10, 110, 210, 310, …
find a^30

Prove by contradiction that in a right triangle with integer sides, the two shorter sides cannot both be odd.

Assume that the two shorter sides, a and b, of a right triangle are both odd integers. Then the hypotenuse, c, must also be an integer. From the Pythagorean theorem, we know that c2 = a2 + b2. We can rewrite this as c2 = (2m + 1)2 + (2n + 1)2, where m and n are integers. We can expand the left-hand side of the equation to get c2 = 4m2 + 4n2 + 4m + 4n + 1. Since c2 is an even integer, 4m2 + 4n2 must be an even integer as well. But, since 4m + 4n + 1 is odd, the only way to make the left-hand side of the equation an even integer is if 4m2 + 4n2 is an odd integer, which is impossible.

Therefore, our initial assumption that a and b are both odd integers is false. Thus, in a right triangle with integer sides, the two shorter sides cannot both be odd.

Learn more about Pythagorean theorem here: https://brainly.com/question/343682

#SPJ11

The value that should go on the flyer from the environmental group can be found to be 60, 000 m ².

The reason why the building developer chose a different unit from the environmental group is to try to understate the amount of land they would be building on.

The conversion factor for square kilometers and meters squared is :

1 km ² = 100, 000 m²

0. 06 km ² would then be :

= 0. 6 x 100, 000

= 60, 000 m ²

The building developer chose to use square kilometers to make it seem as though the amount of land they were using was little so as not to have people being angry with the amount of land they would use. The environmental group chose meters squared for the opposite effect to make it seem like a lot of land was to be used.

Find out more on square kilometers at https://brainly.com/question/29073517

#SPJ1

The required number Justin could have bought 1 pair of jeans and 3 t-shirts.

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Let's assume Justin bought x pairs of jeans and y t-shirts.

We know that the cost of each pair of jeans is $40 and the cost of each t-shirt is $20.

So, the total cost of Justin's purchase can be represented as:

Total cost = 40x + 20y

We also know that Justin bought a total of 4 items. So:

x + y = 4

Now we can use these two equations to solve for x and y:

40x + 20y = 100 (divide both sides by 20)

2x + y = 5 (subtract x from both sides)

Now we have two equations with two variables. We can solve for y in the second equation:

y = 5 - 2x

And substitute this into the first equation:

40x + 20(5-2x) = 100

Simplifying, we get:

40x + 100 - 40x = 100

100 = 100

This equation is true for any value of x and y that satisfy the condition x + y = 4.

So, Justin could have bought 1 pair of jeans and 3 t-shirts.

To know more about Equation visit:

brainly.com/question/649785

#SPJ1

Since it's a rhombus, the the diagonal intersection point is the middle point, so the diagonal should be

d1=5x2=10cm

d2=2x2=4cm

area=(d1xd2)/2=(10x4)/2=20cm^2

The result is (x + 8).

Polynomial is an equation written with terms of the form kx^n.

where k and n are positive integers.

There are quadratic polynomials and cubic polynomials.

Example:

2x³ + 4x² + 4x + 9 is a cubic polynomial.

4x² + 7x + 8 is a quadratic polynomial.

We have,

x² + 12x + 32 and g(x) = x + 4.

Now,

(f/g)(x)

= (x² + 12x + 32) / (x + 4) _____(1)

Now,

We can factorize x² + 12x + 32.

x² + 12x + 32

= x² + (8 + 4)x + 32

= x² + 8x + 4x + 32

= x(x + 8) + 4(x + 8)

= (x + 4) (x + 8) ______(2)

From (1) and (2),

(f/g)(x)

= (x² + 12x + 32) / (x + 4)

=  (x + 4) (x + 8) / (x + 4)

= x + 8

Thus,

The result is (x + 8).

