Answer:
20 students
Step-by-step explanation:
Step 1:
Calculate the percentage of students who brought oranges by taking away the percentage of students who brought bananas and apples from the total percentage of students.
100-(20+35)
=45
Step 2:
Equate the percentage of students who brought oranges to the number of students who brought oranges
45%=9
100%
(100×9)/45
=20 students
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
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
Given the formula A = 5h (B + b); solve for B.
2
Answer:
A=5h(B+b)
A/5h=B+b
A/5h - b= B
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).
____________ 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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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
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:
What is the measure of the angle in red?
70°
Answer:
See pic below.
Answer: C. 380°
Step-by-step explanation:
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
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:
Which of the following quadratic equations is written in general form?
The 3rd one
Step-by-step explanation:
Reason being that it has no factors, meaning it cannot be simplified any further, but quadratic method can be used to attain factors.
hope it makes sense :)
what is heavier ten tons of wool or ten tons of steel
The figure below is a rectangular prism.
Which edge is parallel to segment BD?
A. HK
B. BM
C. DK
D. AH
2. Write the equation of the line in point-slope form.
(-1,3) and (2,9)
Answer:
y - 9 = 2 (x - 2)
Step-by-step explanation:
y2 - y1 / x2 - x1 9 - 3 / 2 - (-1) 6/3 = 2
y - 9 = 2 (x - 2)
18. The maintenance department ordered $3,450 worth of supplies from a valve and fitting supplier. The
supplier will allow a 15% discount because of the large order. How much will the maintenance department
have to pay for the supplies?
A. $2,932.50
B. $3,398.25
C. $3,406.45
D. $2,954.50
Answer:
A) [tex]\$\ 2932.5[/tex]
Step-by-step explanation:
One is given that a certain amount of money was allotted to be spent on supplies. However, there was a discount applied to the purchase. One is asked to find the amount of money actually spent on the supplies.
$3450 was the initial price that was to be spent on supplies, however, a (15%) discount was applied to this price. Subtract (15) from (100) to find the percent value that was actually spent on supplies.
[tex]100-15=85[/tex]
(85%) of the allotted money was actually spent on supplies. Now one has to find out the numerical value of the amount spent. Divide (85) by (100) and then multiply it by the amount of money allotted to the purchase, to fin the amount actually spent on the purchase.
[tex]3450*(\frac{85}{100})\\\\=3450*0.85\\\\=2932.5[/tex]
Simplify Square root (150n^2)
Answer:
12
Step-by-step explanation:
Select the expression that has a value of 13.
9 + 3 x (2 ÷ 3) + 6
(9 + 3) x 2 ÷ 3 + 6
9 − (3 x 2) ÷ 3 + 6
(9 + 3 x 2) ÷ 3 + 6
Answer:
9 − (3 x 2) ÷ 3 + 6 is the answer
Please help me to find this answer
Step-by-step explanation:
angle of a triangle is 180, therefore to get the remaining one, subtract the sum of the two knows from 180, also for the second one; angle on a straight line is as well 180, since you have fine the interior one, subtract it from 180 to get the second answer
Answer:
so angles in a triangle add up to 180,
32+50+m<MQP=180
82+m<MQP=180
m<MQP=180-82
=98°
and angles on a straight line add up to 180 therefore
m<MQR=180-m<MQP
=180-98
=82
I hope this helps and if you don't understand feel free to ask
PLS HELP
Find an equation of the line with a y-intercept of -3 and an x-intercept of -4.5
Answer:
y = - [tex]\frac{2}{3}[/tex] x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (- 4.5, 0 ) ← coordinates of intercepts
m = [tex]\frac{0-(-3)}{-4.5-0}[/tex] = [tex]\frac{0+3}{-4.5-0}[/tex] = [tex]\frac{3}{-4.5}[/tex] = - [tex]\frac{2}{3}[/tex]
The line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = - [tex]\frac{2}{3}[/tex] x - 3 ← equation of line
Hi! I'd appreciate if you could help me on this question.
Liam is buying bottles of soda in packages that contain 8 bottles each. If the total number of sodas Liam bough t was between 45 and 50, how many did he buy? Explain your answer.
Answer:
48
Step-by-step explanation:
We need to find the multiples of 8
8,16,24,32,40,48
48 is between 45 and 50 so he must have bought 48
Answer:
6 bottles
Step-by-step explanation:
For this question we need to know the multiple of 8 which are:
8 x 1 = 8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32
8 x 5 = 40
8 x 6 = 48
8 x 7 = 56
There is only one multiple, which is greater than 45 but less than 50, which is 8x6 l.
This means he bought 6 bottles.
Answered by g a u t h m a t h
Prove that: sec⁴B - sec²B = tan⁴B + tan²B.
Step-by-step explanation:
sec⁴B - sec²B = sec²B(sec²B - 1)
= (1 + tan²B)(tan²B)
= tan⁴B + tan²B
= Right-hand side (Proven)
Find the value of x.
A. 57
B. 72
C. 90
D. 124
Answer:
90
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)
105 = 1/2 (120+x)
210 = 120+x
Subtract 120 from each side
210-120 = x
90 =x
The value of Intercepted Arcs x will be 90. so option C is correct.
What is the relation between line perpendicular to chord from the center of circle?If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.
Or
|AC| = |CB|
Angle Formed by Two Chords= 1/2 (Sum of Intercepted Arcs)
105 = 1/2 (120+x)
210 = 120+x
Subtract 120 from each side;
210-120 = x
90 =x
Hence, the value of Intercepted Arcs x will be 90. so option C is correct.
Learn more about chord of a circle here:
https://brainly.com/question/27455535
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Help me please and thank you
Step-by-step explanation:
jlejej
are u using chrome os
1. In the past, Sam cashed his paycheck each month at Ready Cash, a check cashing service that
charges a 5% fee. He recently opened a checking account at Bank of America so he can now
deposit and/or cash his paycheck without a fee. If Sam is making $28,500 per year, how much will
he save by not going to Ready Cash anymore?
Step-by-step explanation:
28000 ÷ 100
=280
280 × 5
=1400
I need the answer explained
Answer:
1.33
Step-by-step explanation:
62 can only be subtracted from 82 once. So 82.46-62 would be 20.46. Since you can't subtract anymore you put a decimal point. 62x3=186 and 20.46-186=1.86 and you can subtract 186-186=0.
help! due august 12th
Please Answer This!!! I NEEEDDD TOOO KNOWWWWW ANSWER!!!
Answer:
77.5
Step-by-step explanation:
Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B
Find an equation of a plane containing the line r=⟨0,4,4⟩+t⟨−3,−2,1⟩ which is parallel to the plane 1x−1y+1z=−5 in which the coefficient of x is 1.
..?.. = 0.
The plane you want is parallel to another plane, x - y + z = -5, so they share a normal vector. In this case, it's ⟨1, -1, 1⟩.
The plane must also pass through the point (0, 4, 4) since it contains r(t). Then the equation of the plane is
⟨x, y - 4, z - 4⟩ • ⟨1, -1, 1⟩ = 0
x - (y - 4) + (z - 4) = 0
x - y + z = 0
Surface Area of cones
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
9514 1404 393
Answer:
64.1 ft²
Step-by-step explanation:
The area of the cone is given by ...
A = πr(r +h) . . . . for radius r and slant height h
A = π(2 ft)(2 ft +8.2 ft) ≈ 64.1 ft²
I need help on this problem
9514 1404 393
Answer:
see attached
Step-by-step explanation:
(a) The graph is scaled by a factor of 2, and shifted up 1 unit. The scaling moves each point away from the x-axis by a factor of 2. The points on the x-axis stay there. The translation moves that scaled figure up 1 unit.
__
(b) The graph is reflected across the x-axis and shifted right 4 units. The point on the x-axis stays on the x-axis.
