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Please help me with these proofs Part 4

Answer:

2602,02008

Step-by-step explanation:

25000*(1+0,02)^5 - 25000 = 2602,02008

10.5 is the median of the given dataset.

The median is a statistical measure that determines the middle value of a dataset listed in ascending order (i.e., from smallest to largest value). The measure divides the lower half from the higher half of the dataset. Along with mean and mode, the median is a measure of central tendency.

Given the List of numbers 3, 12, 18, 2, 18, 9, 12, 16, 4, 5

Sort from smallest to largest number

2, 3, 4, 5, 9, 12, 12, 16, 18, 18

The median is a statistical measure that determines the middle value of a dataset listed in ascending order (i.e., from smallest to largest value).

The middle values of the dataset are 9 and 12

thus median  = (9+12)/2

Median = 10.5

Therefore, the median of the given dataset is 10.5.

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Answer:

aicd

Step-by-step explanation:

Esmeralda must deposit $53,637.38 to have $80,000 in 20 years.

What is compound interest?

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It refers to the interest on a deposit or loan that is calculated not only on the initial principal but also on the accumulated interest from previous periods.

To find out how much Esmeralda must deposit now in order to have $80,000 in 20 years, you can use the formula for compound interest:

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

where:

A = the future value (what Esmeralda wants to have in 20 years)

P = the present value (what Esmeralda wants to deposit now)

r = the annual interest rate (1.75% in this case)

n = the number of compounding periods per year (monthly in this case)

t = the number of years (20 in this case)

By substituting the given values into the formula, we get:

80,000 = P(1 + 0.0175/12)^(12*20)

Solving for P:

P = 80,000 / (1 + 0.0175/12)^(12*20)

The present value of Esmeralda's deposit is $53,637.38, rounding to the nearest cent.

Hence, Esmeralda must deposit $53,637.38 to have $80,000 in 20 years.

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The equivalent expressions are:

1.

-21 - 15g

2.

x + 7 + 3y

3.

(10 - 9x)/45

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,

1.

-3 (7 + 5g)

= -3 x 7 + -3 x 5g

= -21 - 15g

2.

(x + 7) + 3y

= x + 7 + 3y

3.

2/9 - 1/5 × x

= 2/9 - (1/5)x

= (10 - 9x)/45

Thus,

The equivalent expression is given above.

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The given system of equations represents the cost of 4 cups of tea and the total cost of tea and lemonade.

What is the system of equations?

A system of equations usually referred to as an equation system, is a collection of finite equations for which common solutions are sought.

Here, we

Suppose the number of cups of tea and lemonade is t and l respectively.

Then, the following equations can be formed for the given case,

The equation for total cost is given as,

4t + 2l = 120...(1)          

And, the equation for the number of cups is given as,

l = 5t...(2)                    

Now, the term 4t in equation (1) represents the cost for 4 cups of tea, and 120 represents the total cost.

Hence, the given system of equations represents the cost of 4 cups of tea and the total cost of tea and lemonade.

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Answer:

Step-by-step explanation:

D

Answer:

no they dont

Step-by-step explanation:

The length of the longer side of the rectangle is, 5 inch.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The area of a rectangle is 17 1/2 inches squared.

And, it's shorter side is 3 1/2 inches squared.

Now, We know that;

Area of rectangle = Length × width

Here, it's shorter side is 3 1/2 inches squared.

Hence, We get;

⇒ Area of rectangle = Length × width

⇒ 17 1/2 = Length × 3 1/2

⇒ 35/2 = Length × 7/2

⇒ Length = 35/2 × 2/7

⇒ Length = 5 inch

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Answer: C

Step-by-step explanation:

The problem says that one side of a right triangle has a length of 12 feet.

This means that when you use the Pythagorean theorem on the triangle, it should work.

The lengths that the Pythagorean theorem doesn't work are the ones that don't work.

I is true.

5^2+12^2=13^2

II is also true.

63+9^2=12^2

III is false, however. The Pythagorean theorem doesn't work.

Therefore, the answer is C. I and II only.

Answer: id say it would be C

Step-by-step explanation:

The equation that can be used to find the value of 'x' will be x² = (10)² + (8)². Then the correct option is C.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

If x represents the hypotenuse of this right triangle. then the value of the variable 'x' is calculated as,

x² = (10)² + (8)²

The equation that can be used to find the value of 'x' will be x² = (10)² + (8)². Then the correct option is C.

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Answer:

ccccccccccc

Step-by-step explanation:

took test

If you have a system of linear equations, the solution for the system is the value that makes all of the equations true

Image search results for Make a graph showing the inequality’s solution. ≥b+9/5

Graphing a System of Linear Inequalities

Make a graph of the first inequality. Draw the border line.

