This year’s favorite to win the frog jumping event is Newton. The objective is to take the longest jumps and stop as close as possible to 120 steps. Pythagoras and Fermat are Newton’s toughest competition. ● Newton takes 4 jumps and falls short of the mark by 4 steps. ● Pythagoras takes 5 jumps and overshoots the mark by 5 steps. ● Fermat hits the mark exactly after 6 jumps. How long, in steps, is each frog’s jump?

A. 5/10, -6/11, 7/12, -8/13

B. f(n) = n/(n+5)

C. Positive

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.

Here, we have

A. From inspection of the sequence, the pattern is:

Add 1 to the numerator of the previous term.

Add 1 to the denominator of the previous term.

Make every other term negative.

Hence, assuming the pattern continues, the next four terms in the sequence will be:

5/10, -6/11, 7/12, -8/13

B. An explicit formula for an arithmetic sequence allows you to find the [tex]n^{th}[/tex] term of the sequence.

f(1) = 1/6

f(2) = -2/7

We can see that the numerator is the position of the term (n) in the sequence.  So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.

The denominator is 5 more than the position of the term in the sequence.  So when n = 1 the denominator is 1 + 5 = 6, and when n = 2 the denominator is 2 + 5 = 7.

We observe that if the numerator (the value of n) is odd then the term is positive, and if the numerator  (the value of n) is even then the term is negative.

Hence, the rule for the nth term is:

f(n) = n/(n+5)

If n is odd then f(n) is positive.

If n is even then f(n) is negative.

C. 53 is an odd number.

As the function f(n) is positive when n is odd, the sign of f(53) is positive.

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Answer:10

Step-by-step explanation:

got the same question

Answer:

Step-by-step explanation:

We know that : Percentage means 'divided by 100'

therefore, 1/2 percent = 1 / 2 ÷ 100 = 0.5 ÷100 = 5÷1000= 0.005

A. The amplitude of the sinusoidal function 's' would increase.

B. The midline of the sinusoidal curve will upshift.

A function that repeats its values at regular intervals is said to be periodic. For instance, periodic functions include trigonometric functions, which repeat every 2 pi radian. In science, periodic functions are used to describe oscillations, waves, and other periodic events. Aperiodic refers to any nonperiodic function.

We know the moving mechanism of the pendulum can be graphed as a periodic function.

A. If the pendulum is pulled farther away from its resting point it will reach a greater height on both sides this would have an effect of an increase in the amplitude of the sinusoidal curve.

B. If the pendulum is pulled farther away from its resting point the midline of the sinusoidal curve would move up along the y direction as a result of an increase in magnitude.

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Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them.

Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them. The difference between the two numbers is the sum's product.

Subtracting two integers from each other is a type of subtraction.

The process for determining the difference between two decimals and two whole numbers is the same.

We only add a new step.

Finding the difference between 8.967 and 7.2, for instance, could appear more difficult.

To give them all the same amount of decimal places, we must first convert each decimal.

7.2 becomes 7.200 as a result.

The computation may now be done as before:

8.967 - 7.200 = 1.767

Therefore, there is a 1.767 discrepancy between these figures.

In order to find the difference between two fractions, simplify and find the lowest common denominator of each fraction.

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Answer:

$22

Step-by-step explanation:

27.50 20 present off so you get 5.5 substract and u get 22

The best approach to solve the problem is writing an equation. Given Avelina earns half of what Gus earns, the equation becomes Avelina's earnings = Gus's earnings / 2. On substituting Gus's earnings with $125, we get Avelina's earnings to be $62.50.

The best problem-solving strategy that would be apt to solve this problem, 'Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn?' is to write an equation. We know that Avelina earned half of what Gus earned. This can be represented by the equation: Avelina's earnings = Gus's earnings / 2.

Since we know that Gus earned $125, we can substitute this value into our equation: Avelina's earnings = $125 / 2. Solving this equation gives us the answer: Avelina earned $62.50.

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In each shape there are 4 wholes hence the answer is yes.

