Answer:
21
Step-by-step explanation:
The following stem-and-leaf plot represents the test scores for 26 students in a class on their most recent test. Use the data provided to find the quartiles.
Stem Leaves
6 0 1 2 2 4 7 8
7 0 1 2 5 8
8 3 6 6 7 9 9
9 0 1 2 2 2 4 5 8
Key:
6|0=60
Find the first quartile and third quartile
Considering the given data-set, the quartiles are given as follows:
The first quartile is of 67.5.The third quartile is of 91.5.What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, the first half is the 12 elements from 1 to 12, and the second half is the 12 elements from 15 to 26.
The first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:
Q1 = (67 + 68)/2 = 67.5.
The third quartile is the mean of the 6th and 7th elements of the second half, hence:
Q3 = (91 + 92)/2 = 91.5.
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18. Identify a transformation of the function f(x) = « by observing the equation of the function g(x) = x + 3.
The function shows a horizontal shift of the function to the right by 3 units
Transformation of functionsTransformation is a techniques used to change the position of an object on an xy-plane. Given the parent function f(x) = x
The translated function g(x) = x + 3 shows a horizontal shift of the function to the right by 3 units
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In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now?
Choose the most logical value for the variable to represent.
Let x = .
Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.
How old is Dianna now?
Given that, in 3 years, Dianna will be 4 times as old as she was 33 years ago.
Let x represent the age of Dianna presently.
Dianna's age in 3 years time will be: x + 3
Dianna's age 33 years ago is: x - 33
Since in 3 years, she will be 4 times as old as she was 33 years ago.
x + 3 = 4( x - 33 )
We solve for x
x + 3 = 4x - 132
3 + 132 = 4x - x
135 = 3x
x = 135/3
x = 45
Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.
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Find the trigonometric form of the number 3 + √3i.
Any complex number [tex]z[/tex] can be written in trigonometric form as
[tex]z = |z| e^{i\arg(z)} = |z| \left(\cos(\arg(z)) + i \sin(\arg(z))\right)[/tex]
where [tex]|z|[/tex] is the modulus of [tex]z[/tex] and [tex]\arg(z)[/tex] is its argument, i.e. the angle [tex]z[/tex] makes with the positive real axis in the complex plane.
We have
[tex]|z| = \sqrt{3^2 + \left(\sqrt3\right)^2} = \sqrt{12} = 2\sqrt3[/tex]
and
[tex]\arg(z) = \tan^{-1}\left(\dfrac{\sqrt3}3\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6[/tex]
Then
[tex]3 + \sqrt3 \, i = \boxed{2\sqrt 3 \left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)}[/tex]
NEED ANSWER ASAP
The graph of F(x), shown below, resembles the graph of G(x) = x², but it has
been changed somewhat. Which of the following could be the equation of F(x)
[tex]f(x) = - 3(x + 3) {}^{2} + 3[/tex]
Option DAustin taxi charges $5 plus $0.30 per mile for fare city. What will be the linear equation for the charges if use Austin’s taxi?
I need help please. Trying to get my HS diploma. I did not graduate :(
Find the holes of the function
Answer:
(a) none
Step-by-step explanation:
A "hole" in the graph of f(x) is located at an x-value where the left limit of the function and the right limit are the same finite value, but the function is undefined at that value of x.
ExampleThe function f(x) = (x -2)/(x -2) can be reduced to the function f(x) = 1, which is defined everywhere. That reduction occurs when the numerator factor (x-2) cancels the same binomial denominator factor. A graph of the original function will be a straight horizontal line with a "hole" at (2, 1).
The attachment shows a graph.
Given FunctionThe given function can be reduced, but the reduced function remains undefined at x=1/2. Not all of the denominator factors are cancelled there. The function is graphed in the second attachment. At x=1/2, there is a vertical asymptote, not a hole.
[tex]g(x)=\dfrac{(2x-1)(x+4)^2(x-1)(3x+2)}{3x(x-4)(2x-1)^3}\qquad x\notin \left\{0,\dfrac{1}{2},4\right\}\\\\g(x)=\dfrac{(x+4)^2(x-1)(3x+2)}{3x(x-4)(2x-1)^2}\qquad x\notin \left\{0,\dfrac{1}{2},4\right\}[/tex]
There are no holes in the function's graph.
