Data regarding fuel efficiency of an 18-wheel truck were collected. The graph shows the correlation between the average speed above 40 miles per hour (in miles per hour) and the money spent on gas (n dollars): Estimate the average rate of change from x = 5 to x = 9.​

Answer:

The 1st option

Step-by-step explanation:

Because x can be anything that's not imaginary and y has to be below 2 always because of the negative value added before the 3. Also it's impossible to reverse the sign of the negative because negative x would only result in 3 becoming a fraction.

Answer:

I hope this helps!

Step-by-step explanation:

Please mark brainiest

Answer:

a.

x $         0 $         50         $ 100

p (x)    25/36      5/36        6/36

b. 23.61%

c. 23.61%

Step-by-step explanation:

We have that "x" is the amount of money earned:

we have to fail twice, the probability of failure is 5/6 and the probability of hitting is 1/6, therefore if you lose the probability would be:

5/6 * 5/6 = 25/36

the one to win 50 $, would be:

1/6 * 5/6 = 5/36

and the one to win $ 100 would be:

1/6 * = 6/36

that is to say:

a.

x $         0 $         50         $ 100

p (x)    25/36      5/36        6/36

b. the expected amount you'll win would be:

0 * 25/36 + 50 * 5/36 + 100 * 6/36 = 23.61

c. The normal thing is to pay at least the expected amount, that is, $ 23.61, since something greater than that would already be profit.

The expected value is the sum of the product of values and their respective probabilities. Hence ;

To win $100 :

To win $50 :

To win nothing :

The probability distribution table :

The expected value :

E(X) = (0 × 25/36) + (50 × 5/36) + (100 × 1/36)

E(X) = 0 + 9.7222

E(X) = 9.722

Therefore, the expected amount to be won is $9.722

Willing amount to be paid to play the game :

Any value below the expected value,

Therefore, the willing amount will be < 9.722

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h(x) = f(x)g(x) represents the product of two functions, combining their behaviors into a new function.

In mathematics, the expression h(x) = f(x)g(x) represents the product of two functions, f(x) and g(x). When evaluating h(x) for a given value of x, it involves multiplying the corresponding values of f(x) and g(x).

The product of two functions allows for the combination of their individual behaviors and characteristics. The resulting function, h(x), inherits properties from both f(x) and g(x). The behavior of h(x) will depend on the specific functions involved.

For example, if f(x) represents a linear function and g(x) represents an exponential function, their product h(x) = f(x)g(x) will exhibit a combined behavior reflecting both linearity and exponential growth. The specific form of the functions will determine the precise behavior of h(x) and its graph.

It is important to note that the product of two functions assumes that the functions are defined for the given values of x and that the multiplication operation is valid for the corresponding function values.

h(x) = f(x)g(x) represents the product of two functions, combining their behaviors to form a new function. The specific nature of h(x) depends on the characteristics of f(x) and g(x).

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Answer:

\(115 \dfrac{1}{2}\:cm^3\)

Step-by-step explanation:

The volume of a rectangular prism is the product of each of the sides of the prism

Given the sides have lengths
\(3\dfrac{1}{2}, 6 \;and\; 5 \dfrac{1}{2} cm\)

the volume would be
\(3\dfrac{1}{2} \times 6 \times 5 \dfrac{1}{2}\)

To perform this multiplication, convert mixed fractions to improper fractions first

Use the rule that mixed fraction
\(a\dfrac{b}{c}=\dfrac{a\times \:c+b}{c}\)

\(3\dfrac{1}{2}=\dfrac{3\times 2+1}{2} = \dfrac{7}{2}\)

\(5\dfrac{1}{2}=\dfrac{5\times 2+1}{2}= \dfrac{11}{2}\)

Therefore
\(3\dfrac{1}{2}\times \:6\times \:5\dfrac{1}{2}\\\\= \dfrac{7}{2}\times \:6\times \dfrac{11}{2}\\\\= \dfrac{7}{2}\times \dfrac{6}{1}\times \dfrac{11}{2} \quad(6 = \dfrac{6}{1})\)

\(=\dfrac{7\times \:6\times \:11}{2\times \:1\times \:2}\\\\= \dfrac{462}{4}\\\)

Divide numerator and denominator by 2 to get
\(\dfrac{231}{2}\\\)

Convert improper fraction \(\dfrac{231}{2}\) to mixed fraction using quotient/remainder

\(\dfrac{231}{2} \\\\\rightarrow Quotient: 115\\\\\rightarrow Remainder = 231 - 115 \times 2 = 231 - 230 = 1\)

\(\dfrac{231}{2} = 115 \dfrac{1}{2}\)

The inequality corresponding to the equation -4x + y = -3 is either y > 4x - 3 or y < 4x - 3, depending on the relationship between 4x - 3 and 0.

