Answer:
The IQR (interquartile range) of 13 is the most accurate measure of variability to use in this case, since the data is skewed and contains some outliers.
The IQR is a measure of variability that is less sensitive to extreme values than the range, and is calculated as the difference between the upper and lower quartiles (the 75th and 25th percentiles). It provides a measure of the spread of the middle 50% of the data, which is useful for understanding the typical range of donations received.
In this case, the IQR is calculated as follows:
- The median of the data is 51 (the value in the middle).
- The lower quartile (Q1) is the median of the lower half of the data, which is 42.
- The upper quartile (Q3) is the median of the upper half of the data, which is 54.
- The IQR is the difference between Q3 and Q1: IQR = Q3 - Q1 = 54 - 42 = 12.
So the IQR of 13 is a useful measure of variability to use for this data set, since it captures the spread of the middle 50% of the data while being less sensitive to the outliers at the higher end of the distribution.
How to solve -10(x-1.7)=-3 by expanding first
To solve the equation -10(x-1.7)=-3 by expanding first, we need to apply the distributive property of multiplication.
Expanding -10(x-1.7), we get
-10x + 17 = -3
Now we can solve for x by isolating the variable on one side of the equation. To do this, we'll add 10x to both sides of the equation
-10x + 17 + 10x = -3 + 10x
Simplifying, we get
17 = 10x - 3
Next, we add 3 to both sides of the equation
17 + 3 = 10x - 3 + 3
Simplifying, we get
20 = 10x
Finally, we divide both sides of the equation by 10 to isolate x
20/10 = 10x/10
Simplifying, we get
2 = x
Therefore, the solution to the equation -10(x-1.7)=-3 by expanding first is x = 2.
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Construct a 90 % confidence interval of the population proportion using the given information.
x = 105 n =150
The 90% confidence interval based on the data provided will be (0.6152, 0.7848)
How to calculate the confidence intervalIt should be noted that standard error = ✓[(p * q) / n]
p = population proportion
q = 1 - p
n = sample size
sample proportion = x / n = 105 / 150 = 0.7
standard error = ✓(p * q) / n] = sqrt[(0.7 * 0.3) / 150] = 0.0516
margin of error = 1.645 * 0.0516 = 0.0848
Confidence interval = sample proportion ± margin of error
= 0.7 ± 0.0848
= (0.6152, 0.7848)
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Solve for x. Round to the nearest tenth, if necessary.
Answer:
160
Step-by-step explanation:
The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp)
Adjacent = 80
Hypotenuse = x
therefore, cos(60) = 80/x
1/2 = 80/x
x = 80 x 2 = 160
Please if you know the answer put the steps on thank you.
Answer:
1. # of people who predicted they would pass = 30
2. # of people who predicted they would fail = 20
3. # of people who predicted they would pass and actually passed = 27
4. # of people who predicted they would pass and actually failed = 3
5. # of people who predicted they would fail and actually passed = 11
6. # of people who predicted they would fail and actually failed = 9
Step-by-step explanation:
1. # of people who predicted they would
The total number of people who took the test is 50.The number of people who predicted they would pass is 30.The number of people who predicted they would fail is 20 (since 50 - 30 = 20)Let x be the number of people who predicted fail and actually passed the test. Since three times as many people who passed predicted pass than predicted fail, we know that 3x is the number of people who predicted pass and actually passed the test. Therefore, the total number of people who passed the test is x + 3x = 4x, and we know that 36 people passed the test, so 4x = 36, and x = 9.Since x is the number of people who predicted fail and actually passed the test, then the number of people who predicted fail and actually failed the test is 20 - x = 20 - 9 = 11.The number of people who predicted pass and actually passed the test is 3x = 3(9) = 27.The number of people who predicted pass and actually failed the test is 30 - 27 = 3.I also filled in the frequency table by extracting it from Brainly and drawing on it to show how the math works and fits in the table.
Which of the following pairs consists of equivalent fractions? 3/9 and 5/15 ,12/20 and 20/25,5/6 and 6/5,6/12 and3/4
Answer:
[tex]The[/tex] [tex]Answer[/tex] [tex]Is:[/tex] [tex]\frac{3}{9}[/tex] [tex]&[/tex]& [tex]\frac{5}{15}[/tex]
Step-by-step explanation:
Divide by 4 , 2nd fraction Divide by 5:
3/4 ≠ 4/5
5/6 ≠ 6/5 We can already see it.
