Steve bought 10 gallons of gas at the gas station with the highest price. how much more than cole did he pay for gas?

please help, thank you.​

Solution 1

Inspecting a 7th-degree polynomial of 'n' by taking its derivatives

From the given conditions,

 2n7+n6+2n4+2n3+2n2

=(n+1)7+(n+1)5+(n+1)4+2(n+1)3+(n+1)2+2(n+1)+1.

 2n7+n6+2n4+2n3+2n2

=n7+7n6+21n5+35n4+35n3+21n2+7n+1

 +n5+5n4+10n3+10n2+5n+1

 +n4+4n3+6n2+4n+1

 +2(n3+3n2+3n+1)

 +(n2+2n+1)+2(n+1)+1.

n7-6n6-22n5-39n4-49n3-42n2-26n-9=0 .....[1].

Let A(n)=n7-6n6-22n5-39n4-49n3-42n2-26n-9.

For n>2, A(n)<n7-6n6-22n5.

Since A(n)=0,

0<n7-6n6-22n5.

0<n5(n-3+√31)(n-3-√31).

Since n>2, n>3+√31, which means n≥9 .....[2].

Now, to differentiate A(n),

A'(n)=7n6-36n5-110n4-156n3-147n2-84n-26.

A''(n)=42n5-180n4-440n3-468n2-294n-84.

A'''(n)=210n4-720n3-1320n2-936n-294.

A(4)(n)=840n3-2160n2-2640n-936.

 A(5)(n)

=2520n2-4320n-2640

=2520{(n-6/7)2-262/147}.

If A(5)(n)=0, n=6/7±√(262/147).

Therefore, A(5)(n)>0 for n≥3.

Although n≥9 according to [2], I try inspecting A(n) for n≥10.

When n≥10, A(4)(n) increases monotonously.

A(4)(10)=840000-216000-26400-936>0.

Therefore, A(4)(n)>0 for n≥10.

And when n≥10, A'''(n) increases monotonously.

A'''(10)=2100000-720000-132000-9360-294>0.

Therefore, A'''(n)>0 for n≥10.

And when n≥10, A''(n) increases monotonously.

A''(10)=4200000-1800000-440000-46800-2940-84>0.

Therefore, A''(n)>0 for n≥10.

And when n≥10, A'(n) increases monotonously.

 A'(10)

=7000000-3600000-1100000-156000-14700-840-26>0.

Therefore, A'(n)>0 for n≥10.

And when n≥10, A(n) increases monotonously.

 A(10)

=107-6000000-2200000-390000-49000-4200-260-9>0.

Therefore, A(n)>0 for n≥10 .....[3].

From [2] and [3], A(n)=0 only when 9≤n<10.

In consequence, n=9.

Answer: 5n+14-11n-2

Step-by-step explanation:

Answer: 7313

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

First we combine like terms, so y2 - 5y = - 3y

Now we get - 3y = 3

Then we divide both sides by - 3

Now we get y =-1

Answer:

Step-by-step explanation:

The answer is y= +/- 5 sqrt 37/2

Answer:

2 degrees

Step-by-step explanation:

1) The temperature at 12:00 PM was -8 degrees celsius

2) The temperature at 1:00 PM was 10 degrees higher than at 12:00 PM

3) -8 + 10 = 2

4) The temperature at 1:00 PM was 2 degrees celsius

5) Draw a number line with the labels 12:00 PM and 1:00 PM on either end

6) Label above 12:00 PM -8 degrees celsius, and above 1:00 PM 2 degrees celsius

7) Draw an arrow pointing from 12:00 PM towards 1:00 PM to show that the temperature changes between 12:00 PM and 1:00 PM  

I hope this helps :D

Answer:the answer is -4f

Step-by-step explanation:

Answer:

Perimeter=10.25cm

Area=5cm²

Step-by-step explanation:

Perimeter=4+3.5+2.75=10.25cm

Area=1/2(4)(2.5)=5cm²

The statement is true.

When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.

When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.

