1. The exponential function modeled below represents the number of square
kilometers of land occupied by cane toads x years after this animal was first
introduced into Australia,
Area Occupied by Cane Toads
Time
Area
1,200
(y)
(km)
1,100
1,000
0
36,500
900
5
53,600
800
700
10
78,800
600
15
115,780
500
20 170,120
400
25
250,000
300
200
30 367,300
100
539,700
0 5 10 15 20 25 30 35
Time (y)
Based on the data, which measurement is closest to the number of square
kilometers of land that will be occupied by cane toads 40 years after this
Area (thousands of km)
35
< PREVIOUS

The number of days it will take Sharon to hit her target 700 points is 21 days

490 + 10g = 700

Subtract 490 from both sides

10g = 700 - 490

10g = 210

divide both sides by g

g = 210 / 10

g = 21

Therefore, it will take Sharon 21 days to meet her target points.

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Answer:

-3/2

Step-by-step explanation:

Let's call the number we're trying to find "x". When we double x and then subtract 3, we get 2x-3. The statement says that this is the same as if we had quadrupled x, which would be 4x. We can set these two expressions equal to each other to create an equation:

2x - 3 = 4x

We can solve this equation by first adding 3 to both sides to get rid of the negative number:

2x - 3 + 3 = 4x + 3

This simplifies to:

2x = 4x + 3

We can now subtract 4x from both sides to get rid of the 4x term:

2x - 4x = 4x + 3 - 4x

This simplifies to:

-2x = 3

Finally, we can divide both sides by -2 to solve for x:

(-2x) / (-2) = 3 / (-2)

This simplifies to:

x = -3/2

Therefore, the number we were trying to find is -3/2.

Answer:

Let's call the number we're trying to find "x". If we double x and then subtract 3, we get the expression 2x - 3. If we quadruple x instead, we get the expression 4x. We are looking for a value of x that makes these two expressions equal, so we can set them equal to each other and solve for x:

2x - 3 = 4x

To solve this equation, we can first combine like terms on each side by adding 3 to both sides and then dividing both sides by 2:

2x - 3 + 3 = 4x + 3

2x = 4x + 3

Combining like terms on the left side gives us:

2x - 4x = 4x + 3 - 4x

0 = 3

This equation is clearly false, since no value of x can make 0 equal to 3. Therefore, there is no solution to this problem, and the original number cannot be determined.

In general, if you are trying to solve a problem involving algebraic equations and you end up with a false equation (like 0 = 3 in this case), it means that there is no solution to the problem. This can happen for a variety of reasons, but in this case it is because the original problem statement was not possible or did not make sense.

Step-by-step explanation:

Answer:

Equations of parallel and perpendicular lines The equation of a straight line is represented as \ (y=ax+b\) which defines the slope and the \ (y\)-intercept. Here \ (a\) represents the slope of the line. Since two parallel lines never intersect and have the same slope, their slope is always equal.

Step-by-step explanation:

Subtraction property of equality is B, -4.

What is subtraction property?

The Subtraction Property of Equality states that if two expressions are equal, then the same expression minus any number will also be equal. In other words, if a = b, then a - c = b - c. This property is important in algebra, as it allows us to solve equations by subtracting the same number from both sides. This property is also known as the Subtraction Property of Equality or the Subtraction Property of Equality of Two Values. It is an important concept that allows us to solve equations, and it is used in all levels of mathematics.

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Mean of the given numbers is 5.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

given numbers are 2 3 5 7 8

Mean is given by the formula

       Mean = Sum of all the items/Number of items

           x = 2 +3 + 5 + 7 + 8/5

           x = 25/5

           x = 5

Mean of the given numbers is 5.

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​

The interpretation of the x-intercept in the context of the given problem is: B. After 16 months, the business will have $0 remaining in their technology budget.

To find the x-intercept of an equation, substitute the value of y = 0, and solve for x. It is the value of x when y or the output = 0.

Given the equation, T(x) = −135x + 2160, where T(x) is the amount of money remaining in the budget for technology, and x is the number of months, the x-intercept would be the number of months that the business will have $0 in their budget for technology.

To find the x-intercept, substitute T(x) = 0, into T(x) = −135x + 2160:

0 = −135x + 2160

135x = 2160

Divide both sides by 135

135x/135 = 2160/135

x = 16

This means after 16 months, the technology budget that the company will have remaining is $0.

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Answer:

To find the mean height of all 10 children, we need to find the total height of all the children and divide it by the number of children. The total height of the four girls is 4 * 1.4 = <<41.4=5.6>>5.6m

The total height of the six boys is 6 * 1.7 = <<61.7=10.2>>10.2m

The total height of all 10 children is 5.6 + 10.2 = <<5.6+10.2=15.8>>15.8m

The mean height of all 10 children is 15.8/10 = <<15.8/10=1.58>>1.58m. Answer: \boxed{1.58}.

