Answer: The IQR of this data set is 5.5
Step-by-step explanation: Ok so first you line the data set up in correct order.
Here's the correct order:
13, 15, 15, 16, 18, 19, 22, 28
Then you find the median and since there's even amount of numbers you add the two numbers in the middle which is 16 and 18 and divide that by 2 which is 17. So the median is 17. Then you split the data set into halves. The first quartile is 15 and the third quartile is 20.5. Then to find the IQR, you would minus 20.5 - 15 = 5.5. Hope this helps!
a 110 minute meeting should have a 10 minute break in the middle of two equal parts. How long after the meeting start should the break begin
Answer: 24 minutes and 30 seconds after the meeting as started
Step-by-step explanation:
110 minutes into 2 equal parts = 55 minutes in each section.
In the middle of 55 minutes = subtract the 10 minutes for a break from the 55 minutes that leaves you with 45 minutes. 24 minutes and 30 seconds before and after the 10 minute break.
Total session minutes - 110
Two equal parts of session: 55 minutes in each session
10 minute break in each session: 55-10 =45.
24 minutes and 30 seconds + 10 min break (in middle) + 24 minutes and 30 seconds
After 50 minutes the break will start.
The metting is 110 minutes long. According to the Question the metting have 'a'(only one) break of 10 minutes in between of two equal parts of metting.
so, duration of metting without the break=100 minutes
duration of each part=50 minutes
Now, the break should be after First part which is of 50 minutes.
=> The break should 50 minutes after the starting of metting.
Subtract t⁴-3t²+7 from 5t³-9.
Answer:
t⁴+5t³-3t²-2
Step-by-step explanation:
You can't subtract a variable with a different exponent:
Example:
CAN'T BE SUBTRACTED - 3x²-3x⁴
CAN BE SUBTRACTED - 4x²-2x²=2x²
[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]
Step-by-step explanation:1. Write the expression.[tex]\sf (5t^{3} -9)-(t^{4}-3t^{2} +7 )[/tex]
2. Remove the parenthesis.Beware of the terms of the right hand side parenthesis, as we'll have to change the symbol of all of them because of the minus (-) symbol infront of the parenthesis.
[tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]
3. Work with like terms.Like terms are terms that contain the same variables and can be added and subtracted simply. For example, 7x and 2x are like terms, because they are both expressed in terms of x. However, 7x and x² are not like terms, because one os expressed in terms of x and the ither in terms of x².
• Note: All natural numbers not being multiplied by any variables are like terms.
So now let's identify those like terms:
From this expression: [tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]
Only -9 and -7 are like terms. And, since -9-7= -16, the resulting expression should be the following:
[tex]\sf 5t^{3} -t^{4}+3t^{2} -16[/tex]
4. Order the terms correctly.So even though the last expression is the answer to this problem, we can polish it a little bit by ordering the terms. In math and other exact sciences, terms are normally ordered alphabetically and from greatest to least of it's the same variable with different exponents. Therefore, the final answer is:
[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]
Use mathematical induction to prove that the statement is true for all positive integers: 30 + 138 + 318...
The mathematical induction has been used to prove that the statement is true for all positive integers: 30 + 138 + 318.
What is mathematical induction?In mathematics, mathematical induction is a way of proving propositions. The method entails demonstrating that a statement is true for a base case, usually the smallest feasible value, and then demonstrating that if the statement is true for some value, it is likewise true for the next value.
The key to the proof is the inductive step. It is typically accomplished by assuming that the statement is true for some value and then utilizing that assumption to establish that the statement is true for the following value.
Check the attachment.
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11. Which of the following are not meaningful?
(b) XXXI
(a) VXXIX
(C) XLIV
12. Write 'Divide the difference of 91 and 7 by 6' using brackets and solve.
(d) CXCLXV
what type of number is 15/10?
Answer:
1.5
Step-by-step explanation:
its a decimal number
Answer: the number 15/10 is a fraction.
Step-by-step explanation:
any two numbers that have a slash in the middle are fractons. :)
Please help !!!!!!!!!!!!!!!!!!!!!!
2) The way the coordinates show the given scale factor is that the ratio of both x and y coordinates to the mapped coordinate before dilation are all equal.
3) The coordinates after dilation are: (5.4, 27)
How to use scale factor dilation?2) The coordinates transformed points after dilation are completed as:
B(2, 4) → B'(3, 6)
K(4, -4) → K'(6, -6)
N(-6, 0) →N'(-9, 0)
The scale factor is same because using the ratio of the x coordinates gives:
3/2 = 1.5
6/4 = 1.5
-9/-6 = 1.5
3) The point W of the vertex of the polygon has coordinates as (2, 10)
Thus, if dilated by a scale factor of 2.7, we have the new coordinates as:
(2*2.7, 10*2.7) = (5.4, 27)
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20x-12 factor out gcf in order to rewrite expression
Question 20 of 42
Which of the following is a type of data that is likely to be normally
distributed?
A. The weights of all the 5-year-olds in the United States
B. The outcomes of a fair die rolled 100 times
C. The number of students in a class who get a perfect score on a
test
D. The number of students in a class who get a B on a test
Answer: Option B, the outcomes of a fair die rolled 100 times, is likely to be normally distributed.
Step-by-step explanation:
Answer: Option B, The outcomes of a fair die rolled 100 times
Step-by-step explanation:
that would most likely be normally distributed.
hope it helped! Good luck!!! :)
2y+3y-18=-83?????????????
Answer:
-13
Step-by-step explanation:
What meaning of the statement this?
We can see here that the statement means that H is a subgroup of a group, and aЄ H is an element of that subgroup.
What is a mathematical statement?We can define a mathematical statement to be a claim that, depending on the circumstances, may be true or false. It frequently incorporates mathematical objects and their relationships or characteristics, such as integers, sets, functions, or geometric shapes.
We can see here that it shows that a is an element of the subgroup of H.
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A man has 16 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.50, how many dimes and how many quarters does he have?
Let d = number of dimes, q = number of quarters.
Step one:
A man has 16 coins in his pocket, all of which are dimes and quarters.
Set up the first equation for the number of dimes and quarters. Help PLS
Answer: 10 dimes and 6 quarters, see below for the equations.
Step-by-step explanation:
We know how much a dime is worth and how much a quarter is worth, and they give us the total number of coins and the total number of change.
This equation shows the total number of coins:
d + q = 16
This equation shows the worth of these coins:
0.10d + 0.25q = 2.5
Now, we can graph these equations. See attached. The point of intersection, where the lines cross, is our solution. In the graph, d = x and q = y.
This point is (10, 6) meaning he has 10 dimes and 6 quarters in his pocket.
Pls help
The shape below contains a rectangle and four semi-circles.
Round your responses to two decimal places.
What is the perimeter of the shape above?
What is the area of the shape above?
Answer:
perimeter: 47.12 unitsarea: 151.60 square unitsStep-by-step explanation:
You want the perimeter and area of a figure consisting of a 4 × 11 rectangle with semicircles attached to each straight edge.
PerimeterIf you trace the perimeter of the figure, you see you are tracing the circumference of a circle 4 units in diameter and the circumference of a circle that is 11 units in diameter. The circumference of a circle is given by ...
C = πd
so the total circumference is ...
C1 +C2 = π(4) +π(11) = π(4+11) ≈ 47.12 . . . . units
The perimeter of the figure is about 47.12 units.
AreaThe area of two half-circles is the area of one whole circle of the same diameter. The area of a circle of diameter d is given by ...
A = (π/4)d²
The total area of the circles of diameters 4 and 11 is ...
A1 +A2 = (π/4)·4² +(π/4)·11² = (π/4)(4² +11²)
The area of the central rectangle is added to the areas of the semicircles. Its area is ...
A = LW
A = (11)(4)
TotalThe area of the entire figure is the sum of the circle areas and the rectangle area:
total area = (π/4)(4² +11²) +(4)(11) ≈ 151.60 . . . . square units
The area of the figure is about 151.60 square units.
__
Additional comment
You usually see the formula for the area of a circle as ...
A = πr²
Since r = d/2, we can express this using d as ...
A = π(d/2)² = π(d²)/(2²) = (π/4)d²
You may notice that a square that circumscribes the circle will have a side length of d, and an area of d². The fraction π/4 tells you the fraction of that enclosing square that is covered by the circle. This fact can help you estimate areas and volumes of circles and cylinders.
