#3 a. Complete the table for f(x) = 2x

#3b Use the coordinate points from the table to graph f(x) = 2^x

The explicit form of the arithmetic sequence is

5, 13, 21, 29, .....

What is arithmetic sequence?

A sequence of numbers is said to be in arithmetic progression if the difference between the consecutive terms of the series are same

If the first term is a, common difference is d, then nth term of the sequence is given by

[tex]a_n = a + (n-1)d[/tex]

The recursive form of the given arithmetic series is

[tex]a_n = a_{n-1} + 8[/tex]

First term [tex]a_1 = 5[/tex]

[tex]a_2 = a_1 + 8\\a_2 = 5 + 8\\a_2 = 13[/tex]

[tex]a_3 = a_2 + 8\\a_3 = 13 + 8\\a_3 = 21[/tex]

[tex]a_4 = a_3 + 8\\a_4 = 21+8\\a_4 = 29[/tex]

So the explicit form of the arithmetic sequence is

5, 13, 21, 29, .....

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The 80,000 BD Villa in Saar Mr. Abbas plans to sell at a 40% profit , with the annual house price growth rate of 7% (compounded) gives the number of years Mr. Abbas has to wait as approximately 5 years

The growth rate is the rate at which the value changes within a specified period.  

The amount Mr. Abbas bought the Villar in Saar = 80,000 BD

The profit at which he intends to sell it = 40% = 0.4

The rate at which the house prices rise on average = 7 % per annum

The formula for future value, FV is presented as follows;

[tex]FV = PV\cdot \left(1+\dfrac{r}{100} \right)^n[/tex]

Where;

FV = The future value = 80,000 BD + 0.4 × 80,000 BD = 112,000 BD

PV = The present value = 80,000 BD

r = The rate at which the house prices increases annually

n = The number of years

Which gives;

[tex]112,000 = 80,000\cdot \left(1+\dfrac{7}{100} \right)^n[/tex]

[tex]n = \dfrac{ln\left(\dfrac{112,000 }{80,000}\right) }{ln\left(1+\dfrac{7}{100} \right) } \approx 5[/tex]

The number of years Mr. Abbas has to to wait, n ≈ 5 years

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The probability that at least 12 are delinquent is given as 0.3155

Probability can be defined as the likelihood of getting an outcome out of other outcomes.

We have the mean u = np

where n = 400

p = proportion = 2.5% = 0.025

= 400 x 0.025

= 10

we have to find the population standard deviation

= [tex]\sqrt{np(1-p)}[/tex]

= √400 x 0.025 (1 - 0.025)

= 3.1225

P (X ≥ 12)

= P(X ≥ 11.5)

= 11.5 - 10 / 3.1225

= 1 - P(z < 0.4804)

= 1 - 0.6845

= 0.3155

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Answer:

  2.  $19,547.04

  3.  $10,276.54

  4.  $16,758.38

Step-by-step explanation:

You have three problems in compound interest with different initial payments, interest rates, and compounding intervals. You want the relationship between the initial payment and the future value.

The multiplier of a single payment earning annual interest rate r compounded n times per year for t years is ...

  k = (1 +r/n)^(nt)

For this problem, r=0.09, n=1, t=9. The multiplier of the payment is ...

  k = (1 +0.09/1)^(1·9) = 1.09^9 = 2.17189328

Then the future value of $9000 will be ...

  FV = $9000 × 2.17189328 ≈ $19,547.04

For this problem, r=0.10, n=12, t=4. The multiplier of the payment is ...

  k = (1 +0.10/12)^(12·4) = 1.08333...^48 = 1.48935410

Then the future value of $6900 will be ...

  FV = $6900 × 1.48935410 ≈ $10,276.54

For this problem, r=0.13, n=12, t=13. The multiplier of the payment is ...

  k = (1 +0.13/12)^(12·13) = 1.0108333...^156 = 5.3704484

Then the payment that gives a future value of $90,000 will be ...

  P = $90,000/5.3704484 = $16,758.38

__

Additional comment

For the spreadsheet calculation, we used the "Goal Seek" capability to adjust the value of cell F4 to 90000 by changing the value in cell B4.

We could have calculated the multiplier as above, then used it different ways for the different problems. Instead, we used one FV( ) function for all of the problems.

The area of the piece of land with coordinates (0, 0), (-100, 300) and (200, -200) is as measured by the surveyor is 4000 square meter

The given coordinates being plotted as

A (0, 0)

B (-100, 300)

C (200, -200)

Area of triangle is solved by 0.5 * base * height

dimensions from attached plot, BC = 316.2, Aa = 253

= 0.5 * BC * Aa

= 0.5 * 253 * 316.2

= 39 999.3 approximately 40 000

The plot gave an area of 40 000 square units on paper converting using the given scale which is: One unit in the coordinate plane represents 1m

1 unit = 1 m

1 square unit = 1 square meter

4000 square units = ?

cross multiplying

? = 4000 square units

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1. The completion of the inventory table is as follows:

                                   Units  Unit Cost    Total Cost

Jan. 1  Beg. Inventory     8       $6.00                 $48

Apr. 11 Purchases         24       $11.00              $264

May 17 Purchases        30      $14.00              $420

Dec. 5 Purchases         19      $16.00              $304

2. The Cost of Ending Inventory and the Cost of Goods Sold under LIFO, FIFO, and Weighted-Average, are as follows:

                                      LIFO           FIFO         Weighted-Average

Ending inventory          $704          $845                $767.40

Cost of goods sold       $332          $191                $268.60

FIFO (First-in, First-out) is based on the assumption that the physical flow of goods sold depends on the chronological order of acquisition.

LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.

The weighted-average method uses the average cost of goods to determine both the ending inventory and the cost of goods sold.

LIFO:

Ending inventory = $704 ($48 + $264 + 28 x $14)

Cost of goods sold = $332 ($1,036 - $704)

FIFO:

Ending inventory = $845 (11 x $11 + 30 x $14 + 19 x $16)

Cost of goods sold = $191 ($1,036 - $845)

Weighted Average:

Ending inventory = $767.40 (60 x $12.79)

Cost of goods sold = $268.60 (21 x $12.79)

                                   Units  Unit Cost    Total Cost

Beg. Inventory Jan. 1     8       $6.00                 $48

Apr. 11 Purchases         24      $11.00              $264

May 17 Purchases        30     $14.00              $420

Dec. 5 Purchases         19     $16.00              $304

Total                              81                           $1,036

Units sold                      21

Ending inventory         60

Average cost per unit = $12.79 ($1,036/81)

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The exchange rate of US dollars per Australian dollar is 0.72

The exchange rate of Australian dollars per US dollar is 1.39

Exchange rate

Exchange rate is the price of a country's money in relation to another country's money and it is “fixed” when countries use gold or another agreed-upon standard, and each currency is worth a specific measure of the metal or other standard.

Given,

After arriving in Australia, Jason exchanged $750 of US currency for $1,041.67 Australian dollars. Complete the two statements based on this currency exchange.

Here we need to find the exchange rate of US dollars per Australian dollar and Australian dollars per US dollar then round it to the nearest hundredth.

According to the given details,

Total amount in US dollars = $750

Converted amount in Australian dollar = $1,041.67

When we divide the US dollar by the Australian dollar then we get the value of one dollar rate,

=> 750/1041.67

=> 0.719

When we round off it to the nearest hundredth then we get the exchange rate of $1 is 0.72

Similarly, now we have to divide the Australian dollar by the US dollar then we get the value of one dollar rate,

=>  1041.67/750

=> 1.388

When we round off it to the nearest hundredth then we get the exchange rate of $1 is 1.39.

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Answer:

b < 3

Step-by-step explanation:

3 ( b - 5 ) < - 2b

3 ( b ) - 3 ( 5 ) < - 2b

3b - 15 < - 2b

3b + 2b < 15

5b < 15

b < 15/5

b < 3

Answer:

Step-by-step explanation:

ZT=YT

x+3=3x-11

x-3x=-11-3

-2x=-14

x=-14/-2=7

YT=3×7-11=21-11=10

YT=10

The axis of symmetry of the parabola, having the equation, f(x) = 3·(x - 5)² + 1 is the line x = h = 5

A parabola is the locus of a point that moves such that the distance of the point from a fixed point is the same as the distance of the moving point from a fixed line.

The graph of a parabola has the shape of an open umbrella

The given equation for the parabola is; f(x) = 3·(x - 5)² + 1

The equation is given in the vertex form, f(x) = a·(x - h)² + k, where;

(h, k) = The vertex of the parabola

The axis of symmetry of a parabola, which is the line that divides the parabola in two, passes through the vertex of the parabola

Comparing the equation, f(x) = 3·(x - 5)² + 1, to the vertex form of a parabola,  gives;

a = 3

(h, k) = (5, 1) (The vertex of the parabola)

Which gives; h = 5

The equation of the axis of symmetry is therefore the line, x = h = 5

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In the given triangle JKL , NO = 26 units and JK = (7x + 17) units, then the value of x is equal to 5 units.

As given in the question,

In the given triangle JKL,

M, N ,O are the mid-points of the side JK, JL, KL of the triangle respectively.

Measure of NO is equal to 26 units

Measure of JK is equal to (7x + 17) units

Using mid- point theorem we have,

In triangle JKL,

NO is half the measure of opposite side JK

NO = 1/2 ( JK)

⇒ 26 = 1/2 ( 7x + 17 )

⇒ 7x + 17 = 26 × 2

⇒ 7x + 17 = 52

⇒ 7x = 52 - 17

⇒ 7x = 35

⇒ x= 5 units

Therefore, for the given triangle JKL , NO = 26 units and JK = (7x + 17) units, then the value of x is equal to 5 units.

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a. The annual base premium when Danielle cecils driver rating factor is 1.60 and her car is in age group is $709.

b. The annual premium is $1134.40

It should be noted that the annual premium simply refers to the amount of premium that's paid yearly by the entity. The insurance company has premium payment options for the clients.

The annual base premium will be:

= Liability premium + Collision premium + Comprehensive premium

= $383 + $240 + $86

= $709

The annual premium will be:

= Annual base premium × Driver rating factor

= $709 × 1.60

= $1134.40

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Abdiel's total if he uses a coupon for 12% off the subtotal and leaves a 25% tip before the discount is $27.46

The correct answer option is option B

Amount of total after discount = 12% × $24.30

= 0.12 ×24.30

= $2.916

Amount of abdiel's tip = 25% × $24.40

= 0.25 × 24.30

= $6.075

Abdiel's total after discount before tip = (Amount of abdiel's tip + Abdiel's subtotal) - Amount of total after discount

= (6.075 + 24.30) - $2.916

= $30.375 - $2.916

= $27.459

Approximately,

$27.46

Therefore, the total amount Abdiel paid after discount before tip is $27.46

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The equation of the line is y = (-2/3)x + 8/3

What is a perpendicular line?

Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular line can be used to graphically depict the condition of perpendicularity. It can be defined between any pair of lines, any pair of planes, or any pair of lines and planes.

The slope-intercept form of a line is written in the form:

y = mx + b

where:

y = y-coordinate

m = slope

x = x-coordinate

b = y-intercept

Here, We have

y= 3/2x + 1/2 that passes through the point (-2,4)​

But we do not know the value of b.

We can do this by substituting the point(-2,4), into the equation and we get

y = mx + b

4 = (-2/3)(-2) + b

b = 8/3

Now that you know all your values, rewrite the equation in slope-intercept form:

y = (-2/3)x + 8/3

Hence, the equation of the line is y = (-2/3)x + 8/3

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The expression that represents the age of randy's brother is

2x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Randy age = 8 years old

Randy's brother age = 2 x 8 = 16

Randy's sister age = 8 - 3 = 5

The expression that represents the age of randy's brother.

Let the age of Randy = x.

=  2x

= 2x

= 2 x 8

= 16 years old.

Thus,

The expression that represents the age of randy's brother is

2x.

Where x is the age of Randy.

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A number line is a simple graph with numerical increments spaced evenly. The numbers on the line determine how the number on the line can be answered. The number's application is determined by the question to which it corresponds, such as when plotting a point.

A number line is a horizontal line with evenly spaced numerical increments. The numbers on the line will determine how to answer the number on the line. The number's use is determined by the question that goes with it, such as plotting a point.

The number line is a straight line with divisions at equal intervals, similar to a scale. You can choose any point as "0," and all positive numbers will be to the right of the "0," and all negative numbers will be to the left of the "0." Q.

Therefore,

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According to the solving Probability the value are as follows.

a) P(Blue)= 0/10

b) P(Red)= 5/10

c) P(Red or Yellow)= 9/10

The definition of probability is "How likely something is to happen."

Probability is indeed a number ranging from 0 to 1 that expresses the likelihood that an event will take place as specified.

First, 0 P(E) 1 (where P(E) specifies the probability of an event E) and second, the sum of the probabilities of any collection of mutually and exclusive exhaustive occurrences equals 1 are the two characteristics that define a probability.

We have a Bag of marbles has 4 yellow, 5 red, and 1 purple.

Total balls in a bag= 4+5+1=10 balls.

Something that is IMPOSSIBLE to happen.

P(Blue)= 0/10

Something that is EQUALLY LIKELY to happen.

P(Red)= 5/10

Something that is LIKELY to happen.

P(Red or Yellow)= 9/10

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20 amount of 30% salt solution

How to find the salt solution percentage?

Divide the solute's gram weight by the total weight of the solution, then multiply the result by 100 to get the mass/mass percent of the solution. The amount of solute (measured in grams) per milliliter of solution is known as the mass/volume percent.

Let x be the amount of 30% salt solution

Then, 60-x = amount of 15% salt solution

Salt content of the first solution + salt content of second solution = salt content of the mixture

∴ 0.30x + 0.15(60-x) = 0.20*60

  0.30x + 9 - 0.15x = 12

             0.15x = 3

                   x = 20

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Answer:

[tex] \sqrt[2]{15} = 7.5[/tex]

Answer:

(10 + 8) - (7 * 2) = x, 4 pounds of birdseed left

Step-by-step explanation:

      For the first part of our equation, we will find the total amount of pounds of seeds among the bags (addition).

      For the next part, we will find out how much of the bird seed is used (subtraction).

      Then, it will equal whatever is left.

(10 + 8) - (7 * 2) = x, x = pounds of bird seed left

      Now, we will solve.

(10 + 8) - (7 * 2) = x

(18) - (14) = x

x = 4 pounds of birdseed left

Step-by-step explanation:

Jim has 65 coins in his pocket. All of the coins are nickels and dimes. If the total value of his coins is $5.10, how many nickels or dimes does he have?

nickels = n

dimes = d

We use:

d + n = 65

0.10d + 0.05n = 5.10

solve for d:

d + n = 65

d + n - n = 65 - n

d = 65 - n

substitute in for the second equation: d = 65 - n

0.10(65 - n) + 0.05n = 5.10

6.5 - 0.10n + 0.05n = 5.10

6.5 - 0.05n = 5.10

6.5 - 0.05n - 6.5 = 5.10 - 6.5

- 0.05n= -1.4

n = 28

so there are 28 nickels

Now, solve for d: when n = 28

d + n = 65

d + 28 = 65

d = 37

so there are 37 dimes

Jim has 28 nickels and 37 dimes in his pocket. which is determined by the substitution method.

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

Let the number of nickels would be n

Let the number of dimes would be d

As per the given question,

d + n = 65  ....(i)

0.10d + 0.05n = 5.10  ....(ii)

From equation (i),

d + n = 65

d + n - n = 65 - n

d = 65 - n

Substitute in for the equation(ii): d = 65 - n

0.10(65 - n) + 0.05n = 5.10

6.5 - 0.10n + 0.05n = 5.10

6.5 - 0.05n = 5.10

6.5 - 0.05n - 6.5 = 5.10 - 6.5

- 0.05n = -1.4

n = 28

This means there are 28 nickels

Substitute the value of n = 28 in the equation (i),

d + n = 65

d + 28 = 65

d = 37

So there are 37 dimes

Thus, Jim has 28 nickels and 37 dimes in his pocket.

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Answer:

Depends on the gravitational force. On Earth, one pound equals 4.41N.

Step-by-step explanation:

The formula for Newton's Second Law of Motion is F=ma, which is Force = mass × acceleration.

The SI unit of mass is the kilogram (kg), so we'll have to convert one pound to kilograms. For practical purposes, one pound equals 0.45kg.

The gravitational force of the Earth is 9.8m/s^2. It is worth noting that each planetary body has its own gravitational force in respect to its mass.

Force = mass × acceleration = 0.45kg × 9.8m/s^2 = 4.41N

This number is only applicable on Earth, and may and will change on a planetary body with a mass different from Earth's.

The total amount accumulated after 2 years is $3704. 0

The formula for calculating compound interest is expressed as;

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

Where;

Now, let's substitute the values into the formula, we have;

A = $3500 ( 1 + 0. 03 / 0. 25) ^(0.25× 2)

Find the exponent

A = $3500 ( 1 + 0. 03 / 0. 25) ^0.5

A =  $3500( 1+ 0. 12)^0. 5

Expand the bracket

A = $3500 (1. 12)^0. 5

A = $3500(1. 05)

multiply the values

A = $3704. 0

Hence, the value is $3704. 0

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Step-by-step explanation:

use formula

[tex](x - y) {2} = x {}^{2} - 2xy + y {}^{2} [/tex]

The total cost of the hooded sweatshirts will be 29 × 31 = $899.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.

Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

As per the given,

Number of hooded sweatshirts = 29

Cost of one hooded sweatshirt = $31

Total cost = 29 × 31 = $899.

Hence "The total cost of the hooded sweatshirts will be 29 × 31 = $899".

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In given word problem ,

a) 2040  more kilojoules of energy would you use in an hour of jogging than an hour of swimming .

b)  45 minutes 2 seconds of walking would you have to do to burn up the 1,130 kilojoules in a candy bar.

What is word problem ?

   Our extensive collection of math word problems ranges from addition, subtraction, multiplication, and division to more specialised operations. Mathematical questions that are written as one or more sentences and ask students to use their mathematical understanding to solve problems from "real-life" situations are known as word problems. As a result, for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are already used to.

Here the given ,

=> 1 minute walking = 25 kilojoules

=> 1 minute jogging = 84 kilojoules

=> 1 minute swimming = 50 kilojoules.

a) 1 hour = 60 minutes.

1 hour jogging = 60*84 = 5040 kilojoules.

1 hour swimming = 60*50 = 3000

Then , => 5040-3000=2040 kilojoules.

Therefore 2040  more kilojoules of energy would you use in an hour of jogging than an hour of swimming .

b) x minute of walking = 1130 kilojoules.

=> 25*x=1130

=> x = 1130/25 = 45minutes 2 seconds.

Therefore 45 minutes 2 seconds of walking would you have to

do to burn up the 1,130 kilojoules in a candy bar.

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The probability that the selections are both boys is 7/10

The given parameters in the question are

Seventh grade

Boys = 7

Girls = 3

Eight grade

Boys = 4

Girls = 4

The probability of selecting a boy is calculated as

P(Boy) = Number of boys/Number of students

So, we  have

Seventh grade

Boys = 7

Girls = 3

P(boy) = 7/10

Eight grade

Boys = 4

Girls = 4

P(boy) = 4/8

The probability that the selections are both boys is

P = P(boy) * P(boy)

So, we have

P = 7/10 * 4/8

Evaluate

P = 7/20

Hence, the probability is 7/20

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It would take Amanda 2.25 hours to catch up with Ben

Speed is the ratio of distance to time. It is given by:

Speed = distance/time

Given that Ben covers a distance d at time t, hence:

3 = d/t

d = 3t

Since Amanda leaves One and a half hours (1.5) after Ben leaves, hence Time = t - 1.5

5 = d/(t - 1.5)

d = 5t - 7.5

Since they catch up, hence:

3t = 5t - 7.5

2t = 7.5

t = 3.75 hours

Time for Amanda = t - 1.5 = 3.75 - 1.5 = 2.25 hours

Hence it would take Amanda 2.25 hours to catch up with Ben.