A fraction is referred to as the portion of a whole in mathematics. There are two components to a fraction: a numerator and a denominator. The numerator is the number at the top, and the denominator is the number at the bottom.

13a. There are 4 wholes, hence the answer is yes.

13b. Every whole is divided into 2 parts hence the total number of equal parts is 4 *2 = 8. Hence the answer is yes.

13c. The answer is yes.

13d. No

13e. No

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Answer:

  2x +3y = 15  or  y = -2/3x +5

Step-by-step explanation:

You want the equation of the line with y-intercept 5 and x-intercept 7.5.

The intercept form equation can be written ...

  x/a +y/b = 1

where 'a' is the x-intercept and 'b' is the y-intercept.

The given intercepts of a=7.5 and b=5 mean we can write the equation as ...

  x/7.5 +y/5 = 1

Multiplying by 15 gives the standard-form equation ...

  2x +3y = 15

Solving for y gives the slope-intercept equation ...

  y = -2/3x +5

y = 0.25x + 50 and y = 0.3x + 40 will be the equation to find the cost to rent a car.

A mathematical formula known as a cost function is used to visualize how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.

Costs are the dollar amount spent on materials, labor, services, goods, equipment, and other items for use by a company or other accounting organization.

y = 0.25x + 50

y = 0.3x + 40

The equations will be written as y = mx + b, or slope-intercept form. You must determine what you have in order to determine what belongs where.

They receive $50 per day plus $0.25 per mile from Rent-A-Wreck. This indicates that the $0.25 per mile is the number that changes daily. Thus, y = 0.25x + 50 will be the equation.

They receive $40 per day with $0.30 per mile from Drive-A-Lemon. This indicates that the $0.30 per mile is the number that changes daily. y = 0.3x + 40 will be the formula.

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The fish is closer to sea level. Sea level is defined as the mean sea level, which is a fixed point of reference for measuring altitude.

The altitude of the fish is -20.2 meters, which is closer to sea level than the altitude of the bird at 38.1 meters. This means that the fish is closer to sea level than the bird.  To explain further, sea level altitude is a point of reference that is used to measure the altitude of other objects. Sea level altitude is defined as the mean sea level which is a fixed point.

Therefore, when trying to determine which animal is closer to sea level, it is important to look at the altitude of both the fish and the bird. The altitude of the fish is -20.2 meters, which is closer to sea level than the altitude of the bird at 38.1 meters. This means that the fish is closer to sea level than the bird.

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Answer:

Step-by-step explanation:

set 1 is the work, then 60 works finish 1/21 per day. [tex]\frac{1}{21*60}[/tex] is the work for per workers. so, the days for 70 workers is [tex]\frac{21*60}{70}=18[/tex] days.

it will spend 18 days to complete

Basic quadratic expression:

[tex]ax^2+bx+c[/tex]

[tex]2x^2+5x-42[/tex]

Factoring a quadratic expression when a ≠ 0

1.  Multiply a and c values (ac=k)

[tex]2(-42) = -84[/tex]

2. Find a factor pair whose sum adds to b and has the product of k

[tex]-7,12[/tex]  

[tex]-7(12)=-84[/tex]           [tex]-7+12=+5[/tex]

3. Replace the middle term (bx) with newfound values

[tex]2x^2 +12x-7x-42[/tex]

4. Factor by grouping

[tex]2x(x+6) -7(x+6)[/tex]

5. Perform the last factorization

[tex](2x-7)(x+6)[/tex]

If 1 Swedish krona was worth 0.12 US dollar , and if he took d dollars for the trip then the equation that is used to find the value in Swedish krona (k) of the dollars is option (a) [tex]k = 0.12\times d[/tex] .

The value of 1 Swedish krona is = 0.12 US dollar ,

the number of dollar that Souta took on the trip is = d dollars ;

we have to find the equation that can be used to find the equation in Swedish krona "k" of the dollars ,

According to the question ,

the equation for Swedish krona can be represented as [tex]k = 0.12\times d[/tex] ;

Therefore , the required equation is [tex]k = 0.12\times d[/tex] .