Graph the second inequality on the same grid. Draw the border line.

The place where the shading overlaps is the solution.

Select a test point to verify.

Rearrange the equation so that one side corresponds to the graphed function.

Plot the function y= the opposite side of the equation.

To get the answers, draw vertical lines down to the x-axis from the junction spots.

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The percentage of pages of books that Olivia has not read would be = 35%

Percentage is defined as the part of a whole value per 100 which is represented with the symbol of %.

The number of pages left is the 70-pages book = 70 - 40 = 30 pages.

The number of pages left in the 85-page book = 85 -60 = 25 pages.

The number of pages left in the 65-page book= 65-43 = 22

The total number of pages she has to read = 70+85+65 = 220

The total number of pages she has not read = 30+25+22= 77

Therefore the percentage of the pages she has not read :

= 77/220× 100

= 7700/220

= 35%

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40 quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid to obtain a mixture containing a 40% solution of acid

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The quart of the solution must be added be 'x'.

Therefore, According to the given information,

0.5x + 0.2(20) = 0.4(x + 20).      (0.5 represents 50% solution)

0.5x + 4 = 0.4x + 8.

0.1x = 4.

x = 40.

So, 40 quarts of acid must be added.

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Rounded to the nearest cubic mm, the volume is 615 cubic mm.

To calculate the volume of a cylinder, you can use the formula: V = πr^2h, where r is the radius, h is the height, and π is approximately equal to 3.14. In this case, the radius is 6mm and the height is 7mm. So, the volume of wax needed is approximately: V = 3.14 * 6^2 * 7 = 615.44 cubic mm. Rounded to the nearest cubic mm, the volume is 615 cubic mm.

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I started to learn English recently and I’m struggling doing this homework. Can someone give me a hand?

The requried solution of the given equation is x = -1. Mai's statement is incorrect.

Reasoning is defined as math in the form of a puzzle for the living world such as codded sequences, relations, correlation, etc. is called reasoning.

here,
Mai says that the equation 2x+2=X+1 has no solution because the left-hand side is double the right-hand side.
So,
2x + 2 = x + 1
2x - x = 1 - 2
x = -1, Mai's statement is incorrect because the equation has a solution.

Thus, the requried solution of the given equation is x = -1. Mai's statement is incorrect.

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The total surface area painted black = 90.5 square feet to the nearest tenth.

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

Given:

Three large cones hang from the ceiling in an office building in front of a bank of windows.

The height of each cone is 12 feet, and the circumference of the base of each cone is 8π feet.

The base and 40% of the lateral surface of each cone is painted red, and the rest of each cone is painted black.

Circumference of the base of the cone = 8π feet.

2πr = 8π

πr = 4π

The surface area of the cone = πr x height

The surface area of the cone = 12 x 4π

The surface area of the cone = 48π.

The total surface area painted black = 60% of 48π.

The total surface area painted black = 90.5 square feet to the nearest tenth.

Therefore, the result is 90.5 square feet to the nearest tenth.

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Answer: 90.5 square feet is the correct answer

Step-by-step explanation:

They can create 100 shoes in a day if they work together. They will have 150 shoes left if they donate 150 shoes to the less fortunate.

Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.

Ryle can make 35 shoes in 3 days and Andrei can make 65 shoes in 5 days.

⇒ 35 + 65

Apply the addition operation,

⇒ 100

Together, they can make 100 shoes in a day.

If they work for 3 days, they will make 300 pairs of shoes.

⇒ 300 - 150

Apply the subtraction operation,

⇒ 150

If they donate 150 shoes to the less fortunate, they will have 150 shoes left.

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Answer:

True

Step-by-step explanation:

The ideal congressional district size (Standard Divisor) in 1790 was 34437.33.

The number of persons each House of Representatives seat represents is known as the "Standard Divisor" (SD). By dividing the total population of all the states by the total number of seats available for voting, the SD is determined. SD is calculated as Total U.S. Population / Total Number of Voting Seats.

The ratio of the entire population to the available seats (or other allocations) is known as the standard divisor. • The Hamilton system divides up any extra seats among the states with the largest fractional parts after allocating each state its lower quota initially.

Given,

population in 1790 was 3,615,920,

number of objects = 105

⇒ Standard divisor = total population / number of objects

⇒ Standard divisor = 3,615,920 / 105

⇒ Standard Divisor = 34437.33

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The simplified form of the given mathematical expression (7⁵/7³) include the following: A. 7^2.

In Mathematics, an exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.

