Which graph represents a function?

The graph below shows the total cost for lunch, c, when Will and his friends buy a large salad to share and several slices of pizza, p.

A graph titled Lunch Cost. The x-axis shows the number of slices purchased, numbered 1 to 8, and the y-axis shows the cost in dollars, numbered 5 to 40. Blue diamonds appear at points (0, 7.5), (1, 10), (2, 12.5), (3, 15), (4, 17.5), (5, 20), (6, 22.5), (7, 25), (8, 27.5).

For each additional slice of pizza that is purchased, by how much does the total cost of lunch increase?

$1.50
$2.00
$2.50
$3.00

By simplifying a system of equations we will see that the correct option is the second one:

(2a - 7) + a  = 41

Let's define the variables:

We have the statements:

"Taylor's sister is 7 years less than twice Taylor's age"

s = 2*a - 7

"The sum of Taylor's age and her sister's age is 41"

s + a = 41

So we have a system of equations:

s = 2a - 7

s + a = 41

Replacing the first equation in the second one we get:

(2a - 7) + a  = 41

So the correct option is the second one, that is the equation that represents this relationship.

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To fill the pool 3/4 full it will take 240 minutes

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in mathematical problems.

3/4 of the volume the pool is 3/4×16000= 12000gallons

it takes 1 minutes to fill 50gallons

therefore to fill 12000 gallons it will take 12000×1/50 =240minutes

therefore the number of minutes it will take to fill 3/4 of the pool is 240minutes

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The probability for success is not the same for each trial, then the option D cannot be modelled using a geometric distribution.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

One of the assumptions to consider before the use of a geometric distribution can be valid is that, the probability of success must be the same for each outcome.

In the option D, selection is done without replacement, meaning that, the number total possible outcome will decrease as we make each selection and will also depend on how the colours are being chosen.

Hence, the probability of success will differ for each outcome, thus the option D is correct.

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Answer:

102.375

Step-by-step explanation:

hope it helps :)

multiply 6.5 x 2.25, get 14.625

multiply 14.625 x 7, answer is 102.375

The given sets written in interval notation are

C = (4, ∞), and  = (-∞, 9]

From the question, we are to write the given sets using the interval notation

The given sets are

C = {v | v > 4}

D = {v | v ≤ 9}

For set C,

C = {v | v > 4}

The elements of the sets are 5, 6, 7, 8, 9, ...

This can be written in interval notation as (4, ∞)

For set D,

D = {v | v ≤ 9}

The elements of the sets are 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, ...

This can be written in interval notation as (-∞, 9]

Hence, the interval notation form of the sets are

C = (4, ∞)

and

D = (-∞, 9]

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Answer:

y=-3/4x + 11/4

Step-by-step explanation:

First thing is to minus 3x from 3x and 12.
You will get 4y=-3x+12.
Divide all the sides by 4.
You will get y=-3/4+3.
Now input 1(x), and 2(y) into the slope-intercept form equation.
2=-3/4(1)+b
2=-3/4+b
+3/4 +3/4
2 3/4=b
You can simplify it into 11/4
So, the equation will be y=-3/4x + 11/4
I hope I got this right.

A) The monthly deposit is $503.77

B) Interest per month ≈0.42

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

Let A be the amount in future.

Monthly deposit= [tex]P= \frac{A \times \frac{r}{n}} {(1 +\frac{r}{n})^{t*n} - 1}[/tex]

n= 12, 12 months in a year

So, monthly deposit= [tex]P= \frac{300000 \times \frac{0.05}{12}} {(1 +\frac{0.05}{12})^{25*12} - 1}[/tex]

                                 = 1250/2.4813

                                 = $503.77

So, monthly deposit= $503.77

To find interest:

Interest per year = 5%

Interest per month = 5/12 = 0.416 ≈0.42

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Answer: $503.77

Interest earned: $148,869

Step-by-step explanation:

Let A be the future amount.

Monthly Deposit= P=A*r/n÷ (1+r/n)^t*n-1

n=12 months in a year

P= (300,000*0.05/12)÷ [(1+0.05/12)^25*12]-1

P=1250/2.4813

P=$ 503.77

Interest earned.

