Answer:
[tex]thank \: you[/tex]
Integration 4t√t+adt
Answer:
Step-by-step explanation:
Integration (4t√t+a)dt
[tex]\int \left ( 4 t\sqrt t +a \right )dt\\\\=\int\left ( 4 t^{(\frac{3}{2})} +a\right ) dt\\\\= 4\times 2\times \frac{t^{\frac{5}{2}}}{5} + a t\\\\= 8 \frac{t^{\frac{5}{2}}}{5} + a t[/tex]
Two camp counselors take 5 kids to the movies and sit in a row of 7 seats. if the counselors must sit in consecutive seats (in either order), how many seating arrangements are possible?
Answer:
the total number of arrangements possible is 1,440 ways
Step-by-step explanation:
Given;
total number of kids = 5
total number of counselors, = 2
Since the counselors must sit together in any order, first treat them as a single option. This gives 6! possible arrangements for all the participants.
Also, If they can sit in any order, then the total possible arrangements = 2(6!)
= 2( 6 x 5 x 4 x 3 x 2 x 1)
= 1,440 ways
Therefore, the total number of arrangements possible is 1,440 ways
Seating arrangement is unique way in which people can sit. The number of seating arrangements possible in this case is 2520
What is the rule of product in combinatorics?If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in [tex]p \times q[/tex] ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
How to find the number of seating arrangements?In such situations, we need to model the situation with the view point which can be evaluated mathematically.
For give case, we can see that there are in total 7 seats. And 5 kids are to sit on them, with 2 camp counselors.
So 7 people have to sit on 7 seats.
But it is given that two counselors must sit together.
Now firstly, two counselors can choose 2 seats out of 7 seats in [tex]^7C_2 = \dfrac{7 \times 6}{2 \times 1} = 21[/tex] ways.
Then , in the rest of the 5 seats, 5 kids can arrange themselves in 5! ways(using permutations).
We have:
[tex]n! = n \times (n-1) \times (n-2) \times ... \times 2 \times 1\\\\5! =5\times 4\times 3\times 2\times 1 = 120[/tex]
Since each of this 120 arrangement is for each of 21 ways of counselors sitting, thus, there are 120 times 21 ways of those 7 people to sit (using rule of product), or total [tex]120 \times 21 = 2520[/tex]
Thus,
The number of seating arrangements possible in this case is 2520
Learn more about seating arrangements here:
https://brainly.com/question/13605688
Deandre can paint a small room in 6 hours. Deandre and Casey together can paint the same room in 4 hours. How long would it take for Casey to paint the room alone? Express your answer as a decimal. If necessary, round to the nearest tenth of hour.
Answer:
Step-by-step explanation:
If D can paint the room in 6 hours, in 1 hour she gets [tex]\frac{1}{6}[/tex] of the room painted;
If C can paint the room in x hours, in 1 hour she gets [tex]\frac{1}{x}[/tex] of the room painted.
It takes 4 hours to paint it together. Setting up the classic work equation gives us
[tex]\frac{1}{6}+\frac{1}{x}=\frac{1}{4}[/tex] and we need to solve for x. Multiply everything through by the LCM which is 12x:
[tex]12x(\frac{1}{6}+\frac{1}{x}=\frac{1}{4})[/tex] making our equation simplify to
2x + 12 = 3x and solve for x:
12 = x
C can paint the room alone in 12 hours.
2. The two equal sides of an isosceles triangle each have a length of 4x + y - 5. The perimeter of the triangle is
10x + 4y - 18. Determine the length of the third side. Explain how you found your answer. (4 marks)
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Answer:
2x +2y -8
Step-by-step explanation:
If the equal sides are 'a' and the third side is 'b', then the perimeter is ...
P = a +a +b = 2a +b
The length of the third side is then ...
b = P -2a . . . . . . subtract 2a from both sides
Substituting the given expressions, we find ...
b = (10x +4y -18) -2(4x +y -5)
b = 10x +4y -18 -8x -2y +10
b = 2x +2y -8 . . . . the length of the third side
Nicole was shopping at a local department store and had a budget of $60. She was
buying shorts (s) priced at $10 and t-shirts (t) priced at $8. She was heading to the
checkout stand when she saw a sign that said all t-shirts are 40% off. Write and simplify
an equation that Nicole could use to find the possible combinations of shorts and t-shirts
she could buy for $60.
Answe YEAH BOIIIIII!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
relative extrema of f(x)=(x+3)/(x-2)
Answer:
[tex]\displaystyle f(x) = \frac{x + 3}{x - 2}[/tex] has no relative extrema when the domain is [tex]\mathbb{R} \backslash \lbrace 2 \rbrace[/tex] (the set of all real numbers other than [tex]2[/tex].)
Step-by-step explanation:
Assume that the domain of [tex]\displaystyle f(x) = \frac{x + 3}{x - 2}[/tex] is [tex]\mathbb{R} \backslash \lbrace 2 \rbrace[/tex] (the set of all real numbers other than [tex]2[/tex].)
Let [tex]f^{\prime}(x)[/tex] and [tex]f^{\prime\prime}(x)[/tex] denote the first and second derivative of this function at [tex]x[/tex].
Since this domain is an open interval, [tex]x = a[/tex] is a relative extremum of this function if and only if [tex]f^{\prime}(a) = 0[/tex] and [tex]f^{\prime\prime}(a) \ne 0[/tex].
Hence, if it could be shown that [tex]f^{\prime}(x) \ne 0[/tex] for all [tex]x \in \mathbb{R} \backslash \lbrace 2 \rbrace[/tex], one could conclude that it is impossible for [tex]\displaystyle f(x) = \frac{x + 3}{x - 2}[/tex] to have any relative extrema over this domain- regardless of the value of [tex]f^{\prime\prime}(x)[/tex].
[tex]\displaystyle f(x) = \frac{x + 3}{x - 2} = (x + 3) \, (x - 2)^{-1}[/tex].
Apply the product rule and the power rule to find [tex]f^{\prime}(x)[/tex].
[tex]\begin{aligned}f^{\prime}(x) &= \frac{d}{dx} \left[ (x + 3) \, (x - 2)^{-1}\right] \\ &= \left(\frac{d}{dx}\, [(x + 3)]\right)\, (x - 2)^{-1} \\ &\quad\quad (x + 3)\, \left(\frac{d}{dx}\, [(x - 2)^{-1}]\right) \\ &= (x - 2)^{-1} \\ &\quad\quad+ (x + 3) \, \left[(-1)\, (x - 2)^{-2}\, \left(\frac{d}{dx}\, [(x - 2)]\right) \right] \\ &= \frac{1}{x - 2} + \frac{-(x+ 3)}{(x - 2)^{2}} \\ &= \frac{(x - 2) - (x + 3)}{(x - 2)^{2}} = \frac{-5}{(x - 2)^{2}}\end{aligned}[/tex].
In other words, [tex]\displaystyle f^{\prime}(x) = \frac{-5}{(x - 2)^{2}}[/tex] for all [tex]x \in \mathbb{R} \backslash \lbrace 2 \rbrace[/tex].
Since the numerator of this fraction is a non-zero constant, [tex]f^{\prime}(x) \ne 0[/tex] for all [tex]x \in \mathbb{R} \backslash \lbrace 2 \rbrace[/tex]. (To be precise, [tex]f^{\prime}(x) < 0[/tex] for all [tex]x \in \mathbb{R} \backslash \lbrace 2 \rbrace\![/tex].)
Hence, regardless of the value of [tex]f^{\prime\prime}(x)[/tex], the function [tex]f(x)[/tex] would have no relative extrema over the domain [tex]x \in \mathbb{R} \backslash \lbrace 2 \rbrace[/tex].
leave your answer in simplified radical form.
Answer:
The .jpeg file is the answer. Others are formulas that I use to solve.
Identify a pattern in the given list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.)
27,-9 ,3 ,-1 ,___
work out the surface area of this solid quarter cylinder in terms of pi. r 10cm.h 16
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Answer:
(320 +130π) cm²
Step-by-step explanation:
The perimeter of the base will be the sum of two radii and the arc length of a quarter circle:
P = 2r +r(π/2) = r(2+π/2)
For a radius of 10 cm, the perimeter of the base is ...
P = (10 cm)(2+π/2) = (20+5π) cm
The lateral area of the quarter-cylinder is the product of this perimeter and the height:
LA = Ph = ((20 +5π) cm)(16 cm) = (320 +80π) cm²
__
The total base area is the area of a half-circle of radius 10 cm, so is ...
BA = 1/2πr² = (1/2)π(10 cm)² = 50π cm²
The total surface area is the sum of the base area and the lateral area:
SA = BA +LA = (50π +(320 +80π)) cm² = (320 +130π) cm²
If f(x) = x³ - 2, find f(3)
Answer:
25
Step-by-step explanation:
Assuming the equation is f(x) = x³ - 2
Plug in 3 for x
f(3) = 3³-2
= 27-2
=25
Answer:
25!
I hope it's helpful
How to divide 6,558 by 4 in long division
This is the solution to your question.
A pizza is to be cut into fifths. Each of these fifths is to be cut into thirds. What fraction of the pizza is each of the final pieces?
the following 3 shapes are made up of square, circles, and semi circles. Find the Area and perimeter of the shaded area. Write your answer as a completely simplified exact value in terms of pi
Answer:
Perimeter = 18 + 9pi
Area = 81 - 20.25*pi
Step-by-step explanation:
Perimeter = 9 + 9 + 2(2 pi r)/2 The twos cancel out.
Perimeter = 18 + 9*pi
Area of the square = 9 * 9 = 81 cm^2
Area of the 2 semicircles = 2 * pi * r^2/2
r = d/2
d = 9
r = 9/2 = 4.5
Area of the 2 semicircles = 2 (pi * 4.5^2)/2
Area of the 2 semicircles = 20.25 pi
Area of the blue figure = 81 - 20.25 pi
I need help with this
Answer:
C
Step-by-step explanation:
In the graph given, we can expect the x axis to be horizontal and the y axis to be vertical. This means that the arm span represents y and the height represents x.
Therefore, if a girl on her team is 63 inches tall, we can say that y=x+2, and since height is x, y = 63 + 2 = 65
For a certain company, the cost for producing x items is 40x+300 and the revenue for selling x items is 80x−0.5x2. The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $300.
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1). The order of the list does not matter. To enter a−−√, type sqrt(a).
Part c: Is it possible for the company to make a profit of $15,000?
Answer:
The profit is maximum when x = 40.
Step-by-step explanation:
Cost function, C = 40 x + 300
Revenue function, R = 80 x - 0.5 x^2
The profit function is
[tex]P = R - C\\\\P = 80 x - 0.5 x^2 - 40 x - 300\\\\P = - 0.5 x^2 + 40 x - 300\\\\\frac{dP}{dx} = - x + 40\\\\So, \frac{dP}{dx} = 0\\\\-x + 40 = 0 \\\\x = 40[/tex]
So, the profit is maximum when x = 40 .
Work out the length x. 14 cm 7 cm Х
Answer:
If you want the area of something with the sides 14cm and 7cm then it would be 98 cm.
Step-by-step explanation:
Area = length * width
Area = 14 cm * 7 cm
Area = 98 cm
A study by researchers at a university addressed the question of whether the mean body temperature of an animal is 98 6°F Among other data, the researchers obtained the body temperatures of 109 healthy animals. Suppose you want to use those data to decide whether the mean body temperature of healthy animals is less than 98.6°F.
Required:
a. Determine the null hypothesis
b. Determine the alternative hypothesis
Answer:
H0 : μ ≥ 98.6
H1 : μ < 98.6
Step-by-step explanation:
The population mean temperature, μ = 98.6
The null hypothesis takes up the value of the population mean temperature as the initial truth ;
The alternative hypothesis on the other hand is aimed at using a sample size of 109 to establish if the mean temperature is less than the population mean temperature.
The hypothesis ;
Null hypothesis, H0 : μ ≥ 98.6
Alternative hypothesis ; H1 : μ < 98.6
Dodi bicycles 14mph with no wind. Against the wind, Dodi bikes 10mi in the same time it takes to bike 20mi with the wind. What is the speed of the wind?
