The largest proper fraction that can be formed is 16/17
What is a fraction?
A fraction (from the Latin fractus, "broken") is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction has a numerator above a line (or before a slash like 12) and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.
The largest proper fraction that can be formed is
= 1+3+12/11+6 = 16/17
To know more about fractions, click on the link
https://brainly.com/question/1622425
#SPJ9
I apologize about the quality the shaded region is the trapezoid part not the square in the middle
First, find the area of the trapezoid.
Area of a trapezoid = 0.5 ( sum of bases ) x height
bases = 15in, 8in
height = 8in
A 1 = 0.5 (15 + 8 ) x 8 = 92 in 2
Then, subtract the area of the rectangle:
Area of a rectangle = lenght x width
L = 5
W= 3
A2 = 5 x 3 = 15 in 2
Area of the shaded region = A1 - A2 = 92 - 15 = 77 in2
Interpreting the parameters of a linear function that models a real-world situation
SOLUTION
The equation relating x and y is
[tex]\begin{gathered} y=27x+600 \\ \text{Where } \\ x=\text{Total number of minutes } \\ y=\text{Total amount of water in the pond} \end{gathered}[/tex]The equation connecting x and y is an equation of the form
[tex]\begin{gathered} y=mx+c \\ \text{Where m is the slope or chnages betwe}enx\&y\text{ } \\ \end{gathered}[/tex]Since slope is also refers to as changes between two variables,
Hence
Cmparing with the equation given,
[tex]\begin{gathered} m=27 \\ \text{Slope}=27 \end{gathered}[/tex]Therefore,
The change per minute in the total amount of water in the pond is 27 litres
The starting amount ot water is when the time is at 0 minutes .
Hence, substite x=0 into the equation given and obtain the value of y which stands for the amount of water at the begining.
[tex]\begin{gathered} y=27x+600 \\ \text{put x=0} \\ y=27(0)+600 \\ y=0+600 \\ \text{Then } \\ y=600 \end{gathered}[/tex]Therefore,
The starting amount of water is 600 litres
Answer: A) 27 litres B). 600 litres
Steve has been training for a 5-mile race. Before the race, he predicts he will finish in 42minutes. He actually finishes the race in 40 minutes. What is the percent error for hisprediction?
To find the percent error
percent error = | (actual - expected)/ actual| * 100 %
The actual is 40 and the expected is 42
percent error = | ( 40 - 42) / 40 | * 100 %
= | -2/40| * 100%
= .05 * 100 %
= 5%
Solve the inequality: -1 <= x - 3 > 7
-1 ≤x-3>7
So:
-1≤x-3
x-3>7
Solve each
-1≤x-3
Add 3 to both sides:
-1+3≤x-3+3
2≤x
x-3>7
add 3 to both sides:
x-3+3>7+3
x>10
Solution:
2≤x or >10
What is the vertex of the graph of the function below?y = x^2 + 10x + 24O A. (-4,-1)O B. (-5, -1)O C. (-5,0)O D. (4,0)
For any given parabola in the form
[tex]f(x)=ax^2+bx+c[/tex]The vertex is the point:
[tex]V=(-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]This way,
[tex]\begin{gathered} y=f(x)=x^2+10x+24 \\ \rightarrow a=1 \\ \rightarrow b=10 \\ \rightarrow c=24 \\ \\ \rightarrow-\frac{b}{2a}=-\frac{10}{2\cdot1}=-5 \\ \\ \rightarrow f(-5)=(-5)^2+10(-5)+24=-1 \end{gathered}[/tex]Therefore, the vertex is:
[tex]V(-5,-1)[/tex]Answer: Option B
The dimensions of a rectangular prism are shown below length 1 1over2 width 1 foot hight 2 1over2
Solution
Given the dimensions of a rectangular prism as
length: 1.5 ft
width: 1 ft
Height: 2.5 ft
Part A.