To write the inequality represented by the equation -4x + y = -3, we first need to manipulate the equation to express y in terms of x.

Starting with -4x + y = -3, we isolate y by adding 4x to both sides:

y = 4x - 3

Now we have y expressed in terms of x. To form the inequality, we consider the relationship between x and y. The inequality depends on whether the expression 4x - 3 is greater than or less than 0.

If 4x - 3 is greater than 0, then y is greater than 0, and we can write the inequality as:

y > 4x - 3

If 4x - 3 is less than 0, then y is less than 0, and we can write the inequality as:

y < 4x - 3

The inequality represents a region in the coordinate plane where the y-values are either greater than or less than the expression 4x - 3, depending on the direction of the inequality sign.

For example, if we choose a point (x, y) in the region above the line y = 4x - 3, where y is greater than 4x - 3, the inequality y > 4x - 3 will hold true. On the other hand, if we choose a point below the line, where y is less than 4x - 3, the inequality y < 4x - 3 will be satisfied.

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The width of the rectangle is 1 in.

A rectangle is a type of parallelogram, having each angle right angle and equal diagonal.

Given that, A rectangle has a length that is five times longer than its width. and the perimeter of the rectangle is 12 inches

Perimeter of a rectangle = 2(length+width)

Let the width be w then length will be (5w)

Therefore,

(w+5w)2 = 12

6w = 6

w = 1

Hence, the width of the rectangle is 1 in.

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A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(x^{4}\)+ c\(x^{3}\). The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set.

Part A: A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(x^{4}\)+ c\(x^{3}\). The coefficient of the highest degree term (x^5) must be non-zero and all the terms must be written in descending order of the degree. This is the definition of standard form for polynomials.

Part B: The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set. In this case, the set is polynomials and the operation is subtraction. An example of this property can be seen by subtracting two polynomials, such as 4\(x^{2}\) + 3x - 5 and \(x^{2}\) + 2. The result of this subtraction would be 3\(x^{2}\) + 3x - 5, which is also a polynomial and therefore an element of the set, demonstrating the closure property.

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A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(y^{2}\)+ c. The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set.

Part A: A fifth-degree polynomial with three terms in standard form would be written as a\(x^{2}\) + b\(y^{2}\)+ c. The coefficient of the highest degree term (\(x^{5}\)) must be non-zero and all the terms must be written in descending order of the degree. This is the definition of standard form for polynomials.

Part B: The closure property states that a set is closed under a certain operation if performing that operation on any two elements of the set produces a result that is also an element of the set. In this case, the set is polynomials and the operation is subtraction. An example of this property can be seen by subtracting two polynomials, such as 4\(x^{2}\) + 3x - 5 and  + 2. The result of this subtraction would be 3\(x^{2}\) + 3x - 5, which is also a polynomial and therefore an element of the set, demonstrating the closure property.

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The quantity of girl scout cookies that will fit into the trunk of the Nissan Rogue with the given volume would be = 0.01 cookie.

The volume of the Nissan Rogue that can be filled with the cookie box = 1.11 m³.

The dimensions of the cookie box;

length = 17.8 cm

width = 5.8cm

height = 11.7cm

The volume = 17.8×5.8× 11.7 = 1207.908cm³

But to convert to m³ is to divide cm³ by 100 = 12.08m³

If 1 cookie = 12.08m³

X cookie = 1.11 m³

make X the subject of formula;

X cookie = 1.11/12.08

= 0.01 cookie

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Answer:

if we divide 114.80 by 8 we get 14.35. We do this to get the 1% of the cost.

since we now know that 14.35 is 1% we can multiply 14.35 by 100 and once we do this we get 1435

Answer: 19

Step-by-step explanation: Since there is no one middle number we have to find the mean of the two middle numbers. Once you find the mean for 24 and 11 you will see that the answer is 19.

Answer:

The median is the middle number in numerical order.

Numerical order - \(11,12,14,24,27,72\)

There are 6 numbers.

The median is 19.

Answer:

Love you

Step-by-step explanation:

Answer: x = √-6 - 4

Step-by-step explanation:

x^2+8x+22=0

(x+4)^2 - 16 + 22 = 0

(x+4)^2 + 6 = 0

(x+4)^2 = -6

√(x+4)^2 = √-6

x = √-6 - 4            

√6 = 2.449

Answer:

Marcus has 17 rocks.