$300,000-(503.77*12*25)

$300,000-151,131= $148,869

Step-by-step explanation:

3a + 3.8 is equal to what when a=1.5?

substitute in 1.5 for a:

3(1.5) + 3.8

3(1.5) + 3.8

4.5 + 3.8

= 8.3

The range of this quadratic function y = x² - 2x - 3 is all real numbers greater than 2.

Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x  is defined.

We know a quadratic function y = ax² + bx + c is a graph of a parabola that opens upwards as the coefficient of x² is positive.

Given,  y = x² - 2x - 3.

y = x² - 3x + x - 3.

y = x(x - 3) + 1(x - 3).

y = (x - 3)(x + 1).

Now the x-intercepts are at 3 and -1 so the vertex is located at (3 - 1)/2 = 2.

So the range of this function is all real numbers greater than 2 as the parabola opens upwards.

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The number that will go in between 0.438 and 44% in the thousandth place is 9 and the number is

This is found by converting all the given number to decimal

0.438

the thousandth place has number 8

44% = 0.440

The thousandth place has number 0

4/9 = 0.44444

this is greater than the two numbers and hence cannot go in between them

9/20 = 0.45

this is greater than the two numbers and hence cannot go in between them

checking the two numbers 0.438 and 0.440 the number that can go in between them is 0.439

9 in thousandth place is 0.009

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Step-by-step explanation:

Let [tex]{ \green{ \tt{y = \sqrt{ \frac{(x - 3)( {x}^{2} + 4)}{3 {x}^{2} + 4x + 5}}}}} [/tex]

Take log on both sides

[tex]{ \purple{ \sf{ log_{e}y = log_{e} [\frac{(x - 3)( {x}^{2} + 4}{3 {x}^{2} + 4x + 5}]^{ \frac{1}{2}}}} } { \to}{ \tt{ {eq}^{n} (1)}}[/tex]

This above expression is in the form of

[tex]{ \boxed{ \red {\sf{ {x}^{n} = nx}}}}[/tex]

[tex]{ \boxed{ \red{ \sf{ log( \frac{m}{n} ) = log \: m \: - log \: n}}}}[/tex]

Let's apply these two formulas to eqⁿ (1) then,

[tex]{ \purple{ \sf{ log_{e}y = \frac{1}{2}[log(x - 3) + log( {x}^{2} + 4) - log( {3x}^{2} + 4x + 5) ]}}}[/tex]

differentiate with respect to x.

[tex]{ \blue{ \sf{ \frac{1}{y} \frac{dy}{dx} = \frac{1}{2}[ \frac{1}{x - 3} (1 - 0) + \frac{1}{ {x}^{2} + 4 } (2x - 0) - \frac{1}{3 {x}^{2} - 4x + 5} (6x + 4 + 0)]}}}[/tex]

[tex]{ \blue{ \sf{ \frac{dy}{dx} = y[ \frac{1}{2(x - 3)} + \frac{x}{ {x}^{2} + 4} - \frac{3x + 2}{ {3x}^{2} + 4x + 5 } ]}}}[/tex]

where [tex]{ \boxed{ \purple{ \sf{y = \sqrt{ \frac{(x - 3)( {x}^{2} + 4) }{3 {x}^{2} + 4x + 5}}}}} } [/tex]

Answer:

[tex]let \: \: y = \sqrt{ \frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } } \\ \\ y =( {{\frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } }})^{ \frac{1}{2} } \\ \\ taking \: \: logarathim \ \: both \: \: sides \: \: \\ \: we \: \:get ⇒ \: ln(y) = {\frac{1}{2} ln(\frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } }) \\ \\ ⇒2 ln(y) = ln(x - 3) + ln( {x}^{2} + 4) - ln(3 {x}^{2} ) + ln(4x) + ln(5) \\ differeciate \: \: both \: \: the \: \: sides \: \: we \: \: get \: \: \\ ⇒ 2 \times \frac{1}{y} (\frac{dy}{dx} ) = \frac{1}{x - 3} + \frac{1}{ {x}^{2} + 4} .2x - \frac{1}{3 {x}^{2} } .6x + \frac{1}{4x} .4 + 0 \\ \\ ⇒ \frac{2}{y} \times \frac{dy}{dx} = \frac{1}{x - 3} + \frac{2x}{ {x}^{2} + 4} - \frac{2}{x} + \frac{1}{x} \\ \\ ⇒ \frac{dy}{dx} = \frac{y}{2} . (\frac{1}{x - 3} + \frac{2x}{ {x }^{2} + 4} - \frac{1}{x} ) \\ \\ put \: \: the \: \: value \: \: of \: \: y \: \: we \: \: get \: \\ ⇒ \frac{dy}{dx} = \frac{\sqrt{ \frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } } \\ }{2} \times (\frac{1}{x - 3} + \frac{2x}{ {x }^{2} + 4} - \frac{1}{x} )[/tex]

Step-by-step explanation:

used formula

[tex] { ln(m) }^{n} = n \: ln \: m \\ \\ ln(mn) = ln(m) + ln(n) \\ \\ ln( \frac{m}{n} ) = ln(m) - ln(n) \\ \\ \frac{d}{dx} ( ln(x) ) = \frac{1}{x} [/tex]

The required measure of angle m ∠A  is 58.7° which is the correct answer would be an option (D).

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.

Angles A and B are supplementary.

We have been given that m angle ∠B= 121.3°,

To determine the measure of angle A if the measure of angle B is 121.3°.

As per the property supplementary angles,

m∠A + m ∠B = 180°

m∠A + 121.3 ° = 180°

m ∠A = 180° - 121.3°

m ∠A = 58.7°

Therefore, the required measure of angle m ∠A  is 58.7°

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Answer:

Kendra will donate $9.86 to her Best Friend's Animal Society.

Step-by-step explanation:

In order to find this answer, we need to multiply $11.60 by the 8.5 hours:

11.60 x 8.5 = $98.60

Now, if she donates 1/10 every week, we can turn 1/10 into 0.10. And on a calculator set up this equation:

0.10 x 98.60 = $9.86

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

1) The amount of time that it will take to have 50 stamps is; 10 months

2) The amount of money that bella will have after 12 months is; $112

1) We are told that Jack received a collection of 30 baseball cards. Now, he decided to start collecting after that and he adds 2 stamps every month. Thus, let m represent the number of months he collects and so we have the equation as;

2m + 30

Now, we want to find out how long it will take to get 50 stamps. Thus;

2m + 30 = 50

2m = 20

m = 10 months

2) Principal = $100

Interest rate = 1% monthly

Thus;

Interest after 12 months = 100(0.01 * 12) = $12

Thus, amount she now has after 12 months = $100 + $12 = $112

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Answer:

y = -9

Step-by-step explanation:

The slope-intercept form is y = mx + b

From two points we can easily determine the slope, m = (y2-y1)/(x2-x1)

You would put in the values into the equation.

m = (-9-(-9))/(-3-1) = 0/-4 = 0

Using the slope-intercept form, y = 0(x) + b ⇒ y = b

But we don't know what the y-intercept (b) is yet.  Using the point-slope form we can determine b.

Point-slope: (y - y1) = m(x - x1)

(y - (-9)) = 0(x - (-3))

y + 9 = 0

y = -9

So the equation is y = -9.

1,858.40

2300-36%=1472

1472-70%=441.60

2300-441.6=1,858.40

The smallest number from the sum of three consecutive even numbers is 14.

Given, The sum of three consecutive even numbers is 48.

we are asked to determine the smallest number of the numbers.

Let:

x= the 1st con.even number

x+2=the 2nd con.even number

x+4=the 3rd con.even number

Add the terms and equate it with the total, 48

x+(x+2)+(x+4) = 48

simplify

x+x+2+x+4=48

combine the like terms.