Volume of a rectangular prism =
[tex]\begin{gathered} V_{RP}=l\times w\times h \\ \\ l\text{ is the length} \\ \\ w\text{ is the width} \\ \\ h\text{ is the height} \end{gathered}[/tex][tex]V_{RP}=1.5\times1\times2.5=3.75\text{ ft}^3[/tex]Volume of small cubes
[tex]V_{SC}=0.5^3=0.125\text{ ft}^3[/tex]Number of small cubes that can be packed in a rectangular prism is 30
[tex]N=\frac{V_{RP}}{V_{SC}}=\frac{3.75}{0.125}=30[/tex]Hence, there are 30 small cubes that can be packed in the rectangular box.
Part B.
The volume is given as
[tex]\sqrt[3]{30}=3.12[/tex]The volume of a square-based rectangular cardboard box needs to be at least 1000cm^3. Determine the dimensions that require the minimum amount of material to manufacture all six faces. Assume that there will be no waste material. The Machinery available cannot fabricate material smaller than 2 cm in length.
We have to find the dimensions of a box with a volume that is at least 1000 cm³.
We have to find the dimensions that require the minimum amount of material.
We can draw the box as:
The volume can be expressed as:
[tex]V=L\cdot W\cdot H\ge1000cm^3[/tex]The material will be the sum of the areas:
[tex]A=2LW+2LH+2WH[/tex]Since the box is square-based, the width and length are equal and we can write:
[tex]L=W[/tex]Then, we can re-write the area as:
[tex]\begin{gathered} A=2L^2+2LH+2LH \\ A=2L^2+4LH \end{gathered}[/tex]Now, we have the area expressed in function of L and H.
We can use the volume equation to express the height H in function of L:
[tex]\begin{gathered} V=1000 \\ L\cdot W\cdot H=1000 \\ L^2\cdot H=1000 \\ H=\frac{1000}{L^2} \end{gathered}[/tex]We replace H in the expression for the area:
[tex]\begin{gathered} A=2L^2+4LH \\ A=2L^2+4L\cdot\frac{1000}{L^2} \\ A=2L^2+\frac{4000}{L} \end{gathered}[/tex]We can now optimize the area by differentiating A and then equal the result to 0:
[tex]\begin{gathered} \frac{dA}{dL}=2\frac{d(L^2)}{dL}+4000\cdot\frac{d(L^{-1})}{dL} \\ \frac{dA}{dL}=4L+4000(-1)L^{-2} \\ \frac{dA}{dL}=4L-\frac{4000}{L^2} \end{gathered}[/tex][tex]\begin{gathered} \frac{dA}{dL}=0 \\ 4L-\frac{4000}{L^2}=0 \\ 4L=\frac{4000}{L^2} \\ L\cdot L^2=\frac{4000}{4} \\ L^3=1000 \\ L=\sqrt[3]{1000} \\ L=10 \end{gathered}[/tex]We now can calculate the other dimensions as:
[tex]W=L=10[/tex][tex]H=\frac{1000}{L^2}=\frac{1000}{10^2}=\frac{1000}{100}=10[/tex]Then, the dimensions that minimize the surface area for a fixed volume of 1000 cm³ is the length, width and height of 10 cm, which correspond to a cube (all 3 dimensions are the same).
Answer: the dimensions are length = 10 cm, width = 10 cm and height = 10 cm.
Find the radius of a circle with a circumstance of 28π
We have the next formula to find the circumference of a circle
[tex]C=2\pi r[/tex]where C is the circumference and r is the radius
In our case we have
C= 28π
we substitute the value in the formula
[tex]28\pi=2\pi r[/tex]then we isolate the r
[tex]r=\frac{28\pi}{2\pi}=14[/tex]the radius is 14.
Question 16
Given AEFHAGFH below, what is the measure of GFH?
F
21.6°
E<
(6x - 12)° H
G
1 pts
The most appropriate choice for congruency of triangles will be given by-
[tex]\angle GFH =68.4^{\circ}\\[/tex]
What is congruency of triangles?
Two triangles are said to be congruent if all the corrosponding sides and the corrosponding angles of the triangle are equal.
There are five axioms of congruency. They are -
SSS axioms, SAS axioms, ASA axiom, AAS axiom, RHS axiom.
