Answer:
The order of finishing is important here, therefore you use permutations rather than combinations. Athlete A winning a gold medal, athlete B silver, and athlete C bronze is not the same as athlete A bronze, athlete B silver and athlete C gold for instance
69P3 = 69! / (69 -3!)
Step-by-step explanation:
1. Determine the intervals on which each function is increasing or
decreasing
(a) f(x) = x^3 - 11/2x^2 - 4x
Answer:
[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]
Step-by-step explanation:
We have the function:
[tex]f(x)=x^3-\frac{11}{2}x^2-4x[/tex]
And we want to determine the intervals for which the function is increasing or decreasing.
We will need to first find the critical points of the function. Note that our original function is continuous across the entire x-axis.
To find the critical points, we need to find the first derivative and then solve for the x. So:
[tex]f^\prime(x)=\frac{d}{dx}[x^3-\frac{11}{2}x^2-4x][/tex]
Differentiate:
[tex]f^\prime(x)=(3x^2)-\frac{11}{2}(2x)-(4) \\ f^\prime(x)=3x^2-11x-4[/tex]
Set the derivative equal to 0 and solve for x:
[tex]0=3x^2-11x-4[/tex]
Factor:
[tex]0=3x^2-12x+x-4 \\ 0=3x(x-4)+(x-4) \\ 0=(3x+1)(x-4)[/tex]
Zero Product Property:
[tex]3x+1=0\text{ or } x-4=0 \\ x=-\frac{1}{3}\text{ or } x=4[/tex]
Therefore, our critical points are -1/3 and 4.
We can thus sketch the following number line:
<————-(-1/3)——————————————(4)—————>
Now, let’s test values for the three intervals: less than -1/3, between -1/3 and 4, and greater than 4.
For less then -1/3, we can use -1. So, substitute -1 for x for our first derivative and see which we get:
[tex]f^\prime(-1)=3(-1)^2-11(-1)-4=3+11-4=10>0[/tex]
The result is positive.
Therefore, for all numbers less than -1/3,f(x) is increasing (since its derivative is positive).
For between -1/3 and 4, we can use 0. Substitute 0 for our derivative:
[tex]f^\prime(0)=3(0)^2-11(0)-4=-4<0[/tex]
The result is negative.
Therefore, for all numbers between -1/3 and 4, f(x) is decreasing (since its derivative is negative).
And finally, for greater than 4, we can use 5:
[tex]f^\prime(5)=3(5)^2-11(5)-4=16>0[/tex]
The result is positive.
Therefore, for all numbers greater than 4, f(x) is increasing (since its derivative is positive.
Therefore:
[tex]\text{$f(x)$ is increasing for $x<-\frac{1}{3}$ and $x>4$}\\ \text{ $f(x)$ is decreasing for $-\frac{1}{3}<x<4$}[/tex]
In interval notation:
[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]
What is 8 divide 1/5?
What is 8 divide by 1/5
Answer:
40
Step-by-step explanation:
Suppose a random sample of n=330 tenneagers 13 to 17 years of age was asked if they use social media. Of those surveyed, 252 stated that they do use social media. Find the sample proportion of tenneagers 13 to 17 years of age who use social media
Answer:
what is
Step-by-step explanation:
The sample proportion of the teenagers 13 to 17 years of age who use social media is 0.236.
What is a Sample Proportion?Sample proportion is defined as the proportion of something from a given sample which has a particular characteristic.
The formula to calculate the sample proportion is,
p = Number of successes in a particular sample / Sample size
Given that,
a random sample of n = 330 teenagers 13 to 17 years of age was asked if they use social media.
Sample size = 330
Of those surveyed, 252 stated that they do use social media.
We have to find the proportion of teenagers 13 to 17 years of age who use social media.
Number of failures = 252
Number of successes = 330 - 252 = 78
Sample proportion = 78 / 330 = 0.236
Hence the sample proportion is 0.236.
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Write the equation of a line parallel to the line y=2x
Answer:
to create an equation that is parallel to a line, you keep the slope or rate of change the same, all you do is change the y intercept. so you have to keep
y = 2x, but then you can add any number to the end.
Simonne, Marco, and Evon were partners in
business. Simonne and Marco each received
twice as much of the profit as Evon received. If
the total profit was $1,800, how much did Evon
receive?
What is 15.23 rounded to the nearest hundredth
Answer:
15.20
Step-by-step explanation:
Find the length of BD and EC.
A
D
9
8
B
с
BD =
EC =
Find the general solution of the given system. Use a computer system or graphing calculator to construct a direction field and typical solution curves for the system
Answer:
hello your question is incomplete attached below is the complete question and solution
answer : general solution ( X ) = [tex]C_{1} e^{3t} \left \{ {{1} \atop {-1}} \right. + C_{2} e^{3t} \left \{ {{1} \atop {-1}} \right.[/tex]
Step-by-step explanation:
attached below is the detailed solution to determine the general solution of the given system
general solution ( X ) = [tex]C_{1} e^{3t} \left \{ {{1} \atop {-1}} \right. + C_{2} e^{3t} \left \{ {{1} \atop {-1}} \right.[/tex]
y= -2x+8
what is the value of y when 0 is the value of x?
Not sure what you mean but will be explaining about y = 0 and x =0 anyway.
So for x = 0, that means the value of x is 0.
y = -2(0)+8
y=0+8
y=8
So when x = 0, the value of y is 8 (y = 8) or we can write (0,8)
For y = 0, that means the value of y is 0.
0=-2x+8
-8=-2x
-2x=-8
x=4
So when y = 0, x = 4. We can write as (4,0)
Find the distance between E(5,3) and F(-4,3).
Answer:
3 - 3 = 0 units There is no distance, the points are in the same place.
Step-by-step explanation:
6x² – x=2
Factor and solve
Answer:
x=2/3 or x=−1/2
Step-by-step explanation:
6x²−x=2
6x²−x−2=2−2
6x²−x−2=0
(3x−2)(2x+1)=0
3x−2=0 or 2x+1=0
x=2/3 or x=−1/2
Seven and nine thousands in decimal form
All the fudge machines at a chocolate factory work at the same rate. Six machines working simultaneously can complete a big order in 22 hours.
b
How many hours would it take to fill the order if the number of working machines increased by a factor of 2?
Answer: 11 hours
Step-by-step explanation:
22/2 = 11
I need help with this can someone help me I have a few other ones as well I don’t understand anyone?
Answer:
x=59
Step-by-step explanation:
The sum of the interior angles of a triangle add up to 180 degrees. That means that (x+12)+(x)+(x-9)=180 degrees in total. If we combine the like terms (combine the xs and regular constant values), the xs add up to 3x (x+x+x) and the regular constants add up to 3 (12+-9=3). If we rewrite this in a more simplified form, we get 3x+3=180. Subtract 3 on both sides to get 3x=177 because we want to isolate x. 3x=177 divide 3 on both sides and we get 59. x=59
Kaley and Tom both work at Publix. for $7.68 per hour. This week Kaley worked 5 more hours than Tom in overtime. Write an expression that represents the weeks' wages for Kaley and Tom if h represents the number of hours Tom worked? What is another way to write the expression?
Could someone please guide me towards solving side x I know I have to use trig but I'm completely lost
Answer:
x = 33.13 units
Step-by-step explanation:
Let the altitude of the triangle be h units.
[tex] \sin 65 \degree = \frac{h}{31} \\ \\ 0.906307787 = \frac{h}{31} \\ \\ h = 0.906307787 \times 31 \\ \\ h = 28.0955414 \\ \\ \cos \: 32 \degree = \frac{h}{x} \\ \\ 0.8480480962 = \frac{28.0955414}{x} \\ \\ x = \frac{28.0955414}{0.8480480962} \\ \\ x = 33.1296556 \\ \\ x \approx 33.13 \: units[/tex]
Answer:
x = 23.7926Step-by-step explanation:
Step 1
Find the length of vertical line segment, lets call it h. Use function cos
h/31 = cos 66°h = 31 * cos 66° = 31*0.4067 = 12.6077Step 2
Find x using another function, sin
h/x = sin 32°x = h / sin 32°x = 12.6077 / 0.5299x = 23.7926a dolphin in a aquaruim is 12 feet long. A scale model of the dolphin is 3 1/2 in long. What is the scale factor of the model
Answer:The scale factor= 1 : 41.14
Step-by-step explanation:
I did research on it
What is the equation of the line that passes through the point (5,2) and has a slope
of -3/5
Answer:y = -0.6x + 5
Step-by-step explanation:
Answer:
yessir the one on top is right btw
Step-by-step explanation:
hope this helped
There are 7 students in a class: 2 boys and 5 girls.If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a girl?
Answer:
two sevenths
Step-by-step explanation:
what kind of graph is this?
Answer:
Linear
General Formulas and Concepts:
Types of Graphs
LinearQuadraticExponentialCubicSquare rootCube rootStep-by-step explanation:
Whenever the graph is a straight line (either a diagonal or a horizontal, NOT a vertical line), it will always be linear.
write the equation of the line in standard form passing through (2,-4) with a slope of -7
Answer:
7x+Y=-2
Step-by-step explanation:
(y-y1)=m(x-x1)
(Y+4)=-7(x-2)
Y+4=-7x+2
Y+7x=2-4
7x+Y=-2
Michael wants to purchase a jeep. The purchase price of the Jeep is $37,000. The
dealership will allow him to pay cash or finance the Jeep with a down payment of
$5,000.00 and 60 monthly payments of $625.00. Michael chose to finance the jeep.
Answer the following questions.
a) What is the amount financed?
b) What is the total amount of monthly payments?
C} What is the amount of the finance charge?
Answer:
A) $32,000 B) $37,500 C) $5,500
Step-by-step explanation:
Price of jeep: $37,000
Michael uses $5,000 of his own money toward that total $37,000-$5,000= $32,000
Monthly payments $625.00×60months=$37,500
After paying $5,000 of his own money, & bringing theamount owed to $32,000. Michael still has to pay back $37,500. Making, the finance chardge $5,500. ($37,500-$32,000= $5,500)
Amount financed = $32000, total amount of monthly payment = $37500 and total amount of the finance charge = $5500.
What is dealership finance ?
"Dealer financing is a type of loan that is originated by a retailer to its customers and then sold to a bank or other third-party financial institution. The bank purchases these loans at a discount and then collects principle and interest payments from the borrower. This is also called an indirect loan."
According to the question,
Given,
Price of jeep = $37000
Down payment = $5000
Total number of monthly payment = 60
Amount to be paid after down payment
= $37000 - $5000
= $32000 ____( 1 )
Amount paid in Monthly payments = $625.00 × 60months
= $37500 ____( 2 )
From ( 1 ) and ( 2 ) we get,
Finance charge amount = Total monthly amount - Total amount financed
= $37500 - $32000
= $5500
Hence, amount financed , total amount monthly payment and total amount of the finance charge is $32000 , $37500 and $5500.
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A baby is 18in long at birth and 27 in long in ten months
Answer:
27-18 = 9, baby grew 9 inches
Step-by-step explanation:
The length of the baby will increase 0.9 inch per month.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.equation modelling : Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis and results of the given problemGiven is that a baby is 18in long at birth and 27in long in ten months
At birth, the length of baby = 18 inches.
After 10 months, the length of the baby = 27 inches.
Increase in length per month will be -
r = (27 - 18)/(10 - 0)
r = 9/10
r = 0.9 inch
Therefore, the length of the baby will increase 0.9 inch per month.
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Determine an expression for dy
dx given that x = sin3
(t)andy = cos3
(t)
Answer:
[tex]\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }[/tex]
Step-by-step explanation:
Recall that using the chain rule we can state:
[tex]\frac{dy}{dt} =\frac{dy}{dx}*\frac{dx}{dt}[/tex]
and therefore solve for dy/dx as long as dx/dt is different from zero.
Then we find dy/dt and dx/dt,
Given that
[tex]x=sin^3(t)\\dx/dt = 3 sin^2(t)* cos(t)[/tex]
And similarly:
[tex]y=cos^3(t)\\dy/dt=-3\,cos^2(t)*sin(t)[/tex]
Therefore, dy/dx can be determined by the quotient of the expressions we just found:
[tex]\frac{dy}{dx} =\frac{dy/dt}{dx/dt} =\frac{-3\,cos^2(t)*sin(t)}{3\,sin^2(t)*cos(t)} =-\frac{cos(t)}{sin(t)}[/tex]
now notice that we can find [tex]cos(t) = \sqrt[3]{y}[/tex] from the expression for y,
and [tex]sin(t) = \sqrt[3]{x}[/tex] from its expression for x.
Therefore dy/dx can be written in terms of x and y as:
[tex]\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }[/tex]
Which expression is equivalent to 4x+6y-8x
Answer:The expression is 6y - 4x
Step-by-step explanation:
Answer:
-4x+6y
Step-by-step explanation:
4x+6y-8x4
(4x-8x)+6y
−4x+6y
. "A number is less than or equal to -11.".
Answer:
x <(with a line underneath the carrot) -11
Step-by-step explanation:
Hope this helps! Could not find the symbol.
The inequality for x which is less than or equal to -11 is written as x ≤ -11 or x + 11 ≤ 0.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
Let the required number is x.
In the given question,
Number x is less than or equal to -11.
The inequality for x which is less than or equal to -11 can be written as,
x ≤ -11
The inequality can be further simplified as,
⇒x + 11 ≤ 0
The inequality for x is x + 11 ≤ 0.
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Which of these shows the following expression factored completely? 6x2 – 13x +5
Answer:
B
Step-by-step explanation:
That's my guess.
Answer:
C
Step-by-step explanation:
Write an equivalent addition expression to : -10 – (-4)
Answer:
-6
Step-by-step explanation:
-10-(-4)=-1+4=-6
Hope this helps plz mark brainliest ;D
Describe the graph of x ≤ −2
Solve for x.
10x−3x+5=26
Answer:
x = 3
Step-by-step explanation:
10x−3x+5=26 (Given)
7x + 5 = 26 (Combine like terms)
7x = 21 (subtraction Property of equaity)
x = 3 (division Property of equaity)