The given question is incomplete , the complete question is

When Souta went to Sweden, 1 Swedish krona was worth about 0.12 US dollar. He took d dollars on the trip. Which equation could be used to find the value in Swedish krona, k, of the dollars ?

(a) k = 0.12d

(b) dk = 0.12

(с) 0.12k = d

(d) k = 1.12d

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Answer: HL

Step-by-step explanation:

HL because the hypotenuse leg theorem shows how a given set of right triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal.

A log 10 transformation is a mathematical operation that is used to change the scale of a variable in a data set. The log 10 transformation is applied to the variable by taking the base-10 logarithm of each value in the data set. The result of this operation is a new variable that is on a different scale than the original variable.

The log 10 transformation is commonly used in statistics and data analysis to normalize data that is on a large scale, such as data that spans several orders of magnitude. By applying the log 10 transformation, the data is transformed into a more manageable scale that is easier to work with and analyze.

The log 10 transformation can also be used to stabilize the variance of a variable, this is particularly useful when the data is positively skewed. The log 10 transformation can also be useful for data that has a multiplicative relationship, for example, population growth or stock prices.

It is important to note that the log 10 transformation can only be applied to data that is positive and greater than zero because the logarithm of zero or a negative number is not defined.

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The y-intercept of (0,4) is 4.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.

The y-coordinate of the y-intercept is determined by computing  f(0) if the curve in question is supplied as y=f(x), y=f(x), etc. There is no y-intercept for functions that have an  value at x = 0.

The constant term a is the y-coordinate of the y-intercept if the function is linear and is written in slope-intercept form as  f(x)=a+bx"

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The factorization of the polynomial x² + 3x + 2 gives (x + 1)(x + 2)

An equation is an expression that shows how numbers and variables relate with each other.

A polynomial is an expression consisting of variables and their exponents with operations of addition and subtraction. Polynomials are classified based on degree as linear, quadratic and cubic.

The standard form of a quadratic equation is:

y = ax² + bx + c

where a, b and c are constants.

Given the polynomial:

x² + 3x + 2

Factorizing the polynomial:

x² + 2x + x + 2

= x(x + 2) + 1(x + 2)

= (x + 1)(x + 2)

The factorization gives (x + 1)(x + 2)

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There are 15 different books and 3 each can be arranged on a shelf i.e., there are 15/3 i.e., 5 shelves to arrange the book in the the display case.

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The plane intercepts on the x,y, z axes are 1, ∞, and 1/2. Hence, the Miller indices for the plane inside the cubic unit cell is (102).

Miller indices are used to specify planes and directions. These planes and directions could be in lattices or crystals. The number of indices will correspond to the size of the lattice or crystal.

In the given graph, the plane intercepts are:

x-intercept : 1

y-intercept : ∞  (since the planes does not intercept y-axes)

z-intercept = 1/2

Take the reciprocal:

1/1 = 1

1/∞ = 0

1/(1/2) = 2

Hence, the miller indices are (102)

The graph in your question is missing. Most likely it was like on the attached picture.

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Answer:

d

Step-by-step explanation:

Answer:

SaS

Step-by-step explanation:

The measure of ∠Z is 165 degrees to the nearest degree.

In a triangle, the measure of each angle is equal to the sum of the measures of the other two angles subtracted from 180 degrees. This is known as the Triangle Sum Theorem.

Given that x = 5.2 inches, y = 9.8 inches, and z = 7.1 inches in triangle XYZ, we can use the theorem to find the measure of angle Z.

∠Z = 180 - (x+y)

∠Z = 180 - (5.2+9.8)

∠Z = 180 - 15

∠Z = 165

So the measure of ∠Z is 165 degrees to the nearest degree.

Therefore, The measure of ∠Z is 165 degrees to the nearest degree.

