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The probability of a cat living more than 16 years can be estimated using the normal distribution. This can be calculated using the following equation: P(X>16) = 1-P(X<16) = 1- Φ((16-12)/2) = 0.1587. This means that the probability of a cat living more than 16 years is approximately 15.87%.

The normal distribution is a continuous probability distribution often used to represent real-world phenomena, such as the lifespan of cats. The distribution is characterized by two parameters, the mean and the standard deviation. The mean is the average value of the data, and the standard deviation is a measure of how spread out the data is around the mean.

To calculate the probability of a cat living more than 16 years, we need to find the cumulative probability of a value less than 16 years. This is done using the normal cumulative probability distribution. We subtract the mean (12 years) from the desired value (16 years) and divide the result by the standard deviation (2 years). We then use this value to calculate the cumulative probability using the cumulative probability function (Φ). The result is 0.1587, meaning that the probability of a cat living more than 16 years is approximately 15.87%.

In conclusion, the probability of a cat living more than 16 years is approximately 15.87%.

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ANSWERS:
A ) x^2 + 5/6x + 25/144 = (x + 5/12)^2

B ) x^2 - 11x + 121/4 = (x - 11/2)^2

EXPLANATION:

a. To complete the square for the equation x^2 + 5/6x + ___,

first divide the coefficient of the linear term (5/6) by 2,

which gives you 5/12.

Then, square the result:

(5/12)^2 = 25/144.

So, the equation becomes:
x^2 + 5/6x + 25/144 = (x + 5/12)^2

b. To complete the square for the equation x^2 - 11x + ___,

first divide the coefficient of the linear term (-11) by 2,

which gives you -11/2.

Then, square the result:

(-11/2)^2 = 121/4.

So, the equation becomes:

x^2 - 11x + 121/4 = (x - 11/2)^2

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The probability of selecting 8 female students from a sample of 8 students from a student body with 60% female students is 0.2187, or 21.87%.

The probability of selecting a sample of 8 students from a student body of 60% female students is calculated using binomial probability. The binomial probability formula is used to calculate the probability of a certain number of successes in a certain number of independent trials. In this case, the probability of selecting 8 students, with 60% being female students, can be calculated using the binomial probability formula.

The probability can be calculated using the following equation:
[tex]P(x=8) = (n!/((n-x)!x!)) * p^x * q^{(n-x)}[/tex]

Where:

In this case, n = 8, x = 8, p = 0.6, and q = 0.4. Plugging these values into the equation gives us a probability of 0.2187. This means that there is a 21.87% chance of selecting 8 female students out of a sample of 8 students from a student body with 60% female students.

It is important to remember that binomial probability is only used when there are two possible outcomes in each trial (i.e. success or failure). Additionally, it is important to remember that the equation only applies when the trials are independent of each other.

In conclusion, the probability of selecting 8 female students from a sample of 8 students from a student body with 60% female students is 0.2187, or 21.87%.

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The vertex of the parabola is approximately (7/32, 17.2), which represents the highest point the rock reaches during its flight.

A parabola is a symmetrical, U-shaped curve that is formed by the graph of a quadratic function. The equation of a parabola in standard form is y = ax² + bx + c, where "a", "b", and "c" are constants, and "x" and "y" are variables.

a. To evaluate h(0), we substitute t=0 in the equation:

h(0) = 15 + 7(0) - 16(0)² = 15

This means that at the instant the boy throws the rock (t=0), the height of the rock is 15 feet above the ground.

b. To estimate the time when the rock hits the ground, we need to find the value of t when h(t) = 0. We can solve the equation 15 + 7t - 16t² = 0 for t, using the quadratic formula:

t = (-7 ± √(7² - 4(-16)(15))) / (2(-16))

t ≈ 1.28 s or t ≈ 1.97 s

This means that the rock will hit the ground approximately 1.28 seconds or 1.97 seconds after it is thrown.

c. The equation h(1) = 6 means that one second after the rock is thrown, its height above the ground is 6 feet.

d. The vertex of the parabola h(t) = 15 + 7t - 16t² can be found by using the formula t = -b/2a, where a=-16 and b=7.

t = -7 / (2(-16)) = 7/32

Substituting t=7/32 into the equation, we get:

h(7/32) = 15 + 7(7/32) - 16(7/32)² ≈ 17.2

Therefore, the vertex of the parabola is approximately (7/32, 17.2), which represents the highest point the rock reaches during its flight.

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We can say with 95% confidence interval that the true mean lifetime of the tires is between 49,020 and 50,980 miles.

To calculate the confidence interval, we use the formula:

CI = x-bar ± z* (σ/√n)

where x-bar is the sample mean (50,000 miles), z is the z-score associated with the desired confidence level (in this case, 1.96 for 95% confidence level), σ is the standard deviation (5,000 miles), and n is the sample size (100).

Plugging in the values, we get:

CI = 50,000 ± 1.96*(5,000/√100)

Simplifying the expression, we get:

CI = 50,000 ± 980.

Therefore, we can say with 95% confidence that the true mean lifetime of the tires is between 49,020 and 50,980 miles.

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Answer: True.

Step-by-step explanation:

Important differences are always statistically significant if small sample size is used

The equation of the line is 9x+8y + 19 = 0 and 5x - 4y+ 19 = 0 According to the given graphs, these are the equations of the graph.

Consider two points on the blue line.

The points are (5, -8) and ( -3,1 ).

Equation of the blue line is:

y - 1 = [tex]\frac{-8-1}{5+3} (x+3)[/tex]

8 (y - 1) = -9 ( x + 3)

8y - 8 = -9x -27

9x + 8y + 19 = 0

Therefore, the Equation of the blue line is 9x + 8y + 19 = 0.

Consider two points on the red line.

The points are (-3, 1) and ( 1,6 ).

Equation of the red line is:

y - 1 = [tex]\frac{6-1}{1+3} (x+3)[/tex]

4 (y - 1) = 5 (x + 3)

4y - 4 = 5x + 15

5x - 4y+ 19 = 0

Therefore, the Equation of the red line is 5x - 4y+ 19 = 0.

Hence, the equations for the given blue and red lines are completed.

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(a) To find P(0 < Z < 2.74), you'll want to look up the z-score for 2.74 in a standard normal table or use a calculator with a built-in normal distribution function. The probability is the area under the curve between 0 and 2.74.

(b) To find P(0 < Z < 1), you'll look up the z-score for 1 in a standard normal table or use a calculator. The probability is the area under the curve between 0 and 1.

(c) To find P(-2.40 < Z < 0), you'll look up the z-score for -2.40 in a standard normal table or use a calculator. The probability is the area under the curve between -2.40 and 0.

(d) To find P(-2.40 < Z < 2.40), you can first calculate the probability for P(-2.40 < Z < 0) and P(0 < Z < 2.40), and then sum the two probabilities.

(e) To find P(Z > 1.63), look up the z-score for 1.63 in a standard normal table or use a calculator. The probability is the area under the curve to the right of 1.63.

(f) To find P(Z < -1.74), look up the z-score for -1.74 in a standard normal table or use a calculator. The probability is the area under the curve to the left of -1.74.

(g) To find P(-1.4 < Z < 2.00), first look up the z-scores for -1.4 and 2.00 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.

(h) To find P(1.63 < Z < 2.50), first look up the z-scores for 1.63 and 2.50 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.

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The percentage of scores greater than 34 is 0.5398 or 53.98%.

Given that the mean of scores (μ) = 35 and the standard deviation (σ) = 10. We need to find the percentage of scores greater than 34. Since the scores are normally distributed, we can standardize the variable by using the z-score formula.

z = (x - μ) / σ

Here, x = 34, μ = 35 and σ = 10z = (34 - 35) / 10z = -0.1

We need to find the area to the right of the z-score line on the standard normal distribution table. The standard normal distribution table provides the probabilities corresponding to the z-scores, i.e. the area under the curve to the right or left of the z-score line on the distribution table. The area to the right of the z-score line represents the percentage of scores that are greater than the given value. Using the standard normal distribution table, the area to the right of the z-score line -0.1 is 0.5398.

The percentage of scores greater than 34 is 0.5398 or 53.98%.

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The experimental probability of landing on blue is found by dividing the number of times blue was landed on by the total number of spins.

Experimental probability of landing on blue = Number of times blue was landed on / Total number of spins

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Therefore, the experimental probability of landing on blue is 4/9 or approximately 0.444 or 44.4% (rounded to the nearest tenth or percentage).

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The lower quartile of the given set of numbers 4, 6, 7, 8, 10, 12, 20 is 6. So, correct option is B.

To find the lower quartile of a set of numbers, we first need to arrange them in ascending order. The given numbers are: 4, 6, 7, 8, 10, 12, 20.

Next, we divide the data set into four equal parts. The lower quartile is the median of the lower half of the data set. In this case, the lower half is 4, 6, and 7.

To determine the median of the lower half, we need to find the middle value. Since we have an odd number of data points in the lower half, the middle value is the single value between the two extremes. In this case, the median is 6.

This corresponds to option (b) in the given choices: 6.

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Hence, the best descriptors for each scatterplot are identified in the answer.

Scatterplots: Identifying the best descriptors for each scatterplot Here are the scatterplots (a) and (b). a) Scatterplot (a) From the above scatterplot, the best descriptors are: Weak Relationship (There is no strong correlation between the two variables)Linear Relationship (The data points follow a linear pattern)Approximate Relationship (The data points appear to follow an approximate trend)No Relationship (There is no correlation between the two variables) b) Scatterplot (b) From the above scatterplot, the best descriptors are :No Relationship (There is no correlation between the two variables)Moderate Relationship (There is a moderate correlation between the two variables)Deterministic Relationship (The relationship between the variables is deterministic and direct)Strong Relationship (There is a strong correlation between the two variables)

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The location of the other 2 fountains, given the coordinates of the fountain would be (-6, 6) and (0, 6).

The fountain at (-3, 6) is located exactly in the middle of the horizontal line segment between the other two fountains, so the distance between each of the other two fountains and the middle fountain is 3 units (half of the total distance of 6 units).

Since the line segment is horizontal, the y-coordinate for both fountains will be the same as the middle fountain, which is 6.

Now we need to find the x-coordinates. We'll add 3 units to the x-coordinate of the middle fountain for one of the other fountains and subtract 3 units for the other one:

Fountain A: (-3 - 3, 6) = (-6, 6)

Fountain B: (-3 + 3, 6) = (0, 6)

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The constant (k) in this inverse variation y = 400/x is 400.

The correct answer choice is option D.

Inverse variation refers to the relationship that exists between two variables, such that the increase in the value of one variable decreases the value of the other variable.

It is written as;

y = k/x

Where,

k = constant of proportionality

x and y = the given variables

So,

y = 400/x

Therefore, it can be concluded that the constant of the inverse variation is 400

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Answer:

Carbon compounds are defined as chemical substances containing carbon i'd say.

f(x) = 3x2 + 4x − 9,  the coefficient of x2 is 3, the coefficient of x is 4, and the constant is -9. This can be written in interval notation as [−9, ∞).

Interval notation is a mathematical notation used to express the range of a variable. It is used to represent intervals on the number line, either on the real line or on the complex plane.

In this case, the domain of f(x) = 3x2 + 4x − 9 is all real numbers. The range of this function is all real numbers greater than or equal to -9. This can be written in interval notation as [−9, ∞).

The function is a quadratic polynomial of the form ax2 + bx + c. The domain of a polynomial function is all real numbers (i.e. any x-value). The range of the function is the set of all y-values that it can produce.

Here the coefficient of x2 is 3, the coefficient of x is 4, and the constant is -9. This means that the minimum y-value that the function can produce is -9. This means that the range of the function is all real numbers greater than or equal to -9.

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The probability that a patient would have a depression score greater than 60 is 0.9878.

The probability that a patient would have a depression score greater than 60 in a pain clinic when the mean depression score on a sample of patients is 78 with a standard deviation of 8 can be calculated using z-score.

Z-score formula

Z-score = (x - μ) / σ

Where,

x = the value to be standardized

μ = the mean of the population

σ = the standard deviation of the population

Given data,

Mean = 78

Standard deviation, σ = 8

Let x be the depression score.

To find the probability that a patient would have a depression score greater than 60, we need to find the z-score first.

Using the formula,

z-score = (x - μ) / σ = (60 - 78) / 8 = -2.25

Now, the probability can be calculated using the z-score table which gives the probability that a value will be less than z.

To find the probability that a value will be greater than z, subtract the probability from 1.

Probability of Z < -2.25 = 0.0122

Probability of Z > -2.25 = 1 - 0.0122 = 0.9878

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P(a number greater than 5 and an even number) = 1/6 or 0.167

Part 1 of 3 (a) To find the probability of getting an even number, divide the number of favorable outcomes (rolling a 2, 4, or 6) by the total possible outcomes (rolling any number between 1 and 6). There are 3 even numbers and 6 total possible outcomes.

