Answer:
Cost ratio of pens:pencils = 9 : 4
Step-by-step explanation:
Pen : Pencil
10/10 : 12/12
22.5 / 10 : 18 / 12
2.25 : 1.5 cost per pen : pencil
HC of 0.25 and 0.5 is 8
8 x 2.25 = 18:
1.5 x 8 = 12
Then place them under their denominator x 10 x 12
pens = 18/10 = 1.8
pencils = 12/12 = 1
HC of 1.8 and 1 is 5
1.8 x 5 = 9
1 x 5 = 5
Answer = 9 : 4
Armando's carpet has an area of 220 square feet. He hires the Carpet Pro carpet cleaning service, which is able to clean 9 square feet of his carpet every minute. Therefore, in the first minute, CarpetPro is able to clean 9 square feet of Armando's carpet (leaving 211 square feet remaining to be cleaned). In the second minute, the cleaner is again able to clean 9 square feet of carpet (leaving 202 square feet to be cleaned), etc. Which of the following functions expresses the number of square feet that still remain to be cleaned after t minutes from the time that the carpet cleaner began cleaning this carpet.
a. A(t) = 220 - 9
b. A(t) = 220 - 0.1
c. A(t) = 220(0.1)
d. A(t) = 220(0.96)
e. A(t) 220 - 0.96
Answer:
The answer is A
Step-by-step explanation:
The answer needs to be in slope-intercept form or y=mx+b because the amount of carpet being cleaned every minute is a constant decrease of 9 square feet.
So our b value (or how much carpet cleaned at 0 minutes) is 220
And our m value (or slope or how much carpet is being cleaned every minute) is 9
So if we plug the variables with the tangible numbers we get A(t) = -9x+220 or A(t) = 220-9x.
provided by gauth math
A group of 6 children and 6 adults are going to the zoo. Child tickets cost $10, and adult tickets cost $14. How much will the zoo tickets cost in all?
Answer:
i believe it'll cost 200 dollars
The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:
Part A: Find and interpret the slope of the function. (3 points)
Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)
Part C: Write the equation of the line using function notation. (2 points)
Part D: What is the balance in the bank account after 5 days? (2 points)
Answer:
see below
Step-by-step explanation:
Part A
The slope is found by
m = ( y2-y1)/(x2-x1)
= ( 1200-1500)/(4-0)
= -300/4
=-75
Part B
point slope y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y-1200 = -75(x-4)
slope intercept y = mx+b where m is the slope and b is the y intercept
y = -75x + 1500
standard form Ax+By =C
75x + y = 1500
Part C
Change y to g(x) in the slope intercept form
g(x) = -75x + 1500
Part D
Let x = 5
g(5) = -75(5) + 1500
=-375+1500
=1125
The sum of 'n' terms of an arithmetic sequence is 4n^2+3n. What is the first term, the common difference, and the sequence?
Answer:
The sequence has first term 7 and common difference is 8.
So the sequence is f(n)=7 + 8(n-1)
Step-by-step explanation:
Let a be the first term.
Let a+d be the second term where d is the common difference.
Then a+2d is the third....
And a+(n-1)d is the nth term.
Adding these terms we get:
an+(n-1)(n)/2×d
For the first term of this sum I seen we had n amount of a's and for the second term I used the well known identity sum of the first n positive integers is n(n+1)/2.
Let's simplify:
an+(n-1)(n)/2×d
Distribute:
an+(n^2d/2)-(nd/2)
Find common denominator:
(2an/2)+(n^2d/2)-(nd/2)
Combine terms into one:
(2an+n^2d-nd)/2
Reorder terms:
(n^2d+2an-nd)/2
Regroup terms:
(n^2d+(2a-d)n)/2
We want the following sum though:
4n^2+3n
This means d/2=4 (so d=8) and (2a-d)/2=3.
So plug d=8 into second equation to solve for a.
(2a-8)/2=3
2a-8=6
2a=14
a=7
The sequence has first term 7 and common difference is 8.
So the sequence is f(n)=7 + 8(n-1).
Help me plz need the steps
In Figure 7 (open photo), GH is a diameter of the circle. What is
x² + y² ?
A)58
(B) 49
(C) 10
D) 9
(E) It cannot be determined from the information given.
Answer:
[tex]A)58[/tex]
Step-by-step explanation:
[tex][Kindly\ refer\ the\ attachment]\\We\ are\ given:\\GH\ is\ the\ diameter\ of\ the\ circle.\\ Also,\\ GM=3\ units\ and\ MH=7\ units\\From\ the\ figure,\\GH\ subtends\ an\ angle\ at\ two\ points\ specifically\ M\ and\ N\ on\ the\\ arc.\\Now,\\We\ know\ that,\\'The\ Angle\ subtended\ by\ the\ diameter\ anywhere\ over\ the\ arc\ of\ the\\ circle\ is\ always\ 90\ degrees'.\\Hence,\\\angle GMH\ = \angle GNH=90\\[/tex]
[tex]Also,\\Pythagoras\ Theorem\ states\ that: 'In\ a\ right\ triangle,\ the\ sum\ of\ squares\\ \ of\ the\ legs\ is\ equal\ to\ the\ square\ of\ the\ hypotenuse'\\In\ \triangle GMH,\\Since\ \angle GMH=90,\\GM^2+MH^2=GH^2[Through\ Pythagoras\ Theorem]\\Hence,\\Substituting\ GM=3,\ MH=7:\\3^2+7^2=GH^2\\GH^2=9+49=58[/tex]
[tex]Similarly,\\In\ \triangle GNH,\\Since\ \angle GNH=90,\\GN^2+NH^2=GH^2\\Hence,\\Substituting\ GN=x\ and\ NH=y:\\x^2+y^2=GH^2\\x^2+y^2=58[/tex]
simplify 7-(3n+6)+10n
Answer:
1 + 7n
Step-by-step explanation:
7-(3n+6)+10n
7 - 3n - 6 + 10 n
1 - 7n
Answered by Gauthmath
Convert 110101 in base 2 to base 10
Answer:
base-2 base-10
110011 = 51
110100 = 52
110101 = 53
110110 = 54
21 more rows
____________ is/are when data is analyzed in order to make decisions about the population behind the data.
A. Experiments
B. Simulations
C. Surveys
D. Statistics
Answer:
statistics are when data analyzed in order to make decisions about the population behind the data.
The correct answer to the question is Statistics (Option D).
What is statistics?
Statistics is a field of study in mathematics which deals with raw data. It is a tool which refines the data to produce meaningful results and a pathway to better understanding of it.
Some examples of raw data can be population sample which loves to see a particular TV show or a sample of students getting so and so marks in Math test.
Data is analyzed mainly by three different measure of central tendency that is mean, median and mode.
Mean is the average value of given discrete data.Median is the middle value when the data is sorted in ascending or descending order.Mode is the value that has highest frequency.Therefore, Statistics the correct answer.
To know more about statistics refer:https://brainly.com/question/10734660
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What is 1.25 x 10^8 in standard form?
Answer:
125000000
Step-by-step explanation:
1.25 x 10^8
Move the decimal 8 places to the right
1.25
We can move it two places
125
We need to add 6 more zeros
125000000
Answer: 125,000,000
Step-by-step explanation:
find the common ratio of the geometric sequence 4,3,9/4
Answer:
3/4
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first term
3/4
Check with the third and second terms
9/4 ÷3
9/4 *1/3= 3/4
The common ratio is 3/4
using the unit circle what is the exact value of tanpi/6
Answer:
[tex] \frac{ \sqrt{3} }{3} [/tex]
Step-by-step explanation:
[tex]\frac{1}{3} \div \sqrt{3} [/tex]
help please i’ll give brainliest
Answer:
3rd option
..................[tex]A) \frac{4-2}{2-1} =2[/tex]
[tex]B)\frac{1-0.5}{4-2} =0.25[/tex]
[tex]C)>2[/tex]
[tex]D) 1[/tex]
~OAmalOHopeO
Answer:
The third one is your answer
What is the dimension of the vector space consisting of five-by-one column matrices where the rows sum to zero and the first row is equal to the second row?
a. 5
b. 4
c. 3
d. 2
Answer:
Option c.
Step-by-step explanation:
If we have a vector of N components (or variables), and we have K linear independent restrictions for these N components (such that K < N, we can't have more restrictions than components.)
The dimension of the vector will be given by N - K.
Here we know that we have a vector of 5 components, that can be written as:
[tex]v = \left[\begin{array}{ccc}v_1\\v_2\\v_3\\v_4\\v_5\end{array}\right][/tex]
And we have two restrictions, so we can expect that the dimension of the vector is:
5 - 2 = 3
But let's see it, the restrictions are:
"the first row is equal to the second row"
Then we can rewrite our vector as:
[tex]v = \left[\begin{array}{ccc}v_1\\v_1\\v_3\\v_4\\v_5\end{array}\right][/tex]
Notice that now we have only 4 variables, v₁, v₃, v₄, and v₅
We also know that the sum of the rows is equal to zero, thus:
v₁ + v₂ + v₃ + v₄ + v₅ = 0
we know that v₂ = v₁, so we can replace that to get:
2*v₁ + v₃ + v₄ + v₅ = 0
Now we can isolate one of the variables, to write it in term of the others, for example, let's isolate v₅:
v₅ = -2*v₁ - v₃ - v₄
Now if we replace that in our vector, we have:
[tex]v = \left[\begin{array}{ccc}v_1\\v_1\\v_3\\v_4\\-2*v_1 - v_3 - v_4\end{array}\right][/tex]
Notice that our vector depends on only 3 variables, v₁, v₃, and v₄, so we can define our vector in a 3-dimensional space.
Then the correct option is c, the dimension of the vector space is 3.
Factorize the following: cos²B + 5cosB - 6
Answer:
(cosB-1)(cosB+6)
Step-by-step explanation:
use u substitution . u = cosB
u^2+5u-6
factor
(u-1)(u+6)
put cosB back in for u
(cosB-1)(cosB+6)
Please help me solve the question...
Answer:
All of area is πr²
Step-by-step explanation:
and we should write the area kind of radian. So if all area is π*(12)²= 144π - this for 360°- and 240° is 96π
but we must add area of the triangle which has two same side and has 6 high so it's area is 6*12√3/2 = 36✓3
our answer is 96π+ 36✓3
What is the measure of the angle in red?
70°
Answer:
See pic below.
Answer: C. 380°
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all fractions 2x-2y=14
Answer: y = x - 7
Slope intercept form: y = mx + b
[tex]2x-2y=14\\\\-2y=-2x+14\\\\y=\frac{-2x+14}{-2} =\frac{-2(x-7)}{-2} =x-7[/tex]
Given the formula A = 5h (B + b); solve for B.
2
Answer:
A=5h(B+b)
A/5h=B+b
A/5h - b= B
Plz answer asap question in picture
Answer:
-1 <x < 7
(-1,7)
Step-by-step explanation:
open circle on the left means the number is greater than
-1 <x
Open circle on the right means the number is less than
x < 7
Since both statements are true. we combine them
-1 <x < 7
open circles means parentheses, closed circles mean brackets
PLEASE HELP THIS IS DUE ASAP (answer in decimal!!!!)
The height of a projectile launched upward at a speed of 48 feet/second from a height of 160 feet is given by the function h(t)=-16sup(t,2)+48t+160. How long will it take the projectile to hit the ground?
Answer:
Hello,
5 s
Step-by-step explanation:
[tex]h(t)=-16t^2+48t+160\\=-16(t^2-3t-10)\\=-16(t^2-5t+2t-10)\\=-16(t(t-5)+2(t-5))\\=-16(t-5)(t+2)\\\\h(t)=0 \Longleftrightarrow\ t=-2\ or\ t=5\\\\Only\ t=5\ is \ a\ answer.(time\ must\ be\ positive)[/tex]
Suppose the volume of the cone is 324pi Find dy/dx when x=6 and y=27
Answer:
[tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = -9[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityCalculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle V = \frac{1}{3} \pi x^2y[/tex]
[tex]\displaystyle V = 324 \pi[/tex]
[tex]\displaystyle x = 6[/tex]
[tex]\displaystyle y = 27[/tex]
Step 2: Differentiate
Substitute in volume [Volume Formula]: [tex]\displaystyle 324 \pi = \frac{1}{3} \pi x^2y[/tex][Equality Properties] Rewrite: [tex]\displaystyle y = \frac{972}{x^2}[/tex]Quotient Rule: [tex]\displaystyle \frac{dy}{dx} = \frac{(972)'x^2 - (x^2)'972}{(x^2)^2}[/tex]Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = \frac{0x^2 - (2x)972}{(x^2)^2}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{-1944x}{x^4}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{-1944}{x^3}[/tex]Step 3: Evaluate
Substitute in variables [Derivative]: [tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = \frac{-1944}{6^3}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = -9[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
I need help please. Thank you
Answer:
0.0009765625
Step-by-step explanation:
This is what i got its probally incorrect
if 2x + 1=7 what is the value of x
Answer:
x=3
Step-by-step explanation:
2x+1=7
2x=7-1
2x=6
x=6/2
x=3
Answer:
Solution,
2x + 1=7
or 2x = 7 - 1
or, 2x= 6
or, x = 6
2
or, x = 3
.:. x = 3
15. Five boys went to see the CIRCUS. Four of them had Rs.5 each and the fifth boy had Re.1 more than the entrance ticket price. IF with the whole amount (which the 5 boys had), the boys were able to just buy the entrance ticket for all the 5, cost of the entrance ticket per person was
Answer:
20+(x+1) = 5x
x=21/4
x= 5.25
The entrance ticket per person can be calculated using algebraic equation. We have create the algebraic expression as per the question.
The entrance ticket per person is Rs. 5.25.
Given:
Total boys are 5
4 boys has 5 rupee each so total rupee are [tex]=5\times 4=20[/tex].
Let the entrance ticket per boy is [tex]x[/tex].
One boy had 1 rupee more than entrance ticket [tex](x+1)[/tex].
Write the algebraic expression to calculate the entrance ticket per person.
[tex]5x=20+(x+1)\\5x=20+x+1\\5x-x=20+1\\4x=21\\x=5.25[/tex]
Thus, the entrance ticket per person is Rs. 5.25.
Learn more about algebraic expression here:
https://brainly.com/question/953809
The sum of two numbers is 41. The larger number is 17 more than the smaller number. What are the numbers?
Larger number:
Smaller number:
The differential equation of a certain system is 20y′′+cy′+80y=0
, where c is called damping constant for what value of c critical damping hapens
Options:
110
64
50
60
Answer:
c=80
Step-by-step explanation:
Based on my reading the critical damping occurs when the discriminant of the quadratic characteristic equation is 0.
So let's see that characteristic equation:
20r^2+cr+80=0
The discriminant can be found by calculating b^2-4aC of ar^2+br+C=0.
a=20
b=c
C=80
c^2-4(20)(80)
We want this to be 0.
c^2-4(20)(80)=0
Simplify:
c^2-6400=0
Add 6400 on both sides:
c^2=6400
Take square root of both sides:
c=80 or c=-80
Based on further reading damping equations in form
ay′′+by′+Cy=0
should have positive coefficients with b also having the possibility of being zero.
The coordinates of the preimage are:
A(−8,−2)
B(−4,−3)
C(−2,−8)
D(−10,−6)
Now let’s find the coordinates after the reflection over the x-axis.
A′(−8,
)
B′(−4,
)
C′(−2,
)
D′(−10,
)
And now find the coordinates after the reflection over the y-axis.
A′′(
,2)
B′′(
,3)
C′′(
,8)
D′′(
,6)
This is also the same as a rotation of 180∘.
9514 1404 393
Answer:
A'(-8, 2) ⇒ A"(8, 2)B'(-4, 3) ⇒ B"(4, 3)C'(-2, 8) ⇒ C"(2, 8)D'(-10, 6) ⇒ D"(10, 6)Step-by-step explanation:
Reflection over the x-axis changes the sign of the y-coordinate. Reflection over the y-axis changes the sign of the x-coordinate. We can summarize the transformations as ...
preimage point ⇒ reflection over x ⇒ reflection over y
A(−8,−2) ⇒ A'(-8, 2) ⇒ A"(8, 2)
B(−4,−3) ⇒ B'(-4, 3) ⇒ B"(4, 3)
C(−2,−8) ⇒ C'(-2, 8) ⇒ C"(2, 8)
D(−10,−6) ⇒ D'(-10, 6) ⇒ D"(10, 6)
What is one thousand minus on hundred and ten
Answer:
The answer is 890 . ...... :D
Cars arrive at an automatic car wash system every 10 minutes on average. The cars inter-arrival times are exponentially distributed. Washing time for each is 6 minutes per car and is purely deterministic (i.e., the waiting line system is M/D/c). Assuming that the car wash has a single bay to serve the cars, what is the average number of cars waiting in line (L.)?
Answer:
the average number of cars waiting in line L[tex]q[/tex] is 0.45
Step-by-step explanation:
Given the data in the question;
Cars arrive at an automatic car wash system every 10 minutes on average.
Car arrival rate λ = 1 per 10 min = [ 1/10 × 60 ]per hrs = 6 cars per hour
Washing time for each is 6 minutes per car
Car service rate μ = 6min per car = [ 1/6 × 60 ] per hrs = 10 cars per hour
so
P = λ/μ = 6 / 10 = 0.6
Using the length of queue in M/D/1 system since there is only one service bay;
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ P² / ( 1 - P ) ]
so we substitute
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ (0.6)² / ( 1 - 0.6 ) ]
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.36 / 0.4 ]
L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.9 ]
L[tex]q[/tex] = 0.45
Therefore, the average number of cars waiting in line L[tex]q[/tex] is 0.45