__
Additional comment
A hole can occur for a variety of reasons. In the graph of a rational function, it will generally be found where numerator and denominator zeros cancel each other completely, and the function can be "reduced" to one that is define at the location of those zeros.
It can also occur in piecewise defined functions, where the pieces are defined on adjoining (half) open intervals. For example:
[tex]f(x)=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x > 0\end{cases}[/tex]
has a hole at (0, 0).
Can u help me with number 7 I
Answer:
Scalene Triangle
Step-by-step explanation:
Defn
When all the three sides of the triangle are of different measures, it is a scalene triangle.
Answer:
It is a scalene triangle since all sides have different measurements.
Step-by-step explanation:
if kokichi has 25 pencils and his classmate nagito borrowed 13, how many pencils does kokichi have?
Answer:
25-13=12 kokichi has 12 left
Step-by-step explanation:
hope it helps sorry if I'm wrong
Answer:
Basic math 25 - 13 = 12
Step-by-step explanation:
Determine the measure of the interior angle at vertex C
A. 180
B. 54
C. 240
D. 144
The measure of the interior angle at vertex C is D. 144.
How to calculate the angle?Based on the information given, the angle will be calculated thus:
8x + 8x + 8x + 3x + 3x = (5 - 2) × 180
30x = 540
Divide both side by 30
30x/30 = 540/30
x = 18
Therefore, at vertex C, we have 8x. This will be:
= 8x
= 8 × 18
= 144
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estimate 10,867+26,186 by first rounding to the nearest thousand.
Answer:
37,000
Step-by-step explanation:
10,867 rounds to 11,000 and 26,186 to 26,000. 11,000 + 26,000 = 37,000
Which distance formula or formulas show(s) a joint variation?
d=r•t , formula show a joint variation , Option C is the answer.
What is a Joint Variation ?The variation when a variable is dependent upon two or more variables and varies directly as either of them are taken constant is called Joint Variation.
According to the question , which among the options shows a Joint Variation.
Option 1 d = 50 t
It shows direct variation , as increase in t will directly increase d 50 times * the increase
Option 2 d = 16t²
It also shows direct square variation .
Option 3 d=r•t
In this variation d is dependent on two variables and so it is a joint variation.
Therefore Option C is the answer.
The complete question is ?
Which distance formula or formulas show a joint variation? d=50t, d=16t^2, d=r•t
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The answer to this problem?
The simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]
How to simplify the expression?The expression is given as:
[tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex]
Divide 162 and 2 by 2
[tex]\sqrt{\frac{81x^9}{x^{27}}}[/tex]
Take the square root of 81
[tex]9\sqrt{\frac{x^9}{x^{27}}}[/tex]
Apply the quotient rule of indices
[tex]9\sqrt{\frac{1}{x^{27-9}}}[/tex]
Evaluate the difference
[tex]9\sqrt{\frac{1}{x^{18}}}[/tex]
Take the square root of x^18
[tex]\frac{9}{x^9}[/tex]
Hence, the simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]
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Write in expanded form. Use parentheses to indicate multiplication.
(-a)^3
The expanded form of the expression; (-a)^3 is; (-a)(-a)(-a).
What is the expanded for. if the expression?It follows from the task content that the expanded form of the expression given is to be written.
On this note, the expression (-a)³ can simply be rewritten in it's expanded form as; (-a)(-a)(-a).
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Type the correct answer in each box.
