Answer:
V = 36 ft3
Step-by-step explanation:
2*6= 12
12*3= 36ft
If m = 2s and n = (2s - 1) / 3 then what is the value of s form m = n ?
Answer:
[tex]s = - \frac{1}{4} [/tex]
Step-by-step explanation:
For m to be equal to n,
[tex]2s = \frac{2s- 1}{3} [/tex]
Multiply both sides by 3:
[tex]6s = 2s - 1[/tex]
Minus 2s on both sides:
[tex]4s = - 1[/tex]
Divide by 4 on both sides:
[tex]s = - \frac{1}{4} [/tex]
Find all x-intercepts of the function.
y = x³ - 9x² + 18x
Answer:
Step-by-step explanation:
X-intercepts mean y=0 so we have
y = x³ - 9x² + 18x = 0
Factoring
x³ - 9x² + 18x = 0
x*(x² - 9x +18) = 0
x*(x-3)*(x-6) = 0
So x-intercepts are at x=0, x=3 and x=6
Answer:
Step-by-step explanation:
see plot, intercepts at 0, 3, 6
A small coffee shop sells bags of two types
of coffee. Bag A contains 24 ounces and
costs $15.60. Bag B contains 30 ounces
and costs $20.40. Which statement is true?
A. Bag A costs 3¢ less per ounce than Bag B.
B. Bag A costs 3¢ more per ounce than Bag B.
C. Bag A costs 2¢ less per ounce than Bag B.
D. Bag A costs 2¢ more per ounce than Bag B.
The
exact solusion of the IVP
Answer:
[tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/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 EqualityAlgebra I
|Absolute Value|FunctionsFunction NotationExponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Algebra II
Logarithms and Natural LogsEuler's number eCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Differential Equations
Separation of VariablesAntiderivatives - Integrals
Integration Constant C
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Logarithmic Integration
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y' = \frac{xy}{2 + x^2}[/tex]
[tex]\displaystyle y(0) = 2[/tex]
Step 2: Rewrite
Separation of Variables
Rewrite Derivative Notation: [tex]\displaystyle \frac{dy}{dx} = \frac{xy}{2 + x^2}[/tex][Division Property of Equality] Isolate y's: [tex]\displaystyle \frac{1}{y} \frac{dy}{dx} = \frac{x}{2 + x^2}[/tex][Multiplication Property of Equality] Rewrite Derivative Notation: [tex]\displaystyle \frac{1}{y} dy = \frac{x}{2 + x^2} dx[/tex]Step 3: Find General Solution Pt. 1
Integration
[Equality Property] Integrate both sides: [tex]\displaystyle \int {\frac{1}{y}} \, dy = \int {\frac{x}{2 + x^2}} \, dx[/tex][1st Integral] Integrate [Logarithmic Integration]: [tex]\displaystyle ln|y| = \int {\frac{x}{2 + x^2}} \, dx[/tex]Step 4: Identify Variables
Identify variables for u-substitution for 2nd integral.
u = 2 + x²
du = 2xdx
Step 5: Find General Solution Pt. 2
[2nd Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle ln|y| = \frac{1}{2}\int {\frac{2x}{2 + x^2}} \, dx[/tex][2nd Integral] U-Substitution: [tex]\displaystyle ln|y| = \frac{1}{2}\int {\frac{1}{u}} \, du[/tex][2nd Integral] Integrate [Logarithmic Integration]: [tex]\displaystyle ln|y| = \frac{1}{2} ln|u| + C[/tex][Equality Property] e both sides: [tex]\displaystyle e^{ln|y|} = e^{\frac{1}{2} ln|u| + C}[/tex]Simplify: [tex]\displaystyle |y| = e^{\frac{1}{2} ln|u| + C}[/tex]Rewrite [Exponential Rule - Multiplying]: [tex]\displaystyle |y| = e^{\frac{1}{2} ln|u|} \cdot e^C[/tex]Simplify: [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|u|}[/tex]Back-Substitute: [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|2 + x^2|}[/tex]Our general solution is [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|2 + x^2|}[/tex].
