answer this question please

Answer This Question Please

Answers

Answer 1

The step function and its graph that represents the relationship between the number x of days and the total cost y of renting the chipper are present in the first option.

What is a step function?A function on the real numbers is referred to as a step function in mathematics if it can be expressed as a finite linear combination of interval indicator functions. A step function is, informally speaking, a piecewise constant function with a finite number of pieces.

Given:

Charge for 1 day = $100

Charge for each additional day = $50

Let's assume

The cost of rent is y.

The number of days is x.

The total cost, y according to the data provided can be calculated by the equation,

y = 100 + 50x

Using y = mx+c, when graphing a step function that represents the relationship between the number of days and the total cost,

The gradient or slope will be always 50 for the graph.

So, when x = 0, y = 100 + 0 = 100

When x = 1, y = 100 + 50 = 150

When x = 2, y = 100 + 50 × 2 = 200

When x = 3, y = 100 + 50 × 3 = 250

Thus the step function is,

f(x) = 100 , if 0 < x ≤ 1

f(x) = 150 , if 1 < x ≤ 2

f(x) = 200 , if 2 < x ≤ 3

f(x) = 250 , if 3 < x ≤ 4

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Related Questions

The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is 114 feet. Find the length and width of the rectangle

Answers

Answer:

length is 28,breadth is 29

Step-by-step explanation:

firstly we need to know the definition of consecutive integers:-Consecutive integers are those numbers that follow each other . They follow in a sequence or in order.

let the length and breadth be represented by n and n+1

since we are given in perimeter

perimeter of a rectangle =2(length+breadth)

114=2(n+n+1)

114=2n+2n+2

114=4n+2

114-2=4n

112=4n

n=28

:-n=28,(n+1)=28+1=29

:-the length is 28 and the breadth is 29

please rate as brainliest

Need help, explaining this to me

Answers

[tex]\begin{gathered} (-3p+9)+(-7-p+2p^2)\text{ Given} \\ \\ \text{First, simplify by taking out the parenthesis and making sure it stays true to the operation} \\ \rightarrow-3p+9-7-p+2p^2 \\ \text{Next, arrange starting from the highest degree }(p^2)\text{ to the constant},\text{ and group them} \\ p^2\rightarrow p\rightarrow\text{constant} \\ 2p^2-3p-p+9-7\text{ (final answer)} \end{gathered}[/tex]

Evalúe the limit. Show steps

Answers

The value of the limit will be equal to -2.

A function may be defined as the one in which for one input variable x there is only one output variable y. The input variable is called independent variable and the output variable is called dependent variable. Limit on a function may be defined as the value of input variable reaches a certain specified value the output of function also reaches a certain specified value. The function [tex]\lim_{x \to-2}[/tex] (x²)/(2x + 4) can be solved by using the rule [tex]\lim_{x \to a}[/tex] f(x)/g(x) = [tex]\lim_{x \to a}[/tex] f'(x)/g'(x).

Here f(x) = x², f'(x) = 2x

g(x) = 2x + 4, g'(x) = 2

Now, [tex]\lim_{x \to-2}[/tex] (x²)/(2x + 4) = [tex]\lim_{x \to-2}[/tex] (2x/2)

[tex]\lim_{x \to-2}[/tex] (x) = -2 which is the required value.

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7. Point E (11, 6) isreflected to E' (11,-6).8.frQ

Answers

By looking at the points, we can see that point E' is a reflection over the x-axis of the point E. That, since the y-component changed it's sign.

Linda has c decks of cards. Each deck has 52 cards in it. Using c, write an expression for the total number of cards Linda has

Answers

Each deck has 52 cards in it. If Linda has c decks of cards, then the expression for the total number of cards that she has is

52 x c

= 52c

An arch is in the shape of a parabola. It has a span of 72 meters and a maximum height of 9 meters.

Answers

Answer:

Equation of the parabola:

[tex]y=-\frac{1}{144}x^2+9[/tex]

The height of the arch 18 meters from the center is 6.75m

Explanation:

The arch feet are 72m apart and the origin half way between them. This means that the axis of symmetry (or the x.coordinate of the vertex) is x = 0

Since it's an arch, the parabola is concave down, with it's maximum at the vertex, y = 9. This means that the vertex is at (0, 9). Also, we can see that the y-intercept is y = 9

Finally, we know the two roots of the parabola: x = -36 and x = 36. This is because the points x = -36 and x = 36 are 72m apart, with the center at the original, as the problem says. SInce x = 36 is a root, this means that at that point the y value is 0.

