The average price of gas in 1990 was $1.22 per gallon. The average price of gas in 2022 was $4.62 per gallon. What was the percent increase in the price of gas?

According to the radioactive isotope disintegration model, the remaining mass of the radioactive isotope after 40 years is approximately equal is 129.622 grams.

The deceasing exponential expression described in the statement models the mass of the radioactive isotope (m), in grams, as a function of time (t), in years, which represents the solution of an ordinary differential equation that represents a simple disintegration.

Now, we need to evaluate the function at t = 40 to find the amount remaining after 40 years:

A(40) = 500 · exp(- 0.028171 · 40)

A(40) = 129.622

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Answer:

Step-by-step explanation:

3x−(12x−6)−42=0

−9x+6−42=0

(−9)⋅x+(−36)=0

x=−(−36)/−9

x=-4

From the provided information we get that Ava's Pin code is 8842.

Ava's pin code is a 4-digit number.

Let the first digit = x                                      equation 1

Reading from left to right, the first and second digits are the same. So,

Second digit = x                                            equation 2

Let, third digit = y

The second digit is twice the third digit. So,

x = 2y

⇒ y = x/2

Third digit = x/2                                            equation 3

Let, fourth digit = z

The first digit is four times the fourth digit. So,

x = 4z

⇒ z = x/4

Fourth digit = x/4                                            equation 4

Sum of the four digits is 22. So, using equation 1 , equation 2 , equation 3 and equation 4 , we can write

x + x + (x/2) + (x/4) = 22

2x + (x/2) + (x/4) = 22

Multiplying both sides by 4 , we get

8x + 2x + x = 88

11x = 88

x = 8

First digit = x = 8

Second digit = x = 8

Third digit = x/2 = 8/2 = 4

Fourth digit = x/4 = 8/4 = 2

So, we can conclude that the Ava's Pin code is 8842.

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The equation of the line is y = -1/3x - 4

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are

Slope, m = -1/3

y-intercept, c = -4

A linear equation is represented as

y = slope * x + y-intercept

i.e.

y = mx + c

So, we have

y = -1/3x - 4

Hence. the linear equation is y = -1/3x - 4

See attachment for the graph

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Answer: 3

Step-by-step explanation:

1. 2 packs of 6

2. 6 packs of 2

3. 3 packs of 2 and one pack of 6

Answer:

Step-by-step explanation:

You want an expression for area, maximum area, and dimensions of a rectangular pen fenced on three sides with a total of 120 m of fencing.

The first attachment shows a sketch of the pen with x defined as the dimension the pen extends from the barn wall. The total length of fence is 120 m, so the side parallel to the barn will be (120 -2x) m in length.

The area is the product of the length and width of the rectangle:

  A = (x)(120 -2x)

The second attachment shows a graph of the area as a function of x.

The value of x that gives the greatest area is the x-coordinate of the vertex of the parabola. It is halfway between the zeros at x=0 and x=60. The maximum area will be had when x=30.

The dimensions of the pen are ...

  x = 30

  120 -2x = 120 -2(30) = 60

The pen is 30 m by 60 m, with the 60 m dimension parallel to the barn wall.

The area function only makes sense for values of x between 0 and 60 meters.

The domain of x is 0 ≤ x ≤ 60.

The length of the bridge that connect the two cities separated by the lake is 3.4 miles.

The mathematical operation that would be used to convert yards to miles is division. Division is the process of putting a number into equal groups using another number. For example, when 6 is divided by 3, 3 divides 6 into 2 equal groups.

In order to convert yards to miles, divide the given length in yards by 1760.

1 yard = 1 / 1760 miles

5927.61 / 1760  = 3.36796 miles

= 3.4 miles

To round off to the nearest tenth, since the hundredth digit is greater than 5, 1 is added to the tenth digit and the digits less than the tenth digit is replaced with zero.

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The angle not congruent to the angle 4 in the options is angle 7(∠7)

When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

Therefore, corresponding angles are equal, alternate angles are equal and vertically opposite angles are equal.

Therefore,

∠4≅∠6(vertically opposite angles)

∠4≅∠2(corresponding angles)

∠4≅∠8(alternate exterior angles)

Therefore the angle not congruent to ∠4 among the option is ∠7

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Assuming that the total number of people that pay the $120 are the 900 that claim the policy, and assuming that out of the 900 cases only the vehicular and job related policies are covered, then the profit for this policy will be:

So, under those assumptions, the profit would be $99 900.

The product of powers, power of a product, and power of a power laws can be used to evaluate the equivalent numerical expressions such as:

According to the Power of a Product Property, you can distribute the exponent to each factor if a term is raised to one.

According to the rule of a power, when a base is raised to a power and then raised to another power, the exponents are multiplied while the base is left unchanged.

According to the product of powers rule, you can multiply two words with the same base by simply adding their exponents to get the result.