The inverse of the function are respectively; f⁻¹(3) = 2 and f⁻¹(8) = 8.5
How to find the inverse of a Function?The formula to find the equation of this function using two coordinates is;
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
Using the first 2 coordinates, we have;
(y - 1)/(x + 1) = (3 - 1)/(2 + 1)
(y - 1)/(x + 1) = 2/3
3y - 3 = 2x + 2
3y = 2x + 5
y = ¹/₃(2x + 5)
Thus, the inverse is;
f⁻¹(x) = (3x - 5)/2
Thus;
f⁻¹(3) = (3*3 - 5)/2
f⁻¹(3) = 2
Similarly;
f⁻¹(x) = (3x - 5)/2
Thus;
f⁻¹(8) = (3*8 - 5)/2
f⁻¹(8) = 8.5
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PLEASE PLEASE HELP THANK YOU SO MUCH UE AMAZING
Answer:
2MN=RA+TP
13×2=x+18
26=x+18
26-18=x
8=x
Amanda, Rafael, and Michael served a total of 92 orders Monday at the school cafeteria. Rafael served 2 times as many orders as Michael. Amanda served 8 more than Michael.
How many orders did they each serve?
The number of orders Michael, Rafael and Amanda served are 16.8, 33.6, and 41.6 servings
respectively.
EquationMichael = xRafael = 2xAmanda = 2x + 8Total servings = 92 ordersx + 2x + (2x + 8) = 92
3x + 2x + 8 = 92
5x = 92 - 8
5x = 84
x = 84/5
x = 16.8 servings
Therefore,
Michael = x
= 16.8 servings
Rafael = 2x
= 2(16.8)
= 33.6 servings
Amanda = 2x + 8
= 33.6 + 8
= 41.6 servings
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Rachel runs 7 miles in 80 minutes. At the same rate, how many miles would she run in 64 minutes?
Answer:
[tex]\huge\boxed{\sf 5.6 \ miles}[/tex]
Step-by-step explanation:
Given that,
Rachel runs 7 miles in 80 minutes.
80 minutes = 7 miles
Using unitary method
Divide 80 to both sides
1 minute = 7/80 miles
1 minute = 0.0875 miles
Multiply 64 to both sides
64 minutes = 0.0875 × 64 miles
64 minutes = 5.6 miles
So, Rachel will run 5.6 miles in 64 minutes.
[tex]\rule[225]{225}{2}[/tex]
HELP PLEASE QUICK!
What is the area of the irregular figure below
3. Anneliese spent $58.00 on music items and paid $35.00 on a lay-away item. If she has
-142.00 left in her account, how much did she start with?
A $-49.00
B$93.00
C$135.00
D-$235.00
The amount Anneliese started with before her deductions is -$235.00.
Account balanceAmount spent on music items = $58.00Amount paid for lay-way item = $35.00Total amount spent = $58.00 + $35.00
= $93.00
Amount left in her account = $-142.00
Amount spent is a negative to her accountAmount Anneliese started with = -$93.00 - $-142.00
= -$235.00
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1. Find the volume of the pyramid.
5 in
11 in
9 in
74
The volume of the pyramid with the given length, width and height is 165in³.
What is the volume of the pyramid?The volume of a right rectangular pyramid is expressed as;
V = ( L × W × H ) / 3
Given that;
Length L = 11inWidth W = 9inHeight H = 5inWe substitute into the equation above.
V = ( L × W × H ) / 3
V = ( 11in × 9in × 5in ) / 3
V = 495in³ / 3
V = 165in³
The volume of the pyramid with the given length, width and height is 165in³.
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Which choice is the correct graph of Ix <3?
A +
-6
B++
-6
C
-6
DH
-4
-5
-5
-6 -5
F++
-6
EH
-6
-4
-3
-4
-3
-3
3
-4
-5
-2
-2 -1
OA. Graph A
OB. Graph B
C. Graph C
-3 -2 -1
-2 -1
-20
-2
-3
0
0 1
0
0
-1 0
1
1
1
1
2
2
2
2
2
2
3
3
e
4
3 4
4 5
01
3
4
3
3 4
5
5
5
5
6
6
6
6
6
5
4
6
Answer:
2347 elevated in the cube
Step-by-step explanation:
nashe
Which is the graph of y = 2 – square root of x?
On a coordinate plane, a curved line approaches the grid line at (3, 2.3), crosses the y-axis at (0, 1.5) and ends at (negative 2, 0).
On a coordinate plane, a curved line approaches the grid line at (negative 3, 2.3), crosses the y-axis at (0, 1.5) and ends at (2, 0).
On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).
Using translation concepts, the graph of [tex]y = 2 - \sqrt{x}[/tex] is described as follows:
On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Function [tex]y = 2 - \sqrt{x}[/tex], in blue in the graph, is the function [tex]y = \sqrt{x}[/tex], in red, reflected over the x-axis and shifted 2 units, as shown in the graph.
Hence the correct statement is:
On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).
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what do both of these functions have in common? f(x)=3/2 (x-7) -2 g(x) = 1.5ln(x-2)+7
(x-7) should be absolute value of that.
Both the function have same vertical stretch of 1.5 , Option B is the correct answer.
What is a Function ?A function is a law that relates a dependent and an independent variable.
The functions given in the question is
f(x) = 3/2 |(x -7)| -2
g(x) = 1.5 ln(x-2)+7
For a function f(x)
f'(x) = a f(x) represents the stretching of a function if a> 1
here the value of a = 1.5 for both the functions , so they have same vertical stretch of 1.5 .
Therefore from the options given , Option B is the correct answer.
The complete question is attached as an Image.
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Which type of function best models the data in the table below
The function represented by the table is therefore y = -x -2 which is linear in nature
Linear functionsLinear function are functions that have a leading degree of 1. using the coordinate points on the graph
(0, -2) and (1, -3)
Note that the function will be linear since the dependent and independent variables both have the same common difference.
Determine the slope
slope = -3+2/1-0
slope = -1/1
slope = -1
For the intercept, it is -2 according to the coordinate (0, -2)
The function represented by the table is therefore y = -x -2 which is linear in nature
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9) James purchased a shirt at 20% off. The regular price was $14.95. What was the markdown? What was the final
price?
O a.) a. $2.89; b. $11.46
Ob.) a. $2.99; b. $11.96
Oc.) a. $2.99; b. $11.86
solve this question in the picture
YOU HAVE TO FIND THE AREA OF THE SHADED REIGON IN THE GIVEN PICTURE
●Give right answers
●please solve fast
●Thank you, please solve this part
●FIND the area of the shaded part
Answer: [tex]64\pi[/tex]
Step-by-step explanation:
Area of the outer circle: [tex](\pi)(10^{2})=100\pi[/tex]
Area of the inner circle: [tex](\pi)(6^{2})=36\pi[/tex]
Subtracting these areas, we get the area of the shaded region is [tex]\boxed{64\pi}[/tex]
The sale price of a laptop is R3 700,00, which is only 65% of the original price. Calculate the original price.
The original price of a laptop that is 65% of the sales price is R3 1076923.07692
How to find the original price when given the percentage?The sale price of a laptop is R3 700,00,which is only 65% of the original price.
Therefore,
let
x = original price
Hence,
700, 000 = 65% of x
700,000 = 65 / 100 of x
cross multiply
70000000 = 65x
divide both sides by 65
x = 70000000 / 65
x = 1076923.07692
Therefore, the original price of the laptop is R3 1076923.07692
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a history book weights 24 oz more than a math book. the marh book is 75% the weight of the history book. how much does each book weight
The weight of the math and the history book are 72 and 96 ounces respectively.
How to find the weight of a book?A history book weights 24 oz more than a math book.
Therefore,
let
x = weight of math book
weight of history book = 24 + x
The math book is 75% the weight of the history book.
Therefore,
math book weight = 75 / 100 (24 + x)
x = 75 / 100 (24 + x)
x = 1800 + 75x / 100
100x = 1800 + 75x
100x - 75x = 1800
25x = 1800
x = 1800 / 25
x = 72
Therefore,
weight of math book = 72 ounces
weight of history book = 72 + 24 = 96 ounces.
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The question is below please answer quickly
Answer:
50 metersStep-by-step explanation:
2cm = 5m, so we know that the length is 5m
4cm = 2cm * 2, so the width is 5m * 2, which is 10m.
Now, we multiply them together.
5*10 = 50
The backyard area is 50 meters
Answer:
50m^2
Step-by-step explanation: