Chee and her children went into a grocery store and she bought $12 worth of bananas and mangos. Each banana costs $0.50 and each mango costs $2. She bought twice as many bananas as mangos. Graphically solve a system of equations in order to determine the number of bananas, x,x, and the number of mangos, y,y, that Chee bought.

Fuel consumption is 53.957 miles per gallon for a car moving at  a speed of 60 miles per hour using least square Regression .

A statistical word for models that evaluate the connections between variables is regression. A single dependent variable Y and one or more independent variables X are studied using a linear regression model.

A technique for employing a goodness-of-fit criterion to fit a curve—not necessarily a straight line—through a collection of points. Regression that is most frequently used is linear regression. Recursion is occasionally used interchangeably with the word regression.

Y = mX + b, where X is the predictor (independent) variable, m is the estimated slope, and b is the expected intercept, is the formula for simple linear regression.

Calculation of Fuel Consumption in 60 miles per hour.

given the least square regression line is

y = 55.3286 - 0.02286x

so, y = 55.3286 - 0.02286 * 60 = 53.957 miles per gallon.

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Answer:

g(- 6) = 11

Step-by-step explanation:

substitute x = - 6 into g(x) , that is

g(- 6) = - (- 6) + 5 = 6 + 5 = 11

Answer:

11

Step-by-step explanation:

g(x) = -x + 5

Let x = -6

g(-6) = -(-6) + 5

         =6+5

         =11

When 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].

Given is the statement -

"8[tex]\frac{1}{4}[/tex] divided by 2/11"

We can write it as -

x = {8[tex]\frac{1}{4}[/tex]} ÷ {2/11}

x = 33/4 x 11/2

x = 363/8

x = 45[tex]\frac{3}{8}[/tex]

Therefore, when 8[tex]\frac{1}{4}[/tex] is divided by 2/11, we get 45[tex]\frac{3}{8}[/tex].

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The answers for the two questions is described below:

a. The balance sheet is a financial statement that shows a company's assets, liabilities, and equity at a specific point in time. Each transaction will affect one or more of these categories in different ways:

An increase in assets will increase total assets.

An increase in liabilities will increase total liabilities.

An increase in equity will increase total equity.

The income statement is a financial statement that shows a company's revenues, expenses, and net income over a specific period of time. Each transaction will affect net income in different ways:

An increase in revenues will increase net income.

An increase in expenses will decrease net income.

b. The statement of cash flows is a financial statement that shows the cash flows from operating activities, investing activities, and financing activities over a specific period of time. Each transaction will affect one or more of these categories in different ways:

An increase in cash from operating activities will increase cash flows from operating activities.

An increase in cash from investing activities will increase cash flows from investing activities.

An increase in cash from financing activities will increase cash flows from financing activities.

It is important to note that it can be complex to classify some transactions into one category or another, and it may require more context of the specific transaction and the company's operations.

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An equation that can be used to find the value of,x=$700.0 - $176.95.

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.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

The statement is not an equation if there is no "equal to" sign in it.

According to our question-

x= $700.0 - $176.95

523.05

Hence, An equation that can be used to find the value of,x=$700.0 - $176.95.

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Therefore , the solution to this problem of equation is y = 16.95  cost for 94 minutes.

A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.

Here,

y = mx + b

(50,13.98)(78,17.06)

slope = (17.06 - 13.98) / (78 - 50) = 3.08 / 28 = 0.11

slope(m) = 0.11

use either of ur points...(50,13.98)...x = 50 and y = 13.98

now sub into the formula and find b, the y int

13.98 = 0.11(50) + b

13.98 = 5.5 + b

13.98 - 5.5 = b

8.48 = b

so our equation is : y = 0.11x + 8.48.......for 94 minutes...sub in 77 for x

y = 0.11(94) + 8.48

y = 8.47 + 8.48

y = 16.95 <=== this is the cost for 94 minutes

Therefore , the solution to this problem of equation is y = 16.95  cost for 94 minutes.

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Answer:

2) The estimated weight, in pounds, of the beaver on June 1.

Step-by-step explanation:

Given function:

[tex]w(t) = 29 + 0.0674t \quad t < 90[/tex]

where:

When t = 0:

[tex]\begin{aligned}\implies w(0)&=29+0.0674(0)\\&=29+0\\&=29\end{aligned}[/tex]

Therefore, the constant of the equation (29) is the estimated weight of the beaver, in pounds, when t = 0.

As t = 0 is June 1:

Answer:

12+14i

Step-by-step explanation:

For -(-9-4i), you need to clean up the parentheses so you would distribute. -1 times -9 and -1 times -4i.

You will get 9+4i

Now you have 3+10i+9+4i. You will now add like terms. 10i+4i= 14i. 9+3= 12.

12+14i

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Answer: We know that the trainer earns $2,456.75 every month, and she earns an extra $4.75 every time she sells a gym membership.

And last month she sold 32 gym memberships

We can calculate the total amount of money the trainer earned from selling gym memberships by multiplying the number of memberships sold by the amount earned per membership:

32 memberships * $4.75 per membership = $152.00

To find the total amount of money the trainer earned last month, we can add the amount earned from selling gym memberships to the amount earned from her salary:

$2,456.75 + $152.00 = $2,608.75

So, the total amount of money the trainer earned last month is $2,608.75

Step-by-step explanation:

Answer:

y = - 3

Step-by-step explanation:

Call the line y = a + bx (d)

Since d go through (-7;-3) so -7 = a - 3b (1)

Since d go through (8;-3) so 8 = a - 3b (2)

From (1) and (2), we have equations: [tex]\left \{ {{a - 3b = -7} \atop {a - 3b = 8}} \right.[/tex]

Solve the equations, we have [tex]\left \{ {{a = 0} \atop {b = -3}} \right.[/tex]

Total 6.5 yards , fabaric are needed to make one costume for the dance recital.

We have , Total lengths of fabaric present for making costumes = 52 yards

Total number of costumes for the dance recital made from 52 yards = 8

we have to calculate the length of fabaric in yards are used for make one constume .

Let the " x yards " be the fabric length used to make one constume.

Now, total fabric length used to make 8 conatumes = 8x yards

but it will be equals to 52 yards . So, we get a simple linear equation with one variable, i.e

=> 8x = 52

=> x = 52/8

=> x = 6.5

So, the required fabric length is 6.5 yards .

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The initial value of the function is equal to 5.

In order to determine the initial value of the function, we would have to find the slope from line graph and then write the required equation based on the data points contained in the table by using the slope-intercept form.

Mathematically, the slope-intercept form of a line is modeled by this mathematical equation:

y = mx + c

Where:

Next, we would determine the slope of the data points as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (5 - 7)/(0 + 1)

Slope, m = -2/1

Slope, m = -2.

At point (0, 5), an equation of this line can be calculated in slope-intercept form as follows:

Note: The y-intercept or initial value is equal to 5.

y = mx + c

y = -2x + 5

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The additive inverse of 6 /- 5 is 6/5

We know that for any real number 'a' an additive inverse is a number 'b' such that a + b = 0

i.e., b = -a

An additive inverse of 'a' is -a.

The means, an additive inverse is nothing but changing sign + to - OR - to +

Here we have been given a rational number 6/(-5)

Let m be the additive inverse of number 6/(-5)

From the definition of additive inverse,

6/(-5) + m = 0

[6/(-5) + m] - 6/(-5) = -6/(-5)            

[6/(-5) - 6/(-5)] + m= -6/(-5)       ...........(associative property of addition)

0 + m =  6/5

m = 6/5

Hence, the additive inverse is 6/5

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The rotation about the center that can map an equilateral triangle onto itself is C. 120 degrees.

There are three equal sides and angles in an equilateral triangle which is 60 degrees each. This means that an equilateral triangle can be divided into  three-axis of symmetry such that there are three lines dividing the triangle.

Should this happen, then the angle to rotate the triangle and map it onto itself would be 120 degrees as each of these axes of symmetry measure 120 degrees.

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All expressions that are equivalent to 8.5x + 0.5 +3.5x - 2x are (12x - 2x + 0.5) and (10x + 0.5).

Expressions that are equivalent perform the same thing even when they have distinct appearances.

When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

By combining like terms, we can create expressions that are equivalent to a given expression. Terms with the same variables raised to the same powers are said to be "like terms". 

Here we have

8.5x + 0.5 +3.5x - 2x

The above expression can be simplified as given below

=>  8.5x + 0.5 +3.5x - 2x  

Add and subtract like terms

=> 8.5x +3.5x - 2x + 0.5

=> 12x - 2x + 0.5

=> 10x + 0.5  

Therefore,

All expressions that are equivalent to 8.5x + 0.5 +3.5x - 2x are (12x - 2x + 0.5) and (10x + 0.5).

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Answer:

x=6

Step-by-step explanation:

then x=6 because replacing x 6+3=9

10L  fuel does Asma's car use per 100 km of highway driving

In this question, we have to use the unitary method

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

What is a unitary in math?

a unitary state. (mathematics, of an algebra) That contains an identity element. (mathematics, linear algebra, mathematical analysis, of a matrix or operator) Whose inverse is equal to its adjoint.

So from the unitary method, we can solve it

12 L of gasoline per 100 km

so for 5/6

12 L * 5/6

= 10 L

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The coefficient of the expression 3x² is the number 3 and constant term is 20

What are the coefficients?

The coefficients are the numbers on the left side or before each variable.

What is an algebraic expression?

Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

If the expression of a single term is:. 3x²

Then the only coefficient will be the number that is placed before it and it is:

Number 3

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The function be f(x) = (6) then growth factor for the given equation (b) = 6.

Quantity grows exponentially over time. It happens when a quantity's instantaneous rate of change with regard to time is proportional to the quantity itself.

A function called exponential growth illustrates an expansion within a population that happens at the same pace across time. When a population's per capita growth rate remains constant across time, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.

The general exponential growth function is given by :-

[tex]$f(t)=A b^t$[/tex] , where A is the initial amount , b is the growth factor and t is the time period.

The given function : [tex]$f(x)=(6)^x$[/tex]

When we compare it to the general exponential equation , we get

The growth factor for the given equation (b) = 6.

The complete question is:

Consider the function f(x) = (6)x. What is the value of the growth factor of the function?

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The function be f(x) = (6) then growth factor for the given equation (b) = 6.

Quantity grows exponentially over time. It happens when a quantity's instantaneous rate of change with regard to time is proportional to the quantity itself.

A function called exponential growth illustrates an expansion within a population that happens at the same pace across time. When a population's per capita growth rate remains constant across time, regardless of population size, exponential growth occurs, causing the population to grow exponentially as the population increases.

The general exponential growth function is given by :-

F(t) = AB^t, where A is the initial amount , b is the growth factor and t is the time period.

The given function : f(t) = (6)^x

When we compare it to the general exponential equation , we get

The growth factor for the given equation (b) = 6.

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The complete question is:

Consider the function f(x) = (6)x. What is the value of the growth factor of the function?

Answer:

[tex] \sf \: (-3) × {( - 3)}^{2} = - 27[/tex]

Step-by-step explanation:

Given expression,

→ (-3) × (-3)²

Let's simplify the expression,

→ (-3) × (-3)²

→ (-3) × ((-3) × (-3))

→ (-3) × 9

→ (-3 × 9) = -27

Hence, the answer is -27.

The average rate of change is the ratio of the difference between the y coordinates of two points to the x coordinate of the same point.

It can be found by using two points on the graph and substitute into the formula: (y₀ - y₁) / (x₀ - x₁)

The square brackets [] is used to mean the end points as shown is inclusive

A quadratic equation is a polynomial of degree two

The average rate of change here is not constant and is usually  specified by the two points to which it is measured

For instance using points (-3, 0) and (0, -1) we have

=  (y₀ - y₁) / (x₀ - x₁)

=  (-1 - 0) / (0 - (-3))

= -1/3

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Answer:

3.23, -1.23

Step-by-step explanation:

Draw the line y=1

See where it intersects x^2-2x-3

The x coordinates of the intersections are your answer

The domain of an exponential function is all real numbers. In the interval notation is (-∞, ∞).

What is interval notation?

A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤ 1 .

Given exponential function is f(x) = B^x.

A function with an exponent as the independent variable is called an exponential function. The general form of an exponential function is y = f (x) = B^x, where B > 0 and a > 1, and x is any real number. The function is undefined for -1 < x < 1 if an is negative, which is why a > 0 is true. The function can have a domain that includes all real numbers by limiting a to positive values.

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The information you gave was presented as a table with three columns: value, x-coordinate, and y-coordinate.

You would need to make a graph with the x-coordinate acting as the horizontal axis and the y-coordinate acting as the vertical axis in order to plot this data point. The size or colour of the data point would serve as a representation of the value.

Here is an illustration of a data point plot:

[tex]x | 12 | 14 | 14 | 34 \\ y | 1 | 1 | 3 | 3 \\ v | 1 | 1 | 3 | 3[/tex]

The value at the position (12,1) will be 1, the value at the point (14,1) will be 1, the value at the point (14,3) will be 3, and the value at the point (34,3) will be 3. It's vital to remember that the values on the graph can be depicted by many colours or shapes.

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Answer:

0.0005

Step-by-step explanation:

this is a binomial experiment -- they are either cured or not, and the outcome is random

probability = n choose r * p^r * q^(n-r)

here, n = number of trials, r = number of successes desired, p = probability event occurs, and q = probability event doesn't occur

probability = n choose r * p^r * q^(n-r) = 6 choose 3 * 0.97^3 * 0.03^(6-3)

= 0.00049284342 rounding to 0.0005

Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.

According to the 30-60-90 triangle theorem, the hypotenuse is twice as long as the shorter leg. Additionally, the sides of this particular triangle have a ratio of 1:2: [tex]\sqrt{3}[/tex].

A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:

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The slope of the line that passes through the graph is 3

From the graph, the points are given as

(0, 0)  and (1, 3)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0)  and (1, 3)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0)  and (1, 3)

Substitute the known values in the above equation

So, we have the following equation

Slope = (3 - 0)/(1 - 0)

Evaluate

Slope = 3

Hence, the slope of the line is 3

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The height of rock 4 seconds after it was thrown is 168 ft.

Speed is measured as distance moved over time.

Speed = Distance/ Time.

Here, given that,

we have

a rock is thrown off a bridge 40 feet above a river at an initial velocity of 96 feet per second.

The height h, in feet, of the rock

t seconds after it was thrown can be modeled by the function

h(t)=-16t^2 +96t+40.

where

h -----> is the height in feet of the rock

t -----> the time in seconds

For , t=4, we get,

substitute the value of t in the function and find the value of h

h(4)=-16×4^2 +96×4+40.

So, h= 168

Hence, the height of rock 4 seconds after it was thrown is 168 ft.

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