Step-by-step explanation:

The correlation coefficient is a numerical measure of the strength of the linear relationship between two variables. It ranges from 0 to 1, with 0 indicating no linear relationship, and 1 indicating a perfect linear relationship. A value of 0.5 or higher is considered a strong correlation.

The correlation coefficient is calculated by taking the covariance between two variables and dividing it by the product of the standard deviations of the two variables. The formula is as follows:

r = covariance(x,y) / (stdDeviation(x) * stdDeviation(y))

The correlation coefficient is a statistical measure used to quantify the strength of the linear relationship between two variables. It takes a value between 0 and 1, with 0 indicating no linear relationship, and 1 indicating a perfect linear relationship. The correlation coefficient is calculated by taking the covariance between the two variables and dividing it by the product of their standard deviations. A negative correlation coefficient means that as one variable increases, the other decreases. A value of 0.5 or higher is considered a strong correlation. The correlation coefficient can be used to determine the strength of the relationships between variables, whether they are linear or non-linear. It is an important tool for data analysis and can help to identify relationships between different variables.

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Answer:

Domain:

[tex]0 \leqslant x \leqslant 4[/tex]

Range:

[tex]0 \leqslant x \leqslant 64[/tex]

After solving the equation, the time in minutes Bob rides the scooter will be equal to 97 minutes.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Total price paid to start the scooter = $3

Price of ride per minute = 11 cents

1 dollar  = 100 cents

So, 11 cents = 11/100 = $0.11 per minute

Then, the equation will be,

$3 + $0.11(x) = $13.67

Here, x is the total number of minutes.

0.11x = 13.67 - 3

0.11x = 10.67

x = 97 minutes.

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Answer:

2) y ≥ 2x - 3

Step-by-step explanation:

3 and 4 would be eliminated because the line does not intersect at (0, 2), but rather (0, -3).

Answer:

$12

Step-by-step explanation:

given:

Stefan sells jin a bicycle for $114 and a helmet for $18.

we're gonna add to get the total cost 114 + 18 = $132

The total cost is 110% of what he spent originally to buy the bike and helmet.

divide 110% by 100 to get the answer in decimal which if you calculate is 1.1

now we're gonna make a simple equation and assume what Stefan spends originally is x

1.1 * x = 132

1.1x = 132

(now we want x to be alone so we can find its value so divide both sides by 1.1 (division is the opposite of multiplication if, for example, we have 1.1 - x   1.1 is positive so take it to the other side it'll be negative))

after dividing x=120

therefore, he originally spent $120

and to find how much money Stefan made we're gonna subtract 132-120 = $12

Stefan made $12

Answer:

There isn't enough information to solve for x.

Step-by-step explanation:

The way the statement of similarity is written, we get this proportion:

TY/CH = TL/CK = YL/HK

Replace segment names with lengths:

TY/10 = 25/CK = (4x - 1)/(x + 5)

There isn't enough information to solve for x.

Answer: The rate of change of the distancebetween the bottom of the ladder and the wall at that instant is 6.67 meter per minute.Let us consider that distance between the top of the ladder and the ground is x meterand distance between the bottom of the ladder and the wall is y meter.So, A right angle triangle is formed.Since, the bottom of the ladder is 21 meters from the wall.So,    Applying Pythagoras theorem,                         Given that,   the distance between the top of the ladder and the ground is decreasing at 7 meters per minute.                           Differentiate below equation with respect to time.                     Thus, the rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute

Step-by-step explanation:

Let x be the coefficient of y^2 in the expression 2x^2y+10xy^2-5y^2. So x=5.

A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves.

As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.

The given algebraic expression is 2yx^2+10xy^2-5y^2.

The terms are xy^2, yx^2 any y^2

So the co-efficient of y^2 is 5.

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Answer:

3 (for the box), p=1

Step-by-step explanation:

Since they want you to follow the instructions, divide by 2 to get (5p-2p) alone.

6p/2 = 3p (exactly like 6/2)

You will get 3p=5-2p

To solve the rest of the equation, add 2p to both sides (once you add 2p to the left side, it gets rid of it on the right side by canceling it out)

3p=5-2p

+2p  +2p

5p=5

Divide 5p by 5 to get p by itself.

5p/5 = 5/5

That is p = 1

The six steps to solve inequality are -:

Add the same number to both sides.

Subtract the same number from both sides.

Multiply both sides by the same positive number.

Divide both sides by the same positive number.

Multiply both sides by the same negative number and reverse the sign.

Divide both sides by the same negative number and reverse the sign.

Inequality—the state of not being equal, especially in status, rights, and opportunities1—is a concept very much at the heart of social justice theories. However, it is prone to confusion in public debate as it tends to mean different things to different people. Some distinctions are common though.

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Add the same number to both sides.

Subtract the same number from both sides.

Multiply both sides by the same positive number.

Divide both sides by the same positive number.

Multiply both sides by the same negative number and reverse the sign.

Divide both sides by the same negative number and reverse the sign.

To rewrite an expression in equivalent form, you can use the distributive property, combine like terms, apply the commutative property, or use identities to simplify and rearrange the expression.