3x+6=48

3x = 48-6

3x=42

x=42/3

x=14

the three numbers are:

x = 14

x+2 = 14+2 = 16

x+4 = 14+4 = 18

smallest number of the three numbers = 14

Hence we get the smallest number as 14.

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The ordering and transportation cost C for the components used in manufacturing a product is c= 100(200/x^2+ x/x+30), x≥1 where C is measured in thousands of dollars and x is the order size in hundreds.

To find the rate of change of C with respect to x when (a) x = 10, (b) x = 15, and (c) x = 20.

The rate of change of the cost with respect to x is its derivative.

The differentiation rules to apply are

Quotient Rule: [tex]\frac{d}{dx} \left[\frac{f(x)}{g(x)}\right] = \frac{g(x)f^{'}(x)-f(x)g^{'}(x)}{\left[g(x)]^{2} }[/tex]

Constant Multiple Rule: [tex]\frac{d}{dx} \left[cf(x) \right] = cf^{'}(x)[/tex]

Power Rule: [tex]\frac{d}{dx} \left[x^{n} \right] = nx^{n-1}[/tex]

Constant Rule: [tex]\frac{d}{dx} [c] = 0[/tex]

So,

[tex]c^{'}(x) = 100 (\frac{x^{2}(200)^{'}-200(x^{2})^{'}}{(x^{2})^{2} }+\frac{(x+30)(x)^{'}-x(x+30)^{'} }{(x+30)^{2} } )[/tex]

[tex]c^{'}(x) = 100 (\frac{x^{2}(0)-200(2x) }{x^{4} } + \frac{(x+30)(1)-x(1+0)}{(x+30)^{2} })[/tex]

[tex]c^{'}(x) = 100 (\frac{0-400x}{x^{4} } + \frac{x+30-x}{(x+30)^{2} })[/tex]

[tex]c^{'}(x) = 100 (\frac{-400x}{x^{4} } + \frac{30}{(x+30)^{2} })[/tex]

From the above values it appears that the rate of change of the cost increases as the size of the order increases

[tex]a) c^{'}(10) = -38.13\\ \\b) c^{'}(15) = -10.37\\ \\c) c^{'}(20) = -3.8[/tex]

Hence the above values it appears that the rate of change of the cost increases as the size of the order increases

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Answer:

3

Step-by-step explanation:

19.861>19.851

look at hundreds column

Line C has a slope of -1. LINE D has a slope of -2.

To Compare the slopes of the lines.

Let us consider the following problem:

In the xy-plane, the point (-1,-2) is on the line j, and the point (-2,-1) is on the line k. Each of the lines has a Negative slope.

We should compare slopes of both the lines to each other, because we may have such kind of two lines

y=x+1 and y=x−1

so we see that their slopes are equal, but we may have also

y=2∗x or slope 2

and

y=1/2∗x or slope 1/2,

Hence, the answer is i think that there is not enough information to compare slopes of the lines.

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The inequality to express the information when Oleg is training for a triathlon is 2x + 2y ≤ 30

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.

Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, Oleg jogged for 2 hours at x miles per hour and then he bicycled for 2 hours at y miles per hour.

The inequality will be:

2(x) + 2(y) ≤ 30

2x + 2y ≤ 30

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Complete question

Oleg is training for a triathlon. One day he jogged for 2 hours at x miles per hour . Then he bicycled for 2 hours at y miles per hour. Finally. He swam a distance. The total number of miles did not exceed 30. Express this as an inequality

The length of the sides of the squares is 3 cm.

A rectangle is a quadrilateral with all four interior angles 90°.

Given that, the dimension of the rectangular tin piece is 40 cm by 50 cm.

Let the length of the sides of the square is x.

Then, the dimensions of the resulting rectangular base are (40 - 2x) by

(50 -2x).

Given that, the area of the resulting base is 1496 square cm.