Here,
[tex]\Delta EFH \cong \Delta GFH[/tex] [Given]
[tex]\angle E = \angle G = 21.6^{\circ}[/tex] [Corrosponding parts of congruent triangles are congruent]
[tex]\angle GFH[/tex] = 180 - (90 + 21.6) [Sum of the three angles of a triangle is 180°]
[tex]\angle GFH = 180 - 111.6\\\angle GFH =68.4^{\circ}\\[/tex]
To learn more about congruency of triangles, refer to the link -
https://brainly.com/question/2938476
#SPJ13
decide whether circumference or area would be needed to calculate the total number of equally sized tiles on a circular floor and explain your reasoning
The total number of equally-sized tiles on a circular floor.
Here, we are covering the region or the total space occupied by all the tiles on the floor.
Hence, the area is calculated.
f(x)=3x-4g(x)=-x^2+2x-5h(x)2x)^2+1j(x)=6x^2-8xk(x)=-x+7calculate (g+j)(x)
To calculate (g+j)(x) we need the function:
[tex]\begin{gathered} g(x)=-x^2+2x-5 \\ j(x)=6x^2-8x \end{gathered}[/tex]and we can made the addition so:
[tex]\begin{gathered} (g+j)(x)=g(x)+j(x) \\ (g+j)(x)=-x^2+2x-5+6x^2-8x \end{gathered}[/tex]and we can simplify
[tex](g+j)(x)=5x^2-6x-5[/tex]The marching band director is standing on a platformoverlooking the band practice. The pit section is located 8feet from the base of the platform. If the angle ofdepression from the band director to the pit section is 67°find the height of the platform.
Through trigonometry, we calculated that the height of the platform is 18.8 feet.
The director of the marching band is observing the band practice from a platform. 8 feet separate the base of the platform from the pit area. If the pit section's angle of depression is 67 degrees from the band director,
The angle formed by the horizontal line and the item as seen from the horizontal line is known as the angle of depression. When the angles and the separation of an object from the ground are known, it is mostly used to calculate the distance between the two objects.
We have,
So, the Angle of Depression = [tex]\alpha[/tex] = 67
Let x be the height of the platform,
Tan [tex]\alpha = \frac{x}{8}[/tex]
[tex]Tan 67 = \frac{x}{8} \\\\2.35 =\frac{x}{8} \\x = 2.35 *8 = 18.8[/tex]
Hence, The height of the platform is 18.8 feet.
To know more about trigonometry, visit https://brainly.com/question/26719838
#SPJ9
In an electrical circuit, the voltage across a resistor is directly proportional to the current running through the resistor. If a current of 14 amps produces 280 volts across a resistor, how many volts would a current of 5.5 amps produce across an identical resistor?
A current of 5.5 amps produce across an identical resistor will produce 110Volts across an identical resistor
What is a current?From above,
Current 1 (I₁) = 14 amps
P.d (V₁) = 280 V
By Ohm's law which states that that for a linear circuit the current flowing through it is proportional to the potential difference across it so the greater the potential difference across any two points the bigger will be the current flowing through it.
V₁ = I₁R
= 280 = 14R
= 20Ω = R
Current 2 (I₂) = 3.5 A
Resistance (R) = 20 Ω
Assuming the resistance stays the same,
Using Ohm's law,
V₂ = I₂R
= 5.5*20
= 110 Volts
110Volts would be produced across an identical resistor
Learn more about current on:https://brainly.com/question/23005284
#SPJ1
What is the midpoint of the x-intercepts off(x) = (x – 4)(x + 4)?(0,0)(0,4)(–4,0)(2,0)
Given:
[tex]f(x)=(x-4)(x+4)[/tex]Required:
To find midpoint of intercepts.
Explanation:
We know that when y=0,x=4,-4
therefore x- intercept of the function are (4,0) and (-4,0)
We know that the midpoint of this intercept is at equidistance from both the graph, therefore the points from which graph is equidistance is at origin (0,0)
Required answer:
Hence the midpoint of the x- intercepts of f(x) will be at (0,0) or at the origin of the graph so option 1 is correct.
Make a table for the graph labeled hours studies average grade
We can easily create a table with the first column labeled "hours studied" and second column labeled "average grade".
The hours studied are:
0, 1, 2, 3, and 4
The respective average grades are:
56, 75, 85, 90, 100
The table can look like this:
Answer:
To make the table, you must correlate the average test grade with the hours spent studying.
The graph shows the idea that the more we learn, the higher will be our test grades.
The table is attached.
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is divisible by 6". Find P(A). Outcome Probability 1 0.394 - 2. 0.152 3 0.001 4 0.09 5 0.112 6 0.047 7 0.053 8 0.151
Problem-Solving in Probability.
Prob( A ) = Prob( Outcome divisible by 6 ):
only outcome 6 is divisible by 6, and it has a probability of 0.047
Hence,
[tex]\text{Prob(A) =Prob(outcome 6) = 0.047}[/tex]Hence, the correct answer is 0.047
C. In which of the two functions is it possible to have negative output?
It is possible to have a negative output on:
[tex]y=a|x|[/tex]Since a can take possitive values and negative ones, and since it isn't inside the absolute value barrs.
its composition of fractions in pre-calculus.I know how to do these types of questions, im just not sure how u would set it up if there are 2 x's in one of the equations.
Answer:
(f o g)(x) = x
Explanation:
Given f(x) and g(x) defined below:
[tex]\begin{gathered} f(x)=\frac{1-x}{x} \\ g(x)=\frac{1}{1+x} \end{gathered}[/tex]The composition (f o g)(x) is obtained below:
[tex]\begin{gathered} (f\circ g)(x)=f\lbrack g(x)\rbrack \\ f(x)=\frac{1-x}{x}\implies f\lbrack g(x)\rbrack=\frac{1-g(x)}{g(x)} \end{gathered}[/tex]Substitute g(x) into the expression and simplify:
[tex]\begin{gathered} f\lbrack g(x)\rbrack=\frac{1-g(x)}{g(x)}=\lbrack1-g(x)\rbrack\div g(x) \\ =(1-\frac{1}{1+x})\div(\frac{1}{1+x}) \\ \text{ Take the LCM in the first bracket} \\ =\frac{1(1+x)-1}{1+x}\div\frac{1}{1+x}\text{ } \\ \text{Open the bracket} \\ =\frac{1+x-1}{1+x}\div\frac{1}{1+x}\text{ } \\ =\frac{x}{1+x}\times\frac{1+x}{1}\text{ } \\ =x \end{gathered}[/tex]Therefore, the composition (f o g)(x) is x.
Use the function below to find the indicated value:4x – 10,x21+12 <33
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Explain the given function
It can be seen from the function that there are three conditions which are defined below:
When x is less than 3, this states that we execute the first function for values of x less than 3
When x is between 3 and less than 7, this means that whenever x ranges from 3 to 6, we execute the second function.
When x is greater than or equals to 7, we execute the last function.
STEP 2: find f(7)
Since the value of x which is 7 is greater than or equal to 7, therefore we use the last function as seen below:
[tex]\begin{gathered} f(x)=f(7) \\ f(x)=\frac{x+1}{x-3} \\ Substitute\text{ 7 for x} \\ f(7)=\frac{7+1}{7-3}=\frac{8}{4}=2 \end{gathered}[/tex]Hence, the result is 2
HELP ME PLS!!!!!!!
Total consumption of fruit juice in a particular country in 2006 was about 2.15 billion gallons. The population of that country in 2006 was 400 million. What was the average number of gallons of fruit juice consumed per person in the country in 2006? using the per person amount from this problem, about how many gallons would your class consume?
Answer:
5.375 gallons/personStep-by-step explanation:
Total consumption of fruit juice in 2006:
2.15 billion gallonsThe population of the country:
400 million people.Average consumption of fruit juice per person in 2006 was:
2.15 billion / 400 million = 2.15 × 10⁹ / 400 × 10⁶ = 21.5 × 10⁸ / 4 × 10⁸ = 21.5 / 4 = 5.375 gallons/personTo find how many gallons of fruit juice would your class consume multiply the average consumption by the number of your class mates.
you started this year with $141 saved and you continue to save $27 per month. Write an equation to model this situation (use m for months and s for savings)
The money we would have at any time can be modeled as
M = 27k + 141
Why?
you started with $141, so that is the base amount,
every month you add 27 dollars,
in one month you add 27 dollars,
in two months you 27 again making 54 dollars,
so , in x months, you have added 27x dollars to the 141 dollars,
thus our equation is
M = 27k + 141
Solve the following equations. (You may leave your answer in terms of logarithms or you can plug your answer into a calculator to get a decimal approximation.)
Given the equation:
[tex]200(1.06)^t=550[/tex]We divide each side by 200:
[tex]\begin{gathered} \frac{200}{200}(1.06)^t=\frac{550}{200} \\ 1.06^t=2.75 \end{gathered}[/tex]Now, we take the natural logarithm:
[tex]\begin{gathered} \ln (1.06^t)=\ln (2.75) \\ t\cdot\ln (1.06)=\ln (2.75) \\ \therefore t=\frac{\ln (2.75)}{\ln (1.06)} \end{gathered}[/tex]I’m the relationship shown by the data linear, if so, model with an equation . A. The relationship is linear;
The relation is data if the difference between every 2 x is equal and the difference between every 2 y is equal
Since:
-5 - (-7) = -5 + 7 = 2
-3 - (-5) = -3 + 5 = 2
-1 - (-3) = -1 + 3 = 2
Since:
9 - 5 = 4
13 - 9 = 4
17 - 13 = 4
Then
The difference between every 2 x is constant and the difference between every 2 y constant
Then the relation is linear
Since the form of the linear equation is
[tex]y-y_1=m(x-x_{1)}[/tex]m is the rate of change of y with respect to x (the slope of the line)
(x1, y1) is a point on the line
Let us find m
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ \Delta y=4 \\ \Delta x=2 \\ m=\frac{4}{2} \\ m=2 \end{gathered}[/tex]Since x1 = -7 and y1 = 5, then
[tex]\begin{gathered} y-5=2(x--7) \\ y-5=2(x+7) \end{gathered}[/tex]Consider the graph shown. Which ordered pairs are on the inverse of the function? Check all that apply.
Notice that the graph of the function is a cubic polynomial. Also, the graph is moved one unit upwards, then, the function f(x) is:
[tex]f(x)=x^3+1[/tex]now, we can see from the y and x intercepts, that if we evaluate x= 0 and x = 1, we get:
[tex]\begin{gathered} f(0)=-1 \\ f(1)=0 \end{gathered}[/tex]then, applying the inverse function on both sides (we can do this since f(x) is a polynomial function and they always have inverse function), we get the following:
[tex]\begin{gathered} f^{-1}(f(0))=f^{-1}(-1) \\ \Rightarrow0=f^{-1}(-1) \end{gathered}[/tex]we can see that the first point that is on the graph of the inverse function is (-1,0). Doing the same on the second equation, we get:
[tex]\begin{gathered} f^{-1}(f(1))=f^{-1}(0) \\ \Rightarrow f^{-1}(0)=1 \end{gathered}[/tex]thus, the points that lie on the inverse function are (-1,0) and (0,1)
Help I’ll give extra points!10. Camilla is saving to purchase a new pair of bowling shoes that will cost at least $39. She hasalready saved $19. What is the least amount of money she needs to save for the shoes?11. Suppose you earn $20 per hour working part time at a tax office. You want to earn at least$1,800 this month, before taxes. How many hours must you work?For problem 12, translate the phrase intoalgebraic inequality.12. A tour bus can seat 55 passengers. A minimum of 15 people must register for the tour to bookthe bus.