Learn more about polynomials here:

https://brainly.com/question/2284746

#SPJ1

The number of chocolates in the jar is given by the equation n = 21 chocolates

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Let the number of chocolates be n

Substituting the values in the equation , we get

The number of strawberries in the jar = 18

The number of cherries in the jar = 24

The number of lime candies in the jar = 19

The total number of candies in the jar = 82 candies

So , the equation will be

Number of strawberries in the jar + number of cherries in the jar + number of candies in the jar + number of chocolates = 82

Substituting the values in the equation , we get

18 + 24 + 19 + n = 82

On simplifying the equation , we get

n + 61 = 82

Subtracting 61 on both sides of the equation , we get

n = 21 chocolates

Hence , the equation is n = 21 chocolates

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ9

Answer:

If the repayment period is the same length for both loans, the interest option that will result in the least amount of interest added to the loan is B. Option A will have the least amount of interest because simple interest generates earnings from principal only.

What is the simple interest?

The simple interest is the interest system that does not compute interest on accumulated interest.

Unlike simple interest, compound interest charges interest on accumulated interest.

Thus, the simple interest system applies the interest rate on the principal only for each period to determine the amount of interest.

Step-by-step explanation:

Have a nice day

The acceleration due to gravity of a falling object is +9.8 m/s²

The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. m/s² is its SI unit. Its nature which includes both magnitude and direction—makes it a vector quantity.

Given:

A linear expression we have

y= k x,

Here, Variation's constant is constant, or k.

The acceleration caused by gravity is stated to be the variational constant in the statement.

So, the linear expression becomes

y = g x, where g is a proportionality constant.

Now, Work is not done against gravity since an object falling downwards accelerates due to gravity at a rate of +9.8 m/s².

Learn more about acceleration due to Gravity here:

https://brainly.com/question/9167280

#SPJ1

The amount of urea per square meter in form of fraction will be 6/29 ounce/meter².

What exactly is a fraction?

In mathematics, a fraction is used to represent a piece or part of a whole. It symbolises the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, while the bottom number is known as the denominator. The denominator describes the total number of equal parts in a whole, whereas the numerator defines the number of equal parts taken.

5/10, for example, is a fraction.

In this case, 5 is the numerator and 10 is the denominator.

Now,

Given that Total area=58 square meter

Total Urea used=12 ounce

then urea used for 1 square meter=12/58

=6/29 ounce/meter².

Hence,

          The amount of urea per square meter in form of fraction will be 6/29 ounce/meter².

To know more about fractions visit the link

https://brainly.com/question/10354322?referrer=searchResults

#SPJ1

The probability of obtaining a z-value less than 1.5 is 0.8531 or 85.31% using normal distribution table.

The probability of obtaining a z-value less than 1.5 can be calculated using the standard normal distribution table or by using software like Excel or statistical calculators.

The standard normal distribution is a probability distribution with a mean of zero and a standard deviation of one. It is denoted by the letter Z and is used to standardize normal random variables. The standard normal distribution table provides the probabilities for different values of Z, ranging from -3.4 to 3.4.

To find the probability of obtaining a z-value less than 1.5, we need to look up the value of 1.5 in the standard normal distribution table. The table provides the area under the standard normal curve to the left of a given Z-value.

Looking at the table, we find that the probability of obtaining a z-value less than 1.5 is 0.8531, which means that approximately 85.31% of the area under the standard normal curve is to the left of 1.5.

This means that if we have a normally distributed variable with a mean of zero and a standard deviation of one, there is a 85.31% chance that the z-value will be less than 1.5.

To learn more about probability click on,

https://brainly.com/question/30895983

#SPJ4

The missing numbers for the respective rows are:

row 1: 4/5

row 2: -4/5 and -2/5

row 3: -3/5 and 6/5

Missing number for row 1(top row):

1 - 1/5 = 4/5

Missing number for row 2 (2nd number for last column):

3/5 - 1 = -2/5

Missing number for row 2 (1st number for first column):

-2/5 - 2/5 = -4/5

Missing number for row 3 (1st number for first column):

1/5 + (-4/5) = -3/5

Missing number for row 3 (2nd number for second column):

4/5 + 2/5 = 6/5

Therefore, row 1 have the missing number; 4/5. Row 2 missing numbers from left; -4/5 and -2/5. Row 3 missing number from left; -3/5 and 6/5

Know more about missing numbers here:https://brainly.com/question/23171011

#SPJ1

Possible question:

If the sum of the first two numbers in row 1 is equal to 1 and the sum of the first two in last column to the right is equal to 3/5. Find the missing numbers.

