Step-by-step explanation:
We can set up the ration of the radian angle θ in your problem in terms of degrees given as the ratio: (Θ/2·pi) = (72/360), solving for Θ we get Θ = 1.26 radians. Then for the arc length s = Θ·r using this value gives s = 1.26·4 = 5.04
The number of gallons of water left in a swimming pool at time t minutes can be modeled by w(1) = -7t+B50. Find the y-intercept and explain what it represents in this situation.
Answer:
I'm not really sure
Step-by-step explanation:
soooooooory
PLEASE HELP QUICK!!!
COMPOUND INTEREST!!!
$600 is deposited in an account that pays 7% annual interest, compounded continuously. What is the balance after 5 years?
9514 1404 393
Answer:
$851.44
Step-by-step explanation:
The balance is given by the formula ...
A = Pe^(rt) . . . . principal P, interest rate r, t years
Using the given numbers, we find the balance to be ...
A = $600·e^(0.07·5) ≈ $851.44
Please help just put answer
The answer is: 15 ft
Hello I need this quickly pls
Answer:
Area = x² + 10x + 21
Step-by-step explanation:
Area = L * W
Length = (x + 7)
Width = (x + 3)
=> Area = (x + 7) * (x + 3)
=> Area = x² + 3x + 7x + 21
Combining like terms would result in;
=> Area = x² + 10x + 21
Hope this helps!
Which equation is true when x = 1/2?
Answer:
D
Explanation:
6/ 1/2 = 6*2, 6*2 not equal to 3
half of 8 is 4, not 16
1/2+2 = 2 1/2
10/ 1/2 = 10*2 = 20
Help me please will be appreciated thx
Answer:
-6 +8d -2c
Step-by-step explanation:
[tex]\frac{-2}{5} (15 -20d +5c) = \frac{-2}{5} \times 15 - \frac{-2}{5}\times20d +\frac{-2}{5}\times5c = -6 + 8d -2c[/tex]
hellp plsssss i need it
I still need help! Please! Help me
Part A = 60
Part B is C
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)
h(-4), h(0), h(4), h(8)
h(x)= {-(x+1)^2 + 7, x<2
{ -1/3x, x>4
h(-4)=
h(0)=
h(4)=
h(8)=
PLEASE HELP
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The first two x-values, -4 and 0, fall in the first part of the function definition.
There is no function definition for x = 4, as the second part only applies for x > 4.
The last x-value, 8, falls in the second part of the function definition.
The function is evaluated by putting the x-value where x is in the expression and doing the arithmetic. For example, ...
h(-4) = -(-4+1)^2 +7 = -(-3)^2 +7 = -9 +7 = -2
h(0) = 6
h(4) = undefined
h(8) = -8/3
What is the solution of log; (3x+2) = log: (4x-6)?
Answer:
x = 8
Step-by-step explanation:
Answer:
x = 8
Step-by-step explanation:
Cancel the log from both sides and you'll get:
[tex]3x + 2 \: = 4x - 6 \: \\ 6 + 2 = 4x - 3x \: \\ x = 8[/tex]
SOMEONE PLEASE HELP ME ANSWER ALL THESE IM IN SUMMER SCHOOL NO LINKS OR FILES I WOULD DEEPLY APPRECIATE IT<33
which expression is equivalent to 6 (3x + 4)?
A) 9x + 4
B) 18x + 4
C) 18x + 24
D) 9x + 10
Answer:
c number is the ans
Step-by-step explanation:
multiply each term with 6
HELPP!!! I need help ASAP
Answer:
the right answer is C
Step-by-step explanation:
___________
what is the mean absolute deviation for 9, 7, 6, 8, 7, and 5? (2 points) a 1 b 2 c 6 d 7
Answer: a. 1
Step-by-step explanation:
Given data: 9, 7, 6, 8, 7, and 5.
Mean absolute deviation: [tex]MAD=\dfrac1n\sum^n_{i=1}|x_i-m|[/tex], where m = mean
mean (m) = [tex]\frac{\text{Sum of values}}{\text{Number of values}}[/tex]
[tex]=\frac{42}{6}\\\\=7[/tex]
Now, [tex]MAD=\dfrac{|9-7|+|7-7|+|6-7|+|8-7|+|7-7|+|5-7|}{6}[/tex]
[tex]MAD=\dfrac{2+0+1+1+0+2}{6}[/tex]
[tex]MAD=\dfrac{6}{6}[/tex]
[tex]MAD=1[/tex]
Hence, the mean absolute deviation=1
Thus correct option is a. 1
The habitable part of Earth's surface has been estimated to cover 60 trillion square meters. Estimate the percent of this area occupied by humans if Earth's current population stood packed together as people do in a crowded elevator.The habitable part of Earth's surface has been estimated to cover 60 trillion square meters. Estimate the percent of this area occupied by humans if Earth's current population stood packed together as people do in a crowded elevator. HINT
Answer:
yay
Step-by-step explanation:
A store purchased a DVD for $12.00 and sold it to a customer for 50% more than the purchase price. The customer was charged a 7% tax when the DVD was sold.
What was the customer’s total cost for the DVD?
Answer:
$19.26
Step-by-step explanation:
12 × .5 = 6
6 + 12 = 18
18 × 0.07 = 1.26
1.26 + 18 = 19.26
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
Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon was studied in detail by George W. Pierce, a physics professor at Harvard. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (°F). These data are also available for download at the online study center.
X 20.0 16.0 19.8 18.4 17.1 15.5 14.7 17.1
Y 88.6 71.6 93.3 84.3 80.6 75.2 69.7 82.0
X 15.4 16.2 15.0 17.2 16.0 17.0 14.4
Y 69.4 83.3 79.6 82.6 80.6 83.5 76.3
Required:
a. Draw a scatter diagram displaying the data.
b. Find X- bar, Y- bar, a and b. Then find the equation of the least squares line y=a+bx.
c. Graph the least squares line on your scatter diagram. Be sure to use the point ( X-bar, Y- bar) as one of the points on the line.
Answer:
a) attached below
b) X - bar = 16.65
Y - bar = 80.04
y = 25.26 + 3.29 ( X )
c) attached in diagram below
Step-by-step explanation:
n = 15
∑ x = 20.0 + 16.0 + 19.8 + 18.4 + 17.1 + 15.5 + 14.7 + 17.1 + 15.4 + 16.2 + 15.0 + 17.2 + 16.0 + 17.0 + 14.4 = 249.8
∑ y = 88.6 + 71.6 + 93.3 + 84.3 + 80.6 + 75.2 + 69.7 + 82.0 + 69.4 + 83.3 + 79.6 + 82.6 + 80.6 + 83.5 + 76.3 = 1200.6
∑ xy = ( 20 * 88.6 ) + ( 16 *71.6 ) + ( 19.8 * 93.3 ) + ( 18.4 * 84.3 ) + ( 17.1 * 80.6 ) + (15.5 * 75.2 ) + ( 14.7 * 69.7 ) + ( 17.1 * 82.0 ) + ( 15.4 * 69.4 ) + ( 16.2 * 83.3 ) + ( 15 *79.6 ) + ( 17.2 * 82.6 ) + ( 16 * 80.6 ) + ( 17 * 83.5 ) + ( 14.4 * 76.3 )
= 20127.47
∑x^2 = 20.0^2 + 16^2 + 19.8^2 + 18.4^2 + 17.1^2 + 15.5^2 + 14.7^2 + 17.1^2 + 15.4^2 + 16.2^2 + 15.0^2 + 17.2^2 + 16.0^2 + 17.0^2 + 14.4^2
= 4200.56
∑ y^2 = 88.6^2 + 71.6^2 + 93.3^2 + 84.3^2 + 80.6^2 + 75.2^2 + 69.7^2 + 82.0 ^2 + 69.4^2 + 83.3^2 + 79.6^2 + 82.6^2 + 80.6^2 + 83.5^2 + 76.3^2
= 96725.86
a) Scatter diagram showing given data
Attached below
B)
X - bar = ∑x / n = 249.8 / 15 = 16.65
Y - bar = ∑y / n = 1200.6 / 15 = 80.04
where: Y = Temperature and X = Chirps per seconds
b = [ n ∑ xy - ( ∑x ∑y ) ] / [ n∑x^2 - ( ∑x )^2 ]
= [ 15 * 20127.47 - ( 249.8 * 1200.6 )] / [15* 4200.56 - ( 249.8 )^2 ]
= 2002.17 / 608.36 = 3.29
a = Y-bar - b( X-bar )
= 80.04 - 3.29( 16.65) = 25.26
equation for least squares line
y = 25.26 + 3.29 ( X )
C) Graph the least squares line on scattered diagram
attached below
O capital de R$ 12.000,00 foi aplicado a juros compostos à taxa de 60% ao ano durante 2 anos. Determine o montante? *
?Answer:
Step-by-step explanation:
In order to complete the square for the equation below, what value should be added to both sides of the equation?
