LCM is 6.

Step-by-step explanation:

The zeros of the function are-

The given expression is-

f(x)=(x-10)^2-49

To find the zero put f(x) = 0.

(x-10)^2-49 = 0

Including both sides of an equation, add 49.

(x-10)^2 - 49 + 49 = 49

(x-10)^2  = 49

To remove the exponent upon that left side of the equation, take the appropriate root of both sides.

x - 10 = ±√49

x - 10 = ±7

Solve each case;

a:  x - 10 = + 7

x = 7 + 10

x = 17 (greatest number)

b: x - 10 = - 7

x = -7 + 10

x = 3 (lesser value)

Thus, the zeros of the function are 3 and 17.

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Answer:

12-12-12+i-12+i =0-i

.

.

.

,

The image of the point (3, 6) by means of the translation formula described in the statement is (5, 1).

Herein we find the coordinates of an ordered pair set on Cartesian plane, whose image has to be found by using a rigid transformation formula known as translation formula, whose definition is described and explained below:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that P(x, y) = (3, 6) and T(x, y) = (2, - 5), then the image of the original point according to the translation formula is now determined:

P'(x, y) = (3, 6) + (2, - 5)

P'(x, y) = (3 + 2, 6 - 5)

P'(x, y) = (5, 1)

The image of the point by translation formula is (5, 1).

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$21.00

25% off 28= 7

28-7=21

The two points that are collinear with the point D are points A and B which are on the same plane, K, as the point D

Collinearity of a set of points in geometry is the property of their being on a single line. A set of points with this property is known as a collinear set. In a broader sense, the term has been applied to aligned objects, that is, things that are "in a line" or "in a row."

If two or more points lie on the same line, they are said to be collinear in geometry. As a result, collinear points are the points that lie on a single straight line.

Therefore, the points are A and B.

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264 naira tax doe he pays in a year.

Amount earned per year = 2460

Rate of interest paid: 10k per naira earned

Tax paid by messenger per year :

100k = 1 naira

10k = (100/10) = 0.1 naira

Hence 0.1 naira is paid as tax on every naira earned

The total amount paid off is 2640 Naira :

Amount paid per naira * total amount earned

(0.1 * 2640) = 264 nairas.

A tax is a compulsory monetary charge or a few other sorts of levy imposed on a taxpayer (a man or woman or criminal entity) by using a governmental agency if you want to fund authorities' spending and numerous public expenses (regional, neighborhood, or countrywide), and tax compliance refers to coverage movements and character behavior geared toward making sure that taxpayers are paying the right amount of tax on the proper time and securing the right tax allowances and tax reliefs. the first known taxation passed off in historical Egypt around 3000–2800 BC. A failure to pay in a well-timed way (non-compliance), together with evasion of or resistance to taxation, is punishable by means of regulation. Taxes consist of direct or oblique taxes and may be paid in cash or as its labor equivalent.

Maximum nations have a tax system in the region, so as to pay for public, common societal, or agreed-on country-wide needs and for the capabilities of the presidency. a few levies a flat percentage rate of taxation on private annual profits, however, maximum scale taxes are modern and based on brackets of annual earnings amounts. most nations charge a tax on a character's profits as well as on corporate earnings. nations or subunits regularly additionally impose wealth taxes, inheritance taxes, estate taxes, gift taxes, property taxes, sales taxes, use taxes, payroll taxes, duties, and/or tariffs.

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Answer:

67%

Step-by-step explanation:

[tex]\frac{268}{400}[/tex] X 100

Answer:

67%

Step-by-step explanation:

268 ÷ 400 = 0.67 = 67%

Given that Phil takes 3 times as long as Meredith to complete the work . Let us take Meredith takes x hrs to complete the work, the Phil will do that work in 3x hrs . Now it is given that they together complete the work in 12hrs . So ,

[tex]\longrightarrow \dfrac{1}{x}+\dfrac{1}{3x}=\dfrac{1}{12}\\ [/tex]

[tex]\longrightarrow \dfrac{3+1}{3x}=\dfrac{1}{12} \\[/tex]

[tex]\longrightarrow \dfrac{4}{3x}=\dfrac{1}{12}\\[/tex]

[tex]\longrightarrow x =\dfrac{(4)(12)}{3}\\[/tex]

[tex]\longrightarrow x = 16\ hrs [/tex]

Hence,

And we are done!

The missing number to complete the proportion is 1

Proportion defines that the two given ratios are equivalent to each other. That is two ratios (or fractions) are equal e.g 2:6 = 1:3

Given: 14 seats in 2 rows = 7 seats in ___rows

If each row in a classroom has equal seats. If there are 14 seats in 2 rows of the classroom then we can say there are 7 seats in each row (1 row).

Thus, 14 seats in 2 rows = 7 seats in 1 row

Therefore,  the missing number to complete the proportion is 1. You should type 1

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Answer:

I believe it's 18x2(14x + 7)

Step-by-step explanation:

I took the test :)

18x² + 14x + 7 ( may be expressed in any order )

= 14x +18x² + 7

Points scored by the last player is 10 points. this can be calculated by using BODMAS rule by forming equation.

What is an equation ?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Main body:

Points scored by 4 players = 6 each

Total points scored by 4 players = 4*6

                                                      = 24

Total points scored by team = 34

Points scored by last player or 5th player = total points - points scored by 4 players

Points scored by 5th player = 34-24

                                              = 10

Hence point scored by last player is 10.

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