If you flip a coin and roll a 666-sided die, what is the probability that you will flip a tails and roll at least a 222?

Answer:

Domain [-5,∞)

Range [0,∞)

Step-by-step explanation:

Part 1) Find the domain

we have

[tex]f(x)=\frac{1}{2}\sqrt{x+5}[/tex]

we know that

The radicand must be greater than or equal to zero

so

[tex]x+5\geq 0[/tex]

solve for x

subtract 5 both sides

[tex]x\geq -5[/tex]

The solution for x is the interval [-5,∞)

All real numbers greater than or equal to -5

Remember that

The domain of a function is the set of all possible values of x

therefore

The domain of the function f(x) is the interval  [-5,∞)

Part 2) Find the range

we have

[tex]f(x)=\frac{1}{2}\sqrt{x+5}[/tex]

Find the value of f(x) for the minimum value of x

For x=-5

[tex]f(x)=\frac{1}{2}\sqrt{-5+5}[/tex]

[tex]f(x)=0[/tex]

The minimum value of f(x) is equal to zero

so

The solution for f(x) is the interval [0,∞)

All real numbers greater than or equal to 0

Remember that

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

therefore

The range of the function is the interval [0,∞)

Answer: 6 root 7

Step-by-step explanation:

The biggest whole number you can take out is 36, so the root of 36 on the outside and the 252/36 remains inside the root.

Answer:

6√7.

Step-by-step explanation:

First find the prime factors of 252:

252 =  2*2*3*3*7

Square root of 2*2*3*3 = 2*3 = 6.

Therefore:

√252 = 6√7.

Answer:

a) [tex]a=225 +0.674*16.5=236.121[/tex]

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.  

b) [tex] P(X \geq 3) = 1-P(X<3) = 1-P(X \leq 2) = 1-[P(X=0)+P(X=1) +P(X=2)]= 1-0.5256=0.4744[/tex]

c) [tex]P(\bar X \geq 225)=1- P(\bar X <225) = 1-P(Z<\frac{225-225}{\frac{16.5}{\sqrt{5}}}) = 1-P(Z<0) = 1-0.5 = 0.5[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Part a

Let X the random variable that represent the cuts of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(225,16.5)[/tex]  

Where [tex]\mu=225[/tex] and [tex]\sigma=16.5[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.25[/tex]   (a)

[tex]P(X<a)=0.75[/tex]   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.75[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.75[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=0.674=\frac{a-225}{16.5}[/tex]

And if we solve for a we got

[tex]a=225 +0.674*16.5=236.121[/tex]

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.  

Part b

For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:

[tex] X\sim Bin(n=10, p=0.25)[/tex]

And we want this probability:

[tex] P(X \geq 3) = 1-P(X<3) = 1-P(X \leq 2) = 1-[P(X=0)+P(X=1) +P(X=2)][/tex]

We can find the individual probabilities like this:

[tex]P(X=0)=(10C0)(0.25)^0 (1-0.25)^{10-0}=0.0563[/tex]

[tex]P(X=1)=(10C1)(0.25)^1 (1-0.25)^{10-1}=0.1877[/tex]

[tex]P(X=2)=(10C2)(0.25)^2 (1-0.25)^{10-2}=0.2816[/tex]

[tex] P(X \geq 3) = 1-P(X<3) = 1-P(X \leq 2) = 1-[P(X=0)+P(X=1) +P(X=2)]= 1-0.5256=0.4744[/tex]

Part c

For this case we know that the distribution for the sample mean is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And we want this probability:

[tex]P(\bar X \geq 225)[/tex]

And for this case we can use the complement rule and the z score given by:

[tex] z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we replace we got:

[tex]P(\bar X \geq 225)=1- P(\bar X <225) = 1-P(Z<\frac{225-225}{\frac{16.5}{\sqrt{5}}}) = 1-P(Z<0) = 1-0.5 = 0.5[/tex]

This problem involves using statistics and probability to interpret and make predictions from data involving the distribution of cutting rates of grinding wheels. It involves understanding mean and standard deviation values and the concept of percentiles in the context of normal distribution. To tackle similar problems, you need to understand how to calculate z-scores, use standard normal tables or functions and probabilities involving multiple events, which may involve the use of formulas such as the binomial probability formula.

