42 a random experiment consists of tossing a fair 6-sided die repeatedly. how many tosses are required to be certain that the probability that at leas

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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The reasons behind GDP is an imperfect measure of economic well being are value of goods and services , economic activity, distributional issues, and depletion of natural resources .

GDP (Gross Domestic Product) is an imperfect measure of economic well-being for several reasons.

First,

GDP only measures the monetary value of goods and services produced within a country's borders.

It does not take into account non-market activities such as household work or volunteer work,

This can be significant contributors to well-being but are not included in GDP calculations.

Second,

GDP does not distinguish between desirable and undesirable economic activity.

For example, expenditures on environmental cleanup or healthcare are counted in GDP

Just as much as expenditures on cigarettes or military weapons.

Even though the former are beneficial for society, while the latter are not.

Third,

GDP does not measure distributional issues such as inequality, poverty, or social welfare.

Even if GDP were to increase,

It does not necessarily mean that all citizens have benefited equally from the economic growth.

Fourth,

GDP does not account for the depletion of natural resources or damage to the environment.

While economic growth may be achieved through unsustainable or environmentally destructive practices.

These costs are not reflected in GDP calculations.

Finally,

GDP does not capture the value of intangible factors such as social cohesion, quality of life, or happiness.

If GDP were to include non-market activities such as household work.

It would provide a more accurate measure of overall economic activity.

However, GDP would still be an imperfect measure of economic well-being.

Because it would not account for the distributional issues or environmental factors mentioned earlier.

Additionally, including non-market activities could potentially create new problems.

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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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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]

EXPAND

2w + 6 = 14

BALANCE OUT (-6 from both sides)

2w = 8

SOLVE

2w =8

÷2 ÷2

w = 4

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:

192

Step-by-step explanation:

320/20=16

12x16=192

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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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 (≡)

"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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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.

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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1. The probability a randomly selected pregnancy is more than 265 days in length is 0.5793.

2. The length of pregnancy that separates the shortest and longest 10% from the rest is (247.4, 288.6).3.

3. The probability of pregnancy that lasts less than or equal to 290 days is 0.9292.

1. The probability a randomly selected pregnancy is more than 265 days in length The length of pregnancy follows a normal distribution with mean, μ = 268 days and standard deviation, σ = 15 days.The probability of pregnancy more than 265 days is:

P(X > 265)P(Z > (265 - 268) / 15)P(Z > -0.2) = 0.5793

2. The length of pregnancy that separates the shortest and longest 10% from the rest The length of pregnancy follows a normal distribution with mean, μ = 268 days and standard deviation, σ = 15 days.We need to find the length of pregnancy that separates the shortest and longest 10% from the rest.The length of pregnancy that separates the lowest 10% from the rest is the first decile.

The first decile is given by:

x1 = μ - 1.28σ x 1 = 268 - 1.28 (15) x 1 = 247.4 days

The length of pregnancy that separates the longest 10% from the rest is the ninth decile.The ninth decile is given by:

x9 = μ + 1.28σ x 9 = 268 + 1.28 (15) x 9 = 288.6 days

Yes, it would be unusual to select a pregnancy that lasts longer than 290 days. We can see from the calculation below:

P(X > 290)P(Z > (290 - 268) / 15)P(Z > 1.47) = 0.0708

The probability of pregnancy that lasts longer than 290 days is 0.0708.The probability of pregnancy that lasts less than or equal to 290 days is:

P(X ≤ 290) = 1 - P(X > 290) = 1 - 0.0708 = 0.9292

We know that if the probability of any event is less than 0.05 or 5%, it is considered unusual. As the probability of pregnancy that lasts longer than 290 days is only 0.0708, which is less than 0.05 or 5%, it is considered unusual. Hence, it is unusual to select a pregnancy that lasts longer than 290 days.

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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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Answer:

1

Step-by-step explanation:

Answer: 1 pair

Step-by-step explanation: Trapezoids only have one pair of parallel sides.

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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Answer:

1. Not necessarily congruent to EFD, since 2 given sides tells us nothing about their congruency.

2. Congruent to QPR, due to SAS congruency.

3. Congruent to LJK, due to SAA congruency.

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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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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Either option A or option E could be the probability distribution for a loaded number cube.

What are statistics' four different forms of distribution?

One of the numerous categories of probability distributions is the normal distribution, which is also categorized as the chi-square distribution, the Poisson distribution, the binomial distribution, and the uniform distribution.

A probability distribution that gives each of the six outcomes positive probabilities, as long as they don't sum up to 1, can be used to describe a loaded number cube (because a fair cube has a flat probability distribution with a probability of 1/6 for each outcome).

The probability distribution for a loaded number cube should satisfy two conditions: the probabilities must sum to 1, and each probability must be between 0 and 1.

Out of the given options, only the following probability distributions satisfy both conditions:

Option A: 1/6, 2/6, 3/6, 4/6, 5/6, 1 (Note that the probabilities are not equally spaced, which suggests that the cube is loaded)

Option E: 0.20, 0.15, 0.20, 0.20, 0.20, 0.20 (Note that the probabilities are equally spaced, but they still add up to 1)

Therefore, either option A or option E could be the probability distribution for a loaded number cube.

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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

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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Answer:

12y-8

Step-by-step explanation:

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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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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According to the given tangent of the circle and angle, the value of x is approximately 38.67.

In geometry, a tangent of a circle is a straight line that intersects the circle at exactly one point, which is known as the point of tangency. The tangent line is perpendicular to the radius of the circle at the point of tangency.

An angle is a geometric figure formed by two rays that share a common endpoint, known as the vertex. Angles are usually measured in degrees or radians and are commonly used to describe the direction or orientation of lines, shapes, or objects in space.

we do know that the angle between the tangent and the radius drawn to the point of tangency is 90 degrees. We can use this fact to set up an equation and solve for x:

(3x - 26) + 90 = 180

3x + 64 = 180

3x = 116

x = 38.67

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Total 42 different types of stir-fry dishes are available at a restaurant.

As per the given information,

In restaurant, there are two types of rices (2 options), three proteins (3 options), and seven sauces (7 options).

This is a question of probability.

When all of these options are combined, they make a total of

2 x 3 x 7 = 42 possible combinations.
For example, a customer could choose white rice, chicken, and teriyaki sauce for their stir-fry. Or, they could opt for brown rice, shrimp, and sesame sauce.

There are 40 more combinations to choose from these.
In conclusion, a restaurant customer can choose from a total of 42 different kinds of stir-fry dishes, each of which is made up of a combination of two types of rice, three proteins, and seven sauces.

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