two step equations
find the value of the unknown variable in the equation
3b+4= - 31

The probability of landing in the color green is P = 0.41, and out of 160 spuns, we can expect to get the color green 66 times.

We have a table and we want to use it to find the probability of the spinner landing on green.

It is equal to the quotient between the number of times that we got green and the total number of times that we spun the spinner.

We got green 325 times, and the total number is:

T = 116 + 325 + 359

T = 800

Then the probability is P = 325/800 = 0.41

b) If it is spun 160 times, then we will get 0.41 times 160 green landings, it is:

160*0.41 = 65.6

This can be rounded up to 66, we can expect to land in the green section 66 times.

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Solving radical equations requires a strong foundation in algebraic concepts and techniques, as well as knowledge of exponents and radicals.

Several mathematical skills and concepts required to  solve radical equations are as follow,

Knowledge of exponents,

Radical expressions involve exponents, which are fundamental to solving these equations.

Understanding of the properties of radicals,

Knowing the properties of radicals.

How to simplify them or manipulate them to isolate the variable, is essential in solving radical equations.

Algebraic manipulation,

In solving radical equations, use algebraic manipulation techniques.

Such as factoring or multiplying by conjugates, to isolate the variable and solve for it.

Familiarity with solving equations,

Process of solving a radical equation is similar to that of solving any other equation.

Follow standard algebraic procedures, such as combining like terms, applying inverse operations, and checking our solutions.

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EXPAND

2w + 6 = 14

BALANCE OUT (-6 from both sides)

2w = 8

SOLVE

2w =8

÷2 ÷2

w = 4

Part a: ∠ABE and ∠DBE share a ray EBC as EBC is a straight line.

Part b: ∠ABE and ∠DBE are opposite to each other. Thus, the are termed as the  vertical angles.

Angles that are opposing each other whenever two lines connect are known as vertical angles. According to the vertical angles theorem, vertical angles are consistently congruent.

When two lines in geometry connect, four angles are created. Vertical angles are those that are not next to one another or that are opposing one another. Since they always utilize the same measure, vertical angles are unique.

Postulate for Angle Addition: When two neighbouring angles combine to make a straight line, its result is 180°.

The given angles:

∠ABE = ∠DBE (vertical angles)

Part a: ∠ABE and ∠DBE share a ray EBC .

Part b: ∠ABE and ∠DBE are opposite to each other. Thus, the are termed as the vertical angles.

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The surface area of the triangular prism is 891 square inches, calculated by finding the area of each face (two triangular and three rectangular) and adding them up.

To find the surface area of the triangular prism, we need to find the area of each face and add them up.

The triangular prism has two identical triangular faces and three rectangular faces. The triangular faces have base 9 inches, height 12 inches, and hypotenuse 15 inches. The area of each triangular face can be found using the formula for the area of a triangle:

Formula for area of each triangular face = (1/2) x base x height

= (1/2) x 9 x 12

= 54 square inches

The prism also has three rectangular faces, each with length equal to the base of the triangle (9 inches) and width equal to the height of the prism (29 inches). The area of each rectangular face can be found using the formula for the area of a rectangle:

Area of each rectangular face = length x width

= 9 x 29

= 261 square inches

Hence, the triangular prism's total surface area is:

Total surface area = 2(Area of each triangular face) + 3(Area of each rectangular face)

= 2(54) + 3(261)

= 108 + 783

= 891 square inches

Therefore, the surface area of the triangular prism is 891 square inches.

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Step-by-step explanation:

I do not have a gameplay experience, but I can tell you that having a fixed, predetermined goal can be very motivating and impactful when it comes to achieving financial objectives like saving money. When you have a clear goal in mind, such as saving $50,000 to make your way to Vegas, it can help you stay focused and motivated to make the necessary sacrifices and changes to your spending and saving habits.

With a clear financial goal, you are able to develop a concrete plan and establish measurable steps to achieve your target. This may include creating a budget, cutting back on expenses, and finding ways to increase your income. By having a predetermined goal, you can also track your progress and adjust your strategies accordingly to ensure that you stay on track towards achieving your financial objective.

The solution is given below.

Financial goals are targets set by an individual to achieve financial milestones or plans. In other words, they are financial objectives that an individual wishes to accomplish within a certain time frame. For example, it could be setting up a fund for their children's education, travel, emergency, health care, etc.

here, we have,

given that,

Enzo’s goal was to save $50,000 to make his way to Vegas.

here, we can tell you that having a fixed, predetermined goal can be very motivating and impactful when it comes to achieving financial objectives like saving money. When you have a clear goal in mind, such as saving $50,000 to make your way to Vegas, it can help you stay focused and motivated to make the necessary sacrifices and changes to your spending and saving habits.

we have,

With a clear financial goal, you are able to develop a concrete plan and establish measurable steps to achieve your target. This may include creating a budget, cutting back on expenses, and finding ways to increase your income. By having a predetermined goal, you can also track your progress and adjust your strategies accordingly to ensure that you stay on track towards achieving your financial objective.

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The total probability is 2.5% + 2.5% = 5.0%, which is equivalent to 0.05 or 95.00% in decimal form.

If a random variable follows a normal distribution, the probability that the random variable is 1.96 standard deviations below the mean is 95.00%.Step-by-step explanation:

Z-value for 1.96 standard deviations below the mean can be calculated as follows:

Z=(x-μ)/σ=(-1.96)

Where x is the value of the random variable, μ is the mean, and σ is the standard deviation.To find the probability, we can use a standard normal distribution table.

The table gives the probability of a standard normal random variable Z being less than or equal to a given value, denoted by P(Z ≤ z).

The Z-value we calculated is -1.96, so we look up the corresponding probability in the table:

P(Z ≤ -1.96) = 0.025.

The probability that the random variable is 1.96 standard deviations below the mean is therefore:

P(Z ≤ -1.96) = 0.025 = 2.5%

However, since we are interested in the probability that the random variable is exactly 1.96 standard deviations below the mean, we need to use a two-tailed test.

The probability of being below the mean by 1.96 standard deviations is 2.5%, and the probability of being above the mean by 1.96 standard deviations is also 2.5%.

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Therefore, the tree is 78.14 feet tall. Rounded to the nearest hundredth of a foot, the answer is 78.14 feet.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is a fundamental part of geometry and is used in many areas of science, engineering, and technology.

by the question.

A represents the top of the tree, and the line segment AB represents the height of the tree, which we want to find. The angle of elevation, which is the angle between the ground and the line of sight to the top of the tree, is 54°. The distance from the point on the ground to the tree is 52 feet, which we'll call d. Finally, h represents the distance from the ground to the point where the line of sight intersects the tree.

Using trigonometry, we know that:

tan (54°) = h/d

We can rearrange this equation to solve for h:

[tex]h = d * tan (54)[/tex]

Plugging in the values we know, we get:

[tex]h = 52 * tan (54) = 78.14[/tex]

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Answer:

12y-8

Step-by-step explanation:

Answer:

192

Step-by-step explanation:

320/20=16

12x16=192

"The heavens proclaim God's glory; the skies proclaim the work of his hands." They pour forth speech day after day, and unveil knowledge night after night. They have no speech, no words, and no sound is heard from them. Nonetheless, their voice reaches all over the world, and their words reach all the way to the ends of the planet. God has set up a tent for the sun in the heavens. It's like a newlywed emerging from his bedroom, or a champion joyful to run his race. It rises at one end of the heavens and circles back; nothing is bereft of its warmth."

This paraphrase captures the essence of the verses, emphasizing the declaration of God's glory through the beauty and order of the heavens, the continuous revelation of knowledge, and the symbolism of the sun's journey across the sky.

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The probability of choosing a 't' or an 'e' from the word 'committee' = 4/9

We know that the formula for the probability of an event is given by,

P = number of favourable outcomes / total number of possible outcomes of an event

Let us assume that event A : choosing a letter 't'  from the word 'committee'

and event B: choosing a letter 'e' from the word 'committee'

Here, sample space is the number of letters in the the word 'committee'

So, n(S) = 9

We know that there are two 't' letters in the the word 'committee'

So, n(A) = 2

And there are 2 'e'  letters in the the word 'committee'

So, n(B) = 2

To find the required probability, the number of favourable outcomes

= 2 + 2

= 4

So, the required probability would be:

P = 4/9​

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The space-mean speed of the four vehicles is approximately 64 mph.

The given information about the speeds of four vehicles measured at the midpoint of a roadway section are as follows:Vehicle Speed (mph)A 55B 50C 74D 78The space-mean speed of the four vehicles can be found out by the following formula:Space-mean speed = {Sum of the individual speeds of the vehicles}/{Number of vehicles}Space-mean speed = (55 + 50 + 74 + 78)/4Space-mean speed = 257/4Space-mean speed ≈ 64 mph (rounded to the nearest mph)

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Answer: C

Step-by-step explanation:

In initial order:

A = 0.14

B = -10.33

C = -9.82

D = 4.5

In descending order:

D = 4.5

A = 0.14

C = -9.82

B = -10.33

As observed, the position of A, B and D change when the order is changed but C remains in it's original position thus proving that it is identical (≡)

In each of these phrases, there is a correlation between two variables, but there is no clear evidence that one variable causes the other.

Correlation without causation occurs when two variables appear to be related, but there is no evidence to suggest that one variable causes the other. In other words, the correlation may be due to other factors that influence both variables, rather than one causing the other. Here are some phrases that imply correlation without causation:

Ice cream sales and murder rates both increase in the summer.

Children who read more books tend to have higher test scores.

People who exercise regularly tend to have lower rates of heart disease.

Higher levels of education are associated with higher salaries.

People who own larger houses tend to have higher levels of debt.

Students who use more highlighters tend to get higher grades.

People who wear glasses tend to be smarter.

Countries with higher levels of chocolate consumption tend to have more Nobel laureates.

People who watch more TV tend to have higher rates of obesity.

In each of these phrases, there is a correlation between two variables, but there is no clear evidence that one variable causes the other. For example, the fact that ice cream sales and murder rates increase in the summer may be due to the fact that more people are out and about in the warm weather, rather than one causing the other.

It is important to remember that correlation does not always imply causation, and that other factors may be at play when two variables appear to be related. Therefore, it is essential to carefully examine the evidence and consider alternative explanations before drawing conclusions about cause and effect.

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The equivalent fraction of the given repeating decimal is: 4/25

A recurring Decimal is defined as a decimal number only that consists of digits repeating after a fixed interval after the decimal.

Let a/b denote the unknown fraction

Thus:

a/b = 0.266666666...   ------(1)

Multiply both sides of the equation by 10 to produce

10a/b = 2.66666666...   -----(2)

Multiply both sides of the equation 1 by 100 to produce:

100a/b = 26.6666666...    -----(3)

Subtract eq 2 from eq 3 to get:

90a/b = 24

a/b = 24/90

a/b = 4/15

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Answer: y-intercept is 6 and x intercept is 2

Step-by-step explanation:

The slope formula explains it all. I have nothing to explain.

Answer: 8800

Step-by-step explanation:

Rounds down because 42 is less than 50

Answer:

[tex]x = \frac{3(6+y)}{4}[/tex]

Step-By-Step Explanation:

First Step:

[tex]4x=18+3y[/tex]

Second Step:

[tex]x = \frac{18+3y​}{4}[/tex]

Last Step:

[tex]x = \frac{3(6+y)}{4}[/tex]

The 16-inch pizza is a better deal as it costs about $0.10 per square inch while the 10-inch pizza costs about $0.13 per square inch.

Donnie's Pizza Palace Diameter (in.) Cost ($) Cost per Square Inch ($/in²)

10-inch 10 10 0.13

16-inch 16 20 0.1

To determine which pizza is the better deal, we need to compare the cost per square inch of each pizza.

For the 10-inch pizza:

Cost per square inch = Cost / (π x [tex](diameter/2)^2)[/tex]

Cost per square inch = 10 / [tex](3.14 x (10/2)^2)[/tex] ≈ $0.13

For the 16-inch pizza: Cost / (πx x [tex](diameter/2)^2)[/tex]

Cost per square inch =[tex]20 / (3.14 x (16/2)^2) ≈ $0.10[/tex]

Therefore, the 16-inch pizza is a better deal as it costs about $0.10 per square inch while the 10-inch pizza costs about $0.13 per square inch.

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Answer:

110.5 inches

Step-by-step explanation:

A=( a + b) / 2 h

A = (8 + 9) / 2 x 13

A = 17 / 2 x 13

A = 110.5 inches

The average speed, in miles per hour, of car X for the 2-hour trip is 56 mph.

The average speed, in miles per hour, of car x for the 2-hour trip is 56 mph.Let’s first identify what the given is.The problem states that car X and car Y started from the same point and traveled on a straight course in opposite directions for 2 hours, at which time they were 208 miles apart. The problem also states that car X traveled, on average, 8 miles per hour faster than car Y.So we have two cars, X and Y, that traveled in opposite directions.

In this problem, we are asked to find the average speed of car X for the 2-hour trip.Let’s use the formula that relates distance, speed, and time. For any given problem, this formula will help us determine which variable we need to solve for.distance = speed × timeSo, in this problem, we know the time and distance, but we need to find the speed.

We can use the information given in the problem to set up an equation for the two cars.Using the formula, we can set up the following equation for car X:dX = speedX × 2Using the same formula, we can set up the following equation for car Y:dY = speedY × 2Since car X traveled, on average, 8 miles per hour faster than car Y, we can write this as speedX = speedY + 8.

Now we know that the sum of the distances that car X and car Y traveled is equal to the total distance that separates them. Using this information, we can set up the following equation:dX + dY = 208To solve for the speed of car X, we need to isolate speedX in the equation that relates speedX and speedY. We can do this by substituting the equation for dX and dY in the equation that relates speedX and speedY.

This gives us the following equation:(speedY + 8) × 2 + speedY × 2 = 208Simplifying this equation, we get:4 speedY + 16 = 2084 speedY = 192speedY = 48 mphNow that we know the speed of car Y, we can use the equation for speedX and speedY to find the speed of car X. This gives us:speedX = speedY + 8 = 48 + 8 = 56 mph.

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Answer:

below

Step-by-step explanation:

A (0,8)

B (8,0)

C(0,-8)

D(-8,0)

AB ( 4, 4 )

8/2 , 8/2

(x1+x2/2, y1+y2/2)

BC ( 4,-4 )

8/2 , -8/2

CD ( -4,-4 )

-8/2 -8/2

AD ( -4,4 )

-8/2 8/2

The polygon formed is a square because they all have sides with same lengths

If it was repeated it will still be a square

Therefore, the man finished his trip at 8:40 pm with total travelling time of 10 2/3 hours.

In mathematics, a fraction is a representation of a part of a whole or a ratio between two quantities. It consists of two numbers, a numerator and a denominator, separated by a horizontal line, also called a fraction bar or a vinculum. The numerator represents the number of equal parts being considered, while the denominator represents the total number of parts that make up the whole.

Here,

We can solve this problem using the formula:

distance = rate x time

Let's start by finding the time it took for the man to travel 450 kilometers at an average speed of 50 kilometers per hour:

time = distance / rate

time = 450 km / 50 km/h

time = 9 hours

So the man spent 9 hours travelling. However, he also took two breaks: a 40-minute rest and a 1-hour lunch break. We need to convert these times to hours to include them in our calculation.

40 minutes is equal to 40/60 = 2/3 hours, and 1 hour is simply 1 hour. So the total time the man spent travelling, including the breaks, is:

total time = 9 hours + 2/3 hours + 1 hour

total time = 10 2/3 hours

To find the finishing time, we add the total time to the starting time of 10 am:

finishing time = 10 am + 10 2/3 hours

finishing time = 8:40 pm (rounded to the nearest minute)

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Triangle XYZ will be translated to X'Y'Z' and the coordinates of Z' are (6,7).

A transformation known as a translation involves shifting each point in an image uniformly in one direction. It is also a type of transformation where every point in a figure is moved by the same amount in the same direction, producing a new figure that is identical to the original.

From the graph,

The coordinates of X are (7, 11)

The coordinates of Y are (10, 14)

The coordinates of Z are (8, 7)

When triangle XYZ is translated to X'Y'Z', the X-coordinate is given as (5, 11), which means the X-coordinate shifts left 2 points, so we need to subtract 2 from X-coordinate and keep Y-coordinate as it is.

Therefore the coordinate of the triangle X'Y'Z' are as follows,

The coordinates of X' are (7-2, 11) = (5,11)

The coordinates of Y' are (10-2, 14) = (8, 14)

The coordinates of Z' are (8-2, 7) = (6, 7)

Therefore the coordinates of Z' are (6,7)

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The standard form of the given decimal number is 803,133.

The given decimal number in words is "eight hundred three and one hundred thirty-three thousands". We have to write this decimal number in standard form. So, let's do it below.

The standard form of a decimal number is the way it's written normally, such as 3,040.00 instead of 3.04 × 103. To write the decimal number in standard form, we have to represent it in the form of a sum of its place values, which have a power of ten (10).

Therefore the standard form of the given decimal number is 803,133.

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The value of c is equal to 4.

The value of d is equal to 0.

In Geometry, a reflection across or over the x-axis is modeled and represented by the following transformation rule (x, y) → (x, -y). Therefore, a reflection across or over the x-axis would maintain the same x-value while the sign of the y-value would change from negative to positive or positive to negative as the case may be.

One of the vertices of triangle A is given by:

(x, y)                 →         (x, -y)

A (-1, -1)            →         A' (-1, -(-1) = (-1, 1)

When a translation is applied to triangle A', one of the corresponding or resulting vertices of triangle B is given by:

B (3, 1)

A' (-1 + c, 1 + d) → B (3, 1)

-1 + c = 3

c = 3 + 1

c = 4.

1 + d = 1

d = 0

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