Math

Classify each algebraic expression below as polynomial or non-polynomial

Account balance after 2 years $441.

Based on the given condition, here the details:

P = $400

r = 5 % = 0.05

n = 1

t = 2

Formulate and substitute all above:

F = P · (1 + [tex]\frac{r}{n}[/tex][tex])^{nt}[/tex]

F = 400. 1 + [tex]\frac{0.05}{1}[/tex])²

F = $441

From this as general, account balance is:

A checkbook, a savings account, or an investment account, for example, has a balance that shows how much money is available in the account. This is also called the current account value. The current value of account balances is shown by financial institutions on both paper statements and online tools.

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In the two triangles FIH and GHI

IH is a common side

FI = GH

The angles are between the equal sides

Then the two triangles are congruent by SAS postulate

The answer is A

We will use simple division to solve the problem. The number of representatives attended from each country is 706.

In the given question we know that a political gathering in South America was attended by 8475 people and each 12 territories of South America were equally represented. We need to find out how many representatives attended from each country. Inorder to find the number of representatives we can divide 8475 by 12.

number of representatives= 8475/12 =706

Therefore number of representatives from each country is 706.

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The equation of the line is 4y = x + 32 which passes through the point (-8,6) and has a slope of 1/4.

We have been given the required line that passes through the point (-8,6) and has a slope of 1/4.

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Let the required line would be as

⇒ y - y₁ = m (x - x₁ )

The required line passes through the point (-8,6)

Here x₁ = -8 and y₁ = 6 and m = 1/4

Substituting these inputs into the above equation obtains the line equation.

⇒ y - 6 = 1/4 (x - (-8))

⇒ y - 6 = 1/4 (x + 8)

⇒ 4y - 24 = x + 8

⇒ 4y = x + 8 + 24

⇒ 4y = x + 32

Thus, the equation of the line is 4y = x + 32 which passes through the point (-8,6) and has a slope of 1/4.

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The value of interior angle is 60.

What is triangle?

A triangle is a simple polygon with 3 sides and 3 interior angles. It is one of the basic shapes in geometry in which the 3 vertices are joined with each other and it is denoted by the symbol.

What is interior angle?

In a triangle, there are three interior angles at each vertex. The sum of those interior angles is always 180°. The bisectors of these angles meet at an point known as incenter. As the sum of interior angles of a triangle is 180°, there is only one possible right angle or obtuse angle possible in each triangle.

The sum of interior angle is 180

Given angles is 30, 90, x.

Therefore, sum is given by

90 + 30 + x = 180

120 + x = 180

x = 180-120

x = 60

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The amount of charge on the capacitor after 0.06 seconds = 0.042 millicoulombs

An electric circuit is defined as the device that aids in transmission of electricity generated by a battery or a generator.

A capacitor is defined as the device that has the ability to store energy in an electric circuit.

The amount of charge in a capacitor decreases in one second by = 30%

The original charge on the capacitor = 1 millicoulombs

30 % of 1millicoulombs = 30/100 * 1 = 0.3

1millicoulombs - 0.3 millicoulombs = 0.7 millicoulombs .

If 0.7 millicoulombs = 1 second

X millicoulombs = 0.06 second

Make X millicoulombs the subject of formula;

X millicoulombs = 0.06 × 0.7 = 0.042 millicoulombs.

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The inequality of the function is 36 + 4x < 95 and Rahul can use 14 gigabyte while staying within his budget

The given parameters are:

The above means that;

The total charges per month is

C(x) = Flat cost + Rate per gigabyte x Number of gigabyte

So, we have

C(x) = 36 + 4x

For the bill to be under $95, we have

36 + 4x < 95

Solving further, we have

4x > 59

Divide by 4

x < 14.75

Hence, the inequality is 36 + 4x < 95

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Answer:

The exact answer would be:

[tex]\sqrt{39}[/tex] + [tex]\sqrt{7}[/tex] + [tex]\sqrt{46}[/tex]  an approximate answer to the nearest whole number would be 7

Step-by-step explanation:

To find the missing side we would use the Pythagorean Theorem.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] =[tex]c^{2}[/tex]

[tex]\sqrt{7} ^{2}[/tex] + [tex]b^{2}[/tex] = [tex]\sqrt{46} ^{2}[/tex]

7 + [tex]b^{2}[/tex] = 46  Subtract 7 from both sides

[tex]b^{2}[/tex] = 39

[tex]\sqrt{b^{2} }[/tex] = [tex]\sqrt{39}[/tex]

b = [tex]\sqrt{39}[/tex]

The perimeter, the distance around the triangle, is [tex]\sqrt{39}[/tex] + [tex]\sqrt{7}[/tex] + [tex]\sqrt{46}[/tex]

Three pairs of siblings from different families can be seated in two rows of three chairs so that siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling in 96 ways.