Therefore, it follows:

(40 - 2x)(50 -2x) = 1496

2000 - 80x -100x + 4x² = 1496

4x² - 180x + 2000 -1496 = 0

4x² - 180x + 504 = 0

x² - 45x + 126 = 0

x² - 42x - 3x + 126 = 0

x(x- 42) - 3(x - 42) = 0

(x - 3)(x - 42) = 0

x-3 =0 or x - 42 = 0

x = 3 or x = 42

Note that the dimension of the rectangular tin piece is 40 cm by 50 cm, therefore, x = 42 cm cannot be the length of the square.

Hence, the length of the sides of the squares is 3 cm.

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Answer:

[tex]y = \frac{1}{4} x\\[/tex] [tex]- 5[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

The function f(x) in standard form as described in the task content is; 3x³ + 21x² - 23x + 5.

It follows from the task content that the function, f(x) which is as described is to be determined.

Since the polynomial remainder theorem postulates that;

Polynomial = (quotient × divisor) + remainder.

According to the given task content;

The quotient is; 3x² - 3x + 1.

The divisor is; (x + 8) and the remainder is; -3.

Therefore, the required polynomial is;

f(x) = (3x² - 3x + 1)(x + 8) + (-3)

= 3x³ + 24x² -3x² -24x + x + 8 - 3

= 3x³ + 21x² - 23x + 5.

Therefore, the required function, f(x) is; 3x³ + 21x² - 23x + 5.

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Answer: 48 qt

Step-by-step explanation:

The conversion factor between pints and quarts is two which means there are 2 pints in every quart. divide the number of pints by two to find the number of quarts.

96/2 = 48

EX: 24 pints = 12 quarts

24/2 =12

EX 8 quarts = 16 pints

The same rule works in reverse but instead of dividing you multiply.

8x2 = 16

Number of countries would west Virginia be expected to have is  18 countries

The number of campgrounds that North Dakota has = 465 campgrounds

The number of countries = 12 countries

The number of campgrounds that West Virginia has = 711 campgrounds

Given that the North Dakota was proportional to West Virginia in the number of campgrounds to counties.

The proportion will be

465 / 12 = 711 / x

Divide the terms

38.75 = 711 / x

x = 711 / 38.75

Divide the terms

x = 18.4

x ≈ 18 countries

Hence, number of countries would west Virginia be expected to have is  18 countries

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Differentiation of function [tex]y=e^{4x^{4} } (2x^{3} -1)[/tex] is [tex]\frac{dy}{dx} =6x^{2}e^{4x^{4} } +e^{4x^{4} } (2x^{3}-1)(16x^{3} )[/tex]

A differential equation is an equation that contains one or more functions with its derivatives.

Given,

[tex]y=e^{4x^{4} } (2x^{3} -1)[/tex]

We need to apply product rule of differentiation

dy/dx=xy'+yx'

In the given equation

x=[tex]e^{4x^{4} }[/tex]

y=[tex](2x^{3} -1)[/tex]

[tex]\frac{dy}{dx} =e^{4x^{4} } .6x^{2} +(2x^{3}-1)e^{4x^{4} } (16x^{3} )[/tex]

[tex]\frac{dy}{dx} =6x^{2}e^{4x^{4} } +e^{4x^{4} } (2x^{3}-1)(16x^{3} )[/tex]

Hence, differentiation of function [tex]y=e^{4x^{4} } (2x^{3} -1)[/tex] is [tex]\frac{dy}{dx} =6x^{2}e^{4x^{4} } +e^{4x^{4} } (2x^{3}-1)(16x^{3} )[/tex]

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The equation of the tangent line of the function is y = x + 20

f(x)=(x^2+6)(x−4)

expanding the function gives

f(x)=x^3 - 4x^2 + 6x - 24

At a specific point the slope, m is the derivative

finding the derivative of f(x)

f'(x) = 3x^2 - 8x + 6

The derivative at the point (1, -21) is found by substituting the point to the equation

f'(1) = 3 * 1 - 8 * 1 + 6 = 1

the slope, m = 1

equation of the line of slope = 1 passing through point (1, -21) is calculated using the point slope formula which is

(y - y') = m(x - x')

(y - -21) = 1(x - 1)

y + 21 = x - 1

y = x + 20

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Answer:

Step-by-step explanation:

C E F or just E and F