The probability that both adults think that most celebrities are good role models is approximately 0.034.
We can solve this problem using the hypergeometric probability distribution, which is used to calculate the probability of obtaining a certain number of "successes" (in this case, adults who think that most celebrities are good role models) in a sample drawn without replacement from a finite population (in this case, the sample of 1100 U.S. adults).
The probability of selecting one adult who thinks that most celebrities are good role models is:
p = 215/1100 ≈ 0.195
The probability of selecting two adults who think that most celebrities are good role models is:
P(X = 2) = (215/1100) * (214/1099) ≈ 0.034
Therefore, the probability that both adults think that most celebrities are good role models is approximately 0.034, or 3.4%. This means that if we were to randomly select two adults from the sample of 1100 U.S. adults, there is a 3.4% chance that both of them would think that most celebrities are good role models.
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please do this i need help
The total area if each garden bed has a length of 4 feet is given as follows:
A = 48ft².
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The area for a bed of side length s is given as follows:
A = 3s².
Hence the total area if each garden bed has a length of 4 feet is given as follows:
A = 3 x 4² = 48 ft².
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The radius of a right circular cylinder is decreased by $20\%$ and its height is increased by $25\%$. What is the absolute value of the percent change in the volume of the cylinder
The absolute value of the percent change in the volume of the cylinder is 20%.
When the radius of a right circular cylinder is decreased by 20%, its new radius becomes 0.8 times the original radius (1 - 0.20 = 0.8).
Likewise, when its height is increased by 25%, its new height becomes 1.25 times the original height (1 + 0.25 = 1.25).
The volume of a right circular cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. Let V₁ be the original volume, and V₂ be the new volume after the changes.
V₁ = π(r)²(h) and V₂ = π(0.8r)²(1.25h)
V₂ = π(0.64r²)(1.25h) = 0.8πr²h
Thus, the new volume is 0.8 times the original volume. This represents a 20% decrease in volume (1 - 0.8 = 0.20 or 20%). So, the absolute value of the percent change in the volume of the cylinder is 20%.
In summary, decreasing the radius by 20% and increasing the height by 25% results in a 20% decrease in the volume of the right circular cylinder.
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A sector of a circle has a central angle of 135 degrees. Find the area of the sector if the radius of the circle is 13 cm.
Answer:
A ≈ 199.1 cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{135}{360}[/tex] ( r is the radius )
= π × 13² × [tex]\frac{3}{8}[/tex]
= [tex]\frac{\pi (169)(3)}{8}[/tex]
≈ 199.1 cm² ( to the nearest tenth )
The area of the sector with a central angle of 135 degrees and a radius of 13 cm is 507π/8 cm².
To find the area of the sector with a central angle of 135 degrees and a radius of 13 cm, follow these steps:
Determine the ratio of the central angle to the total angle of the circle (360 degrees): 135/360 = 3/8.
Calculate the area of the entire circle using the formula:
Area = πr²,
where r is the radius.
In this case, Area = π(13 cm)² = 169π cm².
3. Multiply the area of the entire circle by the ratio found in step 1 to find the area of the sector:
(3/8) * (169π cm²) = 507π/8 cm².
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The interval within which 95 percent of all possible sample estimates will fall by chance is defined as ______.
The interval within which 95 percent of all possible sample estimates will fall by chance is defined as The sample mean, plus or minus 1.96 standard errors.
The interval within which 95 percent of all possible sample estimates will fall by chance is known as the 95 percent confidence interval. This interval is calculated by taking the sample means and adding or subtracting 1.96 standard errors. The standard error is a measure of the variation or spread of the sample data around the true population mean.
When we calculate a confidence interval, we are trying to estimate the true population mean based on a sample of data. However, due to the inherent variability in the data, any single sample estimate may not be exactly equal to the true population mean. Therefore, we construct a confidence interval to indicate the range of values within which the true population mean is likely to fall.
The use of 1.96 standard errors in the calculation of the confidence interval is based on statistical theory, which tells us that if we repeatedly sample from a population and calculate the sample mean, approximately 95 percent of the resulting confidence intervals will contain the true population mean. Therefore, the 95 percent confidence interval is a commonly used tool for reporting the precision of sample estimates and providing a measure of uncertainty around those estimates.
In summary, the 95 percent confidence interval provides a range of values within which we can be reasonably confident that the true population means falls. It is calculated as the sample mean, plus or minus 1.96 standard errors, and is a useful tool for reporting the precision of sample estimates and providing a measure of uncertainty around those estimates.
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Six measurements are taken of the thickness of a piece of 18-guage sheet metal. The measurements (in mm) are: 1.316, 1.308, 1.321, 1.303, 1.311, 1.310 Make a boxplot of the six values. Should the t distribution be used to find 99% confidence interval for the thickness
To make a boxplot of the six measurements, first arrange them in order from smallest to largest: 1.303, 1.308, 1.310, 1.311, 1.316, 1.321. Then, draw a number line and plot a box that spans the range from the first quartile (Q1) to the third quartile (Q3), with a line inside the box representing the median.
The whiskers should extend to the smallest and largest observations that fall within 1.5 times the interquartile range (IQR) from the box. Any observations that fall outside of this range are considered outliers and should be plotted as individual points.
In this case, Q1 is 1.308, Q3 is 1.316, the median is 1.311, and there are no outliers. Therefore, the boxplot would show a box from 1.308 to 1.316, with a line at 1.311 in the middle.
As for whether the t distribution should be used to find a 99% confidence interval for the thickness, it depends on whether we know the population standard deviation or not. If we know it, we could use a z-score instead of a t-score to calculate the confidence interval. However, if we do not know the population standard deviation, we would need to use the t distribution to account for the extra uncertainty in our sample estimate of the standard deviation. In either case, a 99% confidence interval would be wider than a 95% confidence interval, since we are more certain that the true population mean falls within the wider range.
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When you use your Taylor polynomial to estimate the probability that a value lies within two standard deviations of the mean, what do you get
When using a Taylor polynomial to estimate the probability that a value lies within two standard deviations of the mean, the result will depend on the specific function used to create the polynomial. However, in general, a Taylor polynomial can provide a good approximation of the function within a certain interval.
1. Identify the function: The probability distribution function for a normal distribution is given by the function f(x) = (1/σ√(2π)) * e^(-(x-μ)^2 / 2σ^2), where μ is the mean and σ is the standard deviation.
2. Determine the interval: Two standard deviations from the mean are represented by the interval [μ - 2σ, μ + 2σ].
3. Apply Taylor polynomial: Approximate f(x) using a Taylor polynomial centered at μ. The higher the degree of the polynomial, the more accurate the approximation.
4. Calculate probability: Integrate the Taylor polynomial over the interval [μ - 2σ, μ + 2σ] to estimate the probability.
5. Interpret the result: The estimated probability represents the likelihood that a value lies within two standard deviations of the mean in a normal distribution.
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write an expanded form of the expression
y(0.5+8)
Evaluating and expanding the expression y(0.5+8) gives 8.5y
Evaluating and expanding the expression y(0.5+8)From the question, we have the following parameters that can be used in our computation:
y(0.5+8)
The above statement is a product expression that multiplies the values of y and 0.5 + 8
Also, there is a need to check if there are like terms in the expression or not
This is because we are adding the terms too
So, we have
y(0.5+8) = 8.5y
This means that the value of the expression when expanded is 8.5y
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