A gas station sells regular gas for $2.20 per gallon and premium gas for $2.75 a gallon. At the end of a business day 340 gallons of gas had been sold, and receipts totaled $803. How many gallons of each type of gas had been sold?

The polynomial -6x⁵ - 1/8 - x³ in standard form is -6x⁵ - x³ - 1/8

From the question, we have the following parameters that can be used in our computation:

-6x⁵ - 1/8 - x³

To rewrite polynomial in standard form, we order the powers in decreasing order

Using the above as a guide, we have the following:

-6x⁵ - x³ - 1/8

Hence, the polynomial in standard form is -6x⁵ - x³ - 1/8

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Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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• Given the tables of data, you can find the rate of change (the slope of the line) by applying the following formula:

Where the following are two points on the line:

- Table A:

Knowing these points:

You can substitute the corresponding coordinates into the formula and evaluate:

- Table B:

Given the points:

You get:

- Table C:

Having:

You get that the slope is:

- Table D:

Knowing these two points on the line:

You get the following slope:

• By definition, the equation of a Proportional Relationship has the following form:

Where the slope "m" is the constant.

That indicates that the value of "y" varies proportionally with the value of "x".

As you can notice, its graph is a line that passes through the Origin.

Therefore, knowing the slope of the Proportional Relationships A, C and D, you can set up the following equations for each one of them:

- For Line A:

- For Line C:

- For Line D:

Hence, the answers are:

• Rates of change:

• Function rules for each Proportional Relationship:

Step-by-step explanation:

Improper fractions have a numerator that is larger than the denominator

1 = 6/6

 so  1  1/6  = 7/6

Therefore, the answer to this question is option (C) ex ante forecasts

To face the challenge of improving operational performance while increasing production efficiency, performance forecasting is a crucial service to help decision-making in the idea, design, and operational phases of an asset.

Here,

As to evaluate forecasting performance of a model or compare relative performance of two models,

can be examined on the basis of ex ante forecasts

The term "ex-ante forecast" refers to a forecast that only takes into account the data (i.e., the value of economic variables) that is available at the time of the actual forecast and not the value of some variables that will be available later on.

Therefore, the answer to this question is option (C) ex ante forecasts

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Answer:

9/41

Step-by-step explanation:

Draw a right triangle in quadrant 2 and label your opposite (40) and hypotenuse (41) sides then use the pythagorean theorem to find the missing side (the adjacent side)  which is equal to 9. Then since cosine is adjacent/hypotenuse and you get 9/41.

Answer:

1

Step-by-step explanation:

steps are in picture.Ignore hand writing

The solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

The system of equations is given as

2x - y + 2z = -6

-3y + z = -2

2x - 3z = -4

Subtract 2x - 3z = -4 from 2x - y + 2z = -6

This is represented as

(2x - y + 2z = -6) - (2x - 3z = -4)

This gives

- y + 5z = -2

Multiply - y + 5z = -2 by 3

-3y + 15z = -6

Subtract -3y + 15z = -6 from -3y + z = -2

This is represented as

(-3y + z = -2) - (-3y + 15z = -6)

This gives

-14z = 4

Divide by -14

z = -2/7

Substitute z = -2/7 in - y + 5z = -2

- y - 5 * 2/7 = -2

This gives

- y - 10/7 = -2

Rewrite as:

y = 2 - 10/7

Evaluate

y = 4/7

Substitute z = -2/7 in 2x - 3z = -4

2x - 3 * 4/7 = -4

This gives

2x - 12/7 = -4

So, we have:

2x = 12/7 - 4

Evaluate

2x = -16/7

Divide by 2

x = -8/7

Hence, the solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

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Answer:

this hard

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Answer:

8 in

Step-by-step explanation:

I hope this helps!

Answer:

I think its something like: Money Leftover = 125 - (price of one shirt * 5)

Step-by-step explanation:

just use variables in the place of "price of one shirt" and "Money Leftover".

multiplying the price of one shirt by five since she buys 5 of the same shirt and subtracting that value from her budget will leave you with the amount of money she had left after the purchase.

Answer:

125-5s=money left over (s is the price of one shirt)

Step-by-step explanation: I hope this helps!

When teaching an 8th grade lesson on problem solving, Sylvia begins by utilizing a short video clip. Sylvia uses this video clip as a discrepant event because students attached with science it would look like magic for them.

A discrepant occurrence is an unexpected, counterintuitive result that differs from what an observer would typically anticipate. Oobleck is a classic illustration of a discrepant event.

Most kids (who have never seen it before) wouldn't anticipate that it would have both solid and liquid qualities. They didn't anticipate it to spread out right away once the "ball" was placed on the table instead of rolling into a ball and taking shape.

The main factor is that pupils will develop an obsession with science. They will see this as "magic," and they will be very interested in learning how it worked. After that, they'll be prepared to "amaze" their friends with both the "trick" and their subsequently displayed "smarts."

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Answer:

Choice C: 5

Step-by-step explanation:

55 is a composite number. 55 = 1 x 55 or 5 x 11. Factors of 55: 1, 5, 11, 55. Prime factorization: 55 = 5 x 11 it should be 5 if 11 isn't an option to

Answer:

  x = 1

Step-by-step explanation:

You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.

The two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.

  (43x +2)° +135° = 180°

  43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137

  x = 1 . . . . . . . . . . . . . . . divide by 43

The value of x is 1.

__

Additional comment

Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.

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The linear cost function is C(x) = 15x + 3250 and the cost function in marginal cost: $15; 150 items cost $5500 to produce is $ 5500 .

Let C(x) is that the total value, and x is that the range of things.

The slope "m" is named the cost and "b" is named the charge.

The value of m is $15 and the price of "x" is 150.

Total cost of 150 items are $5500

Substitute all the values within the equation (1) , we get

   5500 = 15 (150) + b

    5500 = 2250 + b

    3250 = b

Hence , linear cost function is given by C(x) = 15x + 3250

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Answer:

$37.5+$3r

Step-by-step explanation:

We can assume that the number of rides is r. Since each ride is $3.00, all rides are $3r ($3xr).

We also know that there are FIVE people going to the fair, with Tory being one and each of her friends. Since the entrance fee is 7.50, we can do 7.50x5 which is $37.5.

Then, you can add it which is $37.5+$3r

Answer:

Step-by-step explanation:

An easy method is to subtract the areas of two rectangles, 5x4 and 3x1:

Divide into two rectangle

In the below one

Area=4(2)=8mm^2

In above one

Area=3(3)=9mm^2

Total area

Answer:

  a) x = 1 ± (3/7)√7

  b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)

Step-by-step explanation:

You want solutions to the relations ...

We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.

  \(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)

The roots of the numerator quadratic are found by ...

  x² -2x -2/7 = 0 . . . . . divide by 7

  x² -2x +1 -9/7 = 0 . . . . add and subtract 1

  (x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7

  x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root

  x = 1 ± (3/7)√7

Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.

  \(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)

This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.

The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.

The inequality is satisfied for ...

Hence, The Isomorphism between Two-Well-Ordered Sets W1  and W2  is UNIQUE

Make a Plan: Understand the Problem

We need to Prove if Two-Well-Ordered Sets W1  and  W2 are ISOMORPHIC, Then there is ONLY ONE ISOMORPHISM.

PROVE the Statement

1 -Assume there are Two Isomorphisms  f  and g between W1  and W2

2 - Define a Set:

A = {x ∈ W1 |f(x) ≠ g(x)}

3 - If A is Empty, Then f(x) = g(x) for all x ∈ W1, and the Isomorphism is Unique.

4 - If A is Non-Empty, Then Since W1 is Well-Ordered, There Exist a Least Element  a ∈ A

5 - Since f and g are Isomorphisms, f(a) and g(a) are the Least Elements in their respective images in W2.

6 - Since f(a) ≠ g(a), One of them, say f(a), is less than g(a).

7 - Let b = f^-1(g(a)).  Then b > a because f is an Isomorphism and f(a) < g(a).

8 - Since b > a, We now have f(b) = g(b) because, a is the Least Element in A.

9 - However, f(b) = g(a), Which Contradicts the Fact that  f  and g  are Isomorphisms

Hence, The Isomorphism between Two-Well-Ordered Sets W1  and W2  is UNIQUE

I hope this helps you!

Answer: \(72z^{2} +55z-7\)

Step-by-step explanation:

We multiply each component with each other:

8z * 9z = 72z^2

8z * -1 = -8z

9z * 7 = 63z

7 * -1 = -7

We then add it all together, 63z + -8z = 55z and get

\(72z^{2} +55z-7\)

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The point where the gradient line intercepts (touches) the y-axis is called y intercept.

The point where the gradient line intercepts (touches) the x-axis is called x intercept.

check the sketch attached.

When the polynomial p(x) is divided by the expression, (x-a), then the remainder of the division is given by p(a).

According to the question,

We have the following information:

Polynomial p(x) is divided by the expression, (x-a), then the remainder of the division is given by p(a) and we need to find whether this is true or not.

Now, this statement is true because this is what the remainder theorem states of long division method states.

It can be better understood with the following example:

p(x) = \(x^{2} +5x-30\) is divided by (x-2) then the remainder of the division can be found out using the remainder theorem by putting the value of x as 2 in the polynomial.

Hence, the statement polynomial p(x) is divided by the expression, (x-a), then the remainder of the division is given by p(a) is true.

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The fraction in form of sum or difference will be;

⇒ 11/6x + 5/6

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The fraction is,

⇒ (11x + 5) / 6

Now,

Since, The fraction is,

⇒ (11x + 5) / 6

It can be written as;

⇒ (11x + 5) / 6

⇒ 11x/6 + 5/6

Thus, The fraction is written as;

⇒ 11/6x + 5/6

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Answer:

f = 6 cm

g =  8 cm

Step-by-step explanation:

ABCD   f*g = 48

ABCE   f*g + 1/2 (4*f) = 60

48 + 2f = 60

2f = 12

f = 6

g = 48/6 = 8

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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A.

1. Mode: No mode. Median: 24. Mean: 30.875. Range: 50.

2. Mode: No mode. Median: 33.5. Mean: 43.9. Range: 85.

3. Mode: No mode. Median: 46. Mean: 43.571. Range: 61.

4. Mode: No mode. Median: 17. Mean: 18. Range: 28.

5. Mode: No mode. Median: 10.5. Mean: 13.5. Range: 27.

6. Mode: 15. Median: 22.5. Mean: 25.857. Range: 31.

B.

7. Mode: 4.3. Median: 4.2. Range: 2.1.

8. Mode: 18.6. Median: 18.6. Range: 0.8.

C.

9. Mode: No mode. Median: 4/9.

10. Mode: No mode. Median: 5/24.

Answer:

169

Step-by-step explanation:

Perimeter of a rectangle= 2(length+breath)

2(18 + 8)

2(26)

52.

A square has four equal sides.

The length will be determined by dividing 52 by 4

\(52 \div 4 = 13\)

The length is 13.

Since the area of a square is

\( {l}^{2} = {13}^{2} \)

L is length.

The answer is

\( {169}^{2} \)