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Answer:6 days

Step-by-step explanation:

62-26=36

36/6=

6

The explicit formula of the sequence is aₙ = -10 + 8n

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

The first term and the common difference

These values of the first term and the common difference are given as

First term = -2

Common difference = 8

The interpretation of the above sequence is that the 8 is added to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

aₙ = aₙ₋₁ + 8

When represented explicitly, we have

aₙ = a + (n - 1) * d

Where

a = -2 and d = 8

Substitute the known values in the above equation, so, we have the following representation

aₙ = -2 + (n - 1) * 8

Evaluate the products

aₙ = -2 + 8n - 8

Evaluate the like terms

aₙ = -10 + 8n

Hence, the explicit formula is aₙ = -10 + 8n

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Therefore , the solution of the given problem of function comes out to be  f(x) = 2871 thousands.

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.

Here,

Given :

=>  f(x) = 225(1.29)×

After 10 year number of years x =10

=> f(x) = 225(1.29)¹⁰

=> f(x) = 12.76 * 225

=>  f(x) = 2871 thousands.

Therefore , the solution of the given problem of function comes out to be  f(x) = 2871 thousands.

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Answer:

Step-by-step explanation: Two quarters, 50 pennies: N = 52 (N+1 = 53) One quarter, 75 pennies: N = 76 (N+1 = 77) 100 pennies, N = 100 (N+1 = 101) 6 nickels, 70 pennies: N = 76 (N+1 = 77)

Answer:

2 quarters, 2 dime's, 1 Nickel, 2 penny's

Step-by-step explanation:

Well u well need to quarters because 2 quarters are $25 cent then u well need 2 dimes because when your counting dime's that 10 20 30 40 50 so to dime's and 1 Nickel that makes $75 cents so u need 2 penny's and that makes 77

The Graph solution to this inequality on the number line is lies between -4 > 8.4 and their numbers are -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3.

Draw a circle around the number to indicate an inequality, such as x>3, on a number line (e.g., 3). In case the sign also states equal to, complete the circle (or ). If the sign doesn't include equal to (> or), leave the circle empty.

When plotting an inequality, use the,, >, or sign as a = sign. If the inequality is either or, graph the equation as a dotted line. If the inequality is either or, graph the equation as a solid line.

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The missing side of a right triangle without using a calculator can be found by using the Pythagoras theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of the hypotnuse (longest side) is equal to the sum of the square of the perpendicular and base .

that means : [tex]Hypotnuse^{2} = Perpendicular^{2} + Base^{2}[/tex]  ;

let the missing side of the right triangle  be the hypotnuse ;

So , missing side can written as :  [tex]Hypotnuse = \sqrt{Perpendicular^{2} + Base^{2}}[/tex] .

For Example : Let the right triangle has sides lengths as perpendicular = 6 and hypotnuse = 10

The length of side "base" is unknown.

So ,  to find length of side b, we put the known values into theorem:

[tex]10^{2} = 6^{2} + Base^{2}[/tex] ;

[tex]base^{2} = 100 - 36[/tex] ;

So , the missing side "base" = 8 ;

Therefore , the missing side without using calculator can be found by the Pythagoras Theorem .

The given question is incomplete , the complete question is

How do you find the missing side of a right triangle without a calculator when the other two sides are given ?

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Yes S lies as the perpendicular bisector as asked in the question .

The distance is calculated with the use of distance formula,

d = √( x2 - x1 )² + ( y2 - y1 )²

Now , we are suppose to calculate the distance between the points S and R, given their values are ,

S=(4,-2) and

R=(3,7)

Using distance formula ,

d = √( 3 - 4 )² + ( 7 - (-2))²

d =  √ 1 + 81

=  √82

Now, the distance between Q and S can be found as ,

Q=(-5,-1)

S=(4,-2)

d = d = √(4 + 5)² + ( -2 + 1)²

d =  √ 81 + 1

=  √82

As the distance between the two ends of the segment and the point S is the same, the point S must lie on the perpendicular bisector of QR, according to the perpendicular bisector theorem.

For question number 9 the distance between Q and S are,

Q=(-5,4)

S=(-2,-5)

d = √( -2 -5)² + ( 5 - 4)²

d =  √ 9 + 1

=  √10

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