The temperature in Helena at 6 a.m. the next morning is 24∘C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

The temperature in Helena, MT was 0∘C at 6 a.m. on Tuesday morning.

The temperature rose at a rate of 78∘C per hour for 12 hours, then fell at a rate of 76∘C per hour for 12 hours.

Now,

Temperature first after 12 hours= 78*12=936

Temperature second after 12 hours= 76*12=912

=936-912

=24

Therefore, the answer will be 24∘C.

More about the temperature  link is given below.

https://brainly.com/question/15267055

#SPJ9

The angle is 144°.

In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The English word "angle" derives from the Latin word "angulus," which means "corner." The vertex and the two rays are referred to as the sides of an angle, respectively, and are the shared termini of two rays. A shared terminal between two rays (half-lines) is joined to create an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.

Thus;

∠AOC + ∠COD + ∠BOD = 180°

Since AOB is a straight line:

⇒3x-10+50+x+20=180

⇒4x = 120°

⇒x = 30°

Thus, ∠AOC = 3x - 18

∠AOC = 3 × 30° - 18

∠AOC = 72°

2(72) = 144°

Learn more about angles:brainly.com/question/25770607

#SPJ1

Answer:

decay

Step-by-step explanation:

Because you are dying every second of the day and are growing only when your body is resting

Answer:

hey, good morning! the answer to this equation is growth!

Step-by-step explanation:

because if you figure out what 115% is as a decimal which is 1.15. and this decimal is above 1.

good luck!

Answer:

1) Wendy

2) Paige

3) 15%

4) 27%

5) Wendy and Vanessa

Step-by-step explanation:

Wendy 29%

Vanessa 21%

Oliver x

Mike 14%

Luke 12%

Paige 9%

Total 100%

First, let's find Oliver's percentage.

29 + 21 + x + 14 + 12 + 9 = 100

x = 15

Now we have:

Wendy 29%

Vanessa 21%

Oliver 15%

Mike 14%

Luke 12%

Paige 9%

Total 100%

1) Wendy

2) Paige

3) 15%

4) 12% + 15% = 27%

5) 29% + 21% = 50%: Wendy and Vanessa

Answer:

Step-by-step explanation:

Y is 2 when X is 6

The valid inferences are (a) and (c)

From the data in the table, we can make the following valid inferences:

Using the above as a guide, we have the following:

Other inferences are invalid

Read more about probability

https://brainly.com/question/251701

#SPJ1

The required ratio of trombones to all the brass section members is 3 : 7.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The total number of members in the brass section of the jazz band is:

4 trumpets + 3 trombones = 7 members

The ratio of trombones to all the brass section members can be expressed as,

= 3 trombones / 7 brass section members

This ratio cannot be simplified further because the numbers are relatively prime.

Therefore, the ratio of trombones to all the brass section members is 3 : 7.

Learn more about Ratio here:

brainly.com/question/13419413

#SPJ1

It will cost $2353.05 to pour concrete for the entire driveway

From the question, we have the following parameters that can be used in our computation:

Dimension = 15 3/4 yards by 3 yards.

Concrete costs $49.80 per square yar

The cost is calculated as

Total = Area * Cost

So, we have

Total = (15 3/4 * 3) * 49.8

Evaluate

Total = 2353.05

Hence, the cost is $2353.05

Read more about area at

https://brainly.com/question/22972014

#SPJ1

(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R'  is 1/2

(B) Coordinates of Δ P"Q"R"

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) Triangles PQR and P"Q"R" are not congruent.

Given

ΔPQR is transformed into ΔP'Q'R'

Coordinates of P, Q, R are

P (8,0),

Q(6,2)

R(-2,-4)

Coordinates of P'Q'R' are

P′(4, 0)

Q′(3, 1)

R′(−1, −2)

(A) By Distance formula we can find the distance between P Q and P'Q'

Distance formula = [tex]D = \sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]

Where D = Distance between two points

from distance formula we can write that

PQ = [tex]\sqrt{(6-8)^{2} +(2-0)^{2} } = \sqrt{4+4} =2 \sqrt{2}[/tex]

Similarly

P'Q'= √2

PQ /P'Q' = 2

hence the scale factor of dilation is 1/2 (Compression)

(B )The Coordinates of Reflection about y axis can be written for a point

(x,y) as (-x,y)

So the Coordinated of Δ P"Q"R" can be written as

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) ΔPQR  and ΔP"Q"R" are similar triangles but they are not  congruent because their sides  are not equal in size.

Learn more about Congruent triangles at:

brainly.com/question/12413243

#SPJ1

The solutions to the equations are;

(-3, 8) and (34/10, 156/16)

1) We can see that;

2x+y=2  ---- (1)

5x+3y =  9 ----- (2)

Multiply (1) by 5 and (2) by (2)

10x + 5y = 10 --- (3)

10x + 6y = 18 ----- (4)

Subtract 3 from 4

y = 8

Now substitute y =8 in (1)

2x + 8 = 2

x = 2 - 8/2

x = -3

Solution is; (-3, 8)

For question 2;

5x - 2y = -2 ---- (1)

3x + 4y =  30 ---- (2)

Multiply 1 by 3 and 2 by 5

15x - 6y = -6 ---- (3)

15x + 20y = 150 ----- (4)

Subtract (3) from (4)

16y = 156

y = 156/16

5x - 2(156/16) = -2

5x - 156/8 = -2

5x = -2 + 156/8

x = 34/10

Solution; (34/10, 156/16)

Learn more about equation:https://brainly.com/question/29657992

#SPJ1

The correct answer is: 2.8 is greater than 2.58.

A decimal value is a number expressed in the decimal system, which is based on the number ten. It includes a decimal point that separates the whole number part from the fractional part. The digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts of a whole number, which are expressed in powers of ten (tenths, hundredths, thousandths, etc.). For example, in the decimal value 3.14, the digit 3 represents the whole number part, and the digits 1 and 4 represent the tenths and hundredths parts, respectively. Decimal values are commonly used in mathematics, science, and everyday life to represent quantities that are not whole numbers, such as measurements, percentages, and money values.

Given by the question.

because the digit in the tenths place is larger in 2.8 than in 2.58. In decimal notation, the digit immediately to the right of the decimal point represents tenths, and larger values in this place indicate a larger overall value. In this case, 2.8 has a digit of 8 in the tenths place, while 2.58 has a digit of 5 in the tenths place. Therefore, 2.8 is greater than 2.58. The location of the numbers on a number line is not relevant for comparing decimal values, unless they have the same digit in the tenths.

To learn more about decimal:

https://brainly.com/question/2976558

#SPJ1

Answer:

Step-by-step explanation:

a) The area covered by algae 10 days after it was first spotted is approximately 32.64 square meters.

b) We can find the area covered by algae one day after it was first spotted by multiplying [tex]12.5^{1/7}[/tex] by 2.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

a.

To find the area covered by algae 10 days after it was first spotted, we need to convert 10 days into weeks, since the growth rate is given in terms of weekly doubling.

There are 7 days in a week,

So 10 days are approximately 1.43 weeks (10/7).

Let A be the area covered by algae in square meters after n weeks.

Then we can use the formula for exponential growth:

A = 12.5 x [tex]2^n[/tex]

Substituting n = 1.43, we get:

A = 12.5 x [tex]26^{1.43}[/tex]

A ≈ 32.64

Therefore,

The area covered by algae 10 days after it was first spotted is approximately 32.64 square meters.

b.

We know that the area covered by algae doubles each week.

One week is equivalent to 7 days, so after one week, the area covered by algae will be twice the initial area of 12.5 square meters, or 25 square meters.

We can represent this mathematically as:

A = 12.5 x [tex]2^1[/tex]

Now, let's consider what happens after two weeks, or 14 days.

The area covered by algae will double again, so it will be four times the initial area of 12.5 square meters or 50 square meters.

We can represent this mathematically as:

A = 12.5 x 2²

Using the same reasoning, we can find that after three weeks (21 days), the area covered by algae will be eight times the initial area or 100 square meters:

A = 12.5 * 2³

In general, we can see that after n weeks, the area covered by algae will be 2^n times the initial area of 12.5 square meters. This can be written as:

A = 12.5 x [tex]2^n[/tex]

If we want to find the area covered by algae after one day, we can use the fact that one day is equivalent to 1/7 of a week.

So, after one day, the area covered by algae will be:

A = 12.5 x [tex]2^{1/7}[/tex]

Simplifying this expression using the laws of exponents, we get:

A = [tex]12.5^{1/7}\times2[/tex]

Therefore,

We can find the area covered by algae one day after it was first spotted by multiplying [tex]12.5^{1/7}[/tex] by 2.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

The value of gravitational force between two masses is,

⇒ Gravitational force (F) = 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Two masses are,

m₁ = 6

m₂ = 8

d = 4

Now, We know that;

Gravitational force (F) = m₁ m₂ / d²

Substitute all the values we get;

Gravitational force (F) = m₁ m₂ / d²

Gravitational force (F) = 6 × 8 / 4²

Gravitational force (F) = 48/16

Gravitational force (F) = 3

Thus, The value of gravitational force between two masses is,

⇒ Gravitational force (F) = 3

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The height of the  building which casts a 103-foot shadow is 95.5 foot.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34.5-foot shadow

We need to find the height of the building.

Let us consider x be the height of building.

Form a proportional equation.

x/103=32/34.5

Apply cross multiplication

34.5x=32×103

34.5x=3296

Divide both sides by 34.5

x=3296/34.5

x=95.5

Hence, 95.5 foot be the height of the  building which casts a 103-foot shadow.

To learn more on Ratios click:

https://brainly.com/question/13419413

#SPJ9

Answer:

1.5748 in

Step-by-step explanation:

Answer:

1 inch = 2.54 cm

4 / 2.54 = 1.5748031496 inches

Step-by-step explanation:

If a data set has an outlier, the median would be the best measure of central tendency to use as it is less sensitive to extreme values compared to the mean.

The presence of an outlier can heavily skew the mean in the direction of the outlier, causing it to become an inaccurate representation of the center of the data. On the other side, the median is less sensitive to extreme values and represents the middle value of the dataset. It is calculated by finding the middle value in a dataset after arranging it in numerical order.

Therefore using the median as the measure of central tendency in a dataset with an outlier can provide a better indication of the typical value compared to the mean.

Learn more about data set brainly.com/question/30154121

#SPJ4

The ratio of the short side to the long side is 9/4 and the ratio of the hypotenuse to the long side is 5/4.

What is triangle ?

A triangle is a two-dimensional shape with three straight sides and three angles. It is one of the most basic and important shapes in geometry.

The three sides of a triangle can be of different lengths, or they can be of the same length, in which case it is called an equilateral triangle. The angles of a triangle can also vary, and they always add up to 180 degrees. Triangles can have acute angles (less than 90 degrees), right angles (exactly 90 degrees), or obtuse angles (greater than 90 degrees).

According to given information :

Ratio of short to long sides:

x/9 = 9/4

To solve for x, we can cross-multiply:

4x = 9 * 9

4x = 81

x = 81/4

So the ratio of the short side to the long side is:

x/9 = (81/4) / 9 = 81/36 = 9/4

Ratio of hypotenuse to long sides:

y/9 = 15/12

To solve for y, we can cross-multiply:

12y = 9 * 15

12y = 135

y = 135/12 = 45/4

So the ratio of the hypotenuse to the long side is:

y/9 = (45/4) / 9 = 45/36 = 5/4

Therefore, the ratio of the short side to the long side is 9/4 and the ratio of the hypotenuse to the long side is 5/4.

To know more about triangle visit :

https://brainly.com/question/1058720

#SPJ1