The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.

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The number of total outcomes is 12.

Here is a tree diagram for the pizza options:

Copy code

     /  |  \

 Thick Thin

  /     |     \

Red White Red White

/  |  \   / |  \   / |  \

Pep Saus Veg Pep Saus Veg Pep Saus Veg

There are two (2) options for the crust, two (2) options for the sauce, and three (3) options for the topping. Therefore, the total number of outcomes is:

Total Outcomes = 2 (options for crust) x 2 (options for sauce) x 3 (options for topping)

Total Outcomes = 12

Therefore, there are 12 total outcomes.

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The reasonable solutions for this situation is (1, 3.5) and (2, 2)

A graph is a visual representation of data or information, typically used to display the relationship between two or more variables. Graphs are used to make it easier to understand and analyze data, and can be used to convey information in a clear and concise manner.

Audrey has x pounds of red grapes and y pounds of green grapes.

She has less than 5 pounds of grapes in all, hence:

x + y < 5

Also, x ≥ 0, y ≥ 0

a) The option (–1, 2) is wrong because x = -1 < 0

b) The option (1, 3.5) is correct because 1 + 3.5 = 4.5 < 5

c) The option (2, 2) is correct because 2 + 2 = 4 < 5

d) The option (4.5, 0.5) is wrong because 4.5 + 0.5 = 5 which is not less than 6.

e) The option (5, 0) is wrong because 5 + 0 is not less than 5

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Answer:

1/4 i think

Step-by-step explanation:

Answer:

y= -- 1/4 x + 7/4

y= -- 1/4 x + 1.75

Step-by-step explanation:

i runed it through desmos and i was just like the picture dont  know how to explain it

The expected value of X given Y = y is 0.5, and the expected value of X^3 given X < 0.5 is 0.03125.

To compute the given expectations, we need to use the concept of conditional expectations.

To compute E[X | Y = y], we need to find the conditional probability density function f(x | y) and calculate the expectation using the conditional density.

The conditional probability density function can be found using the formula:

f(x | y) = f(x, y) / fY(y)

where fY(y) is the marginal probability density function of Y.

In this case, since f(x, y) = 3y^2 and the support of X and Y is 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, we have:

fY(y) = ∫[0,1] f(x, y) dx = ∫[0,1] 3y^2 dx = 3y^2 * x |[0,1] = 3y^2

Therefore, the conditional probability density function is:

f(x | y) = (3y^2) / (3y^2) = 1

Since the conditional probability density function is constant, the conditional expectation E[X | Y = y] is simply the midpoint of the support of X, which is (0 + 1) / 2 = 0.5.

To compute E[X^3 | X < 0.5], we need to find the conditional probability density function f(x | X < 0.5) and calculate the expectation using the conditional density.

The conditional probability density function can be found using the formula:

f(x | X < 0.5) = f(x) / P(X < 0.5)

where f(x) is the marginal probability density function of X and P(X < 0.5) is the cumulative distribution function of X evaluated at 0.5.

The marginal probability density function of X is:

fX(x) = ∫[0,1] f(x, y) dy = ∫[0,1] 3y^2 dy = y^3 |[0,1] = 1

Therefore, the conditional probability density function is:

f(x | X < 0.5) = f(x) / P(X < 0.5) = 1 / P(X < 0.5)

To find P(X < 0.5), we integrate the marginal probability density function of X from 0 to 0.5:

P(X < 0.5) = ∫[0,0.5] fX(x) dx = ∫[0,0.5] 1 dx = x |[0,0.5] = 0.5

Therefore, the conditional probability density function is:

f(x | X < 0.5) = 1 / P(X < 0.5) = 1 / 0.5 = 2

Now we can calculate the conditional expectation:

E[X^3 | X < 0.5] = ∫[0,0.5] x^3 * f(x | X < 0.5) dx = ∫[0,0.5] x^3 * 2 dx = 2 * (1/4) * x^4 |[0,0.5] = 2 * (1/4) * (0.5^4 - 0^4) = 2 * (1/4) * (0.0625) = 0.03125

Therefore, E[X^3 | X < 0.5] = 0.03125.

