How to subtract fraction and a whole number? Please explain step by step

The inequality represented by the graph is given as follows:

y > 3x - 4.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -4, hence the intercept b is given as follows:

b = -4.

When x increases by 1, y increases by 3, hence the slope m is given as follows:

m = 3.

Hence the equation of the line is:

y = 3x - 4.

The inequality is composed by the values to the right (greater) of the line, and has an open interval due to the dashed line, hence:

y > 3x - 4.

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Answer:

y = x + 60

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line

m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1

the line crosses the y- axis at (0, 60 ) ⇒ c = 60

y = x + 60 ← equation of line

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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Answer:

sqrt65+17

Step-by-step explanation:

a^2+b^2=c^2

a^2+4^2=9^2

a=sqrt65

perimeter = sqrt65+97

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Answer:

m=5

c=-7

Step-by-step explanation:

m is slope

c is the intercept on the y axis

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Answer:

Step-by-step explanation:

Typically yes you need to know

Mean

Median

Mode

and Range

Mean = average, add all numbers then divide by how many

Median = midpoint, middle number.  Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers

Mode = numbers that occurs the most in the list of numbers

Range = This is the largest number minus the smallest number.  

The statement "Every set can be considered a class" means that every object in set theory, including sets, can be considered a class. This is because classes are simply collections of objects, and sets are a type of collection.

The statement "If S is a set, consider the formula x S and the class {x: x = S}" means that if S is a set, then we can consider the formula x S, which states that x is an element of S, and the class {x: x = S}, which is the class of all objects that are equal to S.

In other words, the statement is saying that every set can be considered a class, and that we can define a class for any set by considering the formula that defines the set and the class of all objects that satisfy that formula.

For example, the set {1, 2, 3} can be considered a class by considering the formula x ∈ {1, 2, 3}, which states that x is an element of the set {1, 2, 3}, and the class {x: x ∈ {1, 2, 3}} is the class of all objects that are elements of the set {1, 2, 3}. This class is equal to the set {1, 2, 3}.

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The value of the standard deviation does not change and remains the same.

Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.

The mean μ = 82.4

The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]

we have to find the variance,

We now add a constant k to each data value and calculate the new mean μ'.

μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k

We now calculate the new mean standard deviation σ'.

σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]

Note that x + k - μ' = x + k - μ - k = x - μ

also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ

Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ

If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.

Hence, the standard deviation does not change.

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Answer: 392.

Step-by-step explanation:

Given the Kite ABCD.

We want to find the Area of the Kite.

Recall that the Area of a Kite can be expressed as;

Where;

p and q are the diagonals of the Kite.

For the given Kite, the diagonals of the kite are;

AC and BD.

So,

p = AC = 7 units

q = BD = 4 units

Substituting into the formula, we have;

Therefore, the area of the Kite is;

(e) There is no marble with the number 15 on it, so the probability of drawing such a marble is 0.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) The probability of drawing a red marble is the number of red marbles divided by the total number of marbles in the jar. So, the probability is 8/(8+12+4) = 8/24 = 1/3.

(b) The probability of not drawing a red marble is the number of non-red marbles divided by the total number of marbles in the jar. So, the probability is (12+4)/(8+12+4) = 16/24 = 2/3.

(c) The probability of drawing a marble with the number 2 on it is the number of marbles with the number 2 divided by the total number of marbles in the jar. There is only one red marble with the number 2, one blue marble with the number 2, and no white marbles with the number 2. So, the probability is 2/24 = 1/12.

(d) The probability of drawing a blue marble with the number 1 on it is the number of blue marbles with the number 1 divided by the total number of marbles in the jar. There is only one blue marble with the number 1. So, the probability is 1/24.

(e) There is no marble with the number 15 on it, so the probability of drawing such a marble is 0.

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The general sοlutiοn tο the differential equatiοn is \(\mathrm{y = Ce^{(sin(x))}}\).

The derivative οf a functiοn represents the instantaneοus rate οf change οf the functiοn at a specific pοint. It is calculated by finding the limit οf the difference quοtient as the interval between twο pοints οn the functiοn apprοaches zerο. The derivative can be expressed as a functiοn οf the independent variable, and it prοvides valuable infοrmatiοn abοut the behaviοr οf the οriginal functiοn.

The prοcess οf differentiatiοn invοlves applying a set οf rules tο functiοns tο οbtain their derivatives. These rules include the pοwer rule, prοduct rule, quοtient rule, chain rule, and οther mοre advanced rules that are used tο differentiate mοre cοmplex functiοns.

Tο sοlve the given differential equatiοn, we can use the methοd οf integrating factοrs.

First, we can rewrite the equatiοn as:

y'cοsx = ysinx + sin(175x)

Next, we can multiply bοth sides by the integrating factοr, which is \(e^{(\int(cos(x) dx))} = e^{(\sin(x) + C)}\), where C is a cοnstant οf integratiοn:

\(\mathrm {e^{(sin(x)) }y'cosx = e^{(sin(x))} ysinx + e^{(sin(x))}sin(175x) + Ce^{(sin(x))}}\)

Nοw, we can recοgnize the left-hand side as the derivative οf \(e^{(sin(x))}y\):

\((e^{(sin(x))y)}' = e^{(sin(x))} y' + cos(x) e^{(sin(x))}y\)

Substituting this intο the abοve equatiοn, we get:

\(\mathrm{(e^{(sin(x))y)}' = e^{(sin(x)) }ysinx + e^{(sin(x))}sin(175x) + Ce^{(sin(x))}}\)

\(cos(x) e^{(sin(x))}y = e^{(sin(x))y)}'\)

Separating variables and integrating bοth sides, we get:

\(\int e^{sin(x) }dy/y = \int cos(x) dx\)

ln|y| + C = sin(x) + C'

where C' is anοther cοnstant οf integratiοn.

Therefοre, the general sοlutiοn tο the differential equatiοn is:

\(\mathrm{|y| = e^{(sin(x)) }e^{(C' - sin(x))}}\)

\(\mathrm{y = \± e^{(C' - sin(x) + sin(x))}}\)

\(\mathrm{y = Ce^{(sin(x))}}\)

where C is an arbitrary cοnstant.

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The expression tan(arcsec(x/3)) can be written   \(1/3 \sqrt{x^2-9}\)  in algebraic form.

The inverse secant function, or arcsecant, is defined as the inverse of the secant function, which is the ratio of the length of the hypotenuse of a right triangle to the length of the adjacent side. Given x/3 as the length of the adjacent side, arcsec(x/3) is the measure of the angle that has a secant equal to x/3.

The tangent function is the ratio of the length of the opposite side of a right triangle to the length of the adjacent side. By substituting arcsec(x/3) as the measure of the angle in a right triangle, we can use the tangent function to find the ratio of the lengths of the opposite and adjacent sides, which is equal to \(1/3 \sqrt{x^2-9}\).

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Answer: c

Step-by-step explanation:

Just took the test

The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

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Graphing, substitution, and elimination are three methods for solving systems of equations. While they all aim to find the solution(s) to a system of equations, there are some important differences in how they work and when they are most appropriate to use.

Graphing involves plotting the equations on the same coordinate system and finding the point(s) where the graphs intersect. This method is visual and can be useful for understanding the overall behavior of the equations, but it can be time-consuming and inaccurate if the graphs are not precise enough. Graphing is most appropriate when the equations are simple and have integer solutions, or when a visual representation of the problem is necessary.

Substitution involves solving one of the equations for one variable, then substituting that expression into the other equation to create an equation with only one variable. This method is straightforward and can be done by hand, but it can be time-consuming and error-prone if there are many variables or the equations are complex. Substitution is most appropriate when one of the equations is already solved for a variable, or when the equations involve simple linear or quadratic forms.

Elimination involves adding or subtracting the equations to eliminate one of the variables. This method is efficient and can be done systematically, but it can be confusing if the equations are not balanced or there are many variables. Elimination is most appropriate when the coefficients of one of the variables are equal or opposite in both equations, or when there are many equations and variables.

In general, the choice of method depends on the specific equations and the preferences of the solver. Graphing is a good method to use when the equations are simple and easy to plot, substitution is useful when one equation is already solved for a variable or the equations involve simple forms, and elimination is a good choice when the equations have balanced coefficients or there are many equations and variables to consider. It is important to keep in mind the strengths and weaknesses of each method and to choose the most appropriate method based on the specific situation.

Note - While this answer may provide helpful information for your assignment, it is important to remember that using it verbatim could be seen as plagiarism. To avoid this, it is best to use your own words and properly cite any sources used. This will ensure that you are giving credit to the original author and presenting your own unique perspective on the topic.

~~~Harsha~~~

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer:

-40

Step-by-step explanation:

-40+12=-28

-28/4

=-7

Answer: 1/50, or 0.02

Step-by-step explanation:

I'm assuming this is 5*10/25/100. if you just follow the equation, you get 50/25/100, which is 2/100, or 1/50.

Answer: I am confused on what you are asking

Answer:

22

Step-by-step explanation:

4+18=22 if y is solved for 18 in the equation 4+y= the answer would be 22.

Answer:

22

Step-by-step explanation:

Evaluate y + 4 where y = 18:

y + 4 = 4 + 18

Hint: | Evaluate 4 + 18 using long addition.

| 1 |  

| 1 | 8

+ | | 4

| 2 | 2:

Answer: 22

The 46th term of the sequence is 324.

We have,

To find the 46th term of the sequence, we need to determine the pattern or rule that generates the terms.

Since the difference between consecutive terms is a constant value of 7, we know that this is an arithmetic sequence with a common difference

of 7.

To find the 46th term, we can use the formula for the nth term of an arithmetic sequence:

a(n) = a(1) + (n - 1) d

where a(1) is the first term, d is the common difference, and n is the term number we want to find.

Using the given information, we have:

a(1) = 9

d = 7

n = 46

Plugging these values into the formula, we get:

a (46) = 9 + (46 - 1)7

a (46) = 9 + 45 (7)

a(46) = 9 + 315

a(46) = 324

Therefore,

The 46th term of the sequence is 324.

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The SUV will be $5,299.13 worth than the car 5 years after their model years.

What is the meaning of rounded to the nearest cent?

Look at the number to the right of the whole cents when rounding money to the closest cent. In this instance, it is 9. Increase the cents by one if the figure is five or above. The cents should remain the same if the number is four or less. Given that 9 is more than 5, $3.299 equals $3.30.

Given that,

The value of a car can be predicted by using the function

f(x)=12,000(0.89)^x

Where x years from its model year.

To find the current value of the car, put x = 0 in the model equation:

f(0)=12,000(0.89)^0

f(0) = 12,000.

To find the value of the car after 5 years, put x = 5 in the model equation:

f(5)=12,000(0.89)^5

f(5) = 6700.871

The difference of the value of car is 12,000 - 6700.871 = $5299.129 = $5299.13 (rounded to the nearest cent)

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Answer:

Hope you find it helpful

Answer:

I need points so but I dont want to do my home work hi hello

Answer:

Step-by-step explanation:

Perimeter:  

     \(P=(x+y+z) \ cm\)

Semi-perimeter:

     \(SP=\frac{1}{2} (x+y+z) \ cm\)

Answer:

57

Step-by-step explanation:

this is the boybfiend

Answer:

Step-by-step explanation:

208

Answer:

The expression 5 × 2 = 10 means:

Step-by-step explanation:

Given the expression

From the expression, it is clear that we can determine that when we multiply 2 by 5 to get 10.

In other words, we can determine the value 10 by:

It means 10 is 5 times as many as 2.

Therefore, the expression 5 × 2 = 10 means: