Noah spent $66 for 20 gallons of gasoline. Lydia spent $81.25 for 25 gallons of gasoline. How much did each person spend for 1 gallon of gasoline?

The pigeonhole principle can be used to demonstrate that there must be at least one duplicate in the set nums. Each possible number that can appear in nums is a "pigeonhole" in this context, and each number within nums is a "pigeon."

Method or evidence to confirm that Nums must contain multiple duplicate number: Simple Strategy: Utilizing nested loops, it is intended to determine whether or not each element appears in the array more than once for each element.

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(x-3.5), or (x-7/2) are the factors of the polynomial, f(x) = 6x⁴ – 21x³ – 4x² + 24x – 35

Given,

The polynomial, f(x) = 6x⁴ – 21x³ – 4x² + 24x – 35

We have to find the factors of the polynomial;

Here,

This polygon's 35-factor factors, plus or minus 1, plus or minus 5, plus or minus 7, are potential zeros. Determine whether or not there is a non-zero remainder in each example using synthetic division. If none of these solutions work, try rational divisors derived from 35 and 6 such as 5/6, 7/6, 1/6 and so on.

Now,

f(x) = 6x⁴ – 21x³ – 4x² + 24x – 35

If used correctly, this method will eventually reveal one or two zeros of this poly. Of course, it would be lot simpler if you looked at the potential solutions provided to you for this issue.

I plotted this function and discovered that it crosses the x-axis at 7/2. Another root exists.

To determine whether or whether 7/2 is a root, use synth. div.

Then,

        ___________________________

7/2   /   6    -21    -4    24    -35

                  21      0   -14     35          

       ----------- ------------------------------

          6        0     -4    10       0

Since there is no remainder, the polynomial has a root of 7/2 (or 3.5). Therefore, a factor is (x-3.5) or (x-7/2).

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So basically for the first one do 14.0%x 4.6

The values of x for the given quadratic equation 2x² = 4x - 7

are given by:

[tex]x = \frac{2 +i\sqrt{10} }{2}[/tex]

[tex]x = \frac{2 -i\sqrt{10} }{2}[/tex]

What is the solution of a quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations.

According to the given question:

For this case we have the following quadratic equation:

2x² = 4x - 7

Rewriting the equation we have:

2x² - 4x + 7 = 0

From here, we have:

a = 2b = -4c = 7

Substituting values in the quadratic equation we have:

x = (-b ± √b² - 4ac)/2a

x = (-(-4) ± √(-4) - 4(2)(7)/2(2)

Rewriting the equation we have:

x = (4 ± √16 - 56)/4

x = (4 ± √-40)/4

x = (2 ± i√10)/2

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The triangle with sides 54 m , 78 m and 90 m is not a right angle triangle

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ΔABC

Now , the value of the sides of the triangle is

AB = 54 m

BC = 78 m

AC = 90 m

Now , for the triangle to be right angle triangle , it should satisfy the Pythagoras Theorem

So , For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substitute the values in the equation , we get

AC² = AB² + BC²

90² = 54² + 78²

8100 = 2916 + 6084

8100 ≠ 9000

Therefore , the triangle ΔABC is not a right angle triangle

Hence ,

The triangle with sides 54 m , 78 m and 90 m is not a right angle triangle

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Answer: C. 1200$

Step-by-step explanation:

$600 times twice is $1200

The equation of line in slope intercept form is, [tex]y=\frac{3}{4}x+9[/tex].

What is slope point form of the line?

A line's point slope form equation is y - y1 = m. (x – x1). Consequently,

y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.

Let the line passes through the point (-4, 6) and having slope 3/4.

We know that the equation of line passes through the point [tex](x_1, y_1)[/tex] and having slope m is,

[tex]y-y_1=m(x-x_1)[/tex]

Here, [tex](x_1, y_1) = (-4, 6)[/tex]  and slope [tex]m = \frac{3}{4}[/tex]

Plug the values in the above equation.

⇒

[tex]y-6=\frac{3}{4}(x-(-4))\\ y - 6 = \frac{3}{4}(x + 4)\\ y-6=\frac{3}{4} x + 3\\y = \frac{3}{4}x+3+6\\ y=\frac{3}{4}x+9[/tex]

Hence, the equation of line in slope intercept form is, [tex]y=\frac{3}{4}x+9[/tex].

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The margin of error is 0.086 and its C.I is (0.575 , 0.785).

What is margin of error?

n = 117 , x =87

Point estimate for the proportion:

P = x/n

= 81/118

= 0.68644

Confidence = 95%, α = 0.05

From z-table area 0.975 close to z=1.96

Margin of error, E = 1.96 √((0.68*0.55)/130)

= 1.96 * 0.05363

= 0.105

= 0.086

Confidence = P ± E

= 0.68 ± 0.105

=(0.68-0.105 , 0.68+0.105)

= (0.575 , 0.785)

Hence, the margin of error is 0.086 and its C.I is (0.575 , 0.785).

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Answer:

It's A

Step-by-step explanation:

The first part is her purchase before the tax, which should be $32. The second part is her purchase after sales tax, which adds 8% to the shoes and results in the purchase being $34.40

The values of the integers lie between 29 and 39 and is 30,31,32,33,34,35,36,37,38.

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Given that the integers lie between the numbers 29 and 39. The numbers will be,

29, { 30,31,32,33,34,35,36,37,38 }, 39

Therefore, the values of the integers lie between 29 and 39 and are 30,31,32,33,34,35,36,37,38.

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For a sample population of size, n =5, sx = 20 and sx² = 120, the sum of squared deviation is 40.

Therefore, the answer is 40.

Given a sample population of 5 scores, that is n = 5.

sx = ∑x = 20

sx² = ∑x² = 120

Thus mean can be calculated by

mean, x⁻ = ∑x/ n

x⁻ = 20/ 5

x⁻ = 4

The sum of squared deviations

ss = ∑( x - x⁻)²

ss = ∑( x² -2×x×x⁻ + x⁻²)

ss = ∑x² -2×x⁻×∑x + ∑x⁻²

ss = ∑x² -2×x⁻×∑x + nx⁻²

ss = 120 - 2×4×20 + 5×4²

ss = 40

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The coefficient of yA² for the three given expressions are 2, 10 and 5 respectively.

It is a mathematical statement that defines a mathematical concept as well as the system of a mathematical operation express in a symbolic form.

Mathematical expression is made up of at least two numerical terms along with a sign or at least two terms along with a sign. The expression having two or more numerical terms is called numerical expression.

As example 4 + 3 or 100÷4

The expression which has both variables and numbers is called algebraic expression.

As example X+6 or 25+5y

In an expression, the numbers which are accompanied by variables is called coefficient. As example, 24 + 3y, where 3 is the coefficient of y

but 24 is a constant number.

We are given three expressions, these are 2xA²y, 10xyA² and 5yA²

for the 1st expression, 2 is the coefficient of A²y

for the 2nd expression, 10 is the coefficient

for the last 5 is the coefficient.

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You may use the expression to convert the length of 5 rows of ribbons to inches: length = 5w + (5 - 1)s inches, where w is the width of the ribbons and s is the spacing between the rows.

To convert 5 rows of ribbons to inches, you need to know the width of the ribbons and the spacing between the rows.

Let's say the width of the ribbons is w inches, and the spacing between the rows is s inches. In this case, the total length of the ribbons in 5 rows would be 5w + 4s inches, since there are 5 ribbons and 4 spaces between them.

For example, if the width of the ribbons is 0.5 inches and the spacing between the rows is 0.1 inches, the total length of the ribbons in 5 rows would be :5 × 0.5 inches + 4 × 0.1 inches = 2.5 inches + 0.4 inches = 2.9 inches.

In general, to convert the length of n rows of ribbons to inches, you can use the formula: length = nw + (n - 1)s inches, where w is the width of the ribbons and s is the spacing between the rows.

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Answer:

Sequence:

1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex]

. . . . . . . . . .  ⭐ please take a ruler and measure the distance from AA',    . . .  . . . . . BB', CC', DD', and EE', and then write that distance (it should      . . . . . . . .  be the same for each measurement) in place of 5 in -5. I just     . . . . . . . .  wrote -5 because it was my best approximation for looking at     . . . . . . . .  a laptop screen. ⭐

2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex]

3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex]

Step-by-step explanation:

1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex] means that when you move figure ABCDE down by 5 units, it will map onto the image of A'B'C'D'E.

2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex] means that when you rotate figure A'B'C'D'E' 180 degrees counterclockwise about point B', said figure will map onto the image of A''B''C''D''E''.

3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex] means that when you reflect figure A''B''C''D''E'' across segment D''E'', said figure will map onto the image A'''B'''C'''D'''E'''.

The simplification of the given expression is x² - x + 3.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is √x⁴ = x - 3.  The expression will be simplified as,

√x⁴ = x - 3

Solve the radical term first and simplify the expression further,

x² = x - 3

x² - x + 3 = 0

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Isosceles triangle has three sides, three angles, a base, a height, and an area in which two sides are equal to each other .

the sum of triangle is 180, sum of all the interior angles is equal to 180.

so if you know two angles then apply sum of triangles and find out the value of the third triangle.

isosceles triangle

An isosceles triangle is a type of triangle that has any two sides equal in length. The two angles of an isosceles triangle, opposite to equal sides, are equal in measure.

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When given two values in algebra, it is simple to find the third value. The x value is 5.

x Multiplicand Equals Product

X = product / multiplicand

* x = 10

Product

The x value is 5.

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"A binomial is an algebraic expression which has exactly two terms." The examples of binomials are x² + 3, x + y, x³ + 2x, 9 + 7y, xy² + xy, etc.

A polynomial is of various types like monomial, binomial, trinomial, etc.

Monomial contains only single term.

Trinomial contains exactly three terms. All the three are dissimilar.

A binomial is said to have only positive exponents and no negative exponents.

In x³ + 2x, x³ and 2x are two different terms. The variable is only x. The exponent of x³ is 1, the exponent of x is 1. The coefficient of x³ is 1, the coefficient of x is 2.

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1440 combinations ways.

We know that the total arrangements will be

6!= 720 because its a 6letter word

So if we take MI to be a one letter word

Same for IM

which will Also be 6!= 720

SO TOTAL possible combination will be 720+720= 1440

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time.

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Answer:

x = 10

Step-by-step explanation:

7x-22=3x+18

4x -22 = 18

4x = 40

x = 10

The solutions to the quadratic equation x² + 3x - 28 = 0 are 4 and -7.

The quadratic formula is expressed as;

x = (-b±√(b² - 4ac)) / (2a)

Given the equation;

x² + 3x - 28 = 0

Substitute the values of a, b, and c into the formula and solve for x.

x = (-b±√(b² - 4ac)) / (2a)

x = ( -3 ±√( 3² -  ( 4 × 1 × -28) )) / (2×1)

x = ( -3 ±√( 9 -  ( -112) )) / (2)

x = ( -3 ±√( 9 + 112 )) / (2)

x = ( -3 ±√( 121 )) / 2

x = ( -3 ± 11 ) / 2

x = ( -3 - 11 ) / 2, x = ( -3 + 11 ) / 2

x = -14/2, x = 8/2

x = -7, x = 4.

Therefore, -7 and 4 are the solutions to the equation.

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The commutative, associative, and distributive property are the properties of addition and multiplication.

Commutative Property - The Commutative Property is derived from the word commute, which means to move. It states that the product or sum of two numbers do not change even if the places of numbers are changed or if the numbers move from one place to another. The commutative property of addition states that a + b = b + a and the commutative property of multiplication states that a × b = b ×  a.

Associative Property - It is related with the grouping of numbers. It states that the product or sum of three numbers do not change even if the grouping of numbers are changed. The associative property of addition states that (a + b) + c = a + (b + c) and the associative property of multiplication states that: (a × b) × c = a × (b ×  c).

Distributive Property - It is related with the distribution of numbers. It states that the product of three numbers do not change even if the distribution of numbers are changed. The distributive property of multiplication states that: a × (b + c) = (a × b) + (a ×  c).

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Answer:

A. [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

⭐ What is the multiplicative rate?

To find the multiplicative rate of this exponential function, we need to make an equation to see what each y-value gets multiplied by to get the next y-value.