Step-by-step explanation:

Answer:

Diameter is the width =  7.64 ft

Step-by-step explanation:

Perimeter would need to be the arc of a semi circle measuring less than or equal to 12   Where perimeter therefore = 12* 2 = 24   24 / 3.14 = 7.64331210191   where 3.14 the value for pi  and formula of a semi circle we use radius  =  1/2 pi * 3.82 ^2 =  D * pi = 7.65   and radius =7.64 / 2 = 3.82 so answer is the diameter =   7.64 ft

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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Juan's location after 60 seconds, given the starting point and the number of seconds would be ( 18, 14 )

Every 15 seconds, Juan moves 4 yards east and 3 yards north. He is therefore moving along the grid in steps of (4 , 3 ).

After 60 seconds, Juan will have moved 4 times because 15 seconds in 60 seconds gives 4. This means he would have moved east by :

= 4 x 4

= 16 yards

And north by :

= 3 x 4

= 12 yards

His location would be:

= ( 2 + 16 , 2 + 12 )

= ( 18, 14 )

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The rest of the question is:

What will Juan's location be after 60 seconds?

The percent of increase in the temperature of the liquid 67.97% .

We have that these are a few ways to decipher the appropriate safety protocol for this lab experiment

From the question we are told that

Generally

Safety precautions are the unforgettable rules and regulations that governs a laboratory.

This might vary across experiments such as the one in this scenario.

Therefore,  the percent of increase in the temperature of the liquid 67.97% .

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The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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Answer:

3 lb 7 oz

Step-by-step explanation:

Simply substract 6 lb & 3 lb , then substract 13 oz with 6 oz ..... AND YOU ARE DONE

!!! UwU gang !!!

*3ill MoB*

Answer:

Amadi: 20 years old

Chima : 4 years old

Answer:

3rd

Step-by-step explanation:

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

Answer:

2x+3y=10

Step-by-step explanation:

when you solve this equation doesn't have solution but is linear

9514 1404 393

Answer:

 x = x +1

Step-by-step explanation:

For the "no solution" case, we usually want a linear equation that resolves to something of the form 0 = 1. We can multiply this by any (non-zero) factor we may like, and add any linear expression that seems suitable. The simplest treatment would be to simply add x to both sides:

  x +0 = x +1

  x = x +1 . . . . . . linear equation with no solution

__

If you want to see something more complicated, multiply by 12 and add 2x-9

  (2x -9) +12(0) = (2x -9) +12(1)

  2x -9 = 2x +3 . . . . . another linear equation with no solution

Answer:

4 + ( -7 X 2 ) = -10

Step-by-step explanation:

Check work:

-7 times 2 is -14.

4 + -14 = -10

Answer:

there is no context at all

The probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is given by the equation P = 9/17

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

Given data ,

Let the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 be P

Now , the equation will be

The fraction of doctors who are general practitioners be n ( A ) = 7/17

The fraction of doctors who are under the age of 45 n ( B ) = 4/17

And ,

The fraction of doctors who are both n ( A ∩ B ) = 2/17

Now , from the set theory formula ,

n(A∪B) = n(A) + n(B) - n(A⋂B)

And , probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B )

Substituting the values in the equation , we get

Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = ( 7 / 17 ) + ( 4/17 ) - ( 2/17 )

On simplifying the equations , we get

Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = 9/17

Hence , the probability is 9/17

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The solution to the inequality is y < 9

Inequalities are simply described as a relation with the reflection of a non-equal comparison between two numbers, mathematical expressions or even elements.

The comparison of these expressions or numbers is mostly based on their sizes on the number line.

It is used to compare two values such that one is less than, greater than, or simply not equal to another value.

From the information given, we have the inequality;

-3 + y< 6

To solve for y, collect like terms

y < 6 + 3

add the values

y< 9

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The value of that guarantees the equation has exactly one real root is Zero

A quadratic equation has exactly one real number solution, then the value of its discriminant is always zero.

Quadratic

The word Quadratic is derived from the word Quad which means square. In other words, a quadratic polynomial is a polynomial function of degree 2.There are many scenarios where quadratic polynomials are used. When a rocket is launched, its path is described by the zero of a quadratic polynomial.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

A quadratic equation in variable x is of the form ax2 + bx + c = 0, where a ≠ 0.

In the case of one real solution, the value of discriminant b2 - 4ac is zero.

For example, x2 + 2x + 1 = 0 has only one solution x = -1.

Discriminant = b2 - 4ac = 22 - 4 (1) (1) = 0

Thus,  a quadratic equation has exactly one real number solution, then the value of the discriminant is always zero.

The value of that guarantees the equation has exactly one real root is Zero.

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Answer:

$975

Step-by-step explanation:

The car is rented for 3 weeks

the rent is for a week is $280 so for three weeks it would be

3*28 = $840

now we need to add the per mile price to this

1 mile = $0.15 for 900 miles it would be

900*(0.15) = 135

So the total rental cost is

$840 + $135 = $975