Answer:
4.67 mph
Step-by-step explanation:
Speed with no wind = 14 mph
Let wind speed = w mph
Thus;
Speed with wind = 14 + w
Speed against the wind = 14 - w
Now, we are told that against the wind he bikes 10 miles.
Thus, from; time = distance/speed, we have;
Time = 10/(14 - w)
Also, we are told he biked 20 miles with the wind. Thus;
Time = 20/(14 + w)
We are told the times he used in both cases are the same.
Thus;
10/(14 - w) = 20/(14 + w)
Divide both sides by 10 to get;
1/(14 - w) = 2/(14 + w)
Cross multiply to get:
1(14 + w) = 2(14 - w)
14 + w = 28 - 2w
w + 2w = 28 - 14
3w = 14
w = 14/3
w = 4.67 mph
A clients rash measures 5cm x 4cm how much does this measure in inches
Given:
A clients rash measures 5 cm × 4 cm.
To find:
The measure in inches.
Solution:
We know that,
2.54 cm = 1 inch
1 cm [tex]=\dfrac{1}{2.54}[/tex] inch
1 cm [tex]\approx 0.3937[/tex] inch
Using this conversion, we get
5 cm [tex]=5\times 0.3937[/tex] inches
5 cm [tex]=1.9685[/tex] inches
4 cm [tex]=4\times 0.3937[/tex] inches
4 cm [tex]=1.5748[/tex] inches
Therefore, the measure in inches is 1.9685 inches × 1.5748 inches.
1. The equation of a circle is x^2 + y^2 + 6x - 4y + 4 = 0. What are the center and the radius of the circle? Show ALLLLLL your work
Answer:
(2, -3) and r = 3.
Step-by-step explanation:
you can also plug this equation in desmos but I guess it's good to know how to do it also:
The equation of a circle is (x-h)^2 + (y-k)^2 = r^2
Now in order to make a perfect square on both sides, we need to do this:
First add 9 to both sides:
x^2 + 6x + 9 + y^2 -4y +4 = 9.
I purposely shifted it to show the perfect square created when you add 9 to both sides. Factor:
(x+3)^2 + y^2 - 4y + 4 = 9.
now the second bolded part is allso a perfect square. Factor:
(x+3)^2 + (y-2)^2 = 9
Based on the equation of a circle, the center must be at (2, -3) and the radius is the square root of 9 which is 3.
:)
Wich is equivalent to 64^1/4.
Answer:[tex]2\sqrt[4]{4}[/tex]
Step-by-step explanation:
[tex]64^{\frac{1}{4} }= \sqrt[4]{64}=\sqrt[4]{(2)(2)(2)(2)(4)}=2\sqrt[4]{4}[/tex]
Leo is running in a 5-kilometer race along a straight path. If he is at the midpoint of the path, how many kilometers does he have left to run?
Answer:
2.5 km left
The midpoint is half of 5, which is 2.5, so he'll still have 2.5 km left to complete
Verify if : (-30) x ( 13.+ (-3)] =[(-30) x 13] + [(-30) (-3)]
a. A contest entrant has a 0.002 probability of winning $12,165. If this is the only prize and the fee is $35, then find the expected value of winning the contest. b. The probability of winning a lottery is 0.125. What is the probability of winning AT LEAST ONCE in twelve trials?
Answer:
The right answer is:
(a) -10.67
(b) 0.7986
Step-by-step explanation:
(a)
According to the question,
X P(X) X.P(X) X2.P(X)
12130 0.002 24.26 294274
-35 0.998 -34.93 1222.55
Now,
[tex]\Sigma x.P(x) = -10.67[/tex]
or,
[tex]\Sigma x^2.P(x) = 295496.35[/tex]
hence,
The mean will be:
[tex]\Sigma x.P(x) = -10.67[/tex]
(b)
According to the question,
n = 12
p = 0.125
q = 1 - p
= 0.875
Now,
⇒ [tex]P(X=x) = \binom{n}{x} p^x q^{n-x}[/tex]
By substituting the values, we get
⇒ [tex]P(X \geq 1)=1-(\binom{12}{0} 0.125^0. 0.875^{12-0})[/tex]
⇒ [tex]=1-(1 (0.125^0) (0.875^{12}))[/tex]
⇒ [tex]=1-(1(1.0)(0.2014))[/tex]
⇒ [tex]=1-(0.2014)[/tex]
⇒ [tex]=0.7986[/tex]
Write out the first 5 terms of the following sequence:
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Answer:
2, 1, -1/2, -1/4, 1/8
Step-by-step explanation:
Use n = 1 through 4:
[tex]a_{1+1}=\dfrac{(-1)^{1+1}\cdot a_1}{2}\ \Rightarrow\ a_2=\dfrac{1\cdot2}{2}=1\\\\a_3=\dfrac{(-1)^3\cdot 1}{2}=-\dfrac{1}{2}\\\\a_4=\dfrac{(-1)^4\cdot(-\dfrac{1}{2})}{2}=-\dfrac{1}{4}\\\\a_5=\dfrac{(-1)^5\cdot(-\dfrac{1}{4})}{2}=\dfrac{1}{8}[/tex]
The first 5 terms are ...
2, 1, -1/2, -1/4, 1/8
Find the length of AC
A. 377.19
B. 378.63
C. 2.89
D. 33.13
Answer:
AC = 377.19
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 5 = 33/AC
AC tan 5 = 33
AC = 33/ tan 5
AC = 377.19
michael has an average of 68% in his 3 papers but that is below the pass mark of 70%. what must be his least score in the fouth paper to enable him pass?
Answer:
His least score for him in the fourth paper has to be 76.
Step-by-step explanation:
Given that Michael has an average of 68% in his 3 papers but that is below the pass mark of 70%, to determine what must be his least score in the fouth paper to enable him pass the following calculation must be performed:
(70 x 4) - (68 x 3) = X
280 - 204 = X
76 = X
Therefore, his least score for him in the fourth paper has to be 76.
Work out giving ur answer as a mixed number
Answer:
6 11/12
Step-by-step explanation:
4 1/6 + 2 3/4
Get a common denominator of 12
4 1/6 *2/2 + 2 3/4 *3/3
4 2/12 + 2 9/12
6 11/12
Find the solution to the system of equations.
x + y + z = 25
y+z= 18
Z= 7
Answer:
x=7
y=11
z=7
Step-by-step explanation:
x + y + z = 25
y+z= 18
Z= 7
Substitute the third equation into the second
y+z=18
y+7 = 18
y = 18-7
y = 11
Now substitute y=11 and z=7 into the first
x +y+z = 25
x+11+7 = 25
x+18 = 25
x = 25-18
x=7
SCALCET8 3.9.026.MI. A trough is 10 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 13 ft3/min, how fast is the water level rising when the water is 5 inches deep
Answer:
The answer is "0.624"
Step-by-step explanation:
[tex]b = 5x\\\\h = x\\\\ l = 10 \\[/tex]
Using formula:
[tex]V = (\frac{1}{2})(b)(h)(l) \\\\[/tex]
[tex]= \frac{1}{2} \times (5x)\times (x) \times (10)\\\\= 5x\times x \times 5\\\\= 25x^2[/tex]
[tex]\frac{dV}{dt} = 50x \ \frac{dx}{dt} \\\\\text{(where x represents the height in feet and}\ \frac{dv}{dt} = 13\ \frac{ft^3}{min})\\\\\frac{dx}{dt} = (\frac{1}{50})(\frac{1}{x}) \ \frac{dV}{dt}\\\\[/tex]
When the water is 5 inches deep then:
[tex]x = (\frac{5}{12})\ ft\\\\13 =50(\frac{5}{12}) \ \frac{dx}{dt}\\\\13 \times 12 =50(5) \ \frac{dx}{dt}\\\\\frac{13 \times 12}{50 \times 5} = \frac{dx}{dt}\\\\\frac{156}{250} = \frac{dx}{dt}\\\\ \frac{dx}{dt}= 0.624[/tex]