Please note that the information provided in your question doesn't directly relate to the grinding wheel problems outlined. However, generally, these types of problems involve an understanding of statistics, probability, and the properties of the normal distribution, especially when using mean and standard deviation values to make calculations and predictions. It also involves understanding percentiles of a distribution and how these relate to the standard normal distribution and z-scores.

For example, if we consider that your calculated 75th percentile of the distribution of cutting rates (236.137 SFM) is correct, you can find the probability of a wheel having a cutting rate greater than this value by finding the corresponding z-score and looking this up on a table of standard normal probabilities, or using a computer program or calculator function that will provide this value. To calculate a probability involving multiple randomly selected wheels, we might need to use a binomial probability formula or similar.

Understanding these methods will allow you to generalise to other such problems. Given the complexity of these concepts however, I would recommend finding a tutor or seeking assistance from your teacher or lecturer to guide you through them.

https://brainly.com/question/30448794

#SPJ12

Answer:

x = 35.98

Step-by-step explanation:

The given triangle is a right angle triangle.

From the given right angle triangle

The unlabelled side represents the hypotenuse of the right angle triangle.

With 17 degrees as the reference angle,

x represents the adjacent side of the right angle triangle.

The length of the opposite side of the right angle triangle is 11

θ = 17 degrees

To determine x, we would apply trigonometric ratio

Tan θ = opposite side/adjacent side. Therefore,

Tan 17= 11/x

0.3057 = 11/x

Crossmultiplying,

0.3057x = 11

x = 11/0.3057 = 35.98

Answer:

a) Unit: College Student

Variables of measurement: Procrastination and illness habits.

b) Unit: SUV cars

Variables: Manufacturing and car damage for two car manufactures.

Step-by-step explanation:

We are given the following in the question:

In a research, a unit is a single individual or object that is measured.

a) A study finds that college students who often procrastinate tend to be sick more often than students who do not procrastinate.

Since college students are asked about procrastination, then the unit in this study is college students.

Unit: College Student

Variables of measurement: Procrastination and illness habits.

b) A study finds that sport utility vehicles (SUVs) made by one car manufacturer tend to be more heavily damaged in a crash test than SUVs made by a second car manufacturer.

Since all SUVs cars are considered, the unit in this research is  SUV cars

Unit: SUV cars

Variables: Manufacturing and car damage for two car manufactures.

The unit of analysis in the first study is individual college students, measuring procrastination and sickness. In the second study, individual SUVs are analyzed, comparing car manufacturer brands with crash test damage.

Understanding Variables and Units of Analysis in Studies

In the first study about college students and procrastination, the individual unit of analysis is each college student participating in the study. The two variables measured are the tendency to procrastinate (independent variable) and the frequency of being sick (dependent variable).

In the second study about SUVs and crash tests, the individual unit of analysis is each SUV manufactured by the car companies. The two variables measured are the brand of car manufacturer (independent variable) and the extent of damage sustained in a crash test (dependent variable).

These studies illustrate the importance of properly identifying units of analysis and measuring variables to avoid errors such as the ecological fallacy and to account for potential lurking variables.

Answer: Our required probability is 50%.

Step-by-step explanation:

Since we have given that

Probability of consuming regularly coffee = 65%

Probability of consuming carbonated soda = 60%

Probability of consuming atleast one of these two products =75%

So, we need to find the probability that they consumes both coffee and soda.

So, using "Probability rules", we get that

[tex]P(C\cap S)=P(S)+P(C)-P(C\cup S)\\\\0.75=0.65+0.60-x\\\\0.75=1.25-x\\\\0.75-1.25=-x\\\\-0.5=-x\\\\x=50\%[/tex]

Hence, our required probability is 50%.

Answer:

(7,-4)

Step-by-step explanation:

Answer:

(7, -4)

Step-by-step explanation: