Graph the line with slope -1/3 passing through the point (2,-5) .

The leap pattern of the frog is up 2 steps then back 1 step. To reach 10th step she have to take 9 leaps up.

Let represent leaps up with positive number and leaps back with negative number.

Hence, the movement of the little green frog can be written as:

2 - 1 + 2 - 1 + 2 - 1 + ....

Notice, that every 4 leaps (both up and back) she reaches 2 steps.

2 - 1 + 2 - 1  = 2

Hence, after 4 x 4 = 16 leaps she will reach the 8th steps. The last leap in this instant is leap back. Hence, the next leap will be leaps up 2 steps, and she reaches the 10th steps.

In every 4 leaps there are 2 leaps up.

Therefore, she have to leaps up 2 x 4 + 1 = 9 leaps up.

You can also write all her leaps to reach the 10th steps:

2 - 1 + 2 - 1 +    2 - 1 + 2 - 1  +    2 - 1 + 2 - 1  +   2 - 1 + 2 - 1   + 2

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The requried days over which the mass of the kitten gets doubled is 9 days.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
Let the number of days be x,
According to the quesiton,
2×90 = 90 + 10x
180 - 90 = 10x
x = 9 days

Thus, the requried days over which the mass of the kitten gets doubled is 9 days.

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There are three main measures of central tendency: mean, median, and mode. Each of these measures has its own strengths and weaknesses, and can be affected differently by outliers.

Mean is the most commonly used measure of central tendency, and is calculated by adding all the values in a dataset and dividing by the total number of values. However, when there are outliers in a dataset, the mean can be significantly distorted. This is because outliers, which are extreme values that are far from the other values in a dataset, can skew the mean, making it a less accurate representation of the data than the median or mode.

On the other hand, the median is the middle value of a dataset, and is not affected by outliers as much as the mean. This is because the median is determined by the middle value of a dataset, and does not take into account every individual value.

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Answer: no

Step-by-step explanation:

The inverse of the function f(x) = 2x - 1  is f(x) = 1/2(x + 1)

An inverse of a function is a function that cancels the action of the given function.

The inverse of a function is obtained by reversing the given function.

In the problem, the function is  f(x) = 2x - 1. Hence,

y = f(x) = 2x - 1

Add  both sides with 1:

y + 1 = 2x -1 + 1

2x = y + 1

Divide both sides by 2:

x = 1/2 (y + 1)

Replace y with x

f(x) = 1/2 (x + 1)

Hence, the inverse function of f(x) = 2x - 1 is f(x) = 1/2 (x + 1)

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In a right-angled triangle, the sum of two acute angles is 90°.

An angle smaller than the right angle is called an acute angle.

An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle (which is equal to 90 degrees). For example, ∠30°, ∠45°, ∠60°, ∠75°, ∠33°, ∠55°, ∠85°, etc. are all acute angles.

The sum of all three angles is 180°, and one angle is 90°. So, the sum of the other two angles will be 90°.

Thus, In a right-angled triangle, the sum of two acute angles is 90°.

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The lines of equations y = 3x - 8 and y = 3x - 12 have same slope but they are parallel to each other and have no solution.

What is system of equations?

A System of Linear Equations is when we have two or more linear equations are working together.

The first equation is y = 3x - 8.

The second equation is y = 3x -12.

Substituting the value of y from equation 1 in equation 2 -

y = 3x -12

3x - 8 = 3x - 12

3x - 3x = -12 + 8

0 = 4

There is no x-intercept.

Substituting the value of x in equation 1 -

y = 3x - 8

y = 3(0) - 8

y = 0 - 8

y = -8

So, the lines do not intersect each other.

Therefore, the equations have same slope but do not have any solution.

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option A is correct, 5+0.5n=11 is the equation and value of n is 12.

Two or more expressions with an Equal sign is called as Equation.

Given sentence is  5 increased by half a number is 11.

In the sentence increases means added and half means 1/2 of a number.

Here the unknown number is n.

5+n/2=11

5+0.5n=11

Subtract 5  on both sides

0.5n=6

Divide both sides by 0.5

n=12

Hence, option A is correct, 5+0.5n=11 is the equation and value of n is 12.

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Answer:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is always the same. In this case, the common difference between the terms 29, 37, 45, is 8.

To find the 59th term of an arithmetic sequence, you can use the formula:

a_n = a_1 + (n-1)d

Where:

a_n is the nth term of the sequence

a_1 is the first term of the sequence

n is the position of the term you are trying to find

d is the common difference between the terms of the sequence

In this case:

a_1 = 29

n = 59

d = 8

So, to find the 59th term of this arithmetic sequence, you would do:

a_n = 29 + (59-1)8 = 29 + (58)8 = 29 + 464 = 493

So, the 59th term of this arithmetic sequence is 493.

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The correct question is

What is the 59th term of the arithmetic sequence 29, 37, 45?

Answer:

x = 7

Step-by-step explanation:

cause the lines on the left are the same and the lines on the upper part are the same so thats why the longer lines are parallel to each other.

that means the the angles are the same.

6x + 1 = 9x - 23

-3x = -24 ... ×(-1)

3x = 24 ... ÷3

x = 7

The inequality that can be used to determine the greatest number of games he can bowl is D. 4.25 + 2.5x ≤ 25.

An inequality is a mathematical statement that compares the value of two expressions using one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), ≠ (not equal to). Inequalities are used to express relationships between numbers and can be used to describe constraints or limitations in real-world problems.

Let x be the number of games Manny can bowl

We can write the inequality as:

$2.50(x) + $4.25 ≤ $25.00

2.5x + 4.25 ≤ 25

To solve for x, we subtract 4.25 from each side. Then, divide both sides by 2.5.

2.5x + 4.25 - 4.25 ≤ 25 - 4.25

2.5x ≤ 20.75

x ≤ 8.3

Hence, Manny can bowl as much as 8 games.

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The domain of f(x) =7 is all real numbers and the range of f(x)= 7 is 7.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

This is a function f(x)=7 defined for all real arguments x, so its domain is all real numbers (−∞,+∞).

Since for any value of an argument the function takes a value of 7, its range is one and only one real number y=7.

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Linear functions are those whose graph is a straight line.

If you have a table to look at instead of a graph, you should look at the rate of change. If the rate of change in the input to the rate of change in the output is the same at all points in the table, the table represents a linear function. Linear functions have a straight line as their graph. There is one independent variable and one dependent variable in a linear function. X is the independent variable, while y is the dependent variable.

Check to verify if the function has a constant rate of change to determine whether it is linear or nonlinear.

Choose any two rows from the database and compute the rate of change between them.

Now choose a different

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The solution to the equation "5*2-3^2 / (3^2-(-2))^2" after solving it is 1/121

To solve the equation 5*2-3^2 / (3^2-(-2))^2, we need to simplify the numerator and the denominator. This will give us this:

5*2-3^2 / (3^2-(-2))^2 =

= 10 - 9 / (9 - (-2))^2

Simplify further to make the number reduced

10 - 9 / (9 - (-2))^2

After the subtraction at the numerator level, the denominator figures have two minus signs which becomes a plus. As a result, we realize the value below

= 1 / (11)^2

In order to remove the bracket in the denominator, it implies that the number in bracket will be multiplied by itself since it is in the superscript of 2 which means 11 multiply by 11 or (11 x 11)

= 1/121

Therefore, to solve the equation 5*2-3^2 / (3^2-(-2))^2, one needs to simplify the equation and do the subtraction and addition from the numerator and the denominator respectively to realize the answer which is 1/121

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Answer: 1/121

Step-by-step explanation:

( 5 * 2 - 3^2 )/[ 3^2 - (-2)] ^ 2

= (10 - 9)/(9+2)^2

= 1 / 11^2

= 1/121

Answer:

the answer is c, I took the test and it's C

The probability that the mean of the next 100 claims is larger than $1000 is 0.1791 or 17.91%.

Since the sample size of 100 claims is large enough, assume that the sampling distribution of the mean is approximately normal.

The mean of the sampling distribution of the mean is equal to the population mean, which is $920 in this case. The standard deviation of the sampling distribution of the mean, also known as the standard error, is equal to the population standard deviation divided by the square root of the sample size. In this case, the standard error is $870/√(100) = $87.

Use the normal distribution to calculate the probability that the mean of the next 100 claims is larger than $1000. Use a z-score to find this probability.

The z-score is given by (x - μ)/σ , where x is the value of interest, in this case is $1000, μ is the population mean, which is $920 and σ is the standard error, which is $87.

z = ($1000 - $920)/$87 = 0.9195

Use a standard normal table or a calculator to find the probability corresponding to z-score = 0.9195.

p = 0.8208529999999999

Subtract it from 1.

p = 1 - 0.8208529999999999 = 0.179147

Therefore, the probability that the mean of the next 100 claims is larger than $1000 is 0.1791 or 17.91%.

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The first three terms of the given sequence are -17, -27 and -37

A sequence is an ordered list of objects. Like a set, it contains elements. The number of ordered elements (possibly infinite) is called the length of the sequence.

Given that, an arithmetic sequence formula an = -10n - 7

We are asked to find the first three terms of this sequence.

Therefore,

Put n = 1 for first term,

a₁ = -10(1)-7

a₁ = -17

Put n = 2 for second term,

a₂ = -10(2)-7

a₂ = -27

Put n = 3 for third term,

a₃ = -10(3)-7

a₃ = -37

Hence, the first three terms are -17, -27 and -37

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The shortest possible distance between Trae and Katrina is 6 feet.

Since Yana, Josh, and Katrina are standing at the vertices of a right triangle, the distance between Yana and Josh is the hypotenuse of the triangle and the other two sides are the legs.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Using the Pythagorean theorem, we can calculate that the distance between Yana and Katrina is 15 feet.

( 18^2 + 12^2 = 15^2)

Since Trae is standing between Josh and Katrina, the shortest possible distance between Trae and Katrina is half of the distance between Josh and Katrina, which is 6 feet.

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Answer:

5

Step-by-step explanation:

slope = rise/run or y-value/x-value

point=(10,50)

50/10=5

slope=5

You can use the distance formula, which is Distance = Speed x Time, to determine the bus's speed. In this instance, the trip is 54 kilometers long and takes 90 minutes.

 To answer a problem quickly, rearrange the formula as follows:

     Speed = Distance / Time

 Therefore, you must convert time from minutes to hours in order to determine the speed. 90 minutes are equal to 1.5 hours because there are 60 minutes in an hour.

After that, you may enter the formula with the known values for time and distance:

54 km travelled in 1.5 hours equals 36 km/h.

therefore , the bus travels at a 36 km/h speed.

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The quantity of medication provided to patient is 20 mcg.

A: The ratio formed with respect to x is x:20.

B: Mark should deliver 20 mcg of medication.

What is multiplication?

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the numbers that are multiplied are referred to as the factors.

The quantity of medication recommend is a = 0.4 mcg / kg

The weight of patient is b = 50 kg

Let x be the amount of medication Mark should deliver.

So, the quantity of medicine provided to patient = Weight of patient (b) × Quantity recommend (a)

The equation formed is - x = b × a.....equation 1

The ratio will be - x/ba.....expression 1

Equating the values in expression 1 -

x:0.4 × 50

x:20

Now, substituting the values in equation 1 -

x =  b × a

Applying the arithmetic rule of multiplication -

x = 0.4 × 50

x = 20

Therefore, the patient should be given 20 mcg of medication.

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The answer is 4-9 is the expression is equivalent to (4−3)−6.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

the expression is,

(4-3)-6

= 1-6

= -5

so,

4-9 = -5

Hence, The answer is 4-9.

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Answer is attached here.

The two equations represent the same line.

Here we have the two linear equations below:

y = (1/6)*x + 5

y - (1/6)*x = 5

Remember that:

Two linear equations are parallel if the slope is equal and the y-intercept is different, and two linear equations are perpendicular if the product between the slopes is -1.

Now we can rewrite the second equation just by adding (1/6)x in both sides:

y = (1/6)*x + 5

y = (1/6)*x + 5

So both equations are equal, then the equation represent the same line.

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The word polynomial is made composed of the phrases poly and nominal, which collectively denote "many" and "terms". Using mathematical operations like addition, subtraction, multiplication, and division, exponents, constants, and variables are combined to form a polynomial (No division operation by a variable).

Depending on how many terms are included, the expression is classified as a monomial, binomial, or trinomial. Polynomials are algebraic expressions that use coefficients and variables. Variables may occasionally be referred to as "indeterminates." Addition, subtraction, multiplication, and positive integer exponents are all arithmetic operations that can be performed on polynomial expressions, however division by variables is not one of them.

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The required way to write logarithmic function is [tex]\log_{b}({b^x})=x[/tex]

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number. If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n. For instance, 23 = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log2 8.

The formula for the logarithmic function is f(x) = log base b of x. The base 10 is used for the common log.

The base used by the natural log is e, an irrational integer with the value 2.71828.

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The difference in the means is about 4.3 to 10.5 times the MAD.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
volleyball: mean = 86, MAD = 19.6
basketball: mean = 185, MAD = 17.7
The difference in volleyball the means to MAD is given as,
= 86 / 19.6

= 4.3  

The difference in basketball the means to MAD is given as,
= 185 / 17.7

= 10.5

Thus, the difference in the means is about 4.3 to 10.5 times the MAD.

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Answer:

√((x2-x1)^2 + (y2-y1)^2)

Step-by-step explanation:

To find the distance between two points in fractions, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

To use the Pythagorean theorem to find the distance between two points, you can think of the two points as the endpoints of one of the legs of the right triangle. Let the two points be (x1, y1) and (x2, y2). The distance between the two points is the length of the hypotenuse of the right triangle formed by the two points and the origin. The distance can be computed using the formula:

distance = √((x2-x1)^2 + (y2-y1)^2)

This will give you the distance between the two points in whatever unit you are using for x and y.

When using the "by substitution" method, one of the equations is solved for one of the variables before being "substituted" back into the other equation and the other equation being solved for. Next, you solve backwards to find the first variable.

What is  substitution method ?

The algebraic technique for resolving multiple linear equations at once is called the substitution method. As implied by the name, this strategy involves replacing a variable's value from one equation with another.

What does the differential equations substitution approach entail?

Differential equations can be transformed and handled in numerous ways using the substitution method, which can also be used to solve them.

                         The main idea is to substitute a new variable that is expressed in terms of both the dependent and independent variables for the original independent or dependent variable.

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The given expression if 23+37=60 does 23+37+9=60+97 is not true.

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,

23 + 37 = 60 ____(1)

Now,

From (1),

23 + 37 + 9 = 60 + 97

23 + 37 + 9 = 157

60 + 9 = 157

69 ≠ 157

This is not true.

Thus,

The given expression is not true.

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