x2 - 8x + ? = 42 + ?
Answer:
? = 16
Step-by-step explanation:
x2 - 8x + ? = 42 + ?
1. Take the coefficient of the middle term 8x, which is 8 and divide it by 2. [tex]\frac{8}{2} = -4[/tex]. Then square it [tex]-4^{2} = 16[/tex]
2. Take 16 and add it to both sides: [tex]x^2 - 8x + 16 = 42 + 16[/tex]
2. Take half of the coefficient 8 that you divided by 2, which is 4 and insert 4 into the equation [tex](x -4)^2 = 58[/tex]
3. ? = 16
Find the circumference of a
circle with diameter, d = 10.8cm.
Give your answer rounded to 3
SF.
Answer:
33.9
Step-by-step explanation:
r = d/2
= 5.4
[tex]2\pi \: r[/tex]
[tex] = (2)(\pi)(5.4)[/tex]
=33.93
Out of 400 people sampled, 56 had kids. Based on this, construct a 90% confidence interval for the true population proportion of people with kids.
Give your answers as decimals, to three places
___ < p < ___
Answer:
because having 90% means big
Wat is the average between 1,000, 2300,1000,2600
Answer:
1180.2
Step-by-step explanation:
The average of 1,000,2300,1000,2600 is 1180.2
13) A rectangular garden has an area of 45 square meters. The garden will be 4 meters longer than its width Write and sowe an equation to find the dimensions in meters.
Answer:
9m ×5m
Step-by-step explanation:
Area of a rectangle= length ×width
Let the width be W meters and the length be L meters.
2 equations can be written from the given information:
45= WL -----(1)
L= W +4 -----(2)
Substitute (2) into (1):
45= W(W +4)
Expand:
45= W² +4W
-45 on both sides:
W² +4W -45= 0
Factorise:
(W +9)(W -5)= 0
W+9=0 or W-5=0
W= -9 or W= 5
(reject)
Substitute W= 5 into (2):
L= 5 +4
L= 9
∴ The dimensions of the garden is 9m ×5m.
What is the slope of y=1/2x
Answer:
1/2
Step-by-step explanation:
If you know slope-intercept form, it is y = mx + b, and the value of m is the slope, so the slope = 1/2
Answer:
I'm not sure if you typed your question correct, But the slope is 1/2
Step-by-step explanation:
dababy less goo
1
Abdullah tracked the scores of his Science tests this year.
93, 71, 86, 95, 72, 81, ?
He lost the score from his final test, but knows he had a mean score of 82.
Calculate his missing score.
76 O
Activate Windows
Go to Settings to activate Windows.
11:30 AM
5/31/2021
Desktop
4») GG ENG
O
10
Answer:
76
Step-by-step explanation:
Answer:
I believe the answer is 76
Which set of equations shows a way to find 771 - 468?
Answer:
The one that has 303 as the answer is the correct one
WILL GIVE U BRAINLIEST
Are these triangles congruent? How do you know?
A. Not sure not enough info
B. Yes, by HL
C. Yes, by ASA
D: yes, by AAS
Answer:
C
Step-by-step explanation:
2 angles and a shared side.
shared side is between the two angles
23+15=7
29+21=8
12+15=6
74+12=?
Step-by-step explanation:
here are all the anwsers