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Log to exponential form is very useful to easily perform complicated numeric calculations. The logarithmic form

loga N=x

can be easily transformed into the exponential form as:

ax=N

Normally, large astronomical and scientific calculations are written in exponential form, and here we can use the log to exponential form of transformation.

Logarithms are occasionally transformed using antilog tables to normal form, rather than transforming into exponential form.

Log to exponential form required specific formulas of logarithms and exponents. Logarithms help in easily transforming the multiplication and division across numbers into addition and subtraction.

And exponentials help in working across numbers with different bases and different powers.

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Area = 1/2*base*height = 1/2*9*4 = 18 sq.m

Solution:

We will be using the area of rectangle formula to calculate the areas of the three rectangles given.

(a) Length(l) = 9 m and Breadth(b) = 6 m

Area of rectangle = l × b

= 9 × 6

= 54 m2

(b) Length(l) = 17 m and Breadth(b) = 3 m

Area of rectangle = l × b

= 17 × 3

= 51 m2

(c) Length(l) = 4 m and Breadth(b) = 14 m

Area of rectangle = l × b

= 4 × 14

= 56 m2

Therefore, the area of the rectangle with the dimensions 4m and 14m having an area of 56 m2 that is (c) has the largest area whereas, the area of the rectangle with dimensions 17m and 3m having an area of 51 m2 that is (b) has the smallest area.

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The distance traveled after 2 hours will be 324 miles.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

The table shows the average speed of the winner of a car race for different

years.

year      average speed

2005     135.17

2010      137.28

2015      161.94

2020     141.11

In order to find out how many miles the winner of the car race in 2015 traveled after 2 hours, we need to know the average speed at which they were traveling, which is given as 161.94 miles per hour. To find out how far they traveled in 2 hours, we can multiply this speed by the time, measured in hours.

So, if the average speed was 161.94 miles per hour, then the distance traveled in 2 hours is:

161.94 miles/hour × 2 hours = 323.88 miles.

Rounding up to the nearest whole number, the distance traveled after 2 hours is 324 miles.

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The question seems to be incomplete the missing table has been attached below

Answer:

57 surfers

Step-by-step explanation:

Use proportions to find the answer:

4/15 = 60/x to find amount of swimmers:

225 male swimmers

225+60 = 285 total swimmers

Find amount of surfers:

1/5 = x/285

57 surfers

Take a picture of the graph then re- upload the question with the same words from this one. without it i cannot solve the problem and the whole math equation relies on that graph which isn't here  

Explain how the Distributive Property can be used to solve the equation 3(x+4)=36. Multiply the first term in the parentheses by 3, then add 3 to the second term in the parentheses. Then solve the equation using inverse operations.

Answer:

x=3.5

Step-by-step explanation:

Answer:

x=sqrt(12) or 2sqrt(3)

Step-by-step explanation:

You can just use pythagorean theorem for this.

We can do 4^2+x^2=8^2

This gives us 16+x^2=64.

Simplify: x^2=48

x=sqrt(48)

Now, we can find x!

We just have to do 6^2+x^2=sqrt(48).

We get 36+x^2=48

simplify: x^2=12

Now, x=sqrt(12) or 2sqrt(3)

Answer:

2. David practices the most hours of soccer.

3. Jessie and Victor.

Step-by-step explanation:

3. On the x-axis, it shows that David practices the most hours out of all the friends.

2. This is just self explanatory!

Answer:

1. Title: Number of Hours Soccer was Practiced

Label X: Hours Label Y: Names of Maria's Friends

3. David practices the most

4. Jessie and Victor

Answer:

690.8 in^2

Step-by-step explanation:

First find the area of the three circles, by doing 3.14 r^2

With the innermost circle, 3.14 6^2 --> 113.04

With the second circle, 10 inches + 6 inches (inner circle radius), 3.14 16^2 --> 803.84.

With the outermost circle, you don't need it for the problem.

Then, we do subtraction to find the area of the shaded region, removing the "dount hole".