The distributive property states that multiplying a term and a sum of two or more terms is the same as multiplying each individual term and then adding the products together. It can be used to simplify expressions by breaking down larger terms into smaller ones. For example, 8(x + 2) can be rewritten as 8x + 16.Combining like terms is another way to rewrite expressions in equivalent form. This involves adding (or subtracting) two or more terms with the same variables. For example, 5x + 3x can be rewritten as 8x.The commutative property states that changing the order of two numbers or variables does not change their value. This can be used to rearrange expressions in equivalent forms. For example, 5x + 2y can be rewritten as 2y + 5x.Finally, identities are equations that are always true. They can be used to simplify and rearrange expressions in equivalent form. For example, (x + y)2 can be rewritten as x2 + 2xy + y2 using the identity (x + y)2 = x2 + 2xy + y2.

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Answer:

Step-by-step explanation:

answer is 3 because formula of mean is Mean = {Sum of Observation} ÷ {Total numbers of Observations}.

so 1+2+3+4+5=15/5=3

so 3

The mean or arithmetic mean* is represented with this symbol [tex]\boldsymbol{\sf{\overline{x}}}[/tex], and it is calculated by adding all the data, and dividing them in total, by the total number of data there is.

The mode of 1,2,3,4,5 is 3✅.

The x and y intercepts of the graphed function are (–1, 0) and ( 0,-3 ) respectively.

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We can solve this question using Linear equations . The answer for the question is Option B.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.

So in the given question the motorboat is 55 km from the shore.

  SO y =55 when x=0

  where y is the distance and x is time.

   after 12 minutes it is 19km from the sea shore.

  So y=-3x +55 is the equation.

We can solve this question using Linear equations . The answer for the question is Option B.

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(4,3) , (0,-4) and (4,3.9) are the solution pairs where x > y .

What does greater than (>) mean ?

Greater than means that the variable or number is more than the given limit. On the other hand, greater than or equal to states that the number or variable is either equal to or more than the given limit. The greater-than symbol is represented as >, whereas the greater than or equal to sign is represented as ≥.

Given :

(4,3)

(4,4)

(0,-4)

(4,3.9)

(0,0)

Since , all the ordered pairs are in the (x,y) form , we can clearly see that (4,3) , (0,-4) and (4,3.9) are the solution pairs where x > y .

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The principal of account A is $3 and the principal of account B is $4, Account B had the greater principal.

What is principal?

The principal is the sum that was first invested or borrowed from the bank. P stands for the principal. Rate: Rate is the interest rate at which the main sum is loaned to a person for a specific period of time; it may be 5%.

Given $15.75 in interest in Account A with interest rate 3.0% and $28.00 in interest in Account B with interest rate 4.0% after 21 months.

The formula of simple interest is I = PRT.

For account A:

R = 3.0% = 0.03

T = 21 month = 21/12 year

I = $15.75

P = I/RT

P = 15.75/ (0.03 × (21/12))

P =$3

For account B:

R = 4.0% = 0.04

T = 21 month = 21/12 year

I = $28.00

P = I/RT

P = 28.00/ (0.04 × (21/12))

P =$4

The principal of account B is more than that of account A.

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Answer: One solution

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

The height of the candle DEPENDS on how many hours it has burned.

Dependent variable = height

Independent = hours

A regression table mainly shows us that what the coefficients values are, and whether each coefficient is significant (likely to be different from from 0) .

A regression table is a statistical technique that describes how strongly a dependent variable and one or more independent variables are correlated (s). A field or variable you are attempting to predict or comprehend could be a dependent variable.

Regression allows researchers to predict or explain the variation in one variable based on another variable. The variable that researchers are trying to explain or predict is called the response variable. It is also sometimes called the dependent variable because it depends on another variable.

In statistics, regression is a technique that can be used to analyze the relationship between predictor variables and a response variable. When you use software (like R, SAS, SPSS, etc.) to perform a regression analysis, you will receive a regression table as output that summarize the results of the regression.

A regression table primarily reveals the values of the coefficients as well as the significance of each coefficient (how likely it is that it will depart from 0).

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Answer: 12 m

Step-by-step explanation:

Answer:

The transformed function is

g(x)=2*|x-4|-6

Step-by-step explanation:

First, you would have to stretch it vertically which is g(x)=2*f(x)

Then you would have to move it 6 units down and 4 units to the right which is g(x)=2*f(x-4)-6

resulting in the actual function

g(x)=2*|x-4|-6

Just type that function into the DESMOS calculator and you should be good

The set of all the real numbers are written as R.

The term set in set theory can be written as the well-defined collection of objects called elements or members of the set.

Here we have to find the way to write all real numbers.

Here we have considered that all the real numbers are collectively put on to the set.

And the set that contain all the real numbers are called R.

We all know that the real number contain all the number like negative , positive numbers.

So, Here we consider that if the domain of a function is all real numbers, then here we can represent this using interval notation as (−∞,∞).

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Answer:

Hello,

Step-by-step explanation:

Just find the longest measure.