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We were given the following details:

Car registration = $90

Car Insurance (annual) = $520

Home Insurance = $1020

Since we are to calculate for the monthly amount to budget for Car Insurance, we have:

herefore, the correct nanswer is A. ($43.00 per month)

Let's summarize the given information:

iles before school: 0.65

Miles after school: 1.5

o find the total mnumber of miles that Franklin jogs we need to add the miles he jogs before and after school:

The result of the addition is:

He jogs 2.15 miles.

nswer: 2.15 miles

The larger cylinder is 16 times as large as the smaller cylinder.

The formula for calculating the volume of cylinder is expressed according to the equation;

V = πr²h

where:

r is the radius

h is the height.

Determine the volume of the smaller cylinder;

V =  π(4)²(8)

V =  128π cm^3

Determine the volume of the larger cylinder;

V =  π(16)²(8)

V =  2048π cm^3

Determine the ratio

Ratio = 2048π/ 128π

Large/Small = 16

Large = 16 Small

This shows that the volume of the large cylinder is 16 times greater than that of smaller cylinder.

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Answer:

Carlos will end up paying 80£ in that month, the standard data plan cost 20£ plus 60£ the price of the extra 4 GB of data used.

Carlos has to pay total $80 in a month if he uses 4 GB data over the limit and if he uses x GB data over the limit then have to pay $20+15x.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Cost of 7 GB data plan = $20,

Cost for extra data = $15 per GB.

Since, Carlos use extra 4 GB data in a month,

Cost of 1 GB extra data = $15

Cost of 4 GB extra data = $60

Total cost = cost of 7 GB data plan + Cost of 4 GB extra data

                 = $20 + $60

                 = $80

Total $80 Carlos have to pay, where he used 4 GB over the limit.

If Carlos uses x GB extra data,

Then cost of x GB extra data = $15x

Total cost = cost of 7 GB data plan + Cost of x GB extra data

                =  20 + 15x

Total $20+15x Carlos have to pay, where he used x GB over the limit.

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Based on the direct variation between x and y, the value of y is 48

The given statements are:

From the above points, we understand that:

The variation is a direct variation

A direct variation is represented as

y = kx

Where k represents the constant of variation

The above equation is a linear equation

As a general rule, linear equations are equations that have constant average rates of change.

So, we have

y = kx

y is 120 when x is 15

This means that

120 = 15k

Divide by 15

k = 8

So, we have

y = 8x

The value of y when x is 6 is

y = 8 x 6

Evaluate

y = 48

Hence, the value of y when the value of x is 6 is 42

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Answer:

$3,289.90

Step-by-step explanation:

65,798 times 5%

Answer:

(a) {-1, 1)

(b) {-11}

(c) {-3, 4}

***(d) { x < -1 or x > 1, I am not sure how else to put it, try {-1, 1} if you are not allowed to put in > or < signs

(e) (-∞, -11] or x ≤ -11

(f) {-3, 4}

(g)  ( -√2, √2)  

***I know the correct solution sets but I am not sure how to represent all of  them given the one box you have in your solution for (a). Maybe the solution boxes for the other parts are different. Without knowing that I am only able to provide what is the correct expression

Step-by-step explanation:

We have
f(x) = x² - 1

g(x) = x + 11

(a) f(x) = 0

=> x² - 1 =

=> x² = 1

x = ± 1  

Answer (a): The solution set is {-1, 1}

(b)
g(x) = 0

=> x + 11 = 0

=> x = -11

Answer (b): Solution set: {-11}

(c)
f(x) = g(x)
=> x² - 1 = x + 11
=> x² -x -12 = 0

This is a quadratic equation which can be solved by factoring:
=> (x - 4)(x+3) = 0

=> x = 4, x = -3

{-3, 4} Answer

(d) f(x) > 0
=>  x² - 1 > 0
Add 1 to both sides

x² > 1

x < -1 or x > 1

[tex]\left(-\infty \:,\:-1\right)\cup \left(1,\:\infty \:\right)[/tex]

(e) g(x) ≤ 0
=> x + 11 ≤ 0

=> x ≤ -11

{-∞, -11}

(f)f(x) > g(x)

=> x²-1 > x +11

=> x² -x - 12 > 0

=> (x + 3)(x +4) > 0

=> x + 3 >0 and x - 4 > 0

=> x > -3 and x < 4

{-3, 4}

(g) f(x) ≥ 1

=> x² - 1 ≥ 1

=> x² ≥ 2

=> x ≥ ± √2

=> x ≤ -√2  or x ≥ √2

=> { -√2, √2}

In the above derivations note that if x² ≥ 1 then two possibilities are
x < - 1 or x > 1

By using the concept of weighted averages, 44.667 pints of 40 % pure fruit juice and 25.333 pints of 70 % pure fruit juice are needed to produce 70 pints of 55 % pure fruit juice.

The situation describes a mixing process with two fruit juices of different concentrations. All pure fruit percentages are known and we are asked to determine the numbers of pints of 40 % pure fruit juice and 65 % pure fruit juice to produce 70 pints of 55 % pure fruit juice. This can be determined by means of the concept of weighted average:

(55 / 100) · 70 = (40 / 100) · x + (65 / 100) · (70 - x)

38.5 = 0.4 · x + 45.5 - 0.65 · x

0.15 · x = 7

x = 46.667

We need 44.667 pints of 40 % pure fruit juice and 25.333 pints of 70 % pure fruit juice to produce 70 pints of 55 % pure fruit juice.

