The expression that represents waste reduction is w - 0.35x.
The paper waste produced now is 5.2 pounds per month.
What is the expression that represents waste production?The exression that represents waste production is the total amount of waste generated less athe reduction in waste.
w - 0.35x
Waste now produced = 8 - 0.35 x 8 = 5.2 pounds
To learn more about mathematical expressions, please check: https://brainly.com/question/11980704
A company produces circular drink coasters. the equation x2 y2 = 18.0625, with units in inches, represents the size of a coaster. each coaster is cut from a square piece of cardboard. what is the minimum possible area of each cardboard piece? 4.25 in2 8.5 in2 18.0625 in2 72.25 in2
The minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².
What is the equation of circle?The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here (h,k) is the center of the circle and (r) is the radius of the circle.
A company produces circular drink coasters. the equation which represents the size of a coaster is,
[tex]x^2+ y^2 = 18.0625[/tex]
The units are in the inches. This equation can be written as,
[tex]x^2+ y^2 = \dfrac{289}{16}\\x^2+ y^2 =\left( \dfrac{17}{4}\right)^2[/tex]
Compare it with the equation of the circle, we get,
[tex]h=0\\k=0\\r=\dfrac{17}{4}\rm\; in[/tex]
The radius of the circular coaster is 17/4. The diameter of it is,
[tex]d=2\times\dfrac{17}{4}\\d=\dfrac{17}{2}\rm \; in[/tex]
Now, each coaster is cut from a square piece of cardboard. The diameter of the circular coaster will be equal to the side of the square piece of cardboard.
[tex]a=d=\dfrac{17}{2}\rm\; in[/tex]
The area of the square is the square of its side. Thus, the area of a square piece of cardboard is,
[tex]A=a^2\\A=\left(\dfrac{17}{2}\right)^2\\A=72.25\rm\; in^2[/tex]
Thus, the minimum possible area of each square cardboard piece which is used to produce circular drink coasters is 72.25 in².
Learn more about the equation of circle here;
https://brainly.com/question/1506955
√2 x √27 use the properties of radicals to simplify
Answer: look at the image
Step-by-step explanation:
An equilateral triangle with side lengths of 8. 7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b. Which statements about finding the area of the equilateral triangle are true? Select three options. The apothem can be found using the Pythagorean theorem. The apothem can be found using the tangent ratio. The perimeter of the equilateral triangle is 15 cm. The length of the apothem is approximately 2. 5 cm. The area of the equilateral triangle is approximately 65 cm2.
The image of the triangle is missing, so i have attached it.
Also, the options are;
A) The apothem can be found using the Pythagorean theorem.
B) The apothem can be found using the tangent ratio.
C) The perimeter of the equilateral triangle is 15 cm.
D) The length of the apothem is approximately 2.5 cm.
E) The area of the equilateral triangle is approximately 65 cm².
Answer:
Options A, B & D are true
Step-by-step explanation:
A) We are told that the triangle is an equilateral triangle.
Thus, the 3 sides equal 8.7 cm.
Now from the image, b is half of one of the sides.
Thus, b = 8.7/2 = 4.35 cm
Now, we want to find the apothem "a".
Using Pythagoras theorem, we have;
a² + 4.35² = 5²
a² = 25 - 18.9225
a² = 6.0775
a = √6.0775
a ≈ 2.5 cm.
Thus, option A is true as Pythagoras theorem was able to calculate the apothem "a"
B) since the main triangle is equilateral, it means each angle is 60°.
Now, the radius line from one corner point to the center will divide the 60° angle into 2 equal parts.
Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°
Now, from tangent ratios, we know that;
Opposite/Adjacent = tan θ
In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm
Thus;
a/4.35 = tan 30
a = 4.35 tan 30
a ≈ 2.5 cm.
Thus, option B is correct as Tangent ratio can be used to find the apothem
C) The perimeter of equilateral triangle = 3x
Where x is length of one side.
One side is 8.7 cm
Thus, perimeter = 3 × 8.7 = 26.1 cm
Thus option C is not correct.
D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.
Thus, option D is true.
E) Area of triangle is;
A = ½ × base × height
Base = 8.7 cm
To get height, we will use trigonometric ratio. Thus;
h/8.7 = sin 60°
h = 8.7 sin 60°
Thus;
A = ½ × 8.7 × 8.7 sin 60°
A = 32.77 cm²
Thus is not equal to 65 cm². Thus, option E is not correct.
The statements that are true for the considered equilateral triangle are:
Option A: The apothem can be found using the Pythagorean theorem.Option B: The apothem can be found using the tangent ratio.Option D: The length of the apothem is approximately 2. 5 cm.For a regular polygon, the apothem is the line segment from the center of the polygon to the mid of one of the sides of the considered polygon.
For this case, referring to the figure attached below, we have:
Length of the apothem = x (assume)The triangle ABC is equilateralLength of line segment from vertex to center (radius) = 5 cmLength of each side of the triangle = 8.7 cmSince the triangle is equilateral, there can be 6 congruent triangles like BOD.
Thus, Area of triangle ABC = 6 × Area of triangle BOD
Area of BOD = [tex]\dfrac{1}{2} \times x \times 4.35 = 2.175x \: \rm cm^2[/tex]
Area of ABC = [tex]6 \times 2.175x = 13.05x \: \rm cm^2[/tex]
The length of the apothem is x cm, and can be obtained by using Pythagoras theorem.
We can also use the tangent ratio as the line segment BO is bisecting the internal angle B (each internal angle is of 60 degrees in an equilateral triangle), so angle OBD is of 60/2 = 30 degrees. So using angle and the fact that tangent ratio is ratio of side opposite to angle and the remaining adjacent side(not hypotenuse).
[tex]tan(30^\circ) = x/4.35 \implies x = 4.35 \times \tan(30^\circ) \approx 2.5 \: \rm cm[/tex]
Using Pythagoras theorem too, we can get the value of x as:
[tex]5^2 = 4.35^2 + x^2\\x = \sqrt{25 - 18.9225} \approx 2.465 \: \rm cm \approx 2.5 cm[/tex]
Thus, area of the equilateral triangle ≈ [tex]13.05 \times x \approx 13.05 \times 2.5 = 32.575 \: \rm cm^2[/tex]
This isn't 65 sq. cm.
Thus, the statements that are true for the considered equilateral triangle are:
Option A: The apothem can be found using the Pythagorean theorem.Option B: The apothem can be found using the tangent ratio.Option D: The length of the apothem is approximately 2. 5 cm.Learn more about tangent ratio here:
https://brainly.com/question/14169279
In a trapezoid the sum of the bases is 28 and the area is 84.
What is the altitude or height of the trapezoid?
Answer: If you sketch this out, you should be able to convince yourself that if you drew a line parallel to the bases and halfway between them, and a vertical at the end of that line, there would be an extra triangle on the longer base that would just fit into the space at the end of the shorter base, if you cut and pasted it.
You should also be able to convince yourself by what you know about similarity that the length of that parallel halfway line is just halfway between the lengths of the bases (you can add them and divide by two).
So your trapezoid (trapezium, we call ’em this side of the pond) has the same area as a rectangle with an altitude equal to the trapezoid’s and a width equal to the sum of those bases divided by two. And since you know about rectangles, you’re home and dry. I suggest you do the sketch, fill in the numbers, and then you’ve completed a model piece of homework that should earn full marks and the teacher’s approval.
Step-by-step explanation:
What is the measure of arc c e d? 106° 108° 148° 212°.
Answer:
Can you please give us figure of following ?
Answer:
its the last one 212°
212°
212°
212°
212°
212°
Step-by-step explanation:
212°
A bag contains 16 blue marbles, 12 red marbles, and 12 green marbles.
If Malik randomly draws a marble from the bag (and puts it back) 25 times, how many times should he expect to pull a blue marble?
The random selection of a blue marble is an illustration of probability
You should expected to pull a blue marble 10 times
How to determine the expected blue marble?The given parameters are:
Blue = 16
Red = 12
Green = 12
The total number of marbles is:
Total = 16 + 12 + 12
So we have:
Total = 40
The probability of selecting a blue marble is:
[tex]P(Blue) = \frac{16}{40}[/tex]
When 25 marbles are selected, the expected number of blue is:
[tex]Blue = n * P(Blue)[/tex]
So, we have:
[tex]Blue = 25 * 16/40[/tex]
[tex]Blue = 10[/tex]
Hence, the expected number of blue marbles is 10
Read more about expected values at:
https://brainly.com/question/15858152
I NEED HELP ASAP!!!!!!!!!!!!!!!
Answer:
The one on the very top left corner is the right one.
Step-by-step explanation:
It shows the exact data that you were looking for: ten small apples were green and 3 out of the 12 large apples were red.
Order Least to greatest
41/5, 8.245, 8.25, 8 1/6
Answer:
8.16, 8.2, 8.245, 8.25
Step-by-step explanation:
8 1/6 = 8.16
41/5 = 8.2
|-9| + |12| = ?
Question options:
A -3
B 3
C -21
D 21
Answer:
21
Step-by-step explanation:
-9=9
9+12=21
The question is below:
[tex]3(x - 2) + 7x = \frac{1}{2} (6x - 2) [/tex]
Solving It[tex]3(x - 2) + 7x = \frac{1}{2} (6x - 2) \\ \\ \implies3x - 6 + 7x = ([\frac{1}{2} \times 6 \: x] - [\frac{1}{2} \times 2]) \\ \\ \implies10x - 6 = ([\frac{1}{ \cancel2} \times \cancel 6 \: x] - [\frac{1}{ \cancel2} \times \cancel2]) \\ \\ \implies 10x - 6 = 3x - 1 \\ \\ \fbox{Bringing (3x )to left side whereas( - 6 )in right side} \\ \\ \implies10x - 3x = - 1 + 6 \\ \\ \implies7x = 5 \\ \\ \therefore x = \frac{5}{7} [/tex]
The Solution is = [tex] \frac{5}{7}[/tex]
[tex]\text\red{One Solution set is possible.}[/tex]
Hope This Helpsyou go to the pet store and see 9 cats and 12 dogs.if this ratio stays the same and there are 108 cats in the store,how many dogs would be in the store?
Answer:
144
Step-by-step explanation:
Because if you multiply 9*12=108 and 12*12=144
Write the expression. Then, check all that apply.
a number cubed increased by four
Answer: C and B
Step-by-step explanation: because its rational.
-LearnWithBrainly
Please help thank you
Answer:
Q = mCpΔT where Q is the energy in heat (joules), m is the mass (grams), Cp is the specific heat capacity (J/g/°C), and ΔT is the change in temperature (T2 - T1) in °C.
Step-by-step explanation:
So, since Q = mCpΔT then m = Q/(CpΔT) or (45.0)/(0.780•2.00) = 45/1.56 = 28.846 grams. Since there are 3 sig figs, we round to:
m = 28.8 g
Which of the following is true? there is a phase shift to the left. there is a phase shift to the right. the graph is reflected across the x-axis the graph is stretched horizontally. the graph is compressed horizontally.
Answer:
a. There is a phase shift to the left
Step-by-step explanation:
The correct statement for the graph of y = cos (x + pi/6) compared to the graph of y = cos(x) is given by: Option A: There is a phase shift to the left.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: [tex]y=f(x+c)[/tex]output, but c units earlier)Right shift by c units: [tex]y=f(x-c)[/tex] (same output, but c units late)Vertical shift:
Up by d units: f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]For this case, the parent function y = cos(x) is transformed to make the function y = cos (x + pi/6)
Thus, there is left shift of the graph of the function y =cos(x).
The graphs of both functions (parent function in red color and transformed function in blue color) is given below.
Thus, the correct statement for the graph of y = cos (x + pi/6) compared to the graph of y = cos(x) is given by: Option A: There is a phase shift to the left.
Learn more about transforming functions here:
https://brainly.com/question/17006186
1. What is the volume, in cubic feet, of a rectangular solid with a length of 12 feet, a width of
3 feet, and a height of 4 feet?
Answer: 144 Cubic Feet
Explanation: Multiply all of your numbers together to get your volume.
Numbers : Length(12) x Width(3) x Height(4) = 144 cubic feet.
I hope this helps you! :)
The angle of elevation to the top of a Building in New York is found to be 4 degrees from the ground at a
distance of 2 miles from the base of the building. Using this information, find the height of the building.
how can you take 20% off of a normal price
try to understand the example.
I used 20/100 since 20% is obviously 20/100 and I used ×1000 cus for 1000, you want 20%
hope it helps...!!!
PLEASE HELP ME I CANT GET IT RIGHT
Answer:
I believe the answer is 760 ft²
Step-by-step explanation:
16×39/2=312
(17+39)(16)/2=448
448+312=760ft²
let me know if it was right. good luck!
Which of the following are exact numbers? Select all that apply.
The liquid has a volume of 10.41 mL
The paper has a length of 5.2 cm.
There are 30 students in the class.
There are 100 cm in 1 m.
The exact numbers listed in this problem are given by:
There are 30 students in the class.There are 100 cm in 1 m.What are exact numbers?Exact numbers are numbers that are not rounded. Volumes and lengths, for example, are usually rounded, hence they cannot be called exact.
Thus, the exact numbers listed in this problem are given by:
There are 30 students in the class.There are 100 cm in 1 m.More can be learned about exact numbers at https://brainly.com/question/14089554
#SPJ1
hey, i'm kinda confused on how you do this again factories 3n+12
Answer:
we should take common first
3n+12
taking 3 common
3(n+4)
PLS HELP ME I WILL MARK THE BRAINLIEST
Answer:
1. 155 yd², 2. 379.54 ft², 5. x = 65.82π
Step-by-step explanation:
1. A = (1/2) · (3 + 13) · 8
A = (1/2)(16)(8)
A = 64
A = bh
A = 13*7
A = 91
64 + 91 = 155
155 yd²
2. A = bh
A = 25x25
A = 625
A = πr²
A = 3.14*12.5²
A = 3.14*156.25
A = 490.625
490.925/2 = 245.4625
625 - 245.4625 = 379.5375
379.54 ft²
3. and 4. Sorry, I don't know how to solve these
5. A = πr²
A = 3.14*7²
A = 3.14*49
A = 153.86
x/154 = 153.86π/360
360x = 154*153.86π
360x = 23694.44π
x = 65.8178889π
x = 65.82π
Hope this helps :)
help help please? i need it
Answer:
C, $12
Step-by-step explanation:
Every hour worked the employee earns $12. This is a fixed rate and the answer is shown in the 1st slot of the table -- 1 hour = $12
Answer:
12 dollars per hour
Step-by-step explanation:
For each hour worked, we make 12 dollars as show in the first column, 1 hour is 12 dollars
We can check using the last colum
48 dollars / 4 hours = 12 dollars per hour
The volume of the triangular block is 4 cubic inches. A triangular prism has a volume of 4 cubic inches. The right triangle bases have side lengths of x and a hypotenuse length of y. THe height of the prism is x. What is the approximate length of y? Round to the nearest tenth of an inch. 1. 4 in. 2. 0 in. 2. 8 in. 3. 5 in.
The value of the hypotenuse y will be equal to y = 2.8 inches.
What is volume of prism?The volume of the prism is equal to the product of the area of its base and the height of the prism.
[tex]\rm V=Area \ of\ triangular \ base\times Height \ of \ prism[/tex]
The volume oif the prism is =4 cubic inches
Height of the prism = x inches
Base of the right angle isosceles triangle will be =x inches
The hypotenuse is given = y
Now
[tex]\rm V=\dfrac{1}{2}\times Base\times Height \times height \ of \ prism[/tex]
[tex]V=\dfrac{1}{2} \times x \times x \times x[/tex]
[tex]x^3=8[/tex]
[tex]x=2[/tex]
Now by pythagorus theorem
[tex]y^2=h^2+b^2[/tex]
[tex]y^2=x^2+x^2[/tex]
[tex]y^2=2x^2=2\times 2^2[/tex]
[tex]y=2\sqrt{2}=2.82[/tex]
Thus the value of the hypotenuse y will be equal to y = 2.8 inches.
To know more about Volume of prism follow
https://brainly.com/question/23963432
Answer:
2.8 INCHES
Step-by-step explanation:
The first term of a geometric sequence is 4 and grows exponentially by a factor of 3. Murphy writes out the terms and says that the sum of the 4th and 5th terms is 1,296. Explain Murphy's error and correct it. (Fill in the blanks)
Murphy added terms
____
together. The correct sum of the 4th and 5th terms is ___
(Simplify your answer.)
The geometric sequence can increase or decrease exponentially
The correct sum of the 4th and the 5th terms is 432
How to determine the correct sum?The given parameters are:
Initial value (a) = 4
Growth factor (r) = 3
The nth term of a geometric sequence is calculated as:
[tex]T_n = ar^{n-1}[/tex]
This gives
[tex]T_n = 4 * 3^{n-1}[/tex]
For the 4th term; we have:
[tex]T_4 = 4 * 3^{4-1}[/tex]
[tex]T_4 = 108[/tex]
For the 5th term, we have:
[tex]T_5 = 4 * 3^{5-1}[/tex]
[tex]T_5 = 324[/tex]
Add the 4th and the 5th terms
Sum = 108 + 324
Sum = 432
Hence, the correct sum of the 4th and the 5th terms is 432
Read more about geometric sequence at:
https://brainly.com/question/24643676
2. What number would you divide by to calculate the mean of 3, 4, 5, and 6?
a. 6
b. 3
c. 5
d. 4
Answer:
its 4 i think tell me if i am wrong
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIEST
Answer:
y = 1/2x - 1
Step-by-step explanation:
The x value is divided by 2 and then has 1 subtracted from it.
also for future posts, put the question in the title that way people know what you need and can click if they know the answer.
What is the area of this trapezoid?
Answer:
(b1+b2)h divided by 2 is the formula for a trapezoid
Step-by-step explanation:
ANSWER: 468 ft (squared?)
Lisa is checking out at the bookstore. Each book (b) costs $1.50 and she has a $5 off coupon she can use. She wants to spend $25 or less in the bookstore. How many books can Lisa buy?
Answer:
20
Step-by-step explanation:
Given:
Lisa is checking out at the bookstore.
Each book (b) costs $1.50 and she has a $5 off coupon she can use.
She wants to spend $25 or less in the bookstore.
Solve:
Since there is a $5 off coupon..
$1.5b - $5.00<=$25.00
$1.5b<= $30.00
$1.5b/1.5 = $30.00/1.5
b=20
Lisa can buy 20 book.
~lenvy~
someone help me please
Answer:
3x + 5y = 15
Find gradient:
coordinates taken: (5, 0), (0, 3)
[tex]\rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\rightarrow \sf \dfrac{3-0}{0-5}[/tex]
[tex]\rightarrow \sf -\dfrac{3}{5}[/tex]
Here the y-intercept: 3gradient: -3/5
equation:
[tex]\sf \bold{ y = m(x) + b}[/tex]
[tex]\rightarrow \sf y = -\dfrac{3}{5} x + 3[/tex]
[tex]\rightarrow \sf y = -\dfrac{3}{5} x + \dfrac{15}{5}[/tex]
[tex]\rightarrow \sf 5y =-3x+15[/tex]
[tex]\rightarrow \sf 3x+5y =15[/tex]
Take two points
(0,3)(5,0)x intercept=a=5y intercept=b=3So
equation of line in intercept form
[tex]\\ \rm\rightarrowtail \dfrac{x}{a}+\dfrac{y}{b}=1[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{x}{5}+\dfrac{y}{3}=1[/tex]
Multiply each by 15[tex]\\ \rm\rightarrowtail 3x+5y=15[/tex]
A plane traveling with the wind travels 900 miles in 5 hours. the return trip is against the wind and takes 9 hours. find the rate of the plane in still air and the rate of the wind.
Using the relation between velocity, distance and time, it is found that:
The rate of the plane in still air is of 140 mph.The rate of the wind is of 40 mph.What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
A plane traveling with the wind travels 900 miles in 5 hours, hence:
[tex]v_a + v_w = \frac{900}{5}[/tex]
[tex]v_a + v_w = 180[/tex]
The return trip is against the wind and takes 9 hours, hence:
[tex]v_a - v_w = \frac{900}{9}[/tex]
[tex]v_a - v_w = 100[/tex]
From the first equation, we have that:
[tex]v_w = 180 - v_a{/tex]
Replacing on the second:
[tex]v_a - v_w = 100[/tex]
[tex]v_a - 180 + v_a = 100[/tex]
[tex]2v_a = 280[/tex]
[tex]v_a = 140[/tex]
[tex]v_w = 180 - 140 = 40{/tex]
Hence:
The rate of the plane in still air is of 140 mph.The rate of the wind is of 40 mph.More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569