4. If 2 is subtracted from three times a number, the result is equal to 5 less than three times
the number. Find the number.

An equation system's solution is a collection of values for the variable that concurrently fulfill each equation.

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The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution. In order to solve an equation system, all sets of variable values that could possibly exist must be found. The second equation, however, is initially without a solution (5, 4).

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution.

If both variables are eliminated and you are left with a true statement, there are an infinite number of ordered pairs that satisfy both equations. In reality, the equations' lines are the same.

Let cost token be x and golf games be y, i.e.

16x + 3y = 30

22x + 5y = 43

Lets Solve by using Elimination method both the expression in equal terms

 80x + 15y = 150

- 66x + 15y = 129

14x = 21

x = 21/14

x = 1.5

Then, for y

16(1.5) + 3y = 30

y = 2

Thus, The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

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Answer:

3x - 24

Step-by-step explanation:

24 less is the same as: - 24

3 times itself is: 3x

The order from least to greatest is: A, B, C

The order of the sectors from least to greatest according to their areas is:

Sector A, Sector B, Sector C

To find the area of each sector, we need to multiply the central angle measure (in degrees) by the radius squared and divide by 360.

Sector A: 4 units * (1690 / 360) = 46 square units

Sector B: 6 units * (820 / 360) = 69 square units

Sector C: 9 units * (820 / 360) = 103.5 square units

Hence, the order from least to greatest is: A, B, C

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Answer:

45%

Step-by-step explanation:

Answer:

45%

Step-by-step explanation:

[tex]\frac{9*5}{20*5}[/tex] = [tex]\frac{45}{100}[/tex]

The surface area of the rectangular prism is 100m²

The formula for calculating the surface area of a rectangular prism is expressed as;

Surface area = 2(wl + hw + lh)

Given that;

From the diagram shown, let's substitute the values, we have;

Surface area = 2(2× 7 + 4× 2 + 7 × 4)

multiply the values, we get;

Surface area = 2(14 + 8 + 28)

Add the values

Surface area = 2(50)

Expand the bracket

Surface area = 100m²

Hence, the value is  100m²

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Answer:

Step-by-step explanation:

6 2/5

Number 5 is denominator, keep it for denominator.

Numerator will be 6x5+2 =32

so, a fraction of 6 2/5 greater than 1 is 32/5

Answer: DJ appears to be moving at the same speed as the car

Step-by-step explanation:

DJ is inside of the car, so he moves with it. Jabari is outside of the car and is standing still, so both DJ and the car he is in seems to be moving at 40 miles per hour at the same time

Answer: B. The speed limit changing from 40 mph to 55 mph represents the least percent of change.

In A, a watch selling for $90 from $125 represents a 28% decrease,

In C, the stock market dropping from 250 to 175 points represents a 30% decrease,

In D, Marissa's math grade increasing from 75 to 99 represents a 32% increase.

While in B, the speed limit changing from 40 mph to 55 mph represents a 37.5% increase.

So, B represents the least percent of change.

Step-by-step explanation:

The square root of 2 or root 2 is represented using the square root symbol √ and written as √2 whose value is 1.414. This value is widely used in mathematics.

Well, the basic answer is that the value of root 2 (i.e., 2) is 1.412. We must first understand the concepts of power and roots in order to comprehend what root 2 (2) is and how to calculate its value. √2 = 1.414

You may determine the values of non-perfect square values like root 3, root 5, etc. using the long division method.

The square root or root of a number "n" is a number that, when multiplied by itself, has the value "n". For instance, the square root of 4 is equal to 2. thus 2 + 2 Equals 4. The opposite of squaring a number is finding the square root of that integer. 

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The total number of $12 tickets are 120 while the $15 tickets are 180.

In addition to using operational signs, algebraic expressions also include numbers and variables. Examples include multiplication, multiplication with the natural exponent, division, and addition, subtraction, and exponentiation. The term "fractional expression" refers to division in an algebraic expression with variables.

The term "rational numbers" refers to numbers that can be expressed as fractions. Integers, repeating decimals, and terminating decimals are a few examples.

Given that x stands for $12 tickets and y stands for $15 given as the equation

12x + 15y = 4140

x + y = 300

y = 300 - x

Substitute the value of y in the first equation

12x + 15(300 - x) = 4140

12 x + 4500 - 15x = 4140

12x - 15x = 4140 - 4500

-3x = −360

x = 360/3

x = 120

y = 300 - (120)

y = 180

Thus, The total number of $12 tickets are 120 while the $15 tickets are 180.

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Nelson hourly wage is $11.8

Nelson earned $379.25 in net pay for working 40 hours

He paid $56.64 in federal and state taxes

He also paid $36.11 in FICA tax

Therefore Nelson hourly wage can be calculated as follows

The first step is to calculate the total earnings

= 379.25 + 56.64 + 36.11

= 472

The next step is to calculate the hourly wage

472/40

= 11.8

Hence Nelson hourly wage is $11.8

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Answer: Annie made a mistake in step 1 by plotting the point (1, -3) instead of (1, 0) which is the x-intercept of the given equation.

Step-by-step explanation:

She should have used the x-intercept of the equation instead of just any point.

To fix her mistake, Annie should find the x-intercept of the equation by setting y to 0, and solve for x. Then she can plot the point (1,0) and proceed with step 2 and 3.

Answer: A) The decay constant (λ) is a measure of the rate at which a radioactive isotope decays. It is defined as the probability per unit time that an atom of the isotope will decay. The decay constant can be calculated using the formula:

λ = -ln(1 - x) / t

Where x is the fraction of the original activity that has decayed (in this case, 0.40), and t is the time over which the decay occurred (in this case, one week).

B) The half-life (T1/2) is the amount of time it takes for half of the original activity of a radioactive isotope to decay. It can be calculated using the formula:

T1/2 = ln(2) / λ

C) The mean lifetime (τ) is the average amount of time an atom of a radioactive isotope will survive before it decays. It can be calculated using the formula:

τ = 1 / λ

It's important to note that the above formulas are based on the exponential decay model, which assumes that the decay process is random and that the decay constant is constant over time. If the isotope does not decay in this way, these formulas may not give accurate results.

Step-by-step explanation:

The simplest form of √12x⁸/√3x² is 2x³.

What is simplification?

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Here, we have

Given: √12x⁸/√3x²

We have to simplify this function.

We combine both terms in one and we get

= √12x⁸/3x²

= √4x⁶

= 2x³

Hence, the simplest form of √12x⁸/√3x² is 2x³.

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The weight lies between the whole numbers 8 and 9.

The length, breadth, and height of a package are multiplied using the longest point on each side to determine the dimensional (DIM) weight.

If each of the 4 boxes has the same weight, the weight of each box can be found by dividing the total weight by the number of boxes. Given that the total weight is 34 kilograms, the weight of each box is:

w = 34 kg / 4 boxes = 8.5 kg

So, each box weighs 8.5 kilograms. The weight lies between the whole numbers 8 and 9.

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The length of the ladder, if it is resting against the wall at the height of 48 feet and it forms an angle of 53 degrees with the ground being 63.7 ft.

First, we need to draw a figure according to the conditions given in the question.

Now, let AC be the length of the ladder, AB is the length of the wall, and BC is the length of the ground, as shown in the figure.

As we know,

tan θ = perpendicular/hypotenuse

tan 53 = AC/AB

AC = tan 53 × AB

AC = 1.327 × 48

AC = 63.7 ft

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The sum of the two consecutive numbers is 31.

Let the two consecutive number are n and n+1.

Given the difference between square of two consecutive Numbers is 31.

Then, two consecutive number = n, n+1 = 15, 16

Therefore

( A ): the sum of two consecutive number = 15 + 16 = 31

( B ): Their difference = 16 – 15 = 1

( C ): Subtract their sum by 8 = 31 – 8 = 23

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Answer: 6 2/3

Step-by-step explanation: 2 5/12 + 4 1/4  29/12 + 4 1/4 29/12 + 17/4 (3/3) 29/12 + 51/12 80/12/4/4 20/3 6 2/3

The probability that ben and tom will pass is 0. 87 and 0. 7 respectively will be 0.38

The answers to the questions are as follows:

Please refer to the attached file for point a.

Since both of them pass their driving tests at the same time, we double the odds of each one passing, which results in a probability of "56%".

Tom passes but Ben fails, or Tom passes but Ben succeeds. Therefore, the likelihood and the response is "38%."

(a)The tree diagram is attached.

P(Ben Fails)=1-0.8=0.2

P(Tom Fails)=1-0.7=0.3

(b)Probability that both will pass their driving test.

P(both will pass)=0.8 X 0.7 =0.56

(c)Probability that only one of them will pass their driving test.

P(Tom Bass, Ben Fails OR Ben Pass, Tom Fails)

=(0.7 X 0.2)+(0.8 X 0.3)

=0.14+0.24

=0.38

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The first car consumed 35 number of  gallons and the second car consumed 15 gallons.

1. Calculate the total efficiency of both cars: 35 mpg + 15 mpg = 50 mpg

2. Calculate total gallons consumed: 1150 miles/50 mpg = 23 gallons

3. Divide total gallons by each car: 23/2 = 11.5 gallons (round down to 11 for the first car and round up to 12 for the second car)

4. The first car consumed 11 gallons and the second car consumed 12 gallons.

The first car consumed 35 gallons and the second car consumed 15 number of gallons.

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The equivalent expression for the amount of sports drinks that pass inspection is 23x milliliters.

The inspector at a bottling plant checks 25 bottles, and two bottles do not pass inspection.

To find the amount of sports drinks in milliliters that pass inspection, we can subtract the amount in the two bottles that do not pass inspection from the total amount in all 25 bottles.

Let x be the amount of sports drinks in milliliters in each bottle.

The expression for the milliliters of sports drink that pass inspection is = 25x - 2x

Now, simplifying the expression, we get,

25x - 2x = (25-2)x = 23x

Hence, the equivalent expression for the amount of sports drinks that pass inspection is 23x milliliters.

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The complete question is -

The inspector at a bottling plant checks 25 bottles. Two bottles do not pass inspection. All the bottles hold the same number of milliliters of sports drinks. Write an expression for the milliliters of sports drink that pass inspection. Then simplify it to create an equivalent expression.

(x^4+10x^3+10x^2-15x-6)/(x+2) Synthetic Division

The synthetic division for the polynomial (x^4+10x^3+10x^2-15x-6) divided by (x+2) would be:

x^3 + 8x^2 - 19x - 12 + (R)

Where R is the remainder.

The quotient is x^3 + 8x^2 - 19x - 12

A synthetic division, also known as long division of polynomials or polynomial synthetic division, is a method of dividing polynomials that is faster and simpler than the traditional polynomial long division method. It is particularly useful for dividing a polynomial by a linear factor of the form (x - a), where a is a real number.

Synthetic division allows you to divide a polynomial by a linear factor without having to perform the traditional long division algorithm, by using the polynomial's coefficients instead of the polynomial itself. Synthetic division is also useful for finding the remainder of a polynomial division. The quotient and the remainder are written in a form of simplified polynomials.

Therefore, the correct answer is as given above

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The amounts of liters of gasoline that you need to drive from the first town to the second is given as follows:

1.5 liters.

The amount of gasoline needed is obtained using the proportions in the context of this problem.

The scale is given as follows:

1 inch = 25 km.

Meaning that each inch on the drawing represents an actual distance of 25 km, then the actual distance of the towns separated by 3 inches on the map is given as follows:

3 x 25 = 75 km.

A liter of gasoline lasts for 50 kilometers, hence the amount of liters of gasoline needed for 75 kilometers are given as follows:

75/50 = 1.5 liters.

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The English sentences that are translated from single letters, such as P, Q, R, etc., can either be true or false depending on the context in which they are used.

For example, if P is translated as "the sky is blue," then this sentence is true. However, if P is translated as "the sky is orange," then this sentence is false. In order to determine the truth value of the translated sentence, we must first identify the context in which the letter is being used. Then, we can decide whether the translation is true or false by using logic and reasoning. For example, if we know that the sky is not orange, then the translation of P can be determined to be false.

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The solution for given linear inequalities is (-0.5,4.25) from the given graph.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

As we know the solution for the lines which intersect at a certain point is that point or the coordinates of that point i.e. (-0.5,4.25).

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A right triangle is created by the wall and the ladder's base. 9.3 feet are horizontally between the wall and the ladder's base.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides.

The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

So, the parameters listed are:

69-degree angle.

Ladder length (l) equals 26 feet.

The following cosine ratio is used to compute the horizontal distance (h).

cos(θ) = h/l

Replace known values:

cos(69) = h/26

Make the topic "h":

h = 26 * cos(69)

Consider the product:

h = 9.3

Therefore, a right triangle is created by the wall and the ladder's base. 9.3 feet are horizontally between the wall and the ladder's base.

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1. These excerpts from the Code of Hammurabi identify crimes such as theft, assault, and damage to property.

2. Some of these crimes, such as theft and assault, are still considered crimes today. However, some of the punishments specified in the code, such as the punishment for a son striking his father, would not be considered appropriate today.

3. These excerpts from the Code of Hammurabi identify punishments such as fines, imprisonment, and physical punishment such as whipping or amputation.

4. Physical punishments such as whipping or amputation are no longer used in most modern legal systems.

5. Fines and imprisonment are still used as punishments today.

6. Based on these short excerpts from the code, it seems that Hammurabi defined justice as a system of strict punishment for crimes, with different punishments for different classes of people and different severity of crimes.

Our codes of law today show similarities to the Code of Hammurabi in that they both have a system of punishment for crimes. However, there are also many differences, such as the fact that our legal system is considered more fair and equal, and places a greater emphasis on rehabilitation and protecting the rights of the accused.

7. Today's view of justice has changed significantly from Hammurabi's in that it places a greater emphasis on protecting the rights of the accused, rehabilitation, and equality before the law. This change can be attributed to a number of factors, including the development of democratic societies, the influence of human rights movements, and the advancement of legal scholarship and philosophy.

The 282 rules that make up the Hammurabi code of laws established norms for business dealings and established fines and penalties to satisfy the demands of justice.

A large, finger-shaped black stone stele with Hammurabi's Code carved on it was looted by invaders and only recently found in 1901. One of the most well-known examples of the ancient maxim known as "lex talionis," or the law of retribution, is the Hammurabi Code.

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