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We are asked to solve the following system of equations using the elimination method:

x + 2 y = 16

-7 x- 3 y = 24

so we select to multiply the first equation by "7", that way we will be able to eliminate the term in "x" by simple combining term by term the two equations:

7 (x + 2 y) = 7*16

7 x + 14 y = 112

now we combine this new expression term by term with the second equation:

7 x + 14 y = 112

-7 x - 3 y = 24

_____________

0 + 11 y = 136

solve for y by dividing both sides by 11:

y = 136/11

Now we use this value to solve for x in the first equation:

x + 2 (136/11) = 16

x +

The selling price is $224.75.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Cost price= $155

Cost marks up = 45%

Then the selling price is

=155 + 155 x 45/100

= 155 + 155 x 0.45

=155 + 69.75

= $224.75

Hence, The selling price is $224.75.

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Answer:

y = 3x-8

Step-by-step explanation:

The image's coordinates are:

A = (-2,5),

B = (3,-3),

C = (-4,-1).

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair od numerical coordinates, that are the signed distances from two lines that are fixedly perpendicular to the point and are measured in the same length.

The reverse is done in order to determine a point's coordinates in a coordinate system. Start at the point and move along a vertical line either up or down to the x-axis. Your x-coordinate is located there. To get the y-coordinate, repeat the previous steps while following a horizontal line.

The graph's coordinates are as follows:

A = (-2,5)

B = (3, -3)

C =  (-4,-1)

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The inverse statement is If an angle is not obtuse, then it is a right angle False. Option C

An inverse statement can be defined as a type of conditional sentence having a prompt or immediate inference made from original statement.

It carries the negation of both the hypothesis and conclusion from the

It states the opposite of the original statement given.

The statement is formed by negating the hypothesis and conclusion of a given conditional statement.

An inverse statement is expressed  the form:

Original statement:  If p, then q

Inverse statement: If not p, not q

Given the statement as;

Obtuse angles are not right angles

The inverse statement is:

If an angle is not obtuse, then it is a right angle

Hence, the inverse statement is False. Option C

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The water pressure on a submerged object is given by P = 64d, then the

a. The answer to the subject of the formula, "d," is d = P/64.

b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.

A function can be defined as an expression, law or rule that shows the relationship between two variables.

These variables are namely;

given the role as;

P = 64d

Where;

P stands for pounds per square foot of pressure.

d represents the object's depth in feet.

Let's now make the variable "d" the focus of the formula.

The coefficient of the variable "d," which is 64, is used to divide both sides of the equation. So that the variable can stand on its own, this is done.

We get,

P/64 = 64d/64

d = P/ 64

P equals 672 pounds per square foot if there is pressure.

When the variable's value is substituted into the formula, we get;

d = P/64

Then,

d = 672/64

Discover the quotient.

d = 10. 5 ft.

The value is 10.5 feet.

Therefore,

a. The answer to the subject of the formula, "d," is d = P/64.

b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.

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Based on the interest compounded by the bank monthly, and the amount deposited by Sean in the account, the amount of money that will be in that account in a year is $3,668.09

First, find the monthly rate because the interest is compounded monthly:
= 4.7% / 12

= 4.7/12 %

The number of periods would be:

= 1 x 12 months a year

= 12 periods

The amount that Sean will have in a year can be found by the formula:

= Amount invested x (1 + periodic rate) ^ number of periods

Solving for the amount in the account after 1 year gives:
= 3,500 x (1 + 4.7%/12) ^ 12

= 3,500 x 1.0480257937581146250656044647993

= $3,668.09

In conclusion, the amount that Sean will have after saving for a year in the account would be $3,668.09

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⇒Parallel line have the same gradient if the gradient of the given equation is m=-6  it means that the gradient of the new equation is also m=-6

The general equation of a straight line is y=mx+c

⇒plug in the points and find the value of the unknown c

[tex]6=-6(9)+c\\6=-54+c\\c=6+54\\c=60[/tex]

⇒This means that the new equation parallel to the given equation is⇒

[tex]y=-6x+60[/tex]

Answer:

y = 15x - 30

Hope this helps!

Step-by-step explanation:

The slope can be found with the equation [tex]\frac{y_{2} -y_{1} }{x_{2} - x_{1} }[/tex].

Add in the numbers from the two points to get [tex]\frac{15-0}{3-2}[/tex] which is [tex]\frac{15}{1}[/tex] : 15.

That means slope is 15. To get the other numbers, you can do y = 15x and then plug in one of the points, for example (0) = 15(2), which is 0 = 30. To make this equation true, you need to minus 30 so it would be 0 = 30 - 30 and this is true, so putting it all together would get y = 15x - 30.

If the coordinates of two points are (x_1,y_1) and (x_2,y_2), the distance between them is given by the formula:

Substitute for the coordinates: (-12,1) and (12,-1):

Therefore, the distance between (-12,1) and (12,-1) is approximately 24.08.