The 20th percentile of the given data set is 36. The 40th percentile of the given data set is 50. The 70th percentile of the given data set is 66.4.
To find the percentiles of a data set, we first arrange the data in ascending order:
16, 33, 42, 50, 53, 63, 76, 80.
(a) To determine the 20th percentile, we use the formula:
Percentile = (P/100) * (n + 1),
where P is the desired percentile and n is the total number of data points.
For the 20th percentile:
Percentile = (20/100) * (8 + 1) = 0.2 * 9 = 1.8.
Since 1.8 is not an integer, we interpolate between the values at positions 1 and 2 to find the 20th percentile:
20th percentile = 33 + (1.8 - 1) * (42 - 33) = 36.
(b) Similarly, for the 40th percentile:
Percentile = (40/100) * (8 + 1) = 0.4 * 9 = 3.6.
Interpolating between the values at positions 3 and 4:
40th percentile = 42 + (3.6 - 3) * (50 - 42) = 50.
(c) For the 70th percentile:
Percentile = (70/100) * (8 + 1) = 0.7 * 9 = 6.3.
Interpolating between the values at positions 6 and 7:
70th percentile = 63 + (6.3 - 6) * (76 - 63) = 66.4.
Therefore, the 20th percentile is 36, the 40th percentile is 50, and the 70th percentile is 66.4 for the given data set.
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Consider the following data set.
16, 76, 33, 50, 63, 80, 53, 42
a) Determine the 20th percentile
b) Determine the 40th percentile
c) Determine the 70th percentile
WILL MARK YOU BRAINLIEST HURRY
Answer:
Step-by-step explanation:
flip the 2nd triangle right side :) or another answer (They both have a right angle)
Answer:
Because if you flip the triangle on the right to the side with the 2 lines downward they look exactly the same
Step-by-step explanation:
(a) at point a or point b is the gradient vector more horizontal? why? (b) at point a or point b is the gradient vector longer? why?
The definition of the gradient vector for point a to b is defined below.
Vector:
In math vector value consists of magnitude and direction.
Given,
Here we need to find the gradient vector of point a or point b.
According to the definition of vector, a multidimensional input have partial derivatives, you might wonder what the full derivative of such a function is. Here in the case of scalar-valued multivariable functions, meaning those with a multidimensional input but a one-dimensional output, the answer is the gradient.
Where as the gradient of a function f, denoted as ∇f,
Where f, is the collection of all its partial derivatives into a vector.
Here the point a and b is more horizontal because of the partial derivative nature of vector.
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Answer these questions
Answer:
1. -1
2. 25°
3. 26 1/4
Step-by-step explanation:
1. 14-8 is 6, -2 - 4 = -6, 6 ÷ -6 is -1
2. 75 + 80 = 155, 180 - 155 = 25°
3. cross multiply 4/5 = 21/x (4x= 105) = 26 1/4 or 105/4
I hope this helped, please mark Brainliest, thank you!
Answer:
What she said
Step-by-step explanation:
Click to select the figure in the image that would portray the rotation of the given preimage. The arrow represents both the direction and angle measure of the rotation.
Pre-image:
Image:
Based on the First image, the correct option is the fourth image while based on the second image, the correct option is the fourth image also.
Wat is the rotated in the above direction about?Given that the pre-image is rotated in the direction of the arrow as seen an the first image.
It is required to find the image formed also in that given direction.
Based on the fact that the arrow is rotating counter-clockwise, we get that, the shape of the pre-image will also rotate upwards towards the left hand side of the image shown.
So, based on the options (Taking the 1st image as pre-image), we have,
The fourth image where the shape is at the highest height will be the the fourth image after rotating the pre-image.
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What is 7/10 in standard form?
Answer:
0.7 I googled it :) if its wronge I'm sorry
Set up an equation to calculate the following (create your own variable names):
a. The area of a room.
b. The wall area of a room including windows and doors.
c. The wall area of a room not including two windows and a door.
d. The number of miles given a number of feet. (Use 5,280 feet per mile. )
e. The percent increase (or decrease) of a value given the beginning number and the ending number. How would the result differ between increase and decrease?
The result will differ between increase and decrease because the numerator in the formula represents the change (E - B). If the ending number is greater than the beginning number, it will result in a positive value, indicating an increase.
a. Let's use the variable A to represent the area of a room.
b. We can use the variable WA to represent the wall area of a room, including windows and doors.
c. For the wall area of a room not including two windows and a door, let's use the variable WNA.
d. To calculate the number of miles given a number of feet, we can use the variable M to represent the number of miles and F to represent the number of feet. Since there are 5,280 feet in a mile, we can set up the equation as:
M = F / 5280
e. To calculate the percent increase or decrease of a value given the beginning number (B) and the ending number (E), we can use the variable P to represent the percent change. The formula for percent change is:
P = ((E - B) / B) * 100.