I am picking the y-values 2 and 2/5, but you can choose any two consecutive y-values.

Equation (let x= the multiplicative rate of change):

[tex]2x = \frac{2}{5}[/tex]

Solve for x:

[tex]\frac{2x}{2} = \frac{2}{5}(2)[/tex]

[tex]x = \frac{2}{10}[/tex]

Simplify:

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

∴ The multiplicative rate of change of the function is 1/5.

F=9/5C+32 is the required equation and Greg statement is true

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that Greg is expressing temperature in farenheit and Josh expressing it in the celsius.

C=5/9(F-32)

We need to rewrite the formula so that Josh can quicly convert the temperature that Greg describes F.

F=9/5C+32

The temperature where John leaves has 77 F.

Let us convert to celsius.

C=5/9(77-32)

C=5/9(45)

C=5(5)

C=25 degrees.

25 degress< 30 degrees.

Hence, F=9/5C+32 is the required equation and Greg statement is true.

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Answer:

Step-by-step explanation:

If the derivative of g(x) with respect to x (denoted d/dx g(x)) is equal to 0, then the derivative of the product g(x)sin(x) with respect to x can be found using the product rule for derivatives.

The product rule states that if f(x) and g(x) are two functions, then the derivative of the product f(x)g(x) with respect to x is given by:

d/dx (f(x)g(x)) = f(x) * d/dx g(x) + g(x) * d/dx f(x)

In our case, f(x) is g(x) and g(x) is sin(x). Substituting these values into the equation above, we get:

d/dx (g(x)sin(x)) = g(x) * d/dx sin(x) + sin(x) * d/dx g(x)

Since the derivative of sin(x) with respect to x is cos(x) and the derivative of g(x) with respect to x is 0, we can simplify this expression to:

d/dx (g(x)sin(x)) = 0 * cos(x) + sin(x) * 0

Which simplifies to:

d/dx (g(x)sin(x)) = 0

Therefore, if the derivative of g(x) with respect to x is equal to 0, then the derivative of the product g(x)sin(x) with respect to x is also equal to 0.

The three steps for graphing linear inequalities are consists of solving the variables, plotting the points on graph and bound the region.

while solving the inequalities of two variables the inequal sign are changed by equal sign for a certain time. After determining the unknown value, we plot the points on the XY axis.

while graphing the inequal variables the region that satisfy the inequality is bounded by solid line or dashed line depends on the inequal sign.

hence, we need to plot the linear inequalities on XY axis in three steps.

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Repeat the procedure of dividing, multiplying, subtracting, and bringing the next digit down until you have solved the division problem's quotient.

For example, consider the long-division problem:

4567 ÷  123

In this problem, we need to repeat the process of dividing, multiplying, subtracting, and bringing the next digit down three times, since the divisor has three digits.

However, in some cases, you may need to repeat the process more or fewer times than the number of digits in the divisor.

For example, if the dividend has fewer digits than the divisor, you may need to repeat the process fewer times. Or, if you need to carry a digit over to the next step, you may need to repeat the process more times.

Thus, in general, you should repeat the process of dividing, multiplying, subtracting, and bringing the next digit down until you have found the quotient of the division problem. This will typically be the number of digits in the divisor, minus one, but it may be more or fewer in some cases.

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Using AutoSum in Excel is one quick and simple method of adding numbers. Simply click in a blank cell immediately underneath a column of data. Click AutoSum > Sum next on the Formula tab.

Sum is the outcome of adding two or more numbers or quantities. There may be only two terms, or there may be one hundred, thousand, or a million. There are some summations that have an infinite number of terms.

here

Click AutoSum on the Home tab, choose a cell next to the numbers you wish to add, then hit Enter when you're finished.

When you choose AutoSum, Excel automatically creates a formula (using the SUM function) to add the values.

Simply click in a blank cell immediately underneath a column of data. Click AutoSum > Sum next on the Formula tab.

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Answer:

ƒ(6) = − 50

Step-by-step explanation:

ƒ(x) = − x² – 14, Find f(6)

ƒ(6) = − 6² – 14

ƒ(6) = − 36 – 14

ƒ(6) = − 50