A right triangle has a hypotenuse of length 20 cm and another side of length 16 cm. what is the length of the third side of the triangle?
For sample sizes greater than 40, the results of hypothesis tests and confidence intervals using the t distribution are highly sensitive to non-normality of the population from which samples are taken
b.the use of the t distribution assumes that the population from which the sample is drawn is normally distributed
c.for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers
d.since the t distribution procedure is robust, it can be used even for small sample with strong skewness and extreme outliers
[tex]\boxed{{\text{Option b}}}[/tex] is correct as the the use of the t distribution assumes that the population from which the sample is drawn is normally distributed.
[tex]\boxed{{\text{Option c}}}[/tex] for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers.
Further Explanation:
For sample sizes greater than [tex]40[/tex].
a) the results of hypothesis tests and confidence intervals using the t distribution are highly sensitive to non-normality of the population from which samples are taken is not correct as the sample size is large the data is normally distributed.
b) the use of the t distribution assumes that the population from which the sample is drawn is normally distributed is correct as the condition to apply t-distribution is that the data is normally distributed.
c) for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers is correct as the sample size is small the data set is less normally distributed.
d) since the t distribution procedure is robust, it can be used even for small sample with strong skewness and extreme outliers is not correct as it is the contradiction of option (c).
[tex]\boxed{{\text{Option b}}}[/tex] is correct as the the use of the t distribution assumes that the population from which the sample is drawn is normally distributed.
[tex]\boxed{{\text{Option c}}}[/tex] for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers.
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Answer details:
Grade: College
Subject: Statistics
Chapter: Normal distribution
Keywords: Z-score, Z-value, standard normal distribution, standard deviation, criminologist, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion.
Evaluate. 58−(14)2=58-142= ________
The correct answer is (-138).
Sure, let's break down the calculation step by step:
1. Follow the Order of Operations (PEMDAS/BODMAS):
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
2. Calculate Exponents:
[tex]\(14^2 = 14 \times 14 = 196\)[/tex]
3. Substitute the Exponent Result Back into the Equation:
(58 - 196 = -138)
So, [tex]\(58 - (14)^2 = -138\).[/tex]
The expression you provided is [tex]\(58 - (14)^2\).[/tex] According to the order of operations (PEMDAS/BODMAS), you first need to perform the operation inside the parentheses, which is squaring 14.
[tex]\[14^2 = 14 \times 14 = 196\][/tex]
After finding that \(14^2 = 196\), you substitute this value back into the original expression:
[58 - 196]
Finally, subtract 196 from 58:
[58 - 196 = -138]
Therefore, the correct answer is (-138).
Complete question
Evaluate. 58−(14)2=58-142= ________
When originally purchased, a vehicle costing $24,840 had an estimated useful life of 8 years and an estimated salvage value of $2,600. after 4 years of straight-line depreciation, the asset's total estimated useful life was revised from 8 years to 6 years and there was no change in the estimated salvage value. the depreciation expense in year 5 equals:?
simplify the expression 2x - 4 + 3x
Which measure of central location is meaningful when the data are categorical?
a. the range
b. the mean
c. the median
d. the mode?
write 18/24 as a percentage
divide 18 by 24 for a decimal number:
18 / 24 = 0.75
multiply 0.75 by 100 for the percent
0.75 * 100 = 75%
What is the result of factoring out the GCF from the expression (24 + 36)?
A)12 × (12 + 18)
B)12 × (2 + 3)
C)6 × (8 + 12)
D)12 × (4 + 6)
Answer:
Option B is correct .i.e., 12 × ( 2 + 3 )
Step-by-step explanation:
we are Given an Expression = 24 + 36
we have to find an Expresion after factoring out GCF
Full form of GCF is Greatest Common Factor.
First we find factors of 24 and 36 then their GCF
factors of 24 - 1, 2, 3, 4, 6, 8, 12, 24
factors of 36 - 1, 2, 3, 4, 6, 9, 12, 13, 36
⇒ GCF = 12
W have,
24 + 36
⇒ 12 × 2 + 12 × 3
⇒ 12 × ( 2 + 3 )
Therefore, Option B is correct .i.e., 12 × ( 2 + 3 )
The average annual income I in dollars of a lawyer with an age of x years is modeled with the following function I=425x^2+45,500x-650,000
Which choice is the GCF and LCM of 24 and 48? A) GCF = 12, LCM = 12 B) GCF = 24, LCM = 48 C) GCF = 12, LCM = 24 D) GCF = 12, LCM = 48 PLZ HELP FAST
Find an equation of a parabola that has curvature 8 at the origin.
The curvature of a parabola y = ax^2 at the origin is given by 2a. If the curvature is 8 at the origin, a = 8/2 = 4. Therefore, the equation of a parabola that has a curvature of 8 at the origin is y = 4x^2.
Explanation:The question involves finding an equation of a parabola that has a given curvature at a specific point, the origin, in this case. This falls into the field of calculus. The curvature, also known as concavity, of a parabola y = ax^2 at the origin is given by 2a. Therefore, if the curvature is 8 at the origin, a = curvature/2 = 8/2 = 4. Hence, the equation of the parabola would be y = 4x^2 .
As an example, if we needed to find the curvature of this parabola at any other point, we can use the second derivative, which in this case is constant and equal to 8, meaning the curvature is the same at every point on the parabola. So our quadratic equation meets the given condition of having a curvature of 8 at the origin.
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Irving spent the day shopping and made the following purchases: Item Cost ($) Novel 8.75 Shirt 21.66 Lunch 9.13 Potted plant 16.89 When Irving was done, he checked his account balance and found he had a total of $95.06. How much money was in Irving’s account to begin with? a. $56.43 b. $151.49 c. $38.63 d. $142.36
Solution:
Amount spent by Irving:
Item cost($)
Novel 8.75
Shirt 21.66
Lunch 9.13
Potted plant 16.89
Total money spent = $56.43.
Amount of money In Irving account= $95.06.
Amount of money was in Irving’s account to begin with =$56.43+$95.06=$151.49.
Answer:$151.49.
A parking garage holds 300 cars on each level. There are 4 levels in the garage. How many cars can the parking garage hold in all?
I need help with all of them
A cylinder and a cone each have a radius of 3 cm. and a height of 8 cm. What is the ratio of the volume of the cone to the volume of the cylinder?
14x^2-8x+3 + -6x^2+7x-11
Which set of ordered pairs contains only points that are on the graph of the function y = 12 − 3x?
In bowling you get a spare when you knock down the ten pins in two throws how many possible ways are there to get a spare
Answer:
6
Step-by-step explanation:
or more
Joseph needs to find the quotient of 3.216 ÷8. In what place is the first digit in the quotient?
Suppose that battery life is a normal random variable with μ = 8 and σ = 1.2. using the standard deviation rule, what is the probability that a randomly chosen battery will last between 6.8 and 9.2 hours?
The probability that a randomly chosen battery will last between 6.8 as well as 9.2 hrs will be "0.68".
According to the question,
μ = 8 σ = 1.2The probability that data values lies within standard deviation i.e.,
→ [tex](\mu -6) (\mu +6)[/tex] will be [tex]0.68[/tex]
The probability that data values lies within two standard deviation i.e.,
→ [tex](\mu -26)(\mu +26)[/tex] will be [tex]0.95[/tex]
The probability that data values lies within three standard deviation i.e.,
→ [tex](\mu -36) (\mu +36)[/tex] will be [tex]0.997[/tex]
Throughout the above examples,
→ [tex]\mu-6 = 8-1.2[/tex]
[tex]= 6.8[/tex]
→ [tex]\mu +6 = 8+ 1.2[/tex]
[tex]= 9.2[/tex]
Thus the above answer is correct.
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The probability that a randomly chosen battery will last between 6.8 and 9.2 hours, given a normal distribution with a mean of 8 hours and a standard deviation of 1.2 hours, is approximately 68.2% according to the empirical rule.
Calculating the Probability Using the Standard Deviation Rule
To calculate the probability of a battery lasting within this range, we find the z-scores for both limits and look up the corresponding areas under the normal distribution curve.
The standard deviation rule (or the 68-95-99.7 rule) tells us that for a normally distributed variable with mean (μ) and standard deviation (σ), approximately:
68% of the data falls within 1 standard deviation of the mean (μ ± σ).
95% of the data falls within 2 standard deviations of the mean (μ ± 2σ).
99.7% of the data falls within 3 standard deviations of the mean (μ ± 3σ).
Z-scores:
For 6.8 hours: (6.8 - μ) / σ =α- 1 hours)
For 6.8 hours: (6.8 - 8) / 1.2 = -1
For 9.2 hours: (9.2 - 8) / 1.2 = 1
The z-score corresponds to the number of standard deviations a value is from the mean. A z-score of -1 or 1 for a normal distribution typically encapsulates around 68.2% of the data (as part of the empirical rule).
Thus, we can say that the probability of a battery lasting between 6.8 and 9.2 hours is approximately 68.2%.
From beginning to end, explain the steps required to make a peanut butter and jelly sandwich.
Answer:
take 2 peices of bread
apply jelly
apply penut butter
Put the two peices of bread together
Step-by-step explanation:
edmentem
At a local hospital, 35 babies were born. if 26 were boys, what percentage of the newborns were boys?
Compute r6r6, l6l6, and m3m3 to estimate the distance traveled over [0, 3] if the velocity at half-second intervals is as follows:
For R6 and L6, t= (3- 0) / 6= 0.5. For M3, t= (3- 0)/ 3 = 1. Then
For R6 we will add all the velocity given from 12 to 20 and then multiply it by 0.5 seconds
R6 = 0.5 s ( 12 + 18 + 25 + 20 + 14 + 20 ) m/ sec = 0.5 (109) m = 54.5 m,
For L6 we will add all the velocity given from 0 to 14 and then multiply it by 00.5 as well.
L6 = 0.5 sec ( 0 + 12 + 18 + 25 + 20 + 14 ) m/ sec = 0.5 (89 ) m = 44.5 m.
For M3:
M3 = 1 sec (12 + 25 + 14) m/ sec = 51 m.
The question relates to integral calculus and the concept of Riemann sum approximation. The values r6r6, l6l6, and m3m3 need to be calculated given they represent velocities at half-second intervals. The estimated distance travelled would be the sum of these velocities multiplied by their respective time intervals.
Explanation:The task here is to compute the expressions r6r6, l6l6, and m3m3, and use those to estimate the distance traveled over the interval [0,3], if the velocity changes at half-second intervals. From the details, it is indicative this is a problem involving the mathematical concept of integral calculus, specifically the area under velocity-time curve. The overall distance travelled is given by the area under the curve which is the integral of the velocity function over the given interval.
Let's suppose the values r6r6, l6l6, and m3m3 represent velocities at different half-second intervals of time. In order to estimate the total distance travelled, you would need to sum these velocities and multiply by the duration of each interval (0.5 seconds). This concept is also known as Riemann sum approximation in integral calculus.
For example, if r6r6 = 10 m/s, l6l6 = 12 m/s, and m3m3 = 8 m/s, the estimated total distance travelled would be calculated as (10*0.5 + 12*0.5 + 8*0.5) = 5 m + 6 m + 4 m = 15 m.
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Karen works for $10 an hour. A total of 25% of her salary is deducted for taxes and insurance. She is trying to save $450 for a new set of tires. Write an equation to help determine how many hours she must work to take home $450 if she saves all of her earnings.
Find (3 × 104) − (5 × 102).
a 60 foot tree casts a shadow 85ft long. the sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree is approximately?
The sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree is approximately 0.7059.
Explanation:To find the sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree, we can use the properties of similar triangles. Let's label the height of the tree as 'a' and the length of the shadow as 'b'. We have a right triangle with the height as the opposite side and the shadow as the adjacent side. The sine of the angle can be found using the formula sine(angle) = opposite/hypotenuse, which in this case is a/b. So, the sine of the angle is a/b = 60/85 = 0.7059 (rounded to four decimal places).
Compare and contrast Euclidean geometry and spherical geometry. Be sure to include these points:
1. Describe the role of the Parallel Postulate in spherical geometry.
2. How are triangles different in spherical geometry as opposed to Euclidean geometry?
3. Geodesics
4. Applications of spherical geometry
Final answer:
Euclidean geometry and spherical geometry have distinct characteristics. The Parallel Postulate, triangle properties, geodesics, and applications differ between the two. Euclidean geometry relies on parallel lines, triangles with interior angles summing to 180 degrees, and straight geodesics, while spherical geometry lacks parallel lines, features triangles with angles >180 degrees, and utilizes great circles as geodesics. Spherical geometry finds applications in astronomy, navigation, Earth sciences, and cartography.
Explanation:
Euclidean Geometry vs Spherical Geometry
Euclidean geometry and spherical geometry are two different branches of geometry that have distinct characteristics and applications. Let's compare and contrast them:
1. Role of the Parallel Postulate
In Euclidean geometry: The Parallel Postulate states that given a line and a point not on that line, there is exactly one line that passes through the point and is parallel to the given line.
In spherical geometry: The Parallel Postulate is not true. In fact, there are no parallel lines in spherical geometry. On a sphere, any two lines will eventually intersect.
2. Triangles in Euclidean Geometry vs Spherical Geometry
In Euclidean geometry: Triangles have interior angles that sum up to 180 degrees. The angles of a triangle are classified as acute, obtuse, or right.
In spherical geometry: Triangles have interior angles that add up to more than 180 degrees. In fact, the sum can be greater than 540 degrees. Spherical triangles on a sphere are classified as acute-angled, right-angled, or obtuse-angled based on their angles.
3. Geodesics
In Euclidean geometry: Geodesics are straight lines and shortest paths between two points.
In spherical geometry: Geodesics are great circles or the arcs of circles on the surface of the sphere. They represent the shortest path between two points on a sphere.
4. Applications of Spherical Geometry
Spherical geometry has practical applications in various fields, including:
Astronomy: Spherical coordinates are used to locate celestial objects.
Navigation: Spherical trigonometry helps navigate across the Earth's curved surface.
Earth sciences: Spherical harmonics are used to represent the Earth's gravitational field.
Cartography: Representing the Earth's surface on a map or globe.
Simone paid $12 for an initial years subscription to a magizine. The renewal rate is $8 per year. This situation can be represented by the equation y=8x+12, where x represents the number of years the subscription is renewed and y represents the total cost.
The table shows the solution for the linear equation.
What is linear equation?"An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line".
For the given situation,
Cost for initial year subscription = $12
Cost for renewal = $8
The number of years the subscription is renewed be 'x' and
The total cost be 'y'.
This situation can be represented by the equation y = 8x+12.
For this linear equation, we need to make table by substituting different values of x to get y.
For [tex]x=1[/tex]
⇒[tex]y=8(1)+12[/tex]
⇒[tex]y=20[/tex]
For [tex]x=2[/tex]
⇒[tex]y=28[/tex]
For [tex]x=3[/tex]
⇒[tex]y=36[/tex]
For [tex]x=4[/tex]
⇒[tex]y=44[/tex]
For [tex]x=5[/tex]
⇒[tex]y=52[/tex]
The table below shows these interpretations.
Hence we can conclude that the table shows the solution for the linear equation.
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In the figure shown, what is the area of the rectangle, if the radius of each circle is 6 cm?
To find the area of the given rectangle with circles at its ends, we need to know the radius of the circles and the length of the rectangle in between. Length of the rectangle would be equal to the diameter of a circle plus the length between the two circles. Then, we multiply this length with the width equivalent to the diameter of the circle.
Explanation:In this Mathematics question, the student is asked to find the area of a rectangle with two circles, each with a radius of 6cm, at its ends.
As we know, the area of a rectangle is found by the formula, Area = Length x Width.
The length of the rectangle can be determined from the radii of the circles, it's equal to the diameter of one of the circles (because the radius of the circle is 6, the diameter would be 2*6=12) plus the length of the rectangle that is between the two circles.
However, the width of the rectangle is smoothly equivalent to the diameter of one of the circles (which is 12cm as calculated).
Once we have both the length and width of the rectangle (assuming the length inside the rectangle is given or predetermined), we can easily determine the area of the rectangle by multiplying these two.
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4/25, 13%, 0.28, 7%, 21/100, 0.15 least to greatest