P(an even number) = [tex]3/6 = 1/2 or 0.500[/tex]

Part 2 of 3 (b) To find the probability of getting a number less than or equal to 4, count the favorable outcomes (rolling a 1, 2, 3, or 4) and divide by the total possible outcomes (6). There are 4 favorable outcomes and 6 total possible outcomes.

P(a number less than or equal to 4) =[tex] 4/6 = 2/3 or 0.667[/tex]

Part 3 of 3 (c) To find the probability of getting a number greater than 5 and an even number, count the favorable outcomes (rolling a 6) and divide by the total possible outcomes (6). There is 1 favorable outcome and 6 total possible outcomes.

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The relationship between the mean and median depends on the shape of the distribution of the data, therefore correct options are

(a) The mean is approximately the same as the median

(b) The mean is greater than the median

(c)  The mean is less than the median.

The relationship between the mean and the median depends on the shape of the distribution of the data. In a symmetric distribution, the mean and median will be approximately the same. In a skewed distribution, the mean will be pulled in the direction of the skew, and the median will be a better representation of the "typical" value.

If the distribution is symmetrical (i.e., evenly distributed around the center), the mean and median will be approximately the same.

If the distribution is positively skewed (i.e., has a long tail on the right side), the mean will be greater than the median.

If the distribution is negatively skewed (i.e., has a long tail on the left side), the mean will be less than the median.

Therefore, correct options are

(a) The mean is approximately the same as the median

(b) The mean is greater than the median

(c)  The mean is less than the median.

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Answer: x is equal to 1

Step-by-step explanation:

280 dogs in all of the city's animal shelters are puppies. The solution has been obtained by using ratios.

What is ratio?

The ratio between two amounts of the same unit can be used to determine how much of one quantity is included in the other.

We are given that different animal shelters in a city shows that 10 of the 70 dogs are puppies and the city's animal shelters collectively house 1,960 dogs each year.

So, from this we get the ratio as

⇒ [tex]\frac{10}{70}[/tex] = [tex]\frac{x}{1960}[/tex]

Now, by cross multiplying, we get

⇒ 19,600 = 70x

⇒ x = 280

Hence, 280 dogs in all of the city's animal shelters are puppies.

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Answer:  4

Step-by-step explanation:

Given when y = 2,   x =  -2

Therefore  2 = -2 + ?

? = 2 + 2

? = 4

Answer:76904685 ways

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answer

6 divided by 54 is equal to 9

therefore

answer = d=9

The mean of the differences was 1.33 and the standard deviation of those differences was 2.90. The test statistic for this procedure is 1.90. The correct option is D.

Makers of generic drugs are required to show that their generic drugs do not differ significantly from the "reference" or brand name drugs that they imitate. One aspect in which the generic drugs might differ is their extent of absorption in the blood. Twelve subjects were available for the study. Six were randomly selected to receive the generic drug first and then, after a washout period, receive the "reference" drug. The remaining six received the "reference" drug first, followed by the generic drug after the washout period. Assume that all conditions are met.

The mean of the differences was 1.33 and the standard deviation of those differences was 2.90.

A t-test statistic for a paired sample is to be calculated to find out whether or not there is a statistically significant difference between the two treatments. The formula for a t-test statistic is given below:

t= x¯d/sd / √n

where x¯d is the mean difference,

sd is the standard deviation of the differences, and

n is the number of subjects.

Using the given values, we can substitute in the formula and solve for t as follows:

t=1.33/2.90 / √12t=1.90

Hence, the test statistic for this procedure is 1.90.

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Answer:

Step-by-step explanation:

-8+35 = 27

-16+4 = -12 but when you take the absolute value it turns positive.

So 27+ 12 is 39

The plane's average speed in still air is 270 mph.

The plane's average speed in still air can be calculated as follows:

x = Speed of plane in still air (unknown)            y = Speed of wind (unknown)

Speed of plane with wind = (x + y)

Speed of plane against wind = (x - y)

Using the formula, distance = speed x time, we can equate the above quantities to get two equations as shown below:

1200 = 4(x + y) ... (i)

1200 = 5(x - y) ... (ii)

Simplifying equation (i) and (ii), we get:

x = 270

Therefore, the plane's average speed in still air is 270 mph.

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Answer:

B.

Step-by-step explanation:

I just took the test