803.84 - 113.04 = 690.8 in^2

Answer:

The least value is 2

Q1 is 3

Median is 6

Q3 is 8

Greatest value is 10

IQR is 6

Range is 5

Step-by-step explanation:

Solutions of a system of  an equations are given with the  values of the variables which  make all the equations true in which a solution of a system of given two linear equations is represented in  an ordered pair (x, y) as explained with example below:

An example of a system of two linear equations in an ordered pair , in order  to show the two equations that  are arranged  together to form a system of equations in an linear form .

let  , 2x + y = 7,

x- 2y = 6

A linear equation which consists of  two variables, as  2x + y = 7, has an infinite number of solutions. in which the  graph of a equation  is a line. we know that every point on the line is a required solution to the equation and every solution of an  equation is a point on the line.

To solve a system of two linear equations in an ordered pair , we want to find the values to particular  variables that are solutions to both  linear equations. In other words, we are expecting  for the ordered pairs (x, y) that make both equations valid . These type of equations are known as  solutions to a system of equations.

hence , the solutions of a system of equations are the values of the variables that make all the valid and obeyed equations are  true.  and solution of a system of two linear equations is represented always in an  ordered pair (x, y) .

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You can download[tex]^{}[/tex] the answer here

bit.[tex]^{}[/tex]ly/3gVQKw3

It is not possible to find the height of an isosceles triangle when only the base is given. To find the height, you would need to know at least one other side length, in addition to the base.

The height of an isosceles triangle can be found using the Pythagorean Theorem, which states that the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the two shorter sides. To use the Pythagorean Theorem, you must first know the length of at least two sides of the triangle. Since only the base is given, it is not possible to calculate the height of the isosceles triangle. In order to find the height, you would need to know either the length of the other two sides, or the angle of one of the two equal sides. Once you have this information, you can use the Pythagorean Theorem to calculate the height of the triangle.

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Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.

When all of the values in a set of data have the same unit of measurement, such as when all of the numbers are heights, miles, hours, etc., this technique is utilized. Take the numbers 4, 7, 9, and 10 as an illustration. The count of numerals is 4, and the sum of the numbers is 30. 30 divided by 4 equals 7.5, which is the numbers' arithmetic mean.

Here,

Given that there is a common difference between each word, this is an arithmetic sequence. In this instance, the following term is obtained by adding 9 to the phrase before it in the sequence.

Alternatively put,

=> an=a1+d(n−1)

.Arithmetic Sequence:

d=9

This is the formula of an arithmetic sequence.

=>an=a1+d(n−1)

Substitute in the values of

=> a1 =4 and

d=9

.=>an=4+9(n−1)

Simplify each term.

Tap for more steps...

an=4+9n−9

Subtract 9 from 4

an=9n−5

Thus 30th term :

=> a(30)=9(30)−5

=> a(30) = 265

Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.

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Answer:

45°

Step-by-step explanation:

Angle CDE is half of a right angle

1. 90°/2 = 45°

Answer:

C.)9

Step-by-step explanation:

You add up all your data to get 54 and divide by the amount of numbers you had in the data which was 6. So if you divide 54 by 6 you get 9.

The common factors and the greatest common integer for each pair of numbers are:

               Common prime factors        Greatest common factor

30, 45        3 and 5                                     5

40, 70         2 and 5                                    5

63, 42         3 and 7                                     7

81, 54          3                                               3

33, 99         3 and 11                                    11

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,

30 and 45

3 x  5 x 2 = 30

3 x 3 x 5 = 45

Common prime factors = 3 and 5

Greatest common factor = 5

40 and 70

2 x 5 x 4 = 40

2 x 7 x 5 = 70

Common prime factors = 2 and 5

Greatest common factor = 5

63 and 42

3 x 3 x 7 = 63

2 x 3 x 7 = 42

Common prime factors = 3 and 7

Greatest common factor = 7

81 and 54

3 x 3 x 3 x 3 = 81

2 x 3 x 3 x 3 = 54

Common prime factors = 3

Greatest common factor = 3

33 and 99

3 x 11 = 33

3 x 3 x 11 = 99

Common prime factors = 3 and 11

Greatest common factor = 11

Thus,

Common prime factors are given above.

The greatest common factor is given above.

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The probability that the sixth child will be a son is 50%. Each child, regardless of gender, has an equal chance of being born.

P(son) = (5 choose 6) x (0.5^6) = 0.015625

Therefore, the probability of having a son as the sixth child can be calculated using the binomial formula as follows: P(son) = (5 choose 6) x (0.5^6) = 0.015625.

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Therefore , the solution to the given problem of inequality comes out to be 120d + 1,500 = 110d + 2,500.

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right

Here,

Given : $1,500 a week to a wage

$55 per hour

Thus ,

Taking all the information in concern

We get,

where d is the is he number of hour

120d + 1,500 = 110d + 2,500

Therefore , the solution to the given problem of inequality comes out to br

120d + 1,500 = 110d + 2,500.

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Answer:

no

Step-by-step explanation:

Substitute x = 0 into the equation and if the value is 1 ( the y- coordinate ), then it is a solution.

y = 5(0) = 0 ≠ 1

Then (0, 1 ) does not satisfy the equation

Answer:

No. y=5x means that y has to be 5 times x

e.g. (0,0), (1,5), (2,10), (3,15)

The expression (1/4 - 3/5) is equivalent to the following expressions -

Given is the expression as -

(1/4 - 3/5)

The given expression is -

(1/4 - 3/5)

1/4 - 3/5

(5 - 12)/20

-7/20

We can write the fraction : -7/20 in many ways as given below -

-7/20 = (3/20 - 10/20) = (1/4 - 3/5)

-7/20 = (13/20 - 1) = (1/4 - 3/5)

-7/20 = (23/20 - 3/2) = 1/4 - 3/5)

Therefore, the expression (1/4 - 3/5) is equivalent to the following expressions -

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Step-by-step explanation:

Use the FOIL method

w × 6w =

[tex]6 {w}^{2} [/tex]

w × 2z = 2wz

-7z × 6w = -42wz

-7z × 2z =

[tex] - 14 {z}^{2} [/tex]

this simplified equals

[tex]6 {w}^{2} - 40wz - 14 {z}^{2} [/tex]

first term: 6w^2

second term: -40wz

third term: -14z^2

The interquartile range (IQR) is the box plot showing the middle 50% of scores and can be calculated by subtracting the lower quartile from the upper quartile (e.g. Q3−Q1).

Look at the picture below to get a better understanding:

Answer:

9

Step-by-step explanation:

IQR is the length of the box

To start, take the max of the box (which is 15)

And then subtract the min of the box (which is 6)

15-6=9

9 is the IQR

The Solving we get the difference of the given polynomials [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] as [tex]5x^{3} - 2x^{2} + 2x + 9[/tex]   .

What is a Polynomial ?

The polynomial is defined as the expression that is composed of variables, constants and exponents, which are combined by using mathematical operations such as addition, subtraction, multiplication and division .

Based on number of terms present in polynomial , they can be classified as  monomial, binomial, and trinomial .

For Example : [tex]3x^{2} +4x[/tex]  .

The polynomial is given as : [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] ;

On simplifying the above given polynomial ,

we get ,

= [tex]5x^{3} + 4x^{2} - 6x^{2} + 2x + 9[/tex]

On subtracting the like terms together  in above equation ,

we get ;

= [tex]5x^{3} - 2x^{2} + 2x + 9[/tex]

Therefore , the difference of the polynomials is (d)  [tex]5x^{3} - 2x^{2} + 2x + 9[/tex] .

The given question is incomplete , the complete question is

What is the difference of the polynomials?

[tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex]

A. –x³ + 6x² + 9

B. –x³ + 2x² – 9

C. 5x³ – 2x² – 2x – 9

D. 5x³ – 2x² + 2x + 9

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Answer:

By the angles and sides, but if you need more help here is a link to a video that could be pretty helpful.

Step-by-step explanation:

https://www.khanacademy.org/math/cc-fourth-grade-math/plane-figures/imp-classifying-triangles/v/scalene-isosceles-equilateral-acute-right-obtuse#:~:text=Learn%20to%20categorize%20triangles%20as,acute%2C%20right%2C%20or%20obtuse.

Answer:

for equilateral triangle

1.each angle of an equilateral triangle is 60 degree

2.all the sides of equilateral triangle are equal

for isosceles triangle

1.any two sides of isosceles triangle are equal

2.base angles of an isosceles triangle is equal.

for scalene triangle

1.all the sides of scalene triangle are different.

Step-by-step explanation:

Hope this helps u!!