Solve the following for θ, in radians, where 0≤θ<2π.
2cos2(θ)−8cos(θ)−1=0
Select all that apply:
1.07
1.69
4.59
2.49
2
2.33
Answer:correct answers 1.69
4.59
Step-by-step explanation:
We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
2u^2 - 8u - 1 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 2, b = -8, and c = -1. Substituting these values, we get:
u = (8 ± sqrt(8^2 - 4(2)(-1))) / 2(2)
u = (8 ± sqrt(72)) / 4
u = 2 ± sqrt(18)
Therefore, either:
Let p be the constant function p (z) = 1,000,000,000. Let q be the exponential function q (2) = 10
The product of the two functions is (pq) (z) = 10ª-2, where a is a constant. What is the value of a?
C2023 Illuminate Education, Inc.
P
C
[tex]\large \boxed{\mathrm{10}}[/tex]
The constant function p has a fixed output of one billion, while the exponential function q has a base of two and an output of 10. As the input increases by one, the output of q doubles. For example, q(3) = 20 and q(4) = 40. The rate of growth of q is much faster than p. In fact, q will eventually surpass p for large enough inputs. This demonstrates the power of exponential growth and highlights the importance of understanding the functions used in equations and models.
Answer:
10 or 1b
Step-by-step explanation:
Determine which of the following statements is true concerning the values described in column #1 and column #2. (1 point)
Column #1
Column #2
The x-coordinate of the vertex of the graph of The x-coordinate of the vertex of the graph of
y=-2x² - 4x + 12
y=x²-4x+3
O The value found in column #1 is greater than the value found in column #2.
The value found in column #1 is less than the value found in column #2.
O The value found in column #1 is equivalent to the value found in column #2.
The relationship between column #1 and column #2 cannot be determined by the information given.
8
The statement which is true concerning the values described in column #1 and column #2 is: B. The value found in column #1 is less than the value found in column #2.
How to determine the x-coordinate of the vertex of the graph?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = -2x² - 4x + 12, we have:
Axis of symmetry, Xmax = -(-4)/2(-2)
Axis of symmetry, Xmax = 4/-4 = -1.
For the vertex of f(x) = -2x² - 4x + 12, we have:
f(-1) = -2(-1)² - 4(-1) + 12 = 14.
For the given quadratic function f(x) = x²-4x+3, we have:
Axis of symmetry, Xmax = -(-4)/2(1)
Axis of symmetry, Xmax = 4/2 = 2.
For the vertex of f(x) = x²-4x+3, we have:
f(2) = (2)²-4(2) +3 = -1.
Therefore, 2 is greater than -1.
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what are the coordinates of the point that corresponds to -5pi/4 on the unit circle
The coordinates of the point that corresponds to -5π/4 on the unit circle is (-1/√2, 1/√2).
Given that,
We have to find the coordinates of the point that corresponds to -5π/4 on the unit circle.
We know that any point on the unit circle can be defined as,
(cos θ, sin θ)
where θ is the angle formed with the X axis.
-5π/4 will be the point the corresponds to -225°.
Cos(-5π/4) = cos (5π/4)
= cos (π + π/4)
= -cos (π/4)
= -1/√2
sin (-5π/4) = -sin (5π/4)
= -sin (π + π/4)
= sin (π/4)
= 1/√2
Hence the coordinate of the unit circle is (-1/√2, 1/√2).
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Given the unit circle what is the value of y PLEASE HELP
Answer: √35/6
Step-by-step explanation:
see image for explanation
A quantity shrinks at a continuous rate of
per year. Its effective growth rate is
per year.
Answer:
Based on the information provided, there seems to be a discrepancy between the given information about the quantity shrinking at a continuous rate and the requested information about its effective growth rate. If a quantity is shrinking continuously, it is not experiencing growth, and therefore there is no effective growth rate. Nonetheless, assuming that the requested information was about the effective shrinkage rate of the quantity per year, this information can be extracted from the given information that "A quantity shrinks at a continuous rate of 33% per year." The effective shrinkage rate of the quantity can be calculated as follows:
Let r be the continuous shrinkage rate of the quantity
The effective shrinkage rate of the quantity is given by the expression (1 - r).
From the given information , r = 33% = 0.33.
Therefore, the effective shrinkage rate of the quantity is (1 - r) = (1 - 0.33) = 0.67 or 67% per year.
Note that if the phrase "effective growth rate" was a mistake, and the original intent was to ask for the shrinkage rate, then the above calculation gives the answer. Otherwise, further clarification is needed.
You may be interested in visiting A quantity's size after t years is given by A(t) =...
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Step-by-step explanation:
The question refers to the concept of continuous growth or shrinkage, and the effective growth rate in a financial context. Despite missing figures, assuming a quantity shrinks at a continuous rate of 3% and its effective growth rate is 2%, it implies a net shrinkage is 1% annually.
Explanation:The question pertains to the subject of compound interest in finance, but it appears that some of the figures and percentages are missing. However, generally speaking, continuous growth or shrinkage refers to the rate at which a quantity increases or decreases for a specific period of time. The effective growth rate is a term in finance that is used to compare the annual interest rates between financial products that have different compounding terms. For instance, if a quantity shrinks at a continuous rate of 3% per year, and its effective growth rate is 2% per year, it means that net shrinkage is 1% per year.
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Which of the following is a statistical question that can result in numerical data?
What is the name of the librarian at your local library?
Which park is the best one to take your dogs to play?
What is the name of a local farm in your area?
How many students at your school ride horses?
Calculator
What is the volume of this figure?
Enter your answer in the box.
ft³
4
3 ft
5 ft
6 ft
7 ft
2 ft
Answer:
The answer should be 1,260
Answer:
75
Step-by-step explanation:
.
which equation represents a parabola opening downward with a vertex of the origin and a focus at (0,-1)?
y= -1/4x^2
y=1/4x^2
y=1/12x^2
y=-1/12x^2
prove the identity tan3x-tanx =2sinxsec3x
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and do all 3. :) (Do the one highlighted)
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions.
Which of the following is not an exponential function?To determine which option is not an exponential function, we will apply general equation of an exponential function.
f(x) = aⁿ
where;
a is the base of the functionn is the exponentSo from the given options;
(³/₅)ˣ is an exponential function, because ³/₅ is the base while x is the exponent.
4ˣ is an exponential function, because 4 is the base while x is the exponent.
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions, so there is no one base.
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You invest $4000 in an account to save for college.
a. Option 1 pays 5% annual interest compounded semi-annually. What would
be the balance in the account after 2 years?
b. Option 2 pays 4.5% annual interest compounded continuously. What would
be the balance in the account after 2 years?
c. At what time t (in years) would Option 1 give you $100 more than Option 2?
The answers to the given questions about annual interest are given below:
a. $4,415.25b. $4,376.70c. 2.27986 yearsHow to solvea.
A = 4,000 (1 + 0.05/2)^(2 x 2)
= $4,415.25
b.
A = 4,000 x e^(0.045 x 2)
= $4,376.70
c. $100 more than option 2 = 4,376.70 + 100
= $4,476.70
t (in years) = ln(4,476.70/4,000) / ln(1 + 0.05/2)
= 2.27986 years
Annual interest denotes the rate of interest levied or gained on a loan or investment for a duration of one year. This indicates the portion, expressed as a percentage, of the original amount that is utilized for interest payments or gained as a profit within a twelve-month period.
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Pls help Thanks!!!!!!!!!!!
Answer:
Put your calculator in degree mode.
[tex] \cos(x) = \frac{12}{13} [/tex]
[tex]x = {cos}^{ - 1} \frac{12}{13} = 22.6[/tex]
Angle x measures 22.6°.
Consider the line y=8x-7
Find the equation of the line that is parallel to this line and passes through the point (5,-3)
Find the equation of the line that is perpendicular to this line and passes through the point (5,-3)
Answer:
Parallels lines:
y = 8x - 43
Perpendicular line:
y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]
Step-by-step explanation:
y = 8x -7
Parallel lines have the same slope.
The slope will be 8. We will use the x from the point (5,-3) and the y from the point (5,-3) to find the y-intercept (b)
y = mx + b Substitute in -3 for y, 8 for m, and 5 for x.
-3 = 8(5) + b
-3 = 40 + b Subtract 40 from both sides
-3 - 40 = 40 - 40 + b
-43 = b
Substitute in 8 for m and -43 for b to write the equation
y = mx + b
y = 8x - 43
Perpendicular slope are opposite reciprocals of each other, so the perpendicular slope is [tex]\frac{-1}{8}[/tex]
Substitute [tex]\frac{-1}{8}[/tex] doe m, -3 for y and 5 for x.
y = mx + b
-3 = [tex]\frac{-1}{8}[/tex](5) + b
-3 = [tex]\frac{-5}{8}[/tex] + b add [tex]\frac{5}{8}[/tex] from both sides
-3 + [tex]\frac{5}{8}[/tex] = [tex]\frac{-5}{8}[/tex] + [tex]\frac{5}{8}[/tex] + b
[tex]\frac{-24}{8}[/tex] + [tex]\frac{5}{8}[/tex] = b
[tex]\frac{-19}{8}[/tex] = b
Substitute [tex]\frac{-1}{8}[/tex] for m and [tex]\frac{-19}{8}[/tex] for b
y = mx + b
y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]
Helping in the name of Jesus.
Need help with this 50 Points
Answer:
8.) is D
9.) is B
10.) is A
Step-by-step explanation:
mark brainliest
Answer: D, B, A
Step-by-step explanation:
When multiplying or dividing - and + numbers, rules are as follows:
If the signs are the same, your answer will be +
[tex]\frac{-a}{-b} =+\frac{a}{b}[/tex]
[tex]\frac{+a}{+b} =+\frac{a}{b}[/tex]
If the signs are different, your answer will be -
[tex]\frac{-a}{+b} =-\frac{a}{b}[/tex]
[tex]\frac{+a}{-b} =-\frac{a}{b}[/tex]
If there is no sign in front of number, it is positive
8.
a. 18 / -9 = -2 negative because signs are diff
b. -35 / -7 +5 signs same so +
c. -12 / -6 = +2 same signs so +
d. 70 / -10 = -7 diff signs so -
Order from least to greatest:
-7 -2 2 5
Answer: D
9. Follow rules from above:
Be careful with fractions 1/5 is not the same as 5/1.
With the fraction problems they do not divide into the number because 1 cannot be divided by 5 evenly, leave as a fraction and we are only taking care of the signs.
a. +1/5
b. -1/5
c. +1/10
d. +1/10
Order from least to greatest:
-1/5 1/5 1/10 1/10
Answer: B
10.
a. -2/3
b. +1/25
c. +3/25
d. +1/50
The smallest number is the negative number
Answer A
POSSIBLE POINTS: 10
Find the area of the composite figure below. Area of Triangle = bh, Area of Rectangle = lb Use Pythagorean formula to find the length () of the
Rectangle.
7 mm
10.4 mm
15.3 mm
The total surface area of the composite figure is: 288.62 mm²
What is the area of the composite figure?From the attached image, we can see that the composite figure is made up of 2 triangles and one rectangle. Thus:
Formula for area of rectangle is:
A = Length * Width
Formula for area of triangle is:
A = ¹/₂ * base * height
Using Pythagoras theorem, length of rectangle is:
L = √(10.4² + 15.3²)
L = 18.5 mm
Thus:
TSA = (18.5 * 7) + 2(¹/₂ * 15.3 * 10.4)
TSA = 129.5 + 159.12
TSA = 288.62 mm²
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Financial aid letters show your aid and costs of attendance for
one year
O four years
the entire time you plan on attending
a semester
Financial aid letters display aid and attendance costs for one year only. Some schools offer a financial aid letter for four years of undergrad, aiding in budget planning for the program.
What is the Financial aid?A few schools may give a budgetary help letter that ventures aid and costs for all four a long time of an undergrad program. This could offer assistance understudies arrange and budget for their whole undergrad instruction.
In a few cases, Financial aid letters may show aid and costs for a single semester, instead of the complete scholarly year. This could be valuable for understudies who are as it were going to part-time or who got to take a semester off.
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What is the equation of the line shown in this graph?
Answer:
The equation is y=-3
Step-by-step explanation:
The line is horizontal, cutting across the y-axis, which means it will be a y= line. The point it hits the y-axis is -3, so it is y=-3.