Divide by 3. . .
2/4 ≠ 3/4
Divide by 3 , 2nd fraction Divide by 5:
1/3 = 1/3 [tex]Perfect![/tex]
The answer is, [tex]\frac{3}{9}[/tex] & [tex]\frac{5}{15}[/tex]
Solve for x. Round to the nearest tenth, if necessary.
The calculated value of x in the right triangle is 8.7
Calculating the value of x in the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The value of x in the right triangle can be calculated using the following sine ratio
sin(75) = x/9
Cross multiply the equation
So, we have
x = 9 * sin(75)
Evaluate the products
x = 8.7
Hence, the value of x in the right triangle is 8.7
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a math teacher gave her class two test 70% of the class passed both tests and 80% of the class passed the first test what percent of those who passed the first test also passed the second test this statement is an example of supplementary probability true or false
87.5% of those who passed the first test also passed the second test.
The given statement in the question is an example of conditional probability rather than supplementary probability. Therefore, the statement is false.
We are given the following information:
- 70% of the class passed both tests.
- 80% of the class passed the first test.
We want to find the percentage of those who passed the first test and also passed the second test.
To do this, we will use the concept of conditional probability.
Let A be the event of passing the first test, and B be the event of passing the second test.
We are asked to find the conditional probability P(B|A), which is the probability of passing the second test given that the student has passed the first test.
Using the formula for conditional probability, we have:
P(B|A) = P(A ∩ B) / P(A)
We know that P(A ∩ B) = 0.7 (since 70% of the class passed both tests) and P(A) = 0.8 (since 80% of the class passed the first test).
Now, we can calculate P(B|A):
P(B|A) = 0.7 / 0.8 = 0.875.
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Find the surface area of the triangular prism. A triangular prism. The base is a right triangle with base and height 4 millimeters, and the third side 5.7 millimeters. The height of the prism is 3 millimeters.
The surface area of the triangular prism is approximately 44.29 square millimeters.
What is surface area?
Surface area is the total area that the surface of a three-dimensional object covers. It is a measure of the amount of space that the surface of an object occupies. Surface area is usually measured in square units such as square meters, square centimeters, square inches, or square feet.
What is the area?
The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.
The area of a plane figure is the space enclosed by its boundary.
According to the given information:
To find the surface area of a triangular prism, we need to add up the area of all the faces. A triangular prism has three rectangular faces and two triangular faces.
Let's start by finding the area of the triangular faces. The base of the triangular prism is a right triangle with base 4 millimeters, height 4 millimeters, and hypotenuse 5.7 millimeters. We can use the Pythagorean theorem to find the missing side:
[tex]a^2 + b^2 = c^2\\4^2 + 4^2 = 5.7^2[/tex]
16 + 16 = 32.49
32 = 32.49 - 0.49
32 = 32
So the missing side has length [tex]\sqrt{(5.7^2 - 4^2)} =3.69 millimeters.[/tex] This is the base of each triangular face.
The height of the triangular prism is 3 millimeters, so the height of each triangular face is also 3 millimeters.
The area of each triangular face is:
(1/2) × base × height
= (1/2) × 3.69 × 3
≈ 5.54 square millimeters
So the total area of the two triangular faces is:
2 × 5.54= 11.08 square millimeters
Now let's find the area of each rectangular face. The length of each rectangular face is the same as the base of the triangular face, which is 3.69 millimeters. The width of each rectangular face is the height of the triangular prism, which is 3 millimeters.
The area of each rectangular face is:
length × width
= 3.69 × 3
≈ 11.07 square millimeters
So the total area of the three rectangular faces is:
3 × 11.07
= 33.21 square millimeters
To find the surface area of the triangular prism, we add up the area of all five faces:
11.08 + 33.21
= 44.29 square millimeters
Therefore, the surface area of the triangular prism is approximately 44.29 square millimeters.
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I-Ready
What is the distance between point P and point Q?
PLEASE SOMEONE !! 15 POINTS!!!
Answer:
The answer is -5
Step-by-step explanation:
Each number moves down 5 as it moves to the right 1. Right is positive, and down is negative. -5 divided by 1 is -5.
true or false ? is (b^9)^3 = b^27
It is true that the product of the index [tex](b^9)^3 = b^2^7[/tex]
What is indices?Indices track asset performance in finance and specify array elements in math and programming; their use varies by subject. Different methods refer to list, vector, or matrix elements. Power law of indices: larger number or letter must match.
This can be expressed mathematically as am+n.
Additionally, there are several Laws of Indices that provide rules for simplifying calculations or expressions involving powers of the same base.
The given question is true or false is [tex](b^9)^3[/tex]= [tex]b^27(b^9)^3[/tex] = [tex](b^9)^3 = b^2^7[/tex]
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Suppose a normal distribution has a mean of 34 and a standard deviation of
2. What is the probability that a data value is between 30 and 36? Round your
answer to the nearest tenth of a percent.
Answer:
it’s 86.6%
Step-by-step explanation:
could be wrong
I need some assistance with this ? Please
Answer:
I am sorry this is just so new for me like what even is an "imaginary" solution, i am in 6th grade wth
What is the equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number? How can the equation be simplified if the vertex is at the origin?
Note that equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number is (y-k)² = 4p(x-h).
How can the equation be simplified if the vertex is at the origin?The equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number, is:
(y - k)² = 4p( x - h)
If the vertex is at the origin (h = 0, k = 0 ), the equation an be simplified to....
y² = 4px
where p is still a nonzero real number.
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Natasha is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 20 inches × 15 1 4 inches. She needs to cut another rectangle that is 10 1 2 inches by 10 1 4 inches. How many total square inches of construction paper does Natasha need for her project? Mixed number
What is the value of X? (Thx for any help!)
Answer:
x=109 y=100
Step-by-step explanation:
Answer:
x=100
y=109
Step-by-step explanation:
For any quadrilateral (4-sided shape) inscribed in a circle (all 4 vertices of the quadrilateral are on the edge of the circle), there is a special relationship between certain pairs of angles within the quadrilateral.
Specifically, opposite angles (angles across from each other) must sum (add) to 180 degrees.
The angle measuring 80 degrees is opposite the angle measuring x degrees, so x + 80 = 180, implying x = 100.
In this case, the angle measuring 71 degrees is opposite the angle measuring y degrees. So, 71 + y = 180, which implies y = 109.
On Low Budget Airlines, the maximum weight of the luggage a passenger can bring without charge is 50 pounds. Mary Ellen has decided to weigh each item as she packs her bag. Use rounding to the nearest one pound to estimate the weight of her luggage.
The estimated weight is pounds.
Answer: 50 pounds
Step-by-step explanation:
The maximum weight of the luggage a passenger can bring without charge is 50 pounds.
Mary Ellen has decided to weigh each item as she packs her bag.
weight of Suitcase = 3.65 lbs
weight of clothing = 4.35 lbs
weight of shoes = 8.67 lbs
weight of toiletries = 11.35 lbs
weight of extras = 21.63 lbs
Now we will add the weights of each items
Total weight = 3.65 + 4.35 + 8.67 + 11.35 + 21.63 = 49.65
Rounding to the nearest to the one pound will be = 50 lbs
(Since 0.65 is greater than 0.5 so by rounding off 0.65 will become 1.)
Therefore the estimated weight is 50 pounds.
A small country emits 80,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 2.5% per year for the next 7 years. In the first year of the agreement, the country will keep its emissions at 80,000 kilotons and the emissions will decrease 2.5% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 7 year period, to the nearest whole number?
Using an exponential function and integration, it is found that over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.
Exponential function:
A decaying exponential function is modeled by:
⇒ A (t) = A (0) (1 - r)ⁿ
In which:
A(0) is the initial value.
r is the decay rate, as a decimal.
In this problem:
In the first year, the country emits 80,000 kilotons, hence . A (0) = 8000
Emissions will decrease 2.5% in each successive year, hence r = 0.026
Then, the equation for the amount emitted each year is:
⇒ A (t) = A (0) (1 - r)ⁿ
⇒ A (t) = 80000 (1 - 0.025)ⁿ
⇒ A (t) = 80,000 (0.975)ⁿ
The total amount emitted over the course of the 11 year period is:
T = ∫ 0 to 11 ( A (t) ) dt
Hence:
T = ∫ 0 to 11 ( 80000 (0.974)ⁿ ) dt
Applying the Fundamental Theorem of Calculus:
T = 763,968 kilotons
Hence, Over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.
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Mrs. Hopkins gives her students a math quiz every 8 and a science quiz every 6 days. If she gives math and science quizzes today, how many days will it be before both quizzes are given on the same day again?
Therefore , the solution of the given problem of unitary method comes out to be once more administer maths and science quizzes on the same day.
Definition of a unitary method.The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.
Here,
List the multiples of each integer until we discover a common multiple as one method to determine the least common multiple:
=> 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80 are all multiples of 8.
=> 6, 12, 18, 24, 30, 36, 42, 48, 54, and 60 are multiples of 6.
As an alternative, we can use the prime factorization technique to identify the smallest common multiple:
=> 8's prime factors are 2 x 2 x 2
=> 6's prime factors are 2 x 3
=> 2 x 2 x 2 x 3 = 24
We can see that 24 is the smallest common multiple once more, and in 24 days,
Mrs Hopkins will once more administer maths and science quizzes on the same day.
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100 POINTS!!!
Question
Answer:
A) Sequence 2: 15,13,11,9,7
A) Ordered pairs (12,15), (16,13), (19,11), (22,9), (25,7)
B) Sequence 1: 1,5,17,53,161
B) Sequence 2: 6,15,33,69,141
B) Ordered pairs (1,6), (5,15), (17,33), (53, 69) (161,141)
Step-by-step explanation:
Helping in the name of Jesus.
Answer:
A) Sequence 2: 15,13,11,9,7
A) Ordered pairs (12,15), (16,13), (19,11), (22,9), (25,7)
B) Sequence 1: 1,5,17,53,161
B) Sequence 2: 6,15,33,69,141
B) Ordered pairs (1,6), (5,15), (17,33), (53, 69) (161,141)
Step-by-step explanation:
Helping in the name of typing.
pleaseeeee i need helppp in this
The resulting matrix formed by performing R2 -> 4R1 + R2 on M is given as follows:
[tex]M = \left[\begin{array}{ccc}-4&3&1\\-18&9&8\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]M = \left[\begin{array}{ccc}-4&3&1\\-2&-3&r\end{array}\right][/tex]
The rows of the matrix are given as follows:
R1: -4, 3 and 1.R2: -2, -3 and 4.Hence the row 2 of the resulting matrix has the elements given as follows:
Column 1: 4 x -4 - 2 = -18.Column 2: 4 x 3 - 3 = 9.Column 3: 4 x 1 + 4 = 8.More can be learned about operations with matrices at brainly.com/question/16901354
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A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took
13.5
m
2
13.5 m
2
13, point, 5, start text, space, m, end text, squared of material to build the cube.
What is the volume inside the giant sugar cube?
Give an exact answer (do not round).
The volume of the inside of the giant sugar cube would be = 3.375cm³
How to calculate the volume of a cube using the given surface area?To calculate the volume of a cube, the side length should first be determined from the surface area given.
But the formula for surface area of a cube = 6a²
That is;
surface area = 13.5cm²
a = ?
13.5 = 6(a)²
13.5/6 = a²
a = √13.5/6
= √2.25
= 1.5cm
Therefore the volume of the cube = a³
= 1.5³
= 3.375cm³
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Complete question:
A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 13.5m² of material to build the cube. What is the volume inside the giant sugar cube? Give an exact answer (do not round).
Enter your answer by filling in the boxes.
The correct statement regarding the end behavior of the function is given as follows:
As x -> -∞, f(x) -> +∞.As x -> +∞, f(x) -> +∞.What is the end behavior of a function?The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.
The function in this problem is given as follows:
f(x) = 2(x - 4)² + 3.
We have the square of a number, which is always positive, hence the function goes to positive infinity when the input goes to negative infinity/positive infinity.
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the slope between the points -3, 0 and 0, -1 ?