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Did I graph this equation right?
Equation: P=125+50w
Answer:
yes
Step-by-step explanation:
You want a graph of P = 125 +50W.
Slope-intercept formThe given equation is in slope-intercept form. The independent variable is W, and the dependent variable is P.
Axes assignmentsUsually, the independent variable is graphed on the horizontal axis, which you have done.
The dependent variable is graphed on the vertical axis, which you have done.
The axes are correctly labeled and graduated.
InterceptThe "y-intercept" (P value) when the independent variable is zero is the constant in the equation, 125. You have correctly shown that on the graph.
SlopeThe slope of the line is the coefficient of the independent variable (W) in the equation. You have correctly shown that P increases by 50 when W increases by 1.
Yes, you properly graphed the equation.
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A nearby school for wizardry is larger. They have 14 times as many students.
How many students attend the school for wizardry?
Answer:
14 times more than the larger school
Step-by-step explanation: This makes no sense, there is no problem to solve, just a statement
I don’t know how to solve this.
Answer:
24
Step-by-step explanation:
put 2 over 3 and then simplify it then add the answer with 24
7 cm
D
What is the sum of the areas of circle C and circle D?
O7ft units²
O 14 units²
O 49 units²
O98 units²
The sum of areas of circle C and circle D exists 98 square units.
How to estimate the sum of the areas of circle C and circle D?Given: Radius of circle = 7 units
Area of circle \(=\pi r^2\) ..............(1)
Where, r be the radius of circle
The radius of circle C, r = 7 units
(1) becomes
Area of circle, C \(= \pi 7^2\) square units
\(= 49\pi\) units²
Area of circle, D \(= \pi 7^2\) square units
\(= 49\pi\) units²
Sum of areas of circles C and D,
= Area of circle C + Area of circle D
= 49 + 49
= 98 units²
The sum of areas of circles C and D exist 98 units².
Therefore, the correct answer is option d) 98 units².
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Which sentence is correct?
OA) -3 > 2
OB) -3 <-6
OC) -3>-8
OD) -3>-2
HELP IM BEING TIMED I WILL GIVE BRAINLIEST
Answer:
OC is correct
Step-by-step explanation:
The greater answer is always gonna be the closest one to zero on the number line.
Hopefully this helps!
help pls i don't understand
Answer:
the answer is B) (3√25)+7-5
D IS CORRECT
a.
\( \sqrt{25} = 5 \\ 5 \times 3 = 15 \\ 15 + 7 = 22 \\ 22 - 5 = 17\)
b. same as A), the parentheses dont change any of the math
c. same as A), the parentheses dont change any of the math
d.
\( \sqrt{25} = 5 \\ 5 + 7 = 12 \\ 12 \times 3 = 36 \\ 36 - 5 = 31\)
sin² x + cos²x = 1
Which Trigonometric Identity is given above?
- Pythagorean Identity
- Lagrange's Trigonometric Identity
- Angle Sum and Difference Identity
- Tangent Identity
The Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.
What is Pythagorean Identity?The Pythagorean Identity which tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one is known as or called a trigonometric identity.
The Pythagorean identity can be expressed as:
sin² x + cos² x = 1
This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.
Therefore the correct option is A.
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Small library contains 700 novels. how many ways can You check out three novels
The first book you select can be any one of 700.
. . . For each of those ...
The second book can be any one of the other 699.
. . . For each of those ...
The third book can be any one of the remining 698.
The total number of ways to gather three books from the shelves into your hands is (700 · 699 · 698) = 341,531,400 ways .
BUT ...
When you bring three books to the check-out counter, Marian the Librarian doesn't know in which order you took them down off the shelves. You could have gathered the same three books in (3 · 2 · 1) = 6 different ways.
So, even though there are 341,531,400 ways to gather up three books, there are only (341,531,400 / 6) = 56,921,900 different GROUPS of three books that you can choose to take home.
The graph on the right shows the theoretical probability of getting a given number heads in ten flips of a fair coin.
If this experiment was performed many times you would expect an average of
heads.
If this experiment was performed many times you would expect that the average number of heads is 5.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
From the graph,
The theoretical probability of getting 5 heads in ten flips of a fair coin.
= 0.25
= 25%
And,
The theoretical probability of getting 0 and 10, 1 and 9, 2 and 8, 3 and 7, and 4 and 6 heads is equal.
The average number of heads.
= (0 + 10)/2 = 5
Similarly,
(1 + 9)/2 = 10/2 = 5
(2 + 8)/2 = 10/2 = 5
(3 + 7)/2 = 10/2 = 5
(4 + 6)/2 = 10/2 = 5
So,
If this experiment was performed many times you would expect that the average of heads is 5.
Thus,
The expected average number of heads is 5.
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Answer:
5
Step-by-step explanation:
The answer above is correct.
factorise y^3 - 8y^2 + y-8
Answer:
\((y-8)(y^2+1)\)
Step-by-step explanation:
\(y^3 - 8y^2 + y-8\)
\(= (y-8)(y^2+1)\)
Please help as soon as you can
A line passing through (3/2,2) and (-1,3)
m= (-1)-3/2/(3-2)= -5/2.
Y=Mx+b
Y= -5/2x+b
A line passing through (-1,3) so 3= -5/2*(-1)+b
B= 6/5
The y intercept of the line on the graph y= -5/2x + 6/5
equivalent of 100 sqrt 2
Answer:
141.421356237
Using the information given on the
diagram, which congruence postulate
or theorem can be used to prove
PSR = RQP?
Step-by-step explanation:
ps||pr are parallel
pQR=Rsp
Erica runs 5.3 kilometers every morning. One day, she runs 0.95 kilometers and then stops to take a break. How much further does Erica have left to run?
Answer:
1foot(ft.)1yard(yd.)1mile(mi.)===12inches(in.)3feet(ft.)5,280feet(ft.)
Step-by-step explanation:
calculate the coefficient of variation for a sample of cereal boxes with a mean weight of 340 grams and a standard deviation of 5.2 grams.? 0.15% A
1.53% B
15.29% C
0.65% D
The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.
In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.
CV = (Standard Deviation / Mean) * 100
CV = (5.2 / 340) * 100
CV ≈ 1.53%
Therefore, the correct answer is option B: 1.53%.
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Grade 8
B.
A completely full gasoline tank is drained at a constant rate, as shown in the graph below-
Gasoline in the Tank
Over Time
50
40
30
Remaining Gasoline
(in gallons)
10
0 1 2 3 4 5 6 7 8 9 10
Amount of Time (in minutes)
Zhich statement best describes the rate of change for the gasoline in the tank?
There were 5 gallons of gasoline drained C. There were 0 gallons of gasoline in tl
each minute.
tank after 9 minutes.
There were 40 gallons of gasoline in the D. There were 45 gallons of gasoline in
tank after 1 minute.
tank when it was full.
Answer:
A gallons and a half a minute
Step-by-step explanation:
9 minutes it fills up a gallons and a half
Graph the relation shown in the table. Is the relation a function? Why or why not? {(-1, 9), (0, -1), (-1, 4), (4, 9)}
Answer:
Not a function
Step-by-step explanation:
For an equation to be a function, there should be only one y-coordinate per x-coordinate. Since this relation has both (-1,9) and (-1,4), this is not a function.
Answer:not a function
Step-by-step explanation:
because when you put the points on the coordinate plane your shape will come out as a v shaped object. In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers
Find X? x+14+x3=78 How can I find X? Please answer. Thanks so much! (This is my older sister's account btw)
The value of variable x in the equation is 16.
How to find the variable x in the equation?The equation represented as follows:
x + 14 + x³ = 78
The value x is the variable.
A variable is number represented with a letter in an equation.
Therefore,
x + 14 + 3x = 78
subtract 14 from both sides of the equation
x + 3x + 14 - 14 = 78 - 14
x + 3x = 64
Therefore,
4x = 64
divide both sides by 4
4x / 4 = 64 / 4
x = 16
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a population consists of
Answer:
Step-by-step explanation:
A population consists of a complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.
Since there are 4 sides with a length of `x`, `4x` feet of fencing has been used so far. Since we know that there is 180 feet of fencing, how much feet of fencing is left? Submit your answer as an expression in terms of `x` below.
Using the perimeter relation, the amount of fencing left is obtained using the subtraction operation. Hence, amount of fencing left is 90 feets
Recall :
Perimeter = 2(length + width)Hence,
180 = 2(x + 4x)
180 = 2(5x)
180 = 10x
x = 180 / 10
x = 18 feets
Amount of fencing left :
180 - (18 + 4(18))
180 - (18 + 72)
180 - 90
= 90 feets
Therefore, there is 90 feets of fencing left.
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What is the surface area of this square pyramid?
o 72 cm2
o 384 cm
o 204 cm
o 240 cm2
The surface area of this square pyramid is,
⇒ SA = 296 cm²
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
To find the surface area of this square pyramid
Now, We know that;
the surface area of this square pyramid is,
⇒ SA = B + 1/2 pl
Where, B represents the area of the base. p represents the perimeter of the base. l represents the slant height.
Now, We get;
B = 12 x 8
B = 96
p = 2 (12 + 8)
p = 40
l = 10
Thus, the surface area of this square pyramid is,
⇒ SA = B + 1/2 pl
⇒ SA = 96 + 1/2 x 40 x 10
⇒ SA = 96 + 200
⇒ SA = 296 cm²
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A study examined the average pay for men and women entering the workforce as doctors for 21 different positions.
(a) If each gender was equally paid, then we would expect about half of those positions to have men paid more than women and women would be paid more than men in the other half of positions.
(b) Men were, on average, paid more in 19 of those 21 positions. Complete a hypothesis test using your hypotheses from part (a).
4. Write the appropriate hypotheses to test this scenario
5. Calculate a test statistics and p-value
6. Does this sample provide a convincing evidence that men are paid more than women at a significance level $\alpha$ of 0.05?
The following parts can be answered by the concept of Standard deviation.
4. To test the scenario, we can set up the following hypotheses:
Null Hypothesis (H0): The proportion of positions where men are paid more than women is equal to 0.5 (equal pay).
Alternative Hypothesis (H1): The proportion of positions where men are paid more than women is greater than 0.5 (men are paid more).
5. To calculate the test statistic and p-value, we'll use a one-sample proportion test. In this case, the sample proportion (p-hat) is 19/21. The hypothesized proportion (p0) is 0.5. The sample size (n) is 21.
Test Statistic (z) = (p-hat - p0) / √((p0 × (1 - p0)) / n)
z = (19/21 - 0.5) / √((0.5 × (1 - 0.5)) / 21)
z ≈ 6.43
To find the p-value, we look at the upper tail of the standard normal distribution corresponding to the z-score of 6.43. Since this z-score is very large, the p-value is extremely small (approaching 0).
6. With such a small p-value (close to 0) and a significance level (α) of 0.05, we reject the null hypothesis in favor of the alternative hypothesis. This sample provides convincing evidence that men are paid more than women in the examined positions at the 0.05 significance level.
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The following parts can be answered by the concept of Standard deviation.
4. To test the scenario, we can set up the following hypotheses:
Null Hypothesis (H0): The proportion of positions where men are paid more than women is equal to 0.5 (equal pay).
Alternative Hypothesis (H1): The proportion of positions where men are paid more than women is greater than 0.5 (men are paid more).
5. To calculate the test statistic and p-value, we'll use a one-sample proportion test. In this case, the sample proportion (p-hat) is 19/21. The hypothesized proportion (p0) is 0.5. The sample size (n) is 21.
Test Statistic (z) = (p-hat - p0) / √((p0 × (1 - p0)) / n)
z = (19/21 - 0.5) / √((0.5 × (1 - 0.5)) / 21)
z ≈ 6.43
To find the p-value, we look at the upper tail of the standard normal distribution corresponding to the z-score of 6.43. Since this z-score is very large, the p-value is extremely small (approaching 0).
6. With such a small p-value (close to 0) and a significance level (α) of 0.05, we reject the null hypothesis in favor of the alternative hypothesis. This sample provides convincing evidence that men are paid more than women in the examined positions at the 0.05 significance level.
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What is the value of w?
2/5 (w+5) = 4/5
Answer:
W = -3
Step-by-step explanation:
Answer:
w = - 3
Step-by-step explanation:
Given
\(\frac{2}{5}\) (w + 5) = \(\frac{4}{5}\)
Multiply both sides by 5 to clear the fractions
2(w + 5) = 4 ( divide both sides by 2 )
w + 5 = 2 ( subtract 5 from both sides )
w = - 3
May I please get help with this math. I have tried so many times but still could not find the right answer
In any triangle, the greatest angle is opposite to the greatest side and the smallest angle is opposite to the smallest side.
Knowing that, first let's find the measure of the third angle, using the property that the sum of internal angles in any triangle is equal to 180°:
\(\begin{gathered} C+D+E=180 \\ 42+55+E=180 \\ E=180-55-42 \\ E=83\degree \end{gathered}\)The smallest angle is C, so the smallest side is DE.
The greatest angle is E, so the greatest side is CD.
Therefore the order is:
DE < CE < CD