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The answer to part a) is that next year, in 2023, NCSSM will use approximately 55,485 sheets of paper. In part b), total of approximately 363,353 sheets of paper will be used from 2018 through the end of 2030.


a) To calculate the paper used in 2023, we start with the initial amount used in 2018, which is given as 60,000 sheets of paper. We then need to calculate the decrease in paper use over the years. The rate of decrease is given as 2.25%, which can be written as 0.0225 in decimal form. To find the paper used in 2023, we multiply the initial amount by (1 - rate of decrease)^5, since five years have passed from 2018 to 2023.

b) To calculate the total paper used from 2018 to 2030, we need to sum up the paper used for each year in that time period. We start with the initial amount used in 2018, which is 60,000 sheets. Then we calculate the paper used each year using the same formula as in part a), multiplying the initial amount by (1 - rate of decrease)^n, where n represents the number of years since 2018. We sum up these values for the years 2018 to 2030, which is a total of 13 years.

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The check using addition, the value of difference is added to the smaller value which should give the larger wingspan value.

The value of the wingspan of the butterflies aren't given, however, we could take hypothetical values for the wingspan of the two butterflies :

Wingspan of Butterfly A = 5.55 cm

Wingspan of Butterfly B = 4 cm

This means that, the difference in the wingspan is :

Wingspan of A - Wingspan of B

5.55 cm - 4 cm = 1.55cm

To check using addition :

The value of the difference added to the value of the butterfly with the lower wingspan should give the value of the wingspan of butterfly B(larger wingspan).

This means:

4cm + 1.55cm = 5.55 cm

Hence, the value of the difference is correct.

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Answer:

2

Step-by-step explanation:

The base of a shape can be found by measuring the width of the cross section. In the example you provided, the base of the plank is 2 feet.

Answer:

x = 4

Step-by-step explanation:

Rewrite the given equation as b^(2x) = b^8.

The exponents 2x and 8 must be equal, and so 2x = 8, and x = 4

The remaining soup can feed 15 - 3 = 12 adults.

In this problem, we are given that a can of soup can feed 3 adults or 5 children. Let's assume that a can of soup is denoted by 'x'. Therefore, according to the given information, x = 3a = 5c ... equation (1), where 'a' stands for the number of adults and 'c' stands for the number of children.

Next, we are given that 5 cans of soup are available, i.e., 5x = 15c ... equation (2). Let's put equation (1) in equation (2) to get 5 (3a/5) = 15c, which simplifies to 5a = 15c. Therefore, we get a = 3c ... equation (3).

Now, we are asked to find how many adults can the remaining soup feed? Thus, the remaining soup can be found as 5x - 15c. Substituting the value of 'x' from equation (1), we get 5 (3a/5) - 15c = 15a - 15c. Therefore, the remaining soup can feed 15 - 3 = 12 adults.

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Answer:

72 grams of tea leaves.

Step-by-step explanation:

288/24=12

12*6=72

The completing square form of the equation is  \((x+1)^2=-25\).

What is completing square method?

By altering the equation's form so that the left side is a perfect square trinomial, a quadratic equation can be solved using the "Completing the Square" approach. One approach to locating the roots of the given quadratic equation is to complete the square method.

Here the equation \(x^2+2x=-26\)

To completing the square of the equation add 1 on both sides then,

=> \(x^2+2x+1=-26+1\)

=> \(x^2+2.x.1+1^2=-25\)

=> \((x+1)^2=-25\)

Hence the completing square of the equation is  \((x+1)^2=-25\).

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First one

1. XW≅ZW        1. Given     It's good to start with given

2.∠XWY ≅ ∠ZWY  2. Given     Again, get the given out of the way

3.WY ≅ WY    3.  Reflexive        This reason basically means that the line is equal to itself

4.ΔXWY ≅ZWY 4.  SAS                  We have a side, an angle and a side: SAS

Second Problem

Again, let's get the givens out of the way. I'm lazy, so just put the things in the given section in the boxes.