the least amount of money she needs to save is 20
the number of hours you must work is at least 90hours
Explanation:
10) The pair of shoes cost at least $39
at least $39 means: the cost is ≥ 39
≥ means greater than or equal to
Amount saved = $19
Let the least amount of money = x
x + 19 ≥ 39
x ≥ 39-19
x ≥ 20
This means the least amount of money she needs to save is 20
11) Let the number of hours worked = x
Amount earned per hour = $20
Amount to be earned this month is at least $1,800
This means amount to be earned this month ≥ 1800
[tex]\begin{gathered} 20\times x\text{ }\ge\text{ 1800} \\ 20x\text{ }\ge\text{ 1800} \\ \text{Divide through by 20} \\ x\text{ }\ge\text{ }\frac{1800}{20} \\ x\text{ }\ge\text{ 90} \end{gathered}[/tex]This means the number of hours you must work is at least 90hours
Consider the following functions.S(x) = x2 - 4x + 4 and g(x) = x - 2Step 1 of 2: Find• ()a). simplify your answer.AnswerKeybo(*)(x) =Subn
Answer:
[tex]x-2[/tex]Explanation:
Here, we want to simplfy the given expression
From what we have:
[tex](\frac{f}{g})(x)\text{ = }\frac{f(x)}{g(x)}[/tex]Substituting the values, we have it that:
[tex]\frac{x^2-4x+4}{x-2}\text{ = }\frac{(x-2)(x-2)}{x-2}\text{ =x-2}[/tex]Find the value of x in this equation.
|2x − 3| − 11 = 0
Answer:7
Step-by-step explanation:
Answer:
x=−4
x=7
Step-by-step explanation:
1. Combine similar terms and use the equality properties to get the variable on one side of the equals sign and the numbers on the other side. Remember to respect the order of operations.
2. Add 11 to both sides of the equation.
3. Use the absolute value definition.
4. Add 3 to both sides of the equation.
5. Divide both sides by 2.
6. The answer is: x=7
x=−4
Sorry for the bad English, love from Vanuatu!
Sketch the vectors u and w with angle θ between them and sketch the resultant.|u|=45, |w|= 25, θ=30°
Step 1
Find the resultant of the vectors
[tex]undefined[/tex]I need help on this please! Assignment is called “Periods and Amplitudes” not sure if that helps lol
Solution:
The sine function is generally expressed as
[tex]\begin{gathered} y=A\sin(B(x+C))+D\text{ ---- equation 1} \\ where \\ A\Rightarrow amplitude \\ C\Rightarrow phase\text{ shift} \\ D\Rightarrow vertical\text{ shift} \\ \end{gathered}[/tex]The period of the function is expressed as
[tex]period=\frac{2\pi}{B}[/tex]Given the function:
[tex]y=\sin((\frac{7\pi}{4}x))\text{ ---- equation 2}[/tex]Comparing equations 1 and 2, we see that
[tex]B=\frac{7\pi}{4}[/tex]Thus, by substituting the value of B into the period formula, we have
[tex]\begin{gathered} period=\frac{2\pi}{\frac{7\pi}{4}} \\ =2\pi\times\frac{4}{7\pi} \\ =\frac{2\times\text{4}}{7} \\ =\frac{8}{7} \end{gathered}[/tex]Hence, the period of the function is
[tex]\frac{8}{7}[/tex]What is the height of a parallelogram with an area of 50 square meters
and a base length of 5 meters?
The height of a parallelogram with an area of 50 square meters and a base length of 5 meters is 10 meters
What is a parallelogram?The word "parallelogram" is a translation of the Greek phrase "parallelogrammon," which means "bounded by parallel lines." As a result, a quadrilateral that is bound by parallel lines is called a parallelogram. It has parallel and equal opposite sides on all sides. Square, rectangle, and rhombus are the three primary varieties of parallelograms, and each one has distinct characteristics. If a quadrilateral's opposite sides are parallel and congruent, it will be a parallelogram. So a quadrilateral with both pairs of opposite sides being parallel and equal is known as a parallelogram.
Various forms of parallelograms can be distinguished from one another based on their unique characteristics. It can be broadly classified into three distinct types:
RectangleSquareRhombusArea = 50
Base = 5
Area of ║gm = base (height)
50 = 5(X)
x = 10
To know more about parallelogram ,visit:
brainly.com/question/16287616
#SPJ13