With all this, we can try to find the general form of a parabola. The general form is:

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

c is the y-intercept. We know that c = 9

We can find the value of b, because we know the coordinates of the vertex. The x-coordinate of the vertex is:

[tex]x_{vertex}=-\frac{b}{2a}[/tex]

SInce the x-coordinate of the vertex is x = 0

[tex]0=-\frac{b}{2a}[/tex]

If we solve:

[tex]b=0[/tex]

So far we have:

[tex]y=ax^2+9[/tex]

Finally, to find a, we can use the point (36, 0) (one of the roots)

[tex]0=a(36)^2+9[/tex]

And solve:

[tex]\begin{gathered} 324a=-9 \\ . \\ a=-\frac{9}{1296}=-\frac{1}{144} \end{gathered}[/tex]

Thus, the equation of the arch is:

[tex]y=-\frac{1}{144}x^2+9[/tex]

Evaluating this equation for x = 18, we can find the height of the arch:

[tex]y=-\frac{1}{144}(18)^2+9=-\frac{9}{4}+9=-6.75[/tex]

The entire graph of the function f is shown in the figure below.
Write the domain and range of f as intervals or unions of intervals.

Answers

For given function f,

domain = (-3, -1) ∪ (2, 5]

range = (0, 3) ∪ (1, 5]

In this question, we have been given the graph of the function f.

We need to write the domain and range of f.

From the graph of function f we can observe that, function f is a piecewise function.

For first part x takes vales which are greater than -3 and less than -1

And y takes values between 0 to 3

For first curve the domain is (-3, -1) and the rage of function f is (0, 3)

For the second part, x takes value which are greater than 2 and less than or equal to 5.

And y has values between 1 to 4.

So, for the second part the domain is (2, 5] and the range is (1, 5]

Therefore, for given function f,

domain = (-3, -1) ∪ (2, 5]

range = (0, 3) ∪ (1, 5]

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A(-3,-2) and M (2,6) find the coordinates of the other endpoint

Answers

The other endpoint of the segment is (7, 14)

How to determine the coordinate of the other endpoint?

From the question, we have:

On the segment, we have the following endpoints

Endpoint 1, A = (-3,-2)

Midpoint, M = (2,6)

The midpoint of the segment is calculated using

Midpoint (x, y) = 1/2 * (x1 + x2, y1 + y2)

Where

(x1, y1) = (-3,-2)

(x, y) = (2,6)

Substitute the known values in the above equation

So, we have

(2, 6) = 1/2 * (-3 + x, -2 + y)

Multiply both sides of the equation by 2

So, we have

(4, 12) = (-3 + x, -2 + y)

By comparison, we have

-3 + x = 4

-2 + y = 12

Evaluate the like terms in the above equation

So, we have

x = 7

y = 14

When the above solution is represented as a coordinate, we have the following

(x, y) = (7, 14)

Hence, the other endpoint of the segment where the segment has the endpoint (-3,-2) and midpoint (2,6) is (7, 14)

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EX: Let X₁ and X₂ have the ķ $ joint proib. density function. f(x₁, x₂ ) = [ Kx1,x2, 0<=x1,<=1,0<=x2<=1 and 0 elsewhere.find the value of k

Answers

Answer:

17

Step-by-step explanation:

To find k, we use

∫∞−∞∫∞−∞fXY(x,y)dxdy=1.

Thus, we have

1=∫∞−∞∫∞−∞fXY(x,y)dxdy=∫10∫10x+cy2dxdy=∫10[12x2+cy2x]x=1x=0dy=∫1012+cy2dy=[12y+13cy3]y=1y=0=12+13c.

Therefore, we obtain c=32.

To find P(0≤X≤12,0≤Y≤12), we can write

P((X,Y)∈A)=∬AfXY(x,y)dxdy,for A={(x,y)|0≤x,y≤1}.

Thus,

P(0≤X≤12,0≤Y≤12)=∫120∫120(x+32y2)dxdy=∫120[12x2+32y2x]120dy=∫120(18+34y2)dy=332.

We can find marginal PDFs of X and Y from their joint PDF. This is exactly analogous to what we saw in the discrete case. In particular, by integrating over all y's, we obtain fX(x). We have

Marginal PDFs

fX(x)=∫∞−∞fXY(x,y)dy, for all x,fY(y)=∫∞−∞fXY(x,y)dx, for all y.

Example

In Example 5.15 find the marginal PDFs fX(x) and fY(y).

Answer:

17

Step-by-step explanation:

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Brainliest po kapag tama, Please help na po, Need na po talaga.

Directions: Solve for the number of subsets of the following items. Input your answer inside the box provided for each item.


1. A = {U, S, T, A, C}

2. B = {red, blue, yellow}

Answers

1) If  A = {U, S, T, A, C}, then the Subsets of  {U, S, T, A, C} are;

as detailed below

2) If B = {red, blue, yellow}. then the Subsets of {red, blue, yellow} are;

as detailed below

What are the subsets?

Subsets are a part of one of the mathematical concepts called Sets. For example If a set A is a collection of odd numbers and set B consists of {1,3,5}, then B is said to be a subset of A.

Thus;

1) Subsets of  {U, S, T, A, C} are;

{U}, {S}, {T}, {A}, {C},

{U, S}, {U, T}, {S, T}, {U, A}, {S, A}, {T, A}, {U, C}, {S, C}, {T, C}, {A, C},

{U, S, T}, {U, S, A}, {U, T, A}, {S, T, A}, {U, S, C}, {U, T, C}, {S, T, C}, {U, A, C}, {S, A, C}, {T, A, C},

{U, S, T, A}, {U, S, T, C}, {U, S, A, C}, {U, T, A, C}, {S, T, A, C},

{U, S, T, A, C}

2) Subsets of {red, blue, yellow} are;

{Red}, {Yellow}, {Blue},

{Red, Yellow}, {Red, Blue}, {Yellow, Blue},

{Red, Yellow, Blue}

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3. Perform the indicated operation. Show all necessary work.
(a) -1.424-2.9
(b) 1.424-(-2.9)
(c) -1.424-(-2.9) -0.576
Answer:

Answers

The result of the indicated operations are:

(a) -4.324.

(b)  4.324.

(c) 0.9

What are operations on decimals?Addition, subtraction, multiplication, and division are the basic operations on decimals.We shall first convert the decimal integers to like decimals before adding and subtracting them. Decimals having the same number of decimal places are said to be like decimals. The decimal points of the addends will be aligned, and if necessary, zeroes will be added at the end of one number to equalize the decimal places. then carry on adding (or removing) as usual. The decimal point should be positioned exactly where it is in the extra numbers in the response (or subtracted)

(a) -1.424-2.9

Calculate the sum of the decimals,

The result is -4.324.

(b) 1.424-(-2.9)

Remove the bracket and change the sign in the middle and add the decimals to get the sum,

1.424 + 2.9 = 4.324.

(c) -1.424-(-2.9) -0.576

Remove the parentheses and change the sign,

-1.424 + 2.9 - 0.576

Add the negative decimal numbers and subtract them from the positive decimal number.

-2 + 2.9 = 0.9

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The ratio of girls to boys who participated in the quiz bowl was 7:5. There were 42 girls in the competition. How many boys participated?
Responses
A 3535
B 4949
C 3030
D 28

Answers

Answer: 28

Step-by-step explanation: the other responses seem too much and do you know if the girls are 7 and the boys are 5?

Find the equation of the line having
undefined slope and passing through (0,5).

Answers

Answer:

x = 0

Step-by-step explanation:

A line that has undefined slope is a vertical line. A vertical line has an equation in the form "x = anumber"

In the given information, (0,5), x is 0 and y is 5. What we need is the information on x.

x is 0.

x = 0 is the equation of the line.

Answer:

x=0.

Step-by-step explanation:

undefined slope is a vertical line. if it passes through (0,5) it means its on the y line

I need to know what is negative and whats positive.​

Answers

Easier way to understand it is that positive is basically (+) and negative is (-)

Positive numbers usually have no sign in front of them. So a number like 67 is taken to mean a positive number.

Negative numbers are indicated by placing a dash ( – ) sign in front, such as –5, –12.77. A negative number such as –6 is spoken as 'negative six'.

The function is positive

A tree grows 1 3/4 feet per year. How long will it take the tree to grow from a height of 21 1/4 feet to a height of 37 feet?

Answers

A tree grows x =[tex]1\frac{3}{4}[/tex] feet per year. It take 9 years to grow from a height of x=[tex]21\frac{1}{4}[/tex] feet to a height of 37 feet

What is basic algebra ?

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.

A tree expands by [tex]1\frac{3}{4}[/tex]  = [tex]\frac{7}{4}[/tex] feet annually.

You can calculate this using the methods below if you'd want to know how long it will take the tree to grow from a height of  [tex]21\frac{1}{4}[/tex] = [tex]\frac{85}{4}[/tex] feet to a height of 37 feet:

37 -  [tex]21\frac{1}{4}[/tex]

= 37 - [tex]\frac{85}{4}[/tex]

= [tex]\frac{63}{4}[/tex]

= [tex]\frac{63}{4}[/tex] × [tex]\frac{4}{7}[/tex] = 9 years

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help meeeeeeee please

Answers

The value of the average price per square foot in 2002 is  $101. 5

What is a function?

A function can simply be defined as a rule, a law, an equation or an expression that is made up of two variables and shows or explains the relationship between them.

The variables are;

Independent variableDependent variable

Given the function;

P(t) = 0. 018t³ - 0. 294t² + 3. 065t + 55. 190

Where;

P is the average price per square feett is the number of years since 1992

For the year 2002 , the value of t would be 10

Substitute the value into the formula

P(10) = 0. 018(10)³ - 0. 0294(10)² + 3. 05(10) + 55. 190

expand the bracket, we have

P(10) = 0. 018(1000) - 0. 0294(100) + 30. 5 + 55. 90

multiply through

P(10) = 18 - 2.  + 30. 5 + 55. 90

Add the values

P(10) = $101. 5

Hence, the value is  $101. 5

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2 divided by the sum of 2 and a number

Answers

The given statement can be written as an algebraic expression as: 2/(x + 2).

What is an Algebraic Expression?

A mathematical statement that expresses phrases or words using numbers, variables, and operation signs can be referred to as an algebraic expression.

How to Translate a Statement into an Algebraic Expression?

To translates a given statement in to algebraic expression, we can use "x" as a variable to represent the unknown number in the given word problem.

For example, the number that is added to 2, in the above given scenario, can be represented as "x" in order to translate the given statement into an algebraic expression.

The word "sum" will be represented with the operation sign, "+". Therefore, "the sum of 2 and a number" will be translated as an algebraic expression as, (x + 2).

Therefore, the whole statement, "2 divided by the sum of 2 and a number" will then be expressed in algebraic expression as: 2/(x + 2).

In conclusion, the statement, "2 divided by the sum of 2 and a number", can be written as an algebraic expression as: 2/(x + 2).

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combine the like terms in the expression 6a-4b-2a+c-3b+a

A. 5a- 7 b + c
B. 8a + b + c
C. 9 a b c
D. 3a + b + c

Answers

Answer:

A

Step-by-step explanation:

that is just straight forward work :

we group all like terms together (after all, addition and multiplications are commutative operations) :

6a - 2a + a - 4b - 3b + c = 5a - 7b + c

Consider the line y = (5/8)x - 4.
Find the equation of the line that is perpendicular to this line and passes through the point (8,4).

Find the equation of the line that is parallel to this line and passes through the point (8,4)..

Answers

Considering the definition of parallel and perpendicular line, you get:

the equation of the line that is perpendicular to this line and passes through the point (8,4) is y= -8/5x + 84/5.the equation of the line that is parallel to this line and passes through the point (8,4) is y=5/8 -1.

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

Parallel line

Parallel lines are two lines that are always at the same distance from each other.

Two lines are parallel if they have the same slope and different y-intercepts.

Perpendicular line

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

Equation of perpendicular line in this case

The line is y= 5/8x -4, with a value of slope m of 5/8 and ordinate to the origin b of -4.

If you multiply the slopes of two perpendicular lines, you get –1, the slope perpendicular line can be calculated as:

5/8× slope perpendicular line= -1

slope perpendicular line= (-1)÷ 5/8

slope perpendicular line= -8/5

So, the perpendicular line has a form of: y= -8/5x + b

The line passes through the point (8, 4). Replacing in the expression for perpendicular line:

4= -8/5×8 + b

4= -64/5 + b

4 + 64/5= b

84/5= b

Finally, the equation of perpendicular line is y= -8/5x + 84/5.

Equation of parallel line in this case

In this case, the line is y= 5/8x -4, with a value of slope m of 5/8 and ordinate to the origin b of -4.

If two lines are parallel if they have the same slope, the parallel line has a slope of 5/8 and has a form of: y= 5/8x + b

The line passes through the point (8, 4). Replacing in the expression for parallel line:

4= 5/8×8 + b

4= 5 + b

4 -5 = b

-1 = b

Finally, the equation of parallel line is y= 5/8x - 1

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Let f(x)=x^2-5x and g(x)=3-x find (fg)(4)

Answers

Given:

[tex]\begin{gathered} f\mleft(x\mright)=x^2-5x \\ g\mleft(x\mright)=3-x \end{gathered}[/tex]

Required:

Find (fg)(4)

Explanation:

Given functions are

[tex]\begin{gathered} f(x)=x^{2}-5x \\ g\mleft(x\mright)=3-x \end{gathered}[/tex][tex]\begin{gathered} (fg)(4)=f(4)g(4) \\ (fg)(4)=[(4)^2-5(4)][3-4] \\ (fg)(4)=[16-20](-1) \\ (fg)(4)=(-4)(-1_) \\ (fg)(4)=4 \end{gathered}[/tex]

Final answer:

The value of (fg)(4) = 4

What is the equation of the line that passes through the point (5, -4) and
has an undefined slope?

Answers

Answer:

x=5

Step-by-step explanation:

If the slope is undefined, it is a vertical line. Since the slope-intercept equation is y=mx+b, but the slope is undefined, the equation would have to be the x coordinate, because that is the unchanging variable in a vertical line. So, the answer is x=5.

There are 3 circles and 9 squares. What is the simplest ratio of circles to squares?

Answers

Answer:

1 is to 3

Find the lowest common factor of both numbers, which is 3. Then divide it into both numbers

3 divided by 3 = 1
9 divided by 3 = 3
1:3

Find two pairs of conjugates with a product of 3. Please

Answers

The two pairs of conjugates are ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]).

What is the conjugates pair?

In mathematics, a pair of binomials with identical phrases that part opposite arithmetic operators in the midst of these similar terms are referred to as conjugates. Below are a few more instances of conjugate pairs: p + q, p - q. 3 + 1, 3 - 1. 4 - 3i, 4 + 3i.

Let the two pair of conjugates is

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex])

Use the formula,

(a+b) and (a-b) = [tex]a^{2}-b^{2}[/tex]

Then,

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) = [tex]\sqrt{2} ^{2}-i^{2}[/tex]

We know that,

[tex]i^{2}=-1[/tex]

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) = 2-(-1)

 ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) =  3

Hence, The two pairs of conjugates are ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) with a product 3 .

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According to the solving the  two pairs of conjugates with a product of 3:

(√2 - i ) & (√2 + i ).

What does "pair of conjugates" mean?

When two binomials are identical except for the signs separating the terms, they are said to be conjugates. You only need to rephrase a binomial and alter the sign of the second term to create its conjugate.

According to the given data:

given number = 3.

lets the two pair of conjugates is:

(√2 - i ) & (√2 + i )

Use the formula:

a² - b² = (a + b) and  (a - b)

So,

(√2 - i ) & (√2 + i ) = (√2)² -( i )²

We know that,

i² = -1

So,

(√2 - i ) & (√2 + i ) = 2 - (-1)

(√2 - i ) & (√2 + i ) = 3

According to the solving the  two pairs of conjugates with a product of 3:

(√2 - i ) & (√2 + i ).

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Find a formula for the nth term in this
arithmetic sequence:
a1 = 8, a2 = 4, a3 = 0, a4 = -4, ..

Answers

Answer:

an = -4n +12

Step-by-step explanation:

the nth term in this arithmetic sequence is : an = a1 + (n -1 )d

a1 = 8 d = a2-a1 = 4-8 = -4 ( common difrence)

an = 8 + (n -1 )(-4) = 8 - 4n +4

an = -4n +12

Find the value of x so that f(x) = 7.

Answers

For the given function f(x) = 7 , the value of x is 5.

solution:

We have a linear function in the figure, and linear functions have the same slope for all values of. We can determine the value of f using the secant line equation:

(yB -yA) / (xB - xA) = (yC - yA) / (xC - xA)

Where:

(xA , yA) , (xB , yB)  given

to find ,  (xC , yC)

(xA , yA) = (2,0) , (xB , yB) = (5,7)  and yC = 7

to find xC ,

xC - xA = (yC - yA) / (yB - yA) . (xB - xA)

xC =  xA + (yC - yA) / (yB - yA) . (xB - xA)

xC = 2 + (7-0)/(7-0) x (5 - 2)

xC = 2 + (5 - 2)

xC = 2 + 3

xC = 5

so the value of x in given function f(x) = 7 is 5.

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2. Jay needs 19 quarts more paint for the outside of his barn than for the inside. If he uses 107 quarts in all,
how many gallons of paint will be used to paint the inside of the barn?

Answers

4 gallons of paint will be used to paint the inside of the barn.

What is equation?

In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.

Given Data

Jay needs 19 quarts more paint for the outside of his barn than for the inside.

he uses 107 quarts in all

Paint needed for Inside = x

Paint needed for outside =  x + 19

So,

Total paint = Paint for outside + Paint for inside

107 = x + x+ 19

107 = 2x + 19

2x = 88

x = 44

Number of gallon = [tex]\frac{44}{4}[/tex]

Number of gallon = 4

4 gallons of paint will be used to paint the inside of the barn.

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There was a big snowstorm on Friday night. By Saturday afternoon, 3 inches of the snow had melted. There were still 8 inches of snow left. Solve an equation to find how many inches of snow fell during the snowstorm.

Answers

Answer:

13 correct me if i am wrong

Step-by-step explanation:

y varies directly as x. y = 90 when x = 6. Find y when x= 12.y=(Simplify your answer.)

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Answer

When x = 12, y = 180

Explanation

We are told that y varies directly as x, which can be written as

y ∝ x

Introducing the constant of variation, k, we have

y ∝ x

y = kx

We can then solve for k knowing that

y = 90 when x = 6

y = kx

90 = (k) (6)

90 = 6k

Divide both sides by 6

(90/6) = (6k/6)

15 = k

k = 15

We can then write the relationship between y and x as

y = kx

y = 15x

when x = 12, y = ?

y = 15x

y = 15 (12) = 180

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Suppose times for the 100m sprint for the average person are Uniondale and symmetric with mean 14 seconds and standard deviation 0.8 seconds. What is the probability that the average person has a time faster than Usain Bolt’s record of 9.58 seconds?

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The probability that the average person has a time faster than Usain Bolt’s record of 9.58 seconds

P(x>9.58)=1

This is further explained below.

What is the probability?

Mean[tex](\mu)[/tex]=14 seconds

Standard deviation[tex](\sigma)[/tex]=0.8 seconds

To determine the likelihood that the average individual will beat Usain Bolt's record of 9.58

To express the statement "the probability that the average person has a time faster than Usain Bolt’s record of 9.58 seconds" in a mathematical equation we have:

[tex]&P(x > 9.58)=P\left(\frac{x-\mu}{\sigma} > \frac{9.58-14}{0.8}\right) \\\\&P(x > 9.58)=P\left(z > -\frac{4.42}{0.8}\right) \\\\ &P(x > 9.58)=P(z > -5.525)[/tex]

P(x>9.58)=1

Note: we would make use of the normal table in reading z>-5.525

In conclusion, By using standard normal distribution we get

P(x>9.58)=1

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uestion #5 Nevaeh pays a total of $24 for two sets of paint brushes. Each set costs the same amount of money and contains three paint brushes. What is the cost per paint brush? A $12 B $8 С C $4 D $3 Question #6

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If we have 2 sets, and each set has 3 brushes. We have 6 brushes in total, so each brush costs:

[tex]\frac{24}{6}=4[/tex]

So the cost per brush is $4

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