Step 6: Find Particular Solution
Substitute in point: [tex]\displaystyle |2| = Ce^{\frac{1}{2} ln|2 + 0^2|}[/tex]Evaluate |Absolute Value|: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2 + 0^2|}[/tex]|Absolute Value| Evaluate exponents: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2 + 0|}[/tex]|Absolute Value| Add: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2|}[/tex]|Absolute Value| Evaluate: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln(2)}[/tex][Division Property of Equality] Isolate C: [tex]\displaystyle \sqrt{2} = C[/tex]Rewrite: [tex]\displaystyle C = \sqrt{2}[/tex]Substitute in C [General Solution]: [tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/tex]∴ Our particular solution is [tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/tex].
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differential Equations
Book: College Calculus 10e
A square pyramid has a volume of 1350 ft3. If the base is a square with side
lengths 15 feet, what is the height?
PLZ HELP WILL GIVE 50 POINTS - QUADRATIC APPLICATIONS
find how far away (ground distance) from the catapult will white bird be at its highest. (round to the nearest 2 decimal points)
h= -0.114x^2+2.29x+3.5
Answer:
The bird will be at a ground distance of 10.04 units away.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Equation for the height:
The height of the bird after x seconds is given by:
[tex]h(x) = -0.114x^2 + 2.29x + 3.5[/tex]
Which is a quadratic equation with [tex]a = -0.114, b = 2.29, c = 3.5[/tex].
When the bird is at its highest?
Quadratic equation with [tex]a < 0[/tex], and thus, at the vertex. The ground distance is the x-value of the vertex. Thus
[tex]x_{v} = -\frac{b}{2a} = -\frac{2.29}{2(-0.114)} = 10.04[/tex]
The bird will be at a ground distance of 10.04 units away.
You can transform V to V' by translating it and then performing a dilation centered at V'. Find the translation rule and scale factor of the dilation. Simplify the scale factor and write it as a proper fraction, improper fraction, or whole number. Translation: (x, y) -> (___,___) Scale factor: ___
Answer:
Translation rule → (x + 10, y + 1)
Scale factor = 4
Step-by-step explanation:
Coordinates of V → (-8, -2)
Coordinates of V' → (2, -1)
Therefore, point V has been translated from x = -8 to x = 2,
Translation on x-axis → 2 - (-8) = 10 units
Translation on y-axis → -1 - (-2) = -1 + 2
= 1 unit
If the point V is translated 10 units right and 1 unit upwards,
Rule for the translation → (x + 10, y + 1)
Radius of the circle V = 2 units
Radius of the circle V' = 8 units
Scale factor = [tex]\frac{\text{Dimension of the image}}{\text{Dimension of the original}}[/tex]
= [tex]\frac{\text{Radius of the image}}{\text{Radius of the original}}[/tex]
= [tex]\frac{8}{2}[/tex]
= 4
Therefore, circle V has been dilated by a scale factor of 4 to form circle V'.
What is the name of the following net?
Answer:
[tex]\large\colorbox{gold}{sǫᴜᴀʀᴇ ᴘʏʀᴀᴍɪᴅ}[/tex]
A certain smart phone game app allows the player, once a day, to spin a wheel with 8 different sections. Seven of the sections contain a small prize and one of the sections is the grand prize, in which the player wins all of the other seven prizes. The makers of the game claim that the wheel has an equally likely probability of landing on each section. Andraya has played the game for several months and believes that the grand prize occurs less often than the game makers claim.
Required:
What would be appropriate hypotheses for the Andraya to test?
Answer:
The appropriate hypothesis set for Andraya to test is:
[tex]H_0: p = 0.125[/tex]
[tex]H_1: p < 0.125[/tex]
Step-by-step explanation:
The makers of the game claim that the wheel has an equally likely probability of landing on each section.
That is, the makers claim that the probability of earning the grand prize is:
[tex]p = \frac{1}{8} = 0.125[/tex]
Andraya has played the game for several months and believes that the grand prize occurs less often than the game makers claim.
At the null hypothesis, we test if it happens as often as the makers claim, that is, the proportion is 0.125. So
[tex]H_0: p = 0.125[/tex]
At the alternate hypothesis, we test if it happens less ofter than the makers claim, that is, the proportion is less than 0.125. So
[tex]H_1: p < 0.125[/tex]
The appropriate hypothesis set for Andraya to test is:
[tex]H_0: p = 0.125[/tex]
[tex]H_1: p < 0.125[/tex]
Kyle needs to fill the wooden platform he made to make it more stable. What is the volume of the platform?
Answer:
720 in³
Step-by-step explanation:
v = l * w * h
Break into two parts:
Bottom
v = 12 * 6 * 5
v = 360 in³
Top
v = 8 * 5 * 9
v = 360 in³
Total
v = 360 + 360
v = 720 in³
Plz help me well mark brainliest if correct!!..
Answer: A/The LINE graph
Step-by-step explanation:
Why is a square also a rectangle? Use the drop-down menus to complete the explanation.
A square is also a rectangle because it possesses all the properties of a rectangle. Similar to a rectangle, a square has: interior angles which measure 90° each, opposite sides that are parallel and equal, and many more attributes as well. Keep in mind however that a square is a special type of rectangle because it posseses some additional properties which don't apply to normal rectangles like the fact that all four sides of a square are equal, and diagonals of a square bisect each other at right angles.
I hope this helps! <3
Answer:
Step-by-step expl
A square is also a rectangle because it possesses all the properties of a rectangle. Similar to a rectangle, a square has: interior angles which measure 90° each, opposite sides that are parallel and equal, and many more attributes as well. Keep in mind however that a square is a special type of rectangle because it posseses some additional properties which don't apply to normal rectangles like the fact that all four sides of a square are equal, and diagonals of a square bisect each other at right angles.
A two dimensional shape with four angles
Answer:
A rectangle I think
Please help!!! I have a chance to get $50 if I get all of these questions right!!
If you don't know all the answers please don't answer. Please answer all of the questions correctly like be 110% sure that you are correct on all of them please!! I put the questions in as an attachment like a screenshot please please please help and answer all the questions and answer them with 110% certainty that you know what you are doing!!
Answer:
number 4 is 244 number 5 is 43
Step-by-step explanation:
order of operations is key here
4:6 to the power of 3 is first
216+7*4
now do 7*4
216+28
now simplify
244
5: this one is a little bit more tricky
do the stuff inside the parentheses first
4^2+1=17
3(17)-2^3
exponent next
3(17)-8
multiply next
51-8
43 is your answer
there you go
Match the correct word with it's definition
Answer:
Rule by a small group : Oligarchy
Rule by Citizens : Democracy
Rule by No one Anarchy
Rule by king or Queen : Monarchy
Write an equation of the line with a slope of 5/2 and a y intercept of 1
Answer:
y=5/2x+1
Step-by-step explanation:
y=mx+b
where m=slope and b=y-intercept
so
y=5/2x+1
Over the course of one day, a store owner determined that 80% of customers bought a drink and 30% of customers bought a snack
If the store sold 120 snacks that day, how many more drinks than snacks did the store sell? Enter the answer in the box.
The store sold 40
more drinks than snacks.
Which equation represents the parabola with focus (8, 4) and vertex (8, - 2)
Answer:
8.4 whic e querido representante the parábola 8.3
HELP ME PASS THANKS!!!
h ( - 5 ) = - 2 × ( - 5 )
h ( - 5 ) = 10
____________________
f ( h ( - 5 ) ) = f ( 10 )
f ( 10 ) = 10 / 10 - 8
f ( 10 ) = 10 / 2
f ( 10 ) = 5
Please help I am so confused and I would really appreciate it ♥️♥️
Can someone help me answering this question
Answer: Choice D)
Determine the percentage of values occurring above and below that value
==========================================================
Explanation:
Let's go through the answer choices
A) If we add up all the scores and divide by n, which is the number of scores, then we get the sample mean xbar. We can refer to this as simply the mean. This won't get us the percentile, so we can rule out choice A.B) Subtracting the max and min gets us the range. Range = max - min. We can rule out choice B. C) We can rule out choice C. The steps described here determine the mean absolute deviation (MAD) which is similar in nature to the standard deviation. It tells us how spread out the data set is, so it's somewhat related to the range as well. Unfortunately, we can't figure anything about percentiles with this.D) This must be the answer as there isn't anything left. Turns out this set of steps is the correct method to find the percentile. Technically all you need to do is the "below" portion and ignore the "above" portion of the statement. If we say "the 25th percentile is K", then that is another way of saying "25% of the data is below K".Answer:
D
Step-by-step explanation:
Which ordered pair belongs to the function shown by this mapping diagram?
Answer:
{(7, 3), (8, 1), (9, 1), (10, 2)}
Step-by-step explanation:
Options are missing for this given problem, however, let's find the ordered pairs that should belong to the function shown by the mapping above:
We have the x-values (inputs) on our left while the corresponding y-values (outputs) are on our right.
The ordered pairs (x, y) are as follows:
{(7, 3), (8, 1), (9, 1), (10, 2)}
A measuring cylinder of radius 3cm contains water to a height of 49cm.if this water is poured into a similar cylinder of radius 7cm, what will be the height of the water column
Answer:
9 cm.
Step-by-step explanation:
Volume of a cylinder == pi r^2 h.
The volume of the water is constant so:
pi * 3^2 * 49 = pi * 7^2 h
9 *49 = 49 h
h = 9 cm.
Type the correct answer in each box. Use numerals instead of words.
Simplify the following polynomial expression.
(5x2 + 133 – 4) - (17:2 + 74 - 19) + (50 – 7)(3x + 1)
1 2 -
+
Answer:
14
Step-by-step explanation:
The expression for the polynomial is A = 3x² - 10x + 8
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the polynomial equation be represented as A
Now , the value of A is
A = ( 5x² + 13x - 4 ) - ( 17x² + 7x - 19 ) + ( 5x - 7 ) ( 3x + 1 ) = ax² - bx + c
Let's simplify the left-hand side of the equation using the distributive property and combining like terms:
A = (5x² + 13x - 4) - (17x² + 7x - 19) + (5x - 7)(3x + 1)
A = 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² - 16x - 7
A = 3x² - 10x + 8
Now we have:
a = 3, b = -10, and c = 8
Hence , the final equation is A = 3x² - 10x + 8
To learn more about polynomials click :
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The table shows the mean number of minutes spent on homework last weekend. The MAD for both sets of data is 5. Which number correctly completes the statement: The difference between the means is _______ times the value of the MAD of each set of data. (Subtract the two means and then divide that difference by 5.)
A poll states that Hillary Clinton will receive 43 percent of the vote. There is an 8 percent margin of error. What do you think of the poll
Step-by-step explanation:
This system of election result forecast is called a non-representative poll with a high percent margin of error. and used as an alternative to an expensive and tedious representative poll system.
Non-representative polls can be used to produce accurate electoral predictions and may frequently be done faster and cheaper than typical survey procedures.
Not just for the election forecasts, but also for public opinion on a wide variety of social, economic, and cultural topics, non-representative polling appears promising.
Which congruence statement correctly compares the two triangles shown?
A) AABD - ABDC
B) AABD - ACDB
C) ADBA - ADBC
OD) AADB - ABCD
Answer:
B) ABD=CDB
Step-by-step explanation:
who’s tryna help me with
my im3 final pls !!
Answer:
Step-by-step explanation:
Wat
Write an explicit formula for am, the nth term of the sequence 5, 30, 180, ....
Answer:
Am = 5 * 6^(m-1)
Step-by-step explanation:
30/5 = 6
180/30 = 6
Am = 5 * 6^(m-1)
A snail can travel 390 inches in 5 hours. How far does it travel in 10 minutes?