Based on the law of indices for division, we have the following:

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

By applying the law of indices for division, we have the following mathematical expression:

Mathematical expression = 7⁵/7³

Mathematical expression = 7⁽⁵ ⁻ ³⁾

Mathematical expression = 7²

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Complete Question:

Simplify the following expression:

7^5/7^3

A. 7^2

B. 7^8

C. 7

D. 1

The words and numbers are important in this problem are the poster has 2 sides of equal length.

What is an equal length?

Equal length sides indicate that they measure the same. In plain English, the sides of a shape that are equal in length are the sides of the shape. Congruent sides are also described as having equal lengths of each side.

Here, we have

Given: Jon is making a poster for safety awareness week. His poster has 2 sides of equal length.

We have to determine which math words and numbers are important in this problem.

We concluded from the given problem that the important words and numbers are the poster has 2 sides of equal length.

Hence, the words and numbers are important in this problem are the poster has 2 sides of equal length.

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Answer:

To find the percentage of games won by the school, you can divide the number of games won by the total number of games played, and then multiply by 100.

In this case, the school won 15 games and lost 25 games, for a total of 15 + 25 = 40 games played.

So, to find the percentage of games won, you would do:

(15 / 40) x 100 = 37.5%

So, the St. Paul High School basketball team won 37.5% of their games last season.

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Answer:

Step-by-step explanation:

I think it will be

The simplified form of the given expression is cos(∞/2)

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

(sin²(∞/2))/(1-cos(∞/2)) - 1

Use the formula: sin²(x) = 1- cos²(x)

=> (1-cos²(∞/2))/ (1-cos(∞/2)) - 1

Use the identity a²-b² =(a-b) (a+b)

[(1-cos(∞/2)*(1+cos(∞/2)]/ (1-cos(∞/2)) - 1

common terms cancel out

(1+cos(∞/2) - 1

= cos(∞/2)

Thus, the simplified form of the given expression is cos(∞/2)

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The function that represents The value v of your quarters is a function of n the number of quarters you have is v = n×x.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, The value 'v' of your quarters is a function of 'n' the number of quarters you have.

Therefore, the function 'v' in terms on 'n' can be represented as,

Let, the number of quarters be 'x'.

Therefore,

v = n×x.

Where v is the output and n and x are the inputs.

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The surface area of the cylinder is 1714.44 square inches.

A cylinder is a 3D solid form made up of two bases that are parallel and identical and are connected by a curving surface. These bases resemble spherical disks. The axis of the cylinder form is a line drawn through the center or connecting the centers of two circular bases.

Given:

The net of a cylinder is shown.

And the radius = 13 inches, height = 8 inches.

And we have the formula,

surface area of a cylinder, A = 2πr² + 2πrh.

That means,

the surface area of the cylinder = area of the bases + area of curved part.

So,

the surface area of the cylinder = 2(3.14)(13)² + 2(3.14)(13)(8).

The surface area of the cylinder = 1061.32 + 653.12

The surface area of the cylinder = 1714.44 square inches.

Therefore, the surface area is 1714.44 square inches.

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Considering the definition of perpendicular line, the equation of the line that is perpendicular to y=−13x+2 and passes through (2, 8) is y= 1/13x + 102/13.

A linear equation o line can be expressed in the form y= mx + b

where

Perpendicular lines are lines that intersect at right angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= -13x +2

where:

Since you multiply the slopes of two perpendicular lines, you get –1. So:

-13 × slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-13)

slope perpendicular line= 1/13

The line passes through the point (2, 8). Replacing the slope and the coordinates of the point in the expression of a line:

8= 1/13× (2) + b

8= 2/13 + b

8 - 2/13= b

102/13= b

Finally, the equation of the perpendicular line is y= 1/13x + 102/13.

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Answer:

  C.  x = 18/5

Step-by-step explanation:

You want the solution to √(5x -2) -1 = 3.

Add 1 to isolate the radical.

  √(5x -2) = 4

Square both sides.

  5x -2 = 16

Add 2, then divide by 5.

  5x = 18

  x = 18/5

The graph that represents the inequality 5y≤10 is plotted below.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The given inequality is 5y≤10.

In a graph of an inequality, the symbols (<,>) are represented using a dotted line and the symbols (≤,≥) are represented using a straight line.

So, the graph of inequality 5y≤10 will have a straight line.

Now, writing the inequality 5y≤10 in slope-intercept form y = mx + b -

5y = 10

5y = 0x + 10

Substituting the values of x and y with origin (0,0) -

5(0) = 0(0) + 10

0 = 10

Putting the inequality symbol back -

0 ≤ 10

Since, 0 ≤ 10 is true hence the shaded region of graph will cover the origin.

On solving 5y = 10  -

y = 2

Hence the points of the inequality will be (0,2).

Therefore, the graph for the inequality 5y≤10 is plotted.

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