3. Vertical angles             This is just a fun way of saying that the angles on top of each other are equal

4. AAS                                We have an angle, an angle and a side. Whack em' together and you get AAS

this should be ok by now lmk if its not.

The 90% confidence interval for the proportion of all adults in the United States who own an e-reader is 0.32 ± 1.645 * √(0.32 * 0.68 / 1,005). This corresponds to option (B) in your list of choices.

The appropriate formula for calculating the confidence interval for a proportion is:

sample proportion ± z*standard error

where z is the z-score corresponding to the desired level of confidence (90% in this case) and the standard error is:

sqrt((sample proportion*(1-sample proportion))/sample size)

Plugging in the values given in the question, we get:

sample proportion = 0.32
sample size = 1005
z-score for 90% confidence = 1.645 (option B)
standard error = sqrt((0.32*(1-0.32))/1005) = 0.015

So the appropriate 90% confidence interval is:

0.32 ± 1.645(0.015)
= 0.32 ± 0.025
= (0.295, 0.345)

Therefore, the correct answer is option B: 0.32 +1.645,10.3270.68

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The solution set to the given inequality is

(-∞, -4) U (2,∞)

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

5(x – 2)(x + 4) > 0

First we solve for x, we replace the inequality sign by = sign

5(x – 2)(x + 4) = 0

Divide both sides by 5

(x – 2)(x + 4) = 0

Now we set each factor =0  and solve for x

x-2 =0 , so x= 2

x+4 =0, so x= -4

Now we use number line and make three intervals

First interval -infinity to -4

second interval -4 to 2

third interval 2 to infinity

Now we check each interval with our inequality

First interval -infinity to -4, pick a number in this interval and check with our inequality. lets pick -5

5(-5 – 2)(-5 + 4) > 0

35>0 is true

second interval -4 to 2, pick a number in this interval and check with our inequality. lets pick 0

5(0– 2)(0 + 4) > 0

-40>0 is false

Third interval 2 to infinity, pick a number in this interval and check with our inequality. lets pick 3

5(3 – 2)(3 + 4) > 0

35>0 is true

solution set are the intervals that make the inequalities true

(-∞, -4) U (2,∞)

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Question:

What is the solution set to the inequality 5(x – 2)(x + 4) > 0?

The prisoner's dilemma is a classic example of a noncooperative game. This means that the players involved are not working together to achieve a common goal,

But rather competing against each other to achieve their own individual goals. The lack of cooperation means that there is no communication between the players. This lack of communication can lead to inferior results for both players. In the prisoner's dilemma, both players are incentivized to defect and betray the other player,

which ultimately leads to a worse outcome for both parties involved. The game is also a simultaneous game, meaning that both players make their decisions at the same time, rather than sequentially.

Overall, the prisoner's dilemma is a powerful demonstration of the challenges that can arise in noncooperative situations and the importance of communication and cooperation in achieving optimal outputs.

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a. The coordinates after the rotation are: D(-5, 4) → D' (5, -4), E(3, 6) → E'(3, -6), and F(4, 2) → F'(4, -2) b. The general rule below that describes the rotation are: (x, y) → (x, -y).

According to the definition of a transformation in mathematics, a transformation is a geometric shape or formula that has been altered, mapping the shape or formula from its preimage, or initial position, to its image, or after-transformation position. Because transforming a function to a different space offers a fresh viewpoint on the issue, scientists and mathematicians employ transformations to simplify a problem. Scientists frequently shift a function, manipulate it, and then transform it back to its original place because this fresh perspective can make computations easier in the new space than in the old one.

a. The coordinates after the rotation are:

D(-5, 4) → D' (5, -4)

E(3, 6) → E'(3, -6)

F(4, 2) → F'(4, -2)

b. The general rule below that describes the rotation are:

(x, y) → (x, -y)

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Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e)  6200cm = 6200x cm. f)  403 kg = 40x kg.

a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.

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Answer: (7,11)

Step-by-step explanation:

Answer:

Acute

Step-by-step explanation:

The Pythagorean Theorem refers to \(a^{2} + b^{2} =c^{2}\), no (and only on right angled triangles)? We would have to use the cosine and sine rules to answer this question.

First, lets use the cosine rule to get an angle, then use the sine rule to get another, which would allow us to then determine the third, which will allow us to determine the type of triangle.

\(cosA= \frac{b^2+c^2-a^2}{2bc}\) →  \(cosA= \frac{77^2+56^2-59^2}{2(77)(56)}\) → \(cosA= \frac{5584}{8624}\) → \(cos^{-1}\frac{5584}{8624} = A\) → \(A = 49.65 = 50\)~

Now we can use the sine rule to find the other angles:

\(\frac{sin50}{59} = \frac{sinB}{77}\) → \(77\frac{sin 50}{59} = sin B\) → \(sinB = 0.9997529...\) → \(sin^{-1} 0.9997529... = B = 88.726... = 89\)~

So, if A = 50° and B = 89°, that would mean that the remaining angle is \(180 - 50-89=180-139=41\)

A = 50°

B = 89°

C = 41°

As none of the angles exceed or are equal to 90°, it must be an acute triangle!

Answer:

hello there the correct answer is 16−2x

Step-by-step explanation:

Answer:

5/6

Step-by-step explanation:

There are 5 steps to solving this problem:

Using these steps, we see that:

The value of α is 1/2.

The expected value (E(X)) is 2.

To find the value of α, we need to ensure that the probabilities sum up to 1 over the entire range of non-negative integers.

The probability mass function is given by: P(X = i) = α/2^i

For a probability mass function to be valid, the sum of all probabilities must equal 1.

∑ P(X = i) = 1

Substituting the given probability mass function into the sum:

∑ (α/2^i) = 1

Since the range of i is from 0 to infinity, we can rewrite the sum as a geometric series:

α/2^0 + α/2^1 + α/2^2 + ...

Using the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where a is the first term and r is the common ratio, in this case, 1/2.

α / (1 - 1/2) = 1

Simplifying:

α / (1/2) = 1

2α = 1

α = 1/2

Now let's calculate the expected value (E(X)):

E(X) = ∑ (i * P(X = i))

Substituting the probability mass function:

E(X) = ∑ (i * α/2^i)

Using the formula for the sum of an infinite geometric series:

E(X) = α / (1 - r)^2

where a is the first term and r is the common ratio, in this case, 1/2.

E(X) = (1/2) / (1 - 1/2)^2

E(X) = (1/2) / (1/2)^2

E(X) = (1/2) / (1/4)

E(X) = 2

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8.9 yards far you should be from the enormous pumpkin.

Given that,

You ride a hayride to capture pictures of famous places. Two landmarks and your route are shown on the map. The coordinate plane's units are equivalent to 10 yards.

We have to Calculate how far you should be from the enormous pumpkin.

Suppose that we have a linear function defined according to the following rule, in standard notation:

Ax + By + C = 0.

And a point with coordinates given by:

P(x*,y*)

The following formula gives the shortest distance between the line and the point:

d=|Ax*+By*+C|/√A²+B²

The line of the path in this problem has:

Intercept of 0,

0.5 slope means that when x rises by 4, y rises by 2.

We get,

y = 0.5x.

-0.5x + y = 0

-x + 2y = 0.

The coefficients are:

A = -1, B = 2.

The giant pumpkin has coordinates given by:

(x*, y*) = (-4, -3).

Now, the distance in units is

d = |(-1)(-4) + 2(-3)|/√(-1)²+2²

d = |(-1)(-4) + 2(-3)|/√5

d = 2/√5

d = 0.89 units.

Since each unit is equal to 10 yards, the following is the shortest distance in yards:

10.x.0.89 = 8.9 yards

Therefore, 8.9 yards far you should be from the enormous pumpkin.

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