Answer:
Step-by-step explanation:
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m = [tex]\frac{-1-0}{0+3}[/tex]
m = [tex]\frac{-1}{3}[/tex]
Answer: -[tex]\frac{1}{3}[/tex]
Select all true statements about the graph that represents y=2x(x−11) .
The correct answers for the quadratic equation are:
Roots of a quadratic equation are the points where y = 0.
Abscissa of a quadratic equation are the points where x = 0.
If the equation of a quadratic equation is in the vertex form,
y = a(x - h)² + k
Vertex of the U-shaped curve will be (h, k)
Given in the question, where the equation of the u-shaped curve is
y = 2x(x - 11)
Convert the equation in the vertex form,
y = 2x² - 22x
y = 2(x² - 11x)
y = 2 * (x² - 2 ( 5.5x) + (5.5)² - (5.5)²)
y = 2[(x - 5.5)² - 30.25]
y = 2(x - 5.5)² - 60.5
Hence, the vertex of the U-shaped curve will be (5.5, -60.5).
For x-intercepts,
Substitute y = 0,
0 = 2x(x - 11)
⇒ x = 0, 11
Therefore, roots of the parabola will be (0, 0) and (11, 0).
and the ordinate of the vertex is x = 5.5
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I know how to use the explicit formula to find a_1, but having a_n-1 being multiplied by 2 has thrown me for a loop. I am not sure how to fit it into the formula.
The first four elements of the sequence are:
a11 = 5350
a12 = 10702
a13 = 21406
a14 = 42814
How to calculate the sequenceStarting with a11 = 5350, we can use the recursive formula to find a12:
a12 = 2a11 + 2 = 25350 + 2 = 10702
a13 = 2a12 + 2 = 210702 + 2 = 21406
a14 = 2a13 + 2 = 221406 + 2 = 42814
Therefore, the first four elements of the sequence are:
a11 = 5350
a12 = 10702
a13 = 21406
a14 = 42814
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Find the principal needed now to get the given amount; that is, find the present value. To get $4000 after 2 1/4 years at 9% compounded daily The present value of $4000 is $? (Round to the nearest cent as needed.)
Step-by-step explanation:
Compounding formula
FV = PV ( 1 + i )^n FV = Future value (4000) PV = present value
i = decimal interest per PERIOD = .09/365
n = periods = 2 1/4 yrs * 365 days/yr = 821.25 periods
4000 = PV ( 1 + .09/365)^821.25
Solve for PV = $ 3266.83
Please HELPP!!!!! Angles !! Marking brainliest whoever awnsers
Answer: IN ORDER FROM TOP LEFT OVER
Step-by-step explanation:
1. Example
2. Already correct
3. 43
4. 82
5. Supplementary
6. 68
7. 33
8. Adjacent (could be wrong)
9. 51
10. 128
11. 54
12. Complimentary
13. Parallel
14. 29
15. 117
HOPE THIS HELPS. I MAY HAVE GOTTEN 1 OR 2 WRONG.
. Suppose that the following represents the graph of the function f(x).
N
a. (5 points) Determine the x intercepts and give a number line for the function
f(x). Are there any horizontal or vertical asymptotes?
b. (5 points) Give a number line for f'(x) and classify any local maxima or minima.
c. (5 points) Give a number line for f"(x) and list any points of inflection.
The x intercepts are (-2, 0), (2, 0) and (3, 0) and it has vertical asymptotes at x = 4 and x = -4
Determining the x interceptsThe x intercepts are the points where the graph intersect with x-axis
In this case, the points are (-2, 0), (2, 0) and (3, 0)
So, the x intercepts are (-2, 0), (2, 0) and (3, 0)
Are there any horizontal or vertical asymptotes?The graph has no horizontal asymptotes
However, it has vertical asymptotes at x = 4 and x = -4
The local maxima or minimaFrom the graph, the local maxima or minima are
Minima (3, -1) and Maxima (-1, 12)
The point of inflectionThis is the points where the graph changes it concave-ness
From the graph, we have the point to be (1, 13/2)
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Can you guys help me out?
Step-by-step explanation:
For f(3) 3 is >= 2 so you use the second portion of the function :
f(3) = 5x+2 = 5(3) + 2 = 17