There are 3 pairs of siblings. We can name them as a₁, a₂, b₁, b₂, c₁ and c₂, a total of 6 children.

There are 2 rows of 3 seats each.

We will try to find the number of ways each seat can be filled.

So considering the first seat in first row, it can be filled in 6 different ways. Because any one from 6 children, say a₁, can be seated.

Now for the second seat in first row can only be filled by one of b₁, b₂, c₁ or c₂ because the first seated child a₁ along with the sibling a₂ of the same cannot be seated in the second seat. So in 4 different ways.

For the third seat remaining in the first row, one out of the remaining  pair of siblings c₁ or c₂ can be seated. This can be done in 2 ways.

Now after filling the first row in this manner, the second row can be filled in only 2 ways.

So total number of ways the children can be seated = 6 x 4 x 2 x 2 = 96 ways

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Answer: $31,200 per year

Step-by-step explanation:

The question tells us that they are working 40 hours a week and making 15 dollars an hour. We can find out how much they make a week and then multiply by 52 (number of weeks in a year) to find the amount they make in a year.

Per week:

15 * 40 = $600

Per Year:

600 * 52 = $31,200

Answer:

$31,285.74 per year

Step-by-step explanation:

What we know:

- $15 per hour

- 40 hour weeks

- 52.1429 weeks per year

What we need to find out:

- How much money per year

Step 1: Multiply for how much made per week

We know that we need $15 dollars for 40 hours so we start with multiplying them together to see how much we make a year.

40 x 15 = $600 per week

Step 2: Now multiply the amount of weeks a year by the amount made per week

So now we know that we make $600 per week now we have to multiply the amount of weeks in a year by the money made per week so.

52.1429 x 600 = $31,285.74 per year. So the house keeper makes $31,285.74 per year.

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Answer:

x = 7.5

Step-by-step explanation:

[tex] \frac{6}{15} = \frac{3}{x} [/tex]

cross multiply expressions

6x = 45 divide both sides by 6

x = 7.5

The unit rate of Printer B = 25 pages per minute, which is greater than the unit rate of Printer A that is 15 pages per minute.

The unit rate of a graph can b determined by using any point, (x, y), on the graph and solve by finding, m, which is the ratio of y to x, if x and y represents the variables of the relationship that is graphed.

Thus, unit rate (m) = y/x.

The printing rate for Printer A is represented by the graph. To find the unit rate for Printer A, use a point on the graph, (2, 30) to find the unit rate, m.

Printer A's Unit rate (m) = y/x = 30/2

Printer A's unit rate (m) = 15 pages per minute.

The printing rate for Printer B is given as 25 pages per minute. 25 pages per minute is a greater unit rate compared to 15 pages per minute.

Therefore, we can conclude that Printer B has a greater printing rate than Printer A, because the unit rate of 25 pages per minute is greater than 15 pages per minute.

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we have the function

Part A

For t=0

substitute

Part B

For t=5 years -------> Convert to months

t=60 months

substitute

Part C

Determine horizontal asymptote

The horizontal asymptote is given by the ratio of

P(t)=2,400 ---------> horizontal asymptote

that means

as the value of time t increases ------> the value of the population tends to 2,400 insects

the population cannot be greater than 2400 insects

The range for the function P(t) is the interval [20, 2400)

All real numbers greater than or equal to 20 insects and less than 2400 insects

Part D

Using a graphing tool

After performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.

So, the total cost:

Cost of a total of 8 bags of popcorn and 5 drinks:

Therefore, after performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.

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The correct question is given below:

Zahra and some friends are going to the movies. At the theater, they sell a bag of popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags of popcorn and 5 drinks?

          An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power. Alternatively put, none of the exponents can be greater than 1. As an illustration, while x is a variable raised to the first power, x2 is a variable raised to the second power. An illustration of a constant is 5.

The number of deposits will change at a 100 percent rate.

Given that, consider the image of the linear function's graph.

Currently, the graph's two points are (3, 350) and (2, 250).

Rate of change is therefore equal to (250 - 350) / (2 - 3)

= -100/-1

 = 100.

The rate of change will therefore be 100 in relation to the number of deposits.

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Answer:

1/5

Step-by-step explanation:

"percent" means "per hundred"

(because cent means hundred like years in a century or cents in a dollar)

anyway

20% means

20 per 100

write it as 20/100



Now simplify it.

20/100

= 2/10

= 1/5

Answer:

(x² -5x +13) + (x² +3x -6)

Step-by-step explanation:

(x² -5x +13) + (x² +3x -6)

x² -5x +13 + x² +3x -6

|x² + x²| |-5x + 3x| |+13 -6|

2x² -2x +7

The measure of the angle is calculated using the attached figure.

What is an angle?

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. This measurement is the length of a circular arc divided by its radius. The arc is centered at the vertex in the case of a geometric angle.

From figure,

angle x = 180° - 110° = 70° (linear pair)

angle y = 37° (alternate interior angles)

Measure of angle 1 = 70° + 37° (exterior angle in a triangle is equal to the sum of opposite interior angles)

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"When creating a graph, it is important to assign the x and y axis."

Assigning the x and y axes is crucial when making a graph because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally. A point or line's separation from the y-axis can be determined using the x-axis. The y-axis displays a point's location on a Cartesian plane in the y (vertical) direction. Additionally, it serves as the origin (zero) point for calculating how far a point is from the x-axis.

A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.

"When creating a graph, it is important to assign the x and y axis."

Because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally, determining the x and y axes is essential when creating a graph. The x-axis can be used to calculate a point or line's distance from the y-axis. A point's position on a Cartesian plane is shown on the y-axis in the y (vertical) direction. It also acts as the origin (zero) point for determining a point's distance from the x-axis.

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The correct option is option D) it has range of 22

What is the range of a dataset?

It the difference between the minimum and maximum value of the dataset.

We are given a dataset with a histogram and we are asked to find out which of the given options does not describe the data

We find the answer by eliminating the correct option

Our given dataset contains 10 points

Hence the median will be the average of 5th and 6th element

Here the 5th and 6th elements are 17

Hence the median of the dataset is 17

Similarly 17 is repeated 4 times in the dataset. i.e highest number of times

Hence 17 is the mode of the dataset

If you look clearly at the histogram from median it is symmetrical that is left side equal to the right side

But if you look at the range the minimum value is 13 and maximum value is 21

Hence the range of the function is 21-13=8

And not 22

Hence the correct option is option D)

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Proved that if two parallel lines are cut by a transversal then the alternate exterior angles are congruent.

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

By the property of alternate interior angles;

From the figure attached;

∠XWY ≅ ∠ZYW

The Property of the alternate angles states that if two parallel lines are cut by a transversal, then the alternate angles are congruent.

Here, ∠XWY and ∠ZYW shows the interior angles between the parallel lines and the transversal.

The interior alternate angles ∠XWY and ∠ZYW will be congruent.

Hence, Proved that if two parallel lines are cut by a transversal then the alternate exterior angles are congruent.

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Answer:

12

Step-by-step explanation:

You have 15 pencils in your pencil case.1/5 of the pencils are green. How many are not green?

= 1 - 1/5

= 5/5 - 1/5

= 4/5

This means that 4/5 of the 15 pencils are not green. So:

4/5 * 15 = 12 pencils are not green.

Solution

Transform figure using the rule (x , y) = (-x , y - 8)

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

Answer:

Step-by-step explanation:

round up

√3 = √4

70-√4= 70-2

=68

The rate of change are:

a. 3 ft/min

b. 0.5 ft/min

c. -2.2 ft/min

The formula for finding the rate of change of a relationship is given as:

Rate of change = Change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

a. (2, 8) = [tex](x_1, y_1)[/tex]

(5, 17) = [tex](x_2, y_2)[/tex]

Rate of change = (17 - 8)/(5 - 2)

Rate of change = 9/3

Rate of change = 3 ft/min

b. (3.4, 6.8) = [tex](x_1, y_1)[/tex]

(7.2, 8.7) = [tex](x_2, y_2)[/tex]

Rate of change = (8.7 - 6.8)/(7.2 - 3.4)

Rate of change = 1.9/3.8

Rate of change = 0.5 ft/min

c. (3/2, - 3/4) = [tex](x_2, y_2)[/tex]

(1/4, 2) =  [tex](x_2, y_2)[/tex]

Rate of change = (2 - (-3/4))/(1/4 - 3/2)

Rate of change = 11/4 / -5/4

Rate of change = 11/4 × -4/5

Rate of change = -11/5 = -2.2 ft/min

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The probability of no loads occurring during that period is at most 0.3 exists 3.2 years.

Given: Mean time between occurrence = 0.4 year

A number of loads expected to occur during a 4 year period

Period = 4

Mean time = 0.4

Let the formula = Period/Mean Time

The number of loads expected to occur during a 4-year period

= 4/0.4 = 10 loads

B. Probability that more than 11 loads occur during 4 year period

The expected number of loads during 4-year period = 10 (from A above)

mean = 10

Using Poisson distribution,

P(k events in interval)= (λ^k * e^-k)/k!

where: k = 0, 1, 2,3,4, . . ., 11 and λ = 10.

P(k = 0) = (1[tex]0^0[/tex] × [tex]e^{-10[/tex])/0! = 0.000045

P(k = 1) = (1[tex]0^1[/tex] ×  [tex]e^{-10[/tex])/1! = 0.000454

P(k = 2) = (10² ×  [tex]e^{-10[/tex])/2! = 0.00227

P(k = 3) = (10³ ×  [tex]e^{-10[/tex])/3! = 0.007567

P(k = 4) = (1[tex]0^4[/tex] ×  [tex]e^{-10[/tex])/4! = 0.018917

P(k = 5) = (1[tex]0^5[/tex] ×  [tex]e^{-10[/tex])/5! = 0.037833

P(k = 6) = (1[tex]0^6[/tex] ×  [tex]e^{-10[/tex])/6! = 0.063055

P(k = 7) = (1[tex]0^7[/tex] ×  [tex]e^{-10[/tex])/7! = 0.090079

P(k = 8) = (1[tex]0^8[/tex] ×  [tex]e^{-10[/tex])/8! = 0.112599

P(k = 9) = (1[tex]0^9[/tex] ×  [tex]e^{-10[/tex])/9! = 0.12511

P(k = 10) = (1[tex]0^{10[/tex] ×  [tex]e^{-10[/tex])/10! = 0.12511

P(k = 11) = (1[tex]0^{11[/tex] ×  [tex]e^{-10[/tex])/11! = 0.113736

The probability that more than 11 loads occur during a 4-year period is then given by the following Express

1 - [P(k = 0) + P(k = 1) + P(k = 2) + . . . + P(k = 11)]

substitute the values in the above equation, we get

= 1 - [0.000045 + 0.000454 + 0.00227 + 0.007567 + 0.018917 + 0.037833 + 0.063055 + 0.090079 + 0.112599 + 0.12511+ 0.12511 + 0.113736]

simplifying the equation, we get

= 1 - 0.571665 = 0.428335

C. How long must a time period be so that the probability of no loads occurring during that period is at most 0.3

(λ^0 * e^-λ)/0! = 0.3

⇒ e^-λ/1 = 0.3

simplifying the above equation, we get

⇒ e^-λ = 0.3

⇒ -λ = ln 0.3

⇒ -λ = -1.204

⇒ λ = 1.204

The time period = 4 years / 1.204

Time period = 3.2 years

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Answer:

1) multiply and divide by 2 on right hand side

2) multiply by 24 on both sides ( LHS and RHS)

3) divide by -1 on both sides so that negative sign on RHS will be cancelled

Answer:

Step-by-step explanation:

You want the range of amounts of 60% solution that can be added to a 40% solution to achieve 30 kg of a solution that lies in the range of 46% to 50%.

Let x represent the mass in kg of 60% solution added. The fraction of the total solution that is glucose will be ...

  0.46 ≤ (0.60x +0.40(30 -x))/30 ≤ 0.50

Multiplying by 30 and simplifying the inequality, we have ...

  13.8 ≤ 0.20x +12 ≤ 15

  1.8 ≤ 0.2x ≤ 3 . . . . . . . . subtract 12

  9 ≤ x ≤ 15 . . . . . . . . . . divide by 0.2

The least amount of 60% solution that should be added is 9 kg. The greatest amount is 15 kg.

__

Check

  9 kg of 60% +21 kg of 40% has 5.4 +8.4 = 13.8 kg of glucose, the minimum.

  15 kg of 60% +15 kg of 40% has 9 +6 = 15 kg of glucose, the maximum.

(The minimum and maximum values are seen in the solutions steps after the initial multiplication by 30.)